One Size Fits All? Heckscher-Ohlin Specialization in Global Production

Transcription

1 One Size Fits All? Heksher-Ohlin Speialization in Global Prodution Peter K. Shott Yale Shool of Management and NBER November 7, Abstrat Many previous tests of Heksher-Ohlin trade theory have found underwhelming support for the idea that ountries endowments determine their prodution and trade. This paper demonstrates that those efforts suffer from their fous on the narrower of the model s two potential equilibria, whih assumes that all ountries produe all goods. In this paper we introdue a more general tehnique for testing the model that allows for the possibility that ountries with suffiiently disparate endowments speialize in unique subsets of goods. Results using this tehnique indiate strong support for Heksher-Ohlin speialization versus one-size-fits-all homogeneity. Our results also demonstrate that the empirial evaluation of trade models has been hampered by the oarse aggregation of output inherent in existing datasets. Indeed, we show that traditional ategorizations of goods hide a substantial degree of ross-ountry prie and input intensity heterogeneity, violating the assumptions of the fator proportions framework and rendering previous estimation results diffiult to interpret. To overome this problem, we introdue a methodology for aggregating goods that orrets for underlying produt variation. Estimation of the model using orreted aggregates reveals even stronger support for Heksher-Ohlin speialization. The importane of speialization for the evolution of developed ountry wage inequality is also disussed. Key words: International Trade; Heksher-Ohlin Model; Multiple Cones of Diversifiation JEL lassifiation: F; F4; F; C Speial thanks to Ed Leamer for his piering ritiism, generous patiene and earnest enthusiasm, usually in that order. Thanks as well to partiipants in seminars at Chiago, Mihigan, Purdue, Santa Cruz, Stanford, the World Bank and Yale. Yale Shool of Management, 35 Prospet St.; New Haven, CT 65-8; tel: (3) ; fax: (3) ; peter.shott@yale.edu.

2 One Size Fits All? Heksher-Ohlin Speialization in Global Prodution Issues Existing attempts to find support for the idea that a ountry s endowments determine its prodution and trade have foused on the overly restritive, one size fits all equilibrium of Heksher- Ohlin trade theory. That version of the model has all ountries of the world produing all goods, so that both Japan and the Philippines, for example, are assumed to produe idential apparel and eletronis goods. But a seond, far riher equilibrium is possible within the framework. This equilibrium has ountries speializing in the partiular subset of goods most suited to their mix of endowments, so that relatively labor abundant Philippines might produe labor-intensive t-shirts and portable radios while apital abundant Japan manufatures apital-intensive semiondutors and hemials. Ignoring suh speialization undermines efforts to find support for the Heksher-Ohlin model and louds our thinking about the relationship between globalization and inome inequality. This paper introdues an empirial tehnique for testing the fator proportions framework that an differentiate the two versions of the model. This approah is more general than those employed in previous studies beause it allows the effet of fator aumulation on a given setor s output to vary with a ountry s endowments. Apparel output, for example, might rise with apital aumulation in labor abundant developing ountries like the Philippines, but fall with apital aumulation in relatively apital abundant ountries like Japan. In this way, ountries move in and out of setors over time as their eonomies aumulate endowments. By estimating the apital per labor utoffs where suh hanges in the derivative of output with respet to endowments take plae, we an group ountries aording to produt mix. Results indiate that in 99 the world s ountries an be neatly segregated into three suh groups, eah of whih produes a unique mix of manufaturing aggregates. A sensitivity to speialization highlights the inadequaies of existing ategorizations of goods (e.g. the ISIC, SITC and SIC) for estimating trade theory. Under these shemes, aggregates like Food, Apparel and Mahinery are formed by ombining goods loosely aording to end use. However, testing the key insight of trade theory that the fator intensity of goods produed by a ountry be similar to that ountry's relative endowments requires that we group together lose substitutes that are manufatured Examples inlude the Heksher-Ohlin estimations of Leamer (984), Harrigan (995), Trefler (995) and Davis et al (997), as well as the fator ontent study of Deardorff and Staiger (988). Exeptions inlude: Breher and Choudhri (993), who relax the single one assumption in estimating the impliations of the model for prodution in the U.S. and Canada; Debaere and Demiroglu (997), who exploit insights offered by Deardorff (994) to demonstrate that observed ountry and setor apital labor ratios appear inompatible with the existene of a single one of diversifiation; and Davis and Weinstein (998), who allow tehnique to vary with ountry apital abundane. The latter is disussed in greater detail below.

