Letterie, Wilko A.

Pfann, Gerard A.

Polder, J. Michael

English

Research Papers in Economics

Factor adjustment spikes and interrelation:
an empirical investigation
Wilko A. Letterie
a, Gerard A. Pfann
b, J. Michael Polder
c,*
aBusiness Investment Research Center, Department of Organization and Strategy, Maastricht University, The Netherlands
bBusiness Investment Research Center, CEPR, Maastricht University, The Netherlands
cDepartment of Quantitative Economics, Business Investment Research Center, Maastricht University, P.O. Box 616,
6200 MD Maastricht, The Netherlands
Received 15 July 2003; received in revised form 4 January 2004; accepted 9 March 2004
Available online 2 July 2004
Abstract
We take a descriptive look at interrelated factor demand starting from the observation that adjustment of capital
and labor is lumpy. We find that the adjustment dynamics of an input factor are affected by large adjustments in the
other.
D 2004 Elsevier B.V. All rights reserved.
Keywords: Investment; Labor demand; Interrelated factor demand; Non-convex adjustment costs
JEL classification: D21; D92; J23
1. Introduction
Empirical research over the last decade has documented that factor demand is ‘lumpy’ at the micro-
level, in the sense that firms tend to concentrate adjustments in short periods of time, see e.g. Doms and
Dunne (1998) for investment, and Hamermesh (1989) for labor adjustment. Structural models that stress
the importance of non-convex adjustment costs and irreversibilities in this context have been proposed
by e.g. Abel and Eberly (1994).
Empirical work along these lines has focused on models with a single quasi-fixed input factor, see
e.g. Barnett and Sakellaris (1998). Recently, some theoretical studies have investigated interrelated
factor demand with multiple quasi-fixed input factors where one or more factors are subject to non-
0165-1765/$ - see front matter D 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.econlet.2004.03.017
* Corresponding author. Tel.: +31-433-88-3673; fax: +31-433-88-4856.
E-mail address: m.polder@ke.unimaas.nl (J.M. Polder).
www.elsevier.com/locate/econbase
Economics Letters 85 (2004) 145–150convexities or irreversibility (e.g. Dixit, 1997). As a first step towards a more structural empirical
analysis, this paper provides a descriptive investigation into the relevance of interrelation starting
from the observation that adjustment of capital and labor is lumpy. We find that adjustment lumps
for one factor affect the dynamics of the other.
2. Data and descriptive statistics
We analyze annual data collected by Statistics Netherlands (CBS) concerning product plants in the
Dutch manufacturing sector. For convenience, we will refer to all units as firms. The data is available
for firms with more than 20 employees, and only positive investments are observed (more details on
the definition and construction of the variables are given in Letterie and Pfann, 2003).The entry and
exit of firms is likely to be due to major investment and disinvestment decisions, which do not reflect
the regular adjustment pattern of a firm. Therefore we prefer to analyze a balanced set of data,
although this may bias the information towards larger and successful establishments. To avoid
contamination of the results by exceptional outliers, we also exclude firms for which the investment
ratio exceeds one for one or more periods. We end up with 659 firms for which all information is
available for the period 1978 to 1992. The first 5 years of the sample are used to construct a capital
stock measure according to a perpetual inventory method.
To determine whether firms conduct major investment efforts during a particular year we employ the
so-called relative and absolute spike definitions. The former classifies an observation as a spike if the
investment rate exceeds the median investment rate over a certain period by 75% (Power (1998)); with
the latter definition an observation is called a spike if the investment rate exceeds 20% (e.g. Cooper et
al., 1999). Following Sakellaris (2001), we categorize an observation as a positive employment spike if
the adjustment rate of employment exceeds 10%, and as a negative employment spike if it is smaller
than  10%.
Table 1 displays some descriptive statistics with respect to the adjustment of employment and capital.
The investment rate is about 10% on average, but with a median of about 6% it is positively skewed.
Average labor adjustment is around zero with only a slight positive skewness. About 12% are absolute
investment spikes, while the relative spike definition gives as much as 22%. This difference is striking.
The percentage zero-adjustment is considerably higher for labor, although this observation is somewhat
