A Cross-Country Estimation of the Elasticity of Substitution. between Labor and Capitalin Manufacturing Industries.

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1 A Cross-Country Estimation of the Elasticity of Substitution between Labor and Capitalin Manufacturing Industries. Sebastian Claro Universidad Cat olica de Chile September Abstract This paper presents a simple methodology to estimate the elasticity of substitution between labor and capital for rms operating in perfectly competitive markets with CRS production functions. It is applied in a cross-country sample to 8 -digit ISIC manufacturing industries. The econometric procedure relies on measures of sectorial capital stock, that are estimated for a sample of more than countries. Unlike older studies, the estimates are consistent with hicks-neutral cross-country technology di erences. The results reveal that in most industries the elasticity of substitution is smaller than one, rejecting the null hypothesis of Cobb-Douglas production functions. The paper provides then an estimation of ¾ LK at a level of aggregation extremely useful for research in the international trade literature. Sebastian Claro (sclaro@faceapuc.cl) Instituto de Economia, Universidad Cat olica de Chile, Casilla 7, Correo 7, Santiago - Chile. Phone ( ) 8 Fax( ) 77.

2 Introduction This paper presents an estimation of the elasticity of substitution between labor and capital - ¾ -(as the only two production inputs) for 8 -digit ISIC manufacturing industries. A crosscountry estimation for 99is presented based on thepredictions ofthe relationship between relative factor prices and relative factor intensities that follow from the optimizing process of perfectlycompetitive rms which technologies can be represented with simple CES production functions. It is assumed that there exists many identical rms within each country-industry pair, so that each rm takes factor prices as given and chooses its capital-labor ratio according to traditional rst-order conditions. An estimation of ¾ LK is relevant for its implications for growth theory, income distribution, employment impact of trade ows, labor demand, etc. of di erent substitution possibilities between factors within di erent sectors. The estimation for only two production factors is limited by the availability of data. This is of course a disputable approach, as we may think that factors of production in manufacturing industries could be classi ed in broader categories. The interpretation of such elasticity is subject to thefeasibility ofaggregatingdi erenttypesoflabor intoonecategory. (SeeBerndtand Christensen (97a) for a discussion on the conditions for aggregating factors.) Although apriori one may think that aggregating skilled labor and capital is more viable than aggregating di erent employment categories, evidence presented for Chile by Corbo and Meller (98) suggests that this is not necessarily the case. They argue that for most manufacturing industries there exists some evidence for building an aggregator of unskilled and skilled labor rather than skilled labor and capital. This is implicitly the approach developed here. Section of the paper presents the methodology used to estimate the elasticity of substitution,

3 and a comparison with alternative methodologies. Section discusses brie y the data. Section reports the results and compares them with other results in the literature. Methodology Consider a CRS production function with constant elasticity of substitution between two factors of production labor L and capital K X ic = f(l ic ;K ic ) = (a ic L ½ i ic +b ick ½ i ic )=½ i () where X ic refers to real value-added of good i in country c; L ic and K ic represent labor and capital inputs in sector i and ½ i : Note that we are allowing for a and b to di er across countries. As discussed bellow, this feature will make our estimation of a common ¾ i across countries relevant even in the presence of cross-country hicks-neutral technology di erences. The rst order conditions of the maximization process of each rm that take factor prices as given are w c = r c = (a ic L ½ i ic + b ick ½ i ic ) ½ i=½ i a ic L ½ i ic () (a ic L ½ i ic + b ick ½ i ic ) ½ i =½ i bic K ½ i ic () Combining () and () wegetfor each industryi in country c thefollowing relationship between factor prices - w=r and factor usage - K=L. lnw c =r c = ln a ic =b ic +(½ i )ln L ic =K ic () Strictly speaking, equation () suggests a relationship between factor intensities and relative factor prices at the sectorial level. Without a theoryforcross-industrydi erences infactorprices, () reveals thatfora common vector of relative factor prices, di erent industries choose di erent production techniques. In the empirical section we account for possible di erences in factor prices at the sectorial level.

4 The elasticity of substitution between labor and capital is given by ¾ i = =( ½ i ). Equation () reveals the traditional movement along a production isoquant of changes in relative factor prices. An increase in the relative cost of labor makes the rm use relatively more capital than before, at any scale of production. The size of the elasticity of substitution measures the ease of substitution alongthe isoquant, and have implications on the factor shares in value-added. Equation () provides the basis for the empirical estimation developed in section. I estimate for each - digit ISIC manufacturing industry the relationship in () for a cross-section sample of more than countries. The assumption of a common coe±cient for ln L ic =K ic implies that the elasticity of substitution is the same across countries. However, a common ¾ is compatible with technology di erences revealed through di erences in a and b. An estimation based on a single intercept within each industry implies that a=b is similar across countries, meaning that (potential) technology di erences are hicks neutral. This can be seen by dividing () and () to get f L = w f K r = a µ L ½ () b K Di erences in a and b that keep the ratio constant imply no change in the optimal K=L for any given relative factor prices. This is exactly what hicks-neutral technology di erences imply. As discussed in section, the lack of a panel data structure mandates the estimation with a common cross-country intercept for each industry. This is only consistent with hicks-neutral technological di erences. An alternativeapproach to estimate elasticities of substitution is developed by Behrman (98) and others. Starting from a CES production function like the one in equation () we can derive See Arrow, Chenery, Minhas and Solow (9) and Hamermesh (99).

