Columbia University. Department of Economics Discussion Paper Series THE FACTOR CONTENT OF TRADE. Donald R. Davis and David E.

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1 Columbia University Department of Eonomis Disussion Paper Series THE FACTOR CONTENT OF TRADE Donald R. Davis and David E. Weinstein Disussion Paper #: Department of Eonomis Columbia University New York, NY January 2002

2 Columbia University Department of Eonomis Disussion Paper No The Fator Content of Trade * Donald R. Davis, and David E. Weinstein January 2002 Abstrat: Study of the fator ontent of trade has beome a laboratory to test our ideas about how the key elements of endowments, prodution, absorption and trade fit together within a general equilibrium framework. Already a great deal of progress has been made in fitting these piees together. Nevertheless, the existing researh raises a great many questions that should help to fous empirial researh in the oming years. Among the more pressing issues is a deeper onsideration of the role of intermediates, the role of aggregation biases, and of differenes in patterns of absorption. This work should provide a more substantial foundation for future poliy work developed within a fator ontent framework. * The National Siene Foundation provided support for the researh reported in this hapter.

3 The Fator Content of Trade Donald R. Davis and David E. Weinstein The onept of the fator ontent of trade originates with Vanek (1968). The original formulation is based on a simple model of international fator prie equalization, or what is more preisely termed the integrated equilibrium [Helpman and Krugman (1985)]. Under onditions of ompetition in goods and fator markets, free international arbitrage, ommon onstant returns to sale tehnologies, and adequate restritions on the distribution of world endowments, both goods and fator pries will be equalized internationally. Under these onditions, a good will embody fixed amounts of the servies of the produtive fators, independently of where it is produed. Trade then an be oneived of in two ways. The first is as the overt exhange of goods that traditional theory addresses. Vanek s ontribution was to reognize that we ould equally think of trade as the international exhange of the servies of fators embodied in those goods. Vanek s formulation of the problem allowed an extension of the logi of the Heksher- Ohlin theory to settings in whih the pattern of trade may be indeterminate but in whih the net fator ontent of trade may nonetheless be determinate. Expression of the theory in this form also highlights the deep logi of the Heksher-Ohlin theory in its fous on the relative availability of fators. When we move beyond a fully integrated world eonomy, as we do at length below, we will have to take are in defining the fator ontent of trade appropriate to eah setting. A reasonable first question is why we should are about the fator ontent of trade. We think there are two good reasons. The first is that the study of the fator ontent of trade is a laboratory for general equilibrium. A first statement of general equilibrium is that the elements of the system should hang together. In the ase of international trade, the elements of interest

4 are the tehnologies, produtive endowments, outputs, and demands of all ountries in the world. Study of the fator ontent of trade then beomes a first test of the reasonableness of our assumptions about how these elements interat. If our theories perform poorly in mathing measured and predited fator ontents of trade, then this may point in diretions in whih our theories need to be modified for understanding the world. If our theories perform well, then this indiates that the relevant framework may be a reasonable representation of the world and so also a reasonable framework for poliy studies. Indeed, the seond important reason for onsidering studies of the fator ontent of trade is preisely that they may one day prove helpful in addressing poliy questions of the impat of openness on national inome levels and distribution. There already is a substantial applied literature mapping measures of the fator ontent of trade into impats on domesti relative wages for the United States and other members of Organization for Eonomi Cooperation and Development (OECD). Likewise, there has developed a theoretial literature seeking to establish the onditions under whih suh a mapping makes sense. We believe that these literatures have been very important in larifying the issues that need to be addressed in future work. However, we also believe that the results of the empirial studies must be treated with aution, sine the theoretial frameworks in whih suh alulations have been shown to make sense bear little resemblane to the frameworks preferred in the studies of the fator ontent of trade. We onlude that a major area for future work is taking the empirial frameworks favored by the studies of fator ontent and working out within them the onsequenes of international integration on inomes and inequality. The last fifteen years have seen wide swings in trade eonomists views of models of the fator ontent of trade. Early studies, suh as Bowen, Leamer and Sveikauskas (1987, hereafter 2

5 BLS) and Maskus (1985), seemed very damning. It was not so easy to see that this represented only a phase in the development of the literature. More reent studies, suh as Trefler (1995) performed the signal servie of identifying anomalies in the data whih further researh ould aim to understand. The most reent studies, suh as Davis and Weinstein (2001a), have been muh more positive for amended versions of the theory. We do not at all want to suggest that all issues about the fator ontent of trade are settled. Future work needs to gather better and more extensive data sets, to onsider more arefully the role of traded intermediates, ross-ountry differenes in demand, the role of trade osts, and so on. But the progress made in the last fifteen years surely holds promise that this will ontinue to be a fertile area for researh. 1. Theory The Simple Heksher-Ohlin-Vanek Model We begin with the standard model of Heksher-Ohlin-Vanek (HOV). Let there be G goods, eah produed under perfet ompetition with onstant returns to sale. Let there be F primary fators of prodution with fator markets ompetitive. Let tehnologies for all goods and quality of all fators be ommon for all ountries of the world. Let there be at least as many goods as fators, i.e.g F. Assume that trade between ountries is free, so that goods pries are equalized. Assume that the distribution of world endowments among ountries satisfies the requirements to repliate the integrated equilibrium. 1 Then fator pries will be equalized (FPE), and for all ountries C, there is a ommon tehnology matrix: B= B (1) 3

