A specification test of the Heckscher-Ohlin theory

dournal of International Economics 25 (1988) 129-141. North-Holland

R&ert W. STAIGER Sta@ord University, Stanjbrd, CA 94305, USA

Receive4 June 1986, re-vise4version receive4fune 1987 Under strong assumptions, the Heckscher~hlin model predictsnot only that factorendowment dietezz% alone 4etermine ma4e patterns,but that they 40 so in a particularlysimple way: the lktor content of trade ahcv~ld be a linear function of national an4 world f-or endowments. The evklent empirical shortcomingsof this simple relationshipnee4 not, however, imply the more generalempiricalfailureof cn4owmcnt-bad tradetheories.This paperprovidesempirical evidence consistent with a more general endowment-base4modei, by showing that the strong HeckscherXMin relationship excludes important additional channels through which f-or endowments alkct the pattern of trade.

Under strong assumptions, the Heckscher-Oh!in (HO) theory provides a model of internationa! trade in which relative factor endowment differences alone distinguish one country from another, and in whicb~through the desire of each country to consume factors in proportion to world rather than national endowments, the factor content of trade is a linear function of national and world factor cndowments~ The !ong empirical tradition of testimg the implications of the HO theory, beginning with the pioneering efforts of Leontief (1954), can be viewed more or less as attempts to test the empirical relevance of this strong theoretical result.’ As Learner(1980) has stressed, in the absence of a well formulated model against which the HO theory can be tested, we can do little more tkan document the model’s ‘accuracy’, and whether one rejects the model on empirical grounds is ultimately a matter of taste. Nevertheless, the bulk of the empirical evidence suggests that the strong HO theory ought not to be viewed as an empirically reliable description of the pattern of international trade.’ an4 two anonymous re data on factor etutowrnents.

LOn the frequency0

onald McKinnon,Steve Colt, gan and StanfordUniversity, n for making availableto me o of my Ph.D. Thesis, The rovi4e4 by the Rackham Fellowship is ). (1985).

130

R. W Sraiger, Test of the Heckscher-Ohlin theory

empirical shortcomings of the strong HO predictions take, however, a second question: Is the notion of factor endowment differences inevitably flawed as a basis from which to construct an empirically acceptable theory of trade, or is it simply that the focus of the strong H8 theory has excluded important channels through which endowments affect the pattern of trade? Certainly, there are theoretical results to suggest that the latter may be the case. For example, relative endowments may affectthe pattern of trade by placing countries in diRerentcones of diversification,a theoretical possibility explored by Brecher and Choudhri (1982) in a two-factor setting Here, though the essence of the factor content version of the strong HO theory is preserved, the precise linear relationship between endowments and factor trade is destroyed. Alternatively, Linder’s (1961) emphasis on nonhomothetic preferences provides a link between international differences in demand patterns and relative capita!,?aborabundance, raising the possibility of a demand-sidechannel though which endowments a&ct trade. And Magee and Young (1987) develop a theory of endogenous tariff formation linking the level of protection to a country’s factor endowments, providing an additional link through which endowments can affect trade patterns. While these and other theoretical results suggest that rejection of the strong HO prediction need not imply a rejection of a more general endowment-basedtheory of trade, no empirical evidence exists on the degree to which the actual effects of endowments on trade are adequately reflected in the strong HO theory. In this paper, a specification test described in Hausman and Taylor (1981) is used to test for evidence that endowments affect trade in important ways not captured by the strong HO relationship. The results indicate that they do. The remainder of the paper proceeds as fallows. Section 2 develops the methodobgy under which estimation and hypothesis testing will be carried out. Section 3 describes the data and considers several issues of measurement. Wesuits are presented in section 4. A u’iscussion of the results are contained in section 5. The 3pparent

General equilibrium trade theories such as the model focus by necessity on a subset of the potential sourxs of comparative advantage. One important empirical question with regard to the strong HO model concerns its ability to explain observed patterns of trade. The extensive em&ical literature that began with Leontief (1954) is an attempt to provide an answer to this question. A second empirical issue concerns whether the contribution of re!ative endowments to the determination of comparative advantage and the pattern of trade is adequately captured by the assumptions 0 model. This section describes a methodology for explorin issue.

