FACTOR PRICES AND THE FACTOR CONTENT OF TRADE REVISITED: WHAT S THE USE?

RESEARCH SEMINAR IN INTERNATIONAL ECONOMICS School of Publc Polcy The Unversty of Mchgan Ann Arbor, Mchgan 48109-1220 Dscusson Paper No. 409 FACTOR PRICES AND THE FACTOR CONTENT OF TRADE REVISITED: WHAT S THE USE? Alan V. Deardorff The Unversty of Mchgan August 8, 1997 Recent RSIE Dscusson Papers are avalable on the World Wde Web at: http://www.spp.umch.edu/rse/workngpapers/wp.html

Factor Prces and the Factor Content of Trade Revsted: What s the Use? Alan V. Deardorff The Unversty of Mchgan Paper prepared for a conference, Responses to Internatonal Lberalzaton Chrstchurch, New Zealand, August 25-27, 1997. August 8, 1997 2

Paper: use.doc ABSTRACT Factor Prces and the Factor Content of Trade Revsted: What s the Use? Alan V. Deardorff The Unversty of Mchgan Ths paper examnes the usefulness of a result of Deardorff and Stager (1988), who showed that the factor content of trade can be nterpreted under certan assumptons as ndcatng the nature of the factor prce adjustments that can, n a specfed sense, be attrbuted to that trade. Ths paper elaborates on the sense n whch ths result says anythng about the factor market effects of trade. It also examnes several of the assumptons that were used by Deardorff and Stager to determne whether they can be relaxed. These nclude the assumpton, used for only one of Deardorff and Stager s several results, of Cobb-Douglas technology, whch s shown to be easly extended to Constant Elastcty of Substtuton. Also examned s the assumpton of nonspecalzaton, or that all mported goods are produced or producable n the domestc economy. Wth Cobb-Douglas technology that assumpton s shown not to be needed. Wth more general technology, however, the presence of non-competng mports requres a renterpretaton of the factor content of trade. Whereas wthout noncompetng mports, trade tself s analogous, n terms of ts effects on factor markets, to a change n factor endowments equal to the factor content of trade, wth noncompetng mports trade has an addtonal effect analogous to a Hcks-neutral technologcal mprovement enablng those noncompetng mports to be produced compettvely. Keywords: Factor Content of Trade Correspondence: Trade and Wages Alan V. Deardorff JEL Subject Code: F11 Department of Economcs Unversty of Mchgan Ann Arbor, MI 48109-1220 Tel. 313-764-6817 Fax. 313-763-9181 E-mal: alandear@umch.ed

August 8, 1997 I. Introducton Factor Prces and the Factor Content of Trade Revsted: What s the Use? Alan V. Deardorff The Unversty of Mchgan A few years ago, Bob Stager and I, n Deardorff and Stager (1988) (D-S), derved some curous lttle results from versons of a generalzed Heckscher-Ohln (H-O) trade model concernng the relatonshp between the factor content of trade and assocated changes n factor prces. A few years later, frst several labor economsts, then trade economsts, began to try to account emprcally for the 1980s rse n the relatve wage of sklled labor compared to unsklled labor n the Unted States. They pad partcular attenton ntally to the possblty that changes n trade or trade polcy mght explan ths rse, along the lnes of the Stolper-Samuelson Theorem. One technque was to measure the sklled and unsklled labor emboded n the trade ts factor content and then compare ths to quanttes n the relevant factor markets. Only after ths technque, whch was used frst by labor economsts, was crtczed by trade economsts as havng no theoretcal bass, was t notced that the D-S result dd n fact provde such a ratonale. However, Ed Leamer (1996) has dsagreed, argung that the D-S result was almost completely useless for ths purpose. I wll suggest that he spoke too soon. I agree that the D-S result should be used only wth care and that some wrters have gone way too far n usng factor content to nfer factor-market effects of trade when the true culprt could easly le elsewhere, and I have tred to say as much n Deardorff and Hakura (1995). But