6 Columns of this matrix represent input oeffiients for a given good. Rows represent the input oeffiients for a given fator aross all goods. by For ountry, let the output vetor be given by X and the primary input vetor be given V. Then under the maintained assumption that the tehnology matrix B is ommon to all ountries, full employment of resoures implies that BX = V (2) Demand is assumed to be idential aross ountries and homotheti. Let s vetor of final goods demand, W X be the world output vetor, and world spending. Then, with free trade equalizing goods pries, D be ountry s be ountry s share of W D = s X (3) Equation (3) provides a statement about demand for goods. By pre-multiplying by the ommon tehnology matrix B, we an onvert this to a statement about the fator ontent of onsumption. First, we note that under the hypothesis of a ommon B, Then it follows that Finally, noting that the net trade vetor is to arrive at the statement of the simple HOV model: For future referene, it is onvenient to all W W BX = V (4) W BD = s V (5) T = X D, we an differene equations (2) and (5) W BT = V s V (6) BT the measured fator ontent of trade (MFCT) and V s V the predited fator ontent of trade (PFCT). The first depends on trade flows W weighted by a tehnology matrix. The latter is based on endowments relative to average endowments for a ountry that size in the world. 4

7 It is straightforward to inorporate non-traded goods into the model with FPE. 2 Let be ountry s devotion of primary fators to non-traded prodution. Then the residual N V endowments available for prodution of exportables are T N V V V. Similarly, for the world as a whole, the endowments devoted to prodution of tradables are WT T V V. The predited fator ontent of trade will then be the differene between the residual fators available for prodution of exportables and the fator ontent of onsumption of tradables, or T WT BT = V s V. However, with FPE and free trade, it is also true that N WN V = s V. If we note this and add N WN V s V = 0 to the right-hand side of T WT BT = V s V, we see that this returns us to equation (6). That is, so long as there is FPE, the presene of non-traded goods affets the predited fator ontent of trade not at all, and empirial researhers are free to ignore them in spite of the fat that non-traded setors are in pratie very large. As we will see below, this hanges importantly when FPE no longer holds. Inorporating Intermediates Into the HOV Model When output of goods requires inputs both of primary fators and other goods as intermediates, we need to amend the foregoing. The matrix B should now be interpreted as the matrix of primary, or diret, fator inputs. In addition, there is an input-output matrix A, with dimension G G. Eah element in the input-output matrix is the unit input requirement of one good in the prodution of another good, where it is important to remember that industries may use their own output as an input. A row of the input-output matrix indiates the unit input requirement of a given good in the prodution of all other goods (e.g. how muh steel is used in the prodution of a unit of truks, planes, et.). A olumn, then, indiates how a given good uses all other goods (e.g. how muh steel, truks, et. are used in the prodution of a unit of planes). With the 5

8 presene of intermediate usage, we have to distinguish between gross output, whih we now all X and net output available for final demand, whih we denote by Y. Let I be the G identity matrix. Then the relation between net and gross output is given simply by G Y = ( I A) X (7) Equations (2) and (4) ontinue to hold as fator market learing onditions even in the presene of intermediates. Of ourse, only net output is available for final onsumption, so (3) must be amended to W D = s Y (8) Assuming ( I A ) is invertible, we an define a new matrix of total, or diret plus indiret, fator inputs, given by B= B( I A ) 1 (9) With a little algebra, this allows for a statement of HOV in the presene of intermediates W BT = V s V (10) First Tests of the HOV Model Equation (10) is based on observable variables, so an provide a test of the HOV model. A welome feature for empirial implementation is that it an be implemented even if the researher has data on only a subset of the primary fator inputs. Let f B be the f th row of the tehnology matrix, f fw V be ountry s endowment of fator f, and V be the orresponding sum for the world. Then we an imagine onstruting matries of HOV preditions with dimension F C equal to the number of fators times the number of ountries on eah side of the equation. The typial elements of suh matries will be of the form: 6

9 f f fw BT = V s V (11) Various tests ould be applied to this. Sine orresponding elements of the matries are supposed to be equal, one would at least like them to have the same sign. That is, one would like ountries to be measured to export the servies of fators that the theory identifies as abundant there. This may be alled a sign test. An alternative is to note that orresponding olumns and rows of the matries are supposed to be equal, so one an test the weakened hypothesis that they will have a high rank orrelation. For olumns, this implies that, holding fixed a ountry, measured net exports by fator orrespond to the abundane aross these fators indiated by endowments relative to typial ountry endowments. For a row, this implies that, holding fixed the fator, measured net fator servie exports aross ountries orrespond to those predited based on national and world endowments. One strong requirement for implementing (10) is that it requires data on world fator endowments. This motivates an alternative that is frequently employed. Divide both sides of the equation by the inome share and you get BT V W = V (12) s s Do this for two ountries, and, take the differene and multiply through by the inome share of the first, and you obtain: s s BT ( T ) = V V (13) s s As noted, this has the strong advantage in empirial implementation that one needs data only on the ountries for whih the bilateral omparisons are to be made. However, there is also a disadvantage. Suppose that the true model, instead of being (10) is instead: W, BT = V s V + s Λ (14) 7