R.H! Staiger, Test o,f the Heckscher-Ohlin theory

131

To begin, consider the following specification of the ‘true’ model explaining the factor content of commodity trr--J1 QU_gwith j and m indexing countries and factor:;, respectively:

where q =net exports of the services of tke mth factor by country j, V’i”=endowment of the mtk factor in country jg Vrn =world endowment of the mth factor, % = ( Y,,- Bj)/Y = country j’s share of world expenditure, yi =income of country j, Y = world income, Bi =trade balance of country j, and ZY = the mjth observation on a vector of ‘additional’ explanatory variables. The disturbance term E;”is distributed normally with zero mean and variance a:, and is assumed to be independent of all right-hand-side variables in (1). The true model includes the HO variable, relative factor endowments, entering linearly as one possible determinant of the factor content of trade, but also includes a vector of additional variables q which may enter nonlinear!y through the function g(a). The strong HO model’s exclusive focus on the (linear) contribution of relative factor endowments in explaining the factor content of trade would be empirically justified if the effects of the ZT on the factor content of trade were essentially random and independent of releative endowments. In this case, g( *) could be treated as a zero-mean random vz~=%!~;;‘;”independent of ~7 and of all right-hand-side variables in [I). The strong HO hypothesis can then be written as

a>O,

E@ylVY -SjV”]

@a) =O.

As embodied in conditions

.

W)

(2), (2a) and (2b), the hypothesis says that relative factor abundance is positively and linearly related to tine factor content of net commodity trade, and that the linear effect of endowments on the factor content of trade can be considered independently of the effects of trade determinants not captured by the strong capture the flavor of a commonly held interp re!ationship, as expressed for example by aldwin (1971): Obviously, tke various conditions require osition to be logically valid do not all

RN! Staiger, Test q.f the Heckscher-Ohiin theory

132 Ho~vep,

tiris does not necessarily mean that the Heckscher-Ohhn

theory is a poor theory. IFthe failure of any of the aumptions to hold of the does not systematicallly dnd significar?tSybias the conc!uLGions model, the theory will generally still accurately predict the nature OF trade patterns Froma knowledge OFrelative Factorendowments and thus be a ‘good’ theory (p. 127). Much OFthe existing empirical work on the Factorcontent version of the HO model can ‘becharacter&l i.‘isattempts to test various implications of this joint hypothesis. The early work of Leontief and the voluminous literature that Followedcan be viewed as an attempt to test the empirical relevance OF the model by noting that iF all assumptions OFthe model hold exactly, then ~7 =$’ =!I for al! I and _&and a equals unity. This leads to an exact linear re!ationship between the factor content of trade and relative factor endowments: Fp

VjkJV”.

(3)

Consequently, ‘large’ discrepancies between measures OF Q and either measures of or accepted wisdom about y3(-sqP would imply an empirical refutation OFthe model as a useful approximation of reality. For a model concerned with the direction of trade between countrieq a natura! definition OF‘large’discrqancies would be differencesin sign between the MUand and the right-hand sidt..OF(3). Given the Frequencywith which sign violations have been found in the literature, one would hesitate to consider the HO mode! an empirica!!y re!iab!e description of observed patterns of trade.3 A second iine OFresearchFollowedby Harkness (1983) and Bowen, Learner and Sveikauskas (1987) was to estimate some variant of (2) under the maintained assumption oF(2b) and to test either that a equals unity or that a is positive as in (2a). The conclusions OFthese studies generally support the notion that a positive and linear relationship exists between endowments and the Factorcontent of trade. The implications of such findings are that, while the effects OFendowments as captured by the stro-m UA lLlrwrJ hM,..*=aW a-- ‘I”‘ ..-* lL nr5law * only important determinant OF trade, and may not even be the most important determinant OFtrade, they are at least one important element OF the story, and a model of trade which centers on them is not wholly without empirical content4 l

jThough much of the empiricalwork along these lines was not firmly based iii HO rheory. See, for example, the discussion in DeardartT(198+, Lcamer(1980,1984),or the comments of Learnerand Bowen (1981). 4Eq.(1) in Harkmess(1983)which WBI~ estimatedusing OLS for the United States and Canada follol;?sdirect!yfrom eq. (2) above. Bowen, LBCGI~~ sad Sveikauskas(1987)estimte 11 separate equationsrelatingfactortradeto measuresof factorendowmenrs.Each au&n is derivedfrom a modificationof the HO assumptionswhich leads to a variant of eq. (2) above.

