An Account of Global Factor Trade - Columbia Universitydrd28/hov.pdf · 2009-01-22 · An Account...

An Account of Global Factor Trade

By DONALD R. DAVIS AND DAVID E. WEINSTEIN*

A half century of empirical work attempting to predict the factor content of trade ingoods has failed to bring theory and data into congruence. Our study shows how theHeckscher-Ohlin-Vanek theory, when modified to permit technical differences, abreakdown in factor price equalization, the existence of nontraded goods, and costsof trade, is consistent with data from ten OECD countries and a rest-of-worldaggregate.(JEL F1, F11, D5)

A central objective of international economicresearch has been to account for the factorcontent of trade. There are two principal rea-sons. The first is that economists want to tracethe effects of international influences on rel-ative and absolute factor prices within a coun-try. The Heckscher-Ohlin model and itsvariants, with their emphasis on trade arisingfrom differences in the availability of produc-tive factors, provide a natural setting for suchinvestigations.1

The second reason for the focus on the factorcontent of trade is that it provides a concreteprediction against which to measure how wellour models work. The models are extraordinaryin their ambition. They propose to describe,with but a few parameters and in a unifiedconstellation, the endowments, technologies,

production, absorption, and trade of all coun-tries in the world. This juxtaposition of extraor-dinary ambition and parsimonious specificationhave made these theories irresistible to empiri-cal researchers.

In recent years, empirical research has fo-cused on the Heckscher-Ohlin-Vanek (HOV)theorem because of the sharp predictions thatthis theory has for the links between trade,technology, and endowments. The HOV theo-rem yields a simple prediction: The net exportof factor services will be the difference betweena country’s endowment and the endowment typ-ical in the world for a country of that size. Theprediction is elegant, intuitive, and spectacu-larly at odds with the data.

Wassily Leontief’s (1953) “paradox” iswidely regarded as the first blow against theempirical validity of the factor proportions the-ory. Confirmation of the paradox in later workled Keith E. Maskus (1985) to dub it the“Leontief commonplace.” In one of the mostwidely cited and seemingly damning studies,Harry P. Bowen et al. [henceforth BLS] (1987)report that country net factor service exports areno better predicted by measured factor abun-dance than by a coin flip. In a major contribu-tion, Daniel Trefler (1995) documented the“mystery of the missing trade”—that measuredfactor service trade is an order of magnitudesmaller than that predicted based on nationalendowments. This point is underscored in workby Xavier Gabaix (1997). Davis et al. (1997)[henceforth DWBS] do report positive resultsfor a variant of the HOV model. However theyaccomplish this by restricting the sample forwhich factor price equalization (FPE) is as-sumed to hold to regions of Japan and by

* Department of Economics, Columbia University, NewYork, NY 10027, and National Bureau of Economic Re-search. We are grateful to Alan Deardorff, Gene Grossman,and Elhanan Helpman for very helpful comments. Much-appreciated support for this project has come from theNational Science Foundation, the Harvard Institute for In-ternational Development, and the Clark Fund. Davis thankscolleagues at the Federal Reserve Bank of New York, wherepart of the work on this paper was completed. The viewsexpressed in this paper do not necessarily reflect those of theFederal Reserve. We have benefited from excellent researchassistance by Paris Cleanthous, Joshua Greenfield, WilliamPowers, and especially Pao-Li Chang. Shang-Jin Wei gra-ciously provided us with distance data.

1 One measure of the importance and freshness accordedthis issue is that theJournal of International Economicsdevoted much of its February 2000 Jubilee Issue to a seriesof articles by Edward E. Leamer et al., debating preciselythis question of when and how one can convert from mea-sured factor contents to implied effects on national factorprices.

1423

remaining agnostic about the degree to whichthe FPE framework can be extended acrossnations.

Our current research follows the recent lit-erature in asking if parsimonious amendmentsallow the model to match the data. However,in contrast to all prior work, we have suffi-cient data on technology and absorption toestimate the structural parameters directly.Having estimated these directly from the dataof interest, we then impose the resulting re-strictions in our tests of the HOV model. Bystarting with the basic model and relaxing oneassumption at a time, we see precisely howimprovements in our structural model trans-late into improvements in the fit of the HOVpredictions.

The results are striking. The step-by-step in-troduction of our key hypotheses yields corre-sponding improvement in measures of modelfit. Countries export their abundant factors andin approximately the right magnitudes. The re-sults are remarkably consistent across variationsin weighting schemes and sample. As in priorstudies, the simple HOV model is strongly re-jected by the data. However a model that allowsfor technical differences, a breakdown of factorprice equalization, the existence of nontradedgoods, and costs of trade, is consistent with datafor ten OECD countries and a rest-of-worldaggregate.

I. Theory

Various hypotheses have been advanced toaccount for the divergence of theory and data,such as technical differences and divergences indemand structure. These have so far provedwholly insufficient to bridge the gap betweentheory and data. Nonetheless, they are likely tobe part of a complete account. We advanceseveral new hypotheses with the hope of pro-viding a first successful match.

A successful account should provide a par-simonious and plausible set of departuresfrom the standard model. In order to under-stand the role played by each of the assump-tions, it is important, both in the theory andempirics, to begin with the standard model,relaxing the assumptions one at a time. Thenovel elements of the theory are two. The firstis to show, in an approximate FPE world, how

aggregation may systematically bias mea-sured factor trade downward relative to thetheoretically appropriate measure. The secondis to develop factor content predictions for thecase with no FPE that recognize the crucialrole played in this case by the nontradedsector. These theoretical departures are devel-oped in this section and implemented empir-ically in the following section.

A. The Standard HOV Model

We begin by developing the standard HOVmodel from first principles. Assume that allcountries have identical, constant returns toscale production functions. Markets for goodsand factors are perfectly competitive. There areno barriers to trade and transport costs are zero.The number of tradable goods is at least as largeas the number of primary factors. We assumethat the distribution of these factors acrosscountries is consistent with the world replicat-ing the integrated equilibrium (cf. Avinash K.Dixit and Victor Norman, 1980). Then factorprices will be equalized, so all producers willchoose the same techniques of production. Letthe matrix of total (direct plus indirect) factorinputs for countryc be given byBc. This hasdimension equal to the number of factors timesthe number of goods. The foregoing implies thatfor all countriesc:

Bc 5 Bc9 5 B ; c, c9.

These assumptions enable us to use a singlecountry’s technology matrix (in prior studies,typically that of the United States) in orderto carry out all factor content calculations. Wenow can relate endowments and production:

BcYc 5 Vc 5 BYc

whereVc is the endowment vector for countrycand Yc is the net output vector for countryc.The first equality is effectively a factor market-clearing condition, while the second embodiesthe assumption of FPE.

The standard demand assumption is based onidentical and homothetic preferences acrosscountries. With free and costless trade equaliz-

1424 THE AMERICAN ECONOMIC REVIEW DECEMBER 2001

ing traded goods prices and FPE equalizingnontraded goods prices, the demand in a coun-try will be proportional to world net output:

Dc 5 scYW

whereYW is net output for the world. Premul-tiplying this by the matrix of total factor inputsconverts this to the factor contents:

Bc9Dc 5 scBc9YW 5 scVW.

The first equality follows simply from the as-sumption of identical homothetic preferencesand common goods prices. The second relies onthe fact that FPE insures that all countries usethe common technology matrixBc9.

Collecting terms, we can state the two keytests of the standard HOV model:

Production Specification (P1):Bc9Yc 5 Vc for a specified common

technology matrixBc9.Trade Specification (T1):

Bc9Tc 5 Bc9(Yc 2 Dc) 5 Vc 2 scVW @c.

Here and in subsequent specifications of bothproduction and trade it will be convenient todistinguish the left- and right-hand sides of theequation respectively as themeasuredandpre-dicted factor contents of trade.

B. A Common Technology MatrixMeasured with Error

The foregoing assumes that both the true andmeasured technology matrices are identicalacross countries. A glance at the measured tech-nology matrices reveals this is not the case.Before we pursue more elaborate hypotheses onthe nature of actual technological differences, itis worth investigating the case in which thetechnology matrices are measured with error.Assume that for countryc the measured tech-nology matrix is given as:

ln Bc 5 ln Bm 1 «c

where each element of lnBm is the naturallogarithm of the corresponding element of thetrue technology matrix and«c is a matrix of

normal error terms. This gives rise to our sec-ond set of tests:

Production Specification (P2):BmYc 5 Vc.

Trade Specification (T2):BmTc 5 Vc 2 scVW ; c.

C. Hicks-Neutral Technical Differences

A wide body of literature, both in productiv-ity and in trade, suggests that there are system-atic cross-country differences in productivity,even among the richest countries [e.g., Dale W.Jorgenson and Mashiro Kuroda (1990)]. This isvery likely an important reason why Trefler(1995) found that the data suggests poor coun-tries are “abundant” in all factors and vice versafor the rich countries. BLS (1987) and Trefler(1995) have focused attention on Hicks-neutraltechnical differences as a parsimonious way tocapture these effects. Under this hypothesis, thetechnologies of countries differ only by a Hicks-neutral shift term. This can be characterized viacountry-specific technology shiftslc:

Bc 5 lcBl ; c.

In order to implement an amended HOV equa-tion, it is convenient to think of the productivitydifferences as reflecting efficiency differencesof the factors themselves (rather than technol-ogy per se). For example, if we take the UnitedStates as a base, and U.S. factors are twice asproductive as Italian factors, thenlItaly 5 2. Ingeneral, we can express a country’s endow-ments in efficiency terms:

V cE 51

lc Vc ; c.

The standard HOV equation then holds whenthe endowments of each country are expressedin efficiency units:

Production Specification (P3):BlYc 5 VcE.

Trade Specification (T3):BlTc 5 VcE 2 scVWE ; c.

All succeeding models and the associated em-pirical specifications will be in efficiency units,

1425VOL. 91 NO. 5 DAVIS AND WEINSTEIN: AN ACCOUNT OF GLOBAL FACTOR TRADE

although we will henceforth suppress the super-script E for simplicity.

D. Dornbusch-Fischer-Samuelson Model

So far we have allowed differences in inputcoefficients across countries only as a Hicks-neutral shift, which we refer to as “adjustedFPE.” For cases of adjusted FPE, this impliesthat capital to labor ratios are fixed by industryacross countries. However, there is good reasonto believe this is not the case. The simpleRybczynski relation suggests that countrieswith a relatively large stock of capital shouldhave an output mix shifted toward relativelycapital-intensive goods, but with FPE theyshould not use different input coefficientswithin any individual sector. David Dollar et al.(1988) estimated cross-country differences incapital to labor usage and found this was cor-related with country capital abundance.

From a theoretical perspective, the correlationbetween country factor abundance and industryfactor usage could arise for either of two reasons.First, as Dollar et al. argued, it could reflect abreakdown in factor price equalization. We con-sider this possibility in the next subsection. Beforedoing so, however, we want to consider a simplerhypothesis. This is the hypothesis that FPE isapproximatelycorrect and that the differences ininput usage by industry that we observe acrosscountries arises almost exclusively due to aggre-gating goods of heterogeneous factor contentwithin industry categories.

