NBER WORKING PAPER SERIES SPECIALIZATION AND THE VOLUME OF TRADE: DO THE DATA OBEY THE LAWS? James Harrigan

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1 NBER WORKING PAPER SERIES SPECIALIZATION AND THE VOLUME OF TRADE: DO THE DATA OBEY THE LAWS? James Harrigan Working Paper NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massahusetts Avenue Cambridge, MA Deember 2001 This paper will appear as a hapter in The Handbook of International Trade, London: Basil Blakwell, forthoming 2002, edited by Kwan Choi and James Harrigan. The paper benefited from omments by other Handbook authors at the Spring 2001 NBER meeting of the ITI group. The views expressed herein are those of the author and not neessarily those of the National Bureau of Eonomi Researh, the Federal Reserve Bank of New York or the Federal Reserve System by James Harrigan. All rights reserved. Short setions of text, not to exeed two paragraphs, may be quoted without expliit permission provided that full redit, inluding notie, is given to the soure.

2 Speialization and the Volume of Trade: Do the Data Obey the Laws? James Harrigan NBER Working Paper No Deember 2001 JEL No. F1 ABSTRACT The ore subjets of trade theory are the pattern and volume of trade: whih goods are traded by whih ountries, and how muh of those goods are traded. The first part of the paper disusses evidene on omparative advantage, with an emphasis on arefully onneting theory models to data analyses. The seond part of the hapter first onsiders the theoretial foundations of the gravity model, and then reviews the small number of papers that have tried to test, rather than simply use, the impliations of gravity. Both parts of the paper yield the same onlusion: we are still in the very early stages of empirially understanding speialization and the volume of trade, but the work that has been done an serve as a starting point for further researh. James Harrigan International Researh Department Federal Reserve Bank of New York 33 Liberty Street New York, NY and NBER james.harrigan@ny.frb.org

3 Speialization and the Volume of Trade: Do the Data Obey the Laws? James Harrigan International Researh Department Federal Reserve Bank of New York The ore subjets of trade theory are the pattern and volume of trade: whih goods are traded by whih ountries, and how muh of those goods are traded. Most of the rest of trade theory, suh as the analysis of poliy and the effets of trade on fator pries and welfare, is grounded in models whih explain the pattern and/or volume of trade. As a onsequene, it is impossible to assess the relevane of trade theory as a whole unless we understand the empirial performane of the ore explanations for trade. The oldest explanation for the pattern of trade, originally due to Riardo, is omparative advantage. The law of omparative advantage is an unassailable intelletual ornerstone of eonomis, but until reently empirial researh on it has been sant and only loosely onneted to theory. In ontrast, the law of gravity as applied to explaining the volume of trade has been the foundation for literally hundreds of applied studies, but the gravity model has had a omparatively shallow (if not shaky) theoretial foundation. This purpose of this hapter is to review and ritique the last deade or so of empirial researh on omparative advantage and gravity. The first part of the hapter disusses evidene on omparative advantage, with an emphasis on arefully onneting theory models to data analyses. The seond part of the hapter first onsiders the theoretial foundations of the gravity model, and then reviews the small number of papers that have tried to test, rather than simply use, the impliations of gravity. Both parts of the paper yield the 1

4 same onlusion: we are still in the very early stages of empirially understanding speialization and the volume of trade, but the work that has been done an serve as a starting point for further researh. 1 Testing the General Theory of Comparative Advantage Eonomists are proud of the theory of omparative advantage, seeing it as both beautiful and profound: beautiful beause of its simpliity and elegane, profound beause it is surprising and has deep impliations for eonomi poliy and our understanding of real eonomies. But is the theory of omparative advantage atually useful for helping understand the world? The most fundamental problem about omparative advantage is that it relates observables (trade flows and speialization patterns) to things whih are by their nature almost always unobservable (autarky pries). For example, in Deardorff's definitive modern statement of the theory (1980), the general theorem of omparative advantage for a single ountry is stated as The value of net exports evaluated at autarky pries is non-positive (Deardorff 1980, pg. 948). The assumptions required to prove this result are standard but minimalist: they inlude onvex tehnology, perfet ompetition, and the existene of ommunity indifferene urves. Tariffs and transport osts are allowed, but not trade subsidies. Like all statements of the theory of omparative advantage, Deardorff s is a omparative general equilibrium result: allowing all goods and fator markets to lear simultaneously, it expresses a relationship that must hold between an endogenous variable in one equilibrium (autarky pries) and an endogenous variable in another equilibrium (net exports) 1. 1 Stronger statements, suh as a ountry will export all goods whih are heaper in autarky, and import all other goods, are not possible exept in 2

5 If it were possible to test this theory there would be a lot at stake. The most interesting reasons why the predition ould fail inlude non-onvex tehnology and/or imperfet ompetition, as well as perverse trade poliies suh as export subsidies. Alternatively, markets simply might not work the way we think they do. In short, failure or onfirmation of the law of omparative advantage would be very interesting for theorists as well as poliy-makers. Perhaps surprisingly given the general invisibility of autarky pries, there are two reent papers whih offer evidene on the relationship between autarky pries and trade flows. The first of these is An Experimental Investigation of the Patterns of International Trade" by Noussair, Plott, and Riezman (1995). Noussair et al run laboratory experiments that are intended to satisfy the assumptions of omparative advantage theory. The experimental eonomy has two ountries and two goods, with given linear prodution funtions that differ aross ountries and idential preferenes for all agents. The experimental subjets are undergraduates at Cal Teh and the University of Iowa. The autarky and free trade equilibria in this eonomy an be easily omputed analytially, so the purpose of the experiment is to see how lose the data is to the analytial equilibrium. Before onsidering the results, it is worth asking what an possibly be learned from this exerise. The authors themselves pose the question Sine the world's international eonomies are vastly more ompliated than the eonomies reated for this study, of what relevane are laboratory data? (NPR, pg. 462) The author's don't satisfatorily answer this query. Their best attempt at an answer is restrited models. 3