R.W Stuiger, Test of the l-kk~&r-Ohki~ theory

133

What h& not been tested is the orthogonality assumption (25). The empirical validity of this assumption seems important for two reasons. First, it is a maintained assumptioa that underlies ;sheempirical work of studies such as those of Harkness and of Bower, et al., which employ specifications similar to (2). Second, if there exist empirically important effects of factor endowments on factor trade that are not captured in the linear relationship predicted by the strong HO theory, then these effects will show up in @, resulting in a correlat.ion rbetweenit and relative endowments, and violating the orthogonality condition (2b). As such, violation of (2b) can be interpreted as evidence that the strong HO theory does not adequately capture the empirical relationship between factor endowments and trade. This, in turn, would suggest the potential empirical importance of theories which explore alternative channels through which endowments can affect trade. The orthogonality condition (2b) can be tested by pooling data on J countries and M factors over ‘F time periods under the assumption that the fl are time-invariant.5 The time-invariance of the &’ should be exmed for T spanning a relatively short horizon, since the country-specificcharacteristics excMed from the strong HO model are likely to vary widely across countries but to be relatively stable in any particular country over a short period of time. This leads to an error-components rpecification of the HO model as

A test for a specification error in (4) of the form

can be performed following a prczedure outlined in Hausman (1978) and Hausman and Taylor (1981). In particular, define for any variable X$ the following notation:

Thus, X7 is the mean of Xz across time periods, and ;: is the deviation from the mean in each period. Letting X; represent the mjfth observation on swMo muckem@i& woririi- centered on the predictions of the HO theory for a given year across countries and factors, a growing lirerature has explored the model’s empirical performance over time as well. See, for temple, Balasm (1979), who uses cross-sectional data to RI&~ infkmws s&t &G~H ia +Xdowm ts and their elkts on trade patterns, and also Bowen (1983), H&r (1976) and Stem and

134

R.W! Stdger, Test

of fk HeckscMhiin theory

a k-vector of regressors, y a column vector of k coeficients, and Y;: the dependent variable, consider the error-components model given by

possible estimators of the vector of parameters y in (5) are given by the ‘between-groups’ and the ‘within-groups’ estimators. The between-groups estimator, A, can be obtained from OLS applied to the tnrnsformed equation: TWO

q

=xj!y+rc;“+Ej!.

(6)

Under the orthogondity assumptions of the error-components model, A will be an unbii and consistent estimator of y, but will be biked and inconsistent if fl is not orthogonal to the included set of regressors. The within-groups estimator, iv, is obtained from OLS applied to the transformed equation:

Since the time-invariant fl has been eliminated by the within-groups transformation, fW will provide an unbiased and consistent estimate of y regardless of tk orthogonahty properties of ~7. To test the orthogonality property that

against the alternative given by

(9) Hnusman and Taylor (1981) exploit the fact that the within- and betweengroups estimators of y are affecteddifferentlyby violation of (8). Forming the vector

the test statistic 6 can be constructed as

rit= $[cov

(@)I- %j

(11)

Fhere grimes denote transposes and cov(4) PSany consistent estimate of the variance-sovariance matrix of 0 under the nu!) hy thesis in (8). The authors

R.W! Staiger, Test

of the

He&scher-Ohlin

theory

135

show that

and that liz is distributed asymptotically under the null as central & Consequently, a test of the orthogonality n # and the included set of regressors involves calculating ril and comparing it to the critical 2: value at the chosen confidence level.

TO catry out the procedure described in the previous section, data were obtained oka commodity trade, factor endowments, and income for 29 countries over two time periods. A listing of the countries in the sample is contained in table 1. Trade data for the years 1970 and 2976 were obtain& from UN. sources and concorded to the 22 tradable sectors listed in table 2. National income data were collected for 1970 and 1976 from the United Nations Stitistical Abstracts, while trade balances were derived from calculations based on the U.N. trade data. Factor endowment data for the years 1969 and I975 were obtained from H. Bowen, bas& on calculations in Bowen (1980). Finally, U.S. total (direct plw indirect) factor requirement data were used to calculate the factor content of each nation’s net commodity trade v&cir. To mtitruci measures of total factor requirements, the U.S. input/output table for 1972 was used in combimtion with data on direct requiments of labor of three skill groups - skilled, semiskilled and unskilled - and capitai.” A detaiied description of the steps in constructing this data set is included in the appendix. ‘l’hese steps provide data on the f&or content of trade, factor endowments, and expenditure levels for 29 countries, four factors and two time periods. What remaius is to obtain measures of world endowments and expenditure, both of which enter into the right-hand-side of (4). This brings up an important measurement issue, since data on these world variables are aat __svai!nble. In particulia9,while random errors in measuring the factor a___ _ ‘celle for estimation of ( content of trade are not a particularly serious Lmeasurement errors in the right-hand-side variables of (4) would well-known errors-in-variables problems which could themselves lead to a rejection of the orthogonality condition. While it may be reasonable to assume the absence of measurement errors in the national endowment variable V$ for the 29 countries of t sample, any measure of world *U.S. factor coefficientsfor 1972 were applied k0 each country’snet commodity tradev~Xor Ior 1970 and for 1976 The im@is. assumption is that these represent the ‘World’ factOr coefficientsimplid by the HO rn@de8with factor-priceequalization, and that techni~tes Of productiondid not change between 1970 and 1976.

