Review of'Ifllernationo1 Economics 5(1), 20-31, 1997

Adjustment in General Equilibrium: Some Industrial Evidence

Henry Thompson

Abstract The link belween output changes and factor-mix adjustments in general equilibrium is examined for each of nine industries using pooled datia from 12 developed countries over the years 1MO-85. Specihcations of the Stolper-Samuelson theorem and the specific-facton model of production are built on the-ussumptionr and scruaure of theory with each industry isolated in turn. In their simplest version with only capital and Labor input, these competitive general-equilibrium models explain a goad deal of the o b s e ~ e d variahioos in iodusIrial favtor mLres. The specific-facto~s model perfom better.

1. Introduction

The theory of production and trade is built in large part on the competitive paradigm contained in general-equdibrium models of production. The Stolper-Samuelson theo- rem (1941) of the Heckscher-Ohlin model captures the link between an industry's price and the return to its intensively used factor of production, illustrated inEdgeworth box and Lerner-Peatce diagrams. The specific-factors model assumes every industry is characterized by productive capital used only in that industry, creating a direct link between the price of an output and its specific factor.

This paper provides some empirical evidence for the Stolper-Samuelson theorem and specific-factors model. Model specifications are estimated using data for each of nine manufacturing industries across 12 OECD countries horn 1970-85. In the Stolper- Sarnuebon ~pecilication, a rising price in an industry causes the capital-labor ratios to adjust accorhg to factor intensity. In the specilic-factors model, e higher price in an industry is expected to increase labor input.

There are data available for many industries, suggesting a model with many goods. When the prices of goods a e exogenously given at world levels, however, a production model with two factors shared by each industry is overdetermined. Inttoducing de- mand allows a tractable model, but relaxes the intensity links. The present paper isolates each industry and aggregates the others into a single sector, developing a series of two-sector models to coincide with the Stulper-Samuelson theorem.

Learner (1994a) argues that an idea needs nn issue, a theory, and evidence to survive. The Stolper-Samuelson theorem meets Lhe Erst two conditions. but lacks much of the third. The theorem was originally presen(ed and applied largely in the context of

*Rassekb: Universiry of Hartford, CT Q6117, USA. Tel: 8604'68-5007, Pax: 4198. E-mail: ra6sekh~avax.hartford.edu. ?'bornpaon: Aubum University, AL 36849, USA. Tel: 334-844-2910, F a x 4615. E-mail: hthompsn@bluiness.aubum.edu. A1 Radkee I11 and Michael SpoUacy provided excellent research assistanw. Joy Steward kindly provided helpEu1 comuliation on SAS for the empirical estimation. Tbanks forsuggestioosoffered by Kei-Mu Yi, Pat Conway. md WlcnhuiXu at the 1944Southeast Economic Theory and Lnlernational Trade Conference 81 the University 01 Virginia. Manouchehr Mokhrari was s helpful consdtant Two referees Of this journal made detailed suggestions which improved the paper. The usual diillimer applies.

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22 Farhad Russekh and Henry Thompson

known that there are more than two separable inputs in these production processes. Branson and Monoyios (1977) argue that skilled labor is m important input in ob- served trade. Clark, Hofler, and Thompson (1988) show that there are at least nine separable sku types of labor in a cross-section study of US manufacturing. Learner (1984) successfully speci!ies a model with different types of labor, capital, and resource inputs.

Magee (1980) makes the 6rst attempt at empirical investigation of the Stolper- Samuelson theorem, pointing out that the theorem predicts labor and capital would lobby on opposite sides ol trade policies. Testimony of groups representing labor and capital before the US Congress on the Trade Reform A d of 1973 shows that lobbying activity occurred along industry k s rather tban factor tines. Magee points out, how- ever, that lobbying is more concerned with the short run, while the Stolper-Samuelson theorem is a long-run proposition. Magee's interpretation is in accordwith the point of Learner (1994a) that trade theories should not be "tested" in order to be accepted or rejected. Learner argues that tests should simply suggest conditions under which a theory is applicable and capable of making predictions.

Leamer (1984) points out that direct econometric estimation of Stolper-Samuelson effects is difficult because of the high degree of couinearity between prices of goods and prices of factors. Detailed and reliable data on factor prices, especially capital, are not available. Moreover, a change in technology or other exogenous supply shocks would alter the relation between prices of goods and factor prices. Leamer appeals to Samuelson's reciprocity relation between the Stolper-Samuelson and Rybczynski theorems in order to estimate Stolper-Samuelson effects, focusing on the effects of tariffs on factor prices. The model is not judged by the estimates but is used as rhe hamework for estimation. Leamer (1994b) applies the same procedure to estimate the wage effects of free trade between the US and Mexico.

