Production Technology Estimates and Balanced Growth
| Date | 01 February 2015 |
| Author | Miguel A. León‐Ledesma,Peter McAdam,Alpo Willman |
| Published date | 01 February 2015 |
| DOI | http://doi.org/10.1111/obes.12049 |
40
©2013 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 77, 1 (2015) 0305–9049
doi: 10.1111/obes.12049
Production Technology Estimates and Balanced
Growth*
Miguel A. Le ´on-Ledesma†, Peter McAdam‡,§ and Alpo
Willman†,‡
†School of Economics, University of Kent, Keynes College, Canterbury, CT27NP, UK
(e-mail: m.a.leon-ledesma@kent.ac.uk)
‡Research Department, European Central Bank, Frankfurt am Main, D-60311, Germany,
(e-mail: peter.mcadam@ecb.europa.eu; alpo.willman@gmail.com)
§School of Economics, University of Surrey, Guildford GU2 7XH, UK
Abstract
Capital-labour substitution and total factor productivity (TFP) estimates are essential
features of many economic models. Such models typically embody a balanced growthpath.
This often leads researchers to estimate models imposing stringent prior choices on tech-
nical change. We demonstrate that estimation of the substitution elasticity and TFP growth
can be substantially biased if technical progress is thereby mis-specified. We obtain ana-
lytical and simulation results in the context of a model consistent with balanced and near-
balanced growth (i.e. departures from balanced growth but broadly stable factor shares).
Given this evidence, a constant elasticity of substitution production function system is then
estimated for the US economy. Results show that the estimated substitution elasticity tends
to be significantly lower using a factor-augmenting specification (well below one). We are
also able to reject conventional neutrality forms in favour of general factor augmentation
with a non-negligible capital-augmenting component. Our work thus provides insights into
production and supply-side estimation in balanced-growth frameworks.
I. Introduction
A balanced growth path (BGP) defines an equilibrium in which macroeconomic variables
such as output, consumption, etc., tend to a common growth rate, whilst key underlying
ratios (e.g. factor income shares, capital–output ratio and the real interest rate) are constant,
Kaldor (1961). In terms of neoclassical growth theory (Uzawa, 1961), it requires that
either, technical progress be labour-augmenting (i.e. Harrod neutral), or production is
Cobb–Douglas (i.e. exhibits a unitary elasticity of substitution between input factors).
*Thisarticle is a substantially updated and revised version of an earlier draft distributed as ‘In Dubio Pro CES’(ECB
WorkingPaper No. 1175). We thank two anonymous referees, Beata Javorcik(editor), YoungjaeChang (discussant),
Manuel G´omez-Su´arez, Rainer Klump, Kangwoo Park (discussant), Efthimios Tsionas (discussant),Anders Warne
and participants at numerous seminars for comments. Opinions are the authors’ and not necessarilythose of the ECB.
JEL Classification numbers: C15, C32, E23, O33, O51.
Production technology estimates and balanced growth 41
Although balanced growth looks a reasonable description of many economies and is a
common and tractable modelling narrative, these two explanations are widely disputed.1
For instance, there is now mounting evidence in favour of a below-unity aggregate sub-
stitution elasticity (e.g. Chirinko, 2008). Likewise, that all technical change is labour
augmenting appears unduly restrictive. Recent theoretical literature (Acemoglu, 2007)
also argues that while technical progress is asymptotically labour-augmenting, it may
become capital-biased in transition reflecting incentives for factor-saving innovations.2
Despite these concerns, researchers, guided by tractability and the apparent ‘stylized facts’,
invariably impose BGP conditions for estimating key supply side parameters such as the
elasticity of capital–labour substitution and total factor productivity (TFP).
Arguably, though, the costs of doing so are unknown. To fill this important gap we
hence analyze the potential consequences of imposing prior beliefs on the form of tech-
nical progress for such estimates. In particular, we study how estimates of the elasticity
of substitution and TFP are affected by imposing a priori restrictions on the direction of
technical change where the economy may depart to a large or small extent from BGP. To
motivate matters, we first use some theory to highlight a set of (potential) pitfalls related to
parameter inference and TFP approximations. Then, we analyze the practical importance
of these biases in a simulation experiment. Finally, in light of our analysis, we estimate a
production-technology system of the US economy over 1952–2009 under different techni-
cal progress specifications and compare the resulting estimates of the substitution elasticity
and TFP. Our reference point is the flexible ‘factor-augmenting’ Constant Elasticity of
Substitution (CES) production function.
Following our earlier contribution, Le´on-Ledesma, McAdam and Willman (2010), we
exploit Monte-Carlo methods. Compared to that article, though, the set up and motivation
are quite different. Le´on-Ledesma et al. (2010) analyzed means to estimate production-
technology parameters (linear, non-linear, single and multi-equation) and showed that the
normalized (or indexed) nonlinear system estimation allowed for identification of the key
technology parameters. Here, we take that approach as givenbut use it to explore the more
applied and more specific topic of econometric mis-specification and the robustness of
balanced growth and particular neutrality assumptions.
Our analysis shows that, generally, when the true nature of technical progress is factor-
augmenting, imposing Hicks-neutrality leads to biases towards Cobb–Douglas (unit elas-
ticity). Imposing Harrod-neutrality would generally lead to upward biases in the estimated
elasticity if the true elasticity is below unity and downward biases if it is above unity. We
rationalize these various biases as attempts by the estimator to control for trends in the
data (e.g. in capital deepening) otherwise incompatible with the presumed neutrality con-
cept. We also show that TFP growth approximations from CES estimates crucially depend
on the elasticity of substitution, which governs the transmission of capital deepening and
technical progress components into the evolution of TFP. Hence, biases in the estimated
elasticity will be reflected in biases in estimated TFP growth.
1See Attfield andTemple (2010) for an empirical assessment of the BGP conditions and a discussion of previous
studies of the empirical validity of the BGP.
2Other perspectives drawon the distributional for m of technical change overtime, Jones (2005), Growiec (2008),
or the endogenous choice of production technology, Le´on-Ledesma and Satchi (2011).
©2013 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
To continue reading
Request your trial