3 with idential tehnology. Traditional aggregates an fail on both ounts. The three-digit ISIC aggregate Eletrial Mahinery, for example, enompasses both portable radios assembled by hand and ommuniations satellites. It seems reasonable to assume that ountries will produe these goods at different stages in their development, and that they therefore should be grouped separately. Indeed, we present substantial evidene that three-digit ISIC manufaturing aggregates exhibit signifiant variation in both input intensity and prie aross ountries. Interpreting both piees of evidene as signals of underlying produt mix heterogeneity, we introdue an empirial methodology designed to ontrol for it. When the model is re-estimated using these orreted, Heksher-Ohlin aggregates, support for the idea that output is a funtion of endowments and that ountries speialize inreases. The emphasis in this paper on the prodution impliations of the Heksher-Ohlin model is most losely related to work by Harrigan (995, 997) and Bernstein and Weinstein (). Those studies, however, fail to allow for the possibility that oarse aggregation an obsure prodution patterns. Our fous on international speialization is omplementary to reent researh into the speialization of US regions by Hanson and Slaughter () and Bernard, Jensen and Shott (). The latter, whih relies upon muh more detailed data than is available for a ross setion of ountries, shows that relative fator prie disparity aross US regions is at least partly responsible for heterogeneity in regional industry omposition. By putting speialization at enter stage, this paper also illustrates how a failure to aount for produt mix heterogeneity has hampered efforts to verify the trade preditions of the Heksher-Ohlin model and has perhaps lead to researh over-emphasizing international tehnology differenes as a ause. A prinipal onlusion of existing researh is that observed trade flows are small relative to the disparity in ountries endowments (Maskus 985; Bowen et al 987; Trefler 995; and Davis et al 997). But this onlusion is based upon the joint assumption that every ountry produes all goods and that all ountries employ the same tehnique for making them. Indeed, the US input-output matrix is often used as a proxy for these tehniques. But if a labor abundant ountry like the Philippines produes labor-intensive eletronis rather than the apital-intensive eletronis upon whih US tehniques are based, both parts of this joint assumption are inorret and the true labor embodied in Philippine trade will be underestimated. In this sense, we show that at least part of what Trefler (995) has ogently dubbed the Mystery of the Missing Trade an be resolved by more areful onsideration of speialization. Of ourse, as Trefler and others have pointed out, tehnology an play a role in this mystery by leading us to over- or underestimate ountries fator endowments. If, for example, Philippine labor is less effiient than US labor, its effiieny-orreted labor abundane is less than its raw labor abundane and therefore loser to the true labor embodied in its trade. Our emphasis on speialization in this 3

4 paper is not meant as an argument against a role for tehnology. Rather, it is to highlight an important part of the puzzle that has thus far largely been ignored. Determining whether or not ountries speialize has relevane beyond mehanial tests of trade models. It is a key fator, for example, in helping us understand urrent and future effets of globalization on developed ountry wages. If rih and poor ountries export the same mix of goods in an open world eonomy, their workers ompete diretly. As a result, wage-prie arbitrage mandates that a deline in the (world) prie of labor-intensive goods perhaps due to the redution of trade barriers fores rih ountry wages down if those setors are to remain viable. However, to the extent that ountries speialize, or are in the proess of speializing, this prie-wage link is weakened and may even be broken. Thus, if the US and other developed ountries will soon abandon setors also produed by developing ountries, future prie delines in these produts may not have adverse onsequenes for unskilled workers in rih ountries. Indeed, a reent study by Harrigan (999) indiates that US pries were relatively unaffeted by world prie delines assoiated with the East Asian urreny risis. The paper proeeds as follows: setion outlines the basis of the fator proportions framework and introdues the empirial speifiation designed to estimate it; setion 3 tests the model on traditional ISIC aggregates, highlights the inadequay of those aggregates and develops an alternate Heksher- Ohlin aggregation sheme; setion 4 re-estimates the model using the new aggregates; and setion 5 onludes. To promote readability of the main text, detailed desriptions of the data and eonometris are reserved for two appendies. Theory. The Two Fator Model The ore impliation of the Heksher-Ohlin framework is that ountries produe a mix of goods most suitable to their relative fator endowments. This model assumes: A A A3 Produtive fators (e.g. apital, labor) are perfetly mobile from setor to setor within a ountry, but immobile internationally; Countries are small, open and possess perfetly ompetitive markets; Countries share idential, onstant returns to sale tehnology. The standard version of the model is known as a single one equilibrium, the word one referring to the set of endowment vetors that all selet the same mix of produts. In this version of the model, there is only a single mix of goods and all ountries produe it. 4

5 With A through A3, the mapping of endowments into output is a result of ountries maximizing GDP subjet to the resoure onstraints: Aq v, where A is the (FxI) inputs per unit of output tehnology matrix, q is the (Ix) output vetor, v is the (Fx) endowment vetor and F and I are the respetive number of fators and setors. If the number of fators equals the number of produts (i.e. if A is square), and if there are no linear dependenies among the olumns of A, then this system an be inverted to solve for output as a funtion of endowments, or q = A v, where the elements of A - (known as the Rybzynski derivatives) relate the effet of fator aumulation on the output of eah setor. In a two-good, two-fator world at onstant ommodity pries and within a given one of diversifiation, these derivatives indiate that an inrease in the supply of a fator leads to an inrease in the output of the ommodity that uses that fator intensively and a redution in the output of the other ommodity. In a world with more goods than fators, inspetion of the GDP maximization problem indiates that ountries may produe different subsets of goods (equal to the number of fators) depending upon endowments. In that ase, the vetor q in equation ontains a number of zeros equal to the number of non-produed goods, and the mix of goods with positive output hanges as ountries develop. Thus, with speialization, the vetors and matrix of equation should be interpreted as ontaining only the rows and olumns pertaining to produed goods. The alloation of prodution aross setors within a one may be indeterminate if pries are suh that more goods than fators are viable. This possibility of an uneven (i.e. more goods than fators) equilibrium is disussed further below. Framing the a ountry s problem in terms of its dual (i.e. pries and wages), the (Fx) vetor of fator rewards (w) an be found by minimizing the ost of GDP (w v) subjet to the zero profit ondition A w p, 3 where p is the (Ix) vetor of world pries. The wages assoiated with eah mix of produts (i.e. eah one of diversifiation) are then w = A p. 4 We an interpret q as value added if we reognize that the resulting Rybzynski oeffiients are net of intermediate inputs (Davis and Weinstein 998). 5

