Abstract

1
Introduction
When firms adjust their labor forces, they face adjustment costs (e.g., hiring and firing costs), such that they need to dynamically determine their labor demand. 1  It is then important to understand the structure of adjustment costs because these costs are critical in determining the pattern of labor demand in response to environmental shocks. While hiring costs comprise expenditure on advertising and the time spent on interviewing, testing and so on, it is argued that firing costs depend more on institutional aspects, for example, job security laws.  This implies that a relaxation in job security laws leads to lower firing costs. However, there are few studies that empirically verify this effect. The purpose of this paper is then to investigate causality between job security laws and firing costs. Although the statute of employment security in Japan stipulates that employers can freely discharge their employees, case law established after the 1973 oil shock severely limits mass dismissal. 2 Several cases established four basic requirements that employers must meet before proceeding to dis- miss workers: (a) the necessity of redundancy (i.e., the firm faces serious administrative difficulties), (b) efforts at avoiding redundancy (e.g., reduc- ing working hours, hiring freezing, and conversion of the work-place), (c) the reasonableness of selection criteria, and(d) the reasonableness of the proce- dure itself.  Legal protection, of course, is not sufficient to provide protection in itself, especially in the case of Japan where legal actions may take many years to run through the courts and can be quite costly for the litigants. In particular, workers in small, nonunionized firms are unlikely to believe that they have much protection from the law. Nevertheless, there is a social convention in Japan that a reduction in the number of workers should only be used as a last resort. Job security system as case laws is not clear in the aspect of the rule of judgment but it is suitable for the changes in economic environments. In actuality, several recent studies point out the possibility of changing job security laws in Japan. Ohtake (2002), for example, quantitatively analyzes the cases for redundancy, and argues that the job security laws changed from the latter half of the 1990s. However, Inoue (2000) argues that there were some cases that relaxed the criteria of unjust dismissal in 1999 and 2000. Thus, we can consider cases since the end of 1990 as being indicators of the relation of Japanese job security laws. Although many studies on firms' employment adjustment typically as- sume that adjustment costs are symmetric, we assume an asymmetric form to distinguish between hiring and firing costs, and focus on the changes in firing costs.  Jaramillo et al.  (1993) and Phann and Palm (1993) propose use of the Euler equation for a dynamic labor demand model that allows for asymmetry between hiring and firing. In a more recent study, Azetsu and Fukushige (2005) develop a dynamic labor demand model with asymmetric adjustment costs for the number of workers and working hours. 3 In this paper, we investigate the structural change of adjustment costs using the model developed by Azetsu and Fukushige (2005). If structural changes in adjustment costs occur, change may be gradual rather than more drastic. We therefore allow the structure of adjustment costs to change gradually over time with the gradual switching model proposed by Ohtani and Katayama (1985) and Ohtani et al. (1990). This model can detect when the change in firing costs starts and allows the causality between firing costs and job security laws to be established. The structure of the paper is as follows. In the next section, we develop the dynamic model of labor demand that is the basis of our empirical work. In section 3, we describe the data used, the empirical specification and the results. In section 4 we discuss the implications of the result and conclude the paper.