6 The preonditions for the operations of the priniples [of omparative advantage] have been introdued by the experimenters. The experiments are able to provide some insights into how models [...] are able to organize the data, given that the situation is one in whih the model an meaningfully be applied. The experiment annot, however, answer the equally important questions about the relative likelihood that nature has reated a situation for whih the parametri and institutional features of the model are relevant (NPR, pg. 464). Despite the poor writing, this passage illuminates what the ontribution of the paper is. The paper is really about how markets work, about whether they an effetively exploit all the gains from trade that we know are there. It is hard to see how any experimental result ould affet our view of the relevane of omparative advantage. The authors' results show that prodution, trade, and pries onverge to the orret values, and they argue that the proess of onvergene is informative about how markets work. In partiular, the paper has an extensive disussion of dynamis and the proess of onvergene to the full general equilibrium. This may be of interest to theorists but has little relevane for the appliability of the theory of omparative advantage. In ontrast to Noussair et al, Bernhofen and Brown (2000) provide atual historial evidene on the relationship between autarky pries and trade through an examination of Japan's opening to trade in the 1860s. This is a well-exeuted paper in several ways. First, the authors orretly apply Deardorff's (1980) general statement of the theory of omparative advantage. Seond, they argue arefully and (to this non-expert) onviningly that Japan in the mid-19th entury met the requirements needed to apply the theory: Japan was ompletely losed to trade before 1854, and had fairly free trade (in partiular, no export subsidies) by the late 1860s. They also reognize the biggest potential problem with applying the omparative advantage predition to this episode: pries within Japan might 4

7 have hanged between 1854 and 1870 even in the absene of the opening to trade. The requirements for using 1854 pries in a test of omparative advantage are that eonomi growth was unrelated to trade, and that growth was not biased in favor of exportables 2. They make a plausible historial ase that these onditions held true. A short table onfirms that the Deardorff ondition is satisfied: Japan's trade was orretly predited by her autarky pries 3. Bernhofen and Brown argue that, besides being losed to trade before 1854 and having no export subsidies after opening up, Japan's eonomy was fairly ompetitive before and after opening to trade. Does this mean that their results were foreordained? No. As Noussair et al emphasize, just beause the ompetitive and tehnologial onditions of an eonomy satisfy the assumptions of the theory doesn't mean that the post-trade equilibrium will satisfy the law of omparative advantage - after all, humans and their institutions work in mysterious ways. Put differently, if the data had violated the law of omparative advantage, would it have shaken our faith in the theory? Yes: given the evidene that the authors provide about the struture of the Japanese eonomy in the mid-nineteenth entury, Japan's trade should have been predited by autarky pries, and if it hadn't we would have had to explain why. The fat that the post-trade general equilibrium behaved as expeted is genuine news, and is evidene for the relevane of the theory of omparative advantage. The result is partiularly interesting beause it involves a large ountry whih beame one of the greatest trading nations ever. In short, the standard view that the theory of omparative advantage has never been tested needs to be modified: with Bernhofen and Brown's ontribution, 2 A further ondition whih they do not mention is that tastes must have stayed the same. 3 The paper hooses a normalization for pries suh that the magnitude by whih the Deardorff ondition is satisfied is uninformative. The authors tell me that the next version of the paper will express this magnitude relative to autarky GDP, giving a measure of the size of the gains from trade. 5

8 we now have one paper that tests a very general version of omparative advantage, and omparative advantage passes. I think I an speak for many eonomists who have taught this theory with great fervor when I say "thank goodness". 2 Testing Classial and Neolassial Models Bernhofen and Brown is the exeption to the rule: for all other ontemporary and historial trading eonomies, we have no evidene on autarky pries. As a onsequene, any appliation of omparative advantage theory must have an intermediate step between autarky pries and trade, one that relates autarky pries to observable features of eonomies. This means that empirial researhers must usually model prodution possibilities and preferenes. In this setion I disuss reent empirial work on these models, but first I will lay out a general model of omparative advantage that an be used to frame the disussion. 2.1 The Neolassial Theory Of Prodution and Trade Comparative advantage is a property of what I will all neolassial trade models. These models all have at least two goods (so that there is a potential motive for trade), fators whih are mobile between alternative uses, onvex tehnology, and perfetly ompetitive markets for goods and fators. The equilibrium onditions for suh eonomies inlude zero profit onditions for eah setor: p = a ( w ) g g g = 1,...,G, w! " F (1) where p is the produer prie of good g in ountry, and a ( w ) is the unit ost g funtion for good g given the tehnology and fator pries w that prevail in ountry. Constant returns to sale implies that the unit ost funtions an be rewritten as a ( w ) = a ( w ) w + a ( w ) w a ( w ) w g 1g 1 2g 2 Fg F where eah a fg is the ost-minimizing amount of fator f used to produe one unit of good g, whih depends on w. Colleting all the zero profit onditions together 6 g (2)