5 the following expression for the rst-order condition of maximizing rms (under constant returns to scale) ln X ic =L ic = +¾ lnw ic () with = ¾ lna. This approach has been widely used, even for estimation of aggregate measures ofelasticity ofsubstitution between labor and capital (see Harmermesh (99)). Econometric estimations of equation () provide direct measures of the elasticity of substitution. A complete estimation of equation () requires a panel structure of the data in order to allow for di erent intercepts that are consistent cross-country technology di erences. Behrman avoids that problem by estimatingapooled regression for several countries and 7 -digit ISIC manufacturingindustries using average values for value-added, employmentand wages between 97and 97and including industry and country dummies that allow him to di erentiate the elasticity of substitution across di erent units ofanalysis. Thegreat advantageof his method is that nodata on capital stock and return on capital are required. Indeed, the United Nations database that he uses does not provide data to estimate capital stocks. This allows him to work with a sample of countries broader than the one used here (about 7 countries). Thegreat disadvantage is that helacks degrees of freedom to allow for cross-country di erences in the elasticity of substitution and technology level. This problem is not relevant in an estimation based on equation () Taking logarithm from the rst order condition with respect to labor (equation ()) we get that lnw = lna+ ( ½)ln(X=L) that can be written as ().

6 Data The data is obtained from UNIDO Statistical Database for 8 countries between 9 and 99, containing series on employment, value-added, wages and salaries, output and gross xed capital formation for 8 -digit industry. The series of real capital stock can be estimated using the capital formation series, an estimation of depreciation rates and adequate investment de ators. Table reports the measures ofcapital stock for 99 calculated for di erent countries for each -digit ISIC manufacturing category, in millions of 99 US dollars. The series of capital stock was constructed using the yearly series of gross xed capital formation from 97 until 99 in current US dollars. I considered a % depreciation rate and the investment de ator series for the United States to construct the capital stock series. Due to data restrictions, I perform the empirical analysis in 99 because it is year for which the set of countries with capital stock in maximized across industries. Tables, and report data on employment, nominal value-added and nominal payment of wages and salaries for the set of countries considered. These data allow us to calculate measures of L=K for each country/industry and estimations of wage-rental rate ratios. The wage rate considered is the average yearly wage of workers (Table / Table ) and the rental rate is computed as value-added minus labor payments divided by the capital stock (Table - Table /Table ). Results Table reports the results of regressions of equation () for each industry. (½ i ) represents the coe±cient on ln L=K, n represents the number of countries included in the regression and The results are not a ected by di erent depreciation rates.

7 ¾ i (= = ½ i ) is the implicit value for the elasticity of substitution between labor and capital. In all but ve industries (Beverages, Tobacco, Petroleum Re neries, Iron & Steel, and non-electrical Machinery) the correlation coe±cient between relative factor prices and factor intensity is greater than.7. Figure plots for the 8 ISIC manufacturing industries the cross-country values of ln w=r and ln K=L. These graphs show that the high correlations are not driven by outliers but reveal genuine economic relationships. Moreover, in most cases the assumption of a common intercept implicit in the regression appears to be reasonable. This suggests that if technology di erences exists, a hicks-neutral approximation is a reasonable one. The null hypothesis of Cobb-Douglas technologies (½ = ) is rejected in most cases, as the p-value in the last column of table suggests. Table presents a comparison of the estimates of ¾ reported in table with those obtained by Behrman (98). The rst column in Table replicates column in Table. As already discussed, in most cases ¾ > and the null hypothesis of Cobb-Douglas production functions is in general rejected. Column presents the estimates of Behrman using pooled data for 7 countries. These coe±cients come from an estimation of equation () that includes interactions of lnw ic and sectorial dummies, to allow for cross-industry variations in ¾. This procedure, however, does not include non-interactive dummies, and hence it implicitly assumes similar technologies across countries. The coe±cients in column imply that the null hypothesis of Cobb-Douglas technologies cannot be rejected at high levels of con dence. The correlation coe±cient between the estimators in columns and is. (signi cant at %), but it is mainly driven by the coe±cient of Tobacco industries. Without Tobacco, the correlation drops to. and becomes insigni cant. Column reports estimations of equation using a similar procedure to Behrman but with the data used in this study. It can be easily checked that the results arevery similar tothose in column. Indeed, 7