10 where the last term is any systemati deviation from HOV that is proportional to ountry size but otherwise ommon among the inluded ountries. 3 If we apply the bilateral differene approah to (14), we again end up with (13). That is, the approah of (13) will not detet systemati and potentially large deviations from HOV that are of the form indiated by the last term in (14). Adjusted Fator Prie Equalization The requirement in (1) that input requirements are idential everywhere is stringent, but an be relaxed. Suppose that aross ountries, there are differenes in fator quality of a pure fator augmenting nature. In suh a ase, we need to distinguish between natural and effiieny units of fators. Suppose that there exists a ommon tehnology matrix B and, for eah fator and ountry, an adjustment salar f π that satisfies: f f f B = π B (15) Then we an say that the endowments of ountry expressed in effiieny units are: E 1 V = V (16) f π If all the other requirements of the HOV world are satisfied, this leads to a restatement of the fator ontent of trade in terms of effiieny units of fators: E E BT V s V (17) = If ountry 0 is the base that defines 0 B B, and if the return for fator f in ountry 0 is f 0 w, then for any ountry w f f 0 w = (18) f π 8

11 f f A speial ase of adjusted FPE is when for a fixed, π = π for all fators. This aommodates a world with salar ountry differenes in total fator produtivity, whih here will be interpreted just as ommon differenes in fator quality. Failure of Fator Prie Equalization Under a variety of onditions, fator pries may fail to equalize, even in effiieny terms. There are a variety of ways of dealing with this failure of FPE while ontinuing to work with preditions about fator ontents of trade. An FPE Club. One approah is to ask how HOV should be modified if a subset of the world shares FPE, but not neessarily the whole world. Suppose that there is a set of regions, r R, that shares FPE even though this may not hold for ountries R. Call R the FPE lub. Then lub members share a ommon tehnology matrix R B. Hene for eah r R we ontinue to have R r r BX = V (19) If trade ontinues to equalize goods pries and the other standard HOV demand assumptions hold, then We an always pre-multiply this by r r W D = s Y (20) R B, the differene being that absent world FPE, it is no longer the ase that R W BY will equal W V. Instead, the orresponding equation is that for members of the FPE lub, and a ommon tehnology matrix R B, R r r r R W BT = V s BY (21) 9

12 This restrition an be examined for all members of the FPE lub. Understanding the Breakdown of FPE. A huge advantage of the last approah is that we an apply it to members of the FPE lub without taking a stand on why FPE is breaking down. The big drawbak of this approah is that we are why FPE breaks down. If FPE fails in a systemati way, then we an identify hypotheses that allow us to test an appropriately modified version of HOV. If FPE breaks down, then this should show up in an examination of the tehnology matries of the respetive ountries. Hene, a first approah is to return to equation (1) and hek if there is a ommon B= B for all. FPE would imply that these tehnology matries are equal. Unfortunately, a finding that they are not equal need not invalidate FPE if there are more goods than fators and our industrial ategories, whih define olumns of the B matrix, are themselves omposed of produts of heterogeneous fator ontent. To make this point learly, it is best to depart from generality and think about a world of two fators, say of apital and labor. Let there be two ountries, with home more apital abundant than foreign. Suppose that there is a Dornbush-Fisher-Samuelson (1980) ontinuum of goods with varying apital intensities. Assume as well that the distribution of world endowments is onsistent with re-reating the integrated equilibrium. Then the HOV preditions will hold exatly, even though the pattern of trade in goods may not be fully determined beause the number of goods exeeds the number of fators. Now assume that there are stritly positive osts of trade, although we an think of them as vanishingly small. In this ase, the pattern of trade beomes determinate. The home ountry onentrates its exports among the most apitalintensive goods, and vie versa for the foreign ountry. Goods of intermediate fator intensity are 10

13 non-traded. Formally, the exports of the ountries are disjoint. If, however, our system of lassifying goods into industries aggregates into the same industries goods of very different fator ontent produed in the two ountries, then we will expet to find in the data that ountry apital abundane is orrelated with industry apital intensity. 4 However, this would only be true for traded goods. With the vanishingly small trade osts doing little to disturb FPE, we should not find this orrelation among non-traded goods. A seond issue is that the average input oeffiients that we alulate in the data are a weighted average of the goods that we atually export and our non-traded goods. In this simple framework, goods of intermediate fator intensity fall into the non-traded setor, so we tend to underestimate the true fator ontent of trade. Suppose that we ould orret for this problem and define a tehnology matrix reflets the atual fator intensity of prodution of s exports, ountry be DFS B that E. Let the imports of from a M (and for simpliity, let ountry s demand for its own output be denoted M ), then the appropriate HOV equation is: DFS DFS DFS W B Y B D + B M = V s V (22) The foregoing has allowed for differenes in tehnology matries for tradables by ountry, even though approximate FPE holds. The reason that the matries differed for tradables, but not for non-tradables is that the former refleted heterogeneity of goods in an industry in spite of the approximate FPE, while this implied ommon input oeffiients for the non-traded goods where homogeneity is more plausible. An alternative that an be investigated is a breakdown of FPE, so that there is a systemati orrelation between ountry apital abundane and industry input usage not only in tradables (where this now suggests speialization) but also in non-tradables (where this suggests 11