9 we an ompatly write the system as p = ( A ) w p! " G, A! " F " G (3) where the F G matrix of ost-minimizing input oeffiients A depends on w. The other prodution side equilibrium onditions are that all fators v, whih are in fixed aggregate supply, are fully employed. For a given fator f in ountry, full employment is written as v a x a x a x f = f1 1+ f fg G f = 1,...,F (4) where is output of good g, and the dependene of the on w is impliit. x g Colleting all F full-employment onditions together gives v = A x a fg v! " F (5) The system given by (3) and (5) is F+G equations in the F+2G unknown fator pries, output levels, and output pries. Even at this level of generality, and before speifying G extra equations required to lose the model, we an say something interesting about these eonomies. First, if there are at least as many goods as fators, G # F, then it is possible to solve the zero-profit onditions in (3) for fator pries as a funtion solely of goods pries 4 : w = w (p ) (6) This result, labeled fator prie insensitivity or FPI by Leamer (1995), is remarkable: fator pries do not depend diretly on fator supplies, and if ountry is small (so that produer pries are determined in world markets that are unaffeted by the output of ountry ), then fator pries are ompletely 4 If G > F, then any F equations from (3) an be used to solve for the F fator pries; the other G-F equations will be onsistent by assumption. 7

10 independent of domesti fator supplies 5. Note also that FPI implies that the equilibrium tehnique matrix A will be independent of fator supplies if G # F, sine unit osts depend only on fator pries. We an also say some interesting things about the relationship between fator supplies and outputs. First, if there are exatly as many goods as fators, then A is both independent of fator supplies and square, whih means it an be inverted. Premultiplying both sides of (5) by this inverse gives x = ( A ) v 1, (7) whih is to say that industry outputs are a loally linear funtion of eonomy-wide fator supplies. With more goods than fators, G > F, A is not invertible: there are many output vetors whih satisfy full employment, and whih one will obtain in equilibrium will depend on goods market equilibrium onditions. If G < F, you might be tempted to think that you ould take any G equations from (5) and solve for outputs without referene to the zero-profit onditions (6); the error in that thinking is that with G < F the equilibrium tehniques are not independent of fator supplies. In the G < F ase, outputs are determinate, but they an t be solved for independently of the zero profit onditions. Closing the model under autarky requires G goods-market equilibrium onditions, while with trade the G pries are given by global market learing. With national inome Y a funtion of produer pries and fator supplies, Y ( p, v ) = w ( p, v ) v, (9) we an define the national indiret utility funtion U ( p!, Y ), where 5 For many deades until Leamer oined the term, the FPI result did not have its own name, and the result was often misleadingly referred to as fator prie equalization or FPE. The terminology matters in this ase, beause true FPE - that is, the same fator pries in different ountries - requires more assumptions (inluding fritionless trade and idential tehnology) than FPI, whih is a property of any single eonomy. Suintly, FPI is a neessary but not suffiient ondition for FPE. 8

11 p! = p! ( p, τ ) pries and trade poliy instruments is the vetor of onsumer pries as a funtion of produer τ 6. With the normalization that the marginal utility of inome is unity, Roy s identity gives the Marshallian demands e ( p!, Y )as the negative of the marginal indiret utilities: g e ( p!, Y ) = U ( p!, Y ), e! " G (10) p With the onsumption and prodution sides of the model speified, it is trivial to write down the net export vetor t as the differene between the two: t ( p, p!, v ) = x ( p, v ) e ( p!, Y ( v, p )) The fat that the determination of net exports an be separated into the determination of prodution and onsumption is very far from being a trivial result, and does not generalize to most models with inreasing returns and/or imperfet ompetition: under most suh models, output and onsumption must be determined jointly (see Helpman and Krugman (1985) and Fujita, Krugman, and Venables (1999)). The development of the prodution model of equations (3) and (5) uses primal ost funtions, and is useful for understanding the properties of the resulting equilibrium. But if all one is interested in is the equilibrium outputs and fator pries, then the model an be stated muh more ompatly using duality 7. Under onstant returns and perfet ompetition, national inome is given by (11) 6 I am deliberately nonommital here about how trade poliy auses differenes between onsumer and produer pries. I also ignore the value of trade poliy revenue (tariff revenue plus quota rents) in national inome, and dismiss the possibility of aggregate trade imbalanes, to keep the notation simple. 7 Woodland (1982) offers an espeially lear and detailed development of the dual approah. For a more ompat, if opaque, treatment see Dixit and Norman (1980). 9