In a two-country Dornbusch-Fischer-Samuel-son-type model with approximate FPE and thistype of aggregation problem, we would expect tofind that industry input usage is correlated withcountry capital abundance for tradables, but notfor nontradables.2 The reason is that the necessityfor each country to produce its own nontradables,in combination with the standard assumptions onpreferences, implies that input ratios will differ atmost trivially for the nontraded sectors.

There is one additional assumption that isuseful in thinking about why previous studiesmeasured the factor content of trade to be so

low. This is that the empirical industrial aggre-gates cover a very wide range of goods, somenontraded, some traded, only some of the latterproduced in any one country. Since virtually allprevious studies have used the capital-abundantcountry’s (in practice the United States) tech-nology coefficients to measure the factor con-tent of trade for all countries, there will arise inthis framework a downward bias in the factorcontent of trade for both countries. The reason-ing is as follows. If all goods have the sametrade costs, then nontraded goods will tend to bethose of intermediate factor intensity. Exportsfrom the capital-abundant country in a givenindustry are more capital intensive than totalproduction in that industry because of the pres-ence of these nontraded goods. Thus by em-ploying average input coefficients, there is adownward bias in the measured capital content ofthe capital-abundant country’s exports. Measuredcapital intensity in the importable industry willlikewise be a weighted average of the traded andnontraded goods produced in that empirical indus-try in the capital-abundant country. But thisstrongly understates the labor intensity of imports,because the goods actually imported are noncom-peting, so do not even figure into the calculation ofthe input coefficients. In this two-country frame-work, the factor content of trade will be down-ward biased for both countries.3

These insights motivate a specification whichexplicitly recognizes that (1) The factor contentof production in tradable industries varies sys-tematically with country capital abundance; and(2) The factor content of absorption must bemeasured bilaterally with the producer coun-try’s input coefficients.4 This gives rise to thefollowing specifications:

2 These ideas are developed in greater detail in aDornbusch-Fischer-Samuelson-type setting in Davis andWeinstein (1998). See also Yingfeng Xu (1993).

3 The situation is a little more complicated in a many-country world. What we can say is that the strength of thedownward bias will be greatest for those countries withextreme factor abundance. As predicted factor contents getsmaller, the degree of downward bias would be expected todecline. However, since it is the countries with little mea-sured factor service trade and extreme factor abundancesthat are most important in generating the mystery of themissing trade, this bias is likely to be important.

4 It is worth noting that this ameliorates the aggregationproblem in tradable sectors across countries that arises fromthe fact that they may produce distinct goods; howeverwhen we turn to the data exercises, we will not be able towholly eliminate the aggregation problem caused by thecontrast between average and exportable input coefficients.


Production Specification (P4):BcDFSYc 5 Vc.

Trade Specification (T4):

BcDFSYc 2 FBcDFSDcc 1 Oc Þ c9

Bc9DFSM cc9G5 Vc 2 scVW.

where the superscript inBcDFS reflects the factthat in the continuum of goods, Dornbusch-Fischer-Samuelson model, the unit input re-quirementsin the tradable goods sectorswillvary in accordance with the country’s capital tolabor ratio.

E. Case Without Factor Price Equalization

Elhanan Helpman (1999) proposes an ac-count of the missing trade in the same spirit asthe continuum model, but which focuses onmore substantial departures from FPE and theexistence of specialization “cones” of produc-tion in tradables.5 One consequence of this isthat the common set of nontraded goods will beproduced using different techniques. In turn,this will affect our HOV factor content predic-tions. We now consider the implications.6

To arrive at a definite result, we need to applya little more structure on demand than is stan-dard. Consider a world with any number ofcountries, two factors (capital and labor) and inwhich the extent of differences in endowmentsis sufficient that at least some countries do notshare factor price equalization. We do not re-

strict the number of nontraded goods, althoughwe assume that the number of traded goods issufficiently large that we can safely ignoreboundary goods produced by countries in ad-joining production cones with different produc-tion techniques. Define a countryc’stechnology matrix at equilibrium factor pricesin the Helpman no-FPE model asBcH 5[BcHNBcHT], where the partition is betweennontradables and tradables. Let output be simi-

larly divided, so Yc 5 F YcN

YcT G . Then the

factor content of production, by factor marketclearing, isBcHYc 5 Vc. If we separate outnontradables and rearrange, we getBcHTYcT 5Vc 2 BcHNYcN. Let us call the expression onthe right Vc 2 BcHNYcN [ VcT, so thatBcHTYcT 5 VcT. With no FPE, the prices ofnontraded goods in terms of tradables will typ-ically differ across countries. Assume that pref-erences in all countries between tradables andnontradables are similar and Cobb-Douglas, sofeature fixed expenditure shares. Letsc be coun-try c’s share of world income (in units of trad-ables). Then it follows thatsc is alsoc’s share ofworld spending on tradables.

Assume that preferences across countries fortradables are identical and homothetic. The ab-sorption by countryc of tradable goods pro-duced inc9 is thenDcc9T 5 scYc9T. The factorcontent of this absorption, using the factors ac-tually engaged in production of the good, isBc9TDcc9 5 scBc9HTYc9T 5 scVc9T. DefineVWT [ ¥c VcT and note that forc Þ c9,Dcc9T [ Mcc9 (imports). Then it follows that:

BcHTYcT 2 FBcHTDccT 1 Oc9 Þ c

Bc9HTM cc9G5 VcT 2 scVWT.

That is, under the conditions stated above, weget something very much like the simple HOVequation so long as we restrict ourselves toworld endowments devoted to tradable produc-tion and weight absorption according to theactual coefficients employed in production.

We now need to contemplate the implicationsof this model for what we will observe in thedata. We know that input coefficients both intradables and in nontradables will differ across

5 In the theory, the failure of FPE is taken to be due toendowment differences. Unfortunately the analysis does notcarry over precisely for the case in which the failure of FPEis due to nonnegligible trade costs. The key difficulty is thatin general one would no longer expect the factor content ofconsumption of tradables to bescVWT. If one were willingto place enough structure on the problem, including assum-ing a symmetric geography, then one could get a verysimilar expression with a correction for the overconsump-tion of home goods and underconsumption of goods fromthe remaining countries. However we are not happy dealingin this way with the (important) fact that trade costs matter.See the approach of trade test (T7) below.

6 Adrian Wood (1994) likewise emphasizes that inputcoefficients differ within the same industry for traded goodsproduced in a developing country as opposed to a developedcountry.


countries. The failure of FPE plays a role inboth cases, but they have important differences.The input coefficients differ in tradables be-cause the failure of FPE has led the countries tospecialize in different goods. They differ innontradables because the same goods are pro-duced with different factor proportions. Let usexpand the equation above:


Bc9HTM cc9G5 VcT 2 scVWT

5 @Vc 2 BcHNYcN#

2 scF Oc9

$Vc9 2 Bc9HNYc9N%G .

The right-hand side of this equation can berearranged to be:

5 @Vc 2 scVW#

2 FBcHNYcN 2 sc Oc9

Bc9HNYc9NG .

If we denote byVcN the resources devoted incountry c to production of nontradable goods(and correspondingly for the world), then ourproduction and trade tests can be written as:

Production Specification (P5):BcHYc 5 Vc.



Bc9HTM cc9G5 @Vc 2 scVW# 2 @VcN 2 scVWN#.

where the superscript inBcH reflects the factthat in the no-FPE model, all input coefficientsin a country’s technology matrix will vary ac-cording to the country’s capital to labor ratio.

The first term on the right-hand side in (T5) isthe standard HOV prediction, while the secondis an adjustment that accounts for departures in

factor usage in nontradable goods from theworld average. Note, for example that a capital-abundant country will have high wages, induc-ing substitution in nontradables toward capital.The second bracketed term will typically bepositive then for the case of capital, meaningthat the simple HOV prediction overstates howmuch trade there really ought to be in capitalservices. In the same case, the actual labor us-age in nontradables is less than the world aver-age, and so the simple HOV equation will tendto overstate the expected level of labor serviceimports. In both cases, the new prediction forfactor service trade will be less than that of thesimple HOV model.

In trade specification (T6) we explore how ourestimates of ROW (“Rest of the World”) technol-ogy affect the results. We will discuss this ingreater detail later, but in theoretical terms (T6) isthe same as (T5). We now turn to results focusedon the absorption side of the model.

F. Demand, HOV, and Gravity

Among the more outlandish simplificationsin the HOV model is the assumption that inter-national trade is wholly costless. This is false onits face and overwhelmingly refuted by the data[John McCallum (1995); Charles Engel andJohn H. Rogers (1996)]. The consequence forunderstanding net factor trade is that the fric-tionless model wildly overstates the expectedvolume of trade and so also overstates the op-portunities for arbitrage of factor price differ-ences. This may well be important inunderstanding why the measured factor trade inprevious studies is below that predicted by thefrictionless model.

A key question, then, is how to incorporatetrade frictions into our framework. One ap-proach would be to take direct measures of costsof trade such as tariffs, nontariff barriers, trans-port costs, etc. and to combine this with infor-mation about import demand elasticities tocalculate departures from the predictions of thefrictionless model. While this would likely pushin the right direction, it has severe shortcom-ings. There are good reasons to believe thatthese overt measures of costs of trade are inad-equate to the task. James Harrigan (1993) showsthat the measures we have for nontariff barriersshow very little impact on trade volumes in the


OECD relative to tariffs, which are themselveslow. Nonetheless, as McCallum (1995) hasshown, the international trade volumes aremuch too low to be accounted for by the level oftariff barriers and direct trade costs we observe.David L. Hummels (1999a, b) has undertakenthe important task of improving our measures oftrade costs and thinking hard about the role theyplay. However, we do not believe that the liter-ature is yet sufficiently developed to pursue thisdirect approach.

Since these direct measures of trade costs arelikely to prove problematic, we turn to themodel of trade volumes known as the gravityequation, which uses distance as a proxy forcosts of trade. This model of trade volumes isknown to be very successful. As appears inJames E. Anderson (1979), Jeffrey H. Berg-strand (1990), and Alan V. Deardorff (1998), agravity equation arises very simply when thereis a high degree of production specialization,similarity of preferences, and costs of trade. Thegravity model has not appeared previously inempirical tests of the HOV factor content pre-dictions. The reason is that the bilateral traderelations posited in the gravity model are nottypically well defined in a many-country HOVmodel [see Deardorff (1998) and Trefler(1998)]. However, they are well defined in theproduction model we have developed preciselybecause all countries feature perfect specializa-tion in tradables.

In this case, the demand for imports bilater-ally has to be amended to account for bilateraldistance. Letdcc9 be the distance between coun-triesc andc9. Leaving aside the issue of marketclearing for a moment, a simple way to intro-duce trade costs is to posit that import demandin countryc for products fromc9 takes the formof a standard gravity equation:

ln~Micc9! 5 a0i 1 a1iln~si

TcXic9!