Gaston and Trefler (1994) directly estimate the effect of tariffs on US manufacturing wages, which they find to be negative. They believe less efficient resource allocation under protection may be the cause. Workers may also receive economic rent from tariffs by avoiding the cost of searching for new jobs.

Krugman and Lawrence (1994) examine the factor-price equalization theorem based on the logic of the Stolper-Samueison adjustment process. If factor prices across countries are to become equal through trade, they would generally have to move in the direction predicted by the Stolpcr-Samuclson theorem. Increased international trade is expected to raise the price of a country's abundant factors and reduce h e price of its scarce factors. Such a change would lead all industries to substitute scarce factors for abundant factars as trade increases. In the US, relatively scarce unskilled workers should be substituted for abundant skilled workers. Krugman and Lawrence find that this prediction does not hold between 1979 and 1989, a period when intemational trade increased. Thompson (1985) points out, however, that mcdels of production with as few as three factors do not have such straightforward predictions.

Lawrence and Slaughter (1993) set out to determine whether international trade has caused the slow growth in real hourly compensation and the increase in income disparity in the US since 1973, using the Stolper-Samuelson theorem as a conceptual framework. Their empirical analysis suggests that increased trade and the Stolper- Samuelson process had little influence on relative wages in the US during the 1980s.

Bhagwati and Dehejia (1993) critically evaluate several recent empirical works, mostly by labor economists, which rely on the Stolper-Sarnuelson mechanism to deter- mine the impact of international trade on US wages. They find major theoretical

INDUSTRIAL ADJUSTMENT IN GENERAL EQUILIERIUM 23

pitfalls in these works, and contend that the Stolper-Samuelson theorem is not an adequate guide to reality.

In summary, there is little consensus in the empirical literature. The present paper's contribution lies in specifymg empirical models built directly on the theory, conuolling for exogenous variables.

4. Industrid Factor-Intensity Rankings

The lnternatiom.zl Sectoral Databank (OECD, 1989) providcs data for nine manufac- turing industries in 12 developed countries. Two advantages of this data set are consist- ency across countries and the inclusion of capital input. The data cover the years 1970-85, and are expressed in 1980 US dollars.

The fi~st step in implementing the Stolper-Samuelson theorem is to rank,industries in each country by factor intensity. The average ratio of capital to labor over the entire time period is calculated. Table 1 presents the rankings by capital-labor ratios. For each industry, the fist number shows its ranking, with 1 as the most labor intensive. The number following in parentheses is the capital-labor ratio in thousands of dollars of capital per worker. Indus~ies are compared with the capital-labor ratio in total manufacturing, which appears in parentheses along the last row. Each industry is calssified as either (labor intensive) or K (capital intensive) relative to aggregate manufacturing in each country.

There is a fairly consistent factor-intensity ranking of industries. In every country, textiles ('IX), other manufactures (OM), wood (WD), and machinery and equipment (ME) are labor-intensive industries. Chemicals (CH) and nonmetallic minerals (NM) are capital intensive in cvery country. Basic metals (BM) and food (FD) are also classified as capital-intensive industries, because BM is labor intensive only in the Netherlands and FD only in Canada and Japan. Paper (PA) is a borderline industry, capital intensive in half the counlries. Comparing the distance between the capital-labor ratios and the average in manufacturing, countries with capital-intensive paper industries lie Parther horn the average. Thus, PA is classified as capital intensive.

Industries cau also be consistently compared across countries. For instance, aggre- gatemanufactwing (MF) is the most capital intensive in the Netherlands and Sweden, and the most labor intensive in the UK and Japan. Textiles (TX) is the most labor intensive in the US, and chemicals (CH) the most capital intensive in the Netherlands. The variation in the capital-labor ratio across countries is largest in paper (PA) and basic metals (BM).

5. An Empiricnl Model of the Stolper-Samuelson Theorem

The empirical model incorporates the assumptions and structure of the underlying theory. Variables which are exogenous in theory are included as independent variables in the regressions. Imperfections in the labor market are controlled by the use of independent variables. The key to specifymg a theory is to include the structure of the model which leads to the theoretical outcomes.