12 { } Y = r ( p, v ) = max p x x Y ( v ) x (12) where Y ( v ) is the ompat set of feasible net outputs. Equilibrium outputs and fator pries are then given by x r ( p, v ) p w = r ( p, v ) v (13) (14) Note that the gradient in (13) is a set, refleting the indeterminay in general of the output vetor whih will maximize national inome. As indiated above, this indeterminay disappears if G $ F with no joint prodution, and we an differentiate the output vetor with respet to fator supplies to get x = r ( p, v ) v = [ R ( p, v )] v 2 pv If G=F and there is no joint prodution, then the square matrix R = (A ) -1, it is loally independent of fator supplies, and we just have a restatement of equation (7). The notation R is hosen to evoke the Rybzynski theorem, sine the elements of R give the general equilibrium response of outputs to fator supplies. What an be said in general about R? First, exept in the ase of G=F=2 and no joint prodution, there is no neessary onnetion between a setor s fator intensity and its output response to a fator supply inrease; for example, it is possible in general that the most apital intensive setor will shrink when apital beomes more abundant. A orollary is that it is impossible to generalize the Heksher-Ohlin theorem beyond the 2 2 ase: a ountry will not neessarily export goods that intensively use their abundant fators, even if every other ondition of the theorem is satisfied 8. (15) 8 Although the Heksher-Ohlin theorem doesn t generalize, the result that ountries will export the servies of their abundant fators does generalize to 10

13 Seond, for G>F, we an t say anything about R beause it doesn t exist due to the indeterminay of output. This is alarming from an empirial point of view, but many theorists have argued that this ase is irrelevant, sine even tiny prie hanges will result in G-F industries shutting down, leaving the eonomy with G=F 9. This is a ute theoretial argument, but does not settle the ase empirially. Third, some important results are available for the general G$F ase. A natural extension of the 2 2 prodution struture is to suppose that every setor uses at least two fators, and that there is no joint prodution. As Jones and Sheinkman (1977) show, with these assumptions and G=F, then when a fator supply rises, at least one industry will expand more rapidly than the fator, and at least one industry will ontrat. To state the result more olorfully, in this even ase every fator is a friend to at least one industry and an enemy to another. In the uneven ase of G<F this result does not hold: an inrease in a fator supply may ause all outputs to rise; a fator may be so good-natured that it is a friend to all and an enemy to none 10. But the onverse does not hold: for every industry, there is at least one fator whose aumulation will ause it to deline. That is, every industry has an enemy. This is a rih set of important and testable empirial preditions. If every industry has an enemy, there are lear politial eonomy impliations: there will higher dimensions. See the hapter by Davis and Weinstein for a disussion of the researh on this so-alled Heksher-Ohlin-Vanek hypothesis. 9 The easiest way to understand this argument is to visualize the textbook two-good, one fator Riardian model. If relative pries equal relative labor produtivities, both goods will be produed in indeterminate quantities, and inreases in labor will have unpreditable effets on outputs. But if pries hange even slightly, the eonomy will speialize ompletely in the good whose relative prie has risen, and there will be a unique relationship between labor supply hanges and output hanges. 10 The simplest example omes from the textbook speifi fators model: aumulation of the mobile fator auses both industries to expand. 11

14 be politial opponents to poliies favoring the aumulation of some fators. The opposite an be said for fators whih are friends to all: suh fators are likely to fae less opposition in the quest for favorable treatment. The effets of fator aumulation are also of interest to poliymakers wishing to foreast the future setoral omposition of output. Empirially, there are several points to emphasize. First, the identifiation of friends and enemies an not be aomplished just by looking at input ost shares. Seond, the assumption of no joint prodution is ruial: with joint prodution the magnifiation results in even models do not hold, and the strong friends and enemies results an not be expeted. Third, very little an be said if G>F: there may be no systemati relationship between relative fator supplies and the omposition of output. Most of the above disussion has onerned equilibrium in a single eonomy. Without putting further restritions on how tehnology and tastes vary aross ountries, the model an not say muh about trade or international differenes in outputs and fator pries. The generalized Heksher-Ohlin approah (what I will all the fator-proportions model) to making ross-ountry preditions is to assume away all international differenes in tehnology and preferenes. Further assuming that preferenes are homotheti (so that onsumption shares don t depend on inome), the equation (11) predition for trade simplifies to where t ( p, p!, v ) = r( p, v ) e! ( p! ) Y p e! " G is a vetor of onsumption budget shares. In (16), the output and onsumption funtions are the same aross ountries (the supersripts have disappeared from r(%) and e(%)), and so ould in prinipal be estimated with ross ountry data. The predition an be simplified further by assuming fritionless trade (so that =! = p p p (16) ), G=F, and that endowments are suffiiently lose 12

15 together so that all ountries produe the same goods 11. By equation (6), this means that fator pries and hene prodution tehniques will be the same aross ountries. By equation (7), outputs will vary linearly with fator supplies. Considering (16) as a ross-setion predition at a point in time means that there is no variation in pries, so we an write the predition for a ountry s trade as t ( v, Y ) = R v e! Y In words, trade depends only on relative fator supplies and ountry size. This is an elegant predition, and a version of it was investigated empirially in Edward Leamer's landmark 1984 book (Leamer, 1984). But the elegane of (17) omes at a high prie in terms of empirially dubious assumptions, and muh of the empirial work on the neolassial trade model during the past deade has been aimed at relaxing some of these assumptions without giving up the ability to make ross-ountry inferenes. The assumption of idential homotheti preferenes (IHP) used to derive (17) is implausible, and uninteresting in the sense that there is no real theory behind it. Rather, the IHP assumption is just an analytial simplifiation used to translate the Rybzynski relationship (the mapping from endowments into outputs) into the Heksher-Ohlin relationship (the mapping from endowments into net exports). An empirial rejetion of IHP would rightly have no impat on our view of the underlying prodution model, although it ould be interesting for other reasons 12. Another reason to be uninterested in IHP is that it treats all demand for (17) 11 Together these assumptions are suffiient for trade to reprodue an integrated equilibrium with determinate prodution. The integrated equilibrium is the alloation whih would result in a world with no barriers to the movement of goods or fators. See Dixit and Norman (1980). 12 In a series of well-done papers, Markusen (1986), Hunter and Markusen (1988), and Hunter (1991) explore the role of non-homotheti preferenes in explaining gross trade volumes. 13