2
The Model
Our analysis follows the model developed by Azetsu and Fukushige (2005), which derives and estimates the Euler equation for working hours and the number of workers without specifying the production function. This is of some benefit because it is usually difficult to estimate production functions, especially the aggregate level (e.g., specification problems with functional form and technical progress, measurement problems with physical capital). We start by assuming the form of technology.  Let H t and N t de- note, 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 labor force. We assume that the firm has a production function f(HtNt,€t), with ∂f(H t N t, εt)/∂(H t N t) > 0 and ∂ 2 f(H t N t, εt)/∂(H t N t) 2 < 0. The term εt represents a productivity shock observed at the beginning of period t. Also, we assume that the adjustment costs for the number of workers and working hours are quadratic and asymmetric. The nondifferentiability of adjustment costs causes a discontinuity in the firm's decision rule. For example, Hamer- mesh (1989) argues that labor demand has lumpy or linear adjustment costs at the individual plant level, but continuous costs at the aggregate level. Since we use macro data in this analysis, the discontinuity in labor demand can be ignored. 4 The risk-neutral representative firm adjusts working hours and the num- ber of workers, after the realized current shock is observed, in order to max- imize the present discounted value of expected profits, V , over an infinite horizon. The firm's optimization problem is as follows:
where E t denotes expectations at the end of period t. at, st, it, and d t, re- spectively, represent hiring workers, firing workers, increasing working hours, and reducing working hours. The parameter δ is a discount factor and w t is the wage per working hour. Solving this problem yields the following Euler equations for working hours and the number of workers, respectively:
where Mt ≡ F ′ (t) − wt. When both c 1 and c D (c A and c S ) are positive, the firm will not choose both it and dt ( at and st ) to be positive. Each condition (5) and (6) means that the optimal decision is such that the current marginal return to adjustment of working hours (of the num- ber of workers) is equal to the discounted expected marginal cost for the adjustment itself. The Euler equations (5) and (6) can be combined to yield:
where ât ≡ (at − δαt+1)/Ht, ât ≡ (st − δ st+1)/Ht, ât ≡ (ît − δît+1)/Nt, ât ≡ (dt − δdt+1)/Nt. The α ≡ (cs − ca)/2cN, where cN = (cs + ca)/2, measures the asymmetry between the costs of hiring and firing workers.  Both c A and c S are positive, if and only if − 1 < α < 1 is satisfied. If α is positive (negative), then the adjustment costs for firing workers are relatively larger (smaller) than that for hiring. α = 0 implies that the adjustment costs for workers are symmetric. The parameters, β ≡ c 1 /c N and γ ≡ c D /c N , measure the relative costs of adjusting working hours to costs for adjusting The model cannot be rejected if the estimated the number of workers. parameters satisfied the sign conditions; −1 < α < 1, β, γ > 0.
3
Data and Econometric Estimation
We use seasonally unadjusted monthly data for the Japanese labor market from 1986 to 2004, as reported in the Monthly Labour Survey by the Min- istry of Health, Labour and Welfare. We use indices of working hours, H t , and the number of workers, N t , both normalized to 100 in 2000. The terms it and d t represent the net flow of working hours, H t . The variables a t and s t are represented by the numbers of acquisitions and separations. In gen- eral, the words "dismissal" or "firing" are defined as one-sided cancellation employment contracts by the firm. We use "dismissal" or "firing" when the firm reduces the number of workers. Although early retirement is argued to be voluntary, it is often the case that the company puts heavy pressure on unwanted employees to leave the firm. In this sense, we can regard much voluntary early requirement as "dismissal" or "firing". In order to estimate the model, the realized values of period t + 1 are substituted for unobserved expectations of it+1, dt+1, at+1, St+1, and the disturbances u 1 t and u 2 t are added to (5) and (6), respectively. We obtain the following:
This specification leads (7) to the following equation:
where vt = u1t/Nt – u2t/Ht. Since we use aggregate data, the disturbances u 1 t and u 2 t may be serially correlated, and furthermore, u 1 t / N t and u 2 t / H t , divided by N t and H t , may be heteroskedastic. Accordingly, the composite disturbance v t can exhibit both serial correlation and heteroskedasticity. We now assume the composite disturbance v t = μ t + µ, where µ t is an MA(n) process with heteroskedasticity disturbances and j is constant. 5 We assume the order of the MA process to be n = 23. We allow the parameters, which represent the structure of the adjust- ment costs, to gradually change over time as unexpected change, such that the parameters are specified as follows:
where λ t is a transition function that accounts for a change from α 0 , β 0 , γ 0 to α 0 + α 1 , β 0 + β 1 , γ 0 + γ 1 , over time. The transition function is formed as follows:
where t s , t e represent a start-point and end-point of the gradual shift to be estimated. In order to allow for endogeneity of the regressors, we estimate the equa- tion (10) using the Generalized Method of Moments (GMM) technique de- veloped by Hansen (1982), and employ Newey and West's (1987) weight matrix. The following variable terms serve 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. To allow for the autocorrelation of disturbances in the form of the 23rd-order moving average, the instruments must be lagged at least 24 periods. Table 1 shows the GMM estimation result for equation (10).  A chi-square test (sometimes called the J-test) is used to test the overidentifying restric- tions of the model. In the estimation process, the start-point and end-point of the gradual switching, ts , te , are simultaneously selected as maximizing the Wald statistics, which test the null hypothesis that no parameters have changed. As shown in Table 1, γι and μ 1 are not significant, which implies that there is no structural change in γ and j . Table 2 shows the result for the same equation excluding the parameters γ 1 and μ 1 . By comparing the results in both Table 1 and Table 2, we confirm the robustness of the pa- rameters excluding γι and μ 1 . Hereafter, we focus on the results presented in Table 2. To start with, we check whether the model of labor demand in section 2 can be rejected.  For each parameter, the following condition must be satisfied: asymmetry of adjustment costs for workers − 1 < α < 1, relative adjustment costs for working hours β > 0, γ > 0. The estimated parameters satisfy the sign conditions in every case. To be more specific, before the structural change the estimated α range was from 0.481 to 0.491, and after the structural change from 0.235 to 0.274. All of these are significantly positive and less than 1. The estimated β before the change range was between 0.016 and 0.017; following, between 0.028 and 0.030. The estimated γ is 0.009. All of these parameters are significantly positive and satisfy the sign conditions. Next, we analyze the results for the estimated structure of adjustment costs and the timing of structural change. The significance of α 1 and β 1 sug- gests that structural change in the adjustment costs for labor has occurred. The start-point of the structural change selected is from Sep. 1991 to Apr. 1992. The end-point of the change is selected from Sep. 2001 to Jan. 2002. 6 These results suggest that adjustment costs started to change within one or two years of the bubble burst, and continued to change for nearly 10 years. The estimated α is about 0.5 before the structural change, and falls to 0.25 after the change. All of these are significantly positive. This implies that the costs of adjusting the number of workers are asymmetric, with firing costs exceeding hiring costs. The relative costs of increasing working hours to adjusting the number of workers, β , is estimated to be about 0.015: it is much less costly to adjust working hours than the number of workers. After the change, β rises to 0.03. This means that the relative costs of increasing working hours increase significantly. On the other hand, the relative costs of decreasing working hours, γ , is not significantly zero, but is very small. Structural change in γ is not detected.
4
Discussion and Concluding Remarks
The results of this analysis indicate that structural change gradually took place between 1992 and 2001. We also obtained the estimated parameters before and after the structural change. The measure of asymmetry between the costs for hiring and firing fell, that is, firing costs became large relative to hiring costs. The relative costs of increased working hours and decreasing rose and were unchanged, respectively. For the purposes of this paper, we investigated change in firing costs, not the change in asymmetry between the costs for hiring and firing. Figure 1 shows the change of the parameter c S , c N with setting c A = 1. We can see that firing costs c S have decreased, with hiring costs normally taken to be expenditure on advertising and time spent on interviewing, testing, training new workers, etc.  Of course, in a recession, the labor market is more relaxed such that the firms' costs of searching for new workers could become relatively cheaper when compared to, say, a boom. However, screening costs could also rise because firms select new workers more carefully. It is then natural to believe that hiring costs do not change, regardless of business performance. Figure 2 shows the change of the parameters c 1 and c D . The costs of increasing working hours c 1 rose, and the costs for decreasing working hours cD fell. In this paper we used aggregate data, which does not separate regular from part-time workers. The amount of employed part-time workers in- creased on average by 4.63% per year from 1994 to 2001, while the number of regular workers decreased by 0.39%. In general, the cost of adjusting part-time workers is smaller than the cost for regular workers. It is there- fore possible that a recent increase in the ratio of part-time workers to total workers affects the structure of adjustment costs.  