8 the correlation coe±cient is.87 and the null hypothesis of Cobb-Douglas technologies cannot be rejected, too. Evidence of Cobb-Douglas technologies is also presented in Corbo and Meller (98) for - digit ISIC Chilean manufacturing industries. They use a translog approach to estimate directly the production function rather than the optimal factor usage from optimization processes. I do not have data of real value-added comparable across-countries, so I cannot estimate directly the production function. Moreover, Corboand Meller argue that the directestimation of aproduction function is a more reasonable approach in Chilean manufactures because there is(was) strong danger of speci cation error owing to the presence of non-competitive elements. In the study presented here, I believethattheassumption ofcompetitivedecisionsofmanufacturing rmsin across-section of countries is a-priori a reasonable one. Hamermesh (99) summarizes several studies aimed to estimate the elasticity of substitution between labor and capital at high levels of aggregation - entire manufacturing sector or the whole economy. The most common approach is the one summarized in equation (). The results are mixed, with ¾ ranging from.8 to. depending on the speci cation used. According to the author, direct estimation of ¾ is not a very promising route. His argument is that we know very little about the e ect of changes in the return to work on variations in labor supply over the relatively short periods of time used. This criticism, that also a ects the approach based on equation () seems valid for estimations of the elasticity of substitution based on aggregate production functions, as interactions of factor demands and factor supplies are required toidentify the coe±cients. However, for industry-speci c estimates the criticism is weaker as we can argue that the e ective factor supply for each sector is completely elastic at the factor price level. 8

9 References [] Arrow, K. J.; Chenery, H.B.; Minhas, B.S.; and Solow, R.M (9) "Capital-labor substitution and economic e±ciency" Review of Economics and Statistics :- [] Behrman, Jere R. (98) "Country and Sectorial Variations in Manufacturing Elasticities of Substitution between Capital and Labor" in Trade and Employment in Developing Countries. Chapter. FactorSupplyand Substitution. Ed. by AnneO. Krueger. TheUniversity ofchicago Press. [] Berndt, E., and Christensen, L. R. (97a) "The Internal Structure of Functional Relationships: Separability, Substitution and Aggregation" Review of Economic Studies (July): -. [] Corbo, V and P. Meller (98) "The Substitution of Labor, Skill and Capital: Its Implications for Trade and Employment" in Trade and Employment in Developing Countries. Chapter. Factor Supply and Substitution. Ed. by Anne O. Krueger. The University of Chicago Press. [] Hamermesh, Daniel (99) "Labor Demand" Princeton University Press 9

10 Table : Capital Stock for 99 Millions of 99 US dollars UNIDO Code Country Food Products (/) Beverage () Tobacco () Textile () Apparel () Leather () Footwear () Wood () Furniture () Paper Products () Printing and Publishing () Chemicals () Other Chemicals () Austria Barbados Belgium Bulgaria Canada Colombia Cyprus Czechoslovakia Denmark Ecuador Fiji Finland France Germany, West Hungary Ireland Italy Japan Korea, Rep Kuwait Luxembourg Mexico Mongolia Netherlands New Zealand Norway Poland Portugal Romania Singapore Zimbabwe Egypt United Kingdom United States Source: UNIDO Database, FRED and author s calculations. Petroleum Refineries () Misc. Products of Petroleum & Coal () Rubber () Plastic () Pottery () Glass () Other Non-Metallic Mineral Products (9) Iron & Steel (7) Non-Ferrous Metals (7) Fabricated Metal Products (8) Machinery except Electrical (8) Electrical Machinery (8) Transport Equipment (8) Professional & Scientific Equipment (8) Other Manufacturing Industries (9)

11 Table : Employment Level for 99 Thousands of Workers UNIDO Code Country Food Products (/) Beverage () Tobacco () Textile () Apparel () Leather () Footwear () Wood () Furniture () Paper Products () Printing and Publishing () Chemicals () Other Chemicals () Austria Barbados Belgium Bulgaria Canada Colombia Cyprus Czechoslovakia Denmark Ecuador Fiji Finland France Germany, West Hungary Ireland Italy Japan Korea, Rep Kuwait Luxembourg Mexico Mongolia Netherlands New Zealand Norway Poland Portugal Romania Singapore Zimbabwe Egypt United Kingdom United States Source: UNIDO Database, FRED and author s calculations. Petroleum Refineries () Misc. Products of Petroleum & Coal () Rubber () Plastic () Pottery () Glass () Other Non-Metallic Mineral Products (9) Iron & Steel (7) Non-Ferrous Metals (7) Fabricated Metal Products (8) Machinery except Electrical (8) Electrical Machinery (8) Transport Equipment (8) Professional & Scientific Equipment (8) Other Manufacturing Industries (9)

