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Hb Hb Hb $ > Hb Hb Hb ( U U U U Hb Hb Hb Hb Hb Hb Hb Hb Hb : Preliminary Draft
Notes on the Pure Theory of International Trade
Houston H. Stokes
Note: These "preliminary notes" are geared to the books
1. International Economics 6th edition by Robert Dunn and John Mutti, Routledge (2004)
2. Advanced International Trade: Theory and Evidence by Robert Feenstra Princeton (2004,2016).
3. International Economics by Robert Mundell (1968) Columbia University
4. International Economics Robert Feenstra & Alan Taylor Worth 2008
as well as various key articles in the Handbook of International Economics series. The goal of these notes is to provide a "living" editable document so that students can add material to the basic outline that hopefully will focus the discussion. These notes should be treated as preliminary. Key math setups are given. Please report any errors.
TOC \o "1-3" \h \z \u HYPERLINK \l "_Toc460074080" Notes on the Pure Theory of International Trade PAGEREF _Toc460074080 \h 1
HYPERLINK \l "_Toc460074081" 1. Introduction PAGEREF _Toc460074081 \h 2
HYPERLINK \l "_Toc460074082" 2. Why Nations Trade - Gains from Trade PAGEREF _Toc460074082 \h 11
HYPERLINK \l "_Toc460074083" 3. Modern Theory of Trade. PAGEREF _Toc460074083 \h 22
HYPERLINK \l "_Toc460074084" 4. Basis for Trade: The Ricardian Model vs the Hechscher-Ohlin Models PAGEREF _Toc460074084 \h 26
HYPERLINK \l "_Toc460074085" Stopler- Samuelson Theorem Preliminary graphical analysis. PAGEREF _Toc460074085 \h 34
HYPERLINK \l "_Toc460074086" Math Treatment of Two Factor Model (See Chapter 1 of Feenstra) Optional topic. PAGEREF _Toc460074086 \h 36
HYPERLINK \l "_Toc460074087" Magnification Effect. How do changes in product prices impact factor prices? Optional topic. PAGEREF _Toc460074087 \h 38
HYPERLINK \l "_Toc460074088" Effect of changes in Endowments on Industry outputs PAGEREF _Toc460074088 \h 40
HYPERLINK \l "_Toc460074089" Simple Model of Trade in Intermediate Inputs PAGEREF _Toc460074089 \h 44
HYPERLINK \l "_Toc460074090" Estimation setup PAGEREF _Toc460074090 \h 46
HYPERLINK \l "_Toc460074091" Example Code and results from B34S, Rats and Stata: PAGEREF _Toc460074091 \h 50
HYPERLINK \l "_Toc460074092" Note EMBED Equation.DSMT4 values reported for B34S and Rats agree. Stata made an "adjustment." PAGEREF _Toc460074092 \h 74
HYPERLINK \l "_Toc460074093" STOPSTOP PAGEREF _Toc460074093 \h 74
HYPERLINK \l "_Toc460074094" Code for Leverage Plots with OLS, GAM and Marspline PAGEREF _Toc460074094 \h 74
HYPERLINK \l "_Toc460074095" Edited output from Leverage Plots PAGEREF _Toc460074095 \h 75
HYPERLINK \l "_Toc460074096" Selected Leverage Plots. PAGEREF _Toc460074096 \h 78
HYPERLINK \l "_Toc460074097" 6. Extensions to H-O model suggested by Vanek PAGEREF _Toc460074097 \h 82
HYPERLINK \l "_Toc460074098" 7. H-O Theory, increasing returns and the Gravity Model. PAGEREF _Toc460074098 \h 90
HYPERLINK \l "_Toc460074099" 8. Alternative approaches to trade theory contrasted to Original HO Model. PAGEREF _Toc460074099 \h 99
HYPERLINK \l "_Toc460074100" 9. The Theory of Protection PAGEREF _Toc460074100 \h 104
HYPERLINK \l "_Toc460074101" 10. Arguments for Protection PAGEREF _Toc460074101 \h 109
HYPERLINK \l "_Toc460074102" 11. Mundell Policy Equation PAGEREF _Toc460074102 \h 114
HYPERLINK \l "_Toc460074103" 12. Regional Blocks => Discriminatory Trade Liberalization PAGEREF _Toc460074103 \h 118
HYPERLINK \l "_Toc460074104" 13. Commercial Policy PAGEREF _Toc460074104 \h 119
HYPERLINK \l "_Toc460074105" 14 Trade of Less Developed Countries PAGEREF _Toc460074105 \h 122
HYPERLINK \l "_Toc460074106" 15 International Mobility of Labor and Capital PAGEREF _Toc460074106 \h 123
HYPERLINK \l "_Toc460074107" 16. Balance of Payments Accounting PAGEREF _Toc460074107 \h 125
HYPERLINK \l "_Toc460074108" 17. Market for Foreign Exchange PAGEREF _Toc460074108 \h 126
HYPERLINK \l "_Toc460074109" 18. Impact of trade on determination of National Income PAGEREF _Toc460074109 \h 132
HYPERLINK \l "_Toc460074110" 19. Alternative Models of Balance of Payments or Exchange Rate Determination PAGEREF _Toc460074110 \h 133
HYPERLINK \l "_Toc460074111" 20. Balance of Payments adjustment with fixed exchange rates PAGEREF _Toc460074111 \h 135
HYPERLINK \l "_Toc460074112" 21. Balance of Payments Adjustment through exchange rate changes PAGEREF _Toc460074112 \h 138
HYPERLINK \l "_Toc460074113" 22. The theory of flexible exchange rates PAGEREF _Toc460074113 \h 139
HYPERLINK \l "_Toc460074114" 23. International Monetary Experience 1880-1940 PAGEREF _Toc460074114 \h 140
HYPERLINK \l "_Toc460074115" 24 The International Monetary System 1945-1973 PAGEREF _Toc460074115 \h 144
HYPERLINK \l "_Toc460074116" 25 International Monetary Relations 1973 - Present PAGEREF _Toc460074116 \h 146
1. Introduction
International Trade is concerned with exchange. Important topics include the mechanisms by which trade between countries is caused and the resulting effect on the countries after trade is opened. In the Ricardian Model Trade is caused by comparative or absolute advantage. Production conditions are different in the two countries that are not restricted to have the same technology. The Heckscher-Ohlin approach assumes
1. Two goods and two factors of production where the factors can move between industries.
2. One good is labor intensive while the other is capital intensive.
3. The relative abundance of the factors of production differs by countries. Home country abundant in capital, foreign country abundant in labor.
4. Final products can move between countries. Factors of production cannot move.
5. The technologies used in the two countries the same.
6. Consumer tastes are the same in the two countries
These assumptions can be modified and the effects shown.
Effects of trade:
Welfare changes in both countries. Who gains and by how much? Large and small country assumptions impact the analysis. Can growth actually lower a countries welfare?
The distribution of income changes in both countries. Who owns the factors? Trade alters the relative income of owners of factors of production. Are the factors mobile both into and out of the country?
Factor prices change in both countries. Will factor prices adjust so as to be equalized? Why is factor price equalization so important? How does persistent wage differentials drive immigration? Under what assumptions does immigration of workers lead to EMBED Equation.DSMT4 , to EMBED Equation.DSMT4 constant, to EMBED Equation.DSMT4 ?
The range of goods produced changes in both countries. What is the consumption gain from trade? The production gain from trade? Under what conditions will countries with same tastes and same production conditions trade? Who gains from trade inside the country? Who loses?
Under what assumptions will the relative prices of goods to change after trade, the relative price of factors change?
Key aspects of trade policy include:
The effect of tariff on international trade.
The effect of free trade areas (NAFTA), customs unions and economic unions on welfare.
Why do we need a theory of international trade?
Macroeconomics assumes:
1. economic agents maximize their self interest,
2. such agents are rational.
In trade theory more assumptions are needed.
Within a nation state it is assumed that labor and capital are free to move among regions. This may not be the case across countries. What does this restriction cost?
Within a nation state there are normally no government-imposed barriers to shipment of goods (tariff). Between countries there are many barriers including tariffs, regulations (steering wheel construction laws forced Rolls Royce to buy parts from GM in the 1960s. Cars had to be crash tested, even if they were high priced and hand made.)
The state of the economy within a nation state is usually the same for all regions. Across countries, differences in a countries position in the business cycle can have major ramifications. (In the EU zone Germany and Greece are in different phases.)
Within a country there is only one currency. Exchange rate changes complicate the analysis. (In world of fixed exchange rate and perfect capital mobility there is only one interest rate. In a world of flexible exchange rates, different interest rates across countries are possible.)
[3 Table 1-2] Trade /GDP ratio and GDP (billions) in 2005
Hong Kong 192% $178
Malaysia 111% $130
Switzerland 49% $366
South Korea 42% $788
Germany 38% $2,782
Canada 36% $1,115
China 33% $2,229
Mexico 31% $768
UK 28% $2,193
France 27% $2,110
India 20% $785
Japan 14% $4,506
US 13% $12,455
US share is low compared to most other countries but has increased substantially in recent years. US is now being impacted by the world to an increased degree. Politically workers displaced by foreign competition have become active! These political issues have been impacting the EU zone, which allows labor to be mobile, as well as the US.
Table 1
Ratios of Merchandise Trade to GDP (percent)
Country 1890 1913 1960 1970 1980 1990
Australia 15.7 21.0 13.0 11.5 13.6 13.4
Canada 12.8 17.0 14.5 18.0 24.1 22.0
Denmark 24.0 30.7 26.9 23.3 26.8 24.3
France 14.2 15.5 9.9 11.9 16.7 17.1
Germany 15.9 19.9 14.5 16.5 21.6 24.0
Italy 9.7 14.4 10.0 12.8 19.3 15.9
Japan 5.1 12.5 8.8 8.3 11.8 8.4
Norway 21.8 25.5 24.9 27.6 30.8 28.8
Sweden 23.6 21.2 18.8 19.7 25.0 23.5
United Kingdom 27.3 29.8 15.3 16.5 20.3 20.6
United Statesb 5.6 6.1 3.4 4.1 8.8 8.0
Notes: Merchandise trade is measured as the average of imports and exports
In recent years the development of container shipping has lowered costs and reduced theft. In 1959 .627 tons per man hours which increased to 4,234 tons per man hour in 1976 [4, page 14)
In the period 1970-2000 the total capital outflows of the US increased from 10.88 to 580.65. Inflows from 6.24 to 1024.23. These numbers are greater for UK (3.16 to 777.68 and 1.64 to 801.58). This data is nominal, not real!
US faces increased vulnerability to foreign shocks (such as 1974 oil price shock). As of 2016, the EU and the China slow-down are the biggest risks. Changes is exchange rates under the flexible exchange rate system provides a damper of shocks to the US economy. (In early 1980's high US interest rates attracted capital from abroad causing the dollar to appreciate and making sales overseas more difficult.)
Recent experience in the fall of 2008 indicates how vulnerable the world economy is to the financial system. The degree of leverage in many parts of the world has caused a general loss of confidence in financial institutions. The distribution of income has become a political problem with no easy solution without a political census on what is the best policy. Political pressure in 2016 to raise tariffs might push us back to what we experienced after the Smoot Hawley tariff in 1930.
The real side is being impacted by the monetary side to a degree not seen for a long time.
Euro now gives Europe one currency like the US. The EEC is like what was setup in the US in 1796. US now faces a potential economic rival.
"Pure Theory" of International Trade provides a framework by which all kinds of exchanges can be analyzed, both graphically and using statistical (econometric) methods.
"Monetary Theory" of International trade is concerned with balance of payments adjustment. Increasingly it appears that the monetary side can have substantial real side effects. It remains to be seen if the crisis of the fall of 2008 will result in higher tariffs such as were enacted in the US and other countries in 1932 and which proved so damaging.
Positive Economics
- Develops a framework of analysis
- Constructs various alternative hypothesis
- Tests hypothesis
Normative Economics
- Determines what ought to be
- Can lay out costs and benefits (defense vs welfare)
- Want to look at gains from exchange.
- Want to look at the costs and benefits of differing policies.
Trade can be shown from supply and demand analysis.
Figure 1
Def: An indifference curve drawn on the X and Y diagram contains the locus of points showing different bundles of X and Y to which the consumer (country) is indifferent. Assume barter ratio is fixed. Country at f producing and consuming oc of steel and od of food. The domestic relative price line is a a'. The world relative price line is a a'' . EMBED Equation.DSMT4 causing producers to stop producing food and go 100% to steel (o a). At position g the country consumes ob of steel and gives up ab of steel to get oe of food. Trade moved the country from U1 to U2. Trade is caused by the relative price differing between regions. As a result of trade steel workers gain and food workers need to change jobs. The country as a whole gains. Political question: How are gains distributed? What is the cost of changing jobs? Can it be done?
Figure 2
For complements the indifference curve approaches a 900 angle. For substitutes the indifference curve approaches a 1800 angle.
The above analysis assumes we have a community indifference curve. A major unsolved problem in economics is how to construct the community indifference curve.
Key idea: Normative economics is in the indifference curve and changes:
- Over time
- Due to advertising
- Due to consumption itself
Trade theory assumes exchange in the presence of some fixed factor. The fixed factor does not have to be location related. Examples are land, tastes, skills, climate.
Gains from trade can arise:
Due to changing consumption patterns as a result of changes in relative prices.
Changes in the degree by which a country specializes.
Both changes in consumption patterns and specialization.
Key idea: "Under what conditions can trade gain one country more than another? Who gains in the country?
Changes is specialization imply changes in the returns to factors and thus possible dislocation.
This can cause political problems. Wheat farmers in Mass lost out to Iowa when US Constitution outlawed internal tariffs. Historic international trade models assumed perfect competition and constant returns to scale. Assuming increasing returns was not studied sufficiently. The effect of Monopolistic Competition can be added to the H-O model to explain trade between relatively similar countries.
Growth. Sources of growth in the United States include:
Population (immigration)
Education (increases in technology)
Resources
Will of People (WWII increased productivity)
Some assumptions used to simplify analysis. (How sensitive are results to these assumptions?)
Neutrality of Money: Real variables determined independently of monetary variables. Each sector looks at relative prices not absolute prices (which are a function of money supply).
All prices are flexible (determined by competition)
Assume initially the amount of factors of production are fixed.
Assume initially that factors are immobile between countries.
Assume initially that same technology is available to all consumers.
Assume that initial income patterns are known.
Assume initially no barriers to trade in form of transportation, information, communication.
Key questions:
Direction of trade
Volume of trade and prices of traded goods
Effects of trade restrictions
Effect of free trade and restricted trade on welfare
Approaches:
- Partial equilibrium approach uses supply and demand. The problem is that as you move on the supply and demand curve, the assumptions underlying these curves are not met resulting in the curves shifting. (See Above figure)
- General Equilibrium Approach. Uses production possibility curve (PPP), Community indifference curves, and relative price line to determine trade welfare. This approach will be the main focus of the course.
Technical problems in Trade Analysis:
Time period of analysis. If the period is too short, then substitutes cannot be developed and analysis leads to misleading results. Example. Gas crisis in 1974. Gas prices increased and in the short run people drove old cars. In the longer run more fuel efficient cars were produced and demand for gas fell. => Negative balance of payments effects of an increase in import prices are most severe in the short run.
Simultaneity Both supply and demand may be shifting. Need to identify the supply and demand curves using 2SLS or 3SLS methods.
Errors of Measurement. Trade data may be poor. Example: US used value of disks and manuals to measure software sales.
Aggregate elasticity. Aggregate elasticity measures biased toward zero since greatest price fluctuation is observed in goods with inelastic response => goods with inelastic S & D are likely to be given too much weight in the calculation of the aggregate price index.
Adjustment. During the time path of adjustment we may see points not on the true curve.
Elasticity measurement is critical. Assume two countries initially in equilibrium. The home country (A) imports X and exports Y. Define the income elasticity of demand in A as:
EMBED Equation.DSMT4
If EMBED Equation.DSMT4 then as A and B grow the balance of payments will move against B. It will be in B's interest to have growth in A increase. => Economic stagnation in the foreign country implies balance of payments problems in the home country. The lower the income elasticity of demand, the faster a country can grow and still maintain balance of payments equilibrium.
2. Why Nations Trade - Gains from Trade
- Nations trade because they benefit from it.
- Adam Smith stressed that nations traded due to absolute advantage. Absolute cost advantage => the real cost (labor ) was less in one country than another. Smith was thinking in terms of labor theory of value. Modern economics (not Marxism) discards this approach and looks at other costs of production such as land and capital.
- Assuming labor is mobile, labor is the only input and competition within a single country => goods will trade at prices that are a direct proportion of their labor costs. This further assumes away retraining problems. But between countries labor may not be mobile due to a number of reasons.
- Ricardo stated that absolute advantage was not a necessary condition for trade. Trade could occur due to comparative advantage. Ricardo's example involved the number of hours to produce two goods:
Cloth Wine
Portugal 90 80
England 100 120
Portugal has absolute advantage in both goods since it takes less labor to produce cloth and wine than England. This does not mean that England cannot benefit from trade
In Portugal 90 hours of labor get you 9/8 of a wine barrel or 1C = (9/8)W.
In England 100 hours of labor get you 5/6 of a wine barrel or 1C = (5/6)W.
=> Portugal sell wine, England sell cloth which suggests that it would be desirable for labor in Portugal (England) to move into production of wine (cloth).
Define EMBED Equation.DSMT4 and EMBED Equation.DSMT4 as the # of hours for the ith good in the home (Portugal) and foreign country (England).
EMBED Equation.DSMT4
Assume EMBED Equation.DSMT4 and EMBED Equation.DSMT4 are the labor in the home and foreign country. EMBED Equation.DSMT4 EMBED Equation.DSMT4 Assume cloth is on the x axis and EMBED Equation.DSMT4 are the prices of the ith good in home and foreign country, The slope of the budget lines that are tangent to the indifference curves imply that in the absence of trade
EMBED Equation.DSMT4 in the two countries.
This suggests that cloth (good 1) is relatively expensive in the home country Portugal and wine ( good 2) is relatively expensive in the foreign country England. => England sell cloth and Portugal sell wine.
Define the world price in terms of the relative price of good 1 (here cloth). If EMBED Equation.DSMT4 then the home (foreign) country will produce both cloth and wine.
If EMBED Equation.DSMT4 then the home country will specialize in cloth and the foreign country in wine. Note: comparative advantage determines the wages in each country. Absolute advantage determines the level of wages across countries.
Can setup example in terms of 1 unit of labor.
Broadcloth Linen
England 10 15
Germany 10 20
-=> in England 10 broadcloth = 15 Linen
in Germany 10 broadcloth = 20 Linen
- English broadcloth producers should exchange broadcloth for linen in Germany. Broadcloth produces will benefit if they can obtain more than 15 linen for 10 broadcloth. German linen producers note that to get broadcloth in Germans they have to trade 20 linen but if they trade with England they can only give up 15 linen for 10 broadcloth.
Mill introduced demand to allow us to determine how much each country would trade.
Specie Flow Mechanism. Assume national money is determined by gold stocks. Assume a two country world where trade is initially in balance. Here prices in each country are stable. Assume next that increased demand for A's goods causes gold to flow in. EMBED Equation.DSMT4 causes demand for A's goods to fall and demand for B's goods to rise. Specie Flow mechanism implies that EMBED Equation.DSMT4 (Marshall Lerner Condition). If this condition is not met, all gold will flow from B to A. This classical adjustment mechanism relied on change in gold flows to change national money to change prices and costs. This theory did not deal with output and unemployment effects. Note: Two gold standard papers written by Neuburger and Stokes will be discussed in class later this term.
Managed Adjustment. Keynes suggested that a change in demand could change the demand for imports (exports) without a change in prices. Taussig noted that before WWI the system appeared to adjust faster that the level of gold flows would suggest. Neuburger-Stokes (1979) presented time series evidence that suggested that central banks were using interest rate policy to speed the adjustment without having to resort to the level of gold flows that would other wise occur. The current paper (2016) documents that the effect of gold flows on interest rates was relatively small in comparison to interest rates in other countries in a model of the UK, Germany and France.)
Historical notes: Earl Hamilton studied gold flows from the new world to Spain and hence to France and England. During wars (such as the Bullionist Controversy) many countries suspended the gold standard. In this century the gold standard was suspended during WWI. After the war the UK went back on gold at the overvalued prewar rate. The economic return was protracted and slow. In the late 20's the world moved into depression and countries moved off gold. After WWII the world moved to the gold exchange standard. Here countries pegged to either the pound or the dollar which in turn pegged to gold. Major problems included adjustment, confidence, and liquidity. In the fall of 1967 at the Rio Conference the SDR was setup. The SDR paid interest. No country was required to accept more that 2 times its quota. The SDR was designed to solve the liquidity problem. It did not address the confidence or adjustment problem. In Nov 1967 the pound was devalued from $2.80 to $2.40. In the 20's exchange rates moved in part as a result of changes in prices. This led to purchasing power parity theory or the "law of one price." The problem is that this theory is not general. It does not look at changes in demand, at changes in capital flows and at technological changes, all of which impact on exchange rates. Define EMBED Equation.DSMT4 as the dollar price of one unit of the foreign currency. Theory suggests that:
EMBED Equation.DSMT4 or that foreign inflation is associated with devaluation of the foreign currency.
Technological changes (lower domestic prices) EMBED Equation.DSMT4 A glut of domestic goods floods the market requiring the exchange rate to depreciate to allow country to sell goods.
Capital inflow EMBED Equation.DSMT4 Home currency has strengthened (appreciated).
In 30's moved away from PPP since there were other causes of exchange rate movements. These included large scale speculative capital flows, competitive devaluations by both deficit and surplus countries and problems of exchange stability due to fears. Expectations can alter EMBED Equation.DSMT4 's in countries.
- Before trade the relative prices of goods in A and B differ. After trade they adjust to be the same. Assume EMBED Equation.DSMT4 . This implies that A is willing to sell Y to
B and import X from B. The gains from trade include a consumption effect and a possible production effect. Assuming no changes in production in each country, trade can still result in a gain for both countries. If as a result of trade production changes in both countries there can be a still further production effect. To accurately measure the gains from trade we need:
Community indifference curves in each country.
Production functions in each country (Production possibility curves)
Offer Curves (derived from community indifference curves and production possibility curves to determine the world trade price).
It is important to know how to derive these curves.
Partial equilibrium analysis such as figure 1 can be used to attempt to measure the gains from trade but there are serious problems in moving along country supply and demand curves without the curves themselves shifting. This course will use general equilibrium approach. Basic diagram is given in figure 3. We assume diminishing returns to scale which is seen by the country having a production possibility curve which is bowed outward. The country starts at k with oc of food and oi of steel. After trade with no production change the country is on higher indifference curve and consuming oe of food and on of steel. If production changes, country produces at g. Here food is ob and steel is of. After trade country gives up bd of food to get fp of steel. Country now on highest indifference curve. We assume here that the world trade price does not change as a result of trade (small country assumption).
Figure 3
As we move down the PPC we give up more and more food to get steel. The relative price of steel is increasing relative to food. The factor use more intensively in steel production will see its price increase relative to the factor used most intensively in food. => movements along the PPC are not costless. If trade opens up such that the price of steel increases relative to food. Producers of food will loose relative to producers of steel. => Stopler Samuelson that states that free trade will reduce the income of the scarce factor of production and increase the income of the abundant factor of production in each country. For an example if Chinese steel is reduced in price US steel production will go down and the value of steel mills will fall.
The PPC is derived from the Edgeworth Box with the inputs on the axis. If the isoquants for x any y are tangent along the diagonal then we have constant returns to scale. The tangent points in this case imply the relative price of the inputs is the same in the production of x and y.
Figure 4 shows equilibrium in a closed economy assuming constant returns to scale production.
Here in contrast to figure 3 we have a straight line production possibility curve.
Figure 4
Country reaches U2 by producing oa food and ob steel. Country is at point
C on the production possibility curve. Without trade country cannot get to U3.
Figure 5 shows effect of trade. Country was consuming and producing at k. After
trade county reached higher indifference curve at g. Steel consumption increased from ob to om and food consumption did not change much. Country production point was now all Food and no steel. Na of food was sold for om of steel.
Figure 5
Historical Development of Trade Theory
- Trade theory developed in four areas:
I. Balance of payments and theory of employment
II. Fluctuating Exchange rates
III. Price Theory and International trade
IV. Commercial Policy and The Theory of International Trade
I. Balance of payments and Theory of Employment
- Prior to Keynes - Monetary theory (specie flow mechanism) suggested that system adjusted automatically. Gold out => EMBED Equation.DSMT4 and trade adjusts. The classical theory did have a role for interest rates. The mechanism was EMBED Equation.DSMT4 costs not EMBED Equation.DSMT4 output, EMBED Equation.DSMT4 employment
- Keynes attacked theory suggesting could have unemployment and over production.
- New theory. An external event which causes exports EMBED Equation.DSMT4 => imports EMBED Equation.DSMT4 without EMBED Equation.DSMT4 Pd. The mechanism was exports EMBED Equation.DSMT4 => level of aggregate demand EMBED Equation.DSMT4 => imports EMBED Equation.DSMT4 . This theory covered the balance of payments effects being either EMBED Equation.DSMT4 or EMBED Equation.DSMT4 depending on EMBED Equation.DSMT4 and EMBED Equation.DSMT4 where EMBED Equation.DSMT4 is the income elasticity of the i th country.
- Taussig before WWI noted that the system appeared to adjust faster than gold flows would suggest. He had no theory to explain what was happening. Neuburger and Stokes in
"The Relationship between Interest Rates and Gold Flows Under the Gold Standard: A
New Empirical Approach," , Economica, Vol. 46, August 1979, pp. 261-279.
presented evidence that that is consistent with governments using a variety of policies to force adjustment without a gold flow. Their 2016 paper expands on this result.
- After WWI elasticity measurements appeared to be low. Why did trade adjust? The Keynesian approach provided a missing link.
- Keynesian theory independent of banking policy and implied that banks cannot influence the system. The Keynesian theory did have antecedents in Ricardo and others.
- Capital flow effects. Keynesian theory => unless a disturbance (such as a capital flow) disturbs the circular flow of income (via a change in investment), it will have no effect on the system. The classical theory treated all flows as the same. In classical theory the gold flow => EMBED Equation.DSMT4 M and EMBED Equation.DSMT4 M => changes in prices and the balance of payments etc.
II. Fluctuating Exchange Rates
- During WWI gold standard suspended. After war world's return to the gold standard was protracted and slow. Next the world moved into depression => a period of fluctuating rates.
- In 20's exchange rate moved as a result of war causing prices to increase. This led to purchasing power parity theory (see contributions of Officer) that codified the "law of one price." PPP => exchange rates had to move. Problems with PPP included 1. not looking at effects of shifts in international demand on exchange rates, 2. not looking at effects of capital flows on exchange rates, 3. difficulty in selecting just what price should be used in the index.
- In 30's many countries found depression caused changes in the exchange rate. There was a move away from PPP since here changes in the price level was not the cause of exchange rate movements. The income of all countries fell in the depression but not all countries balance of payments were effected the same. Keynesian theory on the effect of induced income changes implied: Balance of payments deficit => Y down => imports down => balance of payments improves. This line of reasoning suggested that changes in the exchange rate would not adjust the balance of payments. The situation was complicated by:
- large scale speculative capital flows.
- Competitive devaluation by both deficit and surplus countries.
- Problems with exchange stability due to fear => EMBED Equation.DSMT4 .
III. Price Theory and International Trade
- Classical theory measured gain from trade as difference between international rate of exchange on commodities and the rate that would prevail in the absence of international trade. Gain = the savings in resources from trade. This theory rested on the labor theory of value.
- Haberler postulated production possibility curve. Leontief added indifference curves which allowed measurement of the gains from trade. The new approach got away from real costs theories and depended on the ratio of the marginal costs of the two products.
- Viner attacked the new approach on the grounds that the PPC (or production substitution curve) assumed fixed quantities of factors. In Viner's view, P changes caused changes in factor prices. Since as we move along the PPC curve relative prices of factors changes (except in constant returns to scale case) => supply of factors must change. Viner wanted to look at the "real cost" of supplying factors. Viner further noted that the country indifference curves depend on the distribution of goods. Since international trade changes the distribution of goods => Country indifference curves shift as a result of trade. This important point is moot if we assume homogenous tastes for all consumers in the country.
- Samuelson (in 1939 Canadian Journal of Economics and Political Science) showed that after trade, each country if it wants can obtain more of every good while performing less of every production service. => cannot measure the gain but it is a gain never the less. Samuelson showed that some degree of trade can make the country better. This leaves open the possibility of an optimum tariff.
- The more modern H-O Theory shows how trade based on factor endowments alters the distribution of income. H-O Theory argues that in many cases trade originates from the fact that one country had a large supply of one factor. This is contrast to the Ricardian Theory that focused on technology differences in the countries. Using the basic H-O assumptions of two goods, two factors and the same technology in each country and constant returns to scale, the H-O model argues that assuming trade in a good that uses one factor intensively EMBED Equation.DSMT4 => returns to owners of that factor EMBED Equation.DSMT4 relative to other factor owners. H-O Theory showed that assuming constant returns to scale, except for some cases involving complete specialization, trade tended to equalize relative factor returns in the two trading countries. Ohlin showed how changes in relative factor prices might change factor supplies in the longer run. H-O theory can assume fixed factors supplies or variable factor supplies. Recent advances in theory have extended the analysis to the increasing returns case (Krugman, Helpman) that refine the arguments for trade and for protection. Use of the H-O-V Model allows adding more inputs and setting up tests of the Leontief hypothesis using econometric methods.
Looking only at one country producing goods EMBED Equation.DSMT4 where there are N goods. If there are two factors of production EMBED Equation.DSMT4 . Assuming the "even case" which implies an equal number of goods and factors and maximizing the production of good 2 conditional on good 1 we note that EMBED Equation.DSMT4 which defines the production possibility curve. If EMBED Equation.DSMT4 is a concave function of EMBED Equation.DSMT4 then EMBED Equation.DSMT4 which indicates that as we increase production of good 1 the rate of increase in good 2 is reduced, giving the concave shape of the production possibility curve. (See figure 3 of these notes).
Mill introduced demand which allows us to determine how much each country would trade.
IV Theory of Tariffs
- Tariffs and terms of trade. Between WWI and WWII shaky foundation for free trade. In 30's US raised tariffs as did other countries. Samuelson showed that using the optimum tariff (to be defined later) that assumes the elasticity of supply of the foreign country is not EMBED Equation.DSMT4 => country putting up tariff could gain at expense of the other country. Scitovsky showed how such a tariff increased gains from retaliation. => all countries try to gain = all countries lose. Such a result might lead to tariff bargaining. A tariff is like a monopoly. Some gain, some lose. In a tariff war the bigger countries are at an advantage.
- Tariffs and the distribution of income. Tariff EMBED Equation.DSMT4 => certain groups gain. Stolper-Samuelson (RES Nov 41) showed that regardless of tariff effects on the terms of trade and real income as a whole, protection increases return and relative share of factor of production most important in protected industry. Proved for 2 good, 2 factor case. In more than 2 good world cannot tell for sure what will happen since can have complementary relationships. In the 19th century agriculture was governed by land. A tariff on manufacturing made labor relatively scarce => raised return of the working class. This became the "pauper labor" argument for tariffs. 'Pauper Labor" theory not the whole story!! In the Heckscher-Ohlin Model the abundant factor gains from trade and the scarce factor loses from trade.
V Commercial policy
- Mercantilists thought trade was an outlet for a countries surplus production and a way to get gold.
- Classical theory argued against mercantilism. In their view trade was to satisfy wants. A shift in emphasis from exports to imports. In classical view, exports to obtain gold not necessarily the right thing to do since P EMBED Equation.DSMT4 . The goal was not a surplus but balance. In an N country world only N-1 countries can be successful multilateral mercantilists. Only one can be a successful bilateral mercantilist!
- Keynes attacked the classical view that export surplus was not a good thing. Keynes argues exports EMBED Equation.DSMT4 => gold EMBED Equation.DSMT4 =>Yd EMBED Equation.DSMT4 => increased welfare of country. This argument assumes that initially you had unemployment. In Keynes view mercantilists were OK when they argued that exports should be a vent for over production. Keynes noted that not all countries could run a balance of payments surplus. Keynes felt that a policy of trade restriction is a treacherous policy, even in the short run.
Summary.
- Meade integrated income (multiplier) and price theory of balance of payments. He argued looking at two policy targets (internal balance, external balance). To obtain these goals required two instruments. => # of targets = # of instruments.
- Mundell principle of effective market classification => use instrument where it is most effective.
- Meade argued that there is no one rate of exchange. There is one equilibrium rate corresponding to each level of interest rates and income. As interest rates increase, with a fixed level of income, capital will be attracted in. This will appreciate the exchange rate. Given interest rates, if income were to increase => demand for exports would increase implying a depreciation of the exchange rate.
- Alexander looked at income effects on the balance of payments. A balance of payments surplus => total production > total absorption (C + I in real terms). If a devaluation is to improve trade balance it must reduce absorption. This argument is irrespective of elasticities. Absorption theory => balance of payments EMBED Equation.DSMT4 only if hoarding goes up since only in this way can we forestall imports EMBED Equation.DSMT4 as a result of income increasing due to exports EMBED Equation.DSMT4 . This theory has a Keynesian flavor.
- If at full employment and have a devaluation due to a prior deficit, then absorption theory suggests balance of payments will not improve because Y cannot increase. The devaluation has converted demand for the import good to demand for the domestic good. => cannot rely only on EMBED Equation.DSMT4 to help external balance without policies to reduce absorption. Unless absorption EMBED Equation.DSMT4 then country will have nothing to sell! Key idea: Demand is not the only thing to look at. Supply is also important.
- Problems with absorption theory. The theory as stated implicitly assumes a neutral monetary policy or one that maintains the interest rate by changes in M. If this is not done: deficit => devaluation => demand of domestic consumers for foreign goods EMBED Equation.DSMT4 , domestic demand EMBED Equation.DSMT4 => balance of payments gets worse since absorption had to have increased. If were at less than full employment could have domestic income EMBED Equation.DSMT4 > absorption EMBED Equation.DSMT4 and get an improvement in the balance of payments. If drop neutral monetary policy assumption the increased domestic demand => id EMBED Equation.DSMT4 => capital comes in and balance of payments improves.
Metzler Case. Stolper-Samuelson showed how a large factor could gain absolutely as well as relatively from a tariff. Logic: tariff=> internal price of protected good EMBED Equation.DSMT4 => value of scarce factor goes EMBED Equation.DSMT4 . As a counter example, Metzler showed protection may not increase price of the importable good since it may improve the terms of trade sufficiently to shift not only the external terms of trade (price ratio of exports relative to imports without tariff) but also the internal terms of trade in favor of exportables => buy more of the foreign good.
3. Modern Theory of Trade.
- Moved away from theory based only on labor theory of value.
- Initial Assumptions (to be relaxed later):
- Perfect Competition in both commodity and factor markets.
- Given quantities of the factors of production (assume population and capital growth are zero)
- Technology is given.
- Zero transport costs and no barriers to trade.
- Given tastes and preferences.
-Factors of production are perfectly mobile among industries within each country but are immobile between countries.
- Opportunity cost of one unit of X is the amount of Y that you have to give to produce one more unit of X. From opportunity cost you get the production possibility curve which defines the maximum amount of X given Y or conversely the maximum amount of Y given X.
- Production possibility curves show constant returns to scale if they are straight lines from the upper left to the lower right. (See figure 2-1).
- Production possibility curves show decreasing returns to scale if they are convex to the origin. (See figure 2.6).
- Production possibility curves show increasing returns to scale if they are concave to the origin.
- Community Indifference Curves shows the locus of points showing the consumption of X and Y to which the community is indifferent. To derive these curves requires assumptions be made on the distribution of income within a country. => all policy implications have to be somewhat qualified.
- With constant returns to scale, trade drives country to complete specialization (See figure 2-4)
- With decreasing returns to scale trade does not in general drive a country to complete specialization. (See figure 2-6).
- With increasing returns to scale there can be specialization in the wrong direction.
Figure 5B Specialization in right/wrong direction assuming increasing returns.
- The Offer Curve plots the quantities that countries will be willing to export at different prices. Intersection of the offer curves sets the international trade price.
- Draw Increasing, constant and decreasing returns to scale production possibility curves. Recent research by Krugman and others have discussed the implications of product differentiation (monopolistic competition and economies of scale) on the results obtained using the 2 by 2 case and constant returns to scale.
- Draw Gains from trade in case of increasing returns, constant returns and decreasing returns in two cases: 1. where there is no change in production (only Consumption gain) and 2. when there is consumption and production gains. (See book figure 2-9 as a basis upon which to draw). Show specialization in the right and wrong direction.
- Draw the derivation of the offer curve in the case of constant returns to scale (see book figure 2-9) and decreasing returns to scale.
- Draw determination of the equilibrium terms of trade. (see book figure 2-10
- Define the coefficient elasticity of the offer curve => e = % change in quantity demanded / % change in the terms of trade. In figure 2-11 we see e= EMBED Equation.DSMT4 in segment Oa, e > 1 in segment ab and at b e = 1 since for small movements the % change in the terms of trade - % change in the quantity demanded. In the segment bc e< 1. The elasticity of demand the foreign countries offer curves determines whether the optimum tariff is 0 (if e= EMBED Equation.DSMT4 ). In trade the small country assumption => that e < EMBED Equation.DSMT4 for the domestic country but that e = EMBED Equation.DSMT4 for the foreign country.