6 Note that within a one of diversifiation, fator rewards do not respond to hanges in endowments. This ondition is often referred to as fator prie equalization but has been more aptly labeled fator prie insensitivity by Leamer (995). Though partial equilibrium analysis suggests, for example, that an inrease in the supply of labor redues its reward, the general equilibrium formulation of the Heksher- Ohlin framework has wages remaining onstant within a one due to onomitant shifts in output toward labor-intensive setors. Thus, a world populated by ountries with suffiiently dissimilar relative endowments may ontain more than a single region of fator prie insensitivity, thereby limiting or eliminating the tendeny toward global fator prie equalization. The empirial approah developed in this paper diserns these regions by identifying output speialization patterns in a ross-setion of ountries. With an additional assumption about demand, A4 All individuals share idential homotheti preferenes, the Heksher-Ohlin-Vanek (968) relationship between endowments and trade is AN = v s v, 5 w where N is the (Ix) vetor of ountry s net exports, s is ountry s share of global output and v w is the (Fx) vetor of world endowments. Within a two-ountry, two-good and two-fator framework, this relationship is aptured in the Heksher-Ohlin theorem: ountries export the good employing intensively the relatively abundant fator and import the good using intensively the relatively sare fator. In a world with more than a single region of fator prie insensitivity, a ountry s mix of imports and exports hanges, akin to prodution, as ountries aumulate apital. The traditional method of estimating standard trade theory is to examine the strength of the equality in equation 5 by using the US input output matrix as a proxy for A. One advantage of working with the prodution side of the model is that its message that prodution depends upon fators an be evaluated without any assumption about demand. Figure, ontaining a Lerner (95) diagram of a two fator, four setor world, illustrates the path of a small open eonomy aumulating apital relative to fixed labor. The four setors, in order of inreasing apital intensity, are Apparel, Textiles, Mahinery and Chemials. For simpliity of exposition and without loss of generality, eah setor is displayed as having Leontief tehnology and fator intensity reversals are ruled out. As indiated in the figure, the four setors unit-value isoquants delineate three ones of diversifiation. An additional assumption (relaxed below) is inorporated in the figure: 6

7 A5 The world is even in the sense that there are an equal number of fators and goods in eah one. Eah one represents all positive ombinations of the input vetors of two of the four setors. GDP-maximizing ountries speialize by produing only the two goods anhoring the one in whih they reside: prodution of a good outside a ountry s one results in negative profit. The apital-labor ratios marking the borders between ones are labeled τ t for t [,3]. As apital is aumulated relative to labor, output in industry i and ountry per total workfore (Q i /L ) in eah of the four setors evolves as indiated in the four panels of figure (Deardorff 974; Leamer 984). 3 Changes in the derivative of output with respet to endowments always our at one of the four apital-labor ratios delineating ones. Note that development paths an ontain flat spots where ountry does not produe industry i and the derivative of output with respet to endowments is zero. Capital aumulation also moves a ountry into ones with progressively higher wages and lower apital rental rates. This hange in relative fator rewards an be seen by onneting isoquants with their respetive isoost lines. Unit value isoquants are tangent to their respetive isoost lines under perfet ompetition (assumption A). One suh isoost line, tangent to Mahinery and Textiles, is present in the diagram. Note that the absolute value of the slope of this line indiates the ratio of wages to apital rental rates; sine the isoost lines beome steeper as ountries move from the most labor abundant one to the most apital abundant one, relative wages rise. Examination of isoost lines also reveals that a deline in the prie of Apparel lowers nominal wages in the labor abundant one but does not affet nominal wages in the more apital abundant ones. Thus, if the US is suffiiently more apital abundant than the Philippines, their workers nominal wages are not affeted by, for example, a derease in world apparel pries. (Indeed, their real wages rise.) The four ontinuous, piee-wise linear relationships between output and apital abundane depited in figure summarize the basi development paths that an arise within the Heksher-Ohlin framework. Setors an be ranked aording to apital intensity via either the apital-labor ratio at whih peak output per worker ours or the maximum output per worker attained in eah setor. Both riteria are used below to evaluate model performane. The Rybzynski relationships exhibited in figure an be estimated using a ross setion of ountries output and endowment data. If all ountries in a dataset inhabit a single one of diversifiation then output per worker (Q i /L ) in eah setor an be estimated as a linear funtion of the ountry s apital-labor ratio (K /L ), 7

8 Q L i α + K = α i. 6 i L Generalized to ontrol for additional fators suh as human apital and natural resoures, this speifiation has beome standard for estimating the Rybzynski derivatives of the Heksher-Ohlin model. If ountries are distributed among several ones of diversifiation, however, speifiation 6 is inorret. The orret speifiation is that of a spline with T knots where (, T ) t Q L i = T + t= { > } + Ι { > } K K τ β K it t τ β itι t, 7 L t L L t τ represents the apital-labor ratio of the t th estimated interior knot and {} Ι is a vetor of indiator funtions whose elements are unity if the relationship in brakets is true and zero otherwise. This speifiation estimates a separate line segment for eah one. 4 With the appropriate ontinuity restritions ( β it β + i, t β i, t = τ ), this speifiation an be re-written as t Q L i K { τ t, } K = α 8 T + i + αi + αti max L L t = 3 (Poirier 976). This seond speifiation is onvenient beause the slopes of suessive ones are additive: the effet of apital aumulation on output in the most apital sare one is α i while the relationship in the n th one, for n>, is α + n+ i α ti t= 3. Both speifiations allow the derivative of output with respet to endowments to hange disretely at the knots. Speifiation 8 an be estimated on a system of I equations with C observations via maximum likelihood, subjet to the theoretially mandated, system-wide onstraint that eah knot in the development path ours at the same apital-labor ratio in eah industry ( τ = t (, T ) ) it τ t pratie, the loation of interior knots is estimated by gridding over all possible ombinations of T knots for a given interval size. In the estimations to follow, a grid interval of $5 apital per worker is used. Sensitivity analysis using grid values ranging from $ to $ did not hange results substantially. Note that a narrower grid an only inrease evidene against the null.. In 3 The disussion in this setion assumes away non-traded goods. See Leamer (987) for a detailed disussion of their effet on development paths. 8