In the Stolper-Samuelson theorem, the ratio of wages to rents is the dependent variable, while output prices and factor endowments are independent exogenous vari- ables. Including influences due to imperfections in the iabor market, consider the following log h e a r model:

8 Tabk 1. Industrial Facror Irrlensrty, A werage for 1 9 7 W h R

a - n C. &,

Rank ($ WL) K ur L intemiv@ a s n

Cnunlrys a a

Induvrry" BL CN DL1 D N FR IT JP NL N R SW UK US 3 a 2

TX 2(34)L l(24)L 3(30)1, Z(26)L l(31)L 2(22)L 4(29)L 4(56)L l(25)L 2(33)L 2(24)L Z(18)L 3 O M 4(55)L Z(28)L l(24)L l(19)L 3(48)L - l(13)L l(31)L 2(33)L l (7)L

0 A(23)L 2(23)L 3

W D - 4 ( 5 0 ) ~ 4 ( 3 9 ) ~ 4 ( 3 9 ) ~ - l(2.0)~ - - q 4 . 4 ) ~ 4 ( 5 a ) ~ - 3 ( 4 8 ) ~ 3 M E l (3 l )L 3(42)L Z(25)L 3(30)L 2(39)L 3(37)L 2(27)L 3(56)L 3(35)L 3(50)L 3(26)1, 4(32)L 2

PA 3(51) L 6(112)K 5(46) K 5(41)L 4(53)K 4(5fi)K 6(lU9) K Z(48)L 5(49) L 9 (115)K 4(31)L 5(48) L P D 5(68)K 5(58)L 6(55)K 6(55)K 8(75)K 6(65)K 3(29)L 6(78)K 6(64)K 6(78)K S(53)K 6(54)K NM 7(75)K 9(2U)K 8(62)K 9(85)K 6(72)K 5(6l)K S(50)K 7(82)K 7(76)K 5(72)K 6(56)K 7(66)K CH 8(104)K 7(120)K 7(58)K 8(00)K 7(73)K 7(109)K 7(140)K 8(145)K Y(123)K 7(106)K 8(86)K 8(109)K BM 6(70)K 8(164)K 9(79)K 7(74)K 5(60)K 8(191)K X(145)K 5(60)L 8(108)K 8(116)K 7(59)K 9(172)K MF (56) (60) (40) (44) (51 (52) (39) (68) (55) (68) (39) (50)

LSaurue: OECD Infcrnariond Semrnl Darehonk, 1989. "-9, m&lg ham the most labor intensive to ibe most capital incel~sive induslries; (-), Lhou~nds of dollars or K per L: Kor L intensive, capital or lahoc intensive relative Lo average in manukmriltg (MF) in each counQ. 'DL, Belgium; CN, Canada: DU. Germany; DN, Dcnmark; FR, Fmuoe; IT, Italy; JP. lapan; NL. Netherlands; NR, Noway; SW. Sweden; UK, United Kingdom; US, U n i ~ d Statcs. dTX, textiles; OM, other mnnufaclures; WD, wood, wood producls; ME. machinery, equiprnenq PA, paper, printing, publishing; FD. faad, beverages, tabam; NM, M U I I I C U I ~ minerals; CH, chemicals; BM, basic metals, MI:, aggrejyte manuhduring.

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26 Furhod Rassekh and Henry Thompson

domestic supply aud raise the price of output. There is then some ambiguity with respect Lo the h a 1 position of the unit-value isoquant, which would shift away from the origin with the technology shock, but toward the origin with the resulting higher price. The net edeci could be a unit-value isoquant farther from the origin, which would mean a lower relative wage occurring along with the higher price of the labor-intensive good. A price change would then be associated with the opposite of the predicted Stolper-Sarnuelson effect.

Output of industry j is used as a proxy for price. The assumption is lhal technology changes have larger effects onthe unit-isoquant position than the related price changes when supply shocks occur. This assumption works better with more elastic demand. In these competitive models, the typical assumplion is perfect competition, which fits this high level of aggregation. If isolated industry j is labor intensive, higher output is then accompanied by an increase in the ratio of wages to rents. In the process, the capital- labor ratio rises. Higher outputs in capital-intensive industries arc associated with lower capital-labor ratios.

Industrial output is normalized by total manufacturing output. The share of industry j output in total manufacturing output, J ~ , becomes the exogenous variable of interest. Output shares control for the different sizes of the same industry across countries, reflecting performance of each industry relative to all manufacturing. Output shares are not used to proxy the price of the other sector because s, = 1 - sl.

This analysis leads to the estimation of

where qb is the random error term. The Stolper-Samuelson variable si, the share of isolated industry j in manufacturing, is lagged to allow for adjustment over time.

6. Results of the Stolper-SamueIson Estimation

Equation (2) is estimated in a pooled regession for each industry across the 12 sample countries over the 16 years. Although the countries are all developed industrial econo- mies, they differ in institutions, public policy, and business laws. To control for this heterogeneity, (2) is esumated with a separate constant term for each country.

