Cyclical behavior of unemployment and job vacancies in Japan

Japan and the World Economy 23 (2011) 214–225

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Japan and the World Economy journal homepage: www.elsevier.com/locate/jwe

Cyclical behavior of unemployment and job vacancies in Japan Hiroaki Miyamoto * International University of Japan, Graduate School of International Relations, 777 Kokusai-cho, Minami Uonuma-shi, Niigata 949-7277, Japan

A R T I C L E I N F O

A B S T R A C T

Article history: Received 6 July 2010 Received in revised form 5 December 2010 Accepted 14 April 2011

This paper studies whether the Mortensen and Pissarides (MP) search and matching model can explain the observed labor market fluctuations in Japan. To do this, this study first establishes a number of key facts about the cyclical properties of the Japanese labor market. Although the standard MP model correctly predicts the observed regularities in the cyclical fluctuations of unemployment and job vacancies, it cannot generate the observed unemployment and vacancy fluctuations in response to productivity shock of reasonable size. This paper extends the matching model by incorporating firmspecific training costs whose role is emphasized in the Japanese labor market. Relative to the standard MP model, the extended model generates larger cyclical fluctuations in unemployment and job vacancies. However, it still falls short of what observed in the Japanese data. ß 2011 Elsevier B.V. All rights reserved.

JEL classification: E24 E32 J64 Keywords: Search Matching Business cycles Japanese labor market

1. Introduction The Mortensen and Pissarides search and matching model (henceforth MP model) has become a standard framework for analyzing aggregate labor markets. However, the MP model has recently criticized for its inability to explain key business cycle properties of the U.S. labor market (Costain and Reiter, 2008; Hall, 2005; Shimer, 2005). Shimer (2005) demonstrates that the MP model cannot generate the observed unemployment and vacancy fluctuations in response to productivity shocks of reasonable size. This failure of the model has come to be known as the ‘‘unemployment volatility puzzle’’ or the ‘‘Shimer puzzle’’. In the literature, many solutions have been proposed to solve this problem.1 However, less is known about whether this failure of the MP model can be observed in the other countries (Burgess and Turon, 2005; Zhang, 2008). Especially, there has been no study on the Japanese labor market case. In this paper, I study how well the MP model can explain the observed business cycle fluctuations in the Japanese labor market. In the first part of my analysis, I present the relevant Japanese labor market facts over business cycles. Unemployment is counter-

* Tel.: +81 25 779 1464; fax: +81 25 779 1187 E-mail address: [email protected]. 1 Some examples are wage rigidity (Hall, 2005; Shimer, 2005), different calibration strategies (Hagedorn and Manovskii, 2008), on-the-job search (Krause and Lubik, 2007; Nagypa´l, 2007; Tasci, 2006) and informational rents (Kennan, 2010). 0922-1425/$ – see front matter ß 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.japwor.2011.04.001

cyclical, job vacancies are pro-cyclical, and these two variables are negatively correlated over business cycles. Furthermore, both unemployment and vacancies are volatile and persistent. To understand the detail of the unemployment dynamics, I examine the cyclical properties of job finding and separation rates. I construct the job finding rate and the separation rate by using the panel property of the monthly Labour Force Survey. Both job fining and separation rates display considerable variations over business cycles. The job finding rate is pro-cyclical and the separation rate is counter-cyclical. Qualitatively, all these observations are correctly predicted by the MP model. The data also shows that both job finding and separation rates contribute substantially to unemployment fluctuations in Japan. This result is similar to what Fujita and Ramey (2009) and Pissarides (2009) find in the U.S. However, the relative importance of job separation differs between two countries. While the job finding rate is a relatively important determinant of the unemployment fluctuation in the U.S, the separation rate is relatively important in Japan. Specifically, in Japan, the separation rate accounts for 53 percent of the observed fluctuation in unemployment, while the job finding rate accounts for 42 percent of those fluctuations. In the second part of my analysis, I extend the search and matching model by incorporating firm-specific training costs. There are two reasons why I incorporate firm-specific training costs into my model. The first reason is to capture the peculiarity of the Japanese labor market. It is often mentioned that on-thejob training is more common and intensive in Japan than in the