16 traded goods as oming diretly from the demand for final onsumption goods. Intermediate produts are readily introdued into the prodution model and have no impliations for the prodution model results mentioned above, as long as we make the distintion between net and gross outputs. But allowing for trade in intermediate goods means that there will be no simple relationship between net exports and national inome, even if IHP holds. Sine a very large share of the volume of trade is intermediate goods, and essentially all imports require some domesti value added before they enter final onsumption (see Rousslang and To (1993)), a more plausible simple model for trade would be that all trade is in intermediate goods, rather than none as assumed by the models that yield equations (11), (16) and (17). 2.2 When worlds ollide: data meets the neolassial model Whatever assumptions are made about the demand for traded goods, no ross-ountry preditions an be made without taking a stand on how tehnology and pries vary aross ountries. The Leamer (1984) assumptions of idential tehnology, fritionless trade, and G=F lead to a very simple predition: for eah industry at a point in time, output depends linearly on fator supplies: x F g = rfgvf f = 1 (18) This is the model estimated by Harrigan (1995). The empirial model in that paper onsiders ten large manufaturing setors and four fator supplies: apital, skilled and unskilled labor, and land. For eah industry, Harrigan analyzes a panel of 20 OECD ountries and 16 years, using three different strategies for pooling over time: generalized least squares with and without fixed ountry effets, and a timevarying parameter model. Even the fixed effets model has substantial residual autoorrelation, while the non-fixed-effets models all have first-order autoregressive parameters in exess of 0.9. This means that the parameters of the 14

17 model are identified mainly from time series within-ountry variation - an unfortunate fat sine the main interest is in explaining the ross-ountry distribution of prodution. A striking result from Harrigan (1995) is that every industry was found to have at least one enemy, a fator whose abundane and/or aumulation leads to a deline in output (the enemy is usually skilled or unskilled labor, sometimes land). Capital is manufaturing s friend: it is estimated to have a positive effet on output for all ten industries in eah speifiation. Despite the fat that Leamer (1984) used a ross-setion of trade data, in ontrast to a panel of output data, the inferenes about omparative advantage are similar. Although fator supplies are jointly statistially signifiant in eah regression, the model does poorly in explaining the ross-setional variation in the data, with large within-sample predition errors. Harrigan identifies a number of potential explanations for this poor fit (inluding bad data, sale eonomies, and government poliy) but doesn t mention other possibilities (suh as indeterminay in prodution, tehnology differenes, different produt mixes, or prie differenes aused by trade poliy or transport osts). It seems fair to say that the fator proportions view of the world has mixed support from this paper: a poor overall fit, but fairly solid evidene of a systemati relationship between outputs and relative endowments. Several papers have been at least partially motivated by the mixed results of Harrigan (1995). Bernstein and Weinstein (1998) fous on the question of output indeterminay when G>F. They orretly note that this is an empirial question whih has little to do with ounting the numbers of goods and fators in any partiular empirial exerise. They begin by noting that, with idential tehnology, fritionless trade, endowments whih are not too far apart, and G#F, then the full employment onditions (5) will have the same A matrix for all : v = Ax (19) They all this the Heksher-Ohlin-Vanek or HOV model. If, in addition, G is 15

18 exatly equal to F, then outputs are the same linear funtion R of endowments for all, and as noted above R = A -1. They express this impliation as AR = I F (20) where I F is the identity matrix of dimension F. Using data from Japanese regions, they onfirm that (19) holds, whih indiates that tehniques and fator pries are the same in all Japanese regions. This is not a trivial finding: it rules out inreasing returns at the level of industries, and/or tehnologial differenes aross regions. They also argue that it rules out G<F, but that is wrong: with intra-japan mobility of fators, fator pries and tehniques will be equalized regardless of the relative number of goods and fators. Despite the fat that (19) holds for Japanese regions, (20) fails miserably: outputs are not well-explained statistially by endowments alone, and the linear restritions embodied in (20) are rejeted. From this they onlude that G>F and output indeterminay is an empirially important fat about general equilibrium prodution. They then apply (19) to international data, multiplying the Japanese A matrix by national output vetors x to get predited national endowments v: predited Japan v = A x These predited endowments are not at all lose to atual measured endowments, whih leads them to rejet the assumption that all ountries produe the same goods using the same tehniques. This result, while not new (see the hapter by Davis and Weinstein in this volume for more evidene that tehniques vary internationally), is nonetheless worth noting, sine it suggests that eonomists should abandon the simple HOV model of international prodution. Abandoning HOV is one thing, but replaing it with something else is another. One of the most appealing aspets of empirial work based on the even model pioneered by Leamer (1984) is that every parameter estimated has a lear strutural interpretation. The hallenge for researhers wishing to improve on this framework is to develop empirially implementable models whih are equally 16