R.W Staiger,Test of the HeckscheH%lintheory

136

Tabk 1 Countriesincluded in the sample. Australia Austria R&&m-Luxembourg Colombia Denmark Pi&id Frana _Y Greece ;;i Kong Ireland Israel

Italy Japan Korea &#eh Netherlands Norway Portugal Spain Swbdea Swimrlar& Turkey United Kingdom united states Yugoslavia

Table 2 Tradablesectors.= ISICgroup rbsscfiptim 1

310 Ml 322 323 324 331 332 341 342 35A -iPP >zL.y 355 36A 362 371 372 381 382 383 384 3FA

Agriculture,bunting, forestry,Ming Food, bevemgq tobacco Textiks Wearingappare&e&ding footwear Leathera kE<er 8t lb products Footwear Wood products,exluding furniture Furniture& titures, excluding metal paper&gapefP~~ Printins publishing IzdustrialChemicals,other chemicalproducts !%@e~u!sr&e&s. lniacelllrrreaus productionof petroleuma axil Rubberproducts Pottery,china, other noametallii mineralproducts pfoducts Glass& Iron & steel basic industries Nonferrousmetal basic industries Metal produe s&uding machinery,etc. Mach.inery,ezc!udiag :lect&zl Electricalmachinery,apparatus,etc. Transportequipment plastic produb-tsn.e.c, photographicg& etc. other manufactures

These sectorscorrespondto those of the MichiganModel of World Production and Trade - see DeardorlTand Stem (1986, ch. 3).

endowments and expenditure derived from this 29-country sample can be no mere than a proxy. avoid the problems associated with random measurement error of the s in handles, estim wit

RM! Ssaiger, Test

of the

Hecksche~r-Qhk:: :kory

137

be written as

!T E=-Vr

t-l,%

m=l,2,3,4.

t

According to the HO theory, &” ought to be negative for all m and t.’ Finally, since units of measument d&x across the four factors, each &servation in (13) is scakd by V?:to yield:

+ e[

Yjf

-BjJ+p’+&$

(14)

where i=11,2, m=l,2,3,4. The specification test of (14) tests the null hypothesis,

against the alternative,

4. Results

As described above, a test for the presence of misspecitication in the relationship involves estimating (14) under tw ‘temative estimators that w~n-~o~~s and withinare affkcted differently by the violation of (15). ‘Although not considering the possibilityof randommeasurementerrorin the right-hand-side variables,Bowen, Lamer and Sveikauskas(1987) find empiricalsupport for a weakened HO relationship that Pr!ows for Hicks-neutraltechnological differencesbetween countries and for F na!!iple. %incethe ‘mismcasurement’ of national factor endowments by a factor-specific auxem of the present paper is with the degree to which the strong adequately tC co&but.,..i-n of factor endowments to the deterzuinlltioasf trade patWn%tin weakened relationship Consequ~t!;-‘,t!x~gb imply dizztly that a

138

R.CC!Steiger, Test qf the Heckscher-Ohlin theory

grotrps estimates of the parameters of (14) are presented in table 3. Under

the null hypothesis of no misspecification, both sets of estimates will be unbiased and consistent, and on those grounds are expected to be similar if the null hypothesis is correct. Under the alternative 4ypothesis of misspeciication, the between-groups estimates will be biased and inconsistent and should thereforediller from the within-groups estimates, which are unaffected by the violation of (85). It appears that there are important difkrences in the two sets of estimates in table 3. In particular, the between-groups estimate of a is insignificantly differentfrom zero while the within-groups estimate of a is significant and of the theoretically expected sign. On the other hand both sets of estimates contain values for four of the eight O’s -. normal&d measures of world endowments with the sign reversed - that are significantly of the wrong sign at the loo/, level. The appropriate statistical framework for assessing the difference in these two sets of estimates is provided by the test statistic rii, given by (11), which is distributed asymptotically as central d under the null hypothesis, where k :S the number of unknown parameters. Calculation of 1 according to (11) yields a value of 248.1 which is well beyond the x$ critical value of approximately 21.7 at the 1% level of confidence. Thw. clear evidence of Table 3 Results ti betweez= and within-pup Coefiicient

Between~up!?