Leamer s objectons to the assumptons needed for factor content to be meanngful can easly be addressed, and I do so here. I wll revew the D-S results n Secton II, emphaszng what I agree are ther lmtatons. However, these lmtatons do not nclude, n my vew, three assumptons that Leamer orgnally dentfed as needed for ther valdty: balanced trade, Cobb-Douglas technology, and nonspecalzaton. I dspense wth balanced trade also n Secton II, snce t was not n fact used n the D-S dervatons, although our handlng of that ssue was evdently unclear. In Secton III I turn to the Cobb-Douglas assumpton that we used for our strongest result: an explct soluton of a model for factor prces n terms of the factor content of trade. Ths can easly be generalzed to a constant-elastcty-of-substtuton (CES) technology wth a common elastcty of substtuton for all producton and consumpton. Leamer may not lke ths much better, but I suspect that some readers wll fnd ths to be an mprovement. In Secton IV I address what I regard as the more serous problem, the assumpton of non-specalzaton. Snce n other work of my own I have often stressed the mportance of the alternatve H-O case of specalzaton and the absence of factor prce equalzaton (FPE), whch I beleve to be a better approxmaton to global realty than FPE, I too have been concerned that the factor content of trade mght be of lttle use n realty for ths and other purposes. Indeed, I have wondered why others were so wllng to assume FPE n tests of the Heckscher-Ohln Theorem usng the Heckscher-Ohln-Vanek verson of t, as n Bowen, Leamer and Svekauskas (1987). Indeed, t turns out that wth general technology the presence of non-competng mports does requre a renterpretaton of the factor content of trade. As dscussed n 5

Secton II, wthout noncompetng mports trade tself s analogous, n terms of ts effects on factor markets, to a change n factor endowments equal to the factor content of trade. However, wth noncompetng mports trade has an addtonal effect that s analogous to a set of Hcks-neutral technologcal mprovements enablng those noncompetng mports to be produced compettvely at home. Snce Hcks-neutral technologcal dfferences do not affect factor prces n a Cobb-Douglas world, t follows that the strong Cobb-Douglas result of D-S s vald after all wth noncompetng mports. However, n other cases, ncludng the CES case of Secton III, nferences about factor markets from trade must take nto account ths addtonal and somewhat more complex effect of trade. In Secton IV I frst verfy the relatve-factor-prce neutralty of Hcks neutral changes n technology, then examne what can be sad about ther effects wth CES technology. II. Factor Content and Factor Prces Revsted The D-S results all grew out of the followng observaton: Under standard assumptons of the H-O model plus nonspecalzaton, t s possble to reproduce any tradng equlbrum for a country as an autarky equlbrum by smply changng the factor endowments of the country by the amounts of the factor content of trade, addng those factors that were net mported through trade and subtractng those that were net exported. It follows that any comparson between two tradng equlbra can also be made between ther two equvalent autarky equlbra. Therefore n partcular, dfferences n factor prces between two tradng equlbra that may n some sense be assocated wth dfferences n ther trade can be nferred from the dfferences n factor prces that would arse n autarky from dfferences n factor endowments. Ths result can be useful to the extent that factor 6

prces are systematcally related to factor endowments. In D-S (1988) we derved one such very strong relatonshp for Cobb-Douglas technologes and preferences, a result that I extend below to CES technologes. We also derved a weaker correlaton result for more general technologes. One of Leamer s objectons to the use of ths result I strongly share. In comparng two tradng equlbra of a country, there are many reasons why the quanttes traded, and therefore the factor content of trade, may dffer. To nterpret a change n trade as some sort of outsde force affectng a country s usually ncorrect, and therefore to assocate any changes n factor prces that may go wth t as beng caused by t s also ncorrect. The changes n U.S. trade that occurred n the 1980s, for example, were undoubtedly the result of a whole host of causes, both nternal and external to the U.S. Usng the factor content of these changes n trade to nfer what changes n factor markets were due to trade mstakenly attrbutes causaton to trade, when t n fact was beng caused to change by other forces. Furthermore, as should be clear from the method of provng the D-S result just descrbed, t s only true that factor content can be related to factor markets f we can hold other thngs constant, ncludng domestc technologes, preferences, and factor endowments. Therefore, f any of these thngs were to have changed durng the perod of a change n trade that s beng analyzed, perhaps even as ther cause, the effects of these other changes on factor markets wll not be captured by the factor content of trade. Therefore, only f trade has changed due entrely to forces other than these, such as changes n trade polcy at home or abroad or changes only wthn the foregn economes, 7