1 d iln~dcc9 ! 1 z icc9

wheresiTc is total domestic absorption (of final

and intermediate goods) as a share of worldgross output,Xi

c9 is gross output in sectori incountryc9, thea’s and thed are parameters tobe estimated, andz is a normal error term. Theparameter estimates can then be used to gener-ate predicted imports,Mcc. While the gravity

model is quite successful at predicting bilateralimport flows, own demand seems to be deter-mined by a quite different process (see McCal-lum, 1995). Rather than trying to model thisprocess directly, we solve the problem with atwo-step procedure. Bilateral import demand isgenerated from the parameters of the gravityequation. We then set demand for domesticallyproduced goods equal to the difference betweentotal country demand in sectori and total im-ports predicted from the gravity equation. Thisimplementation method enables us to imposethe condition that the predicted total demandequals actual total demand. Nonetheless, devi-ations caused by the failure of the gravity equa-tion to describe real trade flows could still causeproblems with our demand approach.

Measured net factor trade will be exactly thesame as in (T5) above. However, in this case thepredicted factor content of absorption of trad-ables is no longerscVWT. Instead the predic-tions for bilateral absorption must be thosegenerated by the gravity specification, weightedby the factor usage matrices appropriate to eachpartner. Let carets indicate fitted values. Thisgives rise to:


BcHYc 2 FBcHDcc 1 Oc9 Þ c

Bc9HM cc9G5Vc 2 FBcHDcc 1 O

c9 Þ c

Bc9HM cc9G .

We wish to emphasize that the approachreflected in trade specification (T7) representsa significant departure from that in earlierspecifications. It incorporates directly fittedvalues for import demand and complementarymeasures of own demand to generate the fac-tor content of consumption. In doing so, ittakes a larger step away from conventionalHOV predictions, which generate the pre-dicted factor content of consumption baseddirectly on endowment data. The reason forpursuing this direction, this shortcoming not-withstanding, is that it will provide insightinto how much further gain can be expectedfrom a more complete model that does a


better job than standard HOV in predictingaggregate trade volumes.7

G. Summary of Specifications

The seven different specifications can begrouped in a variety of ways. In order to helpkeep the assumptions underlying these specifi-cations clear, we summarize the four key group-ings below:

Yes No

I. All countries share a commontechnology matrix (Absolute FPE) (T1)–(T2) (T3)–(T7)

II. FPE (Absolute, Adjusted, orApproximate) (T1)–(T4) (T5)–(T7)

III. Industry capital to labor ratiosidentical across countries (T1)–(T3) (T4)–(T7)

IV. Identical, homothetic preferenceswith zero trade costs (T1)–(T6) (T7).

II. Data Sources and Issues

A. Data Sources

An important contribution of our study is thedevelopment of a rich new data set for testingtrade theories. This has been a major project onits own. We believe that the data set we developis superior to that available in prior studies innumerous dimensions. The mechanics of con-struction of the data set are detailed in the DataAppendix. Here we provide a brief descriptionof the data and a discussion of the practical andconceptual advances.

The basis for our data set is the Organization

for Economic Cooperation and Development’sInput-Output Database [OECD (1995)]. Thisdatabase provides input-output tables, grossoutput, net output, intermediate input usage,domestic absorption and trade data for 34 in-dustries in ten OECD countries.8 Significantly,all of the data are designed to be compatibleacross countries. We constructed the countryendowment data and the matrices of direct fac-tor input requirements using the OECD’s Inter-national Sectoral Database and the OECD’sSTAN Database. Hence for all countries, wehave data on technology, net output, endow-ments, absorption, and trade. By construction,these satisfy:

(1) BcYc ; Vc.

(2) Y c 2 Dc ; Tc.

We also have data for 20 other countries thatwe aggregate and refer to as the “Rest of theWorld” or ROW.9 Data on capital is derivedfrom the Robert Summers and Alan W. Heston(1997) Database while that for labor is from theInternational Labor Organization. For countriesthat do not report labor-force data for 1985, wetook a labor-force number corresponding to theclosest year and assumed that the labor forcegrew at the same rate as the population. Grossoutput data are taken from the United Nation’sIndustrial Statistics Yearbook,as modified byDWBS (1997). Net output is calculated by mul-tiplying gross output by the GDP-weighted av-erage input-output matrix for the OECD andsubtracting this from the gross output vector.

Bilateral trade flows for manufacturing be-tween each of our ten OECD countries as wellas between each country and the ROW weredrawn from Robert C. Feenstra et al. (1997) andscaled so that bilateral industry import totalsmatch country totals from the input-output (IO)

7 The fact that the gravity model is generally known toperform well in predicting trade volumes may make it seemlikely that an improvement will result. Hence it is reason-able to ask what additional insight is gained from thisexperiment beyond a reaffirmation that the gravity model ofdemand fits well. We think that we do continue to learn alot. First, while industry-level gravity regressions do a goodjob of predicting trade volumes, with typicalR2’s of ap-proximately 0.7 in our runs, a great deal of this comes fromsize differences that may mask large proportional predictionerrors. Second, nothing precludes the possibility that theerrors may be systematic in a way that disrupts our HOVprediction. Finally, there is little doubt that there are a largenumber of considerations that potentially could be intro-duced to the analysis (e.g., industry-level scale economies).It is revealing to see how much incremental explanatorypower is attained by better predictions of trade volumes andalso revealing to see how much remains to be explained bythe myriad factors excluded from the analysis.

8 Australia, Canada, Denmark, France, Germany, Italy,Japan, Netherlands, United Kingdom, and the United States.These are the ten available in the IO database.

9 Argentina, Austria, Belgium, Finland, India, Indonesia,Ireland, Israel, Korea, Mexico, New Zealand, Norway, Phil-ippines, Portugal, Singapore, South Africa, Spain, Sweden,Thailand, and Turkey. These are the countries for whicheither gross output or value added is available for all sectors.


tables. Countryc’s bilateral imports from coun-try c9 in nonmanufacturing sectori is set equalto the share of countryc’s total manufacturingimports that came from countryc9 times totalnonmanufacturing imports in sectori .10 ROWabsorption was then set to satisfy condition (2)above.11 Bilateral distance data comes fromShang-Jin Wei (1996).

In sum, this data set provides us with ten setsof compatible technology matrices, output vec-tors, trade vectors, absorption vectors, and en-dowment vectors. In addition we have a data setfor the ROW that is comparable in quality tothat used in earlier studies.

B. Data Issues

We would emphasize several characteristicsof the data to underscore its advantage overprior data sets. The first draws on the nature ofthe tests considered. The prior work is uniformin rejecting the simplest HOV model. Hence themost interesting work has gone on to consideralternative hypotheses. Importantly, the mostprominent of these theories concern alterationsin assumptions about technological similarityacross countries (e.g., Hicks-neutral technicaldifferences) and the structure of absorption(e.g., a home bias in demand). Yet typicallythese studies have only a single observation ontechnology (that of the United States) and no

observations whatsoever on the structure of ab-sorption. The technological and absorption pa-rameters are chosen to best fit the statisticalmodel, but these yield little confidence that theytruly do reflect the economic parameters of in-terest.12 Our construction of the technology ma-trices allows us to test the theories oftechnological difference directly on the relevantdata and similarly for our hypotheses aboutabsorption. This ability to directly test the cross-country theories of interest greatly enhances ourconfidence that the estimated technology andabsorption parameters indeed do correspond tothe economic variables of interest.

A second issue is the consistency with whichthe data are handled. In part this corresponds tothe fact that we are able to rely to a great extenton data sources constructed by the OECD withthe explicit aim to be as consistent as practica-ble across sources. In addition, the OECD hasmade great efforts to insure that the mappingbetween output data and trade categories issound. Finally, the consistency extends also toconditions we impose on the data which shouldhold as simple identities, but which have failedto hold in previous studies because of the in-consistencies in disparate data sets. These re-strictions include that each country actuallyuses its own raw technology matrix, reflected inBcYc [ Vc.13

We would also like to note, though, that thedesire to bring new data sources to bear on theproblem has carried a cost. Specifically, thefactors available to us for this study are limitedto capital and aggregate labor. We would verymuch have liked to be able to distinguish skilledand unskilled workers, but unfortunately thenumber of skilled and unskilled workersbyindustry is not available for most countries.

We would like to note how the reader shouldthink about this factor “aggregate labor,” andwhy we do not believe this presents too great aproblem for our study. There are at least acouple of interpretations that can be given. Afirst fact about our labor variable is that undermost specifications the OECD countries arejudged scarce in labor while the ROW is

10 This is not ideal, but given that the median ratio ofimports to gross output in sectors outside of agriculture,mining, and manufacturing for our sample of countries is 1percent, this is not likely to introduce large errors.

11 It is reasonable to ask why we aggregated the ROWinto one entity rather than working with each country sep-arately. A major strength of this paper is that our data arecompatible and of extremely high quality. Unfortunately,the output and endowment data for the ROW countriesare extremely noisy (see Summers and Heston [1997] fora discussion of problems with the endowment data). It isquite difficult to match U.N. data with OECD IO databecause of aggregation issues, varying country industrydefinitions, and various necessary imputations (seeDWBS [1997] for details on what calculations werenecessary). As a result, the output and absorption num-bers of any individual country in the ROW are measuredwith far more error than OECD data. To the extent thatthese errors are unbiased, we mitigate these measurementerrors when we aggregate the ROW. In view of all this,we decided that we did not want to pollute a high qualitydata set with a large number of poorly measured obser-vations.

12 Helpman (1999).13 See the discussion in BLS (1987) of related difficul-

ties. The only exception to this is the ROW where we wereforced to use an estimatedB. See Section III for details.


abundant in it. This suggests that one appropri-ate interpretation is that our variable labor is avery rough proxy for unskilled or semiskilledlabor. Note, though, that in most of our laterimplementations, labor is converted to effi-ciency units. If this is an appropriate way tomerge skilled and unskilled, then the fact thatthese OECD countries are scarce in it sug-gests that this is true, even when we convertall labor to common efficiency units. We havelittle doubt that if it were possible to distin-guish highly skilled labor separately for ourstudy, the United States and some of the otherOECD countries would be judged abundant inthat factor.

These reservations notwithstanding, we be-lieve that there are good reasons to believe thatchoice of factors does not confer an advantageto us over prior studies. Many of the factors weomit are land or mineral factors, which were thebest performers for BLS (1987) and Trefler(1995). Hence their omission should only workagainst us. As we will see below, the factors thatwe do include exhibit precisely the pathologies(e.g., “mystery of the missing trade” and theLeontief paradox) that have characterized thedata in prior studies. Finally, in our study of thenet factor trade of Japanese regions, DWBS(1997), we were able both to include morefactors and to distinguish between skilled andunskilled workers. The HOV theory performedadmirably in these circumstances. These pointssuggest that, if anything, the unavailability offactor data for our study may make it moredifficult to find positive results for HOV, noteasier.