H. Miyamoto / Japan and the World Economy 23 (2011) 214–225

U.S.2 Furthermore, Japan is typically known to have an economy with high degree of labor market friction. This fact implies that firm-specific skill training widely prevails in Japan.3 The second reason is that the incorporation of firm-specific training costs can potentially amplify the response of labor market variables to productivity shocks. Mortensen and Nagypa´l (2007) argue that the failure of the MP model lies in the large difference between labor productivity and the opportunity cost of employment. Since the incorporation of training costs reduces this gap, the extended model may generate larger labor market fluctuations. The main objective of this study is to examine whether the MP model can explain the observed business cycle fluctuations in the Japanese labor market. First, I ignore the firm-specific training cost and study how well the standard search and matching model can explain the observed business cycle fluctuations in the Japanese labor market. Although the standard model correctly predicts the observed regularities in the cyclical fluctuations in labor market variables qualitatively, the model cannot explain key cyclical properties of the Japanese labor market quantitatively. The calibrated model explains about 25 percent of the observed fluctuations in the vacancy–unemployment ratio.4 The extended model with firm-specific training costs generates larger cyclical fluctuations in unemployment and vacancies compared with the standard MP model. However, the extended model still falls short of what we observed in the Japanese data. This paper develops the matching model with firm-specific training costs and studies the role of training costs in the amplification mechanism of the model. Recently, several studies demonstrate that the incorporation of matching costs (training costs) can significantly improve the ability of the MP model to explain the cyclical volatility of unemployment and job vacancies in the U.S. (Pissarides, 2009; Silva and Toledo., 2009a,b). My model differs from theirs in the way in which training costs are modeled. While they assume that a firm pays training costs only once at the time of job creation, in my model a firm need to pay flow training costs until training period is over. This specification has a natural link to the firm-specific human capital, whose role is emphasized in the Japanese labor market, in the sense that training costs need to be paid every time the worker is hired by a difference firm even if the worker was trained before. This paper establishes a number of key facts about the cyclical properties of the Japanese labor market by examining data from the Labour Force Survey over the past 30 years. Genda et al. (2008) document the size and cyclicality of worker flows in Japan in the 1990s and 2000s. My findings are broadly consistent with their findings. The stylized facts established in this paper are of interest to macroeconomists. For them, this paper can be a reference when they calibrate parameters in the Japanese labor market. Furthermore, this paper provides a guideline of the empirical features that theoretical model should ideally have.

2 Mincer and Higuchi (1988) estimated wage functions of Japan and the U.S., and found that wage-tenure profile in Japan is steeper than that in the U.S. Since wage structure reflects training costs, their finding suggests that the job training plays a more important role in Japan than in the U.S. 3 A number of studies emphasize the role of firm-specific skill training in the Japanese labor market. Genda et al. (2001) argue that a firm-specific training cost plays an important role to explain the low gross job flows in Japan. Miyamoto and Shirai (2006) demonstrate that by incorporating firm-specific skill training, the MP model can explain the often mentioned peculiarity of the Japanese labor market; low rates of unemployment, job creation, and job destruction. Furthermore, a number of studies pointed out that Japanese firms train their employees to equip with firm-specific skills intensively. See for example, Shimada (1981); Mincer and Higuchi (1988); Hashimoto and Raisian (1985, 1992), and Koike (1984, 1988). 4 Shimer (2005) demonstrates that the MP model explains less than 10% of the volatility in US unemployment and vacancies when fluctuations are driven by productivity shocks.