- Define the coefficient of elasticity of demand as
e = % change in Q demanded / % change in terms of trade
- For a straight line offer curve e = EMBED Equation.DSMT4
- For a curved (yet positively sloped) offer curve
e > 0
- For a negatively sloped offer curve e < 0 (See figure 2-11).
- If the offer curve is not a straight line => can have the possibility of an optimum tariff. Complications will occur if the other country "fights back.
- Distribution of the gains from trade. The lower e for the foreign country the more the gains from trade accrue to the home country. Take of a small county trading with the United States. The small country sees the US offer curve as having e = EMBED Equation.DSMT4 . Here no matter what the small country does, the US price is always the same. This will be shown to be true in the case when the small country places a tariff on the US. If e < EMBED Equation.DSMT4 , then as the tariff reduces quantity, the foreign country lowers price. Hence the price net of the tariff falls.
- Effects of trade. If there are production changes due to trade opening, resources will be reallocated. Mechanism: Assume country A exports X and imports Y. After trade, production of X will increase and production of Y will fall. Inputs used more intensively in the production of X will increase in value relative to prices of inputs used intensively in the production of Y. This is will cause changes in income and may have an impact on demand within the country. Those gaining from trade should be able to compensate those hurt by trade. After trade a country tends to specialize in the direction of the good in which it has a comparative advantage. Changes in the production mix are checked by increasing costs.
- Figure 2.10 shows general equilibrium determination of world relative
price. Figure 2.9 can be modified to show total gain consumption gain and production gain. Figure 2-8 shows partial equilibrium approach to same problem.
- Unless the country is driven to complete specialization after trade
(PXA/PYA) = (PXB/PYB). At a later date we will show that the prices of inputs are related to the prices of final products.
- A movement along the production possibility curve may take a great deal
of time and involve much retraining and human cost. There may be political pressures against such moves. The 2008 US election showed that even within a state there are winners and losers of opening trade.
- In the real world with many countries, transport costs and many products analysis can proceed if for each country goods are ranked by their relative comparative advantage. Usually a country exports the good for which it has the greatest comparative advantage and imports goods for which it has the least comparative advantage. The heavier (or more perishable) a good the more likely it will not be traded.
- It is hoped that through trade there can be a reduction of tensions (war). This was an important motivation for the development of the European Common Market and in recent times TPP.
- Free Trade Area. No tariffs between country A and B. A and B maintain separate tariffs for the rest of the world.
- Customs Union. No tariffs between country A and B. A and B maintain a common tariff for the rest of the world.
- Economic Union. => Customs union with labor mobility.
4. Basis for Trade: The Ricardian Model vs the Hechscher-Ohlin Models
-The Ricardian Model stresses that trade is due to technological differences across countries. The Hechscher-Ohlin model stress that trade is due to differences in factor endowments. After first looking at the Ricardian Model using math (See Feenstra Chapter 1), the Heckscher-Ohlin Model is discussed.
- Let EMBED Equation.DSMT4 labor needed for production of good i in the home country.
EMBED Equation.DSMT4 labor needed for production of good i in the foreign country
EMBED Equation.DSMT4 and EMBED Equation.DSMT4 are the labor in the home and foreign country. The marginal product of labor in each industry is EMBED Equation.DSMT4 . If EMBED Equation.DSMT4 the price of the product in industry i and workers are paid their marginal product, then in equilibrium EMBED Equation.DSMT4 . The slopes of the production possibility curve in each country is EMBED Equation.DSMT4 . If the home country has a comparative advantage in good 1, then EMBED Equation.DSMT4 or relatively less labor needed in good 1 in home country. Define p as the relative price of good 1 or EMBED Equation.DSMT4 .
Figure 4.1 Ricardian Model
- Define EMBED Equation.DSMT4 If p is below A and C, then both countries produce good 2. For C
Comparative Advantage determined by supply side. Later we will show a situation where by "tastes outweigh production conditions." Here demand conditions are overwhelming supply conditions.
- H-O theory predicts that trade will increase the price of the abundant factor and decrease the price of the scarce factor. Assuming two factors L and K, then in equilibrium
(PLA/PKA) = (PLB/PKB). This condition holds unless one or both countries are driven to complete specialization.
- If we assume indifference curves are the same in all countries (same tastes) => supply conditions will drive trade.
- Because a nation's comparative advantage is based on relative factor endowment, over time it could change. Physical capital could be accumulated. Human capital could change (more education, trained workers come into country). (After WWII Germany had ruined physical capital but there was still human capital in the population still living.)
- Formal assumptions
- Perfect competition in both commodity and factor markets. (=> price = MC and full employment in both countries)
- Factors of production immobile internationally but mobile nationally.
- Same tastes in both countries.
- Transport costs are zero, no tariffs.
- State of technology given and the same in both countries.
- Constant returns to scale exist in both industries. (Note in the Cobb-Douglas case EMBED Equation.DSMT4 . The production function shows decreasing returns to scale, constant returns to scale of increasing returns to scale as EMBED Equation.DSMT4 is < 1, = 1 or > 1.
- Commodities can be unambiguously ranked in terms of factor intensity.
- Discussion of assumptions. Constant returns to scale => that is all inputs go up by a factor EMBED Equation.DSMT4 then output goes up by EMBED Equation.DSMT4 . Proof:
EMBED Equation.DSMT4
Isoquants are shown in figure 3-4
- The assumption of identical production functions does not mean that all countries operate using the same mix of labor and capital. Figure 3-5 shows isoquants for wheat (W1 W2) and cloth (C1 C2). Initial budget line is MN. (Can buy OM of land or ON of labor. At these relative prices, country will maximize wheat production at E or cloth production at J. Note that the country cannot do both at the same time. Given this budget line, cloth in labor intensive and wheat is land intensive at E. Next assume that the price of land becomes relatively cheaper relative to labor. The budget line rotates clockwise to RS. Given the setup the same amount of cloth is produced (C1) but in a more land intensive way at K. Substantially more wheat is produced (at W2) in a more land intensive way. Note that the slope of MN represents the factor-price ratio. In this case, even with a shift in relative factor prices, wheat is still more land intensive than cloth. If isoquants are drawn where the wheat isoquant shows a high degree of substitution between land and labor while the cloth isoquant shows that land and labor are more complementary, then a reversal in factor intensity is possible.
- Derivation of the production possibility curve
- Place two figure 3.1's back to back to form Edgeworth Box. In figure 3-6 line OO' is the contract curve. It is always more efficient to move from a position such as Z off the contract curve to a position such as Q on the contract curve. Points P, Q and R trace out the production possibility curve. Point Z becomes a point inside the production possibility curve.
- Along the contract curve the marginal rate of substitution between labor and land in the production of wheat is the same as the marginal rate of substitution of labor and land in the production of cloth.
- Define MPP i j as the increase in the production of j for one more input of i. In equilibrium MPP 1 j / P1 = MPP 2 j / P2 where 1 and 2 are inputs.
- Slope of the isoquant = MPP 1 j / MPP 2 j
- Slope of isocost = P1 / P2
- Note: We assume that input 2 is on the vertical axis. (As you get close to vertical axis MPP of that input EMBED Equation.DSMT4 0 => slope EMBED Equation.DSMT4 . As you get to horizontal axis slope of isocqant EMBED Equation.DSMT4 => MPP of that input goes to 0.)
- Along the contract curve slopes of isoquants are the same. => (MPP 1 j / MPP 2 j) = (MPP 1 i / MPP 2 i ) and are equal to the ratios of the input prices P1 / P2
- Figure 3-7 shows effect on production possibility curve of increasing inputs land and labor.
- Slope of PPC = marginal rate of transformation MRT. In equilibrium MRT = ratio of good prices.
- In consumption theory we have
[MUx / Px] = [MUy / Py]
- Slope of indifference curve = MUx / MUy
- In equilibrium ratios of MU, prices and MRT are the same in both countries. => If the assumptions of the analysis are true you will get factor price equalization. For further detail see classic papers by Stolper-Samuelson in 1941 and 1948.
- As the economy moves to equilibrium there are income effects. Owners of factors of production having price increases (decreases) will have their relative incomes increase (decrease). Because it is impossible to make interpersonal comparisons of utility, cannot tell if national welfare went up. If all persons have the same utility functions and because income went up => winners get more than losers lose. If all persons do not have same utility functions, then compensation principle can be used.
- Compensation principle. Can winners pay losers to accept the change? Will they? In practice owners of scarce factors of production favor protection since free trade will lower their rent. In the United States free trade usually impacts unskilled labor negatively. => labor often favors higher tariffs.
- The predictions of H-O theory require that adjustment is complete. In the short run all factors of production in the import competing industry may be hurt. Since these industries are in specific regions, may have negative regional effects.
- Trade is a substitute for factor mobility. H-O theory => can either have factor mobility or international trade. Factor mobility alters the relative prices of factor prices. Rybczynski Theorem show conditions under which relative factor prices do not have to move when one input increases. European economic community allows labor to be mobile but when times get tough in one region labor can go home. EEC found cultural effects of labor mobility. NAFTA allows Mexican workers not to come to the US to produce but to produce in Mexico and send goods here.
- Rybczynski Theorem shows conditions under which an increase in one factor of production does not lead to the relative price of this factor going down. (See figure 3.9). Assume the economy is on the contract curve and that on the axis of the Edgeworth box is Labor and Capital. Assume that labor is on the horizontal axis. Given the production of X and Y does not change and K is labor intensive, then if L EMBED Equation.DSMT4 => [PL/PK] EMBED Equation.DSMT4 . If on the other hand the production of the capital intensive good Y goes down and the production of the labor intensive good X goes up, then the capital released from the production of Y will combine with the new labor such that it is possible that [PL/PK] remains unchanged. This theorem shows that immigration of labor does not necessarily result in a decrease in the wage rate. There are three possible cases. The Rybczynski line can be drawn on the production possibility diagram. In order for [PL/Pk] to stay constant, when the input used most intensively in the production of C goes up, the output of food must decrease to release the other input to now combine with the more plentiful input. See figure 3.9
-Leontief Paradox. Leontief expected that the United States would export goods that were capital intensive and import goods that were labor intensive. We found the converse. Why? (Later using the H-O-V theory we will discuss whether in fact Leontief setup the econometric model correctly.
- US labor may have more (human) capital attached than labor in other countries. => cannot just measure labor.
- H-O theory assumes same tariff on all goods. US tariffs are relatively higher on labor intensive good than capital intensive goods.
- Leontief may have statistical error such that the there may not be a significant difference between the two capital/labor ratios.
- Reversal. The H-O theory assumes that all goods can be ranked in terms of their capital intensity and that the ranking is the same for all price ratios of capital and labor. The usual case is:
Figure 4.2 Non Reversal Case
Figure 4.2 shows the usual case. For relative price # 1 X=Y=1. If (Pk/PL) EMBED Equation.DSMT4 => than x=1 is less expensive than y=1. Hence (PX/PY) and (PK/PL) are positively related.
Figure 4.3 shows a factor intensity reversal.
Assume two goods X and Y. X has low substitutability of capital and labor while Y has high substitutability of capital and labor. In figure 4.3 for isocost line BB [PL/PK] > than [PL/PK] for AA. For BB good Y is relatively more capital intensive than X, for AA good Y is relatively more labor intensive than X. => H-O assumption of ranking goods in terms of their capital intensive does not hold and the prediction of H-O on the intensive of the exports of the United States will not necessarily hold. The importance of a reversal is that some for one P X / PY value there are two values of P L / PK.
Scale induced factor intensity reversal. Analysis to date has assumed that EMBED Equation.DSMT4 and showed under what conditions it was possible for a reversal to take place. Now assume EMBED Equation.DSMT4 and look at figure 8. Here as the isocost shifts out, X continues to be capital intensive and Y continues to be labor intensive. This is the usual case. Figure 9 shows what happens when there is a factor intensity reversal even without a change in relative factor prices. Here due to scale effects at relatively low level of output X is relative capital intensive and Y is relatively labor intensive. At higher levels of output the situation reverses. Example: A small garden may be labor intensive. As the scale of operation increases, the production process becomes more capital intensive.
Figure 4.4 Reversal due to scale
- Since Leontief looked only at labor and capital, all natural resources were lumped into capital. This may have biased the results.
Stopler- Samuelson Theorem Preliminary graphical analysis.
The real return to a nations scarce factor of production will rise with the imposition of a tariff. Logic: Nation 2 the K abundant nation) imposes an import tariff on commodity X (its L intensive commodity). EMBED Equation.DSMT4 for domestic producers and consumers which implies that the real wage of labor (Nation 2s scare factor) will increase. The tariff results in an increase in EMBED Equation.DSMT4 in the production of both goods causing the wage of labor to increase as domestic production of import protected good X increases.
The Edgeworth box which shows endowments has tangency points of the two isoquants that can be moverd to the production frontier (see figure 3.9 of supplementary graphs) If there is not complete specialization there is a maping from the relative prices of goods to relative prices of factors. Factor price equalization can occur due to movement of inputs that change EMBED Equation.DSMT4 or trade opening of trade that changes EMBED Equation.DSMT4 . A quick analysis is shown below:
- Heckscher-Ohlin - Factor price Adjustment. H-O theory shows how trade tends to equalize good prices and factor prices (in the absence of complete specialization.) Figure 11A & 11B shows the conditions under which factor prices adjust (11A) and do not adjust (11B). In 11A The initial endowments of the countries (RI and RII) are more similar than in figure 11B.
AI => complete specialization of X in country I
AII => complete specialization of X in country II
BI => complete specialization of Y in country I
BII => complete specialization of Y in country II
In figure 11A BII < BI < AII < AI while in figure 11B
BII < AII < BI < AI
Because of complete specialization in figure 11B you never can get to the zone between AII - BI => need factor mobility.
Figure 11 R1 and R2 are the endowment ratios in country 1 and 2.
Obstacles to factor price equalization from trade
- Many countries - will only cause problems if all productions functions are not the same.
- Many products and factors - to equalize all factors need an equal number of traded products.
- Imperfect competition - To get equalization need MC = price of product and factors being paid the value of their marginal product.
- Increasing returns to scale breaks down perfect competition since one producer dominates.
- Different production functions in different countries ruins equalization since one country will have an edge.
- Increasing marginal productivity of factors of production => the price of factors EQ \O(=,/) VMP of factor.
- Factor intensity reversals cause problems due to: 1. lack of homogeneity since will not get straight line expansion paths and 2. due to one good's isoquant curve being positioned inside another good's isoquant curve. If a country expands and there is a reversal there will be a switch in the good having comparative advantage.
If trade does not equalize factor prices, factors can move!
Even if factor prices adjust, the formerly scare factor owners will lose relative to the formerly abundant factor owners. This change in the relative position of factor owners sets the stage for political pressure for tariffs. Since the welfare of the country goes up with free trade => gainers should be able to compensate losers. Problem: it may take time to adjust.
Math Treatment of Two Factor Model (See Chapter 1 of Feenstra) Optional topic.
EMBED Equation.DSMT4 (M1)
We assume perfect competition in product and factor markets. This assumption implies that each industry is producing to maximize GDP. By substituting the constraint into the GDP objective function and choosing EMBED Equation.DSMT4 to maximize
EMBED Equation.DSMT4 (M2)
gives the first order condition EMBED Equation.DSMT4 or
EMBED Equation.DSMT4 (M3)
or in words the economy will produce where the relative price of good 1 equals the slope of the production possibility curve. Equation M3 can be seen if we divide the first order condition by EMBED Equation.DSMT4 Differentiation of the GDP function (M1) produces
EMBED Equation.DSMT4 , (M4)
Due to the "envelope theorem" the terms inside EMBED Equation.DSMT4 sum to 0 resulting in EMBED Equation.DSMT4 . In words the derivative of the GDP function with respect to the price of good i is the output of good i. The envelope theorem can be seen once we note that EMBED Equation.DSMT4 from M3. Moving all terms to the left hand side and dividing by EMBED Equation.DSMT4 shows that EMBED Equation.DSMT4 for small movements of EMBED Equation.DSMT4 induced by changes in EMBED Equation.DSMT4 .
The unit cost function
EMBED Equation.DSMT4 (M5)
is the dual of the production function EMBED Equation.DSMT4 . The solution of the maximization of the unit cost function is
EMBED Equation.DSMT4 (M6)
where EMBED Equation.DSMT4 at the equilibrium
EMBED Equation.DSMT4 (M7)
Gives EMBED Equation.DSMT4 since the terms inside EMBED Equation.DSMT4 =0. In words, at equilibrium, EMBED Equation.DSMT4 are the derivatives of the unit cost function with respect to the wage and interest rate, The assumption that profits equal zero (perfect competition) and full employment produces four nonlinear equations that solve EMBED Equation.DSMT4 .
EMBED Equation.DSMT4 (M7 & M8)
The first two equations indicate that provided there are no reversals and both goods are produced, each price vector EMBED Equation.DSMT4 corresponds to a unique wage and interest rate independent of factor endowments. Using the Ricardian model, however, this would not be the case, since any increase in EMBED Equation.DSMT4 would lower wages.
If we totally differentiate the zero profit condition we get equation 1.9 of Feenstra (2016) which is M9 below.
The Samuelson factor price equalization theorem (1949) requires the two sector model. The reason trade can equalize factor prices is that a labor intensive country can keep exporting the labor intensive product so that the wages of labor are kept high.
Magnification Effect. How do changes in product prices impact factor prices? Optional topic.
First differentiate the zero profit equations (M7).
EMBED Equation.DSMT4 (M9)
Which can be transformed to
EMBED Equation.DSMT4 (M10)
Note EMBED Equation.DSMT4 . Define EMBED Equation.DSMT4 or in words the cost share of labor and capital in industry i. Given EMBED Equation.DSMT4 . Define EMBED Equation.DSMT4 which implies
EMBED Equation.DSMT4 (M11)
which can be solved as
EMBED Equation.DSMT4 (M12)
If industry 1 is labor intensive => EMBED Equation.DSMT4 .
Assume the price of good 1 increases so EMBED Equation.DSMT4
EMBED Equation.DSMT4 (M13)
EMBED Equation.DSMT4 (M14)
Wages increases more than price of good 1 since EMBED Equation.DSMT4 . Since both EMBED Equation.DSMT4 and EMBED Equation.DSMT4 workers can buy more of both good 1 and good 2 (real wage up). Since EMBED Equation.DSMT4 and EMBED Equation.DSMT4 the real return to capital has fallen due to EMBED Equation.DSMT4 and EMBED Equation.DSMT4 increasing.
Stopler-Samuelson 1941 theorem "An increase in the relative price of a good will increase the real return to the factor used intensively in that good and reduce the real return to the other factor."
EMBED Equation.DSMT4 EMBED Equation.DSMT4 (M15)
Which is called the "magnification effect" by Jones (1965) since any change in product prices has a magnified effect on the factor prices. Assume tariffs are lowered so that import prices fall this will result in effects on wage rates that are greater than product price changes. Later we will show the conditions of the Rybczynski theorem that shows when increased trade is not changing input prices.
Effect of changes in Endowments on Industry outputs
Holding product prices fixed implies that EMBED Equation.DSMT4 do not change. From (M8)
EMBED Equation.DSMT4 (E1)
Which can be rewritten as
EMBED Equation.DSMT4 (E2)
Define EMBED Equation.DSMT4 where EMBED Equation.DSMT4 .
And rewrite (E2) as
EMBED Equation.DSMT4 (E3)
And solve
EMBED Equation.DSMT4 (E4)
EMBED Equation.DSMT4 (E5)
EMBED Equation.DSMT4 (E6)
Since industry 1 is labor intensive EMBED Equation.DSMT4 . Given that labor is increasing (immigration) and with a fixed capital stock => EMBED Equation.DSMT4 since factor prices and product prices are fixed, then
EMBED Equation.DSMT4 (E7)
Which proves the Rybczynski theorem that the labor intensive industry, 1, increases production (using up the new labor) and the capital intensive industry, 2, decreases production thus releasing capital to combine with this newly more abundant labor force.
When oil was discovered off the Dutch coast. Industries using oil expanded while other industries not using oil contracted. This was called the "Dutch disease."
Remark: The Rybczynski theorem assumes that both goods are produced (in the zone of diversification) and there are no reversals (either relative price reversals or scale reversals).
For any endowment vector (L, K), there is a unique EMBED Equation.DSMT4 such that when EMBED Equation.DSMT4 are multiplied by this vector all endowments will be used. See (M8).
Under what conditions will all outputs be > 0? Consult Feenstra Figure 1.9. The (L' K) must lie inside the vectors EMBED Equation.DSMT4 . For example if too much labor is added, even if industry 2 completely stops, not enough capital can be released to hold relative factor prices constant.
Proof that the Rybczynski line is straight. From (E1) assume EMBED Equation.DSMT4 which implies EMBED Equation.DSMT4 . The slope of the Rybczynski line is EMBED Equation.DSMT4 and fixed since EMBED Equation.DSMT4 are fixed by assumption.
5. Effect on Wages of Outsourcing Intermediate Inputs; Developing an Empirical Model
The goal of this section is to present the key ideas in Feenstra (2004) chapter 4 regarding modeling outsourcing. Preliminary empirical results will also be presented that extend his models reported in his Tables 4.4 and 4.5. The paper "The Impact of Outsourcing and High-Technology Capital on Wages: Estimates for the United States 1979-1990" by Robert Feenstra and Gorden Hanson Quarterly Journal of Economics Vol 114 # 3 (August 1999) pp 907-940 should also be consulted. Feenstra has provided his data and Stata programs which helps in the replication. B34S data files are also distributed to aid in the replication and extension of this important work.
- Since the 1980's the wage of skilled workers has increased relative to unskilled workers. We want to look at the effect of outsourcing to try to explain what has occurred.
- Assume an input is outsourced and is thus lower cost.
- Option 1 is to use the Stopler-Samuelson 1941 Theorem, to show how if a traded good price increases the price of the input used most intensively will increase relative to the other input.
- Option 2 use Heckscher-Ohlin-Vanek approach and compute the change in factor content of trade and the associated changes in factor prices. Assume EMBED Equation.DSMT4 is the equilibrium wage in a county in year t and EMBED Equation.DSMT4 is the factor content of exports where endowments are given. Deardoff-Staiger (1988) show that
EMBED Equation.DSMT4 (5.1)
Which implies that a higher content of imports for some factor k , or EMBED Equation.DSMT4 or EMBED Equation.DSMT4 will be associated with a falling wage for that factor or EMBED Equation.DSMT4 The same effect as immigration on labor wage. Borjas, Freeman and Katz (1997) find that immigration into the US during 1980-1995 explains 25% to 50% of the relative wage of high school dropouts. The increasing factor content of imports from less-developed countries also reduces the wage of high school drop outs but less than immigration.
-Option 3 is to directly model the presence of traded intermediate inputs caused by firms splitting their production across several countries. Key idea Trade in intermediate inputs can have an effect on production and factor prices that is different from trade in final goods.
A fall in the price of imported intermediate inputs decreases the relative wage of the factor used intensively in those imports in the home country. (See Stopler-Samuelson). (Note in this setup the intermediate input is produced in the foreign and domestic country.)
Since the US outsources production of labor intensive intermediate goods, this suggests a fall in the wage of unskilled labor in the United States since there is now less demand for the domestically produced intermediate input. Feenstra (page 117) argues what while unskilled labor in the home country (US) are the most disadvantaged, their real wages may in fact increase never the less due to possible lower prices of the final product.
Assuming a continuum of inputs and the 1980 Dornbusch-Fisher-Samuelson model. The US is more abundant in skilled labor than abroad. Their model predicts that the growth of capital or technology abroad will lead to increased outsourcing of labor intensive inputs from the US and increase the relative wage of skilled labor in both countries. Reason. capital and or technology EMBED Equation.DSMT4 implies the marginal product of foreign labor (both skilled and unskilled) goes up leading to more outsourcing. In the US unskilled labor wages fall relative to skilled wages.
In period 1979-1995 real wages of those with HS fell 13.4%, those with less that 12 years of school fell 20.2% and those with 16 or more years of school increased by 3.4%.
See Figures 4.1 & 4.2. There has been both an increase in the relative wage of nonproduction to production (manufacturing) workers and an increase in the relative employment of nonproduction to production workers. The only explanation is that there has been a movement outward of the demand curve for more skilled workers. The bulk of the increase in relative demand has occurred within the manufacturing industries.
This suggests that trade cannot be a dominant explanation of the wage and employment shifts because the movements between industries are smaller than the movements within industries.
Stopler-Samuelson suggests that if the price of skill intensive products (computers) increases then the relative wages of skilled workers will increase but the prices of computers fell and the relative wages of skilled workers increased. Data from Lawrence and Slaughter (1993) showed that the relative prices of goods produced in low skilled (production) worker intensive industries increased. => Price movements due to international competition could not explain the wage movements.
Trade however can shift the structure of production within an industry and thus on factor demand within an industry.
Simple Model of Trade in Intermediate Inputs
See Feenstra 2004 Chapter 4
EMBED Equation.DSMT4
EMBED Equation.DSMT4 (4.2)
Given the price of traded inputs EMBED Equation.DSMT4 and holding capital fixed the production of the final good EMBED Equation.DSMT4 in terms of inputs 1 and 2 is
EMBED Equation.DSMT4 (5.2)
Where EMBED Equation.DSMT4 implies import of input 1 EMBED Equation.DSMT4 implies exports of input 2.
Ignoring additional labor and capital used in the final "bundling" stage for production of the final product,
EMBED Equation.DSMT4 (4.3)
Optimal output assuming perfect competition maximizes
EMBED Equation.DSMT4 (4.4)
subject to the resource constraints (4.3) and the production technology (4.2)
- The question becomes how will a drop in the relative price of imported inputs affect factor prices?
For locally produced inputs to be competitive to those produced abroad, assume zero profit condition for producing inputs EMBED Equation.DSMT4 for EMBED Equation.DSMT4
EMBED Equation.DSMT4 (5.5)
Totally differencing (5.5) following Jones (1965) express the percent change in prices EMBED Equation.DSMT4 and as a function of the percent change in input prices EMBED Equation.DSMT4 where EMBED Equation.DSMT4 = cost share of factor j in the production of input i. EMBED Equation.DSMT4
EMBED Equation.DSMT4 (5.6)
With two equations and three unknowns EMBED Equation.DSMT4 no solution is possible unless we assume capital has equal shares in the two industries EMBED Equation.DSMT4 and subtract
EMBED Equation.DSMT4 (5.7)
Note that EMBED Equation.DSMT4 EMBED Equation.DSMT4 or EMBED Equation.DSMT4
since EMBED Equation.DSMT4
Activity 1 involves unskilled labor => EMBED Equation.DSMT4 . The importance of this is that it shows that a decrease in the relative price of the unskilled labor intensive import 1 EMBED Equation.DSMT4 leads to a decrease in the relative wage of unskilled labor in the domestic country EMBED Equation.DSMT4
EMBED Equation.DSMT4 (5.8)
In summary, a drop in the price of the imported unskilled labor intensive input 1 leads to a fall in the relative wage of unskilled labor or EMBED Equation.DSMT4 .
What happens to the price of the final product EMBED Equation.DSMT4 ? Define EMBED Equation.DSMT4 = unit cost that is the dual of the production function EMBED Equation.DSMT4 . The change in the final good price is a weighted average of the input prices
EMBED Equation.DSMT4 (5.9)
EMBED Equation.DSMT4 or EMBED Equation.DSMT4 .
We have shown that the relative price of the final product rises relative to the price of the imported input. In the US in the 1980's domestic prices rose faster than import prices.
Note we are comparing import and domestic prices within an industry. While the relative wage of unskilled workers falls in both countries, their real wages need not fall.
Estimation setup
Since (5.4) is linear homogeneous it can be written as
EMBED Equation.DSMT4 (5.10)
A measure of real value-added including real net exports becomes
EMBED Equation.DSMT4 (5.11)
Given that the capital stock and output are fixed in the short run, we define a short-run cost function
EMBED Equation.DSMT4 (5.12)
Note than any structural variables that shift the production function and affect costs should be included. In the empirical implementation imported intermediate inputs will be measured by expenditure on imported inputs for each industry. Structural variables in industry n will be denoted as EMBED Equation.DSMT4 . Feenstra uses the translog production function
EMBED Equation.DSMT4 (5.13)
EMBED Equation.DSMT4 = optimally chosen inputs for EMBED Equation.DSMT4 , EMBED Equation.DSMT4 EMBED Equation.DSMT4 = inputs/shift parameters. There are two optimally chosen inputs, skilled and unskilled labor. The objective is to calculate the effect on the percent change in costs if the price of one labor input changes.
EMBED Equation.DSMT4 (5.14)
Differentiating (5.13) with respect to EMBED Equation.DSMT4 produces a short run model which was estimated in Feenstra 4.4
EMBED Equation.DSMT4 (4.17)
Feenstra imposed symmetry EMBED Equation.DSMT4 and the requirement that (5.13) was homogenious of degree one in wages which implied EMBED Equation.DSMT4 .
Assume a cross section of countries. Equation (4.17) can be estimated over time, for a single year or for the change between two years. Feenstra used this latter approach for the years 1979 and 1990. This approach assumed the same cost function applied across the industries. Feenstra also made the usual assumption of dropping the wage terms to estimate a wage share of skilled labor
EMBED Equation.DSMT4 (4.18)
in table 4.4.
Basic idea page 118 The decision of companies tp purchase intermediate inputs from overseas will most certainly affect their employment at home and can be expected to differentially affect skilled versus unskilled workers. With firms in industrial countries facing a higher relative wage for unskilled labor than that found abroad, the activities that are outsourced would be would be those that use a large amount amount of unskilled labor such as assembly of components and other repitive tasks. Moving these activitied overseas will reduce the the relative demand for unskilled laboer in the industrial country, in much the same way as replacing these workers with automated production Page 122 discusses right hand side variables. Outsourcing and computer share have a positive effect. Rquation very sensitive. We look at
Looks at 447 industries. In some runs drops computers. Dependent variable = change in non production wage share in industry . Controls include shipments Y and change in ln K/Y). EMBED Equation.DSMT4 is structural variable., outsourcing Equation is not stable.
Table 4.5 looks at log change in industry price. Slight changes in the data such as dropping the computer industry have dramatic effects on the results.
Feenstra (page 133) a drop in the price of imported intermediates has effects that are observationally equivalent to the effect of skilled-based technological change.
Files Problem_4.2.do code and data_Chp4.dta are available on class ftp location. This problem is not discussed in Feenstra 2016.
// set mem 300m
* Annotated October 2014
log using log_4_2.log,replace
// use d:\feenstra_course\chap4\data_Chp4,clear
use c:\feenstra_course\chap4\data_Chp4,clear
// use e:\feenstra_course\chap4\data_Chp4,clear
* use /usr/local/lib/hhsfiles/data_Chp4,clear
drop if year==1972|year==1987
drop if sic72==2067|sic72==2794|sic72==3483
egen wagebill=sum(pay), by(year)
gen share=pay/wagebill
sort sic72 year
by sic72: gen lagshare=share[_n-1]
gen ashare=(share+lagshare)/2
by sic72: gen lagnwsh=nwsh[_n-1]
gen chanwsh=(nwsh-lagnwsh)*100/11
gen wchanwsh=chanwsh*ashare
gen wdlky=dlky*ashare
gen wdly=dly*ashare
gen wdsimat1a=dsimat1a*ashare
gen wdsimat1b=dsimat1a*ashare
gen diffout=dsimat1a-dsimat1b
gen wdiffout=(dsimat1a-dsimat1b)*ashare
gen wcosh_exp=dofsh*ashare
gen htsh_exp=dhtsh-dofsh
gen whtsh_exp=(dhtsh-dofsh)*ashare
gen wcosh_exa=dofsh1*ashare
gen htsh_exa=dhtsh1-dofsh1
gen whtsh_exa=(dhtsh1-dofsh1)*ashare
gen wcosh=ci*ashare
gen whtsh=dhtsh*ashare
* Check with the first column of Table 4.4 *
tabstat wchanwsh wdlky wdly wdsimat1a wcosh_exp whtsh_exp wcosh_exa whtsh_exa wcosh whtsh, stats(mean)
tabstat chanwsh dlky dly dsimat1a dofsh htsh_exp dofsh1 htsh_exa ci dhtsh, stats(mean)
* Reproduce the rest of the columns in Table 4.4 *
* replicates table 4.4 col 2
regress chanwsh dlky dly dsimat1a dofsh htsh_exp [aw=ashare], cluster (sic2)
* test ols
regress chanwsh dlky dly dsimat1a dofsh htsh_exp
* replicates table 4.4 col 3
regress chanwsh dlky dly dsimat1a dofsh1 htsh_exa [aw=ashare], cluster (sic2)
* test ols
regress chanwsh dlky dly dsimat1a dofsh1 htsh_exa
* replicates table 4.4 col 4
regress chanwsh dlky dly dsimat1a ci dhtsh [aw=ashare], cluster (sic2)
* test ols
regress chanwsh dlky dly dsimat1a ci dhtsh
* To instead distinguish narrow and other outsourcing, we can reproduce column (1) of table III in Feenstra and Hanson, 1999 *
tabstat wchanwsh wdlky wdly wdsimat1b wdiffout wcosh_exp whtsh_exp wcosh_exa whtsh_exa wcosh whtsh, stats(sum)
* Reproduce the rest of the columns in Table III *
regress chanwsh dlky dly dsimat1b diffout dofsh htsh_exp [aw=ashare], cluster (sic2)
regress chanwsh dlky dly dsimat1b diffout dofsh1 htsh_exa [aw=ashare], cluster (sic2)
regress chanwsh dlky dly dsimat1b diffout ci dhtsh [aw=ashare], cluster (sic2)
log close
* clear
exit
Note the relatively low EMBED Equation.DSMT4 terms. This model was estimated with Stata which uses the weighted regression coefficients on the raw data in a manner that is not used in Rats.
.
. * replicates table 4.4 col 2
. regress chanwsh dlky dly dsimat1a dofsh htsh_exp [aw=ashare], cluster (sic2)
(sum of wgt is 1.0000e+00)
Linear regression Number of obs = 447
F(5, 19) = 6.72
Prob > F = 0.0009
R-squared = 0.1557
Root MSE = .38912
(Std. Err. adjusted for 20 clusters in sic2)
------------------------------------------------------------------------------
| Robust
chanwsh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dlky | .0467948 .0113832 4.11 0.001 .0229695 .0706201
dly | .0197383 .0063797 3.09 0.006 .0063853 .0330912
dsimat1a | .1966658 .0962066 2.04 0.055 -.004697 .3980286
dofsh | .19534 .0915302 2.13 0.046 .0037651 .3869148
htsh_exp | -.0650465 .1371193 -0.47 0.641 -.3520404 .2219474
_cons | .2028764 .0428851 4.73 0.000 .1131169 .292636
------------------------------------------------------------------------------
. * test ols
. regress chanwsh dlky dly dsimat1a dofsh htsh_exp
Source | SS df MS Number of obs = 447
-------------+---------------------------------- F(5, 441) = 4.31
Model | 4.87604716 5 .975209432 Prob > F = 0.0008
Residual | 99.6927448 441 .226060646 R-squared = 0.0466
-------------+---------------------------------- Adj R-squared = 0.0358
Total | 104.568792 446 .234459175 Root MSE = .47546
------------------------------------------------------------------------------
chanwsh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dlky | .0194616 .010929 1.78 0.076 -.0020179 .0409411
dly | .0016347 .0087081 0.19 0.851 -.0154799 .0187492
dsimat1a | .0854863 .0403379 2.12 0.035 .006208 .1647647
dofsh | .1773819 .078036 2.27 0.024 .0240132 .3307505
htsh_exp | -.0063895 .1034685 -0.06 0.951 -.2097421 .1969632
_cons | .3044169 .0345396 8.81 0.000 .2365342 .3722995
------------------------------------------------------------------------------
.
. * replicates table 4.4 col 3
. regress chanwsh dlky dly dsimat1a dofsh1 htsh_exa [aw=ashare], cluster (sic2)
(sum of wgt is 1.0000e+00)
Linear regression Number of obs = 447
F(5, 19) = 8.01
Prob > F = 0.0003
R-squared = 0.1592
Root MSE = .38832
(Std. Err. adjusted for 20 clusters in sic2)
------------------------------------------------------------------------------
| Robust
chanwsh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dlky | .0444529 .0113121 3.93 0.001 .0207764 .0681293
dly | .0173278 .0062906 2.75 0.013 .0041613 .0304942
dsimat1a | .2207528 .0999711 2.21 0.040 .0115109 .4299947
dofsh1 | .4309753 .1671453 2.58 0.018 .0811362 .7808144
htsh_exa | .0052436 .0712031 0.07 0.942 -.1437862 .1542735
_cons | .2064394 .0397614 5.19 0.000 .1232178 .289661
------------------------------------------------------------------------------
. * test ols
. regress chanwsh dlky dly dsimat1a dofsh1 htsh_exa
Source | SS df MS Number of obs = 447
-------------+---------------------------------- F(5, 441) = 3.90
Model | 4.42334831 5 .884669662 Prob > F = 0.0018
Residual | 100.145444 441 .227087174 R-squared = 0.0423
-------------+---------------------------------- Adj R-squared = 0.0314
Total | 104.568792 446 .234459175 Root MSE = .47654
------------------------------------------------------------------------------
chanwsh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dlky | .0210034 .0110506 1.90 0.058 -.000715 .0427218
dly | .0009338 .0089879 0.10 0.917 -.0167306 .0185982
dsimat1a | .0899303 .0407687 2.21 0.028 .0098053 .1700553
dofsh1 | .2866326 .1631938 1.76 0.080 -.0341015 .6073667
htsh_exa | -.0076398 .1360646 -0.06 0.955 -.2750554 .2597758
_cons | .3244891 .0375708 8.64 0.000 .250649 .3983292
------------------------------------------------------------------------------
.