Preliminary tests indicate heteroskedasticity and hst-order autoconelation. The Parks (1967) method is applied because it assumes res idds are heteroskedastic, contemporaneously correlated, and serially correlated of 6 i ~ t order in pooled data. The modelk estimated in logarithms, and the coefficients are interpreted as elasticities.

Regression estimates of (2) are reported in Table 2. The Stolper-Samuelson theorem in the present model predicts Ulat in the labor-intensive industries (TX, OM, WD, ME) an increase io s, would cause an increase in the capital-labor ratio. In the capital- intensive industries (PA, FD, NM, CH, BM) an increase insi should lower the capital- labor ratio. This prediction holds for five of thenine industries: OM, ME, PA, NM, and BM. The coefficients for WD and FD have the right sign, but are insignillcant. Signifi- cant opposite signs are found in only TX and CM. The Stolper-Samuelsonprediction is thus rejected in only two of nine industries. Among the Labor-intensive industries, OM and ME have correct and signacant posilive signs, and WD has the coxect sign but is insignificant. In three of the five capital-intensive industries, correct s i m c a n t negative effects occur. The signs of the other two industries do not coincide with theory, and CH has a significanl positive sign. The Stolper-Samuelson mechanism performs about as well in both labor- and capital-intensive industries.

.th he :e. lld iv e :ed

'PY ge5 . Sn this nen tal- vith

stry yest. tics, ares

(2)

re of

mple :one- r this

, The lastic, 3. The ies. :orem '. m) apital- apital- VI, and ji&- iiction stries, !ct sign lilicant le with hanism

INDUSTRIAL ADJUSTMENT IN GENERAL EQUILIBRIUM 27

Table 2. Stofper-Somuelson Es;inbarion: Regression Resrrlrs of Eyrrution (2) wilh Dependent Variable (KIL),

In vuriabl@ (+- sra fisfic)

sS,, output share;p&. other prioes: K , capital endowment; L;, labor endowment;G, cwl3icient of variationin wages; ul, unemployment. bTX lextiles; OM, other manuEactures; WD. wood, wwd products; ME. machinery, equipment; PA, paper, printing, pubhlishing; PD, food, kverages, Lobacco; NM, mnmerallic miner* CH, chemicals; BM, bmic melills; hF, aggregale manufacturing. 'RZr g 0 0 d ~ 6 ~ of fit. '1 MSE. menu squre error.

The capital endowment KI coefficient is significantly positive in every industry, and the labor endowment Lj signfiwtly negative, which indicates that factor endowments affect input ratios and underlying factor prices. A higher manufacturing capital endow- ment means a higher ratio of wages to rents and a higher capital-labor ratio in each industry. A higher labor endowment lowers both the wage-rent ratio and the industrial - - capitalIlabor ratio. This result implies that the static factor-price equalization property does not hold in this data set. Factor orices depend on factor endowments. Rassekh (1993) uses the same data, however, a id hds &namic wage convergence in each of these industries.

The coeKicient of variation in wages c: is significant except in FD and BM. Signifi- cance means that enough wage variation occurs across industries and time to affect the industry's capital-labor ratio. The significance of c; indicates that labor is not homo- geneous or completely mobile across industries. There are ways to modify the Heckscher-Ohlin model to include imperfections in the labor market and maintain the basic intuition of the Stolper-Samuelson theorem. Induding c; as a variable allows the share coefficient to be interpreted as though the variation in wages were constant. The unemployment term W; is significant in every industry except BM, which indicates that unemployment generally affects the capiral-labor and wage-rent ratios.

28 Farhad Rarsekh and Henry Thompson

Table 3. Specific-Fuciom Model: Regres~ion RaCirlfs of Equution (3) with Dependmi Variable

'Thk model is estimated with rapital inpuLs of other industries individually included, but these wefiients are not reporled 'S;, output shue; &, other prices; K;, capihl stock in hduslry j; L:, labor endo\Yme~t; cl, coefficient of vnrialion in wages; ul, unernplowent. cTX, textiles; OM, other manufactures; WD, wood, woad producb; ME, machine?, equipment; PA, paper, printin:, publishing: FD, food, beverages, tobacco; NM, nometallic minerah; CH, chemicak; BM, b d c metals; MF, aggregate mnufiicturinp. dRa, goodues6 of fit. 'MSB. mean syuare error.