9 P-values for a lassial likelihood ratio test an be omputed to determine whether the null hypothesis of just one one (i.e. T=) an be rejeted in favor of the nested alternative hypotheses of more than a single one (T>) for the system of I industries. These hypotheses an also be evaluated via posterior odds ratios, or Bayes Fators. Coneptually equivalent to Shwarz (978) riteria, Bayes Fators have a natural degrees of freedom orretion whih aounts for the inrease in parameters in moving from a null hypothesis with I parameters to an alternate hypotheses with IT+T parameters. A Bayes Fator equal to unity indiates that the alternate is just as likely as the null after orreting for degrees of freedom, while odds ratios greater than unity indiate the alternate hypothesis is more likely. Further detail on Bayes Fators is available in the Statistial Appendix. An advantage of the empirial speifiation developed in this setion is that it sets up a horse rae between ompeting trade models, albeit models within the same fator proportions framework. Appropriateness of the multiple one model at the setoral level an be gauged informally by heking estimated splines for onformity with theoretial arhetypes. More formally, partial odds ratios an be omputed for eah ISIC aggregate. However, beause the development paths are estimated as a system, these partial odds ratios must be interpreted with aution: they are omputed as if the loation of knots were known. This assumption is not too severe, however, beause information as to the loation of knots in ISIC setor i is derived mostly from the other I- setors.. What is an Industry? Before proeeding with the estimation it is useful to onsider how goods are defined. Surprisingly little attention has foused on their appropriateness for estimating trade theory. 5 The ISIC ategories developed by the United Nations and used below, for example, group output loosely aording to similarity of end use (e.g. Apparel, Mahinery, Eletroni Mahinery), a proedure not neessarily onsistent with the oneptualization of goods developed above. Reoniling the two requires two additional assumptions: A6 A7 Goods in ountry within the same ISIC aggregate i have idential input intensities and pries. Aross ountries, ISIC aggregates have idential input intensities and pries. The virtue of aggregating goods aording to end use rather than input intensity, of ourse, is that they are more likely to be governed by the same prie. Think, for example, of the high ross elastiity of substitution whih presumably exists between white otton tube soks made by hand and white otton 4 In the estimation, τ is assumed to be zero while τ T is assumed to be the upper range of the sample apital-labor ratios. 5 Dollar, Wolff and Baumol (988) note the wide disparity of setoral apital intensities aross ountries. 9

10 tube soks made by mahine. But we usually think of these two kinds of soks as being produed by different tehniques, where tehnique refers to the partiular ombination of inputs along an isoquant. (If the eah type of sok were produed aording to different tehnology, they would posses different isoquants.) Estimations in the next setion rely upon assumptions A6 and A7. In light of the ensuing results, as well as additional evidene ulled from independent data soures, these assumptions are relaxed in setion 4..3 What Happens If There Are More than Two Fators or the World is Uneven? With three or more fators or prodution, Leamer (987) demonstrates that development paths with respet to any two fators, suh as apital and labor, still take the shape of a spline. However, the loation of a development path s knots as well as the slopes of its non-zero line segments are endogenous to all other fator abundane ratios. Land abundant ountries, for example, might exit the labor-intensive Apparel setor at a higher apital-labor endowment ratio than land sare ountries. In a three fator model that inludes land (T), for example, the orret speifiation is Q L i K { T τ t ( ), } T + K T = β + i β i + β ti max. 8 L L L L t= 3 In this equation, both the knot and industry slope are a funtion of land abundane. As a pratial matter, estimation of equation 8 is quite diffiult. In this paper, we fous on two shortuts. The first, used in setion 3, is to allow eduation per worker and rop- and forestland per worker ratios to enter speifiation 8 linearly, so that these other endowments merely raise or lower the estimated spline. The seond shortut, used in setions 3 and 4, follows Leamer (987) and splits ountries aording to a third endowment, like ropland per worker. 6 Equation 8 is then estimated separately for eah ohort of ountries. Note that this proedure allows the splines knots as well as their derivatives of output with respet to the apital-labor endowment ratio to vary rudely with land abundane. An additional ompliation arises if the world is uneven in the sense that more goods an be produed at zero profit than there are fators in a one of diversifiation. In that ase, ountries in the same one may nevertheless produe a different subset of goods, and speialization is not a signal of a violation of the single one model. Thus, a positive orrelation of import mix and ountry endowments is neessary but not suffiient for the existene of multiple ones of diversifiation. Note, however, that any goods produed in ommon by ountries in the same one must sell for the same prie, a ondition, as we 6 We do not use the seond shortut in the initial estimations in setion three given the relatively large number of estimated knots.

