On Lumpiness in the Replacement and Expansion of Capital*
| DOI | http://doi.org/10.1111/j.1468-0084.2009.00577.x |
| Date | 01 June 2010 |
| Author | Sher Verick,Gerard A. Pfann,Wilko Letterie |
| Published date | 01 June 2010 |
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OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 72, 3 (2010) 0305-9049
doi: 10.1111/j.1468-0084.2009.00577.x
On Lumpiness in the Replacement and Expansion
of CapitalÅ
Wilko Letterie†, Gerard A. Pfann‡ and Sher Verick§
†Department of Organization and Strategy, Faculty of Economics and Business Adminis-
tration, Maastricht University, P.O. Box 616, 6200 MD, Maastricht, The Netherlands
(e-mail: w.letterie@os.unimaas.nl)
‡Department of Econometrics, Maastricht University, P.O. Box 616, 6200 MD, Maastricht,
The Netherlands (e-mail: g.pfann@ke.unimaas.nl)
§United Nations; International Labour Organization (e-mail: Verick@ilo.org)
Abstract
We estimate a model of homogeneous capital investment with two installation
possibilities – replacement and expansion using observations at the establishment
level. We find that regime switches identified by ad hoc measures of lumpy invest-
ment do not adequately distinguish expansionary from replacement activities. In fact,
during periods of expansion, firms spend just as much on replacement capital. Also,
using the common 20% rule would not assign a spike to almost 65% of all observations
that include expansionary investment in this dataset. Finally, replacement although
less responsive to fundamentals than expansions cannot be regarded as an autonomous
part of investment.
I. Introduction
The juxtaposition of theoretical and empirical studies supports a firm-level model of
investment decisions under uncertainty including adjustment costs with a convex and
non-convex component.1Non-convex costs can be modelled through sunk fixed costs,
ÅThe authors thank a referee of this journal and seminar participants in Bonn, Melbourne,Warwick and Porto
for constructive comments. The data used in this article is maintained by the IAB, Bundesagentur fur Arbeit,
N¨urnberg, Germany, and the authors thank HolgerAlda for his help and cooperation. Verickgratefully acknow-
ledges the Bonn Graduate School of Economics and IZA for research support. The usual disclaimer applies.
JEL Classification numbers: E22, C23, C24.
1Examples: United States: Doms and Dunne (1998); Cooper and Haltiwanger (2006); Bloom (2009); Inter-
national: Eberly (1997); Norway: Nilsen and Schiantarelli (2003); The Netherlands: Letterie and Pfann (2007);
United Kingdom: Bloom, Bond and van Reenen (2007).
264 Bulletin
or – if the active liquidation of capital stock is included in the model as well – by
the asymmetry between buying and reselling prices of capital goods. The optimal
investment decision is a linear function of its fundamentals (returns and costs), only
if the adjustment costs of capital are quadratic.2Afirm that faces convex adjustment
costs alone has an incentive to smooth investment expenditures through time. Then the
costs of investing increase with the size of the investment and they are reversible. With
a penalty on large capital expenditures firms are predicted to conduct small invest-
ments and investment is likely to exhibit little variation. If adjustment costs include
a non-convex component investment behaviour is characterized by regime switches.
Firms then have an incentive to wait investing until the gap between a desired and
the actual stock of capital is large enough to render a single investment profitable.
A commonly used method to determine regime switches empirically is through an
ad hoc definition of investment spikes. An example is the absolute spike definition
according to which a lump is observed if the investment rate is larger than 20%. The
determination of spikes aims at separating replacement expenditures from invest-
ments intended to expand the firm’s productive capacity. Replacement investment is
meant to maintain output capacity whereas expansion investment is meant to increase
output capacity. Cooper, Haltiwanger and Power (1999), for example, remark that
‘this threshold is intended to eliminate routine maintenance expenditures’ (p. 932).3
Alternatively, ad hoc spike definitions have been employed to identify events where
firms acquire physical resources embodying the latest technologies available (Power,
1998).
To date the use of ad hoc spikes has received few critiques. Barnett and Sakellaris
(1998) presented a dynamic investment model of smooth adjustment under the null
hypothesis of a convex cost structure and lumpy adjustment under the alternative
hypothesis of non-convex costs. They focus primarily on the question whether the
response of firm investment to fundamentals is nonlinear because of regime switches,
which can be argued to result from the presence of non-convexities in adjustment
costs. If the net benefits of investing exceed a certain threshold, reflecting the
irreversibility of investing, investment in the high regime should be rather responsive
to its fundamentals. Conversely, investment in the low regime will be less respon-
sive to fundamentals.4Evidence for non-convex adjustment costs can thus be found
by identification of different investment regimes. Barnett and Sakellaris (1998) find
support for the view that regime switches occur, implying a time-varying elasticity
of investment to its fundamentals. Letterie and Pfann (2007) developed a method-
ology for a structural identification of different investment regimes. They proposed
a structural model that is represented econometrically by an endogenous switching
regime model. The virtues of the structural threshold approach are the testability
of the existence of multiple regimes and the possibility to investigate whether the
2Lucas and Prescott (1971); Rothschild (1971); Nickell (1978); Bernanke (1983); Pindyck (1991); Abel
and Eberly (1994); Bertola and Caballero (1994).
3See also Nilsen and Schiantarelli (2003); Cooper and Haltiwanger (2006).
4See Eberly (1997), Barnett and Sakellaris (1998), Nilsenand Schiantarelli (2003).
©Blackwell Publishing Ltd and the Department of Economics, University of Oxford 2010
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