biased by the fact that we only observe net labour adjustment.
Conditioning on whether a spike occurs in the other production factor or not, large differences are
observed.
1 If there is an investment spike labor adjustment increases to 5% on average. In addition, more
positive employment spikes occur if there is an investment spike, and there occur less negative
employment spikes. There is also some mild evidence that there is less zero adjustment of labor in times
of an investment spike. In times of a positive employment spike the average investment rate is
considerably higher than when there is no employment spike. It is considerably lower if there is a
negative employment spike. Also, there occur more investment spikes if there is a positive employment
spike, and less if there is a negative employment spike. Finally, there is more zero investment in times of
a negative employment spike.
1 The standard errors of the statistics (not reported to save space) show that most differences are highly significant.
W.A. Letterie et al. / Economics Letters 85 (2004) 145–150 146These statistics show that there is a relation between the adjustment of an input factor and whether or
not there is a spike in the other factor. Another thing worth mentioning, however, is the heterogeneity in
response. For example, while average employment adjustment increases considerably if there is an
investment spike, in 7% of the observations it is coupled with a negative employment spike. Also, capital
and labor do not necessarily ‘spike together’. Only about 20% of the positive employment spikes occur
in the same period as an investment spike, for example.
3. Lumpiness and interrelation
The purpose of this section is to investigate how firms adjust the employment level (respectively,
capital stock) in periods of investment (respectively, labor adjustment) spikes, and in periods before and
after such spikes.
2 This does not only offer insight into whether there is above average adjustment in
times of adjustment spikes, but also gives an idea about the dynamics of the interrelation between
investment and employment decisions.
Analogous to Power’s (1998) investment age variables, we use indicator variables to represent the
timing of lumpy investment episodes. We define four indicator variables as 1ku1[investment
period=k], where k={next, current, previous, between}. For instance 1currentu1[investment period=
current] equals 1 if the firm has an investment spike in the current period, and zero otherwise. The
variable 1[investment period=next (previous)] equals 1 if the concerning firm has an investment spike
in the next (previous) period, where it does not have one in the current or previous (next) period.
3
2 See Sakellaris (2001) for a related study.
Table 1
Descriptive statistics
Total ABS=0 ABS=1 REL=0 REL=1
Mean (med.) Mean (med.) Mean (med.) Mean (med.) Mean (med.)
(DL/L)t 0.015 (0) 0.010 (0) 0.050 (0.037) 0.010 (0) 0.034 (0.023)
POS 0.147 (0) 0.133 (0) 0.247 (0) 0.132 (0) 0.196 (0)
NEG 0.096 (0) 0.100 (0) 0.063 (1) 0.103 (0) 0.073 (0)
D[DLt=0] 0.137 (0) 0.141 (0) 0.106 (0) 0.139 (0) 0.128 (0)
Total POS=0 POS=1 NEG=0 NEG=1
Mean (med.) Mean (med.) Mean (med.) Mean (med.) Mean (med.)
(I/K)t 0.098 (0.063) 0.092 (0.060) 0.135 (0.093) 0.101 (0.067) 0.070 (0.034)
ABS 0.124 (0) 0.109 (0) 0.209 (0) 0.128 (0) 0.082 (0)
REL 0.228 (0) 0.215 (0) 0.305 (1) 0.233 (0) 0.174 (0)
D[It=0] 0.042 (0) 0.042 (0) 0.038 (0) 0.038 (0) 0.073 (0)
Explanation of abbreviations: POS=positive employment spike; NEG=negative employment spike; ABS=absolute
investment spike; REL=relative employment spike; D[ ]=1if[ ] is true, zero otherwise.
3 A category ‘between’ is introduced to take account of those observations for which a firm has a spike in the previous as
well as in the next period, while in the current period no spike occurs. Because this is a side category with sometimes very few
observations, we omit it from the discussion.
W.A. Letterie et al. / Economics Letters 85 (2004) 145–150 147To investigate the relation between the timing of a large investment and labor adjustment we consider
the estimating equation
ðDL=LÞit ¼ ai þ kt þ
X
k
bkð1kÞit þ eit ð1Þ
where kt is a year dummy, and eit is an idiosyncratic disturbance. The fixed effect ai accounts for a firm
specific average adjustment rate and makes the results robust to any omitted time-invariant variables. Eq.
(1) is first-differenced and estimated by least squares. The estimation results are presented in Table 2.
The results indicate that firms hire significantly more people in periods close to investment spikes and
the period of the spike itself. This suggests that the employment and the investment decision are
significantly interrelated. The fact that investment spikes tend to have a positive effect on employment