11 illustrate below, that is violated by traditional aggregation shemes. The intuition for the effet of unevenness omes from the indeterminay of equation () when I>F. Bernard, Jensen and Shott () offer a more detailed disussion of the effets on fator prie equality of relaxing traditional Heksher- Ohlin assumptions. 3 Estimating the Multiple Cone Model using Traditional Aggregates 3. Data Desription Value added, apital stok and employment data for up to 45 ountries in 99 are used to estimate equation 8 for the null and nested alternate hypotheses. This relatively large sample of ountries provides broader overage than many previous examinations of the fator proportions framework, thereby inreasing endowment diversity. As should be lear by now, this diversity is partiularly important for the purposes of differentiating a multiple one model from a single one model. 7 Value added data for 8 three-digit ISIC manufaturing aggregates are drawn from the UNIDO INDSTAT3 database, available on diskette from the United Nations. A drawbak of having only manufaturing data is that it prevents verifiation of whether the model works aross a broader range of setors (i.e. mining, agriulture and servies), where disparities in natural resoures or eduation may be partiularly important in induing speialization. One potential benefit or our data onstraint, however, is that manufaturing aggregates may ontain fewer non-tradables than these other setors, so that their atual development paths more losely resemble the theoretial arhetypes desribed above. Eonomy-wide labor statistis ome from the World Bank CD-ROM. Manufaturing apital endowments are omputed from UNIDO measurements of manufaturing gross fixed apital formation. An alternative is to use a measure of eonomy-wide apital, suh as those found in Maskus (99) or the Penn World Tables. The major differene between use of manufaturing versus aggregate apital is that the relative apital abundane of land rih ountries (e.g. U.S., Canada, Norway, Australia, and New Zealand) delines when using manufaturing apital stok rather than total apital stok. This re-ranking an be used to our benefit: use of manufaturing apital to ompute ountry apital abundane allows us to ontrol for the influene on output of endowments other than apital and labor, like land. 8 7 Fousing on a smaller set of ountries does not neessarily inrease the likelihood that they share the same one of diversifiation, partiularly if fators other than apital and labor are onsidered. Gabaix (997), for example, firmly rejets the Heksher-Ohlin model using a sample of the wealthiest European ountries. Even those ountries, however, vary signifiantly in natural resoure endowments, whih, as noted above, an have a signifiant effet on development paths. (See also Leamer et al 999). 8 Using ountry apital abundane also reveals evidene for speialization. Results using manufaturing apital stoks are reported beause they are the most sensible in terms of having fewer outliers obviously due to land.

12 Estimations in this setion ontrol for additional fator endowments by inluding linear terms for forestland, ropland and higher eduation (seondary plus tertiary eduation attainment). As noted earlier, though theory indiates that these ontrols hange the loation of industries knots, their linear speifiation here might be motivated by an assumption of prodution separability. In any ase, the effet of land is dealt with more fully in the estimations on orreted aggregates in setion 4. Data on land and eduation are drawn from the World Bank CD-ROM and Barro and Lee (994), respetively. The ountries and industries ontained in the sample are listed in the Data Appendix. That appendix also ontains a list of goods that an be found in eah aggregate. 3. Estimation Results The first important result of the paper is provided in table. This table ompares the single one null hypothesis to nested alternate hypotheses of from two to five ones (one to four interior knots). Beause estimation of the alternative hypothesis for eah model involves gridding over all possible ombinations of T knots, omputational onstraints prevent estimating more than five ones in any reasonable amount of time. However, given that our main interest is in whether or not speialization exists this limitation does not appear to be too important. The table provides strong evidene of speialization. The first olumn reports p-values for the lassial likelihood ratio (LR) test and indiates that the single one model an be rejeted at the 99% level of signifiane for all alternate hypotheses. The posterior odds ratios indiate that this evidene persists even after orreting for degrees of freedom and that the four-one model, whih is highlighted, provides the best fit beause the Bayes Fator deays after four ones. Table lists the partial Bayes Fator for eah ISIC aggregate under the favored four-one model. As disussed above, the partial posterior odds ratios are omputed under the assumption that the loation of knots is exogenous. 9 The left panel lists the 6 of 8 setors favoring speialization while the right panel lists the setors favoring the null. The setors most favoring speialization are Paper and Wood while the three setors least favoring it are Nonferrous Metals, Iron and Petroleum Refining. A plausible explanation for this relative performane is that ontrols are inluded for forestland and ropland but not for other natural resoures. That Mahinery, Eletronis and Transportation Equipment favor speialization does not seem too surprising sine we expet apital abundant ountries to fous on these (generally) apital-intensive setors. More puzzling, however, is that there does not seem to be muh evidene of speialization for setors suh as Apparel and Footwear that we expeted to be laborintensive.

