The Elasticity of Substitution Between Capital and Labour in the US Economy: A Meta‐Regression Analysis
| Author | Patrick Zwerschke,Michael Knoblach,Martin Roessler |
| DOI | http://doi.org/10.1111/obes.12312 |
| Published date | 01 February 2020 |
| Date | 01 February 2020 |
62
©2019 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 82, 1 (2020) 0305–9049
doi: 10.1111/obes.12312
The Elasticity of Substitution Between Capital and
Labour in the US Economy: A Meta-Regression
Analysis*
Michael Knoblach, Martin Roessler and Patrick Zwerschke
Faculty of Business and Economics, TU Dresden, 01062 Dresden, Germany
(e-mail: michael.knoblach@tu-dresden.de, martin.roessler@tu-dresden.de,
patrick.zwerschke@tu-dresden.de)
Abstract
Despite extensive research, there is no agreement on the value of the elasticity of substi-
tution between capital and labour at the aggregate or the industrial level. Utilizing 2,419
estimates from 77 studies published between 1961 and 2017, this paper provides the first
meta-regression analysis for the US economy. We show that the heterogeneityin previously
reported estimates is driven primarily by modelling decisions for technological dynamics.
Throughout the analysis, the hypothesis of a Cobb–Douglas production function is re-
jected. Based on our meta-regression sample, we estimate a long-run meta-elasticity for
the aggregate economy in the range of 0.45–0.87. Most industrial estimates do not deviate
significantly from the estimate for the aggregate economy.
I. Introduction
The elasticity of substitution between capital and labour, , is an essential concept in
macroeconomics. In theories of economic growth, the value of is crucial for a multitude
of issues, including the diminishment of marginal products (Brown, 1966), the speed of
convergence to the steady state (Turnovsky, 2002) or the role of technological change
(Acemoglu, 2003). As already shown by Solow (1956) and Pitchford (1960), perpetual
growth is possible even in the absence of technical progress if is sufficiently large.
Moreover, the substitutability between capital and labour also plays a key role for the
functional distribution of income. Since the seminal contribution of Hicks (1932), it is
well known that changes in relative factor endowments affect the distribution of income
between capital and labour if differsfrom unity. For example,Piketty’s (2014) explanation
JEL Classification numbers: C11; E23; O30; O40.
*We thank Alexander Kemnitz, Jonathan Temple and three anonymous referees for very helpful suggestions.
We also benefited from the comments of conference participants at the International Economic Association World
Congress 2017 and the Scottish Economic Society Conference 2017. Moreover, we thank Arthur Leon Gabrielian
for valuable research assistance.
: A Meta-Regression Analysis 63
of the observed decline in the labour share of income crucially depends on the assumption
that >1 (Piketty and Zucman, 2014; Acemoglu and Robinson, 2015).
Due to its relevance, consistent evidence on plausiblevalues of would be valuable for
researchers and policy advisers. However, since the introduction of the constant elasticity of
substitution (CES) production function by Arrow et al. (1961), no consensus has emerged
in the empirical literature. For the US economy, Chirinko’s (2008) survey reports values
above, belowand at unity. More recently, Grossman et al. (2017, pp. 1295) state that ‘[t]he
size of the elasticity of substitution is much debated and still controversial’.
Past research has identified several regularities underlying the heterogeneity in esti-
mation results. For instance, Lucas (1969) notes that early time series studies of the USA
typically reject the Cobb–Douglas assumption, whereas cross-sectional estimates tend to
support a unitary elasticity. Another regularity appears to be present with respect to the
choice of the estimation equation. Over a multitude of studies (e.g. Dhrymes and Zarem-
bka, 1970; Kalt, 1978; Young, 2013), the use of the first-order condition for labour yields
estimates exceeding those obtained by the use of the first-order condition for capital. In
addition, Antr`as (2004) reveals a regularity with respect to the treatment of technological
change. Based on theoretical and empirical evidence he demonstrates that the assumption
of Hicks-neutrality biases estimates towards unity in the presence of non-neutral techno-
logical change and roughly constant factor income shares. As will be outlined below, this
list of conjectures can be extended considerably.
The contribution of this paper is the first assessment of heterogeneity in estimates of
the elasticity of substitution between capital and labour in the US economy both at the
aggregate and the industrial level within a meta-regression framework.1In addition to
analyzing the effects of the different specification choices, weestimate meta-elasticities of
substitution based on our collected data. Conditional on these meta-estimates, we provide
evidence that for the economyas a whole, most likely falls in the range of 0.45–0.87. Thus,
the aggregated empirical evidence suggests that the US economy is most likely not well
represented by a Cobb–Douglas production function, which implies =1. Furthermore,
we find that heterogeneity in previously reported estimates is mainly driven by different
specifications of technological dynamics.
The remainder of the paper is structured as follows. Section II briefly reviews central
properties of the CES production function. In section III, we introduce our search strategy,
provide an initial overviewof the collected elasticity estimates and explore various possible
sources of heterogeneity. The actual meta-regression analysis is conducted in section IV,
where we first describe the data set and our empirical strategy. Subsequently, estimation
results are presented, followed by robustness checks and extensions. Section V concludes.
1Although still less applied than in other disciplines, meta-regressions have become increasingly popular in eco-
nomics. For example, Lichter, Peichl and Siegloch (2015) analyze the own-wage elasticity of labour demand and
Doucouliagos and Ulubasoglu (2008) focus on democracy and economic growth. For excellent overviews of meta-
(regression) analysis methods see Feldand Heckemeyer (2011) and Stanley and Doucouliagos (2012). Meta-analyses
based on observational data are usually subject to the limitation that different studies may draw on the same data
sources. This results in an informational overlapbetween the estimates reported in these studies. Since these overlaps
to some extent also exist in our data set, our analysis shares this limitation with other meta-analyses in economics.
However, there is variation in the data sources used by the studies included in our sample. Furthermore, these studies
coverdifferent time periods and different levels of aggregation (firm/industry/country level). Against this background,
applying meta-analytic techniques can provideinformative insights on the heterogeneity in estimates of the elasticity
of substitution.
©2019 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
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