. * replicates table 4.4 col 4
. regress chanwsh dlky dly dsimat1a ci dhtsh [aw=ashare], cluster (sic2)
(sum of wgt is 1.0000e+00)
Linear regression Number of obs = 447
F(5, 19) = 11.87
Prob > F = 0.0000
R-squared = 0.1885
Root MSE = .38148
(Std. Err. adjusted for 20 clusters in sic2)
------------------------------------------------------------------------------
| Robust
chanwsh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dlky | .0399279 .0087378 4.57 0.000 .0216396 .0582162
dly | .0100379 .0062332 1.61 0.124 -.0030084 .0230841
dsimat1a | .1346024 .0883067 1.52 0.144 -.0502257 .3194306
ci | .0180834 .0066465 2.72 0.014 .0041722 .0319946
dhtsh | .0324624 .0519 0.63 0.539 -.0761655 .1410904
_cons | .1569685 .0446895 3.51 0.002 .0634323 .2505048
------------------------------------------------------------------------------
. * test ols
. regress chanwsh dlky dly dsimat1a ci dhtsh
Source | SS df MS Number of obs = 447
-------------+---------------------------------- F(5, 441) = 5.87
Model | 6.52521799 5 1.3050436 Prob > F = 0.0000
Residual | 98.0435739 441 .222321029 R-squared = 0.0624
-------------+---------------------------------- Adj R-squared = 0.0518
Total | 104.568792 446 .234459175 Root MSE = .47151
------------------------------------------------------------------------------
chanwsh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dlky | .0185285 .0105271 1.76 0.079 -.0021611 .0392181
dly | -.0008842 .0086306 -0.10 0.918 -.0178465 .0160781
dsimat1a | .0523652 .0414966 1.26 0.208 -.0291904 .1339207
ci | .013381 .0043628 3.07 0.002 .0048065 .0219555
dhtsh | .0870111 .0613731 1.42 0.157 -.0336091 .2076312
_cons | .2455871 .037316 6.58 0.000 .1722479 .3189263
------------------------------------------------------------------------------
.
In Table 4.4 Feenstra is estimating equation 4.18
For more details see the assignment sheet.
Example Code and results from B34S, Rats and Stata:
/;
/; Uses Align to insure 447 obs
/;
b34sexec options ginclude('Feenstra_ch4.mac') member(table4_4A);
b34srun;
/; b34sexec data set dropmiss; b34srun;
b34sexec matrix;
/; call loaddata;
call get(chanwsh dlky dly dsimat1a dofsh dofsh1 htsh_exp htsh_exa
ci dhtsh );
big=
'chanwsh dlky dly dsimat1a dofsh dofsh1 htsh_exp htsh_exa ci dhtsh';
call align(argument(big));
mod4_42=' chanwsh dlky dly dsimat1a dofsh htsh_exp';
mod4_42=' chanwsh dlky dly dsimat1a dofsh htsh_exp';
mod4_43=' chanwsh dlky dly dsimat1a dofsh1 htsh_exa';
mod4_44=' chanwsh dlky dly dsimat1a ci dhtsh';
n=namelist(argument(big));
do i=1,10;
call describe(argument(n(i)) :print);
enddo;
/; call tabulate(argument(mod4_42));
/; call tabulate(argument(mod4_43));
/; call tabulate(argument(mod4_44));
call olsq( argument(mod4_42) :print :white);
call gamfit( argument(mod4_42) :print );
call marspline(argument(mod4_42) :print);
call ppreg(argument(mod4_42) :print);
call olsq( argument(mod4_43) :print :white);
call gamfit( argument(mod4_43) :print );
call marspline(argument(mod4_43) :print);
call ppreg(argument(mod4_43) :print);
call olsq( argument(mod4_44) :print :white);
call gamfit( argument(mod4_44) :print );
call marspline(argument(mod4_44) :print);
call ppreg(argument(mod4_44) :print);
b34srun;
Note: If Feenstra_ch4.mac is on your computer, unless it is in c:\b34slm, do not use ginclude.
Note: The Stata code [aw=share] weights the regression including the constant by multiplying buy EMBED Equation.DSMT4 . What effect does this transformation have if the variables are not appropriate? Note that Rats and B34S and other software divide the right and left hand sides by EMBED Equation.DSMT4 .
Example code from Problem _4_2.do
set mem 300m
log using log_4_2.log,replace
use d:\feenstra_course\chap4\data_Chp4,clear
* use /usr/local/lib/hhsfiles/data_Chp4,clear
drop if year==1972|year==1987
drop if sic72==2067|sic72==2794|sic72==3483
egen wagebill=sum(pay), by(year)
gen share=pay/wagebill
sort sic72 year
by sic72: gen lagshare=share[_n-1]
gen ashare=(share+lagshare)/2
by sic72: gen lagnwsh=nwsh[_n-1]
gen chanwsh=(nwsh-lagnwsh)*100/11
gen wchanwsh=chanwsh*ashare
gen wdlky=dlky*ashare
gen wdly=dly*ashare
gen wdsimat1a=dsimat1a*ashare
gen wdsimat1b=dsimat1a*ashare
gen diffout=dsimat1a-dsimat1b
gen wdiffout=(dsimat1a-dsimat1b)*ashare
gen wcosh_exp=dofsh*ashare
gen htsh_exp=dhtsh-dofsh
gen whtsh_exp=(dhtsh-dofsh)*ashare
gen wcosh_exa=dofsh1*ashare
gen htsh_exa=dhtsh1-dofsh1
gen whtsh_exa=(dhtsh1-dofsh1)*ashare
gen wcosh=ci*ashare
gen whtsh=dhtsh*ashare
* Check with the first column of Table 4.4 *
tabstat wchanwsh wdlky wdly wdsimat1a wcosh_exp whtsh_exp wcosh_exa whtsh_exa wcosh whtsh, stats(mean)
tabstat chanwsh dlky dly dsimat1a dofsh htsh_exp dofsh1 htsh_exa ci dhtsh, stats(mean)
* Reproduce the rest of the columns in Table 4.4 *
* replicates table 4.4 col 2
regress chanwsh dlky dly dsimat1a dofsh htsh_exp [aw=ashare], cluster (sic2)
* test ols
regress chanwsh dlky dly dsimat1a dofsh htsh_exp
regress chanwsh dlky dly dsimat1a dofsh1 htsh_exa [aw=ashare], cluster (sic2)
* test ols
regress chanwsh dlky dly dsimat1a dofsh1 htsh_exa
regress chanwsh dlky dly dsimat1a ci dhtsh [aw=ashare], cluster (sic2)
* test ols
regress chanwsh dlky dly dsimat1a ci dhtsh
* To instead distinguish narrow and other outsourcing, we can reproduce column (1) of table III in Feenstra and Hanson, 1999 *
tabstat wchanwsh wdlky wdly wdsimat1b wdiffout wcosh_exp whtsh_exp wcosh_exa whtsh_exa wcosh whtsh, stats(sum)
* Reproduce the rest of the columns in Table III *
regress chanwsh dlky dly dsimat1b diffout dofsh htsh_exp [aw=ashare], cluster (sic2)
regress chanwsh dlky dly dsimat1b diffout dofsh1 htsh_exa [aw=ashare], cluster (sic2)
regress chanwsh dlky dly dsimat1b diffout ci dhtsh [aw=ashare], cluster (sic2)
log close
* clear
exit
Table 4.5 in Feenstra(2004) (same as Table 4.1 in Feenstra(2016) estimates equation 4.24 which calculates the implied change in factor prices assuming labor and capital are optimally selected or
EMBED Equation.DSMT4 (4.19)
Total factor productivity is
EMBED Equation.DSMT4 (4.22)
Where the cost shares EMBED Equation.DSMT4 sum to unity and EMBED Equation.DSMT4 is the first difference. While 4.22 could be estimated for the cost shares, a better strategy is to estimate
EMBED Equation.DSMT4 (4.24)
Where EMBED Equation.DSMT4 are the change in factor prices that are mandated by the change in product prices which is the dependent variable in (4.24). If these values are what occurred it is due to the linkage between product and factor prices mandated by the Stopler Samuelson theory.
File problem_3_a.do estimates Feenstra (2004) equation 4.5 or Feenstra (2016) eq 4.1. OLS models are run to test how the results might change if weighting was not used. Run2.b34 uses GAM, MARS and PPREG on the models in Table 4.5 / 4.1
// set mem 3m
log using log_4_3a.log,replace
// use d:\feenstra_course\chap4\data_Chp4.dta, clear
use c:\feenstra_course\chap4\data_Chp4.dta, clear
// use e:\feenstra_course\chap4\data_Chp4.dta, clear
* use /usr/local/lib/hhsfiles/data_Chp4.dta, clear
keep if year==1990
drop if sic72==2067
drop if sic72==2794
drop if sic72==3483
gen etfp=ptfp-err
gen adj1=1/(1-amesh)
gen etfp1=adj1*etfp
gen dlpvad1=adj1*dlpvad
gen apsh1=adj1*apsh
gen ansh1=adj1*ansh
gen aksh1=adj1*aksh
gen mshxpr=amsh*dlpmx
gen eshxpr=aosh*dlpe
* Reproduce Table 4.5 *
gen dlp34=dlp-mshxpr-eshxpr
regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
* OLS Model
regress dlp34 ptfp apsh ansh aksh , robust
preserve
drop if sic72==3573
regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
* OLS Model
regress dlp34 ptfp apsh ansh aksh , robust
regress dlp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
* OLS Model
regress dlp apsh ansh aksh mshxpr eshxpr, robust
restore
regress dlpvad1 etfp1 apsh1 ansh1 aksh1 [aw=mvshipsh],robust noconstant
* OLS Model
regress dlpvad1 etfp1 apsh1 ansh1 aksh1 ,robust noconstant
regress dlp etfp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
* OLS Model
regress dlp etfp apsh ansh aksh mshxpr eshxpr , robust
log close
* clear *
exit
Results are given below. Note that in Feenstra (2016, 90) he appeared to back away from his research in Table 4.1. The estimates in table 4.1 are troubling because they show that the estimates of EMBED Equation.DSMT4 are quite far off the mark: they do not reflect the actual changes in wages that occurred in the United States during the 1980s, are are quite sensitive to the data used used and specificatiuonb of the regression. Run2.b34 shows alternative estimators on the table 4.1 data. More research is needed on this important topic. The output from run2.b34 or run2.out is available on the class ftp location. More detail on this problem is given later in the class notes. The results shown next show how much of a difference using a weighted regression makes in improving the results. See that the R squared improved to .8957 from .6967.
.
.
. * Reproduce Table 4.5 *
.
. gen dlp34=dlp-mshxpr-eshxpr
.
. regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
(sum of wgt is 9.9873e-01)
Linear regression Number of obs = 447
F(4, 442) = 106.29
Prob > F = 0.0000
R-squared = 0.8957
Root MSE = .80656
------------------------------------------------------------------------------
| Robust
dlp34 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptfp | -.9631819 .0702093 -13.72 0.000 -1.101168 -.8251963
apsh | 3.062598 1.22198 2.51 0.013 .6609845 5.464212
ansh | 2.294716 1.430073 1.60 0.109 -.5158719 5.105305
aksh | 7.887571 .7810006 10.10 0.000 6.352634 9.422507
_cons | -.7051116 .3006016 -2.35 0.019 -1.295898 -.1143256
------------------------------------------------------------------------------
.
. * OLS Model
. regress dlp34 ptfp apsh ansh aksh , robust
Linear regression Number of obs = 447
F(4, 442) = 110.62
Prob > F = 0.0000
R-squared = 0.6967
Root MSE = .91728
------------------------------------------------------------------------------
| Robust
dlp34 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptfp | -.6790007 .0709856 -9.57 0.000 -.8185121 -.5394894
apsh | 3.455601 .8328199 4.15 0.000 1.818822 5.09238
ansh | 3.905478 1.754048 2.23 0.026 .4581676 7.352789
aksh | 7.394156 .71982 10.27 0.000 5.979461 8.808851
_cons | -.7849882 .1904677 -4.12 0.000 -1.159323 -.4106534
------------------------------------------------------------------------------
.
. preserve
. drop if sic72==3573
(1 observation deleted)
. regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
(sum of wgt is 9.8179e-01)
Linear regression Number of obs = 446
F(4, 441) = 92.17
Prob > F = 0.0000
R-squared = 0.8059
Root MSE = .74139
------------------------------------------------------------------------------
| Robust
dlp34 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptfp | -.7531151 .0751891 -10.02 0.000 -.9008886 -.6053416
apsh | 2.427856 1.162844 2.09 0.037 .142451 4.713261
ansh | 4.086394 1.722144 2.37 0.018 .7017647 7.471024
aksh | 8.058291 .9411699 8.56 0.000 6.208556 9.908027
_cons | -.8249273 .2930995 -2.81 0.005 -1.400973 -.2488819
------------------------------------------------------------------------------
. * OLS Model
. regress dlp34 ptfp apsh ansh aksh , robust
Linear regression Number of obs = 446
F(4, 441) = 135.75
Prob > F = 0.0000
R-squared = 0.6696
Root MSE = .87366
------------------------------------------------------------------------------
| Robust
dlp34 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptfp | -.6043067 .0418654 -14.43 0.000 -.6865873 -.5220261
apsh | 3.156235 .7864841 4.01 0.000 1.610513 4.701958
ansh | 4.954764 1.5334 3.23 0.001 1.941084 7.968443
aksh | 7.396599 .7390641 10.01 0.000 5.944073 8.849124
_cons | -.8377685 .1852263 -4.52 0.000 -1.201804 -.4737325
------------------------------------------------------------------------------
.
. regress dlp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
(sum of wgt is 9.8179e-01)
Linear regression Number of obs = 446
F(5, 440) = 10.85
Prob > F = 0.0000
R-squared = 0.4289
Root MSE = 1.2034
------------------------------------------------------------------------------
| Robust
dlp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
apsh | 3.605277 1.88524 1.91 0.056 -.0999163 7.310471
ansh | 6.202674 4.036466 1.54 0.125 -1.730475 14.13582
aksh | 9.535214 2.18722 4.36 0.000 5.236518 13.83391
mshxpr | 1.219304 .2471334 4.93 0.000 .7335958 1.705013
eshxpr | -.9301182 .9150299 -1.02 0.310 -2.728491 .8682541
_cons | -1.929187 .9147773 -2.11 0.036 -3.727063 -.1313111
------------------------------------------------------------------------------
. * OLS Model
. regress dlp apsh ansh aksh mshxpr eshxpr, robust
Linear regression Number of obs = 446
F(5, 440) = 24.65
Prob > F = 0.0000
R-squared = 0.3400
Root MSE = 1.2384
------------------------------------------------------------------------------
| Robust
dlp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
apsh | 5.629626 1.284501 4.38 0.000 3.105105 8.154147
ansh | 7.727702 2.065437 3.74 0.000 3.668354 11.78705
aksh | 8.611022 1.272484 6.77 0.000 6.110121 11.11192
mshxpr | 1.448936 .1923696 7.53 0.000 1.070858 1.827013
eshxpr | .0327104 .533676 0.06 0.951 -1.01616 1.081581
_cons | -2.629372 .6429471 -4.09 0.000 -3.893001 -1.365743
------------------------------------------------------------------------------
. restore
.
. regress dlpvad1 etfp1 apsh1 ansh1 aksh1 [aw=mvshipsh],robust noconstant
(sum of wgt is 9.9873e-01)
Linear regression Number of obs = 447
F(4, 443) > 99999.00
Prob > F = 0.0000
R-squared = 0.9998
Root MSE = .07762
------------------------------------------------------------------------------
| Robust
dlpvad1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
etfp1 | -1.000041 .0006831 -1463.88 0.000 -1.001384 -.9986986
apsh1 | 4.680657 .0157718 296.77 0.000 4.64966 4.711654
ansh1 | 5.482807 .0194677 281.64 0.000 5.444547 5.521068
aksh1 | 3.952538 .0083407 473.89 0.000 3.936146 3.96893
------------------------------------------------------------------------------
. * OLS Model
. regress dlpvad1 etfp1 apsh1 ansh1 aksh1 ,robust noconstant
Linear regression Number of obs = 447
F(4, 443) > 99999.00
Prob > F = 0.0000
R-squared = 0.9988
Root MSE = .1685
------------------------------------------------------------------------------
| Robust
dlpvad1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
etfp1 | -.9992624 .0042216 -236.70 0.000 -1.007559 -.9909655
apsh1 | 4.666086 .0550321 84.79 0.000 4.55793 4.774243
ansh1 | 5.437375 .0644382 84.38 0.000 5.310733 5.564018
aksh1 | 3.953762 .0221871 178.20 0.000 3.910157 3.997367
------------------------------------------------------------------------------
.
. regress dlp etfp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
(sum of wgt is 9.9873e-01)
Linear regression Number of obs = 447
F(6, 440) > 99999.00
Prob > F = 0.0000
R-squared = 0.9999
Root MSE = .0262
------------------------------------------------------------------------------
| Robust
dlp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
etfp | -1.000358 .000677 -1477.55 0.000 -1.001689 -.9990273
apsh | 4.700013 .011911 394.60 0.000 4.676603 4.723422
ansh | 5.443315 .0314405 173.13 0.000 5.381523 5.505107
aksh | 3.972308 .0150284 264.32 0.000 3.942772 4.001845
mshxpr | .9974072 .0023115 431.50 0.000 .9928643 1.00195
eshxpr | .9961108 .0057421 173.47 0.000 .9848254 1.007396
_cons | .0010799 .005423 0.20 0.842 -.0095784 .0117382
------------------------------------------------------------------------------
. * OLS Model
. regress dlp etfp apsh ansh aksh mshxpr eshxpr , robust
Linear regression Number of obs = 447
F(6, 440) > 99999.00
Prob > F = 0.0000
R-squared = 0.9989
Root MSE = .05637
------------------------------------------------------------------------------
| Robust
dlp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
etfp | -.9984327 .0024469 -408.04 0.000 -1.003242 -.9936236
apsh | 4.71449 .0145206 324.68 0.000 4.685952 4.743028
ansh | 5.443702 .0521618 104.36 0.000 5.341185 5.546219
aksh | 4.000907 .044225 90.47 0.000 3.913988 4.087825
mshxpr | .9907738 .0089715 110.44 0.000 .9731416 1.008406
eshxpr | .996285 .0058313 170.85 0.000 .9848243 1.007746
_cons | -.0023481 .007124 -0.33 0.742 -.0163494 .0116532
------------------------------------------------------------------------------
.
. log close
name:
log: C:\feenstra_course\chap4\log_4_3a.log
log type: text
closed on: 15 Jun 2016, 15:29:31
---------------------------------------------------------------------------------------------------------------------
. * clear *
. exit
end of do-file
. do "C:\feenstra_course\chap4\Problem_4_2.do"
. // set mem 300m
.
. * Annotated October 2014
.
. log using log_4_2.log,replace
---------------------------------------------------------------------------------------------------------------------
name:
log: C:\feenstra_course\chap4\log_4_2.log
log type: text
opened on: 15 Jun 2016, 15:30:45
.
. // use d:\feenstra_course\chap4\data_Chp4,clear
. use c:\feenstra_course\chap4\data_Chp4,clear
(Matrl Cons (72 SIC), 67-92)
. // use e:\feenstra_course\chap4\data_Chp4,clear
. * use /usr/local/lib/hhsfiles/data_Chp4,clear
. drop if year==1972|year==1987
(900 observations deleted)
. drop if sic72==2067|sic72==2794|sic72==3483
(6 observations deleted)
.
. egen wagebill=sum(pay), by(year)
. gen share=pay/wagebill
.
. sort sic72 year
. by sic72: gen lagshare=share[_n-1]
(447 missing values generated)
. gen ashare=(share+lagshare)/2
(447 missing values generated)
.
. by sic72: gen lagnwsh=nwsh[_n-1]
(447 missing values generated)
. gen chanwsh=(nwsh-lagnwsh)*100/11
(447 missing values generated)
.
. gen wchanwsh=chanwsh*ashare
(447 missing values generated)
. gen wdlky=dlky*ashare
(447 missing values generated)
. gen wdly=dly*ashare
(447 missing values generated)
. gen wdsimat1a=dsimat1a*ashare
(447 missing values generated)
. gen wdsimat1b=dsimat1a*ashare
(447 missing values generated)
. gen diffout=dsimat1a-dsimat1b
. gen wdiffout=(dsimat1a-dsimat1b)*ashare
(447 missing values generated)
. gen wcosh_exp=dofsh*ashare
(447 missing values generated)
. gen htsh_exp=dhtsh-dofsh
. gen whtsh_exp=(dhtsh-dofsh)*ashare
(447 missing values generated)
. gen wcosh_exa=dofsh1*ashare
(447 missing values generated)
. gen htsh_exa=dhtsh1-dofsh1
. gen whtsh_exa=(dhtsh1-dofsh1)*ashare
(447 missing values generated)
. gen wcosh=ci*ashare
(447 missing values generated)
. gen whtsh=dhtsh*ashare
(447 missing values generated)
.
. * Check with the first column of Table 4.4 *
.
. tabstat wchanwsh wdlky wdly wdsimat1a wcosh_exp whtsh_exp wcosh_exa whtsh_exa wcosh whtsh, stats(mean)
stats | wchanwsh wdlky wdly wdsim~1a wcosh_~p whtsh_~p wcosh_~a whtsh_~a wcosh whtsh
---------+----------------------------------------------------------------------------------------------------
mean | .0008702 .0015802 .0034469 .0009452 .0005605 .0003231 .0001573 .0003704 .0146791 .0008836
--------------------------------------------------------------------------------------------------------------
. tabstat chanwsh dlky dly dsimat1a dofsh htsh_exp dofsh1 htsh_exa ci dhtsh, stats(mean)
stats | chanwsh dlky dly dsimat1a dofsh htsh_exp dofsh1 htsh_exa ci dhtsh
---------+----------------------------------------------------------------------------------------------------
mean | .377241 .8334145 1.180938 .3791446 -.0020403 .1839697 -.0127181 .1451851 3.596809 .1819293
--------------------------------------------------------------------------------------------------------------
. * Reproduce the rest of the columns in Table 4.4 *
.
. * replicates table 4.4 col 2
. regress chanwsh dlky dly dsimat1a dofsh htsh_exp [aw=ashare], cluster (sic2)
(sum of wgt is 1.0000e+00)
Linear regression Number of obs = 447
F(5, 19) = 6.72
Prob > F = 0.0009
R-squared = 0.1557
Root MSE = .38912
(Std. Err. adjusted for 20 clusters in sic2)
------------------------------------------------------------------------------
| Robust
chanwsh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dlky | .0467948 .0113832 4.11 0.001 .0229695 .0706201
dly | .0197383 .0063797 3.09 0.006 .0063853 .0330912
dsimat1a | .1966658 .0962066 2.04 0.055 -.004697 .3980286
dofsh | .19534 .0915302 2.13 0.046 .0037651 .3869148
htsh_exp | -.0650465 .1371193 -0.47 0.641 -.3520404 .2219474
_cons | .2028764 .0428851 4.73 0.000 .1131169 .292636
------------------------------------------------------------------------------
. * test ols
. regress chanwsh dlky dly dsimat1a dofsh htsh_exp
Source | SS df MS Number of obs = 447
-------------+---------------------------------- F(5, 441) = 4.31
Model | 4.87604716 5 .975209432 Prob > F = 0.0008
Residual | 99.6927448 441 .226060646 R-squared = 0.0466
-------------+---------------------------------- Adj R-squared = 0.0358
Total | 104.568792 446 .234459175 Root MSE = .47546
------------------------------------------------------------------------------
chanwsh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dlky | .0194616 .010929 1.78 0.076 -.0020179 .0409411
dly | .0016347 .0087081 0.19 0.851 -.0154799 .0187492
dsimat1a | .0854863 .0403379 2.12 0.035 .006208 .1647647
dofsh | .1773819 .078036 2.27 0.024 .0240132 .3307505
htsh_exp | -.0063895 .1034685 -0.06 0.951 -.2097421 .1969632
_cons | .3044169 .0345396 8.81 0.000 .2365342 .3722995
------------------------------------------------------------------------------
.
. * replicates table 4.4 col 3
. regress chanwsh dlky dly dsimat1a dofsh1 htsh_exa [aw=ashare], cluster (sic2)
(sum of wgt is 1.0000e+00)
Linear regression Number of obs = 447
F(5, 19) = 8.01
Prob > F = 0.0003
R-squared = 0.1592
Root MSE = .38832
(Std. Err. adjusted for 20 clusters in sic2)
------------------------------------------------------------------------------
| Robust
chanwsh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dlky | .0444529 .0113121 3.93 0.001 .0207764 .0681293
dly | .0173278 .0062906 2.75 0.013 .0041613 .0304942
dsimat1a | .2207528 .0999711 2.21 0.040 .0115109 .4299947
dofsh1 | .4309753 .1671453 2.58 0.018 .0811362 .7808144
htsh_exa | .0052436 .0712031 0.07 0.942 -.1437862 .1542735
_cons | .2064394 .0397614 5.19 0.000 .1232178 .289661
------------------------------------------------------------------------------
. * test ols
. regress chanwsh dlky dly dsimat1a dofsh1 htsh_exa
Source | SS df MS Number of obs = 447
-------------+---------------------------------- F(5, 441) = 3.90
Model | 4.42334831 5 .884669662 Prob > F = 0.0018
Residual | 100.145444 441 .227087174 R-squared = 0.0423
-------------+---------------------------------- Adj R-squared = 0.0314
Total | 104.568792 446 .234459175 Root MSE = .47654
------------------------------------------------------------------------------
chanwsh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dlky | .0210034 .0110506 1.90 0.058 -.000715 .0427218
dly | .0009338 .0089879 0.10 0.917 -.0167306 .0185982
dsimat1a | .0899303 .0407687 2.21 0.028 .0098053 .1700553
dofsh1 | .2866326 .1631938 1.76 0.080 -.0341015 .6073667
htsh_exa | -.0076398 .1360646 -0.06 0.955 -.2750554 .2597758
_cons | .3244891 .0375708 8.64 0.000 .250649 .3983292
------------------------------------------------------------------------------
.
. * replicates table 4.4 col 4
. regress chanwsh dlky dly dsimat1a ci dhtsh [aw=ashare], cluster (sic2)
(sum of wgt is 1.0000e+00)
Linear regression Number of obs = 447
F(5, 19) = 11.87
Prob > F = 0.0000
R-squared = 0.1885
Root MSE = .38148
(Std. Err. adjusted for 20 clusters in sic2)
------------------------------------------------------------------------------
| Robust
chanwsh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dlky | .0399279 .0087378 4.57 0.000 .0216396 .0582162
dly | .0100379 .0062332 1.61 0.124 -.0030084 .0230841
dsimat1a | .1346024 .0883067 1.52 0.144 -.0502257 .3194306
ci | .0180834 .0066465 2.72 0.014 .0041722 .0319946
dhtsh | .0324624 .0519 0.63 0.539 -.0761655 .1410904
_cons | .1569685 .0446895 3.51 0.002 .0634323 .2505048
------------------------------------------------------------------------------
. * test ols
. regress chanwsh dlky dly dsimat1a ci dhtsh
Source | SS df MS Number of obs = 447
-------------+---------------------------------- F(5, 441) = 5.87
Model | 6.52521799 5 1.3050436 Prob > F = 0.0000
Residual | 98.0435739 441 .222321029 R-squared = 0.0624
-------------+---------------------------------- Adj R-squared = 0.0518
Total | 104.568792 446 .234459175 Root MSE = .47151
------------------------------------------------------------------------------
chanwsh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dlky | .0185285 .0105271 1.76 0.079 -.0021611 .0392181
dly | -.0008842 .0086306 -0.10 0.918 -.0178465 .0160781
dsimat1a | .0523652 .0414966 1.26 0.208 -.0291904 .1339207
ci | .013381 .0043628 3.07 0.002 .0048065 .0219555
dhtsh | .0870111 .0613731 1.42 0.157 -.0336091 .2076312
_cons | .2455871 .037316 6.58 0.000 .1722479 .3189263
------------------------------------------------------------------------------
.
. * To instead distinguish narrow and other outsourcing, we can reproduce column (1) of table III in Feenstra and Han
> son, 1999 *
.
. tabstat wchanwsh wdlky wdly wdsimat1b wdiffout wcosh_exp whtsh_exp wcosh_exa whtsh_exa wcosh whtsh, stats(sum)
stats | wchanwsh wdlky wdly wdsim~1b wdiffout wcosh_~p whtsh_~p wcosh_~a whtsh_~a wcosh
---------+----------------------------------------------------------------------------------------------------
sum | .3889885 .7063639 1.540769 .4225266 .1998607 .2505536 .1444164 .0703266 .1655768 6.561565
--------------------------------------------------------------------------------------------------------------
stats | whtsh
---------+----------
sum | .39497
--------------------
.
. * Reproduce the rest of the columns in Table III *
.
. regress chanwsh dlky dly dsimat1b diffout dofsh htsh_exp [aw=ashare], cluster (sic2)
(sum of wgt is 1.0000e+00)
Linear regression Number of obs = 447
F(6, 19) = 7.00
Prob > F = 0.0005
R-squared = 0.1627
Root MSE = .38794
(Std. Err. adjusted for 20 clusters in sic2)
------------------------------------------------------------------------------
| Robust
chanwsh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dlky | .0421152 .0141103 2.98 0.008 .0125821 .0716483
dly | .0178086 .0080568 2.21 0.040 .0009456 .0346716
dsimat1b | .2454613 .1692732 1.45 0.163 -.1088315 .5997541
diffout | .121362 .0457066 2.66 0.016 .025697 .2170271
dofsh | .2060218 .1021206 2.02 0.058 -.0077192 .4197627
htsh_exp | -.0392957 .1289341 -0.30 0.764 -.309158 .2305665
_cons | .206945 .0415146 4.98 0.000 .120054 .2938361
------------------------------------------------------------------------------
.
. regress chanwsh dlky dly dsimat1b diffout dofsh1 htsh_exa [aw=ashare], cluster (sic2)
(sum of wgt is 1.0000e+00)
Linear regression Number of obs = 447
F(6, 19) = 7.37
Prob > F = 0.0004
R-squared = 0.1650
Root MSE = .38742
(Std. Err. adjusted for 20 clusters in sic2)
------------------------------------------------------------------------------
| Robust
chanwsh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dlky | .0408212 .0141101 2.89 0.009 .0112884 .070354
dly | .0159677 .0078375 2.04 0.056 -.0004365 .0323718
dsimat1b | .2653356 .175142 1.51 0.146 -.1012407 .6319119
diffout | .1537718 .0502819 3.06 0.006 .0485307 .259013
dofsh1 | .4207269 .1707522 2.46 0.023 .0633383 .7781154
htsh_exa | .0143582 .07223 0.20 0.845 -.1368209 .1655373
_cons | .2137716 .0390531 5.47 0.000 .1320326 .2955107
------------------------------------------------------------------------------
.
. regress chanwsh dlky dly dsimat1b diffout ci dhtsh [aw=ashare], cluster (sic2)
(sum of wgt is 1.0000e+00)
Linear regression Number of obs = 447
F(6, 19) = 14.96
Prob > F = 0.0000
R-squared = 0.1995
Root MSE = .37933
(Std. Err. adjusted for 20 clusters in sic2)
------------------------------------------------------------------------------
| Robust
chanwsh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dlky | .0331274 .0119999 2.76 0.012 .0080113 .0582434
dly | .0068629 .0087795 0.78 0.444 -.0115128 .0252386
dsimat1b | .1928059 .1657117 1.16 0.259 -.1540328 .5396445
diffout | .0380044 .0539983 0.70 0.490 -.0750153 .1510241
ci | .0186984 .0068931 2.71 0.014 .0042711 .0331258
dhtsh | .0519438 .0512489 1.01 0.324 -.0553214 .1592091
_cons | .1612801 .0401323 4.02 0.001 .0772822 .2452781
------------------------------------------------------------------------------
.
. log close
name:
log: C:\feenstra_course\chap4\log_4_2.log
log type: text
closed on: 15 Jun 2016, 15:30:45
---------------------------------------------------------------------------------------------------------------------
.
. * clear
. exit
end of do-file
. do "C:\feenstra_course\chap4\Problem_4_3_b.do"
. // set mem 3m
. capture log close
. log using log_4_3b.log,replace
---------------------------------------------------------------------------------------------------------------------
name:
log: C:\feenstra_course\chap4\log_4_3b.log
log type: text
opened on: 15 Jun 2016, 15:31:29
.
. // use d:\feenstra_course\Chap4\data_Chp4, clear
. use c:\feenstra_course\Chap4\data_Chp4, clear
(Matrl Cons (72 SIC), 67-92)
. // use d:\feenstra_course\Chap4\data_Chp4, clear
. // use e:\feenstra_course\Chap4\data_Chp4, clear
.
.
. keep if year==1990
(1,350 observations deleted)
. drop if sic72==2067
(1 observation deleted)
. drop if sic72==2794
(1 observation deleted)
. drop if sic72==3483
(1 observation deleted)
. gen etfp=ptfp-err
. gen adj1=1/(1-amesh)
. gen etfp1=adj1*etfp
. gen dlpvad1=adj1*dlpvad
. gen apsh1=adj1*apsh
. gen ansh1=adj1*ansh
. gen aksh1=adj1*aksh
. gen t4dlpvad=(dlpvad+etfp)*adj1
. preserve
.
. * Reproduce the first column of Table IV *
. * generating difference measure of outsourcing *
.
. gen dsimatd1=dsimat1a-dsimat1b
.
. * generating difference measure of high tech share *
.
. gen dhtdsh=dhtsh-dofsh
.
. * check whether we are using the right variable as described in table II *
.
. sum dsimatd1 dhtdsh dofsh [aw=mvshipsh]
Variable | Obs Weight Mean Std. Dev. Min Max
-------------+-----------------------------------------------------------------
dsimatd1 | 447 .998730832 .1598317 .3220691 -1.763297 2.735888
dhtdsh | 447 .998730832 .1281193 .1962393 -.0841524 .9744269
dofsh | 447 .998730832 .1983744 .244483 -.3634307 .8313999
.
. regress t4dlpvad dsimat1b dsimatd1 dofsh dhtdsh [aw=mvshipsh], cluster(sic2)
(sum of wgt is 9.9873e-01)
Linear regression Number of obs = 447
F(4, 19) = 5.40
Prob > F = 0.0044
R-squared = 0.1534
Root MSE = .14521
(Std. Err. adjusted for 20 clusters in sic2)
------------------------------------------------------------------------------
| Robust
t4dlpvad | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dsimat1b | .0635024 .030585 2.08 0.052 -.0005128 .1275177
dsimatd1 | .0788136 .0472159 1.67 0.111 -.0200103 .1776375
dofsh | .1665693 .0658945 2.53 0.021 .0286505 .3044881
dhtdsh | .075982 .0722494 1.05 0.306 -.0752377 .2272016
_cons | 4.262727 .0322917 132.01 0.000 4.19514 4.330314
------------------------------------------------------------------------------
.
. * Reproduce Table V using the coefficients in column(1) of Table IV *
.
. gen wt=mvshipsh^.5
. gen apsh5=apsh1*wt
. gen ansh5=ansh1*wt
. gen aksh5=aksh1*wt
. gen narrout=dsimat1b*wt*_coef[dsimat1b]
. gen diffout=dsimatd1*wt*_coef[dsimatd1]
. gen comsh=dofsh*wt*_coef[dofsh]
. gen difcom=dhtdsh*wt*_coef[dhtdsh]
.
. sum narrout diffout comsh difcom
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
narrout | 447 .0004107 .0012838 -.0077687 .0131523
diffout | 447 .0005548 .0012192 -.0053996 .0156501
comsh | 447 .0012452 .0021439 -.0028531 .0110437
difcom | 447 .0004038 .0007386 -.0009354 .0064305
.