In sum, we have constructed a rich new dataset with compatible data for ten OECD coun-tries across a wide range of relevant variables.Importantly, we introduce to this literature di-rect testing on technology and absorption dataof the central economic hypotheses in contest.Finally, although in some respects the availabledata fall short of our ideal, we do not believethat this introduces any bias toward favorableresults.

III. Statistical Tests on Technologyand Absorption

Our principal statistical tests will work di-rectly with the data on technology and absorp-

tion. We consider a variety of assumptionsregarding technology and absorption suggestedby theory and let the data select a preferred set.In Section IV we will implement each of themodels of technology and absorption. In doingso, we will gain a rich view of the role playedby each change in improving the working of theHOV model. For reference, we will indicate theproduction specification associated with the dis-tinct models of technology.

A. Estimating Technology

Our first model of technology (P1) is thestandard starting point in all investigations ofHOV: it postulates that all countries use identi-cal production techniques in all sectors. Thiscan be tested directly using our data. For anycountriesc and c9, it should be the case thatBc 5 Bc9. We reject this restriction byinspection.

One possible reason for cross-country differ-ences in measured production techniques issimple measurement error (P2). The Italian air-craft industry is four times as capital intensiveas the U.S. industry. While this may indicatedifferent production techniques, the fact thatnet output in U.S. aircraft is approximately200 times larger than in Italy raises the ques-tion of whether the same set of activities arebeing captured in the Italian data. This raisesa more general point that is readily visible inthe data. Namely extreme outliers in mea-suredBc tend to be inversely related to sectorsize. In tests of trade and production theorythis is likely to produce problems when ap-plying one country’s technology matrix toanother country. If sectors that are large in theUnited States tend to be small abroad, thenevaluating the factor content of foreign pro-duction using the U.S. matrix is likely tomagnify measurement error. Large foreignsectors are going to be precisely the ones thatare measured with greatest error in the UnitedStates.

A simple solution to this problem is to pos-tulate that all countries use identical technolo-gies but each measuredBc is drawn from arandom distribution centered on a commonB. Ifwe postulate that errors are distributed nor-mally, this relationship can be estimated byrunning the following regression:


(P2) ln Bfic 5 bfi 1 «fi

c .

Here bfi are parameters to be estimated corre-sponding to the log of common factor inputrequirement for factorf in sector i . We cancontemplate two sources of heteroskedasticity.The first arises because larger sectors tend to bemeasured more accurately than smaller sectors.This arises from the fact that we have betterinformation about what the average unit inputrequirements are when there is more output.The second arises because percentage errors arelikely to be larger in sectors that use less of afactor than sectors that use more of a factor. Inorder to correct for this heteroskedasticity, in allregressions we weighted all observations by

B# fi Îln~VAic !

B# f

whereB# fi corresponds to the average across allcountries of the unit factor input requirement insectori , B# f is the average ofB# fi factor intensityacross all sectors, andVAic refers to valueadded in sectori in countryc.14

We noted earlier that there is good reason tobelieve that there are efficiency differences evenamong the rich countries. A convenient speci-fication is to allow for Hicks-neutral technicaldifferences (P3) that are common across sec-tors, as developed in Section I, subsection C. Ifwe denote these differences bylc, then we caneconometrically identify these technical differ-ences by estimating:

(P3) ln Bfic 5 uc 1 bfi 1 cfi

c

where exp(uc) 5 lc. Estimation of this speci-fication requires us to choose a normalizationfor theuc. A convenient one is to setuUS equalto zero (or equivalentlylUS 5 1).

We have also suggested the possibility thatproduction might be characterized by a continuumof goods DFS model in which industry input co-efficients in tradables depend on country capital

abundance (P4). These models can be easily im-plemented. We postulate that input coefficients arecharacterized by the following equation:

(P4)

ln Bfic 5 uc 1 bfi 1 gf

TlnSKc

LcDTRADi 1 ffic

whereTRADi is a dummy variable that takes ona value of one if the sector is tradable andffi

c isan error term. If we wish to require that capitalto labor ratios should not affect the aggregateproductivity of the country, we must also re-quire that15

Of

g fT 5 0.

If FPE breaks down and countries are in differ-ent production cones (P5), this will affect pro-duction coefficients in nontraded sectors aswell. This hypothesis can easily be nested with(P4) by estimating

(P5) ln Bfic 5 uc 1 bfi 1 gf

TlnSKc

LcDTRADi

1 gfNTlnSKc

LcDNTi 1 ffic

whereNTi 5 (1 2 TRADi) is a dummy that isone for nontraded goods sectors. Here our as-sumption that capital to labor ratios do not af-fect productivity levels requires us to imposethe following restriction on the estimates:

Of

~g fT 1 g f

NT! 5 0.

14 The few sectors with nonpositive value added weregiven a zero weight in our regressions.

15 A word of caution is in order. For certain specifica-tions of technical differences (i.e., all sectors within a coun-try share a common, country-specific, Hicks-neutral shiftterm), our measure of productivity is identical to total factorproductivity. Within this simple framework, our normaliza-tion scheme makes sense. However, our aggregate produc-tivity number is subject to all of the standard critiques ofany index number. In particular, the weights chosen for eachsector, factor, and country will affect the measured aggre-gate productivity of the country.


Finally, we can consider a more general speci-fication in which we do not force country capitalto labor ratios to have the same effects acrosssectors. This can be estimated by relaxing theassumption that thegf’s are the same acrosssectors, and estimating:

(P59) ln Bfic 5 uc 1 bfi 1 gfilnSKc

LcD 1 ffic

where now we simply require that thegfi ’s sumto zero.

In each specification, we have 68 equations:one for each factor-industry pair. In specifica-tions (P3) and higher we have cross-equationrestrictions that require us to estimate the equa-tions jointly. Ideally, we would use a seemingly

unrelated regressions procedure and exploit thecross-equation correlations in the error terms,but this would have used up more degrees offreedom than we had available. We thereforeestimated these equations as a system of seem-ingly unrelated regressions with cross-equationrestrictions but imposed a diagonal variance-covariance matrix on the residuals.

Table 1 presents the results of estimatingthese equations. As one can see in all specifi-cations, theuc’s (lc’s) are estimated very pre-cisely and seem to have plausible values. TheUnited States is the most productive countrywith a lc of unity and Italy is the least produc-tive with a lc of about two. Interestingly, onealso sees that industry capital to labor ratiosseem to move in concert with country capital to

TABLE 1—TESTS OFTECHNOLOGICAL VARIATION

ModelMeasurement

error

Hicks-neutraltechnical

differences(HNTD)

Continuummodel withHNTD and

FPE

Helpmanno-FPE

model withHNTD

UnrestrictedHelpmanno-FPE

model withHNTD

Impliedlc

(P2) (P3) (P4) (P5) (P59)uAus — 0.531 0.531 0.530 0.528 1.7

(0.035) (0.035) (0.035) (0.035)uCan — 0.381 0.381 0.380 0.381 1.5

(0.035) (0.035) (0.035) (0.034)uDen — 0.508 0.504 0.508 0.508 1.7

(0.036) (0.036) (0.036) (0.034)uFra — 0.494 0.493 0.494 0.492 1.6

(0.034) (0.034) (0.034) (0.035)uGer — 0.112 0.111 0.112 0.111 1.1

(0.034) (0.034) (0.034) (0.035)uItaly — 0.709 0.707 0.709 0.704 2.0

(0.034) (0.034) (0.034) (0.036)uJapan — 0.431 0.430 0.431 0.430 1.5

(0.033) (0.033) (0.033) (0.034)uNeth — 0.057 0.057 0.056 0.058 1.1

(0.035) (0.035) (0.035) (0.035)uUK — 0.520 0.516 0.520 0.542 1.7

(0.034) (0.034) (0.034) (0.040)uUS — 0 0 0 0 1.0gKT — — 0.408 0.364 —

(0.046) (0.061)gKN — — — 0.493 —

(0.071)gLT — — 20.408 20.449 —

(0.046) (0.060)Number of parameters 68 77 78 80 1442Log L 21741.5 2934.4 2855.7 2802.8 2740.7Schwarz criterion 21963.3 21185.5 21110.1 21063.7 21210.3

Notes:Standard errors are reported in parentheses.gLN 5 2gLT 2 gKT 2 gKN. There is very little variation in theu’s aswe move across specifications because of the constraint that capital to labor ratios cannot affect productivity.


labor ratios. Our Schwarz model selection cri-terion favors the model with neutral technicaldifferences and no factor price equalization(P5).16 The continuum model seems to be notonly the statistical model of choice, but veryimportant economically as well. The estimatedcoefficients indicate that a 1-percent increase ina country’s capital to labor ratio typically raiseseach industry capital to labor ratio by about 0.85percent. Given that capital to labor ratios moveby a factor of two across the ten countries forwhich we have IO data, this translates into largesystematic movements in unit input coefficientsacross countries and within industries.17

Furthermore, we can use this approach to testan implication of factor price equalizationwithin our model.18 If (approximate) FPE holds,then specialization in traded goods may giverise to the observed differences in input coeffi-cients within industries across countries. How-ever, in the nontraded goods sector there shouldbe no systematic variation in factor input ratios.Our estimates indicate that a 1-percent increasein a country’s capital to labor ratio correspondsto a 0.8-percent increase in capital intensity intradables and a 0.9-percent increase in nontrad-ables. Furthermore, in both sectors we can rejectthe hypothesis that input coefficients are inde-pendent of country capital to labor ratios.

Hence, the technology data strongly supportthe hypothesis that the OECD production struc-

ture can be best explained by a model of spe-cialization in tradables with Hicks-neutraltechnical differences and no factor price equal-ization (P5).

B. Estimating Demand

In the theoretical section we introduced ourgravity model:

ln~Micc9! 5 a0i 1 a1iln~si

TcXic9!

1 d iln~dcc9 ! 1 z icc9.

In a zero-trade-cost world with perfect special-ization, we have the following parameter re-strictions,a0i 5 di 5 0. If there are trade coststhat increase with distance, these parameter re-strictions cease to hold. We can statistically testfor the existence of trade costs simply by esti-mating this equation and testing whethera0i 5d i 5 0 for all i . Not surprisingly, the dataresoundingly reject this hypothesis.

We therefore decided to use a gravity modelas the basis for our demand predictions in spec-ification (T7). One of the problems that wefaced in implementation, however, was how tocalculate the distance of any individual OECDcountry to the ROW. In all specifications wecalculated this distance as the GDP-weightedaverage distance from a particular country to thecountries in the ROW. In some sectors wefound large systematic errors in predicting tradewith the ROW. This may be the result of mis-measurement of distance or the fact that the trueROW is some multiple of our sample of coun-tries. We therefore added a dummy variablecorresponding to the exporting country beingthe ROW and a dummy corresponding to theimporting country being the ROW.