changes supports the view that labor and capital are complementary inputs. Also, the apparent high labor
demand in periods right before or after an investment spike indicate that there is a dynamic element in
the relation between labor and capital. The fact that firms hire employees in advance of an investment
lump may indicate that employees need to be trained. As soon as the new capital comes in these
employees can start working with it, or manage the employees that are hired in the same period as the
spike. On the other hand, the excess hiring in the period after a spike may reflect labor market scarcities,
or a learning effect by the firm that it needs more labor to get the work done. The results do not depend
on the definition of the investment spike and support those of Sakellaris (2001).
It is also interesting to look at the relation between the investment rate and employment spikes. To
investigate this we estimate
ðI=KÞit ¼ ai þ kt þ
X
k
bkð1kÞit þ eit ð2Þ
where the indicator variables 1k now reflect whether there was an employment spike in period k. The
estimation results are reported in Table 3. It can be seen that there is significantly more (less) investment
in periods of a large positive (negative) employment change. In addition, there is some evidence that
there is more (less) investment in the period after an employment spike.
The results in Tables 2 and 3 should be put in the light of the heterogeneity found in the previous
section. For example, from Table 2 it can be seen that firms hire about 3% more people in periods of an
investment spike on average. At the same time, however, as became clear from Table 1, some firms do
Table 2
Effect of investment spikes on employment changes
Absolute Relative
Next 0.017 (0.007)* 0.011 (0.054)*
Current 0.030 (0.006)** 0.030 (0.005)**
Previous 0.015 (0.007)* 0.011 (0.055)*
Between 0.028 (0.015) 0.033 (0.010)**
Standard errors are reported in parentheses.
* Significant at 5% level.
** Significant at 1% level.
W.A. Letterie et al. / Economics Letters 85 (2004) 145–150 148not adjust employment when there is an investment spike or even exhibit a negative employment spike.
A more structural analysis should be able to distinguish between those cases.
4. Concluding remarks
In this paper, we investigate the dynamic interrelation between factor demand in the context of lumpy
adjustment. With plant-level data for the Dutch manufacturing sector, we find that the dynamics of
employment are significantly related to large investments. Also, investment is related to large
employment changes. Although our results do not necessarily have a causal or structural interpretation,
they indicate that in modeling the demand for production factors the interrelation among them should be
taken into account. While the traditional literature has investigated this in linear-quadratic models
(Nadiri and Rosen, 1969), no empirical research has been carried out with multiple quasi-fixed input
factors where one or more factors are subject to non-convexities. This should prove to be a worthwhile
direction for future research.
Acknowledgements
This paper has benefited from helpful comments by Eric Bartelsman, Sher Verick, participants at the
NAKE-day 2002, at the conference ‘Firms’ dynamic adjustment with nonconvexities and irreversibility
at the University of Bergamo, and in the Q-seminar series at Maastricht University. All errors are our
own. The authors acknowledge the PIONIER program (grant number 400-10-041) of the Netherlands
Foundation for Scientific Research (NWO) and Statistics Netherlands for financial support. The
empirical part of this paper was carried out at the Center of Research of Economic Micro Data (CEREM)
at Statistics Netherlands. We thank our contacts there for their kind cooperation. The views expressed in
this paper are those of the authors and do not necessarily reflect the policies of Statistics Netherlands.
References
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Table 3
Effect of employment spikes on investment
Positive Negative
Next 0.007 (0.055)  0.011 (0.007)
Current 0.031 (0.005)**  0.027 (0.006)**
Previous 0.008 (0.005)  0.013 (0.006)*
Between 0.024 (0.011)*  0.047 (0.011)**
Standard errors are reported in parentheses.
* Significant at 5% level.
** Significant at 1% level.
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W.A. Letterie et al. / Economics Letters 85 (2004) 145–150 150

A unified model of investment under uncertainty.

Factor adjustment spikes and interrelation: an empirical investigation.

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Factor adjustment spikes and interrelation: an empirical investigation.

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