14 fator substitution). Interestingly, the key to distinguishing this from the former ase is to look for this systemati orrelation in the input oeffiients in the non-traded setor. If this indiates a breakdown of FPE, there is yet another adjustment that needs to be made. Capital abundant ountries with high wages will use more apital per worker in nontraded setors, implying that standard measures of exess fator supplies overstate how muh of the abundant fator is available for prodution of exportables, hene tend to predit too high a volume of fator trade. Sine, in pratie, non-traded setors are large, these adjustments to the theoretial model may matter quite a lot. Let the appropriate matrix for ountry in this ase be H B (after Helpman, who suggested suh an approah). Let a supersript T indiate traded output and an N indiate endowments dediated to the prodution of non-traded goods. Then the appropriate measure for this amended HOV model is: H H T W N WN B Y B M = [ V s V ] [ V s V ] (23) Here the measured fator flows of trade are measured using the produer s tehnology. The predited fator flows are also adjusted for the fat that ountries abundant in a fator tend to use that fator more intensively in non-traded prodution, so have less available for prodution of exportables than indiated in the standard HOV equation. Cross Flows of Fator Servies in a Many-Cone World. When endowment differenes lead to a breakdown of FPE, then a set of equilibrium fator pries and the assoiated goods that an be ompetitively produed at these fator pries define a one in fator spae. Countries whose endowments lie within the same one share FPE, while those that lie in different ones do not. 12

15 It is simplest to think about this in the ase of two fators, say apital and labor. Consider a many-one world. For simpliity, ignore non-traded goods, assume that eah one ontains just one ountry and that the number of goods produed is suffiiently large that boundary goods produed by ountries in different ones an be safely ignored. Consider the ase of a ountry of intermediate apital abundane. Suh a ountry will find that it trades both with ountries that are more apital abundant than itself and also ountries where the reverse is true. Importantly, the ountry should be a net importer of apital servies from the ountries more abundant than itself, and simultaneously a net exporter of apital servies to those ountries less abundant in apital. This suggests an important aution on any impliit welfare onlusions based on the magnitude of a ountry s total net fator trade servies. The point is that even if the ountry is lose to a zero net trader in the servies of apital and labor when onsidering its trade with all ountries, it ould nonetheless be enjoying signifiant gains from fator servie trade by being able to trade + with ountries both more and less apital abundant than itself. Let C ( ) denote the set of ountries more apital abundant than, and C ( ) the set of ountries less apital abundant than. Let E be exports from to and M be imports to from. Then, for example, the fator ontent of trade of with those ountries more apital abundant than itself is ' ' ' B E B M = s V s V (24) ' C ( ) ' C ( ) ' C ( ) ' C ( ) Naturally a similar ondition ould be written down for trade with those ountries less abundant in apital than ountry. Moreover, under the onditions stated, whih imply full speialization in tradables, suh fator ontent preditions an be written down bilaterally. 13

16 The Fator Content of Trade with Traded Intermediates If intermediates are traded and all ountries use idential tehniques, the standard HOV equations an be implemented beause goods will always embody the same amount of fators regardless of where they are produed. The mathematis beomes signifiantly more ompliated in the ase where FPE fails and intermediates are traded. The reason is that all exports and imports embody a ombination of domesti and foreign fators. Hene, the fator ontent of any ountry s trade is going to depend on all of the input-output relationships and tehnologial oeffiients in all ountries. Surprisingly, Trefler (1996) laims to have modeled a world with traded intermediates without using any information about the requisite input-output matries. The starting point of his work is the priniple that HOV equations must always be of the form W V s V = F, where the definition of F varies with the model. Note that the fixed point of this approah, W V s V, will only under restritive irumstanes be the predited fator ontent of trade. That is, from the start, he abandons the idea of developing ounterparts to predited and measured fator ontents of trade. By using data identities, market learing, and a stronger than usual assumption on demand that bilateral onsumption patterns are proportional to world inome shares Trefler (1996) derives a relation W V s V = F. Sine Trefler defines V s V to be the fator W ontent of trade, it tautologially follows that F is likewise the fator ontent of trade, even though neither term atually is the net exports of fators embodied in trade. This is an important point that an be lost to the reader. Sine Trefler is only interested in the aggregate restritions 14

17 on fator usage rather than traking fator servie flows, he is able to bypass using a omplete set of input-output matries. This enables him to show that F an be deomposed as follows: W t' ' W' s = Cons + Inter + s ' V V F F B ( D D ) (25) where B t is some transform of the standard tehnology matrix for ountry. The first two terms on the right-hand side might seem to be but are not the fator ontent of trade in final goods and intermediates respetively. As noted, while they might look like the fator ontent of intermediate and final goods trade, Trefler (1996) and lose inspetion makes lear this is not the ase. The final term of F is a term that would equal zero if the strong assumption that bilateral onsumption patterns are proportional to world inome shares were exatly orret. What he has derived is a relationship between endowments, non-standard tehnology matries, and trade, but it is hard to see what the eonomi meaning of these terms may be. This suggests that understanding how to inorporate traded intermediates into fator ontent studies remains an important area for future researh. Cost Restritions on Fator Content Absent FPE. An alternative approah to testing fator ontent preditions in the absene of FPE relies on the properties of ost minimization. Define the fator ontent of imports to from as H V M B M (26) Letting the vetor of fator pries in be denoted on osts implies that w, Helpman (1984) shows that a restrition ( w w ) M 0 (27) V 15