13 Examining performane of the multiple one model setor by setor highlights the mismath between the large number of ISIC aggregates and the relatively small number of estimated ones. One way to preserve evenness (assumption A5) and also inrease the strength of the estimation is to explore whether ountries arbitrarily speialize in ISIC aggregates of similar apital intensity. Labor abundant ountries might produe either Footwear or Apparel, for example, while apital abundant eonomies might manufature either Mahinery or Transportation Equipment. If that were the ase, then merely ombining Footwear and Apparel into one super-aggregate, for example, and Mahinery and Transportation Equipment into another might make speialization more notieable. Note that this reasoning is idential to that whih supports aggregation shemes suh as the ISIC. Indeed, any time a higher level of aggregation (e.g. three-digit ISIC) is hosen over a lower one (e.g. fourdigit ISIC), the lower level aggregates are assumed to be redundant in the sense that their unit value isoquants lie atop one another. As a result, searhing for redundany may help us understand why support for speialization varies so muh aross ISIC setors. Inspetion of the data underlying tables and, however, provides the first hint that this line of reasoning is flawed. Figure 3 ontains a satter matrix of the underlying Q i /L versus K /L data for eah ISIC ategory as well as that setor s estimated development path. Information in the upper right hand orner of eah plot identifies the setor and ISIC ode. Setors are ordered in terms of inreasing apital intensity from left to right, and down, aording to maximum observed value added per worker. Thus Leather the (,) element of the satter matrix is the least apital-intensive ISIC aggregate while Mahinery the (7,4) element is the most apital-intensive. Sales are hosen to provide maximum detail; value added per worker inreases substantially as one moves down the matrix. As detailed in figure 3, estimated splines deviate substantially from the theoretial arhetypes of figure. Many setors, for example, exhibit positive value added per worker in more than two ones. Indeed, the Apparel spline (,4) suggests that all ountries have positive prodution in that setor. This result suggests that forming super-aggregates by summing over existing three-digit ISIC ategories of similar fator intensity (e.g. Footwear (,3) and Apparel (,4)) is not likely to bring estimates loser to theory: output would remain positive for all ountries. Given the widespread use of high-level aggregates in testing trade theory, this feature of the data is quite important. 9 As noted in the statistial appendix, the magnitude of Bayes Fators depends upon sample size. Note that the Bayes Fator of the favored four one model in table is merely the joint produt of the partial Bayes Fators listed in table. Beause estimated splines are plotted as if ountries ontain no land and no skill, development paths for industries suh as Printing (5,4) and Paper (6,4), where land and eduation ontrols are most signifiant, lie furthest from the data. Use of ontrols redues the likelihood that displayed peaks and valleys are due to endowments other than apital and labor, but this assessment is likely truer for setors like Transportation (7,) and Mahinery (7,4) than for Petroleum (,) and Nonferrous Metals (3,7) beause the former are more apt to depend upon unobserved resoures. 3

14 However, though estimated development paths are not a perfet math for theory, they do ontain hints of underlying speialization. Labor abundant ountries do not produe muh of the most apitalintensive setors, whih is one of the reasons why the setoral evidene for Printing (5,4) and Mahinery (7,4) is so high in table. In addition, the oft-hanging relationship between output and endowments in most industries is learly suggestive of multiple ones and a sharp ontrast to the impression given by earlier studies, where the derivative of output with respet to endowments is onstrained to be a onstant. Indeed, the twin-peaked development paths of the Transportation, Food, Eletrial Mahinery and Mahinery setors, all of whih lie along the lowest row of the matrix, appear easily separable into two sub-isic setors, one that is labor-intensive and one that is apital-intensive. This twin-peakedness is manifest in less apital-intensive aggregates as well, inluding Leather (,), Apparel (,4), Furniture (3,), Printing (5,4), Industrial Chemials (6,) and Paper (6,4). Figure 4 illustrates how this twin-peakedness may result from grouping distint produts with different apital intensities in the same ISIC aggregate, a violation of assumption A7. The left panel of this figure traes out an Eletronis development path with just two goods (e.g. portable radios and satellites), while the right panel illustrates the more general point that ombining a ontinuum of distint goods an lead to development paths with positive output in all ones, akin to those for Footwear (,3), Pottery (,4), Textiles (4,) and Tobao (3,) in figure 3. In highlighting the importane of aggregating goods aording to input intensity and substitutability, Figure 4 motivates an inquiry into how well traditional aggregates onform with the model s assumptions. We are unique in taking this approah. Davis et al (997), for example, move to evaluate the Heksher-Ohlin framework at the (Japanese) regional level when their estimation of the trade side of the model provides disappointing results. Working with a Japanese input-output matrix, they assume that this matrix is likely to be more appropriate within Japan than internationally. While that is no doubt true, their approah makes it more diffiult to verify the model s key message: demonstrating that prodution and fators oinide domestially, where fators are substantially more mobile than internationally, leaves us wondering whether fators attrat industry, as the model ditates, or vie versa. It is also ommon to treat traditional ISIC aggregates as sensible and use estimates based upon them to explore other violations of Heksher-Ohlin assumptions, inluding Riardian tehnologial differenes, home bias in trade and non-homothetiity of preferenes (e.g. Bowen et al 987; Trefler 995; and Harrigan 997). The danger in ignoring aggregation and examining those pathologies is that improper aggregation an bias onstrution of input per unit of output (A) matries and render results Debaere (998), on the other hand, responds to the poor performane of multi-lateral Heksher-Ohlin estimations by fousing on how well relative fator abundane explains bilateral trade. Though his results, like those below, suggest that the model works well for disparately endowed ountries, his bilateral fous diverts attention from the global perspetive most useful for understanding issues of inome inequality. 4

