Capital–Skill Complementarity: Does Capital Composition Matter?

• Published date: 01 January 2019
• Author: Miguel Lorca,Juan A. Correa,Francisco Parro
• Date: 01 January 2019
• DOI: http://doi.org/10.1111/sjoe.12267

Scand. J. of Economics 121(1), 89–116, 2019

DOI: 10.1111/sjoe.12267

Capital–Skill Complementarity: Does

Capital Composition Matter?*

Juan A. Correa

Universidad Andres Bello, 7591538 Santiago, Chile

jlcorrea allamand@yahoo.com

Miguel Lorca

University of New South Wales, NSW2052 Sydney,Australia

mlorcaes@gmail.com

Francisco Parro

Universidad Adolfo Ib´a˜nez, 7941169 Santiago, Chile

fjparrog@gmail.com

Abstract

We estimate the effect of capital composition on the size of capital–skill complementarity and

the skill wage premium. Disaggregating the capital stock into different types according to

technological content, we find that: capital is more of a q-complement to skilled labor than

to unskilled labor; the higher the technological component of capital, the larger the size of the

relative q-complementarity between capital and skilled labor; and replacing non-technological

with technological capital might increase the skill wage premium by about 9 percent. Our results

highlight that changes in capital composition matter for understanding changes in the skill wage

premium.

Keywords: Skill wage premium; technological capital; translog function

JEL classification:D24; J24; L60

I. Introduction

The stock of capital can substitute for or complement labor, depending on

the type of labor used in the production process. Griliches (1969) posits

that capital is less substitutable for skilled labor than for unskilled labor

(capital–skill complementarity). Therefore, as stated by Krusell etal. (2000),

in a framework where capital and unskilled labor are perfect substitutes and

have unit elasticity of substitution with skilled labor, capital accumulation

*We thank H´ector Calvo, Mauricio Larra´ın, Alex Mennuni, Carmine Ornaghi, Fernando Parro,

two anonymous referees, and all participants at the LatinAmerican Meeting of the Econometric

Society and the Society of Labor Economists meeting for their comments and suggestions. J.A.

Correa also thanks FONDECYT for financial support (grant no. 11121620).

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The editors of The Scandinavian Journal of Economics 2017.

90 Capital–skill complementarity: does capital composition matter?

increases the relative marginal product of skilled labor and pushes the skill

wage premium up. Since Griliches (1969) first stated his hypothesis, several

studies have attempted to test it. Although some studies in the body of

literature on this topic support his hypothesis, the evidence has been almost

exclusively concentrated in developed countries.

Moreover, most of the related articles regard capital as an aggregate

input and do not consider that the technological composition of capital

might matter. Does software (technological capital) substitute significantly

more for unskilled workers than it does for skilled workers? Does a

non-complex machine (non-technological capital) substitute for roughly

the same number of unskilled and skilled workers? If the answer to

these questions is yes, how does this phenomenon affect the skill wage

premium?

In this paper, we use panel data from Chilean manufacturing plants to

study these three questions. We present evidence on the existence of capital–

skill complementarity, the effect of capital stock composition on the size of

capital–skill complementarity, and the effect of capital composition on the

skill wage premium. Our estimations also allow us to study the magnitude

of the complementarity between non-technological capital and skilled labor,

compared with the magnitude of the complementarity between technological

capital and unskilled labor.

We build and estimate a four-input production function model with

skilled labor, unskilled labor, technological capital, and non-technological

capital as production factors. We disaggregate the stock of capital, defining

two different specifications for the technological stock of capital. Following

Sato and Koizumi (1973), Hamermesh (1985), and Stern (2011), we

estimate the elasticities of complementarity for our four-input production

function. We show that these elasticities allow us to establish a direct

link between capital composition and the skill wage premium. We use

the estimated elasticities of complementarity to quantify the effect of

a change in the technological content of capital on the skill wage

premium.

We find that capital is more of a q-complement to skilled workers than

it is to unskilled workers, in line with the hypothesis of Griliches (1969).

Moreover, we find that the higher the technological component of the capital

stock, the larger the size of the relative q-complementarity between capital

and skilled labor. We use the computed elasticities of complementarity to

quantify the effect of capital composition on the skill wage premium. We

show that as the composition of the stock of capital moves toward more

technological capital, the skill wage premium rises. Moreover, our estimated

elasticities imply that an economy replacing non-technological capital with

technological capital, such that the contribution to output of technological

capital increases by 50 percent while that of non-technological capital falls

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The editors of The Scandinavian Journal of Economics 2017.