The micro elasticity of substitution and non‐neutral technology

• Author: Devesh R. Raval
• Date: 01 March 2019
• DOI: http://doi.org/10.1111/1756-2171.12265
• Published date: 01 March 2019

RAND Journal of Economics

Vol.50, No. 1, Spring 2019

pp. 147–167

The micro elasticity of substitution and

non-neutral technology

Devesh R. Raval∗

This article provides evidence on the micro capital-labor elasticity of substitution and the bias

of technology. Using data on US manufacturing plants, I find several facts inconsistent with

a Cobb-Douglas production function, including large, persistent variation in capital shares. I

then estimate the elasticity using variation in local wages, and several instruments for them,

for identification. Estimates of the substitution elasticity using all plants range between 0.3 and

0.5, with similar estimates across industries. I use these elasticity estimates to measure labor

augmenting productivity, and find that labor augmenting productivity is highly persistent, and

correlated with exports, size, and growth.

1. Introduction

The elasticity of substitution between capital and labor is central for severalpolicy questions

in economics. It determines how firms’ usage of labor and capital respond to policy changes that

affect factor prices, such as investment subsidies (Hall and Jorgenson, 1967); tariffs on capital

goods (Cai, Ravikumar, and Riezman, 2015); changes in trade barriers (Dornbusch, Fischer,

and Samuelson, 1980); minimum wages (Aaronson and French, 2007); and firing costs (Petrin

and Sivadasan, 2013). The elasticity is also important to understand both some of the reasons

why firms innovate (Acemoglu, 2010), as well as how technological change affects relative

factor intensities, either through nonneutral productivity (Hicks, 1932; Sato, 1975), or investment

specific technical change (Greenwood, Hercowitz, and Krusell, 1997).

Most of the recent empirical literature on production function estimation using micro data

(Olley and Pakes, 1996; Levinsohn and Petrin, 2003) sets the elasticity of substitution to one

∗Federal Trade Commission; devesh.raval@gmail.com.

I would like to thank myadvisor Ali Hortacsu and committee members Sam Kortum and Chad Syverson for their support

and guidance on this article. I have also benefited from comments from Chris Adams, Fernando Alvarez, Allan Collard-

Wexler,Alejo Costa, Dan Hosken, Chang-Tai Hsieh, Erik Hurst, Matthias Kehrig, Steven Levitt, Asier Mariscal, Benni

Moll, Emi Nakamura, Ezra Oberfield,Adi Rom, Ted Rosenbaum, Nate Wilson, and Andy Zuppann, as wellas Editor Marc

Rysman and two anonymousreferees. I appreciate the excellent comments that John Haltiwanger provided as a discussant

at the 2011 NBER Summer Institute in Boston, and the help of Frank Limehouse at the Chicago Census Research Data

Center, Randy Becker for assistance with deflators for the micro data, and Ryan Kelloggfor data on amenities at the local

area level. Any opinions and conclusions expressed herein are those of the author and do not necessarily represent the

views of the US Census Bureau, the Federal TradeCommission, or its Commissioners. All results have been reviewed to

ensure that no confidential information is disclosed.

Published 2019. This article is a U.S. Governmentwork and is in the public domain in the USA. 147

148 / THE RAND JOURNAL OF ECONOMICS

by estimating Cobb-Douglas production functions. Beyond setting the elasticity to one, the

Cobb-Douglas production function implies that all productivity differences are neutral, and so

productivity improvements affect all factors proportionately. This assumption on productivity

thus excludes automation technologies that both improve productivity and decrease the amount

of labor used in production. It means that productivity has no effect on factor shares.

In this article, I first develop a set of stylized facts to evaluate the credibility of the Cobb-

Douglas assumption at the industry level using US micro data on manufacturing plants. Plants

with a Cobb-Douglas production function should have a constant capital share. However, plants

within the same industry exhibit substantial variation in capital shares that are persistent over

time. Second, at least for the largest plants, capital shares are correlated with plant revenue.

Finally, capital shares fall when the average wage in a locality rises.

Given these facts, I estimate the elasticity of substitution between capital and labor that a

manufacturing plant faces. Cost minimization implies that the elasticity of substitution measures

how the ratio of factor costs responds to changes in factor prices. I identify the elasticity using

this relationship; no assumptions on demand or information about output quality or prices are

needed. For factor price variation, I use cross-sectional differencesin wages across US localities.1

Because local wage differences are highly persistent over time, this approach should identify the

average effect of a long-run change in factor prices on plant factor shares.

The main identifying assumption I make is that location-specific wages are uncorrelated

with differences in labor augmenting productivity and rental prices across plants. This assumption

might be violated if more productive areas have higher wages, or if the price of capital varies

across locations due to locally built capital or firm-specific interest rates. I address the concern

of endogenous wages by instrumenting for the local wage using three sets of instruments. The

first set of instruments are cross-sectional differences in amenities from Albouy et al. (2016);

locations with greater amenities should have lower wages (Rosen, 1979; Roback, 1982). I also

use two sets of instruments for labor market conditions based on the interaction of local industry

shares and nationwide shocks due to Bartik (1991) and Beaudry, Green, and Sand (2012).

Using ordinary least squares (OLS) regressions, I estimate a plant-level elasticity of sub-

stitution to be between 0.3 to 0.5, using all manufacturing plants. When I allow the elasticity

to vary across two-digit industries, estimates range between 0.15 and 0.75 for most industries.

Using each of the three sets of instruments, or all instruments together, leads to similar estimates

of the elasticity.

These estimates are robust to severalpotential concer ns. Toaddress the concern of correlation

between rental prices and wages, I estimate the elasticity between labor and equipment capital,

because buildings are likely to have much more local construction than equipment capital. I

also estimate specifications with firm fixed effects to control for differences in rental prices

or productivity across firms. To control for industry clustering, I separately examine a set of

narrowly defined industries which have plants located in almost all US localities. I find broadly

similar estimates to my baseline specification in these robustness checks, except for slightly

higher estimates of the elasticity after including firm fixed effects.

I then apply my estimates of the micro elasticity of substitution to identify labor augment-

ing productivity. I identify labor augmenting productivity without placing any assumptions on

demand. Instead, cost minimization allows me to identify labor augmenting productivity using

expenditures of each factor; I construct two productivity measures, the first using capital and

labor, and the second using materials and labor.

Using these measures, I revisit some of the stylized facts of the productivity literature looking

at labor augmenting productivity. In order to account for measurement errors in productivity, I

employ a repeated measures instrumental variables (IV) strategy, instrumenting for one measure

1An earlier literature used cross-sectional differences in wages across countries or US localities to estimate

aggregate or industry elasticities. See, for example, Arrow et al. (1961), Minasian (1961), Solow (1964), Lucas (1969),

Dhrymes and Zarembka (1970), and Zarembka and Chernicoff (1971).

Published 2019. This article is a U.S.Government work and is in the public domain in the USA.