Other than this, the results of our estimationof the gravity model are entirely conventionaland to save space we do not present them.Typically a1i is close to one in most specifica-tions anddi is significant and negative in allsectors. We statistically reject the hypothesis ofcostless trade. We will incorporate the newgravity-based absorption model into trade spec-ification (T7).

We have already noted in the theoretical sec-tion that relying on a gravity specification to

16 Implicitly, we are assuming no problems arising fromthe fact that we had to impute certain elements of ourtechnology matrix. There are two points to bear in mind onthis point. First, since our imputation method replaced miss-ing values with average international values, this tended towork against models (P3)–(P5). Second, when we triedindustry-by-industry estimation ofBKi

c /BLic on a constant

and Kc/Lc we found a very strong positive relationshipbetween industry and country capital intensity in almostevery sector even when we dropped all constructed data.

17 Although we do not report it in our tables, we alsoexamined versions of (P4) and (P5) that do not allow forneutral technical shifts. The idea was to identify the specificrole played by the efficiency adjustments relative to that ofadjusting industry input ratios. These specifications performonly slightly better than (P1) by the Schwarz criterion andonly marginally better than (P2) and (T2) in the productionand trade tests below. In short, in combination with thedependence of industry input ratios on country capital abun-dance, the efficiency adjustmentis playing an important rolein improving the performance of the HOV model.

18 Note that in this paper we do not examine factorprices, so do nottestFPE itself.


generate import demands and the complemen-tary own demands represents a substantial stepaway from the conventional HOV framework.Future work would do well to develop a morefully specified model relating production costs,trade costs, and trade volumes. Nonetheless, webelieve that important insights can be gainedfrom the gravity framework even in our morecircumscribed setting.19

IV. Implications for Net Factor Trade

We have shown how a series of both conven-tional and novel assumptions about how tradelinks production technology and the choice oftechniques can be tested with data on the tech-nology matrices of countries. This allows us toselect as the preferred model within this setproduction model (P5), based on a continuum ofgoods with no FPE. In turn, this would selecttrade specifications (T5) or (T6) as the preferredtrade specifications. If one is willing to take alarger step away from the conventional HOVassumptions determining the underlying struc-ture of demand, as reflected in our gravity esti-mates, then the preferred model is (T7).

This identification of preferred models not-withstanding, we now turn to provide variousmeasures of how closely the production andtrade specifications conform to the restrictionsimposed on them by theory for all of our mod-els. There are two reasons for doing this. First,by its nature, our procedure had to identify a

preferred specification. The reader, though, willwonder whether the preferred specification doeswell in an absolute sense. An examination ofplots and simple regression statistics providesinsight into this question. Second, it is reason-able to ask which of the assumptions are crucialfor any improvements that result as we movebetween models. Because the production mod-els are nested and feature a sensible progressionfrom wholly standard to more novel ap-proaches, it is straightforward to identify theimpact of individual assumptions given the baseof other cumulated assumptions.

The key specifications were developed in Sec-tion I and are summarized in Table 2. We begin byworking primarily on the production side. Oncewe have made the major improvements we antic-ipate in that area, we move on to consider anamendment to the absorption model.

A. Production and Trade Tests

For each specification, we provide two testsof the productionmodel. In all cases the tech-nology matrices that we use are based on thefitted values obtained in the previous section.Furthermore, we express both measured andpredicted factor-content numbers as a share ofworld endowments in efficiency units.20 Thisadjustment eliminates the units problem andenables us to plot both factors in the samegraph. The productionSlope Test examinesspecifications (P1) to (P5) by regressing theMeasured Factor Content of Production(MFCP) on the Predicted Factor Content ofProduction (PFCP).21 For example, in specifi-cation (P1) this involves a regression ofBfYc onVfc. The hypothesized slope is unity, which wewould like to see measured precisely and withgood fit. TheMedian Error Test examines the

19 We outline here a few reasons we chose this path.First, costs of trade are an obviously important feature of theworld which cannot be ignored if there is to be any hope ofmatching theory and data. Second, it is inevitable that anymanner of considering the consequences of trade costs willsimilarly have to use the data if only to calculate importdemand elasticities and relate these to primitive measures oftrade costs—approaches which have serious drawbacks oftheir own. Third, both the theory and our empirical resultson technology strongly endorse a model with specializationin tradables, precisely the setting in which the gravity modelis appropriate. Fourth, each industry gravity regression has110 observations of bilateral imports, which are used toestimate just five parameters. In short, we have deliberatelytreated the data with a light hand in order to avoid undulyprejudicing the results. Finally, we should note that thereare, in principle, many things that could still be wrong withour model. Using the gravity demand specification will atleast provide some insight about how much will remain tobe explained once we have a fundamentals model whichgets average trade volumes correct.

20 In each case, efficiency units correspond to the esti-mated productivity parameters in the specification beingconsidered. As one can see from Table 1, estimated produc-tivity parameters differ only in the third digit as we moveacross specifications. Hence, the fact that country endow-ments measured in efficiency units change slightly acrossspecifications has no significant quantitative impact on ourresults.

21 Measured Factor Content refers to factor content cal-culations obtained by applying a technology matrix to pro-duction or trade data. Predicted Factor Content refers tofactor content calculations based on endowment data.


absolute prediction error as a proportion of thepredicted factor content of production. For ex-ample, for (P1) this isuBf

USYc 2 Vfcu/Vf

c.We provide three tests of thetrade model.

The first is theSign Test. It asks simply ifcountries are measured to be exporting servicesof the factors that we predict they are exporting,i.e., is sign(MFCT) 5 sign(PFCT)? For ex-ample, in trade specification (T1), it asks ifsign(Bf

USTc) 5 sign(Vfc 2 scVf

W). The statis-tic reported is the proportion of sign matches.The tradeSlope Testexamines specifications(T1) to (T5) by regressing the MFCT on thePFCT. For example, in specification (T1) thisinvolves a regression ofB f Tc on (Vfc 2scV fW). The hypothesized slope is again unity,which we would like to see measured preciselyand with good fit. TheVariance Ratio Testexamines the ratio Var(MFCT)/Var(PFCT).One indicator of “missing trade” is when thisratio is close to zero, whereas if the model fitperfectly, the variance ratio would be unity. Wealso consider several robustness checks.22

B. The Simple HOV Model Employing U.S.Technology:(P1) and (T1)

We have the same point of departure as priorstudies: an assumption that all countries share a

common technology matrix and an implemen-tation that uses that of the United States. How-ever, our study is the first to examine directlythe production component of this model. As onecan see in Table 3, specification (P1) fails mis-erably, but in an interesting way. A plot of (P1)for all countries appears as Figure 1. The UnitedStates is excluded, since it fits perfectly byconstruction. A glance at the plot reveals twokey facts. First, for all countries and factors,measured factor content of production is alwaysless than predicted. Second, this gap is mostsevere for ROW. This carries a simple message:if these countries used the U.S. technology ma-trix to produce their actual output, they wouldneed much less of each factor than they actuallyemploy. The slope coefficient of measured onpredicted factor trade is only 0.24. Excludingthe ROW raises the slope coefficient to 0.67,still well short of the theoretical prediction ofunity. The results by factor are presented inTable 4. The median prediction error is 34 per-cent for capital and 42 percent for labor. Thusour direct data on production suggest strongly thatadjusting for productivity differences will be animportant component in getting HOV to work.

Now consider trade specification (T1). A plotappears as Figure 2. Factor abundance correctlypredicts the sign of measured net factor tradeonly 32 percent of the time. This is significantlyworse than relying on a coin flip!23 The22 Not all of these tests have been run in prior work.

However, the prior work does yield a simple bottom line:All prior studies on international data have fared poorly byat least one of these measures. 23 At the 7-percent level of significance.

TABLE 2—KEY SPECIFICATIONS

Key assumptionProduction

specifications Trade specifications

(P1) Conventional HOVwith U.S. technology

BUSY c 5 V c (T1) BUST c 5 B US(Y c 2 D c ) 5 V c 2 scV W

(P2) Average technologymatrix

BmY c 5 V c (T2) BmT c 5 V c 2 scV W

(P3) Hicks-neutral efficiencyadjustment

BlY c 5 V cE (T3) B lT c 5 V cE 2 scV WE

(P4) Continuum model:Different input ratios intraded goods and H-Nefficiency

B cDFSY c 5 V c (T4) B cDFSY c 2 [ B cDFSD cc 1 ¥c9Þ c B c9DFSM cc9] 5 V c 2 scV W

(P5) Helpman no-FPEmodel, different inputratios in all, H-NE

B cHY c 5 V c (T5) B cHY cT 2 [ B cHD ccT 1 ¥c9Þ c B c9HM cc9] 5 [V c 2 scV W] 2 [V cN 2 scV WN]

Forces ROWproduction model towork

(T6) As above

Adds gravity-baseddemand determination

(T7) B cHY c 2 [ B cHD cc 1 ¥c9Þ c B c9HM cc9] 5 V c 2 [ B cHD cc 1 ¥c9Þ c B c9HM cc9]

Note: Hats ( ˆ ) indicate fitted values from estimation of technology and absorption.


variance ratio is 0.0005, indicating that thevariance of the predicted factor content oftrade is about 2,000 times that of measured.This is missing trade big time! And the slopecoefficient is zero (actually20.0022, s.e.50.0048). Moreover, under this specificationour data reveal a Leontief “paradox” in whichthe United States is measured to be a netimporter of capital services and a net exporterof labor.

Since the production specification (P1)performs so poorly, it is perhaps no sur-prise that the trade specification (T1) is like-wise a debacle. Nonetheless, this providesan extremely important baseline for our studyprecisely because it reveals that our dataexhibit all of the pathologies that plagueprior studies. Hence we can rule out thatchanges in the country sample, aggregationof many countries into a composite ROW,or the selection of productive factors suf-fice to account for positive results that mayfollow.

C. An Average Technology Matrix:(P2) and (T2)

Examination of specification (P1) stronglysuggested that the U.S. technology matrix is anoutlier. Is it useful to think of there being anaverage technology matrixBm that is a goodapproximation to a common technology? Thatis the question explored in specifications (P2)and (T2). A plot of predicted and measuredfactor content of production appears asFigure 3. When all data points are included, theslope is 0.33. If we focus only on a regressionbased on our ten OECD countries (so excluding

TABLE 3—PRODUCTION AND TRADE TESTS

ALL FACTORS

Production tests: Dependent variable MFCP

(P1) (P2) (P3) (P4) (P5)

Predicted 0.24 0.33 0.89 0.89 0.97Standard error 0.09 0.11 0.06 0.05 0.01R2 0.27 0.29 0.92 0.94 1.00Median error 0.34 0.21 0.07 0.05 0.03Observations 20 22 22 22 22

Trade tests: Dependent variable MFCT

(T1) (T2) (T3) (T4) (T5) (T6) (T7)

Predicted 20.002 20.006 20.05 0.17 0.43 0.59 0.82Standard error 0.005 0.003 0.02 0.02 0.02 0.04 0.03R2 0.01 0.14 0.31 0.77 0.96 0.92 0.98Sign test 0.32 0.45 0.50 0.86 0.86 0.82 0.91Variance ratio 0.0005 0.0003 0.008 0.07 0.19 0.38 0.69Observations 22 22 22 22 22 22 22

Notes:The theoretical coefficient on “predicted” is unity. The theoretical value of the sign testis unity (100-percent correct matches). The variance ratio is Var(MFCT)/Var(PFCT) and hasa theoretical value of unity.