18 In simple terms, this restrition just says that if instead of importing the fator servies we atually import, we had instead hired these same fators in our loal market at pries w to produe these goods ourselves, the ost would have been at least weakly greater than our import bill (equal to the ost of produing that import vetor in the foreign ountry). Obviously, a orrelative restrition to (27) an be plaed on the osts of fator servie imports to. We an also look at the differene between two suh equations for and to arrive at ( w w )( M M ) 0 (28) On average, ountry imports from the servies of those fators that are relatively ostlier in than. V The restritions in (27) and (28) an in priniple be taken to data, sine they involve observable post-trade fator pries and measurable fator servie flows. However, there are two diffiulties in implementing these. The first is that, in ontrast to the other approahes to HOV derived above, it is ruial to have information about all fators of prodution. A seond diffiulty is that one must be able to measure with onfidene the fator returns in eah ountry, inluding the rental on apital. V 2. Data Issues Empirial analysis requires the researher to onfront a spetrum of questions. What data is required to test the theory? When alternative measures are available, how do we hoose among them? When alternative soures of data exist and they do not provide identially the same values, 16

19 how do we hoose among them? When some analyti elements must be onstruted from more primitive data, how do we hoose the method for suh onstrution? Is there reason to believe that measurement error in the relevant data is large? Is there a way to minimize the impat of suh measurement error on tests of the theory? What is the Data? The data required depends on the variant of the HOV theory to be tested and whether we also want to test some of the subsidiary hypotheses. Tests of HOV always require some measure of a tehnology matrix. Standard HOV theory requires a matrix of total (diret plus indiret) fator requirements. The next hoie is how many tehnology matries one wants to work with. Most of the literature has worked with a single tehnology matrix typially that of the US, although oasionally also of Japan. When these papers (e.g. BLS, Trefler 1993 and 1995) have ontemplated tehnologial differenes, these have been treated as parametri deviations from the US tehnology matrix. An alternative approah is to use distint tehnology matries for the ountries in the study, as in Davis and Weinstein (2001a) or Hakura (2001). Tests of HOV always require some measure of endowments. Standard HOV theory requires endowments of the entire world, although in pratie researhers have worked with endowments for the largest set of ountries they an obtain. When the tests are in the bilateral differene format of equation (13), endowments are only required for the ountries onsidered. In standard tests of HOV, tests are fator by fator, so that omission of some fators from the test does not affet results for inluded fators. By ontrast, tests of ost restritions when FPE fails require data for all fators. An important question in pratie is whether one wants to use oarse or fine definitions of the fators themselves. Alternative implementations of HOV have used 17

20 two, three, up to as many as twelve fators of prodution. At times the hoie is mandated by data availability or ompatibility. At other times, there is a real hoie. For example, do we want to haraterize labor endowments by oupational ategory: managerial, prodution, servie, sales, et.? Or do we want to see it as stoks of high skilled and low skilled labor? The former has the advantage of providing a more detailed division of the labor types. However, the latter is probably loser to our idea of fators that an flow aross oupational ategories. Researhers also must address the issue of the ompatibility of the data. Is a skilled worker in the United States the same fator as a skilled worker in Cambodia? Are there quality differenes? How shall we sum aross ountries to obtain some measure of world endowments? The measurement of trade flows is relatively more straightforward. Standard HOV theory requires for eah ountry only its net trade vetor with the rest of the world. Some variants of HOV require that exports and imports be measured as gross flows, sine they may have different fator ontent under what is nominally the same industry. Further refinements may require that this be refined to examine bilateral trade flows. Implementations that examine the prodution side of HOV typially require some measure of output. Depending on the question at issue, this may require gross or net output. 5 The differene, of ourse, also requires an input-output matrix. Here there are hoies about whether one omputes this with absorption of domesti intermediates separated from those that are imported from various soures. Standard HOV requires some measure of a ountry s share of world absorption. Often this is taken as the ountry s GDP share. Sometimes this is adjusted for trade imbalanes, although these have typially had sant impat on the HOV results. The demand side of HOV also plaes restritions on the pattern of absorption that an be examined more diretly. 18

21 Unfortunately, absorption is often not diretly observed, and so inferenes an only be made indiretly from fator servie flow alulations. Implementation of standard HOV does not require data on fator pries. However, some tests of HOV (e.g. Trefler 1993) have relied on fator prie data in a subsidiary manner to onfirm the plausibility of parameters alulated from the data. When FPE fails, implementation of tests of ost restritions relies importantly on high quality fator prie data for all fators. Data Quality and Compatibility Trade is the differene between output and absorption. The fator ontent of trade is the differene between endowments (the fator ontent of prodution) and the fator ontent of absorption. From this perspetive, trade in goods or fator servies an be thought of as a residual that is frequently an order of magnitude smaller than output or absorption. This fat brings to the fore the issues of data quality and ompatibility. We have already talked about the data inputs required to test fator ontent theories. The researher is then faed with the question of whih data soure to rely on for measures of the relevant variables. An unfortunate fat is that measures of the same variable for the same ountry and time period, but drawn from alternative soures, frequently differ and the differenes need not be small! There are many reasons for this, potentially inluding different definitions, different hoies about whih exhange rates are used to onvert figures, different methodologies for onstruting key variables, and so on. Indeed, at times these problems may be suffiiently large that it might be impossible to observe relationships based on net fator flows even were the relationship to exist. A ase in point is the study of BLS. BLS had stressed the importane of the fat that their tests use three 19