may the factor content of trade, together wth the D-S result, tell us somethng about the effects of those changes on domestc factor markets. Ths does not, however, mean that the result has no meanng. Even for changes n trade that are caused by changes n domestc technology or other thngs held constant n the result, there remans an nterpretaton of the factor content of trade that s vald. Suppose that quanttes of trade change for any reason. We may ask by how much factor prces would have changed dfferently f the changes n trade had been prevented by changes n domestc trade polcy, and the D-S results gve the answer. Thus regardless of whether actual changes n trade have been due to, say, reductons n tarffs, we may stll ask how the economy would have fared dfferently had these changes been prevented by trade polcy. If the changes actually were due to trade lberalzaton, then we wll have captured the effects of that lberalzaton. But f they were due to any other causes, we wll not have captured the factor market effects of those causes. Rather, we wll have measured the factor market effects of accompanyng those causes, whatever they may be, wth trade polces to nsulate any effects on quanttes traded. Thus the factor content of trade does help us to answer a queston. Whether t s one that anybody s askng s another matter. Leamer objected that our result depended on trade beng balanced. That s not the case, as we mentoned n a footnote. However, t may be useful to work through why ths s true and what the meanng of the result s n the context of a changng mbalance of trade, as a way of llustratng what the result can and cannot say. Suppose then that what has truly happened s that a small country has ncreased ts expendture on all goods, ncludng both traded and nontraded, above ts ncome, fnancng 8

the excess by borrowng from abroad. As dscussed n Deardorff and Hakura (1995), snce addtonal nontraded goods cannot be mported, the country s resources wll shft nto producng more nontraded goods, and these resources wll be wthdrawn from the traded sectors. It wll therefore export less of ts prevous exports and mport more of ts prevous mports, thus runnng the trade defct that ts ncreased expendture makes nevtable. The factor content of trade wll also show ths defct, the country now mportng more of some or all factors than t exports. Dependng on the factor requrements of the traded goods, the factor content of trade may be suggestve of a change n relatve factor prces accordng to the D-S result. But n fact, factor prces have not changed at all, as we know from FPE, so what can be the meanng of ths result? The answer s ths: these are the changes n factor prces that would have occurred f the ncrease n expendture had been accompaned by, say, ncreased mport tarffs and export subsdes suffcent to prevent any change at all n the quanttes of trade. Of course, had the ncrease n expendture been accompaned by such polces, domestc prces would have changed and we would ndeed have seen changes n factor prces. The factor content of trade turns out to be a tool for nferrng what these changes would have been. III. A CES Specfcaton I turn now to an extenson of the strongest D-S result. Ths was a smple formula relatng factor prces and the factor content of trade under the assumpton that all producton functons as well as preferences are Cobb-Douglas. Specfcally, 9

D-S Proposton 2. If a country s preferences and technologes are Cobb- Douglas and dentcal n two tradng equlbra for whch factor endowments are also dentcal, then f prces are normalzed to equate total expendture to unty n both equlbra, then 2 1 2 1 w w S S 1 = 2 w B for every factor. Here, w s the prce of the factor, S s the net amount of that factor emboded n the country s trade, and B s the amount of that factor emboded n consumpton (assumed equal to fnal demand). The ratonale for ths result s smply that factor prces depend n autarky on supply and demand for factors, and wth Cobb-Douglas technologes and preferences, the economy s equvalent to one n whch factors are demanded drectly for consumpton, also wth Cobb-Douglas preferences. Thus wth approprate normalzaton the demand for factors has unt elastcty, and demand can be nverted to yeld equlbrum factor prces that also depend unt-elastcally on factor quanttes. Not surprsngly, perhaps, a world of common-elastcty CES technologes and preferences wll be almost equally well-behaved. Suppose, then, an autarkc, representatve-consumer economy n whch goods xj, j = 1,..., n are consumed and enter a CES utlty functon, U ρ ρ j = a j x j 1 (1) where a j > 0 are parameters determnng (but not equal to) expendture shares and ρ s σ 1 related to the elastcty of substtuton, σ > 0, ρ = < 1. Goods are produced from m σ factors,, also wth CES producton functons wth elastcty σ : x 1 j = bjvj ρ ρ (2) 10