31

-o*oam (0.W) -21.14 (7.26)

0: 0: s: @ 0: 0:

e; e:

’ “hpsdeat

-20.42 (7.27) 1470 (7.26) 12.85 (7.26) 19.17 (5.89) 17.23 (5.92) - 8.38

estitmtbs.’

- -.Within-groups 0.038 (0.0097) 10.85 (1.47) 12.12 (1.48) -3.71 (1.43) -0.44 (4.11) 9.02 ii.iS)

( S.te)

(Z, - 2.42 (1.16)

- 16.67 0.q

- 2.6s (2.94)

mij9h!e

_ - factor content of trade:

F;Ufr;. Standard errors arc shown in parentheses.

R.U!

Staiger,

Test

of the

Heckscher4hlin

theory

i39

misspecification in the strong HO relationship is present: the linear contribution of factor endowments is not independent of other country- and factorspeciGc effects that combine to determine the pattern of international trade.8

The results of this paper suggest two important conclusions with regard to empirical concerns of the HO theory. First, the finding of misspecification casts doubt on the interpretation of regression analyses of the HO model that explicitly or implicitly assume an independence between factor endowments and information excluded from the strong HO theory. Second, the findings indicate the potential empirical importance of theories which explore alternative channels through which endowment differencesaffect the pattern of trade. Whether this points toward the kind of endowmentdetermined demand character&ticsemphasixed by Linder (1961) and more rccentty by Htmtcr and Markusen (1988), or toward the role of relative factor endowments in shaping the politically endogenous patterns of protection discussed by Baldwin (1984) and Magee and Young (1987), or toward the need to allow for PO~‘~~ nA~gsa. zr be M1rrtzA~nhz 1 111111tihrr1sdB ..I l il.W Lwes&m.vmfII*j) betwen endowments and trade brought about by countries whose endowments lie in differentcones of diversification as explored in Learner (1988), is not an issue that can be resolved by the findings of this paper. What is implied by these findings is the empirical imp&ance of exploring these and other extensions of the HO theory. AppfSldiX

This appendix describes the method used to construct measures of total unit factor requirements which were employed in the calculation of the factor content of’ each nation’s net commodity trade vector. Direct plus indirect factor requirements for three kinds of labor and for capital were constructed for the 22 tradable sectors listed in table 2 based on U.S. data for 1970 on direct factor requirements and the 1972 U.S. input/output table. The three labor skill groups were chosen to be compatible with the labor endowment data, as described in Bowen (1980). The endowment data defines skilled labor as the number of workers classified as professional or technica!, semiskilled labor as the labor force times the literacy rate minus skilled workers, and unskilled labor as one minus the national literacy rate times the labor force Using U.S. data from the 1971 Survey of Occupational Employment, direct inputs of skilled !abor, as defined above, were calculat for the 22 tradable a&-r endowments are interpretedhere as the *In lceepp~g-withthe HO modeling tradition, f-, exogenous variablesthat kause’ everythingelse_However,an alternativeinterpretationoI’these results is that factor endowments act in kc: cndogzxus.

140

R.R Staiger,Test qf the HeckscMMin

theory

industries of table 2 and seven additionai nontradable sectors. Direct inputs of semiskilled labor for each of the 29 sectors were defined as the number of s&es and clerical -workers,operatives, craftsmen, service workers, managers, and administrators, while direct inputs of unskilled labor were calculated as ?he number of fa-rmand nonfarm laborers. For manufacturing sectors, direct inputs of capital in 1970 wWq con&u&d f&m the Bureau of Labor Statistics Economic Growth Project capital data series compiled by 3ack Faucett Associates. Capital inputs into nomnanuffacturingsectors were estimated using data faom the 1972 Capital .Fio~ Tables published in the Survey of Current Business. For this calcu~ iation, it was assumed that the relationship between capital flows and stocks in each nonmanufacturingsector is the same as in the manufacturing sector as a whole. The 1972 U.S. input/output table was concorded to the 290sectorlevel, and its Leontief inverse used to calculate the direct~pius-indirectfactor requirements for the 22 tradable sectors. Finally, multiplying each country’s net commodity trade vector by the matrix of gross factor inputs yields the factor content of trade used in the empirical work of this paper.

m

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