FIGURE 1. PRODUCTION WITH COMMON TECHNOLOGY (US)(P1)


ROW), the slope in the production test risessharply to 1.27, reflecting most strongly theinfluence of high productivity in the UnitedStates. If we exclude the United States as well,the slope falls to about 0.90. TheR2 in eachcase is respectably above 0.9. Also, in both

cases, the median production errors are approx-imately 20 percent. The ROW continues to be ahuge outlier, given its significantly lower pro-ductivity. These results suggest that use of anaverage technology matrix is a substantial im-provement over using that of the United States,

TABLE 4—PRODUCTION AND TRADE TESTS

CAPITAL

Production tests:Dependent variable MFCP Trade tests: Dependent variable MFCT

(P1) (P2) (P3) (P4) (P5) (T1) (T2) (T3) (T4) (T5) (T6) (T7)

Predicted 0.77 0.99 0.87 0.90 0.99 0.06 0.0220.03 0.25 0.57 0.65 0.87Standard error 0.11 0.15 0.08 0.05 0.01 0.01 0.01 0.02 0.05 0.07 0.15 0.07R2 0.84 0.84 0.92 0.94 1.00 0.80 0.28 0.14 0.77 0.88 0.68 0.95Median error 0.34 0.20 0.07 0.06 0.02Sign test 0.45 0.64 0.73 0.91 0.77 0.80 1.00

PRODUCTION AND TRADE TESTS

LABOR

Production tests:Dependent variable MFCP Trade tests: Dependent variable MFCT

(P1) (P2) (P3) (P4) (P5) (T1) (T2) (T3) (T4) (T5) (T6) (T7)

Predicted 0.07 0.12 0.92 0.87 0.94 20.008 20.008 20.07 0.14 0.42 0.59 0.81Standard error 0.06 0.09 0.09 0.08 0.02 0.002 0.003 0.03 0.01 0.03 0.05 0.03R2 0.15 0.16 0.92 0.93 0.997 0.627 0.529 0.43 0.94 0.96 0.94 0.99Median error 0.42 0.22 0.08 0.05 0.05Sign test 0.18 0.27 0.27 0.82 1.00 0.80 0.81

Notes:The theoretical coefficient on “predicted” is unity. The theoretical value of the sign test is unity (100-percent correctmatches).

FIGURE 2. TRADE WITH COMMON TECHNOLOGY (US)(T1)

FIGURE 3. PRODUCTION WITH COMMON TECHNOLOGY

(AVERAGE)(P2)


since median production errors fall by one-thirdto one-half. Nonetheless, the fact that predictionerrors are still on the order of 20 percent for theOECD group, and much larger for the ROW,suggests that there remains a lot of room forimprovement.

Examination of (T2) can be brief. The signtest correctly predicts the direction of net factortrade only 45 percent of the time. The varianceratio continues to be essentially zero, again in-dicating strong missing trade. The Slope Testcoefficient is 20.006. In short, factor abun-dance continues to provide essentially no infor-mation about which factors a country will bemeasured to export. The plot of predicted andmeasured net factor trade looks essentially iden-tical to Figure 2, indicating massive missingtrade. Overall, this model is a complete empir-ical failure.

D. Hicks-Neutral Technical Differences:(P3) and (T3)

Specifications (P3) and (T3) are predicatedon the existence of Hicks-neutral differences inefficiency across countries.24 The estimation ofthese efficiency differences is discussed abovein Section III and here we view the implemen-tation. A plot of (P3) appears as Figure 4. Therecontinue to be substantial prediction errors, thelargest by far being for the ROW, but alsosizable ones for the United Kingdom and Can-ada. Nonetheless, the median prediction errorfalls to about one-third of its previous level,now around 7 percent. The slope coefficientvaries somewhat according to the inclusion or

exclusion of the ROW, although typically it isaround 0.9. When all data points are included,theR2 is about 0.9. When we exclude ROW, theR2 rises to 0.999. This highR2 is a result of theimportant size effects present when comparingmeasured and actual factor usage acrosscountries.

There is an additional pattern in the produc-tion errors. If we define capital abundance ascapital per worker, then for the four mostcapital-abundant countries, we underestimatethe capital content of production and overesti-mate the labor content. The reverse is true forthe two most labor-abundant countries.25 Thesesystematic biases are exactly what one wouldexpect to find when using a common or neutral-ly-adjusted technology matrix in the presence of

24 In this and all subsequent specifications we wereforced to calculate ROW endowments in efficiency units.Since we did not have a technology matrix for the ROW, wewere forced to estimate this matrix based on our parameterestimates generated in Section III.lROW was set equal tothe average productivity of labor and capital or:

lROW51

2

LROW

~BLROWYROW!

11

2

KROW

~BKROWYROW!

.

In specifications (T6) and (T7), when we force the tech-nology to fit exactly for the ROW, we picktwolROW’s suchthat for each factor:

l fROW5

f ROW

BfROWYROW .

25 If we normalize the U.S. capital to labor ratio to one,then the capital to labor ratios of the remaining countries indescending order are Australia (0.95), Canada (0.92), Neth-erlands (0.92), France (0.88), Germany (0.84), Japan (0.79),Italy (0.71), Denmark (0.62), and the United Kingdom(0.48). For the four most capital-abundant countries we onaverage underestimate the capital intensity of their produc-tion by 10 percent and overestimate their labor intensity by8 percent. For Denmark and the United Kingdom we over-estimate their capital intensity by 25 percent and underes-timate their labor intensity by 16 percent. In addition to thepattern we observe among the six countries discussed in thetext, for the ROW (0.17), we also overestimate the capitalcontent of ROW production and underestimate its laborcontent.

FIGURE 4. PRODUCTION WITH HICKS-NEUTRAL TECHNICAL

DIFFERENCES

(P3)


a continuum of goods. Moreover these biasesare not small. Quite often these biases in over-or underpredicting the factor content of produc-tion were equal to 20 percent of a country’sendowment. Thus, while allowance for Hicks-neutral efficiency differences substantially im-proves the working of the production model,prediction errors remain both sizable andsystematic.

We have seen that the Hicks-neutral effi-ciency shift did give rise to substantial improve-ments for the production model. Will itsubstantially affect our trade results? The an-swer is definitely not. The plot of (T3) looksessentially the same as Figure 2, again indicat-ing massive missing trade. The sign test showsthat factor abundance correctly predicts mea-sured net factor trade exactly 50 percent of thetime. The trade variance ratio is 0.008, indicat-ing that the variance of predicted factor tradestill exceeds that of measured factor trade by afactor of over 100. The slope coefficient isessentially zero. In sum, while the adjustmentfor efficiency differences is useful in improvingthe fit of the production model, it has done nextto nothing to resolve the failures in the trademodel.

E. The DFS Continuum Model with IndustryVariation in Factor Employment:

(P4) and (T4)

As we discussed in Section III, subsection A,there is a robust feature of the data that hasbeen completely ignored in formal tests of theHOV model: capital to labor input ratios byindustry vary positively with country factorabundance. We consider this first within theframework of the DFS (1980) continuummodel, as this allows us to conserve yet awhile longer the assumption of (approximate)factor price equalization.

Consider production specification (P4), as inFigure 5. The production slope coefficient re-mains at 0.89, but the median production errorfalls slightly to 5 percent. What is most surpris-ing is how the continuum model affects thetrade specification (T4). A plot appears as Fig-ure 6. The proportion of correct sign tests risessharply to 86 percent (19 of 22)—significantlybetter than a coin flip at the 1-percent level. Thevariance ratio remains relatively low, although

at 7 percent it is much higher than in any of theprevious tests. (T4) is the first specification thateliminates the Leontief paradox in the U.S. datafor both capital and labor.26 The most impres-sive statistic is the slope coefficient of 0.17,

26 This type of Leontief paradox is absent in all subse-quent tests.

FIGURE 6. TRADE WITH CONTINUUM OF GOODS MODEL

AND FPE(T4)

FIGURE 5. PRODUCTION WITH CONTINUUM OF GOODS

MODEL AND FPE(P4)


where all of the previous trade slopes were zero.Clearly, allowing country capital to labor ratiosto affect industry coefficients is moving us dra-matically in the right direction.

F. A Failure of FPE and Factor Usage inNontraded Production:(P5) and (T5)

Our next specification considers what hap-pens if the endowment differences are suffi-ciently large to leave the countries in differentcones of production. In such a case, FPE willbreak down and nontradables will no longer beproduced with common input coefficientsacross countries. This specification of the pro-duction model was preferred in our statisticalanalysis of technology in Section III. Our tradetests now require us to focus on the factorcontent of tradables after we have adjusted theHOV predictions to reflect the differences infactor usage in nontradables arising from thefailure of FPE.

This is our best model so far. Plots of pro-duction and trade specifications (P5) and (T5)appear in Figures 7 and 8. The production slopecoefficient rises to 0.97, with anR2 of 0.997.The median production error falls to just 3 per-cent. We again achieve 86 percent correctmatches in the sign test. The variance ratio risesto 19 percent. The slope coefficient is 0.43 for

all factors, and 0.57 and 0.42 for capital andlabor respectively. Again, the slopes still fallwell short of unity. But this must be comparedto prior work and specifications (T1) to (T3), allof which had a zero slope, and (T4), which hada slope that is less than half as large. Underspecification (T5), for example, a rise of oneunit in Canadian “excess” capital would lead tothe export of nearly 0.6 units of capital services.The amended HOV model is not working per-fectly, but given the prior results, the surprise ishow well it does.27

G. Corrections on ROW Technology:(T6)

We have seen that production model (P5)works quite well for most countries. There are afew countries for which the fit of the productionmodel is less satisfying. There are relativelylarge prediction errors (ca. 10 percent) for bothfactors in Canada, for capital in Denmark, andfor labor in Italy. Given the simplicity of theframework, the magnitude of these errors is notsurprising. Since we would like to preserve thissimplicity, these errors need not immediatelycall for a revision of our framework.

There is one case, however, in which a closer

27 Implementing production model (P59) (i.e., not forc-ing all sectors to have identicalg’s) yields results that arealmost identical to model (P5), and so we do not reportthem.

FIGURE 7. PRODUCTION WITHOUT FPE(P5)

FIGURE 8. TRADE WITH NO-FPE, NONTRADED GOODS

(T5)


review is appropriate. For the ten OECD coun-tries, we have data on technology which entersinto our broader estimation exercise. But this isnot the case for ROW. The technology forROW is projected from the OECD data basedon the aggregate ROW endowments and thecapital to labor ratio. Because the gap in capitalto labor ratios between the ten countries and theROW is large, there is a large amount of uncer-tainty about the adequacy of this projection. Asit turns out, the prediction errors for ROW arelarge: the estimated technology matrix under-predicts labor usage by 9 percent, and overpre-dicts capital usage by 12 percent. Moreover,these errors may well matter because ROW ispredicted to be the largest net trader in bothfactors and because its technology will matterfor the implied factor content of absorption ofall other countries.