19 losely tied to theory, but that relax the stringent assumptions used to derive equations like (17) and (18). In the fator ontent literature, this has been aomplished using restritive models of international tehnology differenes (Trefler 1993, 1995) or two-fator models where fator prie equalization fails (Davis and Weinstein 1998) 13. These models may or may not be appropriate for studies of the fator ontent of trade, but they are too restritive for studying omparative advantage, as they rule out all but very speial types of ross-ountry tehnology differenes. In searhing for amendments to the fator proportions model, it is natural to onsider general tehnology differenes as a soure of omparative advantage, not least beause there is extensive evidene that, even among advaned eonomies, tehnology differenes are large, ubiquitous, and non-transitory (see, inter alia, Jorgenson, Kuroda, and Nishimizu (1987), Jorgenson and Kuroda (1990), Dollar, Baumol and Wolff (1988), Dollar and Wolff (1993), van Ark (1993), van Ark and Pilat (1993), and Harrigan (1997b, 1999)). Harrigan (1997a) points out that using the dual, rather than the primal, representation of aggregate tehnology makes it possible to estimate more general models of speialization. Harrigan assumes that tehnologial differenes aross ountries are Hiks-neutral and industry speifi. This an be inorporated into the revenue funtion approah in a very straightforward way: = θ = diag{ θ,..., 1 θg} r ( p, v ) r( θ p, v ) θ g, (21) where is a salar produtivity parameter whih gives the level of tehnology in industry g of ountry relative to produtivity in a base ountry. This is a natural extension of the lassial one-fator Riardian model, and it has the virtue that the tehnology parameters are, in priniple, measurable by applying the theory of total fator produtivity (TFP) measurement. The usual derivative property applies to 13 See the hapter by Davis and Weinstein in this volume for details on these modeling strategies. 17

20 (21), so that outputs are given by the gradient of (21) with respet to pries: x = r( θ p, v ) p (22) Note that if there are no ross-ountry differenes in relative industry tehnology levels, that is θ g = θ g, then (by the homogeneity of the revenue funtion) tehnology differenes beome a salar shift parameter, giving outputs as x ( p, v ) = θ x( p, v ) Equation (23) illustrates that tehnology differenes whih are neutral aross setors affet absolute, but not omparative, advantage 14. To implement the model given by (22), Harrigan (1997a) follows Kohli (1991) and assumes that the revenue funtion (21) an be adequately approximated by a translog funtional form. This strategy leads to the following estimation equation: (23) G F gt = kg lnθgt + if ln ft + εgt k= 1 i= 1 s a r v (24) s gt where is the share of good g value added in ountry 's GDP at time t, the a's and r's are parameters to be estimated, and ε gt has a panel struture with fixed ountry and time effets to aount for other unobservable influenes on speialization. There are a number of notable features of this speifiation. First, it allows Harrigan to simultaneously estimate the impat of Riardian and Heksher-Ohlin influenes on speialization. Seond, sine the same tehnology parameters appear in eah equation, it is possible to alulate ross-tfp effets on output shares, whih is a key general equilibrium hannel. Third, the estimated results do not diretly tell us whether eah setor has an enemy, in the sense of a 14 This is the model preferred by Trefler (1995) in his study of the fator ontent of trade. 18

21 fator that auses its output to deline in absolute terms, although the r's tell us whih fators raise or lower a good's share of national inome 15. Fourth, beause of the use of ountry fixed effets, all of the model's parameters are identified by within-ountry time series variation. Fifth, the speifiation of the model requires no assumption about any form of fator prie equalization - this is one of the benefits of using a dual rather than primal approah. Harrigan's results support the view that non-neutral tehnology differenes are important for speialization. For most setors, the own-tfp effets are positive, statistially signifiant, and large. The largest effet is in the biggest setor, Mahinery: a 10 perent improvement in relative Mahinery TFP raises that setor's share of GDP by around 0.25 perentage points. As an example of the ross-tfp effets, tehnologial progress in Mahinery omes at the expense of the Chemials and Metals setors, whose share of GDP delines. The inferenes about fator supplies are roughly onsistent with Harrigan (1995) and Leamer (1984): aumulation of produer durables and High-Shool eduated workers generally lead to expanding manufaturing setors, while growth in strutures and highly eduated workers are assoiated with delining manufaturing. These findings suggest a simple story: the servie setor is intensive in non-residential onstrution (offie buildings and retail stores) and ollege-eduated workers (managers, professionals, eduators), so that abundane in these fators draws other resoures out of manufaturing and into the servie setor. By ontrast, the manufaturing setors are intensive in produer durables and medium-eduated workers, so that abundane in these fators draws resoures out of servies and into manufaturing setors. While plausible, onfirmation of this explanation would require data on diret fator shares whih are not easily available in internationally omparable form. Harrigan (1997a) fruitfully extends the literature on omparative advantage 15 It is straightforward to ompute the effets on levels, rather than shares, of output, but Harrigan does not do this. 19