where v j s the amount of factor used n producng good j, and b j 0 are parameters that permt arbtrary (but non-reversng, snce ndustres share dentcal elastctes of substtuton) factor ntenstes. Defne total demand for a factor, v, as vj = v, (3) j and defne natonal ncome, Y, as wv = Y. (4) By choosng x j, v j, and v to maxmze (1) for gven w and Y, we can derve demands for factors that can n turn be equated to ther supples to derve equlbrum factor prces. Substtutng (2) nto (1) and (3) nto (4), the maxmzaton problem becomes one of selectng factor nputs only: maxu vj = cjvj ρ j 1 ρ where c = b a (5) j j j subj. to wv j = Y (6) j Ths s a conventonal CES demand problem, and the soluton s equally conventonal: v j = Y w j c σ 1 σ j w σ c w j 1 σ 1 1 σ 1 σ. (7) 11

That s, demand for a factor nput departs from the Cobb-Douglas case ( Y a term comparng the wage of factor to a CES ndex of the wages of t and all other factors. Defnng that ndex as / w ) by I = c j w σ 1 σ j 1 1 σ (8) we can sum the v j to get total factor demands v v C Y = j = w w I 1 σ (9) where C = c σ. (10) j j If we now also normalze factor prces so that I=1, then factor demands depend very smply on ther respectve factor prces: v σ = CYw. (11) In equlbrum these factor demands must equal factor supples, v, and we can solve for equlbrum factor prces, w ~, as ~w 1 v = σ. (12) CY Thus, n a CES world, autarky factor prces vary wth respect to factor endowments wth an elastcty 1/σ. It follows, usng the same argument as n D-S, that factor prces n dfferent tradng equlbra wth dfferent factor contents of trade but dentcal preferences, technologes, and factor endowments wll dsplay an elastcty 1/σ wth respect to the factor content of trade relatve to endowments. Thus the Cobb- 12

Douglas case of D-S was specal, but not unque n permttng a strong relatonshp between factor prces and factor content of trade. Of course, even ths CES world s very specal, snce I have assumed the same elastcty of substtuton n all producton and utlty functons. Wthout that, thngs would not be nearly so smple, and probably not worth workng out n tedous detal. However, the general pont s that an autarky economy behaves lke a consumer ndrectly demandng factors for nput to a utlty functon, and the resultng quanttes of factors demanded must depend on factor prces n conventonal ways. It follows that the equlbrum factor prces must also depend, n conventonal but perhaps very complex ways, on factor quanttes, and therefore that these factor prces are also related to the factor content of trade. IV. Noncompetng Imports The D-S result depends heavly on the assumpton that all mports are capable of beng compettvely produced wthn the country. Wth that assumpton, the factors that would be needed to produce them (ther factor content), f they were added to the country s endowments, would not only make t possble to produce them at home wth avalable factors and wthout changng other outputs. It would also, under the other usual Heckscher-Ohln assumptons, cause that addtonal producton to be an equlbrum outcome. Noncompetng mports nterfere wth that reasonng. Suppose that some mports cannot be produced at home wth the avalable technology and at exstng factor prces wthout makng a loss. That s the factors needed to produce a dollar s worth of these mports cost more than a dollar. Then f we nterpret that bundle of factors as the factor 13

