Discussion Papers In Economics
And Business

The Estimation of Asymmetric Adjustment Costs for the Number ofWorkers and Working Hours−Empirical Evidence from Japanese Industry Data

Kenji Azetsu

Mototsugu Fukushige

Discussion Paper 05-18

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANThe Estimation of Asymmetric Adjustment Costs for the Number ofWorkers and Working Hours−Empirical Evidence from Japanese Industry Data

Kenji Azetsu

Mototsugu Fukushige

Discussion Paper 05-18
June 2005
この研究は「大学院経済学研究科・経済学部記念事業」
基金より援助を受けた、記して感謝する。
Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANThe Estimation of Asymmetric Adjustment Costs for the Number ofWorkers and Working Hours－Empirical Evidence from Japanese Industry Data*
Kenji Azetsu†
Graduate School of Economics, Kobe University
Mototsugu Fukushige‡
Graduate School of Economics, Osaka Univeristy

Abstract
In this paper, we investigate the asymmetry of adjustment costs for labour. Using monthly
data on Japanese industries, we estimate a model of dynamic labour demand thatincorporates adjustment costs for hiring and firing workers, and for changing working hours.
Our estimates suggest the following. (1) It is more costly to fire workers than to hire them in
all industries. (2) This asymmetry between hiring and firing costs is more important for
production sectors than for non-production sectors. (3) It is much less costly to adjust working
hours than to adjust the number of workers.
Keywords: Adjustment costs; Dynamic labour demand; Working hours
JEL Classification: J23; J32

We would like to thank Junya Masuda, and the participants of Kansai Econometrics
Workshop for their useful comments. We acknowledge financial support from the 21stCentury COE Research.
† Graduate School of Economics, Kobe University, 2-1, Rokkodai-cho, Nada-ku, Kobe
657-8501, JAPAN. E-mail: 018d201e@y01.kobe-u.ac.jp‡ Graduate School of Economics, Osaka University, 1-7, Machikaneyama-cho, Toyonaka,
Osaka, 560-0043 , JAPAN. E-mail: mfuku@econ.osaka-u.ac.jp*

1. Introduction
The structure of adjustment costs for labour has been investigated in many studies. Whenfirms experience a shock in their technology or product demand, they adjust the labour force,
given these adjustment costs. Therefore, to understand firms' employment adjustment, it isimportant to estimate the structure of adjustment costs for labour.
Early empirical research on firms' employment adjustment typically assumes that
adjustment costs are symmetric, convex and quadratic. Hence, dynamic labour demand is
described by a single partial adjustment equation. However, there are several problems withthese assumptions. A problem with the assumption of symmetry is that it implies that hiringand firing cost functions are equal.§ Jaramillo et al. (1993) estimate Euler equations for a
dynamic labour demand model that allows for asymmetry between hiring and firing. Based on
panel data on Italian firms, their empirical study rejects the hypothesis of symmetricadjustment costs. Pfann and Palm (1993) also found that adjustment costs are asymmetric byusing time series data on the manufacturing sectors of the Netherlands and the UK. Morerecently, in the context of fixed-term contracts, which can be adjusted more cheaply thanpermanent contracts, Goux et al. (2001) have investigated the structure of adjustment costs(the asymmetry of adjustment costs for permanent employees and the relative costs ofadjustment for workers on fixed-term contracts.) However, none of the papers has
investigated the structure of adjustment costs when firms can adjust employment bychanging working hours.
In the context of the Japanese labour market, numerous attempts have been made byresearchers to investigate employment adjustment. Their main objectives were to compare
Japanese employment adjustment patterns with those of other countries. That is, isadjustment in Japan slower than in other countries? Do Japanese companies adjust hours
more than the number of workers? However, most studies use the partial adjustment model,
which is problematic, as has already been mentioned.** Although there are many studies ofEuropean countries, little is known about the structure of adjustment costs in Japan.††In this paper, we assume that firms adjust not only the number of workers but also working
hours, and that both incur adjustment costs. We derive the Euler equation for working hours
and the number of workers, similarly to Goux et al. (2001), without specifying the production
Another problem is the assumption of smooth adjustment costs. The non-differentiability ofadjustment costs causes a discontinuity in the firm's decision rule. Hamermesh (1989) argued
that labour demand has lumpy adjustment costs at the individual plant level. However, at theaggregate level, adjustment costs can appear continuous. In this paper, since we use macro
data, the discontinuity in labour demand can be ignored.
** See, for example, Ohtake (1988) and Muramatsu (1991). Abraham and Houseman (1989)
investigate differences in adjusting the number of workers and working hours in the USA andJapan, but do not specify an employment-adjustment model.
†† Hildreth and Ohtake (1998) examine the discreteness of labour demand by using data
provided by a Japanese company.
§