22 independent soures of information on endowments, tehnology, and trade. To their redit, BLS report in their footnote 14 a hek on measurement error in these data. If you pre-multiply the US gross output vetor by the US tehnology vetor, this should deliver as an identity the US endowments employed. Sine BLS onstruted the endowment data separately from the US tehnology matrix, this identity does not hold in their data, and frequently departs quite sharply from equivalene. For example, the imputed endowment of apital based on the tehnology matrix and the output levels exeeds the endowment of apital by more than 100 perent. Smaller, but substantial errors exist for other fators. Sine one way of interpreting their tests is as a hek of whether the entire world uses US tehnology, it should be more than a little troubling that in their data, even the US does not use US tehnology. Suh onerns lead us to believe that a great deal of attention must be paid to onsisteny in the onstrution of the data. National apital stoks annot be onstruted independently of the way that apital is onstruted when the tehnology matrix is put together. Definitions for other variables likewise must be onsistent. This also suggests the value of using one data soure as an ultimate authority for a given projet. When there are disrepanies between alternate soures, resolve them based on this authority and do re-saling of supplementary data as needed. Naturally, this requires are in the seletion of the highest quality database as the authority. But it at least allows the theory some hane to esape being swamped simply by inonsistent definitions of the same variables. 20

23 3. Fator Content: What are the Tests? In the absene of a lear alternative framework relating endowments and trade, it is not possible to test HOV against a well-speified null hypothesis. As a result, researhers typially run horse raes between various versions of the model, e.g. HOV with neutral tehnial shifts, home bias, et. The statistial framework is typially Bayesian and simply asks whih version of HOV is best supported by the data. A major problem with suh statistial tests of HOV is that one of the models must be deemed best even if it has little explanatory power. As a result, researhers also rely on goodness of fit riteria as a means of testing HOV. Typially researhers have foused on five suh riteria. The first two measures are nonparametri. Sign tests ask whether the sign of MFCT is the same as that of PFCT. These tests identify what share of the data would lie in quadrants one and three if one plotted MFCT against PFTC. A strength of this test is that large outliers are unlikely to affet the results. The major weakness, of ourse, is that ountries with small PFCT may have many sign errors without it indiating a major problem for the theory. Rank tests put a little more struture on the data by asking whether ountries that are predited to be large exporters (importers) of a fator are measured to do so. A problem in these tests arises when there are a large number of ountries that have similar PFCT s. A seond major lass of tests is the regression tests. Here three tests are standard. The first two arise from the slope and R 2 of a regression of MFCT on PFCT. In addition to the slope and R 2 tests, Trefler has utilized the missing (fator servie) trade test (MT) whih is defined as the variane of the MFCT, 2 2 σ M, divided by the variane of PFCT, σ P. 21

24 How these tests are related is best understood by thinking about how eah statisti is alulated. The formulas for the slope oeffiient and R 2 in a linear regression are σ αˆ = and = σ σ 2 MP 2 MP R P σpσm where ˆα is the slope oeffiient of a regression of MFCT on PFCT. A little algebra shows that the three tests are related: MT = 2 αˆ R 2 In other words, any two tests are suffiient for identifying the outome of the third. First Generation Studies: A String of Empirial Rejetions The seminal empirial ritique of Heksher-Ohlin is due to Leontief (1953). Although this was not a test of the HOV theorem, the study learly indiated that something was seriously amiss with how eonomists thought about trade. Leontief used data on input requirements and US trade to measure apital to labor ratios in US imports and exports separately. To universal surprise, widespread dismay, and sattered onsternation, he showed that US imports were more apital intensive than US exports. This suggested that the US is relatively labor abundant a result ever after known as the Leontief Paradox. Leamer (1980) showed, however, that Leontief applied a oneptually inappropriate test of the Heksher-Ohlin hypothesis. When he re-examined the same data in a oneptually orret way, the paradox vanished. Nonetheless, this paradox refused to perish. Breher and Choudhri (1982) pointed out that one (ounterfatual) impliation of Leamer s approah is that US expenditure per worker would have to be lower than for the world as a whole. Stern and Maskus (1981) applied Leamer s (1980) approah to US data for both 22

25 1958 and 1972, finding the Leontief paradox held in the former but not in the latter year. Extensive surveys of previous work on Heksher-Ohlin an be found in Deardorff (1984) and Leamer and Levinsohn (1995). The first real tests of HOV were onduted by Maskus (1985) and BLS (1987). The analyti foundation is given by equation (11). Their results severely undermined onfidene in the robustness of the Heksher-Ohlin framework. Maskus (1985) arried out both sign and rank tests on data for two time periods (1958 and 1972), and for three high quality fators (professional, unskilled labor, and apital). He reports results only for the United States, perhaps beause the Leontief paradox had foused on it. The sign test is orret for only one fator in 1958, but for all three in This might be seen to suggest that the Heksher-Ohlin-Vanek relations fare well, at least in the latter period. However, the test laks power. As Maskus notes, if we onsider the alternative that the signs were determined randomly, we will have two or fewer sign failures out of six tries 34.4 perent of the time. Moreover, even if we limit ourselves to the 1972 data, under the same alternative, there will be no sign violations (as in his data) one in eight times. The results were, if anything, worse in the rank test. The diret measures of US fator abundane relative to the rest of the world were stable, with physial apital most abundant, professionals seond, and unskilled labor least abundant. However, the trade-imputed measures of fator abundane in 1958 suggested the US was most abundant in unskilled labor, and least abundant in physial apital! The 1972 trade-imputed measure of fator abundane showed unskilled labor shifting dramatially to be least abundant, and reverses the relative abundane of physial apital and professionals. A repeat of the tests, restrited to OECD data, yielded no improvement. As Maskus noted, paradoxial outomes may be the rule rather than the exeption. 23