. regress narrout apsh5 ansh5 aksh5, noconstant
Source | SS df MS Number of obs = 447
-------------+---------------------------------- F(3, 444) = 52.29
Model | .000211586 3 .000070529 Prob > F = 0.0000
Residual | .000598861 444 1.3488e-06 R-squared = 0.2611
-------------+---------------------------------- Adj R-squared = 0.2561
Total | .000810447 447 1.8131e-06 Root MSE = .00116
------------------------------------------------------------------------------
narrout | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
apsh5 | -.0095155 .0093511 -1.02 0.309 -.0278934 .0088624
ansh5 | .0986666 .0147744 6.68 0.000 .0696303 .127703
aksh5 | .0026378 .003536 0.75 0.456 -.0043116 .0095872
------------------------------------------------------------------------------
. regress diffout apsh5 ansh5 aksh5, noconstant
Source | SS df MS Number of obs = 447
-------------+---------------------------------- F(3, 444) = 44.65
Model | .000185525 3 .000061842 Prob > F = 0.0000
Residual | .000615016 444 1.3852e-06 R-squared = 0.2317
-------------+---------------------------------- Adj R-squared = 0.2266
Total | .000800542 447 1.7909e-06 Root MSE = .00118
------------------------------------------------------------------------------
diffout | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
apsh5 | .0203644 .0094764 2.15 0.032 .0017403 .0389885
ansh5 | .0628478 .0149723 4.20 0.000 .0334224 .0922732
aksh5 | -.0011399 .0035834 -0.32 0.751 -.0081824 .0059026
------------------------------------------------------------------------------
. regress comsh apsh5 ansh5 aksh5, noconstant
Source | SS df MS Number of obs = 447
-------------+---------------------------------- F(3, 444) = 153.17
Model | .001395044 3 .000465015 Prob > F = 0.0000
Residual | .001347998 444 3.0360e-06 R-squared = 0.5086
-------------+---------------------------------- Adj R-squared = 0.5053
Total | .002743042 447 6.1366e-06 Root MSE = .00174
------------------------------------------------------------------------------
comsh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
apsh5 | -.0049722 .0140295 -0.35 0.723 -.0325447 .0226004
ansh5 | .2480141 .0221661 11.19 0.000 .2044505 .2915777
aksh5 | .0007009 .0053051 0.13 0.895 -.0097253 .0111272
------------------------------------------------------------------------------
. regress difcom apsh5 ansh5 aksh5, noconstant
Source | SS df MS Number of obs = 447
-------------+---------------------------------- F(3, 444) = 68.02
Model | .000099567 3 .000033189 Prob > F = 0.0000
Residual | .000216627 444 4.8790e-07 R-squared = 0.3149
-------------+---------------------------------- Adj R-squared = 0.3103
Total | .000316194 447 7.0737e-07 Root MSE = .0007
------------------------------------------------------------------------------
difcom | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
apsh5 | .0259448 .0056241 4.61 0.000 .0148915 .036998
ansh5 | .0069214 .0088859 0.78 0.436 -.0105422 .0243851
aksh5 | .0043305 .0021267 2.04 0.042 .0001509 .0085102
------------------------------------------------------------------------------
.
. restore
.
. * Reproduce column (2) of Table IV *
.
. preserve
.
. * generating difference measure of outsourcing *
.
. gen dsimatd1=dsimat1a-dsimat1b
.
. * generate difference measure of high tech share with ex ante rental price *
.
. gen dhtdsh1=dhtsh1-dofsh1
.
. * check whether we are using the right variable as described in table II *
.
. sum dsimatd1 dhtdsh1 dofsh1 [aw=mvshipsh]
Variable | Obs Weight Mean Std. Dev. Min Max
-------------+-----------------------------------------------------------------
dsimatd1 | 447 .998730832 .1598317 .3220691 -1.763297 2.735888
dhtdsh1 | 447 .998730832 .1643722 .1506561 .0204334 .9001704
dofsh1 | 447 .998730832 .0534329 .124323 -.2700591 .3795505
.
. regress t4dlpvad dsimat1b dsimatd1 dofsh1 dhtdsh1 [aw=mvshipsh], cluster(sic2)
(sum of wgt is 9.9873e-01)
Linear regression Number of obs = 447
F(4, 19) = 2.42
Prob > F = 0.0844
R-squared = 0.1089
Root MSE = .14898
(Std. Err. adjusted for 20 clusters in sic2)
------------------------------------------------------------------------------
| Robust
t4dlpvad | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dsimat1b | .0795164 .034676 2.29 0.033 .0069387 .1520942
dsimatd1 | .11368 .0440198 2.58 0.018 .0215455 .2058144
dofsh1 | .1924159 .1083624 1.78 0.092 -.0343891 .4192209
dhtdsh1 | -.0477944 .0820494 -0.58 0.567 -.2195258 .1239369
_cons | 4.294261 .0385949 111.27 0.000 4.213481 4.375041
------------------------------------------------------------------------------
.
. * Reproduce column (3) of Table IV *
.
. * generating difference measure of high tech share *
.
. gen dhtdsh=dhtsh-dofsh
.
. regress t4dlpvad dsimat1b dsimatd1 ci dhtsh [aw=mvshipsh], cluster(sic2)
(sum of wgt is 9.9873e-01)
Linear regression Number of obs = 447
F(4, 19) = 5.96
Prob > F = 0.0028
R-squared = 0.2129
Root MSE = .14002
(Std. Err. adjusted for 20 clusters in sic2)
------------------------------------------------------------------------------
| Robust
t4dlpvad | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dsimat1b | .0404059 .0295213 1.37 0.187 -.0213829 .1021947
dsimatd1 | .0351687 .0488208 0.72 0.480 -.0670145 .1373518
ci | .0081792 .0045064 1.82 0.085 -.0012528 .0176112
dhtsh | .093074 .0496036 1.88 0.076 -.0107475 .1968955
_cons | 4.243861 .0334856 126.74 0.000 4.173775 4.313947
------------------------------------------------------------------------------
.
Example Code to Test WLS with "junk" data. Test case shows how WLS can give "significant"
but misleading answers. WLS is shown with Rats and Stata. Note that Stata uses a non standard weighting system. B34S first build a random left hands side variable and a random right hand side variable and a random vector of "weights" to form a "junk" model. Next OLS and weignted least squares are run in three software systems. The results speak for themselves.
/;
/; B34S-Stata-Rats
/;
b34sexec matrix;
* tests weighted regression ;
* illustrates how weighted least squares can give "significance";
n=10000;
k=4;
y=rn(array(n:));
w=abs(rn(array(n:)));
x=rn(array(n,k:));
/;
/; OLS Model
/;
/; quick way to go to weighted least squares assuming
/; vector or matrix input
call olsq(y x :print :savex);
ww=1./afam(sqrt(w));
%xnew=transpose(transpose(afam(%x))*ww);
%ynew=afam(%y)*ww;
call print('Weighted Least Squares':);
call olsq(%ynew %xnew :noint :print);
/; pass data to test WLS with Stata and Rats
call dmfput(y,w :file 'file_1.dmf'
:member file1
:comment 'y and w for weighted regression test'
);
call dmfput(x :file 'file_2.dmf'
:member file2
);
b34srun;
/;
/; test reading the save
/;
b34sexec data file('file_1.dmf') filef=fdmf
dmfmember(file1)
;
b34srun;
b34sexec data file('file_2.dmf') filef=fdmf
dmfmember(file2)
;
b34srun;
/;
/; Merge the two DMF files
/;
b34sexec merge
file1('file_1.dmf')
file2('file_2.dmf')
file3('file_3.dmf')
member1(file1) member2(file2) member3(file3)
outfmt=formatted
/; comment('Test of effect of Weighted Regression')
;
b34srun;
/;
/; illustrate a read of a DMF into the matrix Command
/;
b34sexec matrix;
call dmfget(:file 'file_3.dmf' :member file3 :print);
b34srun;
/;
b34sexec data file('file_3.dmf') filef=fdmf; b34srun;
/;
/; This is the best way to go
/;
b34sexec options open('statdata.do') unit(28) disp=unknown$ b34srun$
b34sexec options clean(28)$ b34srun$
b34sexec options open('stata.do') unit(29) disp=unknown$ b34srun$
b34sexec options clean(29)$ b34srun$
b34sexec pgmcall idata=28 icntrl=29$
stata$
pgmcards$
// uncomment if do not use /e
// log using stata.log, text
// describe
regress y m1*
regress y m1* [aw=1/w]
b34sreturn$
b34seend$
b34sexec options close(28); b34srun;
b34sexec options close(29); b34srun;
b34sexec options
dodos('stata /e stata.do');
b34srun;
b34sexec options npageout
writeout('output from stata',' ',' ')
copyfout('stata.log')
dodos('erase stata.do','erase stata.log','erase statdata.do') $
b34srun$
/$ user places RATS commands between
/$ PGMCARDS$
/$ note: user RATS commands here
/$ B34SRETURN$
/$
b34sexec options open('rats.dat') unit(28) disp=unknown$ b34srun$
b34sexec options open('rats.in') unit(29) disp=unknown$ b34srun$
b34sexec options clean(28)$ b34srun$
b34sexec options clean(29)$ b34srun$
b34sexec pgmcall$
rats
pcomments('* ',
'* Data passed from B34S(r) system to RATS',
'* ',
"display @1 %dateandtime() @33 ' Rats Version ' %ratsversion()"
'* ') $
PGMCARDS$
*
linreg y
# constant m1col__1 m1col__2 m1col__3 m1col__4
linreg(spread=w) y
# constant m1col__1 m1col__2 m1col__3 m1col__4
b34sreturn$
b34srun $
b34sexec options close(28)$ b34srun$
b34sexec options close(29)$ b34srun$
b34sexec options
/$ dodos(' rats386 rats.in rats.out ')
dodos('start /w /r rats32s rats.in /run')
dounix('rats rats.in rats.out')$ B34SRUN$
b34sexec options npageout
WRITEOUT('Output from RATS',' ',' ')
COPYFOUT('rats.out')
dodos('ERASE rats.in','ERASE rats.out','ERASE rats.dat')
dounix('rm rats.in','rm rats.out','rm rats.dat')
$
Results
B34SI Matrix Command. d/m/y 15/ 8/10. h:m:s 21:18:32.
=> * TESTS WEIGHTED REGRESSION $
=> * ILLUSTRATES HOW WEIGHTED LEAST SQUARES CAN GIVE "SIGNIFICANCE"$
=> N=10000$
=> K=4$
=> Y=RN(ARRAY(N:))$
=> W=ABS(RN(ARRAY(N:)))$
=> X=RN(ARRAY(N,K:))$
=> CALL OLSQ(Y X :PRINT :SAVEX)$
Results for the OLS Model of 10,000 observations on "junk" data.
Ordinary Least Squares Estimation
Dependent variable Y
Centered R**2 1.283800318883199E-003
Adjusted R**2 8.841139958492355E-004
Residual Sum of Squares 10083.5816512905
Residual Variance 1.00886259642727
Standard Error 1.00442152327958
Total Sum of Squares 10096.5435971802
Log Likelihood -14231.0024774754
Mean of the Dependent Variable -1.106035532484140E-002
Std. Error of Dependent Variable 1.00486582947752
Sum Absolute Residuals 8006.64281307591
F( 4, 9995) 3.21201963864575
F Significance 0.987921184267561
1/Condition XPX 0.945609242214882
Maximum Absolute Residual 4.03166296169811
Number of Observations 10000
Variable Lag Coefficient SE t
Col____1 0 -0.21613705E-01 0.10089154E-01 -2.1422713
Col____2 0 0.99455008E-02 0.10155609E-01 0.97931108
Col____3 0 -0.25503089E-01 0.99336699E-02 -2.5673381
Col____4 0 -0.83857056E-02 0.10068969E-01 -0.83282667
CONSTANT 0 -0.11056801E-01 0.10044510E-01 -1.1007806
=> WW=1./AFAM(SQRT(W))$
=> %XNEW=TRANSPOSE(TRANSPOSE(AFAM(%X))*WW)$
=> %YNEW=AFAM(%Y)*WW$
=> CALL PRINT('Weighted Least Squares':)$
Weighted Least Squares
Weighted Least Squares of above model that will be validated with Rats and Stata below.
=> CALL OLSQ(%YNEW %XNEW :NOINT :PRINT)$
Ordinary Least Squares Estimation
Dependent variable %YNEW
Centered R**2 0.125430978105311
Adjusted R**2 0.125080975495248
Residual Sum of Squares 104592.075351771
Residual Variance 10.4644397550546
Standard Error 3.23487863065287
Total Sum of Squares 119592.705359240
Log Likelihood -25926.7988036037
Mean of the Dependent Variable -1.522589703452888E-002
Std. Error of Dependent Variable 3.45839075041880
Sum Absolute Residuals 14772.8577916210
F( 4, 9995) 358.371550665769
F Significance 0.999999999999874
1/Condition XPX 0.255815512089038
Maximum Absolute Residual 110.962446369039
Number of Observations 10000
Variable Lag Coefficient SE t
Col____1 0 0.13243375 0.98266760E-02 13.476963
Col____2 0 0.32195210 0.11437311E-01 28.149282
Col____3 0 0.31666619E-01 0.95544411E-02 3.3143350
Col____4 0 -0.15003716 0.11766487E-01 -12.751228
Col____5 0 0.60455770E-01 0.97906901E-02 6.1748221
=> CALL DMFPUT(Y,W :FILE 'file_1.dmf'
=> :MEMBER FILE1
=> :COMMENT 'y and w for weighted regression test'
=> )$
=> CALL DMFPUT(X :FILE 'file_2.dmf'
=> :MEMBER FILE2
=> )$
B34S Matrix Command Ending. Last Command reached.
Space available in allocator 14856808, peak space used 581397
Number variables used 49, peak number used 51
Number temp variables used 45, # user temp clean 0
B34SI 8.11E (D:M:Y) 15/ 8/10 (H:M:S) 21:18:32 DATA STEP Data from Matrix Command PAGE 1
Variable # Cases Mean Std Deviation Variance Maximum Minimum
Y 1 10000 -0.1106035532E-01 1.004865829 1.009755335 3.460313180 -4.001602802
W 2 10000 0.7897850809 0.5970220007 0.3564352694 3.646702144 0.3183224533E-04
CONSTANT 3 10000 1.000000000 0.000000000 0.000000000 1.000000000 1.000000000
Number of observations in data file 10000
Current missing variable code 1.000000000000000E+031
Data begins on (D:M:Y) 2: 1:1960 ends 2: 1:****. Frequency is 1
B34SI 8.11E (D:M:Y) 15/ 8/10 (H:M:S) 21:18:33 DATA STEP Data from Matrix Command PAGE 2
Variable # Cases Mean Std Deviation Variance Maximum Minimum
M1COL__1 1 10000 0.4888179470E-02 0.9956528401 0.9913245780 3.689869729 -3.764639466
M1COL__2 2 10000 0.2011437524E-03 0.9891161269 0.9783507125 3.785540146 -4.161275084
M1COL__3 3 10000 -0.2136661813E-02 1.011215800 1.022557394 3.964659396 -3.849832359
M1COL__4 4 10000 -0.5438502297E-02 0.9976399892 0.9952855480 3.611193295 -3.935043696
CONSTANT 5 10000 1.000000000 0.000000000 0.000000000 1.000000000 1.000000000
Number of observations in data file 10000
Current missing variable code 1.000000000000000E+031
Data begins on (D:M:Y) 2: 1:1960 ends 2: 1:****. Frequency is 1
B34SI Matrix Command. d/m/y 15/ 8/10. h:m:s 21:18:33.
=> CALL DMFGET(:FILE 'file_3.dmf' :MEMBER FILE3 :PRINT)$
DMF File Name file_3.dmf
Member FILE3
Created on date 15/ 8/10
Time 21:18:32
Number of series 6
Number of observations 10000
Frequency 1.00000000000000
File format is FORMATTED
Base Date d/m/y 2/ 1/1960
Header Data from Matrix Command
Number of comments 1
Comments:
Series: Type Label:
Y 0
W 0
M1COL__1 0
M1COL__2 0
M1COL__3 0
M1COL__4 0
B34S Matrix Command Ending. Last Command reached.
Space available in allocator 14856979, peak space used 100370
Number variables used 14, peak number used 14
Number temp variables used 7, # user temp clean 0
B34SI 8.11E (D:M:Y) 15/ 8/10 (H:M:S) 21:18:34 DATA STEP Data from Matrix Command PAGE 3
Variable # Cases Mean Std Deviation Variance Maximum Minimum
Y 1 10000 -0.1106035532E-01 1.004865829 1.009755335 3.460313180 -4.001602802
W 2 10000 0.7897850809 0.5970220007 0.3564352694 3.646702144 0.3183224533E-04
M1COL__1 3 10000 0.4888179470E-02 0.9956528401 0.9913245780 3.689869729 -3.764639466
M1COL__2 4 10000 0.2011437524E-03 0.9891161269 0.9783507125 3.785540146 -4.161275084
M1COL__3 5 10000 -0.2136661813E-02 1.011215800 1.022557394 3.964659396 -3.849832359
M1COL__4 6 10000 -0.5438502297E-02 0.9976399892 0.9952855480 3.611193295 -3.935043696
CONSTANT 7 10000 1.000000000 0.000000000 0.000000000 1.000000000 1.000000000
Number of observations in data file 10000
Current missing variable code 1.000000000000000E+031
Data begins on (D:M:Y) 2: 1:1960 ends 2: 1:****. Frequency is 1
output from stata
___ ____ ____ ____ ____ (R)
/__ / ____/ / ____/
___/ / /___/ / /___/ 11.1 Copyright 2009 StataCorp LP
Statistics/Data Analysis StataCorp
4905 Lakeway Drive
College Station, Texas 77845 USA
800-STATA-PC http://www.stata.com
979-696-4600 stata@stata.com
979-696-4601 (fax)
Single-user Stata perpetual license:
Serial number: 30110535901
Licensed to: Houston H. Stokes
University of Illinois at Chicago
Notes:
1. (/m# option or -set memory-) 120.00 MB allocated to data
2. Stata running in batch mode
. do stata.do
. * File built by B34S on 15/ 8/10 at 21:18:34
. run statdata.do
Stata validates the B34S results. Note command setup.
. regress y m1*
Source | SS df MS Number of obs = 10000
-------------+------------------------------ F( 4, 9995) = 3.21
Model | 12.9619459 4 3.24048647 Prob > F = 0.0121
Residual | 10083.5817 9995 1.0088626 R-squared = 0.0013
-------------+------------------------------ Adj R-squared = 0.0009
Total | 10096.5436 9999 1.00975534 Root MSE = 1.0044
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
m1col__1 | -.0216137 .0100892 -2.14 0.032 -.0413905 -.0018369
m1col__2 | .0099455 .0101556 0.98 0.327 -.0099615 .0298525
m1col__3 | -.0255031 .0099337 -2.57 0.010 -.0449751 -.0060311
m1col__4 | -.0083857 .010069 -0.83 0.405 -.0281229 .0113515
_cons | -.0110568 .0100445 -1.10 0.271 -.0307461 .0086325
------------------------------------------------------------------------------
. regress y m1* [aw=1/w]
(sum of wgt is 1.3529e+05)
Source | SS df MS Number of obs = 10000
-------------+------------------------------ F( 4, 9995) = 279.99
Model | 866.267364 4 216.566841 Prob > F = 0.0000
Residual | 7730.9091 9995 .773477649 R-squared = 0.1008
-------------+------------------------------ Adj R-squared = 0.1004
Total | 8597.17646 9999 .859803627 Root MSE = .87948
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
m1col__1 | .1324338 .0098267 13.48 0.000 .1131715 .151696
m1col__2 | .3219521 .0114373 28.15 0.000 .2995327 .3443715
m1col__3 | .0316666 .0095544 3.31 0.001 .012938 .0503952
m1col__4 | -.1500372 .0117665 -12.75 0.000 -.1731018 -.1269725
_cons | .0604558 .0097907 6.17 0.000 .041264 .0796475
------------------------------------------------------------------------------
.
end of do-file
Output from RATS
Rats used to validate B34S and Stata results.
*
* Data passed from B34S(r) system to RATS
*
display @1 %dateandtime() @33 ' Rats Version ' %ratsversion()
08/15/2010 21:18 Rats Version 7.30000
*
CALENDAR(IRREGULAR)
ALLOCATE 10000
OPEN DATA rats.dat
DATA(FORMAT=FREE,ORG=OBS, $
MISSING= 0.1000000000000000E+32 ) / $
Y $
W $
M1COL__1 $
M1COL__2 $
M1COL__3 $
M1COL__4 $
CONSTANT
SET TREND = T
TABLE
Series Obs Mean Std Error Minimum Maximum
Y 10000 -0.011060 1.004866 -4.001603 3.460313
W 10000 0.789785 0.597022 0.000032 3.646702
M1COL__1 10000 0.004888 0.995653 -3.764639 3.689870
M1COL__2 10000 0.000201 0.989116 -4.161275 3.785540
M1COL__3 10000 -0.002137 1.011216 -3.849832 3.964659
M1COL__4 10000 -0.005439 0.997640 -3.935044 3.611193
TREND 10000 5000.500000 2886.895680 1.000000 10000.000000
*
linreg y
# constant m1col__1 m1col__2 m1col__3 m1col__4
Linear Regression - Estimation by Least Squares
Dependent Variable Y
Usable Observations 10000 Degrees of Freedom 9995
Centered R**2 0.001284 R Bar **2 0.000884
Uncentered R**2 0.001405 T x R**2 14.048
Mean of Dependent Variable -0.011060355
Std Error of Dependent Variable 1.004865829
Standard Error of Estimate 1.004421523
Sum of Squared Residuals 10083.581651
Regression F(4,9995) 3.2120
Significance Level of F 0.01207882
Log Likelihood -14231.00248
Durbin-Watson Statistic 1.980979
Variable Coeff Std Error T-Stat Signif
********************************************************************************
1. Constant -0.011056801 0.010044510 -1.10078 0.27101868
2. M1COL__1 -0.021613705 0.010089154 -2.14227 0.03219575
3. M1COL__2 0.009945501 0.010155609 0.97931 0.32745000
4. M1COL__3 -0.025503089 0.009933670 -2.56734 0.01026268
5. M1COL__4 -0.008385706 0.010068969 -0.83283 0.40496239
linreg(spread=w) y
# constant m1col__1 m1col__2 m1col__3 m1col__4
Linear Regression - Estimation by Weighted Least Squares
Dependent Variable Y
Usable Observations 10000 Degrees of Freedom 9995
Centered R**2 0.125431 R Bar **2 0.125081
Uncentered R**2 0.125448 T x R**2 1254.479
Mean of Dependent Variable -0.015225897
Std Error of Dependent Variable 3.458390750
Standard Error of Estimate 3.234878631
Sum of Squared Residuals 104592.07535
Log Likelihood -22690.72492
Durbin-Watson Statistic 1.952328
Variable Coeff Std Error T-Stat Signif
********************************************************************************
1. Constant 0.060455770 0.009790690 6.17482 0.00000000
2. M1COL__1 0.132433752 0.009826676 13.47696 0.00000000
3. M1COL__2 0.321952098 0.011437311 28.14928 0.00000000
4. M1COL__3 0.031666619 0.009554441 3.31434 0.00092188
5. M1COL__4 -0.150037162 0.011766487 -12.75123 0.00000000
B34S normal exit on Date (D:M:Y) 15/ 8/10 at Time (H:M:S) 21:18:40Results:
Note EMBED Equation.DSMT4 values reported for B34S and Rats agree. Stata made an "adjustment."
Code for Leverage Plots with OLS, GAM and Marspline
/;
/; Uses Align to insure 447 obs
/;
b34sexec options ginclude('Feenstra_ch4.mac') member(table4_4A);
b34srun;
b34sexec matrix;
call echooff;
call get(chanwsh dlky dly dsimat1a dofsh dofsh1 htsh_exp htsh_exa
ci dhtsh );
big=
'chanwsh dlky dly dsimat1a dofsh dofsh1 htsh_exp htsh_exa ci dhtsh';
call align(argument(big));
mod4_42=' chanwsh dlky dly dsimat1a dofsh htsh_exp';
mod4_42=' chanwsh dlky dly dsimat1a dofsh htsh_exp';
mod4_43=' chanwsh dlky dly dsimat1a dofsh1 htsh_exa';
mod4_44=' chanwsh dlky dly dsimat1a ci dhtsh';
n=namelist(argument(big));
datamean=1;
dopass1=1;
dopass2=0;
if(datamean.ne.0)then;
do i=1,10;
call describe(argument(n(i)) :print);
enddo;
endif;
if(dopass1.ne.0)then;
call load(contrib);
call contribi;
/;
/; specific settings
/;
do_ppexp=0;
_m=8;
iols=2;
/; _mi=1;
_mi=2;
_nk=40;
/; ppreg code
_m=30;
iols=2;
/; iols=4;
isave=1;
/; rf code
_mtry=2;
_mtree=200;
call character(fsv_info,'1. Model 1');
call character(l_hand_s,'chanwsh');
call character(_args, 'dlky dly dsimat1a dofsh htsh_exp');
call character(_argsg,'dlky dly dsimat1a dofsh htsh_exp');
call contribl;
call contribd;
endif;
/; call tabulate(argument(mod4_42));
/; call tabulate(argument(mod4_43));
/; call tabulate(argument(mod4_44));
if(dopass2.ne.0)then;
call olsq( chanwsh argument(mod4_42) :print :white);
call gamfit( chanwsh argument(mod4_42) :print );
call marspline(chanwsh argument(mod4_42) :print :mi 3 :nk 20);
call ppreg(chanwsh argument(mod4_42) :print);
call olsq( chanwsh argument(mod4_43) :print :white);
call gamfit( chanwsh argument(mod4_43) :print );
call marspline(chanwsh argument(mod4_43) :print :mi 3 :nk 20);
call ppreg(chanwsh argument(mod4_43) :print);
call olsq( chanwsh argument(mod4_44) :print :white);
call gamfit( chanwsh argument(mod4_44) :print );
call marspline(chanwsh argument(mod4_44) :print :mi 3 :nk 20);
call ppreg(chanwsh argument(mod4_44) :print);
endif;
b34srun;
Edited output from Leverage Plots
Settings for Leverage plots
Mars Models
Number of knots for MARS (_knots) 16
Number of interactions (_mi) 2
Max span between each knot (_ms=0) 0
C_rows / r_rows print setting 0
Plot setting 2
GAM Models
Degree of Polynomial for forecasts (degmod) 6
Default degree of GAM model (_gdf) 2.000000000000000
PPREG Models
Number of trees (_m) 30
Exploratory Projection Pursuit turned off (do_ppexp=0)
OLS, GAM and MARS plotted (iols=2)
Plots produced in WMF form (ihp=0)
Data saved in SCA fsv format (isave=1)
Leverage effect of target variable (iversion=1)
Grids placed on graphs (igrid=1)
Show graphs (ishow=1)
Data to write in fsv file (fsv_info) 1. Model 1
Left hand side variable (l_hand_s) chanwsh
Right hand side variables (_args)
_ARGS = dlky dly dsimat1a dofsh htsh_exp
GAM right hand side variables (_argsg)
_ARGSG = dlky dly dsimat1a dofsh htsh_exp
Ordinary Least Squares Estimation using QR Method
Dependent variable CHANWSH
Centered R**2 4.663004197990550E-02
Adjusted R**2 3.582085878239876E-02
Residual Sum of Squares 99.69274477778127
Residual Variance 0.2260606457546060
Standard Error 0.4754583533335028
Total Sum of Squares 104.5687919355227
Log Likelihood -298.9114424425495
Mean of the Dependent Variable 0.3772410371879195
Std. Error of Dependent Variable 0.4842098457728058
Sum Absolute Residuals 154.2697623492203
F( 5, 441) 4.313928363306974
F Significance 0.9992344947238444
QR Rank Check variable (eps) set as 2.220446049250313E-16
Maximum Absolute Residual 2.423346113505557
Number of Observations 447
-2 * ln(Maximum of Likelihood Function) 597.8228848850989
Akaike Information Criterion (AIC) 611.8228848850989
Scwartz Information Criterion (SIC) 640.5407950473939
Akaike (1970) Finite Prediction Error 0.2290950168385605
Generalized Cross Validation 0.2291363007988864
Hannan & Quinn (1979) HQ 0.2341227407534938
Shibata (1981) 0.2290135572121456
Rice (1984) 0.2291787236270834
Variable Lag Coefficient SE t
DLKY 0 0.19461621E-01 0.10929047E-01 1.7807244
DLY 0 0.16346747E-02 0.87081211E-02 0.18771841
DSIMAT1A 0 0.85486338E-01 0.40337870E-01 2.1192576
DOFSH 0 0.17738186 0.78035999E-01 2.2730773
HTSH_EXP 0 -0.63894988E-02 0.10346851 -0.61753074E-01
CONSTANT 0 0.30441686 0.34539594E-01 8.8135623
Using MARS note the number of time any knot figures in model. Also compare EMBED Equation.DSMT4 values for different models.
Multivariate Autoregressive Splines Analysis
Model Estimated using Hastie-Tibshirani GPL routines in
CRAN General Public License (GPL) Library.
Version - 1 March 2006.
Left Hand Side Variable CHANWSH
Penalty cost per degree of freedom 3.000
Threshold for Forward stepwise Stopping 0.1000E-03
Rank Test Tolerance 0.1000E-12
Max # of Knots (nk) 16
Max interaction (mi) 2
Number of Observations 447
Number of right hand Variables 5
tolbx set as 1.000000000000000E-09
stopfac gcv/gcvnull > stopfac => stop 10.00000000000000
prevcrit set as 10000000000.00000
Series Lag Mean Max Min
DLKY 0 0.5129 14.73 -13.03
DLY 0 0.3948 22.53 -13.96
DSIMAT1A 0 0.3653 2.970 -3.900
DOFSH 0 0.1801 0.8314 -0.3634
HTSH_EXP 0 0.1540 0.9744 -0.8415E-01
GCV with only the constant 0.2349848679602379
Total sum of squares 104.5687919355228
Final gcv 0.2243541985438403
Variance of Y Variable 0.2344591747433244
R**2 (1 - (var(res)/var(y))) 9.800778114759146E-02
Residual Sum of Squares 94.32023666063806
Residual Variance 0.2114803512570358
Residual Standard Error 0.4598699286287763
Sum Absolute Residuals 151.8419819292555
Max Absolute Residual 2.356771963985708
# of coefficients after last fwd step 6
MARS Model Coefficients SE t Non Zero % Importance #
CHANWSH = 0.22430248 0.36260299E-01 6.18 447 100.000 1
+ 0.11234242 * max( DLKY{ 0} - 5.1592455 , 0.0) 0.29373323E-01 3.82 23 5.145 99.886 2
+ 0.33196963 * max( DOFSH{ 0} - -0.47806446E-01, 0.0) 0.86699033E-01 3.82 332 74.273 100.000 3
+ 0.16270845 * max(DSIMAT1A{ 0} - 0.20999895 , 0.0) 0.57208979E-01 2.84 287 64.206 74.278 4
-0.70342093 * max( DLKY{ 0} - -0.38131475E-01, 0.0) 0.22217457 -3.16 39 8.725 82.687 5
* max( -0.47806446E-01 - DOFSH{ 0} , 0.0)
+ 0.19893933 * max( 5.1820626 - DLY{ 0} , 0.0) 0.64517991E-01 3.08 87 19.463 80.530 6
* max( -0.47806446E-01 - DOFSH{ 0} , 0.0)
Analysis of GCV, RSS and KNOT by Variable before prune step
Obs _GCV _RSS _KNOT _VAR _LAG
1 0.2308 100.4 5.159 DLKY 0
2 0.2306 98.08 -0.4781E-01 DOFSH 0
3 0.2320 96.41 0.2100 DSIMAT1A 0
4 0.2345 95.22 -0.3813E-01 DLKY 0
5 0.2355 93.38 5.182 DLY 0
6 0.2373 91.87 -7.413 DLY 0
7 0.2394 90.47 3.993 DLY 0
Generalized Additive Models (GAM) Analysis
Reference: Generalized Additive Models by Hastie and Tibshirani. Chapman (1990)
Model estimated using CRAN General Public License (GPL) routines.
Gaussian additive model assumed
Identity link - yhat = x*b + sum(splines)
Response variable .... CHANWSH
Number of observations: 447
Residual Sum of Squares 96.78912935189766
# iterations 1
# smooths/variable 12
Mean Squared Residual 0.2165304907201290
df of deviance 435.9990210388421
Scale Estimate 0.2219939143929292
Primary tolerence 1.000000000000000E-09
Secondary tolerance 1.000000000000000E-09
R square 7.439755628449879E-02
Total sum of Squares 104.5687919355228
Model df coef st err z score nl pval lin_res Name Lag
------------ ---- ------ ------- ------- ------- ---- ---
1. 0.307945 0.3423E-01 8.997 intcpt
2.00 0.182242E-01 0.1083E-01 1.683 0.7998 97.50 DLKY 0
2.00 0.759133E-03 0.8629E-02 0.8797E-01 0.5792 97.17 DLY 0
2.00 0.742341E-01 0.3997E-01 1.857 0.7106 97.34 DSIMAT1A 0
2.00 0.195753 0.7733E-01 2.531 0.6579 97.27 DOFSH 0
2.00 -.177332E-01 0.1025 -.1729 0.7457 97.40 HTSH_EXP 0
-----
11.0
Projection Pursuit Regression
Number of Observations 447
Number of right hand side variables 6
Maximum number of trees 30
Minimum number of trees 30
Number of left hand side variables 1
Level of fit 2
Max number of Primary Iterations (maxit) 200
Max number of Secondary Iterations (mitone) 200
Number of cj Iterations (mitcj) 10
Smoother tone control (alpha) 0.000000000000000E+00
Span 0.000000000000000E+00
Convergence (CONV) set as 5.000000000000000E-03
Left Hand Side Variable CHANWSH
Series Mean Max Min
CHANWSH 0.3772 2.972 -1.184
Right Hand Side Variables
# Series Lag Mean Max Min
1 DLKY 0 0.5129 14.73 -13.03
2 DLY 0 0.3948 22.53 -13.96
3 DSIMAT1A 0 0.3653 2.970 -3.900
4 DOFSH 0 0.1801 0.8314 -0.3634
5 HTSH_EXP 0 0.1540 0.9744 -0.8415E-01
6 CONSTANT 0 1.000 1.000 1.000
Given # of trees 30
# primary iterations used 2
# secondary iterations used 3
# cj iterations used 2
Residual sum of squares 45.74746740785981
Total sum of squares 104.5687919355227
Mean of the Dependent Variable 0.3772410371879195
Std. Error of Dependent Variable 0.4842098457728058
Sum Absolute Residuals 102.4741977233084
Maximum Absolute Residual 1.592191521771080
Residual Variance 0.1037357537593193
Variable Importance for Model with # Trees 30
Series Number Importance
1 1.00000
2 0.582809
3 0.547460
5 0.397385
4 0.343518
6 0.00000
For Random Forest method note effect on EMBED Equation.DSMT4 of bagging and averaging. Note mtry was set as 2!
Random Forest Analysis Ver. 3.1 - 30 May 2009 build
Regression option selected.
Number of Observations 447
Number of right hand side variables 5
Maximum number of trees (maxtree) 200
Maximum number of nodes (nrnodes) 179
Number of Variables to select at each node (mtry) 2
Minimum node size (ndsize) 5
Left Hand Side Variable CHANWSH
Series Mean Max Min
CHANWSH 0.3772 2.972 -1.184
Right Hand Side Variables
# Series Lag Mean Max Min
1 DLKY 0 0.5129 14.73 -13.03
2 DLY 0 0.3948 22.53 -13.96
3 DSIMAT1A 0 0.3653 2.970 -3.900
4 DOFSH 0 0.1801 0.8314 -0.3634
5 HTSH_EXP 0 0.1540 0.9744 -0.8415E-01
Total Sum of Squares 104.5687919355227
Sum of Squared Residuals for last bagged model 85.36903992005276
Sum of Squared Residuals for averaged OOB model 111.6020632996678
Sum of Squared Residuals for averaged model 39.00181645337509
Centered R**2 for %YHAT 0.1836088154036296
Centered R**2 for %YHAT2 -6.725975536259265E-02
Centered R**2 for %YHAT3 0.6270224057152378
Importance Analysis
For details see Hastie-Tibshirani-Friedman (2009, 594)
Variable importance based on Randomization
1 0.0000000
2 0.0000000
3 0.0000000
4 0.0000000
5 0.0000000
Variable importance based on Gini
1 4268.8911
2 3955.2716
3 4179.0395
4 1710.9527
5 1407.7635
Selected Leverage Plots.
It appears that there are thresholds. Only select graphs are shown.
Table 4.5 represents another approach that assumes a long run cost function where both types of labor and capital are jointly solved from
EMBED Equation.DSMT4 (4.19)
Here factor prices differ across industries. (4.19) is linearly homogeneous in inputs and can be written as
EMBED Equation.DSMT4 (4.20)
Where we replaced EMBED Equation.DSMT4 by EMBED Equation.DSMT4 that includes other structural variables. Note that EMBED Equation.DSMT4 is the unit cost function and
EMBED Equation.DSMT4 (4.21)
(4.21) shows that both product prices and structural change EMBED Equation.DSMT4 can affect factor prices. Taking the difference between the log change in factor and product prices and noting that the cost shares sum to 1.0, total factor productivity is
EMBED Equation.DSMT4 (4.22)
Which can be used to form the estimating equation
EMBED Equation.DSMT4 (4.23)
If the data are factor shares EMBED Equation.DSMT4 then the implied change in factor prices EMBED Equation.DSMT4 can be estimated from
EMBED Equation.DSMT4 (4.24)
Which has been used in Table 4.5. EMBED Equation.DSMT4 can be interpreted as the change in factor prices that are mandated by the change in product prices. A code template for further investigation of whether there are nonlinearities in the model that have caused the model not to work well is
Code Template for Estimation of a Long Run Model
b34sexec options ginclude('Feenstra_ch4.mac') member(ch4_3_a);
b34srun;
b34sexec matrix;
call loaddata;
call olsq( dlp34 ptfp apsh ansh aksh :print :white);
call gamfit( dlp34 ptfp apsh ansh aksh :print );
call marspline(dlp34 ptfp apsh ansh aksh :print);
call ppreg(dlp34 ptfp apsh ansh aksh :print);
b34srun;
Stata Template
// set mem 3m
log using log_4_3a.log,replace
// use d:\feenstra_course\chap4\data_Chp4.dta, clear
// use c:\feenstra_course\chap4\data_Chp4.dta, clear
use data_Chp4.dta, clear
// use e:\feenstra_course\chap4\data_Chp4.dta, clear
* use /usr/local/lib/hhsfiles/data_Chp4.dta, clear
keep if year==1990
drop if sic72==2067
drop if sic72==2794
drop if sic72==3483
gen etfp=ptfp-err
gen adj1=1/(1-amesh)
gen etfp1=adj1*etfp
gen dlpvad1=adj1*dlpvad
gen apsh1=adj1*apsh
gen ansh1=adj1*ansh
gen aksh1=adj1*aksh
gen mshxpr=amsh*dlpmx
gen eshxpr=aosh*dlpe
* Reproduce Table 4.5 reprinted at 4.1 in new edition.
gen dlp34=dlp-mshxpr-eshxpr
regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
* OLS Model
regress dlp34 ptfp apsh ansh aksh , robust
preserve
drop if sic72==3573
regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
* OLS Model without sic72
regress dlp34 ptfp apsh ansh aksh , robust
regress dlp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
* OLS Model
regress dlp apsh ansh aksh mshxpr eshxpr, robust
restore
regress dlpvad1 etfp1 apsh1 ansh1 aksh1 [aw=mvshipsh],robust noconstant
* OLS Model
regress dlpvad1 etfp1 apsh1 ansh1 aksh1 ,robust noconstant
regress dlp etfp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
* OLS Model
regress dlp etfp apsh ansh aksh mshxpr eshxpr , robust
log close
* clear *
exit
___ ____ ____ ____ ____ (R)
/__ / ____/ / ____/
___/ / /___/ / /___/ 14.2 Copyright 1985-2015 StataCorp LP
Statistics/Data Analysis StataCorp
4905 Lakeway Drive
Special Edition College Station, Texas 77845 USA
800-STATA-PC http://www.stata.com
979-696-4600 stata@stata.com
979-696-4601 (fax)
Single-user Stata perpetual license:
Serial number: 401406202087
Licensed to: Houston H. Stokes
University of Illinois Chicago
Notes:
1. Stata is running in batch mode.
2. Unicode is supported; see help unicode_advice.
3. Maximum number of variables is set to 5000; see help set_maxvar.
. do Problem_4_3_a.do
.