15 uninterpretable. To see this problem more learly, onsider the twin-peaked Eletronis development path in figure 4. If the A matrix onstruted to determine the equality of AN = v s v is assumed to be an average of the two ountries individual A matries, then apital intensity is underestimated in the apital abundant eonomy and over-estimated in the labor abundant eonomy. As a result, it may appear as if the fators embodied in Philippine trade, for example, are small relative to its manifest labor abundane, giving rise to a mystery of the missing trade (Trefler 995). Mis-measurement an be even more severe for labor abundant ountries if an A matrix from a apital abundant ountry like the US is used a proxy for all ountries tehnology matrix, as is ommon pratie. The solution to this problem is to onsider a muh broader A matrix that has multiple olumns for eah three-digit ISIC ode, so one Eletronis olumn, for example, might represent Philippine eletronis goods while another represents Japanese eletronis goods. Davis and Weinstein (998) make a similar point in researh omplementary to that presented here. Extending their previous work, the authors take a more sophistiated approah to dealing with observed input-output heterogeneity, broadening their estimation of the Heksher-Ohlin model to onsider speialization. Indeed, one interpretation of their results is that eah ountry is in a one of its own. w 3.3 Evidene of Intra-ISIC Output Heterogeneity Figure 5, whih plots setoral apital intensities (K i /L i ) for 39 of 45 ountries for whih data are available, provides an indiation of the extent to whih input intensities an vary aross ISIC aggregates. Countries are sorted in order of inreasing apital abundane from Sri Lanka (LKA) to Belgium (BEL). Here, as above, manufaturing apital is used as the measure of ountry-level apital endowment. ISIC setors are ordered in terms of average apital intensity from Textiles (Tex) to Petroleum (Pet). Note that the vertial sale has been ensored at $6, to provide a learer view of all setors. If eah setor represented the idential good in every ountry, the bars in figure 5 would line up like a wedge of heese rising from the ountry axis toward the bak of the plot. Atual intensities depart from this pattern in two ways. First, within-ountry setoral apital intensity rankings are not uniform. Seond, within-industry ountry rankings vary substantially: Germany s Apparel setor, for example, is almost 3 times as apital-intensive as Colombia s. Setoral apital stoks are onstruted using UNIDO INDSTAT3 data on gross fixed apital formation by setor. Due to missing information, it is not possible to ompute these stoks is not possible for all 45 ountries in the sample. To ompute 99 apital stoks for setor i in ountry (K i ), gross fixed apital formation was aumulated and depreiated (at 3.3%) from 975 to 99, inlusive; results are not sensitive to the depreiation rate. In some ases, missing time-series observations were estimated non-parametrially, though the results in this setion are in general not sensitive to the partiular way in whih this was done. A more omplete desription of how the setoral apital intensity dataset was onstruted is available from the author upon request. 5

16 Table 3 provides a more preise illustration of the extent of this heterogeneity. The table displays the minimum, median and maximum apital intensity in eah ISIC aggregate along with two measures of dispersion, Std( k i Mean( k ) i ) and Max( k i ) Min( k Min( k i ) i ), where k is the apital intensity of ountry in ISIC setor i. Large disrepanies between the two measures (e.g. for Mahinery) are indiative of outliers or mis-measurement. Bolivia s Mahinery setor, for example, has an estimated apital intensity of just $3. Setors are listed in asending order of the first measure of dispersion. In addition, data on four-digit ISIC aggregation and unit values indiates that intra-aggregate, aross ountry input intensity heterogeneity is a signal that the goods produed by labor and apital abundant eonomies are not lose substitutes. Table 4, for example, lists the orrelation of ountry apital abundane and four-digit ISIC prodution shares within the three-digit ISIC Mahinery aggregate. (The four-digit data originates from the same soure as the three-digit data but annot be used in the estimations above beause ountry overage is too sparse.) Correlations in the table are sorted from low to high and indiate that labor abundant ountries tend to manufature the first two types of mahinery (non-eletrial mahinery and agriultural mahinery) while apital abundant eonomies tend to manufature the rest. 3 (We report orrelations for the Mahinery aggregate beause it has the greatest number of sub-setors and the most extensive ountry overage of the pool of three-digit manufaturing ategories; other setors exhibit similar evidene.) Thus, to the extent that substitutability aross fourdigit aggregates is low, variation in setoral apital intensity is a strong signal of speialization. Evidene of unit value variation is ulled from an independent dataset on US imports ompiled by Feenstra (996). This dataset identifies the origin, value and quantity of US imports at the -digit HTS level of aggregation (roughly 6, ategories) for the years 97 to 994. This level of aggregation permits seletion of a very speifi good, like men s otton shirts, to determine whether unit values are orrelated with soure ountry apital abundane. Absene of orrelation supports a null hypothesis of homogeneous output within setors aross ountries. Positive orrelation, on the other hand, is onsistent with an alternate hypothesis of speialization, where shirts from apital abundant ountries are poor substitutes of shirts from labor abundant eonomies and are therefore more likely to lie on distint isoquants. 3 To ompliate analysis even further, note that a given ountry s aggregate may inorporate sub-setors of disparate input intensity as well. 6