26 BLS likewise report results widely viewed as underutting Heksher-Ohlin-Vanek. An important ontribution was extending the test to a muh broader set of ountries (27) and fators (12). Thus, whereas the Maskus test was based on a matrix of only three ells for eah time period, the BLS matrix had 324 entries. Beause of the greater dimensionality of the matrix, it beame possible to ondut sign and rank tests not only for a single ountry aross fators (as in Maskus (1985)), but also for a single fator aross ountries. The sign test was orret more than half of the time for eleven of the twelve fators, but was orret over 70 perent of the time for only four in twelve. The sign mathes were orret more than half the time for 18 of 27 ountries, but over 70 perent of the time for only 8 of the 27. Only 61 perent of the total sign mathes were orret. They note that independene between the signs of orresponding entries an be rejeted at the 95 perent level for only one fator in twelve, and for only four of the 27 ountries. In effet, in determining whih fators servies would on net be exported or imported, Heksher-Ohlin did little better than a oin-flip. The rank proposition fares no better. BLS report both rank orrelations and the proportion of orret rankings when entries are ompared two at a time. A zero orrelation is rejeted for only four of the 12 fators and eight of the 27 ountries. Moreover, one fator and five ountries have the wrong sign on the orrelation. While the pairwise omparisons get over 50 perent orret rankings for 22 of the 27 ountries, the same is true for only three of the 12 fators (all land variables). In sum, BLS note that the sign and rank propositions yield the Heksher-Ohlin- Vanek model relatively little support. It is hard to overstate the impat that the Leontief and BLS studies had on the profession. Krugman and Obstfeld (1994) summarized the thinking at the time in their textbook writing, trade just does not run the diretion that the Heksher-Ohlin theory predits. [p. 78]. The 24

27 problem was that there was no alternative. Riardian and sale eonomies models were useful at explaining many problems, but it was hard to imagine that eduational levels in the US had no impat on the US industrial mix. In large measure beause we had to have some theory about these linkages, empirial researhers ontinued to searh for ways of reoniling the theory with the data. In order to do this, they adopted two main approahes. The first was to see if simple amendments to the theory would yield new insights, and the seond was to test the theory with better data. The pessimism regarding Heksher-Ohlin was partly relieved by Trefler (1993), only to be revived by Trefler (1995). One of his key insights was that it was not enough to simply say HOV fails without understanding why it fails. Trefler s two papers represent alternative approahes to resolving the problems identified by BLS. The former follows up on Leontief s suggestion that the failure of Heksher- Ohlin may be due to fator-based differenes in effiieny. Trefler hoose the effiieny fators so that the Heksher-Ohlin-Vanek equations fit exatly. He then shows that the implied produtivity differentials orrelate niely with evidene on ross ountry differenes in wages and rentals, suggesting a version of adjusted fator prie equalization. Trefler (1995) returned to the simple Heksher-Ohlin-Vanek framework. We had learned from Staiger (1988) that there were systemati ways in whih fator ontent preditions missed the mark; Trefler went on to show us what those systemati problems were. In one exerise, he graphed the net fator trade residuals, ε T = B(I A) -1 T (V sv W ), against the predited net fator trade, V sv W. Theory would predit that these should be entered around the line ε T = 0. Instead they losely followed the line ε T = (V sv W ), or equivalently, MFCT = B(I A) -1 T = 0. This says that measured net fator trade is approximately zero, to whih he applied the olorful moniker the ase of the missing trade. 25

28 An important insight into the work of Trefler was identified by Gabaix (1997). Gabaix tried to understand why the results looked so good in Trefler (1993) and so bad in Trefler (1995). What Gabaix realized that these two sets results were linked. In the first paper, Trefler alulated produtivity parameters, f π, that solved the following problem: F = π V s π V f f f f f The seond paper had demonstrated that the LHS of this equation was very lose to zero. If we set it as exatly zero, then 0 = π V s π V f f f f After a little algebra and remembering that s is the share of ountry s GDP in the world, it is possible to show that π π f f Y W f V V V (1 s ) = W Y (1 s ) f V V V where Y is ountry s GDP. If both and are suffiiently small relative to the world, then the term in brakets on the right onverges to unity. In that ase, the alulated relative produtivities are: π π f f = Y V f Y V f In short, the produtivity parameters would simply be GDP per fator. Hene, as long as wages are orrelated with GDP per apita, it will not be surprising that the measured produtivity parameters would be orrelated with wages. 26