function. Goux et al. (2001) assume that the labour force is the sum of permanent workers andthose on fixed-term contracts, which implies that the marginal productivities of the two types
of worker are equivalent. Therefore, the estimable Euler equation can be derived without
specifying the production function. In our model, the labour force is the product of working
hours per worker and the number of workers. By using monthly data on Japanese industries
from 1992 to 2004, we investigate the structure of adjustment costs. These costs are
represented by measures of asymmetry between hiring and firing costs, and by the relative
costs of changing working hours and the number of workers. Hence, we re-evaluate Japanesefeatures of employment adjustment.
The structure of the paper is as follows. In the next section, we develop the dynamic modelof labour demand on which our empirical work is based. In section 3, we describe the data
used and report the empirical results. In section 4, we present a summary and conclusions.

2. The Model
We start by assuming the form of the technology. Let

H t and N t denote, respectively,

working hours per worker and the number of workers that a representative firm hires. Thus,

H t N t is the firm's effective labour force. We assume that the firm has a production function> 0 and f ' ' < 0 . The term ε t represents a productivity shockf ( H t N t , εｔ) , with ｆ’observed at the beginning of period t .
The risk-neutral firm adjusts working hours and the number of workers, after the realized
current shock is observed, in order to maximize the present discounted value of expected
profits, V , over an infinite horizon. The firm's optimization problem is as follows:where

Et denotes expectations at the end of period t . The parameter δ is a discountfactor and wt is the wage per working hour. C I andI ∈{H +, H −, A, S } , respectively,+−

represent the costs of increasing working hours, ht , reducing working hours, ht , hiring
workers,

at , and firing workers, st . For each I , the function C I is assumed to bedifferentiable and strictly convex. We also assume thatC ' H + (0) = C ' H − (0)andC ' A (0) = C ' S (0) so that the costs of adjusting working hours and the number of workers
are differentiable at zero.
Solving this problem yields the following Euler equations for working hours and thenumber of workers, respectively:

where M t ≡ F ' (t ) − wt . When both adjustment costs, C I , are strictly increasing, the firm+

will not choose both ht−

and htto be positive, and neither will it choose at and st .‡‡We assume the following quadratic form for all adjustment costs:

Given these specifications, the Euler equations (5) and (6) can be combined to yield:wherec N ≡ (c A + c S ) / 2,aˆ t ≡ (at − δat +1 ) / H t,sˆt ≡ ( st − δst +1 ) / H t,

However, if either C H + and C H − ( C A and C S ) is decreasing, the firm may choose both

‡‡

+
t

h

−

and ht(or at and st ) to be positive. Note that, since the adjustment costs, C I , arestrictly convex, if each C I is increasing, the second-order conditions are satisfied. Otherwise,
satisfaction of the second-order conditions is not guaranteed.

hˆt+ ≡ (ht+ − δht++1 ) / N tandhˆt− ≡ (ht− − δht−+1 ) / N t .

The(c S − c A ) / 2c Nparameter

measures the asymmetry between the costs of hiring and firing workers. That

− 1 < (c S − c A ) / 2c N < 1 implies c A > 0 and cS > 0 . The terms c H + / c N and c H − / c N
measure the relative costs of adjusting working hours for a given number of workers.

3. Empirical Analysis
In this section, we present parameter estimates for equation (8). We use seasonallyunadjusted monthly data for Japanese industry from January 1992 to January 2004, asreported in the Monthly Labour Survey by the Ministry of Health, Labour and Welfare. We

H , and the number of workers, N , which are normalized to
100 in 2000. The variables a and s are represented by the numbers of acquisitions andseparations. Although s represents the number of layoffs, data on layoffs by industry are+−
not available. Separations include voluntary quits. The terms h and h represent the net
flow of working hours, H .
use indices of working hours,

To estimate the parameters of the Euler equation (8), we use Generalized Method ofMoments (GMM), following Goux et al. (2001). The GMM estimates are obtained by using thestandard two-stage instrumental variables method. We use the following lagged values of theforcing variable and a constant term as instrumental variables:

Lag indicates the number of lags used for a variable, based on monthly data. For example, if
Lag = 1, the variable xt −1 is used, whereas xt −1 and xt − 2 are used if Lag = 1, 2. Tables 1
and 2 report the empirical results from GMM. The discount rate, δ , is chosen to equal 0.99
in Table 1 and 0.95 in Table 2, but results are robust to variations in the discount rate.
In the industries sampled, the estimate of (c S − c A ) / 2c N is positive, and less than unity.
This implies: (1) hiring and firing costs, C A and C S , are positive, so that c N is positive;and (2) the costs of adjusting the number of workers are asymmetric, with firing costs
exceeding hiring costs. Further, the estimates of c H + / c N and c H − / c N are both positive
but small relative to (c S − c A ) / 2c N . This suggests that it is significantly cheaper to change

working hours than the number of workers.
We get similar results when we focus on each industry. The costs of adjusting the number ofworkers are asymmetric in all industries. However, the asymmetry in costs appears to differ
between production sectors (such as construction and manufacturing) and non-production
sectors (such as transport and communications, finance and insurance, real estate andservices). For the production sectors, the estimated (c S − c A ) / 2c N is about 0.5, whereas
the corresponding estimate for the non-production sectors is 0.3.
For most industries, the estimates of c H + / c N and c H − / c N are small. This implies that it
is much less costly to adjust working hours than the number of workers. For some sectors(electricity, gas, heating supplies and water, transport and communications, finance andinsurance and services), one component of the relative costs of working hours, c H + / c N ,c H − / c N , is significantly less than zero (from about –0.05 to –0.17). This implies that either
C H + or C H − may be negative, since the parameter c N is positive in all industries. As
mentioned in the previous section, if one of these is negative, the firms in those sectors may
increase their working hours and, at the same time, reduce those costs. A possible
interpretation is that firms may apply different working hours policies to different groups ofworkers. In our model, we assume that workers are homogeneous although, in practice,
workers are heterogeneous. Firms in the sector may increase the working hours of someworkers and reduce those of other workers.

4. Conclusion
In this paper, we derived an estimable Euler equation for working hours and the number ofworkers, similarly to Goux et al. (2002), without specifying the production function. Using
data on Japanese industries from 1992 to 2004, we estimated a model of dynamic labourdemand in which there are adjustment costs of changing the number of workers and theirworking hours.
Our results indicate that it is more costly to fire workers than to hire them, in all industries,
and firing during recessions is more difficult than the hiring during upturns. We also foundthat the asymmetry between hiring and firing costs is more important for production sectors
than for non-production sectors. This result is consistent with the empirical findings of Phannand Palm (1993), obtained using data on the Dutch and UK manufacturing sectors. Finally,
since adjustment costs for working hours are small relative to those for the number of workers,

firms typically adjust working hours.

Appendix
In this Appendix, we solve the optimization problem (1) in the text, and derive the estimating
equation (5). First, we define W as follows:−+

The problem in (1) is to maximize W for ht , ht , at , st given the constraints, which are
the transition equations, (2) and (3), and the non-negativity restrictions, (4). That is:

Differentiating W with respect to each variable and taking account of (2) and (3) yields:

M t ≡ ∂F ( H t N t , ε t ) / ∂ ( H t N t ) − wt

where

.

The

Kuhn-Tucker

conditionsare∂W / ∂h + ≤ 0 , ∂W / ∂h − ≤ 0 , ∂W / ∂a ≤ 0 , ∂W / ∂s ≤ 0 with the complementary-slackness++−−
proviso that h (∂W / ∂h ) = 0 , h (∂W / ∂h ) = 0 , a (∂W / ∂a ) = 0 , s (∂W / ∂s ) = 0 ,respectively. When each adjustment cost, C I , is strictly increasing, the firm will not choose+

both ht−

and htto be positive, and neither will it choose both a t and s t . However, if+either C H + or C H − ( C A and C S ) is decreasing, the firm may choose both ht−

and ht(or a t and s t ) to be positive.
By differentiating both sides of (9) with respect of H t −1 and N t −1 , we have the following:

Using the above Kuhn-Tucker conditions and (17) and (18), we can derive following Euler
equations for working hours and for the number of workers:

Specifying each adjustment cost function as quadratic, as in (7), and dividing (19) and (20) by

N t and H t respectively, yields the Euler equations:whereaˆ t ≡ ( at − δat +1 ) / H t , sˆt ≡ ( st − δst +1 ) / H t , hˆt+ ≡ ( ht+ − δht++1 ) / N t , hˆt− ≡ ( ht− − δht−+1 ) / N t.
Combining equations (21) and (22) yields:

where c N ≡ (c A + c S ) / 2 .

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Note: Numbers in parentheses are the standard errors of the parameters. The * indicates thatthe coefficient is significant at the 5% level. const denotes the constant term. Lag indicatesthe number of lags used for the instrumental variable, based on the forcing variable. J
denotes the J-test statistics. The p-value is the probability value associated with the J-test.