Figure 3 shows the ratio of part-time workers to total workers, reported in the Monthly Labour Survey by the Ministry of Health, Labour and Welfare. This only started to rise around 1998, while structural change started around 1991. Therefore, the increase in the ratio of part-time workers to total workers has not been the only cause of structural change. Now, we reach a stage where it is possible to argue that firing costs have gradually fallen since the bubble burst. 7  Why then did firing costs start to fall from about 1992? As already noted in section 1, there were several cases that caused the criterion of unjust redundancy to be relaxed towards the end of the 1990s. This implies that firing costs had fallen gradually, without relaxing job security laws. With the exception of job security laws, bargaining power and the social consensus for firms' reduction of workers establish firing costs. Since almost all workers employed by small, nonunion- ized firms cannot pay the court costs, they are not directly protected by job security laws. But they are, however, protected by the social regulation governing the reduction of workers. When firms reduce the number of their workers, they stand to lose their reputations and to be strongly opposed by trade unions. If the firms obtain a social consensus for the reduction of workers, the costs for reducing workers could be lower. After the bubble burst in 1991, social sympathy for the firms' reduction of workers occurred because of worsening economic performance. We can then understand that relaxation of the social regulation governing firms' reduction of workers led to lower firing costs. Thus, our results are consistent with those of Suruga (1997), who found, using firm micro-level data, a positive correlation be- tween firing and a firm's administrative trouble. Suruga (1997) also argues that a firm could seek and obtain sympathy for the firm's reduction of work- ers, and avoid conflict with workers and trade unions, if the firm has serious administrative problems. Following the Second World War, there were many dismissal conflicts between employees and employers. Workers furiously resisted collective dis- missals, so firing costs gradually increased. Severe job security laws were enacted in 1980s and 1990s after the first oil shock in 1973. After the bub- ble burst in the beginning of the 1990s, Japan suffered from a prolonged period of economic stagnation.  During this period, firms could gain the acceptance of workers for reducing the number of workers, such that firing costs began to gradually decrease. Job security laws also started to relax, but lagging the reduction in firing costs. This analysis shows that firing costs had started to fall one or two years after the bubble burst, and continued to fall for nearly 10 years, while job security laws started to change at the end of the 1990s. We conclude that firing costs in the Japanese labor market can change to suit the economic environment, because change in the social consensus as regards firms that reduce the number of workers corresponds to the economic environment.  We also find that job security laws follow change in the social consensus when such change is quite large.
Appendix
In this Appendix, we solve the optimization problem of the text, and derive the estimation equation (7). First, we define W as follows:
The problem of the text is maximizing W for it, dt, at, st under the con- straints; transition equations (2) and (3), and the Nonnegativity restrictions (4). That is:
(14) Differentiating W with respect to each variable, taking account of (12) and (13), we have:
where M t ≡ ∂F ( H t N t , E t )/∂( H t N t ) – w t . The Kuhn–Tucker conditions are ∂W/∂i ≤ 0, ∂W/∂d ≤ 0, ∂W/∂α ≤ 0, ∂W/∂s ≤ 0, with the complementary- slackness proviso that i(∂W/∂i) = 0, d(∂W/∂d) = 0, a(∂W/∂a) = 0, s(∂W/∂s) = 0, respectively. When all adjustment cost parameters ci, cr, c A , c S are strictly positive, the firm never chooses both it and dt positive, and neither a t nor s t . But, if one of c 1 and c D (c A and c S ) is negative, the firm may choose both it and d t ( at and s t ) positive. By differentiating both sides of (11) with respect to H t − 1 and N t − 1, we have the following:
Using the above Kuhn–Tucker conditions and (19), (20), we can derive the following Euler equations for working hours and for the number of work- ers:
Dividing (21) and (22) by Nt, Ht respectively, the above Euler equations are:
where ât ≡ (at − δαt+1)/Ht, ât ≡ (st − δst+1)/Ht, ât ≡ (ît − δît+1)/Nt, dt ≡ (dt − δdt+1)/Nt. Combining the two equations (23) and (24)as follows:
where c N = (c S + c A )/2.