content of those mports and magne addng them to the country s endowment, whle t wll become physcally possble to produce them, that producton wll not happen n a compettve non-dstorted economy. The factor content of those mports, f added to endowments, would be used for somethng else. Of course t s unlkely that there s now only one possble defnton of factor content. Unless there are dstortons elsewhere n the world, the mports are almost certanly actually beng produced wth a dfferent bundle of factors than would be used domestcally. The foregn producers may be usng less of all factors due to a superor technology, or they may just be usng a dfferent factor mx that costs less for them, though t would not for us, because factor prces are unequal. Ether way, we could use that dfferent bundle of factors to measure the factor content of the mports, but that would not help. Those factors ether would not be suffcent to replace the mports wth domestc technology, or they could do so but not at mnmum cost. In short, as far as I can see, there s no defnton of the factor content of trade that we can apply to noncompetng mports that wll allow us to replcate n autarky all other aspects of a tradng equlbrum and thus move on to the other D-S results. That s one of Leamer s (1996) major crtcsms, and I take t to heart. There are many trade economsts who often seem more than wllng to assume a world of complete factor prce equalzaton, all the world n a sngle dversfcaton cone, where noncompetng mports do not exst. But I have always felt that FPE provdes a poor approxmaton to the world of many dverse countres n whch we lve, and f asked to choose between FPE and, say, a world of two dversfcaton cones and sets of factor prces as my favorte false model of 14

the world economy, I would choose the latter. In that world, the D-S result does not hold. Let me suggest, however, a smple alternatve result that does hold. Suppose as our experment we magne changng not just factor endowments but also technology n constructng our equvalent autarky equlbrum. That s, suppose that nstead of mports we gve a country a Hcks-neutral technologcal mprovement suffcent for t to break even producng the mports, and then also, as before, gve t the factors needed to produce the mports wth that technology. Now, as n the case of only competng mports, we are able to reproduce the tradng equlbrum wth an equvalent autarky equlbrum. And when we move from one tradng equlbrum to another wth both dfferent factor content of trade and possbly wth dfferent noncompetng mports, that wll be equvalent to a combned change n both factor endowments and technology. To the extent that we can nfer factor prce changes from these two exogenous changes n autarky, then we wll also be able to nfer factor prce changes from changes n factor content of trade together wth some nformaton about noncompetng mports. Ths may seem an awkward and pontless exercse, but I wll suggest that t s not. Frst, just thnkng about trade n ths way remnds us of somethng that we have long known, but often forget. In a general Heckscher-Ohln world and even beyond, trade along the lnes of comparatve advantage serves two purposes. It allows a country to consume what t has not the factor endowments to produce, and also what t has not the technology to produce tself. Imports, therefore, are equvalent not only to proxy factor nputs but also to proxy technology as well, or at least that s the case when those mports are noncompetng. 15

When dscussng the gans from trade, many of us fondly quote Ingram s parable of a new and wldly popular technology that turns out to be just nternatonal trade, and we use t to explan why the welfare effects of trade are no less desrable than the welfare effects of technologcal mprovement. But the parable extends beyond just the gans from trade to all other effects of trade as well, ncludng the effects on factor prces. Recognzng that mports are equvalent to a combned transfer of both factors and technology helps to remnd us of that fact. The next queston s whether ths does us any good. The surprsng answer s yes, a great deal, at least n one specal case. Consder the effects of a Hcks-neutral technologcal change n a Cobb-Douglas economy of the sort underlyng D-S s Proposton 2. In such an economy, each factor s share of natonal ncome s fxed, and wll not change n response to any and all Hcks-neutral changes n preferences or technology. All factors wll gan, of course, but f factor endowments do not change they must gan n the same proporton. So t turns out that D-S Proposton 2 s vald after all, even n the presence of noncompetng mports. The reason s that now trade s equvalent to a combnaton of a change n autarky factor endowments equal to the factor content of trade together wth a set of Hcks-neutral technologcal mprovements that would make t effcent to produce all noncompetng mports at domestc factor prces. The equvalent change n endowments has the effects on factor prces gven by D-S Proposton 2, whle the technologcal mprovement causes no further change n relatve factor prces. The argument also clarfes how factor content of noncompetng mports should be measured: 16