Hence we will consider specification (T6),which is the same as (T5) except that we forcethe technology for ROW to match actual ROWaggregate endowments, i.e.,BROWYROW [VROW. A plot appears as Figure 9.28 Thisyields two improvements over specification

(T5). The slope coefficient rises by over one-third to 0.59 and the trade variance ratio dou-bles to 0.38. This suggests that a morerealistic assessment of the labor intensity ofROW production materially improves the re-sults.

H. Adding Gravity to the HOV DemandModel: (T7)

As we note in the theory section, one of themore incredible assumptions of the HOV modelis costless trade. With perfect specialization andzero trade costs, one would expect most coun-tries to be importing well over half of the tradedgoods they absorb. Simple inspection of thedata reveals this to be a wild overestimate ofactual import levels.

We now take a larger step away from thestandard HOV framework by estimating the logform of the gravity equation introduced earlier.This provides us with estimates of bilateral im-port flows in a world of perfect specializationwith trade costs. We then use these estimates ofimport and implied own demand in order togenerate factor service trade predictions. Theresults are presented in column (T7) and illus-trated in Figure 10. By every measure, this isour best model of net factor trade. In movingfrom (T6) to (T7), the slope coefficient risesfrom 0.59 to 0.82. That is, measured factor

28 To maintain consistency with the foregoing, we reportthe results here and in (T7) with all 11 countries. Becausethe move to (T6) forces the production model of ROW to fitperfectly, we will want to consider below whether excludingthe ROW points affects the main thrust of these results. Wewill see that it does not.

FIGURE 9. TRADE WITH NO-FPE, NONTRADED GOODS, AND

ADJUSTED ROW(T6)

FIGURE 10. TRADE WITH NO-FPE, GRAVITY DEMAND

SPECIFICATION, AND ADJUSTED ROW(T7)


trade is over 80 percent of that predicted. Thestandard errors are small and theR2 is 0.98.Signs are correctly predicted over 90 percentof the time. The variance ratio rises to nearly0.7. The results look excellent for each factorconsidered separately, and especially for cap-ital, which has a slope coefficient of 0.87 andcorrectly predicts the direction of net factortrade in all cases. These results strongly en-dorse our use of the gravity equation to ac-count for the role of distance and tradefrictions in limiting trade 1 volumes and netfactor contents.

I. Robustness Checks

We have undertaken a variety of additionalchecks of the robustness of our results. Weexamined the consequences of dropping influ-ential points such as the ROW and the UnitedStates. The results of this exercise appear asTable 5 and indicate the robustness of our re-sults to these exclusions. We have also consid-ered alternative heteroskedasticity correctionssimilar to those of Trefler (1995) and Gabaix(1997).29 While there are minor variations, theimportant point is that all of these checks yieldresults that strongly endorse the conclusions inour central case.

An additional question is why even in (T7)the slope coefficient is only 0.82 while thetheoretical coefficient is unity. Several paths

for exploration seem reasonable. We did lookat the possibility of attenuation bias due tomeasurement error. In the specifications thatperform best, the highR2’s leave little roomfor attenuation bias to be a major factor. Asecond factor at work is that our estimationcan look only at adjustments to the capital tolabor ratio in the average production matrix,not the export production matrix. Hence, evenour estimates may understate the true factorcontent of trade. Third, some error surelyarises from the fact that we have assumed thatintermediates used in the production of ex-portables are all of national origin. We sus-pect these errors are not large, but they areworthy of more careful examination. Finally,and most obviously, trade barriers and homebiases in demand really do exist. Hence, itwould be astonishing if we could ignore all ofthese and describe global factor trade flowsperfectly. The real surprise is just how wellwe do.

V. Conclusion

Our study starts from a simple premise. Sincethe principal hypotheses of the nature of HOV’sfailures in prior work concern technological dif-ferences and absorption patterns, it is crucial toaddress these directly on the relevant techno-logical and absorption data. We develop a smallset of hypotheses, some traditional, some novel,of why prior tests of HOV fail. We then esti-mate the crucial parameters directly from therelevant data and impose these restrictions onour empirical implementation of the HOVtheory.

Our results replicate the feature of priorstudies that the standard HOV theory per-forms miserably. However, our results alsoprovide strong support for a model with asmall number of amendments. Conditional onthese amendments, countries export theirabundant factors and they do so in ap-proximately the right magnitudes. The resultsare extraordinarily consistent across specifi-cations and are robust to changes in thesample.

Perhaps the most exciting feature of our re-sults is the simple and unified picture they drawof the global economy. Technical differencesmatter, even among the rich OECD countries.

29 A full description of these results are available inDavis and Weinstein (1998).

TABLE 5—TRADE TESTS

EXCLUDING ROW AND THE UNITED STATES

ALL FACTORS

Trade tests: Dependent variable MFCT

(T1) (T2) (T3) (T4) (T5) (T6) (T7)

Prediction 20.05 20.04 0.05 0.30 0.35 0.42 0.64Standard error 0.01 0.01 0.07 0.07 0.11 0.14 0.09Sign test 0.28 0.39 0.56 0.61 0.83 0.78 0.89Variance ratio 0.00 0.01 0.09 0.09 0.30 0.49 0.54R2 0.47 0.33 0.03 0.51 0.41 0.36 0.76

Notes:The theoretical coefficient on “predicted” is unity.The theoretical value of the sign test is unity (100-percentcorrect matches). The variance ratio is Var(MFCT)/Var(PFCT) and has a theoretical value of unity.


Rich countries of the OECD cannot even beconsidered part of an efficiency-adjusted FPEset. This comes through most clearly in ourresults about systematic differences in industryfactor usage in nontraded sectors. This failure ofFPE promotes specialization in tradables andfactor substitution in nontradables. The formerimplies that previous studies have underesti-mated the actual factor content of trade, whilethe latter implies that they have overestimated

the relative abundance of factors across coun-tries that are available for production of trad-ables. Finally, there is significantly less tradethan is implied by a frictionless model withperfect specialization in tradables. No doubtmuch is left out of our account. Yet it isstartling that such a plausible and simple setof departures from the conventional modelallows us to so accurately match the interna-tional data.

DATA APPENDIX

Data Sources:

For capital and labor:Data for manufacturing sectors were taken from the 1997 OECD Structural Analysis (STAN)Industrial Database for years 1970–1995.Data for other sectors were taken from the 1996 International Sectoral Database (ISDB) 1960–1995.

For production, demand, and trade:Data were taken from the 1995 OECD Input-Output Database.

Countries:

We used the ten countries included in the OECD IO Database:Australia, Canada, Denmark, France, Germany, Italy, Japan, Netherlands, United Kingdom, andUnited States.

Some countries did not have an IO table for 1985. We chose the closest year to 1985 for which anIO table existed. These countries and their related years are:

Australia (1986), Canada (1986), Germany (1986), Netherlands (1986), United Kingdom (1984).

Sectors:

Data for each of the ten countries is organized into 34 sectors. All sectors were defined as in theIO tables except for sectors 29 and 30 (ISIC 7100 and 7200) which were aggregated due to theinability to disaggregate ISDB data for these two sectors. The individual sectors and their ISICRevision 2 codes are given below:


Capital Stock Data:

Capital stock was calculated using the perpetual inventory method. For nonmanu-facturing sectors, data were taken from ISDB ITD, which contains information on gross fixedcapital formation in 1990 PPP prices in U.S. dollars. All values were then con-verted to 1985 prices. One compatibility problem that arises in these data is that sometimes thevalue added in a sector in ISDB is different from that in the IO tables. To prevent variation inclassification to produce variations in factor intensities we scaled up all investment series by theratio of value added in the IO tables relative to value added in the same sector as reported in theISDB.

Formally, for each nonmanufacturing sectorj , GFCF was calculated as:

GFCFj 5 ITDjISDB p

PUS,1985

PUS,1990 pVAj

IO

VAjISDB .

For manufacturing sectors, the ISDB data was at a higher level of aggregation than we liked.Therefore, data were taken from the STAN database. The investment series we used was GrossFixed Capital Formation (GFCF), in current prices and national currencies. To convert all data

IO Sector ISIC Revision 2 codes Description

1 1 Agriculture, forestry, and fishery2 2 Mining and quarrying3 31 Food, beverages, and tobacco4 32 Textiles, apparel, and leather5 33 Wood products and furniture6 34 Paper, paper products, and printing7 3511352-3522 Industrial chemicals8 3522 Drugs and medicines9 3531354 Petroleum and coal products10 3551356 Rubber and plastic products11 36 Non-metallic mineral products12 371 Iron and steel13 372 Non-ferrous metals14 381 Metal products15 382-3825 Non-electrical machinery16 3825 Office and computing machinery17 383-3832 Electric apparatus, nec [not elsewhere classified]18 3832 Radio, TV, and communication equipment19 3841 Shipbuilding and repairing20 38421384413849 Other transport21 3843 Motor vehicles22 3845 Aircraft23 385 Professional goods24 39 Other manufacturing25 4 Electricity, gas, and water26 5 Construction27 61162 Wholesale and retail trade28 63 Restaurants and hotels29/30 71172 Transport and storage, and communication31 81182 Finance and insurance32 83 Real estate and business services33 9 Community, social, and personal services34 Producers of government services35 Other producers


to 1985 PPP prices, the STAN data were multiplied by a capital stock price deflator, derivedfrom the ISDB. Where ISDB sectors contained several STAN sectors, we used the same capitalstock price information for each sector. Our price deflator consisted of ISDB ITD/IT, whereISDB IT is investment in current prices and national currencies. We then converted thesenumbers into 1985 dollars. Manufacturing data were also scaled by the ratio of ISDB to STANGFCF in total manufacturing. This was done so that the size of manufacturing sectors rela-tive to nonmanufacturing sectors would be consistent if ISDB or STAN consistently under-or overreport the size of manufacturing sectors. Finally, all sectors were scaled by the sectorratio of IO to STAN or ISDB value added (VA). This was done so that sectors would beweighted more heavily if the sector was larger in the IO table than in STAN or ISDB.Ideally, we would have used ISDB data instead of STAN data for this last adjustment but wecould not because the matching between the IO tables and the STAN data was much better formanufacturing.

Hence, for each manufacturing sectori, for each country, and for each year, GFCF was calcu-lated as:

GFCFi 5 GFCFiSTAN p

ITDiISDB

ITiISDB p

PUS,1985

PUS,1990 pGFCFISDB,Total Mfg.

GFCFSTAN,Total Mfg. pVAi

IO

VAiSTAN.