12 Table : Wages and Salaries for 99 Millions of US Dollars UNIDO Code Country Food Products (/) Beverage () Tobacco () Textile () Apparel () Leather () Footwear () Wood () Furniture () Paper Products () Printing and Publishing () Chemicals () Austria Barbados Belgium Bulgaria Canada Colombia Cyprus Czechoslovakia Denmark Ecuador Fiji Finland France Germany, West Hungary Ireland Italy Japan Korea, Rep Kuwait Luxembourg Mexico Mongolia Netherlands New Zealand Norway Poland Portugal Romania Singapore Zimbabwe Egypt United Kingdom United States Source: UNIDO Database, FRED and author s calculations. Other Chemicals () Petroleum Refineries () Misc. Products of Petroleum & Coal () Rubber () Plastic () Pottery () Glass () Other Non-Metallic Mineral Products (9) Iron & Steel (7) Non-Ferrous Metals (7) Fabricated Metal Products (8) Machinery except Electrical (8) Electrical Machinery (8) Transport Equipment (8) Professional & Scientific Equipment (8) Other Manufacturing Industries (9)

13 Table : Value Added for 99 Millions of US Dollars UNIDO Code Country Food Products (/) Beverage () Tobacco () Textile () Apparel () Leather () Footwear () Wood () Furniture () Paper Products () Printing and Publishing () Chemicals () Austria Barbados Belgium Bulgaria Canada Colombia Cyprus Czechoslovakia Denmark Ecuador Fiji Finland France Germany, West Hungary Ireland Italy Japan Korea, Rep Kuwait Luxembourg Mexico Mongolia Netherlands New Zealand Norway Poland Portugal Romania Singapore Zimbabwe Egypt United Kingdom United States Source: UNIDO Database, FRED and author s calculations. Other Chemicals () Petroleum Refineries () Misc. Products of Petroleum & Coal () Rubber () Plastic () Pottery () Glass () Other Non-Metallic Mineral Products (9) Iron & Steel (7) Non-Ferrous Metals (7) Fabricated Metal Products (8) Machinery except Electrical (8) Electrical Machinery (8) Transport Equipment (8) Professional & Scientific Equipment (8) Other Manufacturing Industries (9)

14 Table : Elasticity of Substitution between Labor and Capital CES Production Function Industry ( digit ISIC) r - se n R s p-value (r=) Food Products (/) Beverage () Tobacco () Textile () Apparel () Leather () Footwear () Wood () Furniture () Paper Products () Printing and Publishing () Chemicals () Other Chemicals () Petroleum Refineries () Misc. Products of Petroleum & Coal () Rubber () Plastic () Pottery () Glass () Other Non-Metallic Mineral Products (9) Iron & Steel (7) Non-Ferrous Metals (7) Fabricated Metal Products (8) Machinery except Electrical (8) Electrical Machinery (8) Transport Equipment (8) Professional & Scientific Equipment (8) Other Manufacturing Industries (9)

15 Table : Comparison of Alternative Approaches.8.97 Claro Behrman Claro Industry ( digit ISIC) Eq. () Eq. () Eq. () Food Products (/) Beverage () Tobacco ().. Textile () Apparel () Leather () Footwear () Wood () Furniture () Paper Products () Printing and Publishing () Chemicals () Other Chemicals () Petroleum Refineries () Misc. Products of Petroleum & Coal () Rubber ()..9.9 Plastic () Pottery () Glass () Other Non-Metallic Mineral Products (9)..9.9 Iron & Steel (7) Non-Ferrous Metals (7) Fabricated Metal Products (8) Machinery except Electrical (8) Electrical Machinery (8) Transport Equipment (8) Professional & Scientific Equipment (8)..9 Other Manufacturing Industries (9).8.9

16 Figure : Cross-country Correlations of Relative Factor Prices and Factor Intensities Food Products (/) Beverage () Tobacco () Textile () Apparel () Leather () Footwear () Wood Products () Furniture ()

17 Figure : Cross-country Correlations of Relative Factor Prices and Factor Intensities Paper Products () Printing and Publishing () Chemicals () Other Chemicals () Petroleum Refineries () Misc. Products of Petroleum & Coal () Rubber Products () Plastic Products () Pottery ()

18 Figure : Cross-country Correlations of Relative Factor Prices and Factor Intensities Glass Products () Other Non-metallic Mineral Products (9) Iron & Steel (7) Non-Ferrous Metals (7) 7 8 Fabricated Metal Products (8) 7 8 Machinery except Electrical (8) Electrical Machinery (8) Transport Equipment (8) Professional & Scientific Equipment (8) Other Manufacturing Industries (9) 8