. // set mem 3m
.
. log using log_4_3a.log,replace
-------------------------------------------------------------------------------
name:
log: D:\class\E514\log_4_3a.log
log type: text
opened on: 10 Oct 2016, 10:11:28
.
. // use d:\feenstra_course\chap4\data_Chp4.dta, clear
. // use c:\feenstra_course\chap4\data_Chp4.dta, clear
. use data_Chp4.dta, clear
(Matrl Cons (72 SIC), 67-92)
. // use e:\feenstra_course\chap4\data_Chp4.dta, clear
. * use /usr/local/lib/hhsfiles/data_Chp4.dta, clear
.
. keep if year==1990
(1,350 observations deleted)
. drop if sic72==2067
(1 observation deleted)
. drop if sic72==2794
(1 observation deleted)
. drop if sic72==3483
(1 observation deleted)
. gen etfp=ptfp-err
. gen adj1=1/(1-amesh)
. gen etfp1=adj1*etfp
. gen dlpvad1=adj1*dlpvad
. gen apsh1=adj1*apsh
. gen ansh1=adj1*ansh
. gen aksh1=adj1*aksh
. gen mshxpr=amsh*dlpmx
. gen eshxpr=aosh*dlpe
.
.
. * Reproduce Table 4.5 *
.
. gen dlp34=dlp-mshxpr-eshxpr
.
. regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
(sum of wgt is 9.9873e-01)
Linear regression Number of obs = 447
F(4, 442) = 106.29
Prob > F = 0.0000
R-squared = 0.8957
Root MSE = .80656
------------------------------------------------------------------------------
| Robust
dlp34 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptfp | -.9631819 .0702093 -13.72 0.000 -1.101168 -.8251963
apsh | 3.062598 1.22198 2.51 0.013 .6609845 5.464212
ansh | 2.294716 1.430073 1.60 0.109 -.5158719 5.105305
aksh | 7.887571 .7810006 10.10 0.000 6.352634 9.422507
_cons | -.7051116 .3006016 -2.35 0.019 -1.295898 -.1143256
------------------------------------------------------------------------------
.
. * OLS Model
. regress dlp34 ptfp apsh ansh aksh , robust
Linear regression Number of obs = 447
F(4, 442) = 110.62
Prob > F = 0.0000
R-squared = 0.6967
Root MSE = .91728
------------------------------------------------------------------------------
| Robust
dlp34 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptfp | -.6790007 .0709856 -9.57 0.000 -.8185121 -.5394894
apsh | 3.455601 .8328199 4.15 0.000 1.818822 5.09238
ansh | 3.905478 1.754048 2.23 0.026 .4581676 7.352789
aksh | 7.394156 .71982 10.27 0.000 5.979461 8.808851
_cons | -.7849882 .1904677 -4.12 0.000 -1.159323 -.4106534
------------------------------------------------------------------------------
.
. preserve
. drop if sic72==3573
(1 observation deleted)
.
. regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
(sum of wgt is 9.8179e-01)
Linear regression Number of obs = 446
F(4, 441) = 92.17
Prob > F = 0.0000
R-squared = 0.8059
Root MSE = .74139
------------------------------------------------------------------------------
| Robust
dlp34 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptfp | -.7531151 .0751891 -10.02 0.000 -.9008886 -.6053416
apsh | 2.427856 1.162844 2.09 0.037 .142451 4.713261
ansh | 4.086394 1.722144 2.37 0.018 .7017647 7.471024
aksh | 8.058291 .9411699 8.56 0.000 6.208556 9.908027
_cons | -.8249273 .2930995 -2.81 0.005 -1.400973 -.2488819
------------------------------------------------------------------------------
. * OLS Model without sic72
. regress dlp34 ptfp apsh ansh aksh , robust
Linear regression Number of obs = 446
F(4, 441) = 135.75
Prob > F = 0.0000
R-squared = 0.6696
Root MSE = .87366
------------------------------------------------------------------------------
| Robust
dlp34 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptfp | -.6043067 .0418654 -14.43 0.000 -.6865873 -.5220261
apsh | 3.156235 .7864841 4.01 0.000 1.610513 4.701958
ansh | 4.954764 1.5334 3.23 0.001 1.941084 7.968443
aksh | 7.396599 .7390641 10.01 0.000 5.944073 8.849124
_cons | -.8377685 .1852263 -4.52 0.000 -1.201804 -.4737325
------------------------------------------------------------------------------
.
. regress dlp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
(sum of wgt is 9.8179e-01)
Linear regression Number of obs = 446
F(5, 440) = 10.85
Prob > F = 0.0000
R-squared = 0.4289
Root MSE = 1.2034
------------------------------------------------------------------------------
| Robust
dlp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
apsh | 3.605277 1.88524 1.91 0.056 -.0999163 7.310471
ansh | 6.202674 4.036466 1.54 0.125 -1.730475 14.13582
aksh | 9.535214 2.18722 4.36 0.000 5.236518 13.83391
mshxpr | 1.219304 .2471334 4.93 0.000 .7335958 1.705013
eshxpr | -.9301182 .9150299 -1.02 0.310 -2.728491 .8682541
_cons | -1.929187 .9147773 -2.11 0.036 -3.727063 -.1313111
------------------------------------------------------------------------------
. * OLS Model
. regress dlp apsh ansh aksh mshxpr eshxpr, robust
Linear regression Number of obs = 446
F(5, 440) = 24.65
Prob > F = 0.0000
R-squared = 0.3400
Root MSE = 1.2384
------------------------------------------------------------------------------
| Robust
dlp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
apsh | 5.629626 1.284501 4.38 0.000 3.105105 8.154147
ansh | 7.727702 2.065437 3.74 0.000 3.668354 11.78705
aksh | 8.611022 1.272484 6.77 0.000 6.110121 11.11192
mshxpr | 1.448936 .1923696 7.53 0.000 1.070858 1.827013
eshxpr | .0327104 .533676 0.06 0.951 -1.01616 1.081581
_cons | -2.629372 .6429471 -4.09 0.000 -3.893001 -1.365743
------------------------------------------------------------------------------
. restore
.
. regress dlpvad1 etfp1 apsh1 ansh1 aksh1 [aw=mvshipsh],robust noconstant
(sum of wgt is 9.9873e-01)
Linear regression Number of obs = 447
F(4, 443) > 99999.00
Prob > F = 0.0000
R-squared = 0.9998
Root MSE = .07762
------------------------------------------------------------------------------
| Robust
dlpvad1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
etfp1 | -1.000041 .0006831 -1463.88 0.000 -1.001384 -.9986986
apsh1 | 4.680657 .0157718 296.77 0.000 4.64966 4.711654
ansh1 | 5.482807 .0194677 281.64 0.000 5.444547 5.521068
aksh1 | 3.952538 .0083407 473.89 0.000 3.936146 3.96893
------------------------------------------------------------------------------
. * OLS Model
. regress dlpvad1 etfp1 apsh1 ansh1 aksh1 ,robust noconstant
Linear regression Number of obs = 447
F(4, 443) > 99999.00
Prob > F = 0.0000
R-squared = 0.9988
Root MSE = .1685
------------------------------------------------------------------------------
| Robust
dlpvad1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
etfp1 | -.9992624 .0042216 -236.70 0.000 -1.007559 -.9909655
apsh1 | 4.666086 .0550321 84.79 0.000 4.55793 4.774243
ansh1 | 5.437375 .0644382 84.38 0.000 5.310733 5.564018
aksh1 | 3.953762 .0221871 178.20 0.000 3.910157 3.997367
------------------------------------------------------------------------------
.
. regress dlp etfp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
(sum of wgt is 9.9873e-01)
Linear regression Number of obs = 447
F(6, 440) > 99999.00
Prob > F = 0.0000
R-squared = 0.9999
Root MSE = .0262
------------------------------------------------------------------------------
| Robust
dlp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
etfp | -1.000358 .000677 -1477.55 0.000 -1.001689 -.9990273
apsh | 4.700013 .011911 394.60 0.000 4.676603 4.723422
ansh | 5.443315 .0314405 173.13 0.000 5.381523 5.505107
aksh | 3.972308 .0150284 264.32 0.000 3.942772 4.001845
mshxpr | .9974072 .0023115 431.50 0.000 .9928643 1.00195
eshxpr | .9961108 .0057421 173.47 0.000 .9848254 1.007396
_cons | .0010799 .005423 0.20 0.842 -.0095784 .0117382
------------------------------------------------------------------------------
. * OLS Model
. regress dlp etfp apsh ansh aksh mshxpr eshxpr , robust
Linear regression Number of obs = 447
F(6, 440) > 99999.00
Prob > F = 0.0000
R-squared = 0.9989
Root MSE = .05637
------------------------------------------------------------------------------
| Robust
dlp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
etfp | -.9984327 .0024469 -408.04 0.000 -1.003242 -.9936236
apsh | 4.71449 .0145206 324.68 0.000 4.685952 4.743028
ansh | 5.443702 .0521618 104.36 0.000 5.341185 5.546219
aksh | 4.000907 .044225 90.47 0.000 3.913988 4.087825
mshxpr | .9907738 .0089715 110.44 0.000 .9731416 1.008406
eshxpr | .996285 .0058313 170.85 0.000 .9848243 1.007746
_cons | -.0023481 .007124 -0.33 0.742 -.0163494 .0116532
------------------------------------------------------------------------------
.
. log close
name:
log: D:\class\E514\log_4_3a.log
log type: text
closed on: 10 Oct 2016, 10:11:29
-------------------------------------------------------------------------------
. * clear *
. exit
Code Template for Estimation of a Long Run Model
b34sexec options include('Feenstra_ch4.mac') member(ch4_3_a);
b34srun;
b34sexec matrix;
call loaddata;
call olsq( dlp34 ptfp apsh ansh aksh :print :white);
call gamfit( dlp34 ptfp apsh ansh aksh :print );
call marspline(dlp34 ptfp apsh ansh aksh :print);
call ppreg(dlp34 ptfp apsh ansh aksh :print);
b34srun;
Variable Label # Cases Mean Std. Dev. Variance Maximum Minimum
YEAR 1 Year ranges from 58 to 97 447 1990.00 0.00000 0.00000 1990.00 1990.00
SIC72 2 4 digit SIC code 447 3015.57 608.388 370136. 3999.00 2011.00
EMP 3 Total employment in 1000s 447 39.2085 62.8485 3949.93 631.100 0.400000
PAY 4 Total payroll in $1,000,000 447 1054.33 1892.61 0.358198E+07 18381.6 13.9000
PRODE 5 Production workers in 1000s 447 27.0548 41.5547 1726.79 487.700 0.100000
PRODH 6 Production worker hours in 1,000,000 447 54.2481 83.9769 7052.12 979.200 0.300000
PRODW 7 Production worker wages in $1,000,000 447 607.053 1040.94 0.108355E+07 9789.90 8.70000
VADD 8 Total value added in $1,000,000 447 2959.26 5191.26 0.269491E+08 39504.4 27.6000
MATERIAL 9 Total cost of materials in $1,000,000 447 3469.51 9619.80 0.925406E+08 145885. 10.7000
INVENT 10 End-of-year inventories in $1,000,000 447 875.567 2098.71 0.440458E+07 32271.6 7.90000
INVEST 11 Total capital expenditure in $1,000,000 447 228.052 545.062 297093. 4396.40 0.400000
ENERGY 12 Cost of electric & fuels in $1,000,000 447 126.855 352.896 124535. 4327.90 0.800000
CAP 13 Total real capital stock in $1,000,000 447 2702.68 5862.97 0.343745E+08 59407.3 19.9000
EQUIP 14 Real capital: equipment in $1,000,000 447 1646.90 3676.64 0.135177E+08 38087.0 4.40000
PLANT 15 Real capital: structures in $1,000,000 447 1055.78 2300.93 0.529427E+07 31042.8 12.2000
PISHIP 16 Deflator for VSHIP 1987=1.000 447 1.11687 0.837093E-01 0.700725E-02 1.53300 0.822000
PIINV 17 Deflator for INVEST 1987=1.000 447 1.08237 0.241873E-01 0.585027E-03 1.11900 0.937000
PIEN 18 Deflator for ENERGY 1987=1.000 447 1.06987 0.167540E-01 0.280697E-03 1.25700 1.02200
VSHIP 19 Total value of shipments in $1,000,000 447 6412.92 13641.7 0.186097E+09 170775. 44.5000
PIMAT 20 Deflator for MATCOST 1987=1.000 447 1.12898 0.481798E-01 0.232130E-02 1.52700 1.01400
CI 21 computer investment/total investment 447 5.55268 5.48071 30.0382 43.4804 0.00000
SIC2 22 2 digit SIC code 447 29.6174 6.09484 37.1470 39.0000 20.0000
IMAT 23 imported materials 433 23.3486 109.734 12041.7 1399.06 0.00000
SIMAT1A 24 Share of imported mat -broad outsourcing 447 0.118441 0.875671E-01 0.766799E-02 0.659710 0.00000
SIMAT1B 25 share of imported mat - 2-digit industry 447 0.485957E-01 0.749496E-01 0.561745E-02 0.628002 0.00000
DSIMAT1A 26 change in outsourcing (broad) 447 0.365305 0.563151 0.317139 2.96951 -3.90025
DSIMAT1B 27 change in outsourcing (narrow) 447 0.157793 0.473762 0.224450 2.73056 -4.14979
DLY 28 change in log real shipments 447 0.394762 3.76272 14.1581 22.5287 -13.9630
NWSH 29 nonproduction share of the total wages 447 0.372574 0.120623 0.145500E-01 0.873336 0.109044
MVSHIPSH 30 industry share of total manfg shipments 447 0.223430E-02 0.496680E-02 0.246691E-04 0.703875E-01 0.230466E-04
DLKY 31 change in log capital stock/shipments 447 0.512945 3.13639 9.83696 14.7261 -13.0257
APSH 32 average production share 447 0.132555 0.574340E-01 0.329867E-02 0.364086 0.115928E-01
ANSH 33 average non-production share 447 0.722582E-01 0.393782E-01 0.155065E-02 0.270142 0.638309E-02
AMESH 34 aosh + amsh 447 0.512149 0.123647 0.152887E-01 0.890473 0.171757
AMSH 35 average material share 447 0.487772 0.127229 0.161873E-01 0.877148 0.151759
AOSH 36 average energy share 447 0.243771E-01 0.328570E-01 0.107958E-02 0.275952 0.213427E-02
AKSH 37 average capital share 447 0.283037 0.843416E-01 0.711350E-02 0.636899 0.738303E-01
DLP 38 change in log price 447 3.54611 1.70410 2.90397 11.7933 -12.9502
DLPE 39 change in log energy price 447 3.12686 0.912518 0.832688 8.40714 0.860887E-01
DHTSH 40 (capital=pstk x ex post rental price) 447 0.334085 0.376402 0.141678 1.27976 -0.301242
DHTSH1 41 (capital=pstk x ex ante rental price) 447 0.210975 0.245414 0.602279E-01 1.21186 -0.209675
DOFSH 42 change in office equipment/total capital 447 0.180127 0.307711 0.946862E-01 0.831400 -0.363431
DOFSH1 43 change in office equipment/total capital 447 0.352378E-01 0.151631 0.229921E-01 0.379551 -0.270059
DLPMX 44 change in log material price 447 3.58936 0.887371 0.787427 7.67960 -1.81683
DLPVAD 45 change in log value-added 447 1.77040 1.65821 2.74968 10.5839 -12.6178
PTFP 46 primary TFP 447 0.408978 1.64672 2.71169 14.0399 -5.01075
ADLHW 47 annual change in log production wage 447 4.71405 0.00000 0.00000 4.71405 4.71405
ADLNW 48 annual chage in log non-production wage 447 5.43687 0.00000 0.00000 5.43687 5.43687
ADLPK 49 annual change in log capital price 447 3.95370 0.00000 0.00000 3.95370 3.95370
ERR 50 error as defined in (4.26) of Chapter 4 447 0.464305E-01 1.10714 1.22575 4.49691 -4.63585
ETFP 51 ptfp-err 447 0.362547 1.46871 2.15711 14.8904 -7.65468
ADJ1 52 1.0/(1.0-amesh) 447 2.24364 0.889095 0.790491 9.13017 1.20737
ETFP1 53 adj1*etfp 447 1.00142 3.55532 12.6403 32.8904 -10.8290
B34S 9 (D:M:Y) 10/10/16 (H:M:S) 10:24: 4 DATA STEP Feenstra Chap4 4_3a Data PAGE 2
DLPVAD1 54 adj1*dlpvad 447 3.35799 3.56748 12.7269 14.9729 -29.1263
APSH1 55 adj1*apsh 447 0.270372 0.903109E-01 0.815606E-02 0.488378 0.305658E-01
ANSH1 56 adj1*ansh 447 0.143112 0.558816E-01 0.312275E-02 0.389831 0.266251E-01
AKSH1 57 adj1*aksh 447 0.586515 0.109801 0.120563E-01 0.920277 0.277150
MSHXPR 58 amsh*dlpmx 447 1.69937 0.515041 0.265268 3.39471 -1.58880
ESHXPR 59 aosh*dlpe 447 0.763338E-01 0.115698 0.133861E-01 1.21165 0.206717E-02
DLP34 60 dlp-mshxpr-eshxpr 447 1.77040 1.65821 2.74968 10.5839 -12.6178
CONSTANT 61 447 1.00000 0.00000 0.00000 1.00000 1.00000
Number of observations in data file 447
Current missing variable code 1.000000000000000E+31
Note: Missing data in the data file
B34S Matrix Command. d/m/y 10/10/16. h:m:s 10:24: 4.
=> CALL LOADDATA$
=> CALL OLSQ( DLP34 PTFP APSH ANSH AKSH :PRINT :WHITE)$
Ordinary Least Squares Estimation
Dependent variable DLP34
Centered R**2 0.6967466663385627
Adjusted R**2 0.6940022922782783
Residual Sum of Squares 371.8964985643850
Residual Variance 0.8413947931320926
Standard Error 0.9172757454179701
Total Sum of Squares 1226.355846031963
Log Likelihood -593.1542618937680
Mean of the Dependent Variable 1.770400132847875
Std. Error of Dependent Variable 1.658214939272056
Sum Absolute Residuals 297.4930711130872
F( 4, 442) 253.8818145899300
F Significance 1.000000000000000
1/Condition XPX 6.550394423061074E-04
Maximum Absolute Residual 5.408266825961406
Number of Observations 447
Variable Lag Coefficient White SE t
PTFP 0 -0.67900074 0.70587514E-01 -9.6192754
APSH 0 3.4556009 0.82814894 4.1726805
ANSH 0 3.9054785 1.7442105 2.2391097
AKSH 0 7.3941559 0.71578284 10.330166
CONSTANT 0 -0.78498817 0.18939943 -4.1446174
=> CALL GAMFIT( DLP34 PTFP APSH ANSH AKSH :PRINT )$
Generalized Additive Models (GAM) Analysis
Reference: Generalized Additive Models by Hastie and Tibshirani. Chapman (1990)
Model estimated using CRAN General Public License (GPL) routines.
Gaussian additive model assumed
Identity link - yhat = x*b + sum(splines)
Response variable .... DLP34
Number of observations: 447
Residual Sum of Squares 300.2070345290874
# iterations 1
# smooths/variable 15
Mean Squared Residual 0.6716041040919182
df of deviance 434.0021682741188
Scale Estimate 0.6917178218784257
Primary tolerence 1.000000000000000E-09
Secondary tolerance 1.000000000000000E-09
R square 0.7552039764800347
Total sum of Squares 1226.355846031963
Model df coef st err z score nl pval lin_res Name Lag
------------ ---- ------ ------- ------- ------- ---- ---
1. -1.04728 0.1685 -6.217 intcpt
3.00 -.665252 0.2421E-01 -27.48 1.000 346.8 PTFP 0
3.00 4.03542 0.7551 5.344 0.1748 300.8 APSH 0
3.00 5.63971 1.133 4.979 0.8573 304.0 ANSH 0
3.00 7.58671 0.4869 15.58 1.000 325.1 AKSH 0
-----
13.0
=> CALL MARSPLINE(DLP34 PTFP APSH ANSH AKSH :PRINT)$
Multivariate Autoregressive Splines Analysis
Model Estimated using Hastie-Tibshirani GPL routines in
CRAN General Public License (GPL) Library.
Version - 1 March 2006.
Left Hand Side Variable DLP34
Penalty cost per degree of freedom 2.000
Threshold for Forward stepwise Stopping 0.1000E-03
Rank Test Tolerance 0.1000E-12
Max # of Knots (nk) 5
Max interaction (mi) 1
Number of Observations 447
Number of right hand Variables 4
tolbx set as 1.000000000000000E-09
stopfac gcv/gcvnull > stopfac => stop 10.00000000000000
prevcrit set as 10000000000.00000
Series Lag Mean Max Min
PTFP 0 0.4090 14.04 -5.011
APSH 0 0.1326 0.3641 0.1159E-01
ANSH 0 0.7226E-01 0.2701 0.6383E-02
AKSH 0 0.2830 0.6369 0.7383E-01
GCV with only the constant 2.755841979409840
Total sum of squares 1226.355846031963
Final gcv 0.8411019886991933
Variance of Y Variable 2.749676784825029
R**2 (1 - (var(res)/var(y))) 0.7056440275681013
Residual Sum of Squares 360.9851676062820
Residual Variance 0.8093837838705881
Residual Standard Error 0.8996575925709670
Sum Absolute Residuals 306.7363667559480
Max Absolute Residual 3.945752605427743
# of coefficients after last fwd step 5
MARS Model Coefficients SE t Non Zero % Importance #
DLP34 = 1.1612470 0.13135952 8.84 447 100.000 1
-1.2359379 * max( PTFP{ 0} - 3.1126752 , 0.0) 0.77496252E-01 -15.9 23 5.145 85.560 2
+ 0.57809246 * max( 3.1126752 - PTFP{ 0} , 0.0) 0.31013665E-01 18.6 423 94.631 100.000 3
+ 12.581184 * max( AKSH{ 0} - 0.41347152 , 0.0) 1.9014328 6.61 23 5.145 35.497 4
-7.1731181 * max( 0.41347152 - AKSH{ 0} , 0.0) 0.62994727 -11.3 423 94.631 61.089 5
=> CALL PPREG(DLP34 PTFP APSH ANSH AKSH :PRINT)$
Projection Pursuit Regression
Number of Observations 447
Number of right hand side variables 5
Maximum number of ridge functions 20
Minimum number of ridge functions 20
Number of left hand side variables 1
Level of fit 2
Max number of Primary Iterations (maxit) 200
Max number of Secondary Iterations (mitone) 200
Number of cj Iterations (mitcj) 10
Smoother tone control (alpha) 0.000000000000000E+00
Span 0.000000000000000E+00
Convergence (CONV) set as 5.000000000000000E-03
Left Hand Side Variable DLP34
Series Mean Max Min
DLP34 1.770 10.58 -12.62
Right Hand Side Variables
# Series Lag Mean Max Min
1 PTFP 0 0.4090 14.04 -5.011
2 APSH 0 0.1326 0.3641 0.1159E-01
3 ANSH 0 0.7226E-01 0.2701 0.6383E-02
4 AKSH 0 0.2830 0.6369 0.7383E-01
5 CONSTANT 0 1.000 1.000 1.000
Given # of ridge functions 20
# primary iterations used 1
# secondary iterations used 7
# cj iterations used 2
Residual sum of squares 179.3691430157083
Total sum of squares 1226.355846031963
Mean of the Dependent Variable 1.770400132847875
Std. Error of Dependent Variable 1.658214939272056
Sum Absolute Residuals 210.3559765757928
Maximum Absolute Residual 2.456771179577403
Residual Variance 0.4058125407595211
Variable Importance for Model with # ridge functions 20
Series Number Importance
1 1.00000
3 0.885062
4 0.760611
2 0.636560
5 0.00000
Stata Template
// set mem 3m
log using log_4_3a.log,replace
// use d:\feenstra_course\chap4\data_Chp4.dta, clear
// use c:\feenstra_course\chap4\data_Chp4.dta, clear
use data_Chp4.dta, clear
// use e:\feenstra_course\chap4\data_Chp4.dta, clear
* use /usr/local/lib/hhsfiles/data_Chp4.dta, clear
keep if year==1990
drop if sic72==2067
drop if sic72==2794
drop if sic72==3483
gen etfp=ptfp-err
gen adj1=1/(1-amesh)
gen etfp1=adj1*etfp
gen dlpvad1=adj1*dlpvad
gen apsh1=adj1*apsh
gen ansh1=adj1*ansh
gen aksh1=adj1*aksh
gen mshxpr=amsh*dlpmx
gen eshxpr=aosh*dlpe
* Reproduce Table 4.5 reprinted at 4.1 in new edition.
gen dlp34=dlp-mshxpr-eshxpr
regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
* OLS Model
regress dlp34 ptfp apsh ansh aksh , robust
preserve
drop if sic72==3573
regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
* OLS Model without sic72
regress dlp34 ptfp apsh ansh aksh , robust
regress dlp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
* OLS Model
regress dlp apsh ansh aksh mshxpr eshxpr, robust
restore
regress dlpvad1 etfp1 apsh1 ansh1 aksh1 [aw=mvshipsh],robust noconstant
* OLS Model
regress dlpvad1 etfp1 apsh1 ansh1 aksh1 ,robust noconstant
regress dlp etfp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
* OLS Model
regress dlp etfp apsh ansh aksh mshxpr eshxpr , robust
log close
* clear *
exit
___ ____ ____ ____ ____ (R)
/__ / ____/ / ____/
___/ / /___/ / /___/ 14.2 Copyright 1985-2015 StataCorp LP
Statistics/Data Analysis StataCorp
4905 Lakeway Drive
Special Edition College Station, Texas 77845 USA
800-STATA-PC http://www.stata.com
979-696-4600 stata@stata.com
979-696-4601 (fax)
Single-user Stata perpetual license:
Serial number: 401406202087
Licensed to: Houston H. Stokes
University of Illinois Chicago
Notes:
1. Stata is running in batch mode.
2. Unicode is supported; see help unicode_advice.
3. Maximum number of variables is set to 5000; see help set_maxvar.
. do Problem_4_3_a.do
.
. // set mem 3m
.
. log using log_4_3a.log,replace
-------------------------------------------------------------------------------
name:
log: D:\class\E514\log_4_3a.log
log type: text
opened on: 10 Oct 2016, 10:11:28
.
. // use d:\feenstra_course\chap4\data_Chp4.dta, clear
. // use c:\feenstra_course\chap4\data_Chp4.dta, clear
. use data_Chp4.dta, clear
(Matrl Cons (72 SIC), 67-92)
. // use e:\feenstra_course\chap4\data_Chp4.dta, clear
. * use /usr/local/lib/hhsfiles/data_Chp4.dta, clear
.
. keep if year==1990
(1,350 observations deleted)
. drop if sic72==2067
(1 observation deleted)
. drop if sic72==2794
(1 observation deleted)
. drop if sic72==3483
(1 observation deleted)
. gen etfp=ptfp-err
. gen adj1=1/(1-amesh)
. gen etfp1=adj1*etfp
. gen dlpvad1=adj1*dlpvad
. gen apsh1=adj1*apsh
. gen ansh1=adj1*ansh
. gen aksh1=adj1*aksh
. gen mshxpr=amsh*dlpmx
. gen eshxpr=aosh*dlpe
.
.
. * Reproduce Table 4.5 *
.
. gen dlp34=dlp-mshxpr-eshxpr
.
. regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
(sum of wgt is 9.9873e-01)
Linear regression Number of obs = 447
F(4, 442) = 106.29
Prob > F = 0.0000
R-squared = 0.8957
Root MSE = .80656
------------------------------------------------------------------------------
| Robust
dlp34 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptfp | -.9631819 .0702093 -13.72 0.000 -1.101168 -.8251963
apsh | 3.062598 1.22198 2.51 0.013 .6609845 5.464212
ansh | 2.294716 1.430073 1.60 0.109 -.5158719 5.105305
aksh | 7.887571 .7810006 10.10 0.000 6.352634 9.422507
_cons | -.7051116 .3006016 -2.35 0.019 -1.295898 -.1143256
------------------------------------------------------------------------------
.
. * OLS Model
. regress dlp34 ptfp apsh ansh aksh , robust
Linear regression Number of obs = 447
F(4, 442) = 110.62
Prob > F = 0.0000
R-squared = 0.6967
Root MSE = .91728
------------------------------------------------------------------------------
| Robust
dlp34 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptfp | -.6790007 .0709856 -9.57 0.000 -.8185121 -.5394894
apsh | 3.455601 .8328199 4.15 0.000 1.818822 5.09238
ansh | 3.905478 1.754048 2.23 0.026 .4581676 7.352789
aksh | 7.394156 .71982 10.27 0.000 5.979461 8.808851
_cons | -.7849882 .1904677 -4.12 0.000 -1.159323 -.4106534
------------------------------------------------------------------------------
.
. preserve
. drop if sic72==3573
(1 observation deleted)
.
. regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
(sum of wgt is 9.8179e-01)
Linear regression Number of obs = 446
F(4, 441) = 92.17
Prob > F = 0.0000
R-squared = 0.8059
Root MSE = .74139
------------------------------------------------------------------------------
| Robust
dlp34 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptfp | -.7531151 .0751891 -10.02 0.000 -.9008886 -.6053416
apsh | 2.427856 1.162844 2.09 0.037 .142451 4.713261
ansh | 4.086394 1.722144 2.37 0.018 .7017647 7.471024
aksh | 8.058291 .9411699 8.56 0.000 6.208556 9.908027
_cons | -.8249273 .2930995 -2.81 0.005 -1.400973 -.2488819
------------------------------------------------------------------------------
. * OLS Model without sic72
. regress dlp34 ptfp apsh ansh aksh , robust
Linear regression Number of obs = 446
F(4, 441) = 135.75
Prob > F = 0.0000
R-squared = 0.6696
Root MSE = .87366
------------------------------------------------------------------------------
| Robust
dlp34 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptfp | -.6043067 .0418654 -14.43 0.000 -.6865873 -.5220261
apsh | 3.156235 .7864841 4.01 0.000 1.610513 4.701958
ansh | 4.954764 1.5334 3.23 0.001 1.941084 7.968443
aksh | 7.396599 .7390641 10.01 0.000 5.944073 8.849124
_cons | -.8377685 .1852263 -4.52 0.000 -1.201804 -.4737325
------------------------------------------------------------------------------
.
. regress dlp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
(sum of wgt is 9.8179e-01)
Linear regression Number of obs = 446
F(5, 440) = 10.85
Prob > F = 0.0000
R-squared = 0.4289
Root MSE = 1.2034
------------------------------------------------------------------------------
| Robust
dlp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
apsh | 3.605277 1.88524 1.91 0.056 -.0999163 7.310471
ansh | 6.202674 4.036466 1.54 0.125 -1.730475 14.13582
aksh | 9.535214 2.18722 4.36 0.000 5.236518 13.83391
mshxpr | 1.219304 .2471334 4.93 0.000 .7335958 1.705013
eshxpr | -.9301182 .9150299 -1.02 0.310 -2.728491 .8682541
_cons | -1.929187 .9147773 -2.11 0.036 -3.727063 -.1313111
------------------------------------------------------------------------------
. * OLS Model
. regress dlp apsh ansh aksh mshxpr eshxpr, robust
Linear regression Number of obs = 446
F(5, 440) = 24.65
Prob > F = 0.0000
R-squared = 0.3400
Root MSE = 1.2384
------------------------------------------------------------------------------
| Robust
dlp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
apsh | 5.629626 1.284501 4.38 0.000 3.105105 8.154147
ansh | 7.727702 2.065437 3.74 0.000 3.668354 11.78705
aksh | 8.611022 1.272484 6.77 0.000 6.110121 11.11192
mshxpr | 1.448936 .1923696 7.53 0.000 1.070858 1.827013
eshxpr | .0327104 .533676 0.06 0.951 -1.01616 1.081581
_cons | -2.629372 .6429471 -4.09 0.000 -3.893001 -1.365743
------------------------------------------------------------------------------
. restore
.
. regress dlpvad1 etfp1 apsh1 ansh1 aksh1 [aw=mvshipsh],robust noconstant
(sum of wgt is 9.9873e-01)
Linear regression Number of obs = 447
F(4, 443) > 99999.00
Prob > F = 0.0000
R-squared = 0.9998
Root MSE = .07762
------------------------------------------------------------------------------
| Robust
dlpvad1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
etfp1 | -1.000041 .0006831 -1463.88 0.000 -1.001384 -.9986986
apsh1 | 4.680657 .0157718 296.77 0.000 4.64966 4.711654
ansh1 | 5.482807 .0194677 281.64 0.000 5.444547 5.521068
aksh1 | 3.952538 .0083407 473.89 0.000 3.936146 3.96893
------------------------------------------------------------------------------
. * OLS Model
. regress dlpvad1 etfp1 apsh1 ansh1 aksh1 ,robust noconstant
Linear regression Number of obs = 447
F(4, 443) > 99999.00
Prob > F = 0.0000
R-squared = 0.9988
Root MSE = .1685
------------------------------------------------------------------------------
| Robust
dlpvad1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
etfp1 | -.9992624 .0042216 -236.70 0.000 -1.007559 -.9909655
apsh1 | 4.666086 .0550321 84.79 0.000 4.55793 4.774243
ansh1 | 5.437375 .0644382 84.38 0.000 5.310733 5.564018
aksh1 | 3.953762 .0221871 178.20 0.000 3.910157 3.997367
------------------------------------------------------------------------------
.
. regress dlp etfp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
(sum of wgt is 9.9873e-01)
Linear regression Number of obs = 447
F(6, 440) > 99999.00
Prob > F = 0.0000
R-squared = 0.9999
Root MSE = .0262
------------------------------------------------------------------------------
| Robust
dlp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
etfp | -1.000358 .000677 -1477.55 0.000 -1.001689 -.9990273
apsh | 4.700013 .011911 394.60 0.000 4.676603 4.723422
ansh | 5.443315 .0314405 173.13 0.000 5.381523 5.505107
aksh | 3.972308 .0150284 264.32 0.000 3.942772 4.001845
mshxpr | .9974072 .0023115 431.50 0.000 .9928643 1.00195
eshxpr | .9961108 .0057421 173.47 0.000 .9848254 1.007396
_cons | .0010799 .005423 0.20 0.842 -.0095784 .0117382
------------------------------------------------------------------------------
. * OLS Model
. regress dlp etfp apsh ansh aksh mshxpr eshxpr , robust
Linear regression Number of obs = 447
F(6, 440) > 99999.00
Prob > F = 0.0000
R-squared = 0.9989
Root MSE = .05637
------------------------------------------------------------------------------
| Robust
dlp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
etfp | -.9984327 .0024469 -408.04 0.000 -1.003242 -.9936236
apsh | 4.71449 .0145206 324.68 0.000 4.685952 4.743028
ansh | 5.443702 .0521618 104.36 0.000 5.341185 5.546219
aksh | 4.000907 .044225 90.47 0.000 3.913988 4.087825
mshxpr | .9907738 .0089715 110.44 0.000 .9731416 1.008406
eshxpr | .996285 .0058313 170.85 0.000 .9848243 1.007746
_cons | -.0023481 .007124 -0.33 0.742 -.0163494 .0116532
------------------------------------------------------------------------------
.