as the least-cost factors needed to produce them at domestc factor prces after a Hcksneutral mprovement makes them compettve. What f we do not have Cobb-Douglas technologes? Then the noncompetng mports really do matter, and n ways that could get rather complcated. But they are not hard to understand, and not necessarly hard to deal wth. I wll consder only a smple case for llustraton. Suppose the CES world that was dscussed n Secton III, and suppose only a sngle noncompetng mport, X. What are the effects on factor markets of a Hcks-neutral technologcal mprovement for producng X? The mprovement wll make X cheaper, and ncrease demand for t. But whether expendture on t (and on the factors to produce t) wll expand on contract depends on the elastcty of substtuton, σ. If substtuton s elastc, σ > 1, then demand for the good wll expand more than prce has fallen, expendture wll rse, and that ncreased expendture wll be passed through to the markets for whatever factors the good employs, alterng ther prces as well. If substtuton s nelastc, the reverse wll hold. Only f the elastcty s one, the Cobb-Douglas case already mentoned, wll there be no effect on factor markets. Therefore, for example, f we wsh to compare factor prces n two tradng equlbra that dffer n ther factor content of trade and also n the presence of a new noncompetng mport, X, n the new equlbrum, then n addton to the effects of factor content that we explored n Secton III, we should also account for the technologcal mprovement that the new noncompetng mport represents. For example, f σ > 1 and X s, say, skll ntensve, then we expect a larger ncrease n the relatve wage of sklled labor than we would have predcted based on factor content alone. 17

There are also a number of cases, n addton to the Cobb-Douglas case, where we do not have to do anythng. If our two tradng equlbra do have noncompetng mports but they are the same ones, and f the sze of cost reducton needed to make them compettve s unchanged, then they do not matter for relatve factor prces. Or, f there are many changes n noncompetng mports but ther average factor ntensty s the same as that of the economy as a whole, then agan we can gnore them snce ther effects wll cancel out. Ths s not to say that these cases are at all lkely, however. To take perhaps the smplest and most basc example from the Heckscher-Ohln model, consder the effect of trade (as compared to autarky) on factor prces for a small two-sector economy that s completely specalzed n the skll-ntensve good. The unskll-ntensve good s ts noncompetng mport. If we were to measure ts factor content of trade we would fnd, of course, that t exports skll and mports unskll, and we mght use the D-S result to nfer (correctly, n terms of sgn) that trade has lowered the relatve wage of unsklled labor compared to autarky. If ths s a CES economy wth elastcty, say, three, we mght even use the result of Secton III to calculate the sze of ths declne by measurng the factor content, comparng t to endowments, and usng the elastcty 1/3. But because of the noncompetng mport, ths would be wrong. The noncompetng mport of the unskllntensve good has also had the effect of a Hcks-neutral technologcal mprovement n producng t, of a sze that depends on just how cheap t s on the world market. Snce demand s elastc, that mprovement corresponds to an ncrease n demand for unsklled labor along wth the ncrease n supply represented by ts factor content. Therefore the approprate prce of unsklled labor should be hgher. In ths case, the presence of the 18

noncompetng mport has caused us to overstate the change n factor prces usng just the factor content of trade. V. Concluson Is the factor content of trade of any use? I thnk so. It must be used wth careful attenton to both the questons that answers, and to the assumptons needed for t to provde correct answers. These assumptons are not trval, but they are not qute as specal as may be alleged, and one can understand and deal wth the bases that departures from these assumpton ental. 19

References Bowen, Harry P., Edward E. Leamer, and Leo Svekauskas 1987 "Multcountry, Multfactor Tests of the Factor Abundance Theory," Amercan Economc Revew 77, pp. 599-620. Deardorff, Alan V. and Dala S. Hakura 1995 Trade and Wages -- What Are the Questons? n Jagdsh Bhagwat and Marvn H. Kosters, eds., Trade and Wages: Levelng Wages Down? Washngton, D.C.: The AEI Press, pp. 76-107. Deardorff, Alan V. and Robert W. Stager 1988 "An Interpretaton of the Factor Content of Trade," Journal of Internatonal Economcs 24, (February), pp. 93-107. Leamer, Edward E. 1996 What s the Use of Factor Contents? Natonal Bureau of Economc Research Workng Paper No. 5448, February 1. 20