22 in one diretion, by abandoning the Heksher-Ohlin assumption that ountries share the same tehnology. Another problemati feature of the standard fator proportions approah is the assumption that all ountries produe the same goods and have the same fator pries. This "one one" assumption is expliit in Leamer (1984), Harrigan (1995), and Bernstein and Weinstein (1998), as well as in most of the fator ontent literature (with the notable exeption of Davis and Weinstein 1998). Absolute fator prie equalization is easy to rejet by diret observation: it would be hard to explain mass migration from the South to the North if wages were the same everywhere. In the fator ontent literature, the assumption of equal fator pries in levels is sometimes replaed with the weaker assumption that relative fator pries are equalized (see Trefler 1995). Equal relative fator pries implies that, for a given setor aross ountries, input oeffiients are onstant and in partiular do not vary with aggregate endowments (this is just a orollary of fator prie insensitivity). This hypothesis an be tested by a simple non-strutural ross-setion regression pooled aross goods g and ountries : a a Kg Lg = β + g K β L (25) where the left-hand side is the apital-labor ratio in industry g in ountry, whih is regressed on an industry onstant and ountry 's aggregate apital-labor ratio. Under the one-one/fpi hypothesis,! = 0. There is ample evidene that this is not the ase: Dollar, Wolff, and Baumol (1988, Table 2.3) show that apital per worker in individual industries is highly orrelated with apital per worker in aggregate manufaturing. More reently, Davis and Weinstein (1998, Table 1) show the same thing, finding that tehniques are strongly orrelated with aggregate endowments. A finding that! > 0 in equation (25) an be explained by a failure of fator prie equalization (FPE). Retaining the Heksher-Ohlin assumptions of 20

23 fritionless trade, perfet ompetition, and idential tehnology aross ountries, FPE fails when ountries have endowments whih are too far apart, and as a result ountries produe different goods, the so-alled "multi-one" equilibrium. The fat that we do not observe suh speialization in the output statistis may simply be beause different goods are lumped together into the same industrial lassifiation. If this were true, then the sign of the Rybzynski effets of endowments on observed output aggregates would differ systematially aross ountries, and one-one empirial models like Harrigan (1995) would be misspeified. By using a dual approah, Harrigan (1997a) skirts this issue, but the general sprit of that paper is a one-one model, sine the translog approximation is assumed to be valid at all points in the sample. Shott (2000) takles the multione issue diretly, and develops an empirial model where the set of produed goods and the assoiated Rybzynski effets depend on relative fator supplies. Shott's theoretial model is a standard one of two fators (apital and labor), many goods whose tehniques of prodution are independent of fator pries, and many ountries 16. The equilibrium of this model has every ountry produing just two goods, one more and one less apital intensive than the ountry's aggregate endowment. Define k g = a a Kg Lg and k K = L to be the fixed apital-labor ratio of good g and the apital-labor endowment of ountry respetively, and number goods in order of inreasing apital intensity, k1 < k2 <... < kg. 16 Shott's model in a more general form dates bak at least to Deardorff (1979). 21

24 Then there are three possible linear relationships between the output of a good and a ountry's endowments: x r K r L = 1 1 if 1 g Kg Lg k [ k, k ) xg = r2kgk + r2lgl k [ k, k + 1) g g if (26) g g x g = 0 otherwise, where the r's are positive onstants. In words, if a ountry's apital-labor ratio lies between k g-1 and k g, then apital aumulation leads to an inrease in the output of good g, and the opposite if k lies between k g and k g+1. If k does not lie between k g- 1 and k g+1, then ountry will not produe any of good g at all; it will be produing the two goods losest to its aggregate apital-labor ratio instead. Now imagine that a partiular industrial lassifiation inludes two or more goods with quite different apital intensities (for example, Textiles inludes lowquality otton loth as well as high-teh syntheti fibers). With suh aggregation of goods within a single lassifiation, the Rybzynski effet of apital on output of the aggregate may swith sign more than one: at very low k the Rybzynski effet is positive, then it beomes negative as ountries move out of the labor intensive good, then positive again as prodution of the apital intensive good ommenes, et. In this ase trying to infer the effet of endowments on outputs by pooling aross ountries with very different endowments is a hopeless muddle: any estimated slopes will be a mix of effets of varying size and sign, and will have no strutural interpretation. Shott pursues two strategies for dealing with the omplexities of multiple ones and multiple goods aggregated into a single ategory. The first is to take the existing output aggregates and estimate a piee-wise linear relationship between outputs and endowments. In this model, Shott simultaneously estimates the Rybzynski effets along with the apital-labor ratios at whih the effets hange. 22

25 Shott unovers four ones, whih is to say that for eah output aggregate, four Rybzynski effets are estimated at different point in the sample. This is an intriate empirial model and in the end is not too onvining, as the fitted and atual output levels are not at all lose to eah other, and the points at whih the slopes hange sign seem heavily influened by a very small number of observations (see Shott (2000), Figure 3). Shott's seond empirial strategy is more promising. Rather than work with the usual output aggregates, he onstruts three of his own aggregates based on the apital intensity of eah ountry-industry observation. Sine (as! > 0 in equation (25) verifies) setoral apital intensities are orrelated with aggregate apital abundane, Shott's "Heksher-Ohlin aggregates" group together produts in different output ategories whih are produed by ountries with similar apital abundane. For example, Apparel produed in Guatemala is lumped together with Eletrial Mahinery produed in the Phillippines, while Swedish Apparel is lumped together with Transport Equipment produed in Malaysia. Using these three HO aggregates and estimating a version of equation (26), Shott finds what the multi-one reasoning above suggests: the effet of apital aumulation on the least-apital intensive aggregate is at first negative then zero, the effet is first positive and then negative for the middle aggregate, and is first zero and then positive for the third aggregate. In other words, he identifies two ones: in the first one, ountries produe the Low and Middle apital-intensive HO aggregates, and in the seond one ountries produe the Middle and High apital intensive HO aggregates. There is some irularity in this proedure, sine ountry apital abundane is in effet used to onstrut the HO aggregates, making it unsurprising (for example) that apital abundant ountries speialize in the apital intensive aggregate. Shott's results are also suspet beause he uses total apital within manufaturing, rather than aggregate apital, to measure a ountry's overall apital-labor ratio; this means he is ignoring apital re-alloation between manufaturing and the rest of the eonomy. A broader ritiism is that Shott's 23