. log close
name:
log: D:\class\E514\log_4_3a.log
log type: text
closed on: 10 Oct 2016, 10:11:29
-------------------------------------------------------------------------------
. * clear *
. exit
Code Template for Estimation of a Long Run Model
b34sexec options include('Feenstra_ch4.mac') member(ch4_3_a);
b34srun;
b34sexec matrix;
call loaddata;
call olsq( dlp34 ptfp apsh ansh aksh :print :white);
call gamfit( dlp34 ptfp apsh ansh aksh :print );
call marspline(dlp34 ptfp apsh ansh aksh :print);
call ppreg(dlp34 ptfp apsh ansh aksh :print);
b34srun;
Variable Label # Cases Mean Std. Dev. Variance Maximum Minimum
YEAR 1 Year ranges from 58 to 97 447 1990.00 0.00000 0.00000 1990.00 1990.00
SIC72 2 4 digit SIC code 447 3015.57 608.388 370136. 3999.00 2011.00
EMP 3 Total employment in 1000s 447 39.2085 62.8485 3949.93 631.100 0.400000
PAY 4 Total payroll in $1,000,000 447 1054.33 1892.61 0.358198E+07 18381.6 13.9000
PRODE 5 Production workers in 1000s 447 27.0548 41.5547 1726.79 487.700 0.100000
PRODH 6 Production worker hours in 1,000,000 447 54.2481 83.9769 7052.12 979.200 0.300000
PRODW 7 Production worker wages in $1,000,000 447 607.053 1040.94 0.108355E+07 9789.90 8.70000
VADD 8 Total value added in $1,000,000 447 2959.26 5191.26 0.269491E+08 39504.4 27.6000
MATERIAL 9 Total cost of materials in $1,000,000 447 3469.51 9619.80 0.925406E+08 145885. 10.7000
INVENT 10 End-of-year inventories in $1,000,000 447 875.567 2098.71 0.440458E+07 32271.6 7.90000
INVEST 11 Total capital expenditure in $1,000,000 447 228.052 545.062 297093. 4396.40 0.400000
ENERGY 12 Cost of electric & fuels in $1,000,000 447 126.855 352.896 124535. 4327.90 0.800000
CAP 13 Total real capital stock in $1,000,000 447 2702.68 5862.97 0.343745E+08 59407.3 19.9000
EQUIP 14 Real capital: equipment in $1,000,000 447 1646.90 3676.64 0.135177E+08 38087.0 4.40000
PLANT 15 Real capital: structures in $1,000,000 447 1055.78 2300.93 0.529427E+07 31042.8 12.2000
PISHIP 16 Deflator for VSHIP 1987=1.000 447 1.11687 0.837093E-01 0.700725E-02 1.53300 0.822000
PIINV 17 Deflator for INVEST 1987=1.000 447 1.08237 0.241873E-01 0.585027E-03 1.11900 0.937000
PIEN 18 Deflator for ENERGY 1987=1.000 447 1.06987 0.167540E-01 0.280697E-03 1.25700 1.02200
VSHIP 19 Total value of shipments in $1,000,000 447 6412.92 13641.7 0.186097E+09 170775. 44.5000
PIMAT 20 Deflator for MATCOST 1987=1.000 447 1.12898 0.481798E-01 0.232130E-02 1.52700 1.01400
CI 21 computer investment/total investment 447 5.55268 5.48071 30.0382 43.4804 0.00000
SIC2 22 2 digit SIC code 447 29.6174 6.09484 37.1470 39.0000 20.0000
IMAT 23 imported materials 433 23.3486 109.734 12041.7 1399.06 0.00000
SIMAT1A 24 Share of imported mat -broad outsourcing 447 0.118441 0.875671E-01 0.766799E-02 0.659710 0.00000
SIMAT1B 25 share of imported mat - 2-digit industry 447 0.485957E-01 0.749496E-01 0.561745E-02 0.628002 0.00000
DSIMAT1A 26 change in outsourcing (broad) 447 0.365305 0.563151 0.317139 2.96951 -3.90025
DSIMAT1B 27 change in outsourcing (narrow) 447 0.157793 0.473762 0.224450 2.73056 -4.14979
DLY 28 change in log real shipments 447 0.394762 3.76272 14.1581 22.5287 -13.9630
NWSH 29 nonproduction share of the total wages 447 0.372574 0.120623 0.145500E-01 0.873336 0.109044
MVSHIPSH 30 industry share of total manfg shipments 447 0.223430E-02 0.496680E-02 0.246691E-04 0.703875E-01 0.230466E-04
DLKY 31 change in log capital stock/shipments 447 0.512945 3.13639 9.83696 14.7261 -13.0257
APSH 32 average production share 447 0.132555 0.574340E-01 0.329867E-02 0.364086 0.115928E-01
ANSH 33 average non-production share 447 0.722582E-01 0.393782E-01 0.155065E-02 0.270142 0.638309E-02
AMESH 34 aosh + amsh 447 0.512149 0.123647 0.152887E-01 0.890473 0.171757
AMSH 35 average material share 447 0.487772 0.127229 0.161873E-01 0.877148 0.151759
AOSH 36 average energy share 447 0.243771E-01 0.328570E-01 0.107958E-02 0.275952 0.213427E-02
AKSH 37 average capital share 447 0.283037 0.843416E-01 0.711350E-02 0.636899 0.738303E-01
DLP 38 change in log price 447 3.54611 1.70410 2.90397 11.7933 -12.9502
DLPE 39 change in log energy price 447 3.12686 0.912518 0.832688 8.40714 0.860887E-01
DHTSH 40 (capital=pstk x ex post rental price) 447 0.334085 0.376402 0.141678 1.27976 -0.301242
DHTSH1 41 (capital=pstk x ex ante rental price) 447 0.210975 0.245414 0.602279E-01 1.21186 -0.209675
DOFSH 42 change in office equipment/total capital 447 0.180127 0.307711 0.946862E-01 0.831400 -0.363431
DOFSH1 43 change in office equipment/total capital 447 0.352378E-01 0.151631 0.229921E-01 0.379551 -0.270059
DLPMX 44 change in log material price 447 3.58936 0.887371 0.787427 7.67960 -1.81683
DLPVAD 45 change in log value-added 447 1.77040 1.65821 2.74968 10.5839 -12.6178
PTFP 46 primary TFP 447 0.408978 1.64672 2.71169 14.0399 -5.01075
ADLHW 47 annual change in log production wage 447 4.71405 0.00000 0.00000 4.71405 4.71405
ADLNW 48 annual chage in log non-production wage 447 5.43687 0.00000 0.00000 5.43687 5.43687
ADLPK 49 annual change in log capital price 447 3.95370 0.00000 0.00000 3.95370 3.95370
ERR 50 error as defined in (4.26) of Chapter 4 447 0.464305E-01 1.10714 1.22575 4.49691 -4.63585
ETFP 51 ptfp-err 447 0.362547 1.46871 2.15711 14.8904 -7.65468
ADJ1 52 1.0/(1.0-amesh) 447 2.24364 0.889095 0.790491 9.13017 1.20737
ETFP1 53 adj1*etfp 447 1.00142 3.55532 12.6403 32.8904 -10.8290
B34S 9 (D:M:Y) 10/10/16 (H:M:S) 10:24: 4 DATA STEP Feenstra Chap4 4_3a Data PAGE 2
DLPVAD1 54 adj1*dlpvad 447 3.35799 3.56748 12.7269 14.9729 -29.1263
APSH1 55 adj1*apsh 447 0.270372 0.903109E-01 0.815606E-02 0.488378 0.305658E-01
ANSH1 56 adj1*ansh 447 0.143112 0.558816E-01 0.312275E-02 0.389831 0.266251E-01
AKSH1 57 adj1*aksh 447 0.586515 0.109801 0.120563E-01 0.920277 0.277150
MSHXPR 58 amsh*dlpmx 447 1.69937 0.515041 0.265268 3.39471 -1.58880
ESHXPR 59 aosh*dlpe 447 0.763338E-01 0.115698 0.133861E-01 1.21165 0.206717E-02
DLP34 60 dlp-mshxpr-eshxpr 447 1.77040 1.65821 2.74968 10.5839 -12.6178
CONSTANT 61 447 1.00000 0.00000 0.00000 1.00000 1.00000
Number of observations in data file 447
Current missing variable code 1.000000000000000E+31
Note: Missing data in the data file
B34S Matrix Command. d/m/y 10/10/16. h:m:s 10:24: 4.
=> CALL LOADDATA$
=> CALL OLSQ( DLP34 PTFP APSH ANSH AKSH :PRINT :WHITE)$
Ordinary Least Squares Estimation
Dependent variable DLP34
Centered R**2 0.6967466663385627
Adjusted R**2 0.6940022922782783
Residual Sum of Squares 371.8964985643850
Residual Variance 0.8413947931320926
Standard Error 0.9172757454179701
Total Sum of Squares 1226.355846031963
Log Likelihood -593.1542618937680
Mean of the Dependent Variable 1.770400132847875
Std. Error of Dependent Variable 1.658214939272056
Sum Absolute Residuals 297.4930711130872
F( 4, 442) 253.8818145899300
F Significance 1.000000000000000
1/Condition XPX 6.550394423061074E-04
Maximum Absolute Residual 5.408266825961406
Number of Observations 447
Variable Lag Coefficient White SE t
PTFP 0 -0.67900074 0.70587514E-01 -9.6192754
APSH 0 3.4556009 0.82814894 4.1726805
ANSH 0 3.9054785 1.7442105 2.2391097
AKSH 0 7.3941559 0.71578284 10.330166
CONSTANT 0 -0.78498817 0.18939943 -4.1446174
=> CALL GAMFIT( DLP34 PTFP APSH ANSH AKSH :PRINT )$
Generalized Additive Models (GAM) Analysis
Reference: Generalized Additive Models by Hastie and Tibshirani. Chapman (1990)
Model estimated using CRAN General Public License (GPL) routines.
Gaussian additive model assumed
Identity link - yhat = x*b + sum(splines)
Response variable .... DLP34
Number of observations: 447
Residual Sum of Squares 300.2070345290874
# iterations 1
# smooths/variable 15
Mean Squared Residual 0.6716041040919182
df of deviance 434.0021682741188
Scale Estimate 0.6917178218784257
Primary tolerence 1.000000000000000E-09
Secondary tolerance 1.000000000000000E-09
R square 0.7552039764800347
Total sum of Squares 1226.355846031963
Model df coef st err z score nl pval lin_res Name Lag
------------ ---- ------ ------- ------- ------- ---- ---
1. -1.04728 0.1685 -6.217 intcpt
3.00 -.665252 0.2421E-01 -27.48 1.000 346.8 PTFP 0
3.00 4.03542 0.7551 5.344 0.1748 300.8 APSH 0
3.00 5.63971 1.133 4.979 0.8573 304.0 ANSH 0
3.00 7.58671 0.4869 15.58 1.000 325.1 AKSH 0
-----
13.0
=> CALL MARSPLINE(DLP34 PTFP APSH ANSH AKSH :PRINT)$
Multivariate Autoregressive Splines Analysis
Model Estimated using Hastie-Tibshirani GPL routines in
CRAN General Public License (GPL) Library.
Version - 1 March 2006.
Left Hand Side Variable DLP34
Penalty cost per degree of freedom 2.000
Threshold for Forward stepwise Stopping 0.1000E-03
Rank Test Tolerance 0.1000E-12
Max # of Knots (nk) 5
Max interaction (mi) 1
Number of Observations 447
Number of right hand Variables 4
tolbx set as 1.000000000000000E-09
stopfac gcv/gcvnull > stopfac => stop 10.00000000000000
prevcrit set as 10000000000.00000
Series Lag Mean Max Min
PTFP 0 0.4090 14.04 -5.011
APSH 0 0.1326 0.3641 0.1159E-01
ANSH 0 0.7226E-01 0.2701 0.6383E-02
AKSH 0 0.2830 0.6369 0.7383E-01
GCV with only the constant 2.755841979409840
Total sum of squares 1226.355846031963
Final gcv 0.8411019886991933
Variance of Y Variable 2.749676784825029
R**2 (1 - (var(res)/var(y))) 0.7056440275681013
Residual Sum of Squares 360.9851676062820
Residual Variance 0.8093837838705881
Residual Standard Error 0.8996575925709670
Sum Absolute Residuals 306.7363667559480
Max Absolute Residual 3.945752605427743
# of coefficients after last fwd step 5
MARS Model Coefficients SE t Non Zero % Importance #
DLP34 = 1.1612470 0.13135952 8.84 447 100.000 1
-1.2359379 * max( PTFP{ 0} - 3.1126752 , 0.0) 0.77496252E-01 -15.9 23 5.145 85.560 2
+ 0.57809246 * max( 3.1126752 - PTFP{ 0} , 0.0) 0.31013665E-01 18.6 423 94.631 100.000 3
+ 12.581184 * max( AKSH{ 0} - 0.41347152 , 0.0) 1.9014328 6.61 23 5.145 35.497 4
-7.1731181 * max( 0.41347152 - AKSH{ 0} , 0.0) 0.62994727 -11.3 423 94.631 61.089 5
=> CALL PPREG(DLP34 PTFP APSH ANSH AKSH :PRINT)$
Projection Pursuit Regression
Number of Observations 447
Number of right hand side variables 5
Maximum number of ridge functions 20
Minimum number of ridge functions 20
Number of left hand side variables 1
Level of fit 2
Max number of Primary Iterations (maxit) 200
Max number of Secondary Iterations (mitone) 200
Number of cj Iterations (mitcj) 10
Smoother tone control (alpha) 0.000000000000000E+00
Span 0.000000000000000E+00
Convergence (CONV) set as 5.000000000000000E-03
Left Hand Side Variable DLP34
Series Mean Max Min
DLP34 1.770 10.58 -12.62
Right Hand Side Variables
# Series Lag Mean Max Min
1 PTFP 0 0.4090 14.04 -5.011
2 APSH 0 0.1326 0.3641 0.1159E-01
3 ANSH 0 0.7226E-01 0.2701 0.6383E-02
4 AKSH 0 0.2830 0.6369 0.7383E-01
5 CONSTANT 0 1.000 1.000 1.000
Given # of ridge functions 20
# primary iterations used 1
# secondary iterations used 7
# cj iterations used 2
Residual sum of squares 179.3691430157083
Total sum of squares 1226.355846031963
Mean of the Dependent Variable 1.770400132847875
Std. Error of Dependent Variable 1.658214939272056
Sum Absolute Residuals 210.3559765757928
Maximum Absolute Residual 2.456771179577403
Residual Variance 0.4058125407595211
Variable Importance for Model with # ridge functions 20
Series Number Importance
1 1.00000
3 0.885062
4 0.760611
2 0.636560
5 0.00000
B34S Matrix Command Ending. Last Command reached.
Space available in allocator 99856943, peak space used 133856
Number variables used 145, peak number used 145
Number temp variables used 41, # user temp clean 0
B34S 9 (D:M:Y) 10/10/16 (H:M:S) 10:24: 4 DATA STEP Feenstra Chap4 4_3a Data PAGE 3
Stata Template
// set mem 3m
log using log_4_3a.log,replace
// use d:\feenstra_course\chap4\data_Chp4.dta, clear
// use c:\feenstra_course\chap4\data_Chp4.dta, clear
use data_Chp4.dta, clear
// use e:\feenstra_course\chap4\data_Chp4.dta, clear
* use /usr/local/lib/hhsfiles/data_Chp4.dta, clear
keep if year==1990
drop if sic72==2067
drop if sic72==2794
drop if sic72==3483
gen etfp=ptfp-err
gen adj1=1/(1-amesh)
gen etfp1=adj1*etfp
gen dlpvad1=adj1*dlpvad
gen apsh1=adj1*apsh
gen ansh1=adj1*ansh
gen aksh1=adj1*aksh
gen mshxpr=amsh*dlpmx
gen eshxpr=aosh*dlpe
* Reproduce Table 4.5 reprinted at 4.1 in new edition.
gen dlp34=dlp-mshxpr-eshxpr
regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
* OLS Model
regress dlp34 ptfp apsh ansh aksh , robust
preserve
drop if sic72==3573
regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
* OLS Model without sic72
regress dlp34 ptfp apsh ansh aksh , robust
regress dlp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
* OLS Model
regress dlp apsh ansh aksh mshxpr eshxpr, robust
restore
regress dlpvad1 etfp1 apsh1 ansh1 aksh1 [aw=mvshipsh],robust noconstant
* OLS Model
regress dlpvad1 etfp1 apsh1 ansh1 aksh1 ,robust noconstant
regress dlp etfp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
* OLS Model
regress dlp etfp apsh ansh aksh mshxpr eshxpr , robust
log close
* clear *
exit
___ ____ ____ ____ ____ (R)
/__ / ____/ / ____/
___/ / /___/ / /___/ 14.2 Copyright 1985-2015 StataCorp LP
Statistics/Data Analysis StataCorp
4905 Lakeway Drive
Special Edition College Station, Texas 77845 USA
800-STATA-PC http://www.stata.com
979-696-4600 stata@stata.com
979-696-4601 (fax)
Single-user Stata perpetual license:
Serial number: 401406202087
Licensed to: Houston H. Stokes
University of Illinois Chicago
Notes:
1. Stata is running in batch mode.
2. Unicode is supported; see help unicode_advice.
3. Maximum number of variables is set to 5000; see help set_maxvar.
. do Problem_4_3_a.do
.
. // set mem 3m
.
. log using log_4_3a.log,replace
-------------------------------------------------------------------------------
name:
log: D:\class\E514\log_4_3a.log
log type: text
opened on: 10 Oct 2016, 10:11:28
.
. // use d:\feenstra_course\chap4\data_Chp4.dta, clear
. // use c:\feenstra_course\chap4\data_Chp4.dta, clear
. use data_Chp4.dta, clear
(Matrl Cons (72 SIC), 67-92)
. // use e:\feenstra_course\chap4\data_Chp4.dta, clear
. * use /usr/local/lib/hhsfiles/data_Chp4.dta, clear
.
. keep if year==1990
(1,350 observations deleted)
. drop if sic72==2067
(1 observation deleted)
. drop if sic72==2794
(1 observation deleted)
. drop if sic72==3483
(1 observation deleted)
. gen etfp=ptfp-err
. gen adj1=1/(1-amesh)
. gen etfp1=adj1*etfp
. gen dlpvad1=adj1*dlpvad
. gen apsh1=adj1*apsh
. gen ansh1=adj1*ansh
. gen aksh1=adj1*aksh
. gen mshxpr=amsh*dlpmx
. gen eshxpr=aosh*dlpe
.
.
. * Reproduce Table 4.5 *
.
. gen dlp34=dlp-mshxpr-eshxpr
.
. regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
(sum of wgt is 9.9873e-01)
Linear regression Number of obs = 447
F(4, 442) = 106.29
Prob > F = 0.0000
R-squared = 0.8957
Root MSE = .80656
------------------------------------------------------------------------------
| Robust
dlp34 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptfp | -.9631819 .0702093 -13.72 0.000 -1.101168 -.8251963
apsh | 3.062598 1.22198 2.51 0.013 .6609845 5.464212
ansh | 2.294716 1.430073 1.60 0.109 -.5158719 5.105305
aksh | 7.887571 .7810006 10.10 0.000 6.352634 9.422507
_cons | -.7051116 .3006016 -2.35 0.019 -1.295898 -.1143256
------------------------------------------------------------------------------
.
. * OLS Model
. regress dlp34 ptfp apsh ansh aksh , robust
Linear regression Number of obs = 447
F(4, 442) = 110.62
Prob > F = 0.0000
R-squared = 0.6967
Root MSE = .91728
------------------------------------------------------------------------------
| Robust
dlp34 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptfp | -.6790007 .0709856 -9.57 0.000 -.8185121 -.5394894
apsh | 3.455601 .8328199 4.15 0.000 1.818822 5.09238
ansh | 3.905478 1.754048 2.23 0.026 .4581676 7.352789
aksh | 7.394156 .71982 10.27 0.000 5.979461 8.808851
_cons | -.7849882 .1904677 -4.12 0.000 -1.159323 -.4106534
------------------------------------------------------------------------------
.
. preserve
. drop if sic72==3573
(1 observation deleted)
.
. regress dlp34 ptfp apsh ansh aksh [aw=mvshipsh], robust
(sum of wgt is 9.8179e-01)
Linear regression Number of obs = 446
F(4, 441) = 92.17
Prob > F = 0.0000
R-squared = 0.8059
Root MSE = .74139
------------------------------------------------------------------------------
| Robust
dlp34 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptfp | -.7531151 .0751891 -10.02 0.000 -.9008886 -.6053416
apsh | 2.427856 1.162844 2.09 0.037 .142451 4.713261
ansh | 4.086394 1.722144 2.37 0.018 .7017647 7.471024
aksh | 8.058291 .9411699 8.56 0.000 6.208556 9.908027
_cons | -.8249273 .2930995 -2.81 0.005 -1.400973 -.2488819
------------------------------------------------------------------------------
. * OLS Model without sic72
. regress dlp34 ptfp apsh ansh aksh , robust
Linear regression Number of obs = 446
F(4, 441) = 135.75
Prob > F = 0.0000
R-squared = 0.6696
Root MSE = .87366
------------------------------------------------------------------------------
| Robust
dlp34 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptfp | -.6043067 .0418654 -14.43 0.000 -.6865873 -.5220261
apsh | 3.156235 .7864841 4.01 0.000 1.610513 4.701958
ansh | 4.954764 1.5334 3.23 0.001 1.941084 7.968443
aksh | 7.396599 .7390641 10.01 0.000 5.944073 8.849124
_cons | -.8377685 .1852263 -4.52 0.000 -1.201804 -.4737325
------------------------------------------------------------------------------
.
. regress dlp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
(sum of wgt is 9.8179e-01)
Linear regression Number of obs = 446
F(5, 440) = 10.85
Prob > F = 0.0000
R-squared = 0.4289
Root MSE = 1.2034
------------------------------------------------------------------------------
| Robust
dlp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
apsh | 3.605277 1.88524 1.91 0.056 -.0999163 7.310471
ansh | 6.202674 4.036466 1.54 0.125 -1.730475 14.13582
aksh | 9.535214 2.18722 4.36 0.000 5.236518 13.83391
mshxpr | 1.219304 .2471334 4.93 0.000 .7335958 1.705013
eshxpr | -.9301182 .9150299 -1.02 0.310 -2.728491 .8682541
_cons | -1.929187 .9147773 -2.11 0.036 -3.727063 -.1313111
------------------------------------------------------------------------------
. * OLS Model
. regress dlp apsh ansh aksh mshxpr eshxpr, robust
Linear regression Number of obs = 446
F(5, 440) = 24.65
Prob > F = 0.0000
R-squared = 0.3400
Root MSE = 1.2384
------------------------------------------------------------------------------
| Robust
dlp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
apsh | 5.629626 1.284501 4.38 0.000 3.105105 8.154147
ansh | 7.727702 2.065437 3.74 0.000 3.668354 11.78705
aksh | 8.611022 1.272484 6.77 0.000 6.110121 11.11192
mshxpr | 1.448936 .1923696 7.53 0.000 1.070858 1.827013
eshxpr | .0327104 .533676 0.06 0.951 -1.01616 1.081581
_cons | -2.629372 .6429471 -4.09 0.000 -3.893001 -1.365743
------------------------------------------------------------------------------
. restore
.
. regress dlpvad1 etfp1 apsh1 ansh1 aksh1 [aw=mvshipsh],robust noconstant
(sum of wgt is 9.9873e-01)
Linear regression Number of obs = 447
F(4, 443) > 99999.00
Prob > F = 0.0000
R-squared = 0.9998
Root MSE = .07762
------------------------------------------------------------------------------
| Robust
dlpvad1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
etfp1 | -1.000041 .0006831 -1463.88 0.000 -1.001384 -.9986986
apsh1 | 4.680657 .0157718 296.77 0.000 4.64966 4.711654
ansh1 | 5.482807 .0194677 281.64 0.000 5.444547 5.521068
aksh1 | 3.952538 .0083407 473.89 0.000 3.936146 3.96893
------------------------------------------------------------------------------
. * OLS Model
. regress dlpvad1 etfp1 apsh1 ansh1 aksh1 ,robust noconstant
Linear regression Number of obs = 447
F(4, 443) > 99999.00
Prob > F = 0.0000
R-squared = 0.9988
Root MSE = .1685
------------------------------------------------------------------------------
| Robust
dlpvad1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
etfp1 | -.9992624 .0042216 -236.70 0.000 -1.007559 -.9909655
apsh1 | 4.666086 .0550321 84.79 0.000 4.55793 4.774243
ansh1 | 5.437375 .0644382 84.38 0.000 5.310733 5.564018
aksh1 | 3.953762 .0221871 178.20 0.000 3.910157 3.997367
------------------------------------------------------------------------------
.
. regress dlp etfp apsh ansh aksh mshxpr eshxpr [aw=mvshipsh], robust
(sum of wgt is 9.9873e-01)
Linear regression Number of obs = 447
F(6, 440) > 99999.00
Prob > F = 0.0000
R-squared = 0.9999
Root MSE = .0262
------------------------------------------------------------------------------
| Robust
dlp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
etfp | -1.000358 .000677 -1477.55 0.000 -1.001689 -.9990273
apsh | 4.700013 .011911 394.60 0.000 4.676603 4.723422
ansh | 5.443315 .0314405 173.13 0.000 5.381523 5.505107
aksh | 3.972308 .0150284 264.32 0.000 3.942772 4.001845
mshxpr | .9974072 .0023115 431.50 0.000 .9928643 1.00195
eshxpr | .9961108 .0057421 173.47 0.000 .9848254 1.007396
_cons | .0010799 .005423 0.20 0.842 -.0095784 .0117382
------------------------------------------------------------------------------
. * OLS Model
. regress dlp etfp apsh ansh aksh mshxpr eshxpr , robust
Linear regression Number of obs = 447
F(6, 440) > 99999.00
Prob > F = 0.0000
R-squared = 0.9989
Root MSE = .05637
------------------------------------------------------------------------------
| Robust
dlp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
etfp | -.9984327 .0024469 -408.04 0.000 -1.003242 -.9936236
apsh | 4.71449 .0145206 324.68 0.000 4.685952 4.743028
ansh | 5.443702 .0521618 104.36 0.000 5.341185 5.546219
aksh | 4.000907 .044225 90.47 0.000 3.913988 4.087825
mshxpr | .9907738 .0089715 110.44 0.000 .9731416 1.008406
eshxpr | .996285 .0058313 170.85 0.000 .9848243 1.007746
_cons | -.0023481 .007124 -0.33 0.742 -.0163494 .0116532
------------------------------------------------------------------------------
.
. log close
name:
log: D:\class\E514\log_4_3a.log
log type: text
closed on: 10 Oct 2016, 10:11:29
-------------------------------------------------------------------------------
. * clear *
. exit
Code Template for Estimation of a Long Run Model
b34sexec options include('Feenstra_ch4.mac') member(ch4_3_a);
b34srun;
b34sexec matrix;
call loaddata;
call olsq( dlp34 ptfp apsh ansh aksh :print :white);
call gamfit( dlp34 ptfp apsh ansh aksh :print );
call marspline(dlp34 ptfp apsh ansh aksh :print);
call ppreg(dlp34 ptfp apsh ansh aksh :print);
b34srun;
Variable Label # Cases Mean Std. Dev. Variance Maximum Minimum
YEAR 1 Year ranges from 58 to 97 447 1990.00 0.00000 0.00000 1990.00 1990.00
SIC72 2 4 digit SIC code 447 3015.57 608.388 370136. 3999.00 2011.00
EMP 3 Total employment in 1000s 447 39.2085 62.8485 3949.93 631.100 0.400000
PAY 4 Total payroll in $1,000,000 447 1054.33 1892.61 0.358198E+07 18381.6 13.9000
PRODE 5 Production workers in 1000s 447 27.0548 41.5547 1726.79 487.700 0.100000
PRODH 6 Production worker hours in 1,000,000 447 54.2481 83.9769 7052.12 979.200 0.300000
PRODW 7 Production worker wages in $1,000,000 447 607.053 1040.94 0.108355E+07 9789.90 8.70000
VADD 8 Total value added in $1,000,000 447 2959.26 5191.26 0.269491E+08 39504.4 27.6000
MATERIAL 9 Total cost of materials in $1,000,000 447 3469.51 9619.80 0.925406E+08 145885. 10.7000
INVENT 10 End-of-year inventories in $1,000,000 447 875.567 2098.71 0.440458E+07 32271.6 7.90000
INVEST 11 Total capital expenditure in $1,000,000 447 228.052 545.062 297093. 4396.40 0.400000
ENERGY 12 Cost of electric & fuels in $1,000,000 447 126.855 352.896 124535. 4327.90 0.800000
CAP 13 Total real capital stock in $1,000,000 447 2702.68 5862.97 0.343745E+08 59407.3 19.9000
EQUIP 14 Real capital: equipment in $1,000,000 447 1646.90 3676.64 0.135177E+08 38087.0 4.40000
PLANT 15 Real capital: structures in $1,000,000 447 1055.78 2300.93 0.529427E+07 31042.8 12.2000
PISHIP 16 Deflator for VSHIP 1987=1.000 447 1.11687 0.837093E-01 0.700725E-02 1.53300 0.822000
PIINV 17 Deflator for INVEST 1987=1.000 447 1.08237 0.241873E-01 0.585027E-03 1.11900 0.937000
PIEN 18 Deflator for ENERGY 1987=1.000 447 1.06987 0.167540E-01 0.280697E-03 1.25700 1.02200
VSHIP 19 Total value of shipments in $1,000,000 447 6412.92 13641.7 0.186097E+09 170775. 44.5000
PIMAT 20 Deflator for MATCOST 1987=1.000 447 1.12898 0.481798E-01 0.232130E-02 1.52700 1.01400
CI 21 computer investment/total investment 447 5.55268 5.48071 30.0382 43.4804 0.00000
SIC2 22 2 digit SIC code 447 29.6174 6.09484 37.1470 39.0000 20.0000
IMAT 23 imported materials 433 23.3486 109.734 12041.7 1399.06 0.00000
SIMAT1A 24 Share of imported mat -broad outsourcing 447 0.118441 0.875671E-01 0.766799E-02 0.659710 0.00000
SIMAT1B 25 share of imported mat - 2-digit industry 447 0.485957E-01 0.749496E-01 0.561745E-02 0.628002 0.00000
DSIMAT1A 26 change in outsourcing (broad) 447 0.365305 0.563151 0.317139 2.96951 -3.90025
DSIMAT1B 27 change in outsourcing (narrow) 447 0.157793 0.473762 0.224450 2.73056 -4.14979
DLY 28 change in log real shipments 447 0.394762 3.76272 14.1581 22.5287 -13.9630
NWSH 29 nonproduction share of the total wages 447 0.372574 0.120623 0.145500E-01 0.873336 0.109044
MVSHIPSH 30 industry share of total manfg shipments 447 0.223430E-02 0.496680E-02 0.246691E-04 0.703875E-01 0.230466E-04
DLKY 31 change in log capital stock/shipments 447 0.512945 3.13639 9.83696 14.7261 -13.0257
APSH 32 average production share 447 0.132555 0.574340E-01 0.329867E-02 0.364086 0.115928E-01
ANSH 33 average non-production share 447 0.722582E-01 0.393782E-01 0.155065E-02 0.270142 0.638309E-02
AMESH 34 aosh + amsh 447 0.512149 0.123647 0.152887E-01 0.890473 0.171757
AMSH 35 average material share 447 0.487772 0.127229 0.161873E-01 0.877148 0.151759
AOSH 36 average energy share 447 0.243771E-01 0.328570E-01 0.107958E-02 0.275952 0.213427E-02
AKSH 37 average capital share 447 0.283037 0.843416E-01 0.711350E-02 0.636899 0.738303E-01
DLP 38 change in log price 447 3.54611 1.70410 2.90397 11.7933 -12.9502
DLPE 39 change in log energy price 447 3.12686 0.912518 0.832688 8.40714 0.860887E-01
DHTSH 40 (capital=pstk x ex post rental price) 447 0.334085 0.376402 0.141678 1.27976 -0.301242
DHTSH1 41 (capital=pstk x ex ante rental price) 447 0.210975 0.245414 0.602279E-01 1.21186 -0.209675
DOFSH 42 change in office equipment/total capital 447 0.180127 0.307711 0.946862E-01 0.831400 -0.363431
DOFSH1 43 change in office equipment/total capital 447 0.352378E-01 0.151631 0.229921E-01 0.379551 -0.270059
DLPMX 44 change in log material price 447 3.58936 0.887371 0.787427 7.67960 -1.81683
DLPVAD 45 change in log value-added 447 1.77040 1.65821 2.74968 10.5839 -12.6178
PTFP 46 primary TFP 447 0.408978 1.64672 2.71169 14.0399 -5.01075
ADLHW 47 annual change in log production wage 447 4.71405 0.00000 0.00000 4.71405 4.71405
ADLNW 48 annual chage in log non-production wage 447 5.43687 0.00000 0.00000 5.43687 5.43687
ADLPK 49 annual change in log capital price 447 3.95370 0.00000 0.00000 3.95370 3.95370
ERR 50 error as defined in (4.26) of Chapter 4 447 0.464305E-01 1.10714 1.22575 4.49691 -4.63585
ETFP 51 ptfp-err 447 0.362547 1.46871 2.15711 14.8904 -7.65468
ADJ1 52 1.0/(1.0-amesh) 447 2.24364 0.889095 0.790491 9.13017 1.20737
ETFP1 53 adj1*etfp 447 1.00142 3.55532 12.6403 32.8904 -10.8290
B34S 9 (D:M:Y) 10/10/16 (H:M:S) 10:24: 4 DATA STEP Feenstra Chap4 4_3a Data PAGE 2
DLPVAD1 54 adj1*dlpvad 447 3.35799 3.56748 12.7269 14.9729 -29.1263
APSH1 55 adj1*apsh 447 0.270372 0.903109E-01 0.815606E-02 0.488378 0.305658E-01
ANSH1 56 adj1*ansh 447 0.143112 0.558816E-01 0.312275E-02 0.389831 0.266251E-01
AKSH1 57 adj1*aksh 447 0.586515 0.109801 0.120563E-01 0.920277 0.277150
MSHXPR 58 amsh*dlpmx 447 1.69937 0.515041 0.265268 3.39471 -1.58880
ESHXPR 59 aosh*dlpe 447 0.763338E-01 0.115698 0.133861E-01 1.21165 0.206717E-02
DLP34 60 dlp-mshxpr-eshxpr 447 1.77040 1.65821 2.74968 10.5839 -12.6178
CONSTANT 61 447 1.00000 0.00000 0.00000 1.00000 1.00000
Number of observations in data file 447
Current missing variable code 1.000000000000000E+31
Note: Missing data in the data file
B34S Matrix Command. d/m/y 10/10/16. h:m:s 10:24: 4.
=> CALL LOADDATA$
=> CALL OLSQ( DLP34 PTFP APSH ANSH AKSH :PRINT :WHITE)$
Ordinary Least Squares Estimation
Dependent variable DLP34
Centered R**2 0.6967466663385627
Adjusted R**2 0.6940022922782783
Residual Sum of Squares 371.8964985643850
Residual Variance 0.8413947931320926
Standard Error 0.9172757454179701
Total Sum of Squares 1226.355846031963
Log Likelihood -593.1542618937680
Mean of the Dependent Variable 1.770400132847875
Std. Error of Dependent Variable 1.658214939272056
Sum Absolute Residuals 297.4930711130872
F( 4, 442) 253.8818145899300
F Significance 1.000000000000000
1/Condition XPX 6.550394423061074E-04
Maximum Absolute Residual 5.408266825961406
Number of Observations 447
Variable Lag Coefficient White SE t
PTFP 0 -0.67900074 0.70587514E-01 -9.6192754
APSH 0 3.4556009 0.82814894 4.1726805
ANSH 0 3.9054785 1.7442105 2.2391097
AKSH 0 7.3941559 0.71578284 10.330166
CONSTANT 0 -0.78498817 0.18939943 -4.1446174
=> CALL GAMFIT( DLP34 PTFP APSH ANSH AKSH :PRINT )$
Generalized Additive Models (GAM) Analysis
Reference: Generalized Additive Models by Hastie and Tibshirani. Chapman (1990)
Model estimated using CRAN General Public License (GPL) routines.
Gaussian additive model assumed
Identity link - yhat = x*b + sum(splines)
Response variable .... DLP34
Number of observations: 447
Residual Sum of Squares 300.2070345290874
# iterations 1
# smooths/variable 15
Mean Squared Residual 0.6716041040919182
df of deviance 434.0021682741188
Scale Estimate 0.6917178218784257
Primary tolerence 1.000000000000000E-09
Secondary tolerance 1.000000000000000E-09
R square 0.7552039764800347
Total sum of Squares 1226.355846031963
Model df coef st err z score nl pval lin_res Name Lag
------------ ---- ------ ------- ------- ------- ---- ---
1. -1.04728 0.1685 -6.217 intcpt
3.00 -.665252 0.2421E-01 -27.48 1.000 346.8 PTFP 0
3.00 4.03542 0.7551 5.344 0.1748 300.8 APSH 0
3.00 5.63971 1.133 4.979 0.8573 304.0 ANSH 0
3.00 7.58671 0.4869 15.58 1.000 325.1 AKSH 0
-----
13.0
=> CALL MARSPLINE(DLP34 PTFP APSH ANSH AKSH :PRINT)$
Multivariate Autoregressive Splines Analysis
Model Estimated using Hastie-Tibshirani GPL routines in
CRAN General Public License (GPL) Library.
Version - 1 March 2006.