Note:Japanese ISDB IT data were missing in manufacturing, so a slightly different method wasused for each Japanese manufacturing sectori. An overall capital goods price deflator (CGPD)for each year (from Economic Statistics Annual, Bank of Japan, 1994) was used to first convertall investment levels into 1990 yen prices. We then used the overall capital price deflator fromISDB (ITV/ITD) to convert these prices into 1990 U.S. PPP dollars and then followed ourstandard procedure.

Japanese capital formation was therefore calculated as follows:

GFCFi ,Japan5 GFCFiSTAN p

1

CGPDp

ITDISDB

ITVISDB pPUS,1985

PUS,1990 pGFCFISDB,Total Mfg.

GFCFSTAN,Total Mfg. pVAi

IO

VAiSTAN.

After the gross fixed capital formation was calculated for each year and each sector, a permanentinventory method was used to determine capital stocks. Capital formation for each year from 1975to 1985, inclusive, was used with a depreciation rate of 0.133. Capital formation from 1976–1986(1974–1984), was used for those countries which have IO tables for 1986 (1984). These capital totalswere also converted to 1985 U.S. dollars.

Labor Data:

For manufacturing sectors, data were taken from STAN Number Engaged (NE). For non-manufacturing sectors, the ISDB Total Employment (ET) was used. These labor data includeself-employed, owner proprietors, and unpaid family workers. Labor data were taken fromthe same year as the IO table (1984, 1985, or 1986). Some scaling was also performed onthe labor data. All sectors were scaled by the ratio of IO to STAN value added. In addi-tion, manufacturing sectors were scaled by the ratio of ISDB to STAN total manufacturingemployment.


For each manufacturing sectori, in each country, for the year 1984, 1985, or 1986, labor wascalculated as:

Li 5 NEiSTAN p

ETISDB,Total Mfg.

NESTAN,Total Mfg. pVAi

IO

VAiSTAN.

For each nonmanufacturing sectorj , labor was calculated as:

Lj 5 ETjISDB p

VAjIO

VAjISDB .

Production Data:

Data were taken from Gross Output column of the OECD Input-Output table and converted to 1985U.S. dollars.

Data Problems:

Not all data were available in each database or consistent between databases. The following sectorshave data problems of one sort or another. (Superscripts refer to the type of problem, discussedbelow.)

1. The following sectors have missing ISDB GFCF data or GFCF price data (IT and/or ITD files):Australia (3–15, 17, 19, 23, 28, 35), Canada (23, 35), Denmark (14, 17, 18, 23, 28, 35), Italy(5), Japan (5, 35), Netherlands (14–16, 21–23), United Kingdom (35), United States (35).

2. The following sectors have ISDB or STAN capital data which include or exclude sectors thatdiffer from the IO tables:

Canada (24), Denmark (20, 21, 32, 33), France (5, 10, 20, 23, 24, 32, 33, 34), Germany (32,33), Italy (2, 7, 8, 33), Japan (28–33), Netherlands (19, 20, 31, 33, 35), United Kingdom (5,14, 23), United States (20, 21, 27, 28).

3. The following sectors have missing ISDB value added (VA) data:France (35), Italy (32), United Kingdom (27, 28, 31, 32), United States (35).

4. The following sectors have ISDB or STAN employment data which include different sectors thanthe IO tables:

Australia (25), Canada (24), Denmark (21), France (20, 34, 35), Germany (32, 33), Italy (2,33), Japan (28–31, 33), Netherlands (19, 20), United States (20, 21, 27, 28).

Australia (3–151, 167,8, 171, 188, 191, 205,6,8, 218, 226, 231, 254, 281, 338, 351,5,8)Canada (205,6, 231, 242,4, 351,5)Denmark (141, 158, 168, 171, 181, 197, 202,5,8, 212,4,8, 225,6,8, 231, 281, 322, 332, 351,8)France (51,2, 102, 202,4, 232, 242, 322, 332, 342,4, 353,4)Germany (78, 88, 178, 188, 208, 322,4, 332,4)Italy (22,4, 51,6, 72, 82, 325, 332,3,4,8, 348, 358)Japan (51, 98, 207,8, 227, 248, 282,4, 29/302,4, 312,4, 322,5, 332,4, 351,8)Netherlands (128, 138, 141, 151, 161, 178, 188, 192,4, 202,4, 211, 221, 231, 312, 332, 352)United Kingdom (52, 142, 232, 273,5, 283,5, 313,5, 323,5, 351,5)United States (202,4, 212,4, 272,4, 282,4, 351,3,5).


5. The following sectors have missing ISDB or STAN employment values:Australia (20, 35), Canada (20, 35), Denmark (20, 22), Italy (32), Japan (32), UnitedKingdom (27, 28, 31, 32, 35), United States (35).

6. The following sectors have completely missing ISDB or STAN GFCF values:Australia (20, 22), Canada (20), Denmark (22), Italy (5).

7. The following sectors have ISDB or STAN GFCF values that are missing for some years:Australia (16), Denmark (19), Japan (20, 22).

8. The following have unusual sectors included or excluded from the IO VA values:Australia (16, 18, 20, 21, 33, 35), Denmark (15, 16, 20, 21, 22, 35), Germany (7, 8, 17, 18,20), Italy (33, 34, 35), Japan (9, 20, 24, 35), Netherlands (12, 13, 17, 18).

These omissions and inconsistencies were dealt with in the following ways:

1. The following sectors had missing GFCF price deflators (ITD/IT), for which the averagemanufacturing price deflator for the particular country was used.

Netherlands (14–16, 21–23), Australia (3–15, 17, 19, 23), Canada (23), Denmark (14, 17,18, 23).

2. Otherwise, see the description below for corrections of other missing data.

Construction of Missing Data for Production, Capital, and Labor:

In all but a few cases, missing data were replaced by a two-step process. First, we calculated averageinput coefficients for countries which had output data for the sector. Second, this average wasweighted by the size of gross output in the country with the missing sector.

1. For a countryr with a missing sectori in the three nonmanufacturing sectors 33–35 (SOC, PGS,and OPR), the production data was calculated as follows:

Xir 5

Oc

Xic

Oc

Xc,total p Xr ,total.

This was done in: Australia (33, 35), Italy (33, 34).2. To calculate missing or aggregated production data for manufacturing sectors, where STAN data

were available, the following formula was used:

Xir 5 ~Xi

r!STAN p~Xr ,Total Mfg.! IO

~Xr ,Total Mfg.!STAN.

This was done in: Australia (16, 18, 21), Denmark (15, 16), Germany (7, 8, 17, 18, 20),Netherlands (12, 13, 17, 18).

3. Occasionally, IO, STAN, and ISDB production data were all problematic. In this case, the valueof production in these sectors was taken directly from the IO tables without correction. Den-mark’s sectors 21 and 22 were included in sector 20, and the IO values of zero were used for 21and 22.

This was done in: Australia (20), Denmark (20, 21, 22).4. Some countries had data for OPR recorded as zeros, but this was believed to be the correct value.

These sectors were: Denmark (35), France (35), United Kingdom (35).For all other sectors we setXi

c 5 Xic.

5. For a countryr with a missing sectori , the capital stock in sectori was calculated by first findingthe average input coefficient in other countries. This average was then multiplied by the total


output of the country in the missing sector.

Kir 5

Oc Þ r

Kic

Oc Þ r

Xic p Xi

r.

This was done in: Australia (22, 28, 33, 35), Canada (20, 24, 35), Denmark (19,28, 32, 33), France (5, 10, 20, 23, 24, 32, 33, 34), Germany (32, 33), Italy (2, 5,7, 8, 32, 33, 34, 35), Japan (5, 9, 20, 22, 24, 28 –33, 35), Netherlands (19, 20,31, 33, 35), United Kingdom (5, 14, 23, 27, 28, 31, 32), United States (20, 21,27, 28, 35).

6. Sectors with missing labor data were calculated in an identical way.

L ir 5

Oc Þ r

Lic

Oc Þ r

Xic p Xi

r.

This was done in: Australia (25, 33, 35), Canada (20, 24, 35), France (20, 34), Germany (32,33), Italy (2, 32, 33, 34), Japan (9, 20, 24, 28–33, 35), Netherlands (19, 20), UnitedKingdom (27, 28, 31, 32), United States (20, 21, 27, 28, 35).

7. For sectors where production is zero, capital and labor are set equal to zero;K/X andL/X wereset to average of other countries’ values.

This was done in: Denmark (21, 22, 35), France (35), United Kingdom (35).8. After recalculating the data by the steps above, the total capital and labor for each country no

longer summed to the total value given in the ISDB TET. Thus capital and labor for each sectorwere scaled as follows:

K ir 5

Kir

Oi

K ir Kr ,ISDB TET

L ir 5

L ir

Oi

L ir Lr ,ISDB TET.

Production values were not rescaled. These were the final values (of capital, labor, and produc-tion) used in this paper. Once we had these variables, we then constructed the matrix of directfactor input requirements by dividing the amount of a given factor employed in a sector by grossoutput in that sector.

Construction of the Matrix of Intermediate Input Usage, Demand, and Trade Data:

1. The matrix of intermediate input usage, (henceforth theA matrix) was constructed by firsttaking input-output data from the IO tables and then dividing the input used in each sectorby the corresponding sector’s gross output. Any problematic elements of theA matrix werereplaced by the average value of other countries whose corresponding elements have no


problem. That is,

aijR 5 ~aij

R!avg.

2. Since both theA matrix and production were constructed independently for problematic sectors,ARX did not correspond to the values for total useARXIO given in the IO table, whereAR is theRth row of theA matrix. Therefore, theA matrix was further scaled by the following method:

Let ARX IOPL 5 H ARX IO For values ofX IO that were not constructedARX Otherwise.

Let AX IOPL be the vector whose rows are composed ofARXIOPLFind l such that

1l1 0

l2 ···0 ln

2 A X 5 AX IOPL.

Then A 5 lA was used as the finalA matrix. We then postmultiplied our matrix of directfactor input requirements by (I 2 A)21 to obtain the matrix of direct and indirect factor inputrequirements.

3. Demand data were taken from the IO table as the sum of Private Domestic Consumption,Government Consumption, GFCF, and Changes in Stocks.

For problematic sectors of SOC, PGS, or OPR, the demand data were constructed as:

D 5 (I 2 A)X.This was done in Australia (33, 35), Italy (33, 34) because we believed there to be very littletrade in these sectors.

For sectors where export data were missing from the IO table due to aggregation problems butpresent in STAN, the demand data were constructed as:

D5(I2A )X2(E2M ),

where

EiR 5

~EiR!STAN

~EM,Total Mfg.!STAN p ~EM,Total Mfg.! IO

MiR 5

~MiR!STAN

~MM,Total Mfg.!STAN p ~MM,Total Mfg.! IO.

This was done in Australia (16, 18, 21), Denmark (16, 17), Germany (7, 8, 17, 18, 20),Netherlands (13, 14, 17, 18).

4. Trade data were then constructed in the following way:

T 5 ~I 2 A!X 2 D.


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