17 In 994 the US imported men s otton shirts from half of its 6 trading partners, a relatively large share for suh a narrow good. The unit values of these shirts range from $56 (Japan) to $ (Senegal). In support of speialization, the orrelation of unit value with ountry apital abundane is.56, whih is signifiant at the 99% onfidene level. Indeed, as reported in Shott (), a positive relationship between unit value and soure ountry apital abundane is found aross a wide range of manufaturing aggregates and has been inreasing for the last twenty years, a signal that speialization may be inreasing with time. Furthermore, that study also finds that no signifiant relationship between unit value and soure ountry apital abundane exists in natural resoure goods suh as iron ore and fuel. Taken together, this new evidene of produt heterogeneity strongly suggests that traditional aggregation shemes mask speialization and that they present a formidable problem for estimating trade models. A potential solution is developed in the next setion. 4 Re-estimation the Multiple Cone Model with HO Aggregates Given the evidene presented in the previous setion, we now proeed as if ross-ountry heterogeneity within three-digit ISIC setors is a prinipal ause of the underwhelming performane of the Heksher-Ohlin model. Our first step, therefore, is to develop a tehnique for assembling Heksher-Ohlin Aggregates, hereafter referred to as HO Aggregates, whih groups output aording to ountry-industry input intensity rather than end use. We then use these new industries to re-estimate the model. Our approah in this setion provides a useful ontrast to the more traditional pratie of assuming that observed input intensity heterogeneity is due solely to differenes in international fator produtivity. Thus, this setion explores the gains to be had from proeeding in an alternate diretion. 4. Construting HO Aggregates Relax assumption A7 and use instead A7 The further apart goods within the same ISIC ategory are in terms of input intensity, the more likely they are to be different goods. The most straightforward method of operationalizing this assumption is to rank the (I*C)x list of ountry-isic apital intensities displayed in figure 5 in asending order and split them into ohorts alled HO Aggregates. Let X n denote output of HO Aggregate n in ountry and k i = K i Li represent the apital intensity of ISIC aggregate i in ountry. Then a ountry s output of HO Aggregate n is the sum of that ountry s output in all ISIC aggregates with apital intensity between the maximum and minimum apital intensity for that aggregate, 7

18 X =, 9 n Q i k ] i ( kn, kn where k n and k n are the apital intensity utoffs for aggregate n. Note that this tehnique preserves evenness within ones (assumption A5), so that T=N-. This aggregation sheme relies upon an additional assumption, A8 Pries are suh that the unit value isoquants of all goods within a given derived aggregate are tangent to a single isoost line. whih guarantees that the relationship between derived aggregates and ountry endowments remains as desribed in setion. The intuition for this guarantee omes from the assumption of onstant returns to sale (A3): beause the total output of any ombination of goods along a single isoost line within a one an be represented by the output of a single good tangent to that isoost line, the output of all setors with apital intensity greater than k n in aggregate n and ountry an be attributed to X n. As a result, indeterminate output within a one, even for a ontinuum of goods, is not problemati for our purposes so long as output deviates randomly from that neessary to plae respetive unit value isoquants along true isoost lines. Though this assumption is strong, it is important to note that it is no stronger than the assumption about pries whih lurks behind every estimation relying upon ISIC aggregation. The threedigit Eletronis ISIC, for example, assumes a ommon isoquant for both portable radios and satellites. Thus, our HO Aggregates are better than three-digit ISIC industries in terms of similarity of input intensity and no worse in terms of prie heterogeneity. 4 Finally, note that there is nothing about the proedure for forming HO Aggregates that renders verifiation of the multiple one model a foregone onlusion. By definition, ountry 's apital-labor ratio is a labor weighted average of the apital per labor ratios in eah of its I industries, or K L i I Ki Li Li L i I i. Thus, with at least three HO Aggregates defining two ones of diversifiation, it is possible to test whether the fator intensity of goods produed by a ountry are similar to that ountry's relative 4 In a dynami ontext, our tehnique implies that the underlying pries of the goods in HO aggregates move together, so that, for example, labor-intensive apparel and labor-intensive eletronis pries have a higher orrelation than the orrelations between either labor and apital-intensive apparel or labor and apital-intensive eletronis. Leamer (998) exhibits evidene supporting this assumption. 8

19 endowments. This assertion relies upon the evidene reported in setion 3, whih assoiates heterogeneity of tehnique with the prodution of goods that are not substitutes. 4. A Simple Test for Speialization Using HO Aggregates The simplest method for estimating whether ountries fall into more than a single one of diversifiation is to test if development paths based on extreme HO Aggregates ontain a kink. The intuition for this test is summarized by three panels in figure 6, where eah isoquant is meant to represent one of the IxC ountry-isic pairs from figure 5, kmin and k max represent the minimum and maximum apital intensity of these IxC pairs and k ut represents the apital-labor ratio biseting the isoquants into N= HO Aggregates. Under the null hypothesis of no speialization (left panel), all ountries have positive output of both HO Aggregates irrespetive of how they are split by kut beause all ountries possess at least one ISIC industry with positive output in eah HO Aggregate. As a result, adding a knot at τ = kut to the linear development path of eah of the two HO Aggregates will not improve the model s fit after ontrolling for degrees of freedom. However, under the alternate hypothesis of multiple ones (two right panels), there are two leavages of the IxC ountry-isic isoquants that result in a better fit for the multiple one equilibrium than for the single one equilibrium. The first leavage (middle panel) orresponds to a k ut high enough to exlude any isoquants from a labor abundant ountry. The seond leavage (right panel) orresponds to a k ut low enough to exlude any isoquants from a apital abundant ountry. Note that figure 6 is drawn under the assumption of a three good, two one equilibrium, but this test is general to the atual number of goods. This test unovers evidene of a multiple one equilibrium no matter how many ones atually exist beause it fouses on finding only the most extreme HO Aggregates. We implement it by estimating the N= system of equations X L n = T + t= { } { } K K > τ + β K nt Ι t > τ + ( Land, Skill) β ntι t Φ, L t L L t for a grid of k min, k ) τ knots, where, as above, ( Land, Skill) ( max Φ represents the addition of linear ontrol terms for ropland, forestland and higher eduation. 5 Note that the theoretially implied knot 5 Inlusion of these ontrols does not alter the results substantively. 9