Left Hand Side Variable DLP34
Penalty cost per degree of freedom 2.000
Threshold for Forward stepwise Stopping 0.1000E-03
Rank Test Tolerance 0.1000E-12
Max # of Knots (nk) 5
Max interaction (mi) 1
Number of Observations 447
Number of right hand Variables 4
tolbx set as 1.000000000000000E-09
stopfac gcv/gcvnull > stopfac => stop 10.00000000000000
prevcrit set as 10000000000.00000
Series Lag Mean Max Min
PTFP 0 0.4090 14.04 -5.011
APSH 0 0.1326 0.3641 0.1159E-01
ANSH 0 0.7226E-01 0.2701 0.6383E-02
AKSH 0 0.2830 0.6369 0.7383E-01
GCV with only the constant 2.755841979409840
Total sum of squares 1226.355846031963
Final gcv 0.8411019886991933
Variance of Y Variable 2.749676784825029
R**2 (1 - (var(res)/var(y))) 0.7056440275681013
Residual Sum of Squares 360.9851676062820
Residual Variance 0.8093837838705881
Residual Standard Error 0.8996575925709670
Sum Absolute Residuals 306.7363667559480
Max Absolute Residual 3.945752605427743
# of coefficients after last fwd step 5
MARS Model Coefficients SE t Non Zero % Importance #
DLP34 = 1.1612470 0.13135952 8.84 447 100.000 1
-1.2359379 * max( PTFP{ 0} - 3.1126752 , 0.0) 0.77496252E-01 -15.9 23 5.145 85.560 2
+ 0.57809246 * max( 3.1126752 - PTFP{ 0} , 0.0) 0.31013665E-01 18.6 423 94.631 100.000 3
+ 12.581184 * max( AKSH{ 0} - 0.41347152 , 0.0) 1.9014328 6.61 23 5.145 35.497 4
-7.1731181 * max( 0.41347152 - AKSH{ 0} , 0.0) 0.62994727 -11.3 423 94.631 61.089 5
=> CALL PPREG(DLP34 PTFP APSH ANSH AKSH :PRINT)$
Projection Pursuit Regression
Number of Observations 447
Number of right hand side variables 5
Maximum number of ridge functions 20
Minimum number of ridge functions 20
Number of left hand side variables 1
Level of fit 2
Max number of Primary Iterations (maxit) 200
Max number of Secondary Iterations (mitone) 200
Number of cj Iterations (mitcj) 10
Smoother tone control (alpha) 0.000000000000000E+00
Span 0.000000000000000E+00
Convergence (CONV) set as 5.000000000000000E-03
Left Hand Side Variable DLP34
Series Mean Max Min
DLP34 1.770 10.58 -12.62
Right Hand Side Variables
# Series Lag Mean Max Min
1 PTFP 0 0.4090 14.04 -5.011
2 APSH 0 0.1326 0.3641 0.1159E-01
3 ANSH 0 0.7226E-01 0.2701 0.6383E-02
4 AKSH 0 0.2830 0.6369 0.7383E-01
5 CONSTANT 0 1.000 1.000 1.000
Given # of ridge functions 20
# primary iterations used 1
# secondary iterations used 7
# cj iterations used 2
Residual sum of squares 179.3691430157083
Total sum of squares 1226.355846031963
Mean of the Dependent Variable 1.770400132847875
Std. Error of Dependent Variable 1.658214939272056
Sum Absolute Residuals 210.3559765757928
Maximum Absolute Residual 2.456771179577403
Residual Variance 0.4058125407595211
Variable Importance for Model with # ridge functions 20
Series Number Importance
1 1.00000
3 0.885062
4 0.760611
2 0.636560
5 0.00000
B34S Matrix Command Ending. Last Command reached.
Space available in allocator 99856943, peak space used 133856
Number variables used 145, peak number used 145
Number temp variables used 41, # user temp clean 0
B34S 9 (D:M:Y) 10/10/16 (H:M:S) 10:24: 4 DATA STEP Feenstra Chap4 4_3a Data PAGE 3
6. Extensions to H-O model suggested by Vanek
(Math treatment by Feenstra)
Assume C countries ( EMBED Equation.DSMT4 , N industries EMBED Equation.DSMT4 and M factors indexed by EMBED Equation.DSMT4 . Define EMBED Equation.DSMT4 the requirements of labor and capital to produce one unit of good j using input k. Assuming the 2 by 2 case with Labor L and capital K EMBED Equation.DSMT4 Matrix A includes both direct primary factors EMBED Equation.DSMT4 used in production and indirect factors used through intermediate production.
Remark: [In input-output analysis: Define B as the N by N input-output matrix. Define EMBED Equation.DSMT4 = final demand in industry j and EMBED Equation.DSMT4 = production of good j. Total production needs to take into account final demand and intermediate demand. EMBED Equation.DSMT4 or
EMBED Equation.DSMT4 . (6.1)
Define B such that EMBED Equation.DSMT4 . Final production of goods EMBED Equation.DSMT4 . In terms of the primary and indirect factors, EMBED Equation.DSMT4 ]
Define EMBED Equation.DSMT4 = outputs of the N industries in country i, EMBED Equation.DSMT4 = demands for N industries in country i and EMBED Equation.DSMT4 (Can think of EMBED Equation.DSMT4 as absorption).
Remark: [ S. Alexander (See Dunn-Mutti page 400) argued that if EMBED Equation.DSMT4 it was not possible to export. Other writers have stressed the fact that it was important to determine if the economy was at full employment or not. If an economy is at full employment then the only way to increase exports is to reduce absorption.]
Factor content of trade is EMBED Equation.DSMT4 . Define an individual component of EMBED Equation.DSMT4 as EMBED Equation.DSMT4 . where >0 (<0) determines if the k factor is exported (imported).
Goal of HOV theory is to relate factor content of trade in country i to the underlying factor endowments.
EMBED Equation.DSMT4 = demand for factors in country i.
EMBED Equation.DSMT4 demand for factors in country i that are consumed domestically.
Assuming product prices are equalized across countries => consumption vectors are proportional => can simplify the analysis. Define EMBED Equation.DSMT4 =share of country i. EMBED Equation.DSMT4 , EMBED Equation.DSMT4 . If trade is balanced, EMBED Equation.DSMT4 = country i's share of world GDP.
Given world consumption = world production,
EMBED Equation.DSMT4 . (6.2)
This proves the HOV theorem relating to the factor content of trade EMBED Equation.DSMT4 . Recall EMBED Equation.DSMT4 = total demand for factors in country i. If EMBED Equation.DSMT4 this implies that factor content of trade greater than countries consumption share times total world factor demand.
EMBED Equation.DSMT4 (6.3)
for the kth factor. Equation (6.3) is the basic HOV theorem. Equations (6.19) and (6.25) extend
the HOV model by allowing for factor productivity differences in the EMBED Equation.DSMT4 matrix across countries.
EMBED Equation.DSMT4 (6.4)
A country i is abundant in factor k if
EMBED Equation.DSMT4 (6.5)
Looking at two elements of the factor content of trade vector
EMBED Equation.DSMT4 (6.6)
EMBED Equation.DSMT4 (6.7)
which can be transformed to
EMBED Equation.DSMT4 (6.8)
Define capital to be abundant relative to labor if
EMBED Equation.DSMT4 (6.9)
which simplifies to the Leamer (1980) Theorem "If capital is abundant relative to labor in country i then the HOV theorem for all inputs is
EMBED Equation.DSMT4 (6.10)
and for the EMBED Equation.DSMT4 input
EMBED Equation.DSMT4 (6.11)
Leamer's 1980 theorem states that if capital is abundant relative to labor in country i, then
EMBED Equation.DSMT4 (6.12)
or
EMBED Equation.DSMT4 (6.13)
From (6.7) and (6.13) we have proved that the capital/labor ratio embodied in production for country i exceeds the capital/labor ratio embodied in consumption" if country i is capital abundant.
EMBED Equation.DSMT4 (6.14)
Strict equality holds if there is no trade and EMBED Equation.DSMT4 . Feenstra page 40 reports that (6.14) holds for the US in 1947. => No Leontief paradox! The Leamer theorem does not require balanced trade!
To fully test the Leontief paradox requires data on EMBED Equation.DSMT4 , A, EMBED Equation.DSMT4 and EMBED Equation.DSMT4 . If the number of factors equals the number of goods we can estimate net exports as
EMBED Equation.DSMT4 (6.15)
taking EMBED Equation.DSMT4 from (6.3) as data. The estimated coefficients should estimate the relative abundance of each factor EMBED Equation.DSMT4 . (Note: This is the usual OLS model Y=XB where EMBED Equation.DSMT4 ) If the number of goods is greater than the number of factors, we can estimate EMBED Equation.DSMT4 (adjusted net exports of each industry) as a function of A' (their labor and capital requirements).
EMBED Equation.DSMT4 (6.16)
EMBED Equation.DSMT4 (6.17)
Feenstra (2004, 43) and others have argued that this less than optimum formulation gives a "contaminated estimate" of the vector of relative factor endowments that could be less than zero.
Leamer using an alternative approach treated EMBED Equation.DSMT4 as data and using data for all C countries estimated
EMBED Equation.DSMT4 (6.18)
which is not a test of Leontief. For details on this and other possible approaches, see Freenstra (2004, 44-60).
In an important extension Trefler (1993) assumed different productivity of factors across countries. Let EMBED Equation.DSMT4 represent the relative productivity of EMBED Equation.DSMT4 country for the EMBED Equation.DSMT4 factor relative to the US.
Looking at all countries, equation (6.4) becomes
EMBED Equation.DSMT4 (6.19)
which restates the HOV theory in equation (6.3).
There are MC equations but since both sides sum to 0.0, we drop one country and solve for M(C-1) parameters using an inverse. Equation (6.19) holds as an identity. Given the assumptions of the model, it is thus not testable. Of interest is whether the assumptions are warranted.
One way to proceed is to see if the solutions generated by the inverse are all greater than 0.0. Any value < 0.0 is not reasonable. Another way to proceed is to assume factor price equalization and see if the estimated relative labor productivity EMBED Equation.DSMT4 follows relative wage differences across countries. The empirical results for this hypothesis for the factor labor are given in figure 2.4 on page 51 of Feenstra and tend to support Trefler (1993).
Research Ideas: It would be interesting to generate figure 2.4 for other factors and see what countries are off the line. Figure 2.4 suggests that relative wages in Canada are above what Canadian labor productivity would imply. Hong Kong, Finland, France etc being below the line are more productive in labor than their relative wages. Another research question might be to look at trends over time.
Trefler (1995) approached the same general problem using a method involving differences in the factor requirements matrix EMBED Equation.DSMT4 across countries. One simplifying assumption is to assume a uniform amount change across countries defined as EMBED Equation.DSMT4 . In his 1993 paper defined EMBED Equation.DSMT4 to resent the relative productivity of EMBED Equation.DSMT4 country for the EMBED Equation.DSMT4 factor relative to the US. In the 1995 paper if EMBED Equation.DSMT4 then the EMBED Equation.DSMT4 country is less technologically advanced than the US. In terms of the US technology matrix
EMBED Equation.DSMT4 (6.20)
Starting from the factor requirement equation for total production in country EMBED Equation.DSMT4
EMBED Equation.DSMT4 (6.21)
we define factors needed for trade.
EMBED Equation.DSMT4 (6.22)
Using (6.20) we multiply both sides of (6.22) by EMBED Equation.DSMT4 to express the factor content of trade of the EMBED Equation.DSMT4 country in terms of US factor requirements matrix.
EMBED Equation.DSMT4 (6.23)
Looking at all countries we note
EMBED Equation.DSMT4 (6.24)
which allows simplification of the last term in (6.23). Equation (6.23) can now be written as
EMBED Equation.DSMT4 . (6.25).
Equation (6.25) is a restatement of the HOV theorem when we allow for uniform technological differences across countries. Equation (6.25) needs to be estimated to get the best EMBED Equation.DSMT4 values.
Trefler's results are given in Table 2.5. Significance can be measured for each estimate. The estimates EMBED Equation.DSMT4 themselves are of interest.
Summary of Selected Factor Content Research:
Equation (6.3) is the HOV Model assuming no productivity parameters
Equation (6.19) allows individual country individual factor productivity adjustments.
Equation (6.25) imposes a country-wide adjustment to all the elements of the
EMBED Equation.DSMT4 matrix for a specific country.
Trefler (1998) looked at bilateral trade.
He assumed that output of every good is exported to each country in proportion to the purchasing country's GDP.
Define EMBED Equation.DSMT4 as gross exports of goods from country EMBED Equation.DSMT4 to country EMBED Equation.DSMT4 . This is related to net exports EMBED Equation.DSMT4
EMBED Equation.DSMT4 (6.26)
The bilaterial export assumption EMBED Equation.DSMT4 implies
EMBED Equation.DSMT4 (6.27)
Define EMBED Equation.DSMT4 as the factor content of exports from country EMBED Equation.DSMT4 to country EMBED Equation.DSMT4 .
EMBED Equation.DSMT4 (6.28)
Using (6.21) equation (6.27) becomes
EMBED Equation.DSMT4 (6.29)
which can be transformed to relative endowments of country EMBED Equation.DSMT4
EMBED Equation.DSMT4 (6.30)
From equation (6.31) we prove the Trefler (1998) theorem that is an identity if the assumptions of the derivation are correct.
EMBED Equation.DSMT4 (6.31)
The left term is the relative factor endowments. On the right the first term is the factor content for trade from country EMBED Equation.DSMT4 to all countries. The second term on the right is the factor content from country of imports for all countries to country EMBED Equation.DSMT4 .
Feenstra contains a number of other tests on trade which are not treated here due to time limitations.
It appears although the data fails the rigid assumptions of same tastes and same production conditions of the H-O model, that with adjustments the theory can be made to work.
If the number of goods equals the number of factors, it is possible to have factor price equalization.
If the number of factors is > number of goods factor price equalization does not hold!
If the number of factors is < number of goods "there is a wide range of possible factor endowments across countries such that factor prices equalization continues to hold, provided that technologies are the same across countries. However the amount of production occurring in each country is indeterminate when factor prices are equalized."
Many concerns remain. One key issue is that the H-O theory was developed to explain trade in final goods not intermediate goods. With "outsourcing" increasing, this assumption is not realistic. Outsourcing is usually implemented as a means by which labor intensive intensive can be produced.
Econometrically a drop in the price of imported intermediate goods implies effects that are observationally equivalent to the effect of skill-based technological change.
7. H-O Theory, increasing returns and the Gravity Model.
Figure 5B shows specialization in right and wrong direction with increasing returns. While the H-O theory suggested that factor endowments drove trade between countries, the majority of trade currently is between similar countries. Krugman attempted to explain this finding by investigating the effects of assuming monopolistic competition and increasing returns.
- Monopolistic competition assumes that each firm sets MC=MR where the MR curve is downwardly sloped and firms enter an industry if profits are positive. It is assumed that at equilibrium P=AR=AC. Following Feenstra (2004 139) Assume labor is the only input, w is the equilibrium wage, EMBED Equation.DSMT4 is the marginal cost and EMBED Equation.DSMT4 is the consumption of the EMBED Equation.DSMT4 good. Assume there are L consumers. We initially assume an additive symmetric utility function EMBED Equation.DSMT4 or EMBED Equation.DSMT4 . Dropping subscripts, at equilibrium the supply of each good equals the demand or EMBED Equation.DSMT4 For the ith good
EMBED Equation.DSMT4
Remark: (7.8) and (7.9) solve for the intersection point of the ZZ and PP curves. Equation (7.7) plots as the PP curve in Feenstra figure 5.2 or the figure below. PP is upward sloped and indicates that as demand increases resulting in EMBED Equation.DSMT4 , then equilibrium EMBED Equation.DSMT4 from (7.9). Note that we have a downward sloped AC curve. In a graph with p on the y axis and q on the x axis an outward shift in the demand curve implies EMBED Equation.DSMT4 everything else equal resulting in EMBED Equation.DSMT4 as we move up the curve. Assume two identical countries start trading. This is like EMBED Equation.DSMT4 . From (7.8) we see that Equation (7.5) plots on the graphs as ZZ and is the firms average cost curve.
The next task is to determine the equilibrium number of firms N.
EMBED Equation.DSMT4
which is a function of the equilibrium consumption c which in turn depends on EMBED Equation.DSMT4 and EMBED Equation.DSMT4 .
Graphical analysis of the model that shows how p/w and c are determined is shown below. Assume that EMBED Equation.DSMT4 or that reduced consumption implies a movement up the demand curve and thus an increase in EMBED Equation.DSMT4 in most cases. This insures that the PP curve showing the locus of points that solves EMBED Equation.DSMT4 is upward sloped. Remember that EMBED Equation.DSMT4 . If EMBED Equation.DSMT4 then as it increases from 1.1 to 1.2 to 1.3 assuming EMBED Equation.DSMT4 = 1, EMBED Equation.DSMT4 decreases from (1.1/.1)=11, to (1.2/.2) =6 to (1.3/.3) = 4.333. The ZZ curve which is the firm's average cost curve is downward sloped and solves (6.5) or EMBED Equation.DSMT4 . Increased consumption with increasing returns to scale implies that average cost will fall. Increasing the population L will shift ZZ to Z' Z' and result in a decrease in both EMBED Equation.DSMT4 and EMBED Equation.DSMT4 . In words, consumption of the ith good falls due to individuals spreading their expenditure over more goods. This lowers EMBED Equation.DSMT4 .
Equations (7.8) and (7.9) can provide insight into dynamics. Looking at (7.8) assume there is an increase in L. The initial effect is to lower EMBED Equation.DSMT4 , but this is not an equilibrium value. The solution will involve a move down the PP curve and a fall in EMBED Equation.DSMT4 which from (7.9) will lower c,
Notes for a future setup: In a later setup we will use a CES utility curve that makes a flat PP curve. Here as EMBED Equation.DSMT4 we find that EMBED Equation.DSMT4 but EMBED Equation.DSMT4 does not change.
Using the Krugman assumptions the result of assuming two identical countries with increasing returns that are trading finds:
EMBED Equation.DSMT4 implies EMBED Equation.DSMT4 . Number of firms EMBED Equation.DSMT4 since for each country full employment requires EMBED Equation.DSMT4 and economies of scale allow EMBED Equation.DSMT4 to increase more than proportionally than the increase in L. This can be seen when we note that EMBED Equation.DSMT4 implies that EMBED Equation.DSMT4 as increased returns to scale kick in. In summary the increase in EMBED Equation.DSMT4 as firms exploit economies of scale necessarily implies a reduction in the number of firms in each country. Think of it as the firms are capitalizing on the increased profits obtainable from the increasing returns to scale. It pays for them to specialize due to increased demand.
=> opening trade between countries indeed implies that firms must exit in each, while the remaining firms expand their output and take advantage of scale economies.
Krugman's model makes two predictions concerning the impact of trade productivity of firms: The scale effect as surviving firms expand their outputs and the selection effect as some firms are forced to exit. The evidence is that the scale effect is not all that large. Increased US-Canada trade had only a small effect on scale. It appears that the gains to scale were not all that big in the first place. The selection effect suggests that if the least efficient firms exit this will result in an increase in average industry productivity. (This is outside Krugman's model that did not allow for differences in productivity among firms to simplify the analysis.) The evidence is that productivity in Canada increased but that there was a small scale effect.
Models have been suggested by Head-Reis (see Feenstra (2004 143)) to impose a model with no scale effect. Note "If the elasticity of demand for product varieties is constant then firm scale will not change at all due to tariffs or trade liberalization." To impose this restriction use a CES utility function:
EMBED Equation.DSMT4 . (7.12)
The elasticity of substitution between products EMBED Equation.DSMT4 is equal to EMBED Equation.DSMT4 which when N is large equals the elasticity of demand EMBED Equation.DSMT4 In this model EMBED Equation.DSMT4 which implies a flat PP curve and no scale effect. Another implication is that the markup of prices over marginal costs is fixed or
EMBED Equation.DSMT4 (7.13)
since EMBED Equation.DSMT4 . Equation (7.13) comes directly from a simple transformation of (7.7). This can be seen by looking at the implications of a flat PP curve. In such a world the profit equation is
EMBED Equation.DSMT4 . (7.14)
Equation (7.14) can be derived if we note:
EMBED Equation.DSMT4 (7.15)
Assuming no extra normal profits in the long run for monopolistic competition => output will be fixed
EMBED Equation.DSMT4 . (7.16)
Equation (7.16) insures the term on the right of (7.14) in [ ]) = 0. (Note that the EMBED Equation.DSMT4 can be normalized to 1.0.) The number of products N produced can be solved from the identity EMBED Equation.DSMT4 as
EMBED Equation.DSMT4 (7.17)
and does not change because of the CES assumption. (7.11) can be derived from (7.17) is we use (7.0). (7.17) illustrates there is no selection effect on the production side. But more varieties are consumed due to imports. Melitz and Yeaple allow for heterogeneous firms and thus allow for the selection effect even with a CES utility function.
Summary: The theory is attempting to explain trade between similar countries but is still short of explaining most of what is happening. More work needs to be done in developing the theory and then performing tests. In the last 20 years a major effort has been made to test pure theory trade models. Key articles on the reading list will point to how to proceed with research in this area. The goal of future research might be to explain what has happened and to make predictions on what might occur in the future.
Why does all this matter? In the past 20 years the ratio of skilled wages to unskilled wages has increased in many countries in addition to the US. This has led to political ramifications. How is this to be explained? What is to be done about it? An argument made by Feenstra and others is that "movements in product prices (combined with growth in productivity) are fully consistent with the increase in the relative wage of skilled labor in the United States." A number of authors "have argued that the variables most highly correlated with the movement in wages over the 1980s and 1990s are neither trade prices nor outsourcing nor high-technology capital, but rather, a sharp increase in the price of skill-intensive nontraded goods in the United States as well as a decrease in the price of unskilled-intensive nontradables. This finding poses a challenge to those who believe that either trade of technology is responsible for the change in wages and will no doubt be an important area for further research." Feenstra (134).
Gravity Equation Research
Assume two countries that have similar production conditions and tastes operating under monopolistic competition :
- Gravity equation => bilaterial trade between two countries is directly proportional to the product of the countries' GDP. => larger countries trade more. => more similar countries trade more.
Assume production of two countries sums to 10.
Case one assumes the sizes were equal. 5*5 = 25.
Case 2 assumes sizes were 1 and 9. 1*9=9.
Case 1 implies more trade.
Define EMBED Equation.DSMT4 as trade from i to j . It can be proved, given all countries have the same price, that
EMBED Equation.DSMT4 (7.18)
Proof: Assume N products and C countries. Total GDP in each country is EMBED Equation.DSMT4 and
world GDP is EMBED Equation.DSMT4 . Define EMBED Equation.DSMT4 as country j's share of world expenditure so that EMBED Equation.DSMT4 .
Assume all countries producing different products and demand are identical and homothetic.
Remark: [A homothetic utility function states that the point at which a ray from the origin of an indifference map intersects each indifference curve will find a constant rate of transformation (slope). In words EMBED Equation.DSMT4 .]
Exports from country i to country j of product k is
EMBED Equation.DSMT4 . (7.19)
For all products
EMBED Equation.DSMT4 (7.20)
- An important question is if the assumptions needed for this result are too binding to be of use in empirical models. Focusing on size,
EMBED Equation.DSMT4 (7.21)
or two countries of unequal size will not trade as much as two countries of the same size.
- Assume a region "A" such as OECD with two countries.
EMBED Equation.DSMT4 . (7.22)
Their relative shares are
EMBED Equation.DSMT4 . (7.23)
The size equation can be expressed as
EMBED Equation.DSMT4 (7.24)
Squaring the identity
EMBED Equation.DSMT4 (7.25)
implies that
EMBED Equation.DSMT4 (7.26)
Substituting back into (7.24) proves the Helpman 1987 theorem that states that if countries are completely specialized in their outputs, tastes are identical and homothetic and there is free trade then the volume of trade is:
EMBED Equation.DSMT4 (7.27)
The term EMBED Equation.DSMT4 is a "size dispersion index" that shows how trade is related to the relative size of countries. In the more than two country case look at pairs of countries and define EMBED Equation.DSMT4 The above equation is usually expressed in logs (Feenstra 2004, 147) or
EMBED Equation.DSMT4 (7.28)
For empirical work using fixed effect models the form
EMBED Equation.DSMT4 (7.29)
has been used. The second term, if present assumes country shares are not constant, while if this term is not present the implicit assumption is that the shares are constant and are in the EMBED Equation.DSMT4 term.
Helpman' model assumes EMBED Equation.DSMT4 which is tested by the above form. Results for this and other related models are shown in Feenstra (2004 148-).
- Summary: The Monopolistic Competition model assumes each country will be exporting varieties of the differentiated product to another. It is assumed that such countries are completely specialized in that product but could costlessly move to another product => intraindustry trade.
Equation Estimated in Table 5.2
EMBED Equation.DSMT4
Where Y = income EMBED Equation.DSMT4 indicator of trade between two provences, EMBED Equation.DSMT4 = distance Some models added border effect and a indicator of US trade. Border effect was negative , X = trade. A border effect implies that prices not equalized across i and j.
Remark: [(H-O model only in an extreme case has complete specialization and never has intraindustry trade. When there is a continuum of goods H-O can result in complete specialization. Feenstra asserts that factor prices will not be equal. Johnson shows a special case where they might be). Common assumption of Monopolistic competition model and H-O Continuum of goods model is that # of goods exceeds # factors.]
- Simple Heckscher-Ohlin Model does not allow for intraindustry trade unless there is a continum of goods produced.
-H-O models with a continuum of goods => more goods than factors.
- Using the gains from trade. A country can gain from trade in the following cases:
- Same production conditions, different tastes.
- Different production conditions, same tastes
- Different production conditions, different tastes where tastes do not outweigh production conditions .
- Different production conditions, different tastes where tastes do outweigh production conditions.
- Same production conditions and same tastes implies no gains from trade are possible. (Does this work for marriages?)
Figure 2.7 is the basic diagram. Form this base the above cases can be drawn.
- The gains from trade can be broken down into the production gain and the consumption gain. The consumption gain refers to the gain that occurs when the production of all goods in a country stays the same after trade opens but the consumption pattern changes. If production does not change, then there are usually fewer political repercussions of trade. Note that politicians never complain about the consumption gain, only the costs of obtaining the production gain. The production gain arises as the mix of goods produced changes as a result of trade opening. Figure 9 below shows these gains
Figure 9.
Initially the country is at a for consumption and production. After trade opens the country moves to a higher indifference curve at b but still produces at a. When production of X relative to y increases the country gets to c. The diagram makes the small country assumption. If this is not the case, the terms of trade may deteriorate as production of X increases.
8. Alternative approaches to trade theory contrasted to Original HO Model.
- Product cycle of a new good - Vernon.
- 1. Product development and sale in the US
- 2. Growth in US exports as foreign demand increases.
- 3. Decline in US exports as foreign firms begin to produce for their home markets.
- 4. US becomes a new importer as foreign prices fall.
- Examples Radios, television, synthetic fibers, transistors, pocket calculators. Product cycle theory is short run and dynamic.
- Multinationals. If the product is developed by a multinational, the production may move overseas at once. Note that the product cycle theory is not in conflict with comparative advantage since the US may have a comparative advantage in science and research technology. Continuing product improvements may allow the US to maintain its role as a producer. Since technology and capital are mobile the US may lose its production role. Technology may be stolen!!
- Economies of Scale Considerations - Krugman.
- Products such as aircraft may require large fixed cost to get going. Firms in these industries may require larger markets (and not proceed unless such markets are available). The large startup costs insulate such firms from stages 3-4 of the product cycle.
- Economists have argued that anti trust laws should not be used to prevent US firms from cooperating on major research efforts.
- Preference Similarity Hypothesis - Linder.
- => Countries will export good which has a large domestic market. => countries will find that the most promising markets are those which have preference similarities to their home market. This analysis explains gains from trade in the same tastes different production conditions case but in addition considers the case where a country both imports and exports the same product class, but different models. (US imports cars but also exports cars of different design. Linder model does not explain why production originates in one country.
- Border Trade.
- Trade based on similarities in consumer preferences implies that similar products may cross a border in both directions. Often the product is not quite the same. Shipping costs for bulk products may explain this circumstance.
- Changes in Factor Supplies.
- Figure 10-1 in Dunn and Mutti shows neutral growth. Here the same % increase in factor supplies cause PPC to move out. Exports increase. Relative prices of food and cloth remain the same. This analysis assumes a number of things:
- Income elasticity of demand for all goods is unity.
- Constant returns to scale. (If one good had increasing returns, then the same % increase in both factors would not increase the production of both good the same percentage.
- Analysis assumes that world trade prices do not change (small country assumption.)
- Figure 10-2 in Dunn and Mutti shows same conditions except that demand does not go up by the same percentage as factors of production increased. If final consumption point is along GQ' = > then we have trade biased growth. If final consumption is along Q'K then trade is anti-trade biased growth.
- The production expansion path OPP' assumes that the terms of trade remain the same. If the terms of trade move against the country, then the expansion path will be steeper than OPP'. Immiserizing growth (see figure 10-4 is an extreme case. Here welfare of the country actually falls. This can cause substantial political problems!
- Immiserizing growth can occur due to:
- The country increasing production.
- World trade prices moving against the country which by increasing production tries to stay ahead.
- Increases of one factor of production.
- Figure 10-2 shows effect on PPC of increasing one factor of production. Cloth is relative labor intensive in comparison to wheat. An increase in labor (immigration went up) causes the PPC to move out. The increase in the potential cloth output (C1C2/OC1 is proportionately greater that the increase in potential food output F2F1/OF1. The effect of this change is that at the same world trade price the expansion path can no longer be a straight line.
- A complete analysis looks at both production and consumption effects. Increased supply may cause world trade prices to change. Changes in income inside the home country may have effects on consumption patterns. From figure 10-3 we add indifference curves and generate the new offer curves shown on figure 10.3 These are drawn on figure 10 below.
Figure 10
- Offer curve analysis. Initial offer curve for home country was OA. The offer curve of the rest of the world is ORest of World. The world trade relative price is OT and the home country exports OC1 of cloth for OF1 of food. As a result of the production possibility curve moving out, the home country offer curve moves to OA'. If the small country assumption was in effect, the rest of the world offer curve would be OT and the home country would sell OC3 of cloth and be at point E2. Since the rest of the world offer curve is not completely elastic, then the terms of trade move against the home country EMBED Equation.DSMT4 and the equilibrium point becomes the new terms of trade line OT'. Immiserizing growth (see figure 10-4) is the extreme situation. Prebisch argued that this occurred for less developed countries in the 60's. This fact has been controversial.
- Changes in technology shift the PPC and can be handled like changes in factor supplies.
- Changes in demand can shift community indifference curve and cause changes in relative prices.
- Transport Costs. Have assumed that transport costs are zero. This assumption implies that trade will equalize commodity prices at home and abroad for traded goods and assuming do not have complete specialization. Transport costs imply that price of good in foreign exporting country is less that price in domestic country. => transport costs lower gains from trade. In some cases transport costs preclude trade. IMF data suggests that transport costs have fallen from about 9% of the value to trade to 6% of the value of trade in the last 40 years. Time to deliver a product also makes some products not able to be exported.
- Dumping. Defined as selling a good in one market below the cost charged in another market. For a consumer in a given market, dumping is a gain. For the domestic producer of the domestic good being imported, dumping is seen as "unfair." For the i t h good
EMBED Equation.DSMT4
If EMBED Equation.DSMT4 . If EMBED Equation.DSMT4 are domestic and foreign elasticities of demand for the ith good, then EMBED Equation.DSMT4 ADVANCE \l4
Different elasticities of demand suggest market segmentation. Dumping => a gain to importing consumers but is usually protested by competing domestic firms.
- Cartels. Cartels attempt to reduce supply and raise price. This action will tend to be more successful if:
- The price elasticity of demand for the product is low (=> no close substitutes). In the case of oil initially people were "stuck" with cars that had low mileage. Over time as energy efficient cars were built demand elasticity changed.
- The elasticity of supply for products from outside the cartel is low (new firms cannot enter easily). In the long run firms may be more likely to be able to enter.
- A few members of the cartel must be willing to reduce production. Some way must be found to monitor production and assign quotas This has been a problem within OPEC.
- The cartel must be congenial and small enough to work together.
9. The Theory of Protection
- National money supplies were historically linked with gold. With increasing population and growth outstripping increases in the gold stock, governments were anxious to increase gold reserves. Arguments were been made for bilateral mercantilism where a country ran a surplus with each and every other country. Since in an N country world, at most there can be 1 successful bilateral mercantilism, argument shifted to multilateral mercantilism. where on balance a country ran a surplus but not necessarily with all countries. Tariffs have been used to restrict imports. Retaliation often negates first round effects. Import "regulations" or "standards" have been used to achieve the same goals.
- Partial Equilibrium Analysis - Small country assumption
(Small country assumption assumes that country has no effect on the world trade price) See figure 5-1. We assume area under demand curve = consumer welfare.
- Initially free trade at world price = Pw. Country produces 0Q1. Country consumes OQ4. Imports Q1Q4.
- Tariff increases such that EMBED Equation.DSMT4 . Domestic producers able to produce Q2Q1 more. Domestic consumers consume Q3Q4 less.
As result of tariff imports now Q2Q3. Tariff proceeds [Q2Q3] * [PT-Pw]. b = producer surplus gain. d = consumer surplus loss. c = gov gain due to tariff. After tariff consumer surplus loss = a+b+c+d . But other sectors gain. a = producers gain, c= government gain b+d = consumers loss.
Deadweight loss = reduction in imports * tariff * .5
= (Q3Q4 + Q1Q2)*(PT-PW)* .5 + b+c.
Assumes straight line demand and supply curves.
=> total consumer loss = a+b+c+d. If consumers get benefit of tariff from government then a+b+d is the loss. Producers gain b. => consumers and producers are often on different sides of the politics of tariffs.
- Non Trade Barriers. Regulations regarding packaging may hinder foreign firms. In late 50's size of headlights limited high priced Italian cars from being sold in the US. Crash testing limited low volume cars. RR had to import steering columns from GM. When the requirement is not in the home market => costs of compliance cannot be shifted/shared.
- Quotas. Although GATT outlawed quotas have "Voluntary Export Restraints" (VERs). VER can be used to convince Congress not to place tariff on good. See figure 5-2. In the absence of a quota would import Q1Q4 = 40. VER limits imports to Q2Q3 = 25. Producer surplus = a. Deadweight loss = b + d. c goes to foreign country exporter who has the right to ship to domestic country. In 1950s and 1960s oil companies were given limited rights to ship oil to the US and earn area c. If treasury auctioned quota right, could recapture the monopoly rent. Same holds for NBC's right to channel 5!! Producers can upgrade products to sell a limited number of top of the line products. Producers can send parts to the US and put them together on US soil.
- Subsidies. US producers are given a subsidy of S per unit. In figure 5-3 => supply curve shifts from S to S'. => Domestic producers can sell Q1Q2 more. Imports now Q2Q4 not Q1Q4. Total subsidy = S * OQ2 (paid for by taxes) of which producers get a. b is the deadweight loss since it represents an inefficiency in resource use. The subsidy is less inefficient than a tariff since the level of consumption was the same as before the subsidy. (There is no area d that occurs with the tariff since the tariff implies an increase in price. Subsidies are deemed less politically defensible.
- Lerner "The Symmetry Between Import and Export Taxes" (Caves and Johnson # 11. A tax or subsidy on trade involves a divergence between foreign and domestic price ratios. Equal taxes on exports and imports create the same divergence between foreign and domestic price ratios (if trade is in balance) so the real effect of import and export taxes are symmetrical.
[tariff] + [import subsidy] = 0 effect on price
[tariff] = [consumption tax] + [production subsidy]
[export tax] = [production tax] + [consumption subsidy]
[devaluation] + [import subsidy] = 0 effect on imports
[devaluation] = [tariff] + [export subsidy]
= [consumption tax] + [production subsidy]
[tariff] + [export subsidy] + [appreciation] = 0
[export tax] = [tariff] + [appreciation]
[appreciation] = [consumption subsidy] + [production tax]
[import subsidy] = [consumption subsidy] + [production tax]
- Large Country Case - Here EMBED Equation.DSMT4 tariff => EMBED Equation.DSMT4 foreign price
-Figure 5-4 shows partial equilibrium analysis. Assume A is the home country and B is the foreign country. If there was no trade between A and B, the price of oats would be higher in A than B. With free trade are initially at price PW. B sells q1q4 ) to A. Assume next that country A places a tariff of T on imports from B. Price is not PW+T since B's price falls as tariff drives B down its supply curve. B's price is now P0. In A this is P0 + T. The effect is that A imports Q2Q3. Area c = tariff collected. d+b = deadweight loss and a = production subsidy. In A domestic production goes up by Q1Q2 and consumption goes down by Q3Q4.
- Elastic supply. If B had a perfectly elastic supply curve, then the price in A after the tariff would rise the full amount of the tariff. A would not be able to drive the price lower in B. A has no power over the price it pays!
- Inelastic supply. If B had a perfectly inelastic supply curve and none of the product was sold in B, then the effect of a tariff is to lower the price B gets. A sees the same price. Tariff collections rise but producers in A do not see any increase in sales. This may be the case in some primary product producing countries. Here foreign country pays the tariff.
- Inelastic supply - export tax. In 1973 oil producing countries imposed an export tax and collected more money from the developed countries who need the oil and initially imported what they had in the past, but at a higher cost.