26 theoretial model is quite speial and is taken perhaps too literally as a framework for data analysis; Leamer (1987), in ontrast, also works with a multiple-one model but regards the piee-wise linearity between outputs and endowments implied by the model to be too speial to take seriously. Shott also ompletely ignores the issue of tehnology differenes, whih Harrigan (1997) showed to be important for speialization. Despite these aveats, Shott's study is important for two reasons: it provides some evidene that multiple ones are empirially important, and it fores us to think seriously about the heterogeneity lurking within measured aggregate outputs. Harrigan and Zakrajšek (2000) onsider the multiple-one issue as well as several other open questions about speialization. As noted above, Harrigan (1997a) measures produtivity differenes using TFP indies (whih, beause of data availability, restrits the sample to OECD ountries), and estimates a fixedeffets model of speialization that does not use any of the ross-ountry variation in the sample. Motivated by these limitations of Harrigan (1997a), Harrigan and Zakrajšek develop an empirial model whih permits onsistent estimation of the effets of fator endowments on speialization while allowing for unobservable tehnology differenes. This allows them to analyze a larger number of ountries (inluding a few from Latin Ameria and East Asia), and to exploit the rosssetion variation in the data. Their identifying assumption is that, exept for ountry and time effets, any non-neutrality in tehnology differenes is orthogonal to fator supplies. As in Harrigan (1997a), they adopt a dual-translog approah whih allows them to avoid making any assumptions about fator prie equalization, and whih leads to an estimating equation whih is a simplifiation of (24): F gt = βg + if ln ft + εgt i= 1 s r v (27) If the ountry effets β g are also assumed to be orthogonal to fator supplies, then 24

27 it is possible to use a random-effets estimator whih ombines the time-series and ross-ountry variation in the sample. They also report fixed effets estimates (whih use only the time-series variation) and between estimates (whih use only ross-ountry variation) of (27). Unlike most other papers in this literature, Harrigan and Zakrajšek also onsider alternative hypotheses. The statistial alternative they onsider is simple, that speialization depends on aggregate produtivity rather than on relative endowments: 2 1ln 2 ln gt = g + t + t + gt s β β θ β θ ε (28) where θ t is measured as real GDP per worker. This redued form relationship an be loosely derived from a produt yle model, where new goods are first produed in rih ountries and are later produed in poorer ountries as tehnology is transferred. It an also apture multiple one effets in a flexible way: models suh as Shott's would predit an important role for the seond-order term as ountries move into and out of goods based on their overall per-apita inome. Harrigan and Zakrajšek find that estimating (27) gives a noisy but fairly onsistent story about industrial speialization: human and physial apital abundane raise output in the heavy industrial setors, while physial apital lowers output in food and apparel-textiles. The model has little suess in explaining variation in output in the smaller, more resoure-based setors, probably beause they have no measurements of resoure abundane. Turning to the alternative model (28), results are roughly in line with what would have been expeted from the fator proportions results: higher aggregate produtivity is assoiated with lower output of food and higher output in the heavy industrial setors (fabriated metals and the three mahinery ategories). What about multiple ones? Following Shott's line of reasoning, this should show up in parameter instability aross different regions of relative fator 25

28 supply spae. Harrigan and Zakrajšek used a number of formal and informal strategies to find evidene of suh instability and found nothing. They did find some weak evidene of quadrati effets in equation (28), but the nonlinearity was only eonomially important for a single setor, Food. The bottom line from Harrigan and Zakrajšek (2000) is onsistent with the message whih has been developed in all of the papers reviewed in this setion, as well as the fator ontent literature reviewed in this volume by Davis and Weinstein: Relative fator endowments have a large influene on speialization, in ways that are onsistent with theory and stylized fats about the international eonomy. However, fator endowments leave muh that is unexplained: there is a great degree of ountry-speifi idiosynray in speialization patterns, and there is also a great deal of noise (Harrigan and Zakrajšek (2000), page 23.) 2.3 What about Riardo? The papers disussed in the previous setion all work with variants of multifator models that have roots in the Heksher-Ohlin tradition. This might seem odd to a reader familiar only with a muh earlier literature on testing trade models, whih onluded that Heksher-Ohlin did very poorly (Leontief 1954) while Riardo did quite well (MaDougall 1951, 1952). Empirial researh on the stati Riardian model was quiesent for nearly three deades after Balassa's last word on the subjet (Balassa 1963). In the last few years, however, there have been a few papers on the Riardian model, inluding the innovative work by Eaton and Kortum (2001) whih is disussed in the ontext of the gravity equation below. Here I will disuss two reent papers that are very muh in the spirit of MaDougall and Balassa. Golub and Hsieh (2000) argue that a fous on labor produtivity variation as the soure of omparative advantage is appropriate beause other fators of prodution (suh as apital and raw materials) are internationally mobile. This is 26