29 To drive home the point that missing trade was responsible for Trefler s 1993 results, Gabaix did an experiment in whih he began with the hypothesis that the measured fator ontent of trade is minus the HOV predition, i.e. MFCT = PFCT. Using this equation, he shows that the alibrated f f π differ little from those of Trefler and relative π orrelate with relative wages nearly as well as in Trefler (1993). What this makes lear is that evidene that the alibrated relative of HOV. f π orrelate well with relative wages ould not be used as evidene in favor These were not problems that Trefler ould have foreseen when he wrote the original paper. However, it undersored Trefler s ontention that understanding the mystery of the missing trade would be ritial to understanding what was wrong with HOV. Indeed, one you understand that the MFCT is essentially zero, muh of the HOV eonometris beomes quite simple. Consider, for example, Trefler's preferred speifiation involving an Armington home bias. His estimating equation is Y F V s ( 1 ) V V Y W f f * f * fw f = α + α + µ If we make the assumption that trade balanes are a small share of GNP and hene then this equation ollapses to ( ) F = α V s V + µ f * f fw f or W s Y Y, MFCT = α PFCT + µ f * f f We already know from the first part of Trefler's paper that the LHS of this equation is lose to zero so we may not be surprised to find evidene that * α is muh smaller than unity. 27

30 This may be evidene in favor of an Armington home bias, but it ould be the result of any other proess that results in little measured net fator trade. For example Conway (2001) argues that MFCT will be small if there is little fator mobility sine trade will not move fators away from their autarky alloations. Using Trefler's data he estimates 1 F = V ( β + 1 f ) s V + ε 1+ γ f f fw f where γ f and β are parameters to be estimated. He finds γ f to be signifiantly greater than zero while β is indistinguishable from zero. In other words, for the ase where β is zero, we an rewrite the speifiation as MFCT = α PFCT + µ f f f f Fundamentally, the differene between the two papers is in how they shrink PFCT to math MFCT Trefler does it by ountry, and Conway by fator. In both ases ˆα will be signifiantly less than unity as long as MFCT is small. The relationship between the various tests that we derived earlier gives us an insight into why these speifiations sueed at eliminating the mystery of the missing trade. Reall that these authors delare vitory over the missing trade when 2 2 σ M / σ P' 1 where P' an now be defined as ˆα * PFCT. Realling our earlier disussion of regression tests, we know that this 2 2 ondition an be rewritten as σ / ( ασ ˆ ) 1 or MT/ 2 M P 2 ˆα, whih just equals 1/R 2. This implies that the missing trade statisti is bounded below by 1 and above by infinity in this type of speifiation. Hene any speifiation that an be written as MFCT = α PFCT + µ is f f f guaranteed to deliver a missing trade statisti above one and so appear to solve the mystery of the missing trade. This solution is illusory and provides no information about the eonomis underlying missing trade. Oddly enough, as the fit deteriorates, missing trade will shift toward 28

31 exess trade. This may help explain why in the preferred speifiation of Trefler (1995), the missing trade statisti is muh larger than unity even though Gabaix finds that PFCT has almost no explanatory power. 6 Is this all that is going on? First, we have already noted that suh speifiations are mathematially guaranteed to solve the mystery of the missing trade. The only remaining question is what they tell us about fator servie flows. Gabaix (1997) notied that tests of equation (6) an fail miserably even for preferred eonometri speifiations. In neither Trefler (1995) nor Conway (2001) do the authors take the estimated parameters and go bak to the original puzzle to see if they suessfully reonile MFCT and PFCT. When Gabaix does this using Trefler s data, he finds that the amended model does little to reonile predited and measured fator trade. 7 Putting the Piees Together As researhers puzzled over why HOV performed so badly, they began to ask whih parts of the theory were ausing the problems. As we have already noted, trade theory neessarily ontains a theory of prodution and a theory of absorption. Davis, Weinstein, Bradford, and Shimpo (1997, hereafter DWBS) were the first to reognize that this naturally suggests that tests of HOV an be broken up into tests of prodution and absorption models. This enables one to test the theories diretly on the relevant data rather than trying to infer parameters about demand and prodution from the fator ontent of trade. Aware of many of the problems that had plagued testing of HOV on international data, DWBS developed a new approah to testing HOV. Several elements of that approah are worth noting. First, it examines the prodution and absorption sides separately. Prior HOV tests 29

32 working with trade data ould make inferenes about the soure of diffiulties, but ould not examine them diretly. Seond, we sought to bridge our own and prior work by starting with a strit HOV model and relaxing assumptions one at a time. This allowed us to identify whih assumptions seemed to be ruial in driving the results. Third, we developed an approah that allowed us to make HOV preditions when only a subset of the world shared FPE. This draws on the analytis embodied in equation (21). In our ase the relevant FPE lub was a set of ten regions of Japan. Finally, we worked a data set in whih identities held. The results, in ontrast to prior work, were very positive for HOV. The step-by-step approah in DWBS allowed us to see whih elements of the theory were ausing problems. We first onsidered the Heksher-Ohlin theory of the pattern of prodution under the assumption that all ountries in the world utilize the same input oeffiients. Our results find little support for this version of Heksher-Ohlin, onfirming earlier studies. The results improve dramatially, though, under the more modest assumption that all Japanese regions share a ommon set of input oeffiients. This indiated that although the theory was a powerful means of talking about prodution within an FPE lub, it performed poorly as a desription of international prodution patterns We then turned to the Heksher-Ohlin theory of the pattern of onsumption. We examine this first by onsidering Japanese regional absorption, whih the theory suggests should be proportional to world net output. The Heksher-Ohlin model of proportional absorption does surprisingly well under this assumption. Indeed while Trefler (1995) was fored to estimate home bias parameters from fator ontent data, we ould examine the question on the atual onsumption data. What we found was that the assumption that Japanese onsumption differed from that in the rest of the world did no better than the standard predition of homothetiity. In 30