- General Equilibrium Analysis. (See figure 5-5)
- Small Country Case. Country initially at P1 for production and C1 for consumption. The world relative price line is TT. Tariff on the imported good (food) raises the relative price of food. Hence as [PF / PC] EMBED Equation.DSMT4 the relative price line gets flatter and moves to EE. Tariff has driven a wedge between domestic and world price. The new domestic price => food production EMBED Equation.DSMT4 in country as move along PPC to P2. Consumption is now at C2 on indifference curve i1.
- Large Country Case. See figure 5-6. Initially at P1 for production and C1 for consumption. As a result of tariff domestically [PF/PC] EMBED Equation.DSMT4 but due to large country assumption and assuming that the foreign country has supply elasticity < EMBED Equation.DSMT4 => that the world [PF/PC] EMBED Equation.DSMT4 . Due to the domestic price [PF/PC] EMBED Equation.DSMT4 production shifts to P3 but foreign imports are made at the new world price. Final consumption point C3 is where indifference curve i3 is tangent to the new domestic price ratio.
- Offer Curve Analysis. Figure 6-2 shows the initial position E. Here A supplied OC of cloth for OF of food. The terms of trade are represented by OE. Country A now places a tariff on B => A's offer curve shifts to OA'. Without retaliation, A hopes to obtain the new relative price OE'. Point E' is selected such that A's indifference curve (not drawn) is tangent to B's offer curve. If B retaliates to get back to the original price we move to E"(not shown in ed # 6). Here trade will fall. If B has elasticity of supply of EMBED Equation.DSMT4 , then the effect of A's tariff in would be no change in the terms of trade and equilibrium since A cannot change prices.
- Dynamics of Offer Curve Adjustment.
Usually assume Walrusian adjustment => Excess demand causes price to rise.
Can have Marshallian adjustment where excess demand => supply to increase.
- Effective rate of Protection for industry j,
EMBED Equation.DSMT4
EMBED Equation.DSMT4
Case 1. Value added 50%. Tariff = 33%
=> effective rate of protection = .33/(1-.50) = 66%
Case 2.
tariff on motor cycle = 40%
tariff imported steel = 60%
tariff on imported chrome = 50%
share of steel = .2
share of chrome = .22
% value added = 10% EMBED Equation.DSMT4
effective rate of protection on value added =
[.4 - [(.2*.6) + (.22 * .5)]]/.1 = 1.7 => 170%
without tariffs on imported steel and chrome would be .4/.1 =400%
- Export Subsidies. Governments have various means by which they can stimulate exports. In the 60's JFK gave "tied aid" that required that the foreign country buy American goods (usually military hardware). Other schemes include direct payments to export firms which is illustrated in figure 5-7 for a country facing world demand elasticity = EMBED Equation.DSMT4 . Here the world price is P0. In the absence of any intervention the country would export c. As a result of the subsidy the export firms have a price of EMBED Equation.DSMT4 . The higher price increases exports by d + b ( and reduces domestic consumption by b. Note that the subsidy is not available for domestic sales so the firm raises the domestic price which cuts off b of domestic sales. The deadweight loss is b (loss of domestic consumer surplus) and d (the loss of productive efficiency which results from producing goods at a cost (the area under the supply curve) which is higher than the revenue received from foreign firms. If the small country assumption was not in effect, the effect of the subsidy might be to reduce the world price.
10. Arguments for Protection
- Protectionism and free trade have always been in conflict in the United States. Labor used to be pro free trade but in recent years labor has tried to secure tariffs to "save jobs." In the 25 years after WWII, there was a consensus to reduce tariffs. In this era the United States was economically dominant. JFK made major progress in pushing for free trade. Now protectionism has become far more popular since the world trade market is much more competitive. A number of arguments are made for tariffs.
- Protection of a way of life. The scissors statement in the book on page 142 was a plea to protect an industry from becoming extinct. The statement did not make any attempt to measure the costs of the tariff against the benefits. No attempt was made to make a security argument.
- Increase Output and Employment. These arguments assume that the country will have a net increase of jobs = the protected jobs. What will happen is that there will be less jobs due to the reduction in real income. In the tariff analysis we showed the deadweight loss (d+b) in figure 6-1. There is no way to get around this cost. In a country with flexible exchange rates, a tariff will initially make the balance of payments go more into surplus but, exchange rate changes will nullify this gain. Mechanism: Tariff reduces demand for foreign currency which will fall in value making imports cheaper for a range of goods. The fall in the exchange rate nullifies the effect of the tariff.
- Closing a Trade Deficit. In the short run tariffs on non essential items are sometimes used. In the long run these policies are usually not effective.
- Pauper Labor. The argument is made that foreign labor is less expensive => US labor need protection. Argument assumes that 1. labor is the only input and 2. there are no differences in labor productivity 3. that wages rates have not adjusted for differences in productivity. Argument also ignores that exchange rates adjust to compensate for differences in unit labor costs across countries. Key factor is not wage rates but unit labor costs.
- Heckscher-Ohlin - Factor price Adjustment. H-O theory shows how trade tends to equalize good prices and factor prices (in the absence of complete specialization.) Figure 11A & 11B shows the conditions under which factor prices adjust (11A) and do not adjust (11B). In 11A The initial endowments of the countries (RI and RII) are more similar than in figure 11B.
AI => complete specialization of X in country I
AII => complete specialization of X in country II
BI => complete specialization of Y in country I
BII => complete specialization of Y in country II
In figure 11A BII < BI < AII < AI while in figure 11B
BII < AII < BI < AI
Because of complete specialization in figure 11B you never can get to the zone between AII - BI => need factor mobility.
Obstacles to factor price equalization from trade
- Many countries - will only cause problems if all productions functions are not the same.
- Many products and factors - to equalize all factors need an equal number of traded products.
- Imperfect competition - To get equalization need MC = price of product and factors being paid the value of their marginal product.
- Increasing returns to scale breaks down perfect competition since one producer dominates.
- Different production functions in different countries ruins equalization since one country will have an edge.
- Increasing marginal productivity of factors of production => the price of factors EQ \O(=,/) VMP of factor.
- Factor intensity reversals cause problems due to: 1. lack of homogeneity since will not get straight line expansion paths and 2. due to one good's isoquant curve being positioned inside another good's isoquant curve. If a country expands and there is a reversal there will be a switch in the good having comparative advantage.
If trade does not equalize factor prices, factors can move!
Even if factor prices adjust, the formerly scare factor owners will lose relative to the formerly abundant factor owners. This change in the relative position of factor owners sets the stage for political pressure for tariffs. Since the welfare of the country goes up with free trade => gainers should be able to compensate losers. Problem: it may take time to adjust.
Terms of trade argument. Figure 6-2 shows initially the world is at E. Country A seeing that the elasticity of B's offer curve is not perfectly elastic, decides to impose an "optimum" tariff and move to E'. B does not let this pass and itself passes a tariff moving the world to E". If B did not react, then from A's nationalistic perspective the move to E' is in its interest. OPEC's oil price increases are similar to export taxes. Here OPEC wanted to get the tariff gains. The primary product producing countries have been interested in raising the value of their products. They have suspected that demand for their products has not been growing worldwide as fast as the demand for the products of the developed countries. What is the optimum tariff? If the other countries offer curve has an elasticity EMBED Equation.DSMT4 , => optimum tariff = 0. If the elasticity = 1, then there is no limit to the amount of tariff that can be applied by one country since no matter what the tariff, the other country supplies the same amount. For an example see figure 6-2. The optimum point is where country A's trade indifference curve is tangent to country B's offer curve. The analysis assumes no retaliation.
Infant Industry Argument. Argues that start up industries or infant industries need special protection. Over time the learning curve will => that the PPC curve will shift out and the firm will be competitive. Firms fear that attempts to develop an industry will be defeated by vigorous price competition from existing firms. Argument can be traced to Alexander Hamilton's "Report on Manufactures" (1791). While argument appears to have appeal:
- How do we tell in advance if an industry will ever grow up and have the PPC shift out?
- Will the eventual gains outweigh the costs of protection?
- Why does the market not finance the startup? Why is the government needed?
- If the wrong industry is selected the country will be saddled with a continuing burden.
Many infant industries remain dependent.
Industrial Strategy. Krugman has developed an argument that is an extension of infant industry and product cycle argument. Protectionism is advocated for new or emerging industries while extensive research is carried out or until sufficient economies of scale are realized. Protection of such industries may discourage foreign firms from entering the field. It is suggested that the United States may thus be able to gain permanent dominance of the market. Krugman looked an Japan and detected that this was their strategy.
- Why does the market not finance such an industry?
- How is Washington going to "beat the market" and pick a winner?
How has Japan been doing recently in picking winners?
Secondary Arguments for Protectionism.
- National Defense. This argument was recognized by Adam Smith "defense is more important than opulence." If the product is storable a better strategy might be to buy on the world market at a low price and store the product. It is costly for a country to become self sufficient. International dependence may be a means by which to avoid war. An argument can be made to protect an industry to maintain skills in the work force.
- Cultural or Social Values. Country may want to protect a way of life. What is the cost?
- Protection to Correct Distortions in the Domestic Market. Figure 6-5 illustrates the situation.
D = domestic demand.
SP = domestic supply curve.
Pw = world price.
With no tariff the domestic production = OA, domestic consumption = OF and domestic imports = AF. We assume that SP does not include external economies in the production of the good that, if present, would make the supply curve SS. Solution is to impost a tariff raising the price to PT such that domestic production = OB, domestic consumption = OC and domestic imports = BC. Problem is that tariff induces a deadweight loss of shaded area. A better policy might be to provide a domestic production subsidy of GE. Here domestic consumption = OF, domestic imports = BF and domestic production = OB. The domestic distortion argument has been suggested by economists that think that wages in manufacturing in some developing countries are > that wages for the same labor in agriculture. If true this would imply that the social cost of labor is < than the private cost and suggest a tariff to protect manufacturing. Others suggest that the market is paying a higher wage in the city due to differences in skills of to pay people for the disutility of working in that location.
- Anti-dumping tariffs. Can place a tariff to correct an artificially low price due to dumping. If dumping is long run, the country as a while gains while the industry facing the dumped product is hurt. If dumping is short run (goal to drive domestic competing firm out of business) can have a case to use a tariff to counter dumping.
- Scientific Tariff. Arguments have been made to apply a tariff to "equalize the costs of production at home and abroad." This would cancel the gains from trade. These arguments are usually made in political campaigns.
- Revenues. Tariffs have been used as a source of revenues. (US in late 1700's) and in many developing countries having no income tax. The problem is that the export sector is hurt. In Nigeria farmers in Palm Oil, Ground nuts and Coca were required to sell their produce to marketing boards at a low price which in turn were the only one that could legally export. The result was that agricultural, output was below that which could be realized if the world trade price was used. Since the marketing boards price paid to farmers never changed. Farmers did not get a higher price in lean years and a lower price in good years. => farmer faced the full effect of changes in the crop. HHS argued that the government go into the palm oil business and gradually raise the price that farmers obtained.
11. Mundell Policy Equation
The Mundell policy equation listed on page 41 of his International Economics (1968) provides a way to unify a great deal of the pure trade theory that was first introduced as graphs. The policy equation can be simplified by assuming some effects to be zero. The basic equation is
EMBED Equation (11.1)
which shows how changes in transfers ((T), changes in the terms of trade ((P), changes in tariffs in countries a and b EMBED Equation.DSMT4 , changes in consumption taxes in a and b EMBED Equation.DSMT4 , changes in production taxes in a and b EMBED Equation.DSMT4 , changes in the balance of payments ((B), and changes in productivity in countries a and b ( EMBED Equation.DSMT4 ) are related. Define T > (<0) as a lending of funds from country a to country b in terms of X goods. P is the price of Y in terms of X. If we define EMBED Equation.DSMT4 domestic expenditure in a, then
EMBED Equation.DSMT4
where demand in a (b) is defined in X (Y) goods. Small letters define consumption EMBED Equation.DSMT4 while capital letters EMBED Equation.DSMT4 denote production
Country a (b) exports good X (Y).
EMBED Equation.DSMT4 These are in absolute value form. We note that EMBED Equation.DSMT4 is the marginal propensity to spend on imports in the ith country.
EMBED Equation.DSMT4 (11.2)
EMBED Equation.DSMT4 compensated elasticity of supply of y in a. The elasticity of supply in b is defined as
EMBED Equation.DSMT4 (11.3)
Since country a imports y then
EMBED Equation.DSMT4 (11.4)
which leads to
EMBED Equation.DSMT4 (11.5)
The policy equation provides a way to apply the theory used in the graphs since the parameters of the equation can be estimated. In terms of the Mundell equation, the Marshall-Lerner exchange rate stability relationships is just
EMBED Equation (11.6)
Define the terms of trade P as the foreign price / the domestic price. EMBED Equation.DSMT4 implies an increased surplus or reduced deficit. I = amount of imports. Assume exchange stability or EMBED Equation.DSMT4 where we assume EMBED Equation.DSMT4 is the absolute value of the elasticity of demand for imports of the ith country. The above equation suggests that if the terms of trade move against the country ( EMBED Equation.DSMT4 ) the balance of payments improves EMBED Equation.DSMT4 . Assume a is Germany and b is the UK. After WW I Germany was required to make a payment to the UK, One way to do this would be to place a tariff on UK goods or
EMBED Equation.DSMT4 (11.7)
or have the UK grow and Germany not grow
EMBED Equation.DSMT4 (11.8)
If the terms of trade are to remain fixed, the only way for country A to grow faster than country B is for the marginal propensity to import in A to be less than in B because EMBED Equation.DSMT4 .
Suppose country a wishes to know the rate at which it must tax import goods to relieve disequilibrium caused by an increase in productivity in the foreign country b then
EMBED Equation.DSMT4 (11.9)
or
EMBED Equation.DSMT4 (11.10)
If China is country b who has EMBED Equation.DSMT4 then no tax change is needed. However if Chinese buy more from the US (country a) then the consumption tax in the US must be lowered to stimulate demand for Chinese goods.
The effect on the terms of trade of a tariff is
EMBED Equation.DSMT4 (11.11)
Unless EMBED Equation.DSMT4 the effect of a tariff increase in country a is to improve the terms of trade for country a which implies that EMBED Equation.DSMT4 or in words the price of the foreign good/domestic good falls.
The effect on the domestic price ratio EMBED Equation.DSMT4 of a tariff change is
EMBED Equation.DSMT4 (11.12)
if we assume P and EMBED Equation.DSMT4 initially were 1. A tariff raises the domestic price of imports if the sum of the foreign demand for imports, EMBED Equation.DSMT4 plus the domestic marginal propensity to import, EMBED Equation.DSMT4 is greater than one. Other interesting related items are
EMBED Equation , (11.13)
which relates changes in utility in country A to the growth of productivity in country A. Multiply out to get
EMBED Equation.DSMT4 (11.14)
which highlights the result that the gain in productivity comes at the cost of a loss in the terms of trade. If EMBED Equation.DSMT4 we have immeriserizing growth!
The effect of a production tax in country a on the imported good y, increases demand for the foreign good and worsens the terms of trade.
EMBED Equation.DSMT4 (11.15)
The effect of a consumption tax in country a on the imported good has the reverse effect
EMBED Equation.DSMT4 (11.16) EMBED Equation.DSMT4
The policy equation allows us to net out the effect of a number of policy instruments being applied. The basic idea is that any policy will cause either excess demand or excess supply which requires some other variable to change. The advantage of the policy equation is that more than one policy can be changed at the same time. For further details and extensions see Mundell (1968)
Application: Since WW II the US has tried to promote growth of first Europe and later other sectors of the world. Assuming the US is country A and that there is US growth EMBED Equation.DSMT4 , the policy equation suggests that unless we can get growth going in the rest of the world (B), the terms of trade are going to move against the US.
A country can grow faster than the rest of the world if its marginal; propensity to import is lower.
12. Regional Blocks => Discriminatory Trade Liberalization
- United States has the following trading classes:
- Free trade (NAFTA)
- Most favored nation status
- tariff not at MFN level
- embargo
- Free Trade Area. Easiest to setup since do not have to agree on a common tariff but there is always the problem of reshipment of goods. Usually setup when the countries are quite different and a common tariff makes little sense and/or when the countries are quite far apart and the reshipment problem is less.
- Customs Union. (free trade area with a common tariff) avoids the reshipment problem. Customs union has trade creation and trade diversion. Trade diversion arises from the higher costs of trading from the new partner country rather than a third lower cost country outside the customs union. Trade creation is the added trade with the partner country that was not possible in the past.
- Economic Union. (Customs union with capital and labor freely mobile). An economic union is a large step toward one economy. The United States became an economic union when the constitution was passed since tariffs between the states were outlawed and capital and labor were freely mobile. Figure 7-1 shows trade creation and diversion due to a customs union. Before the customs union was formed between France and Germany, France had a tariff T which was added to the US supply curve SUS. At that time imports were Q2Q3 from the US. After the formation of the customs union, there was trade diversion from the US which was the low cost producer to Germany. Imports are now Q1Q4 from Germany. Total consumer surplus increases by a + b + c + d. The French government loses c + e of tariff revenue. The efficiency gains for the expansion of trade = b + d. The result of the customs union was that local producers lost sales but customers gained. Since e = the loss and b + d = the gain, if e > (<) (b + d) then on balance the customs union hurt (helped) country.
- Dynamic Effects. Europe noted that in many cases the complete output from an industry in one country was less than the output from one firm. => Form the EEC to allow bigger firms since the market would be bigger. Another gain from the common market was that national firms faced increased competition. New changes in the works include:
- Removal of border controls.
- Standardization of industrial standards (TV).
- Removal of limitations on movement of professional people (common licensing standards for doctors etc)
- Standardization of legal systems.
- Removal of capital controls.
- Removal of restrictions on trade in services such as banking, insurance and air transport.
- All cross country government procurement.
Major problem with economic unification - Distribution of the seignorage. How do we coordinate monetary policy? What happens if different parts of Europe want a different rate of monetary growth?
13. Commercial Policy
- The rise of nationalism in the Western world (1500-1800) associated with mercantilism and close and detailed regulation of trade. The objective was to amass gold to increase the national money supply. The classical economists fought against these theories. They argued that imports were desirable. To get imports you had to export. In the UK the Corn Laws were repealed in 1846. UK was a leader in the free trade movement which reached a peak in 1870 when Germany, France and Italy wanted tariff protection for their new industries against the established UK industries.
- Period 1875 - 1914 European countries developed preferential relationships with their colonies.
- Protectionist tide swelled until middle of depression.
Tariffs over the history of the United States. In the period 1789-1934 tariffs set by Congress and were in general relatively quite high. Tariff of 1789 was designed to generate revenue. After 1812 Southern and Western interests who exported agricultural good and imported manufacturing goods, wanted low tariffs. Eastern and Mid Atlantic States wanted higher tariffs to protect their industry. In 1828 Southerners added high tariffs on manufacturing goods usually imported into the East in the hopes the tariff would fail. The south wanted low tariffs while the North wanted high tariffs to protect their industry. Much to their surprise the "Tariff of the Abominations" passed. In 1833 some of the worst tariff abominations were removed.
After the civil war Southerners had little political power. Tariffs were raised since the North was in power and remained high until the Underwood tariff of the 1920's. In 1930 Smoot-Hawley tariff passed. Trade soon fell. In 1934 President Roosevelt was given the authority to negotiate bilateral tariff agreements (Reciprocal Trade Agreements Act). In the period 1934-1947 agreements with 29 nations were made. All agreements stressed the unconditional most-favored nation clause and the chief supplier rule where the US only negotiated with the countries who were the chief supplier of the product. By many agreements the US was able to lower world tariffs.
After WWII there was a move toward multilateralism. The International Trade Organization, International Monetary Fund and the World Bank were setup. The Reciprocal Trade Agreement provided the authorization for the United States to participate under the GATT agreement which was established in 1947. The main principle of GATT is nondiscrimination. However if all countries get the same tariff on a product but not all products get the same tariff, and all countries do not produce the same range of products, there is a possibility that what appears nondiscriminatory is in fact discriminatory.
In the period 1933 - 1960's tariffs fell from ~ 53% to 10%. 1962 Trade Expansion Act authorized Kennedy Round. Eventually in 1967 tariffs were cut about 35%. While most reductions were across the board, there were special cases for individual countries. Trade Expansion Act provided "adjustment assistance" to workers impacted. This good idea did not work out too well in practice due to administrative problems. Workers may have problems learning new skills. How do we tell it is foreign competition that was the problem? An escape clause in the act allowing firms to partition for relief provided a warning to foreign firms that a tariff was possible. Many foreign firms a voluntary limits on exports to the United States. In the negotiations many countries questioned whether tariffs contained water and as a result tariff reductions were not meaningful.
The Tokyo Round began in 1973 and was completed in 1979. The President was authorized to reduce tariffs up to 60% and eliminate "nuisance tariffs." After the Tokyo round the European Community reduced tariffs 29%, Japan reduced tariffs 49%, the United States reduced rates 31% and all industrial countries reduced 34%. The US participated in the Tokyo Round under the 1974 Trade Reform Act which again contained an "escape clause" and "adjustment" help and gave the President's hand in dealing with certain unfair trading practices. The President was authorized to give special treatment to developing countries in the form of a Generalized System of Preferences. Only some commodities qualified to be on the GSP list.
The Uruguay Round began in 1986 and as concerned with trade in services, intellectual property rights, and Voluntary Export Restraints. GATT passed in late 1995.
The 1988 Omnibus Trade Act included provisions allowing retaliation against the exports of countries whose governments do not make reasonable efforts to enforce U. S. patents and copyrights within their borders (Super 301).
During the Clinton years NAFTA open trade with Canada and Mexico. So far this legislation has been a success. Bush II wants fast track authority to extend trade with other South American Countries.
14 Trade of Less Developed Countries
Issues: In the 60's primary product producers felt that the terms of trade were moving against them. That the prices of primary products were low and that production in the developed countries prevented industry from developing in the developing countries.
In recent period many of same countries have experienced rapid growth. Two types of countries:
- Those that have partially or totally broken away from the past trading pattern and now export manufactured goods.
- Those that still export primary products (OPEC).
Price instability of primary product producing countries:
Competitive markets more volatile than oligopolies.
Elasticities of demand and supply are lower for primary products than manufactured products (use Mundell equation to determine the effect on growth.
Possible policies:
- Marketing boards => Government gets the profits. Farmer's earnings fluctuate as yield changes.
- Buffer stock system. (Clinton released oil from US reserve in May 1996).
- Figure 10-3 Shows decline in concentration of merchandise for least developed countries. Many countries tried to reduce impact of foreign trade by a policy of import substitution. A costly way to proceed. Infant industry argument a temporary import substitution policy.
- "Four tigers" (Hong Kong, Taiwan, Singapore, South Korea) were countries that pursued an export-led growth policy. Indonesia, Thailand, Malaysia and China also were successful. Countries exported labor intensive goods.
15 International Mobility of Labor and Capital
Without mobility of labor => high wages can persist is a labor scarce region.
If a country is driven to complete specialization BEFORE factor prices are equalized => need labor mobility to equalize relative factor prices.
Trade and factor mobility are close substitutes.
AFL-CIO supports immigration restrictions to raise wages. Also support protectionism.
If production patterns stay the same more labor immigrating => PL/PK EMBED Equation.DSMT4 . If the production of the capital intensive good goes down, it is possible to release enough capital to combine with the now more abundant labor to keep PL/PK fixed.
Assume Y = F(K, LABOR, LAND, TECHNOLOGY)
K includes education and training
LABOR = a(population) where a = labor force participation rate
Y/C = output per capita
Y/C = F(K/LABOR, LAND/LABOR, TECHNOLOGY
EMBED Equation.DSMT4 (Y/C) / EMBED Equation.DSMT4 (K/LABOR) > 0
EMBED Equation.DSMT4 (Y/C) / EMBED Equation.DSMT4 (LAND/LABOR) > 0
EMBED Equation.DSMT4 (Y/C) / EMBED Equation.DSMT4 (TECHNOLOGY) > 0
It is in the interest of the US to let in highly educated and talented immigrants. Reverse brain drain.
Most of the world's largest firms are multinationals. Direct investment of capital by Multi National Corporations) MNC improves the world's allocation of capital. Owners of capital in capital scare countries may not want foreign capital to come in since relative return on capital will fall. Their position in society may change!!
MNC adjust prices and move money to reduce taxes.
Source Country Issues:
- Return to labor goes down in country exporting capital.
- For tax reduction reasons, MNC may "over" export capital to reduce tax.
- Home country labor force feels export of capital => export of jobs.
- Source country may feel that in many cases host country pressures MNC to distort trade flows.
Host country issues:
- Host country gains BUT does it get a fair deal? How controls this capital?
- MNC may improve host countries ability to export by developing a capability to produce certain products.
- Host country may not get its "share" of research.
- Host countries often complain that MNC's change prices in order of avoid taxes. Money can be moved from one country to another in "payment" of input goods.
- Host countries try to impose their laws on MNC that are under different laws.
- Developing countries, increasingly find it difficult to borrow funds. Have turned to MNCs as a source of capital.
16. Balance of Payments Accounting
CA = current account
KA = capital account
d(FXR) = change in country's foreign exchange reserves
CA + KA = d(FXR)
Under fixed exchange rates d(FXR) EQ \O(/,=) 0
Under flexible exchange rates d(FXR) ~ 0.
Y = C + I + G +(X-M)
Y = C + Sp + T
I + (X-M) = Sp + (T-G)
I -(Sp + (T - G)) = M - X
T - G = Sg
St = Sp + Sg
=> I - St = M - X
=> Excess of investment over total savings = imports - exports
Assume a sharp decline in US total savings caused by large government budget deficits and lower personal savings.
=> I > St implies that M > X
System will come into equilibrium at a higher interest rate. US investing more than it saves, a capital inflow. Rest of world is the mirror image.
17. Market for Foreign Exchange
XRr = real effective exchange rate
XRn = nominal effective exchange rate
Pd = domestic price level
Prow = price level for rest of world
XRr = (XRn * Pd) / Prow
Purchasing power parity (PPP) => nominal exchange rates should move to just offset changes in inflation.
Change notation to be specific
St = dollar price of one unit of the foreign currency for delivery today
t + n F t = dollar price of one unit of the foreign currency for delivery in t+n
t + nS eADVANCE \l4t = expected spot rate in period t for period t+n
EMBED Equation.DSMT4 ADVANCE \l4 = 90 day interest rate in domestic county
EMBED Equation.DSMT4 = 90 day interest rate in foreign country
Be careful how the exchange rate is defined!!
Equilibrium Interest parity condition
EMBED Equation.DSMT4
Interest Parity Diagram shows parity condition graphically along diagonal line.
Positions 1, 2 and 3 are outflows while positions 4, 5 and 6 are inflows. Along the parity line are no flow points.
1 => making it on exchange > loss on interest
2 => making it on both exchange and interest
3 => making it on interest > loss on exchange
4 => making it on exchange > loss on interest
5 => making it on both interest and exchange
6 => making it on interest > loss on exchange
Define EMBED Equation.DSMT4
Inflow condition
EMBED Equation.DSMT4
or
EMBED Equation.DSMT4
Outflow condition
EMBED Equation.DSMT4
or
EMBED Equation.DSMT4
Outflow: 1. Buy foreign currency spot.
2. Buy foreign security.
3. Sell enough of foreign currency forward to bring back principle and interest in period t+n.
4. In 90 days unwind forward contract.
Equilibrium spot speculation condition
EMBED Equation.DSMT4
Which can be written as
EMBED Equation.DSMT4
Inflow condition
EMBED Equation.DSMT4
or
EMBED Equation.DSMT4
Outflow condition
EMBED Equation.DSMT4
or
EMBED Equation.DSMT4
Outflow: 1. Buy foreign currency spot.
2. Buy foreign security.
3. In 90 days bring funds home hopefully at a rate EMBED Equation.DSMT4
Forward speculation
Do nothing if EMBED Equation.DSMT4
Sell forward if EMBED Equation.DSMT4
Buy forward if EMBED Equation.DSMT4
Define:
EMBED Equation.DSMT4 = desired stock of forward contracts held by arbitragers in period t.
EMBED Equation.DSMT4 = desired stock of forward contracts held by forward speculators in period t.
EMBED Equation.DSMT4 = desired stock of domestic currency held by spot speculators in period t.
EMBED Equation.DSMT4
With no intervention
EMBED Equation.DSMT4
EMBED Equation.DSMT4 = return to spot speculation
EMBED Equation.DSMT4 = return to forward speculation
EMBED Equation.DSMT4 = return to arbitrage
Return to spot speculation = return to arbitrage plus return to forward speculation.
EMBED Equation.DSMT4 = EMBED Equation.DSMT4 + EMBED Equation.DSMT4
Non intervention cases
EMBED Equation.DSMT4
Intervention cases
EMBED Equation.DSMT4
See Stokes (1973 figures 1 and 2)
Define dMd = new flow of money to the domestic country due to forward intervention, then (dropping subscripts)
dMd = dF[( EMBED Equation.DSMT4 Se/ EMBED Equation.DSMT4 F)Z + EMBED Equation.DSMT4 ] where EMBED Equation.DSMT4
dMd = dI[( EMBED Equation.DSMT4 Se/ EMBED Equation.DSMT4 I)Z + 1] where EMBED Equation.DSMT4
and I = the dollar amount of forward contracts of the foreign currency sold by the central bank.
The key problem is the sign of EMBED Equation.DSMT4 Se/ EMBED Equation.DSMT4 F.
If EMBED Equation.DSMT4 Se/ EMBED Equation.DSMT4 F < 0 => central bank causes F to fall but the market believes that the attempt will fail and as a result Se rises.
Tension index based on hypothesis that not all values for EMBED Equation.DSMT4 imply the same degree of tension in the market. Weighing each market as EMBED Equation.DSMT4 for n countries the weighted tension index EMBED Equation.DSMT4 is defined as
EMBED Equation.DSMT4
18. Impact of trade on determination of National Income
Under assumptions of fixed exchange rate the business cycles of major trading partners tend to be linked.
=> Recession in UK causes less demand for US goods which in turn shows US production.
=> Small countries do not export business cycles.
=> During Vietnam war US inflation caused an outflow of money from the US. causing world wide inflation.
=> If Canada knows the US is moving into recession, it can adopt an expansionary fiscal policy.
19. Alternative Models of Balance of Payments or Exchange Rate Determination
- Under fixed exchange rates a balance of payments deficit => loss of reserves.
- If M > X => a recessionary factor. Loss of competitiveness.
- Balance of payments deficit for US => stock of US dollars builds up outside country. US central bank forced to sell foreign currency for US dollars. => reduction is US money supply.
- Trade surplus => expansionary effects.
- In the 60' and 70' the US sterilized US deficits. => no domestic effects of the deficit. => caused the world to bear burden of adjustment.
Keynesian View of balance of payments
BOT = Px* Qx - Pm* Qm
Q m = F(Yd, XR r) EMBED Equation.DSMT4 Qm/ EMBED Equation.DSMT4 Yd > 0, EMBED Equation.DSMT4 Q m / EMBED Equation.DSMT4 (XR r ) > 0
XR r = foreign price of domestic money. UK def
Qx = F(Yf, XRr) EMBED Equation.DSMT4 Q f / EMBED Equation.DSMT4 Yf > 0, EMBED Equation.DSMT4 Q f / EMBED Equation.DSMT4 (XR f ) < 0
BOT = Px * F(Yf, XR r) - Pm* F(Yd, XR r)
+ - - + -
BOT = F(Px, Pm,Yd, Yf, XRr)
KA = capital account
+ - - +
= F(rd, rf, riskd, riskf)
+ - - + - + - - +
BOP = F(Px, Pm, Yd, Yf, XRr, rd, rf, risk d, risk f)
Monetarist Approach to balance of payments
- Excess money creation drives down domestic interest rate => BOP deficit => money flows out to adjust system.
- In recent years velocity has been changing up, then down. => hard to determine the appropriate increase in money supply.
- Figure 13-2 shows US dollar appreciation in period 80-85 due to tight US monetary policy. The exchange rate also appreciated in the period 95-2000, After 2000 US growth and government deficits together with lower foreign growth causes the effective exchange rate to depreciate.
In a world of flexible exchange rates speculative flows of money have a large impact. Economists have not been able to effectively model these flows.
20. Balance of Payments adjustment with fixed exchange rates
Hume "Specie flow mechanism"
=> Money linked to gold. Deficit => money flows out increasing domestic interest rate, and lowering domestic prices, reduces domestic income.
=>Sets into motion corrective forces that will adjust system.
Need IS/LM/BB analysis to under stand what happens.
IS Curve => locus of points where S=I
LM Curve => locus of points where Money Demand = money supply
BB Curve => locus of points where BOP=0
IS curve goes from upper left to lower right. See fig 16-1.
Assumptions: EMBED Equation.DSMT4 I/ EMBED Equation.DSMT4 r < 0, EMBED Equation.DSMT4 S/ EMBED Equation.DSMT4 Y > 0
Points to right (left) or IS are points of excess supply or S > I. (excess demand or S < I).
Assume any point on r, Y axis. Move right. Here Y up => S up. Since r = fixed then S > I. In order to increase I, need to move down. As r falls I increases.
The more sensitive investment is to interest rates, the flatter the IS. IS curve drawn on Y r axis where r is real interest rate.
LM curve goes from lower left to upper right. Figure 16-2. Points to right (left) are points of excess demand (supply).
Assumptions Ms = m1 + m2 where
m1 = transactions demand for money,
m2 = speculative demand for money
EMBED Equation.DSMT4 m1 / EMBED Equation.DSMT4 Y > 0, EMBED Equation.DSMT4 m2 / EMBED Equation.DSMT4 r < 0
The more sensitive the speculative demand for money is to interest rates the flatter the LM. The less sensitive the transactions demand to income the flatter the LM.
Ms up => LM to right.
P up => LM to left.
BB curve goes from lower left to upper right. See figure 16-6. Assert a point. Move right. => Y up causes BOP < 0. r must increase to attract capital into country.
The more sensitive capital flows are to changes in r the flatter the BB.
The less sensitive the BOP to changes in Y the flatter the BB.
If the dollar price of the foreign currency goes up => BB moves right.
Figures 16-3 shows closed economy equilibrium where IS=LM. We assume away problem that IS a function of real interest rate r and LM is function of nominal interest rate i. If we were to assume
EMBED Equation.DSMT4
then Mundell draws GG such that difference between IS and GG is EMBED Equation.DSMT4 . If this world equilibrium is where LM = GG.
Figure 16-4 shows effect of fiscal policy.
Figure 16-5 shows effect of monetary policy.
Both curves assume Y is below full employment. If Y is at full employment fiscal policy will move IS right. Prices will increase and LM will move left resulting is same level of income but higher interest rates.
Figure 16-7 shows open economy equilibrium where BB, IS and LM intersect.
Figure 16-8 shows domestic equilibrium at A but at a BOP deficit since are to right of BB.
Figure 16-9 shows money flowing out of country causing LM to move left to equilibrium.
Figure 16-10 shows Brenton Woods adjustment. Here central bank moves LM by reducing money supply. After adjustment Y down , r up.
Figure 16-11 shows fiscal policy being used to adjust system. Here after adjustment Y down and r down.
Mundell "Principle of Effective Market Classification" => use the instrument that is most effective in adjusting the system.
Figure 16-12 shows that if LM is flatter than BB = > use monetary policy rather than fiscal policy since there will be less of a loss of income. A steep BB curve => BOP not sensitive to changes in interest rates.
Figure 16-13 shows that if LM is steeper than BB => use fiscal policy to adjust a deficit since here need to move IS right not left as in case of figure 16-12. A flat BB => the BOP payments sensitive to interest rate changes!
Figure 16-14 shows Mundell diagram. y axis is government surplus. On horizontal axis is interest rate.
- Along FF have balance of payments equilibrium. To left (right) have deficit (surplus).
- Along DD have domestic equilibrium. To left (right) of DD have recession (inflation).
Slopes of FF and DD represent relative impacts of monetary and fiscal policy on equilibrium. Note that fiscal policy is relatively strong at achieving domestic balance and monetary policy is relatively effective at achieving BOP equilibrium.
Figure 16-15 Shows how if fiscal policy (monetary policy) is used on the BOP (domestic balance), system moves away from equilibrium.
Figure 16-16 shows Reagan policy. Tight money to help BOP, expansionary fiscal policy to help obtain domestic balance.
21. Balance of Payments Adjustment through exchange rate changes
Marshall-Lerner Case. We have assumed that if the domestic price of one unit of the foreign currency goes up, then exports up, imports go down and the BOP improves. This is exchange stability and forms the basis of the Mundell Equation.
If the demand for imports and exports is inelastic => as foreign prices go up will buy less but spend more. On export side as price fall exports increase but prices fall faster.
F i g u r e 1 7 - 3 s h o w s a s m a l l c o u n t r y f a c i n g a h o r i z o n t a l s u p p l y c u r v e . D e v a l u a t i o n s h i f t s u p s u p p l y c u r v e . O n i m p o r t s i d e e l a s t i c i t y = %1 %. D e m a n d c u r v e f o r e x p o r t s i s v e r t i c a l . D e v a l u a t i o n h a s n o e f f e c t .
F i g u r e 1 7 - 4 s h o w s c a s e w h e r e D f o r e x p o r t s i s n o t c o m p l e t e l y i n e l a s t i c . H e r e d e v a l u a t i o n h e l p s s i n c e d e m a n d f o r i m p o r t s i s %1 % a n d d e m a n d f o r e x p o r t s i s n o t 0 .
F i g u r e 1 7 - 5 s a m e a s f i g u r e 1 7 - 3 e x c e p t o n i m p o r t s i d e e l a s t i c i t y <