Adjustment in the capital-labor ratio and the underlying wage-rent ratio can be expected to take some time. Equation (2) was also estimated including various combi- nations of several lags of the share variable. To determine the long-run impact, an econometric procedure described by Harvey (1990, chapter7) is applied. Accordingly, (2) is estimated for each industry with the first and second lags of the share variable. The equation is then re-estirnated with three lags. To determine the optimum lags, the Akaike Information Criterion described by Harvey (1990. p. 176) is applied. Results suggest that OM and WD need three lags, while the other industries need only two lags. The reported parameters for the share variable in Table 2 are calculated by summing the coefficients of the optimum lags.

7. An Empirical Specific-Factors Model

Jn estimating the specik-factors model, the capital input K$ is assumed to be the specific factor in the isolated indushy, and should be held constant. Therefore, Kj, becomes an exogenous variable. Indusbial labor input Lj, is treated as the dependent variable. Capital input in each of the industries is also separately held constant. The following spedc-factors equation is then cstimnted for each i~~dustry j:

aper, basic

n be mbi- t, an ng'y, able. I, the :suits r two :d by

se the :e, K\i ndent t. The

INDUSTRIAL ADJUSTMENT IN GENERAL EQUILIBRIUM 29

Most variables in (3) are repeated from (2), and pii represents a random-error term. Equation (3) is also estimated with a separate intercept for each country. The same discussion about using output shares as the Stolper-Samuelson variable applies in the specific-factors model.

A higher price in any industry in the specificifactors model lowers the ratio of wages to rents in the industry. In the present estimation, a higher output share in an industry should raise labor input. A positive c , is expected for every industry.

The total endowment of manufacturing labor is included as an exogenous variable. Coefficients for the total labor endowment and the capital inputs are nor predicted to be zero as in the Heckscher-Ohlin model. Other i nd~ l r i a l capital Kj ( j # i ) represents the input of capital in each of the orher industries. An increase in the capital of another sector causes labor to be drawn away from sector j. Thus, the coefficients for Kj, are expected to be negative. An increase in the labor endowment L; causes every industry to hire labor as wages fall. Thus, the coefficient c, should be positive.

Table 3 presents results from the pooled esrimalion of the specific-factors model in (3) for each industry. Heteroskedasticity and serial correlation of order one are again detected, and the Parks method is applied. The model is estimated in logarithms.

The coefficient c, of h e output share qi is positive in every industry and significant except in TX and EM. The fact that c, is not negative in any industry is strong support for the specific-factors model.

An increase in the capital input Kji in an industry should raise the labor input in the industry, as labor k, attracted kom other industries. Sigruficant positive coefficients for Kj occur in five industries (TX, ME, FD, CH, and BM) and only two significant negative signs occur (PA and NM). These coefficients are not reported to economize on space.

Increases in the labor endowment would be spread across industries, as the consist- ently significant positive coefficients indicate. The coefficient of variation in wages ct is significant for every industry, as is unemployment u; except for industry NM.

The Parks method used to estimate the two models does not automarically report the RZ. TO cdculate measures of goodness of fit, actual values of the dependent variables are regressed on their fitted values. The resulting measures are reported in Tables 2 and 3. These values should be interpreted only as an indication of goodness of fit because they may not have the usual distribution associated with ordinary least squares.

8. Conclusions

The specification in this paper captures the general-equilibrium predictions of ihe Stolper-Samuelson theorem and the specific-factors model using industrial data. In the Stolper-Samuelson theorem, the dependent variable is the ratio of capital to labor in each industry. Independent variables in the estimation are suggested by the assump- tions of theory. In five of nine industries, results conform with the Stolper-Samuelson theorem, and its basic implication is rejected in only two industries. Treating industrial capital as s p e d c and exogenous, an empirical specific-factors model is specified. Seven of nine industries conform with the basic prediction of the specific-factors model, and no industry presents a contradictory significant resull.

The present paper's focus is on the general-equilibrium siructure of production, not on diierellces in countries nr nn le.v.v~lc nf intern~tinnal trurlr Var in t inn in n i ~ t n i i t

30 Faritad Rasekh and Henry Thompson

prices, positively correlated with outputs, typically have the predicted general-equitib- rium effects on inputs. The Stolper-Samuelson theorem and specific-factors model apply across a wide range of common ci~cumtances. These core theoretical models should not be dismissed ofhand as empirically irrelevant.

The factor-proportions model springs from the way economists since Ricardo and Walras view an economy. There is a continuing challenge to formulate general- equilibrium models with many goods which clarify links between the prices of goods and the prices of factors. The present study shows that the Siolper-Samueison theorem and speci6c-factors model, even in rheir simplest two-factor versions, have empirical content. Comparing the performance of the two models, the specific-factas model generates somewhat stronger results.

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