215

In response to the unemployment volatility puzzle, this paper studies the ability of the search and matching model to account for the cyclical properties of the Japanese labor market. Recently, Esteban-Pretel et al. (2010) also study if the unemployment volatility puzzle holds for the Japanese economy.5 My paper differs from theirs in the following points: first, I construct the Japanese worker flows data from the Labour Force Survey, and study how much of the observed unemployment fluctuations can be accounted for by variations in unemployment inflow and outflow rates. Second, instead of performing numerical stimulations of the model to compare the model implications with the data, I use very competently the method available in the literature to address the issue. Third, I develop a search and matching model with firmspecific training costs in order to capture the peculiarity of the Japanese labor market. While the methodology to answer the question is different between these two studies, both papers reach the same conclusion that the unemployment volatility puzzle hold for the Japanese economy. The reminder of the paper is organized as follows. Section 2 presents salient features of the Japanese aggregate labor market over the business cycle. Section 3 describes the theoretical model. I develop a search and matching model with firm-specific training costs. In Section 4, I calibrate the model parameters and present the quantitative results. In Section 5, I study the role of firm-specific training costs. Conclusions and suggestions for future research are presented in Section 6. 2. Japanese labor market facts In this section, I present some of the salient features of the Japanese aggregate labor market over the business cycle. I focus on labor productivity and four labor market variables: unemployment, vacancies, the job finding rate, and the separation rate. The first variable of interest is unemployment, which is measured as the number of workers who are looking for a job and ready to work immediately if a job is available, yet not working. I obtain the data from the Labour Force Survey (LFS), conducted by the Statistics Bureau and the Director-General for Policy Planning.6 My focus is cyclical fluctuations in unemployment and hence low-frequency movements in the data are filtered out by using a Hodrick–Prescott (HP) filter with smoothing parameter of 105, as in Shimer (2005). In Fig. 1, I present the quarterly time series of unemployment and its trend. Until the early 1990s unemployment had been low but it climbed gradually and exhibited strong fluctuations. The difference between log unemployment and its trend has a standard deviation of 0.143. Thus, unemployment is often as much as 29 percent above or below its trend. The cyclical component of unemployment also exhibits a large persistence with quarterly autocorrelation of 0.96. The flip side of unemployment is job vacancies. The conventional measure of job vacancies is obtained from the monthly Report on Employment Service (Shokugyo Antei Gyomu Tokei) conducted by the Ministry of Health, Labour and Welfare.7 The Report on Employment Service is administrative data set and it measures only a number of firms that post advertisements at the Employment 5 Both papers were developed simultaneously and without the knowledge of each other. Since these papers use the different methodology to address an important question if the unemployment volatility puzzle holds for the Japanese economy, they are complementary, rather than competing. 6 The Labour Force Survey is conducted in the last week of each month. The survey defines completely unemployed workers as persons who satisfy the following conditions: (i) with no job and did not work at all during the reference week (other than employed person); (ii) ready to work if work is available; (iii) did any job seeking activity or preparing to start business during the reference week (including waiting the outcome of the job seeking activity done in the past). 7 The data are available from the portal site of Official Statistics of Japan, http:// www.e-stat.go.jp/.

H. Miyamoto / Japan and the World Economy 23 (2011) 214–225

216

4000

0.4

Unmployment (in thousands)

Unemployment trend

Unemployment Vacancy

0.3

3500 0.2 3000

0.1 0

2500

-0.1 2000

-0.2 -0.3

1500

-0.4 1000 1980

1985

1990

1995

2000

2005

2010

Year

-0.5 1980

1985

1990

1995

2000

2005

2010

Year Fig. 1. Quarterly unemployment (in thousands) and trend, 1980Q1–2009Q4. Note: Unemployment is a quarterly average of the monthly series constructed from the LFS. The series are seasonal adjusted by using the Census’s X-12-ARIMA algorithm. The trend is an HP filter of the quarterly data with smoothing parameter 105. Shaded areas indicate ESRI-dated recessions.

Vacancy trend

Vacancy (in thousands)

2200 2000 1800 1600 1400 1200 1000 800 1980

1985

1990

1995

2000

2005

2010

Year Fig. 2. Quarterly vacancies (in thousands) and trend, 1980Q1–2009Q4. Note: Job vacancies are defined as the difference between the number of job openings and the number of job placements, and constructed from Employment Security Service Statistics. The series are seasonal adjusted by using the Census’s X-12-ARIMA algorithm. The trend is an HP filter of the quarterly data with smoothing parameter 105. Shaded areas indicate ESRI-dated recessions.

Agency to find workers.8 Job vacancies are defined as the difference between the number of active job openings (yuko-kyuujin-suu) and the number of job placements (shushoku-ken-suu). It is important to note that job vacancies are not measured on the same basis as economy-wide unemployment.9 Although the data on vacancies are not perfect, this study uses this data source because it is the only available data that covers long periods consistently.10 Fig. 2 shows the vacancies and its trend. Similar to unemployment, job vacancies exhibit remarkable variation. The cyclical component of job vacancies has a standard deviation of 0.180, and it also exhibits a large persistence with quarterly autocorrelation of 0.943. 8 Sasaki (2008) uses this data set and estimates outflow equations for unemployed and job vacancies under random and stock-flow matching formations. 9 Unemployment is given in the LFS, while the measure of job vacancies is given in the Report on Employment Service. These two data sets are not collected using the same standards. The Report on Employment Service does not cover all sources of available vacancies because the vacancies in the data are registered vacancies in the Employment Agency. 10 Admitting the data on vacancies in Japan are somewhat imperfect, Sakurai and Tachibanaki (1992) use these two data sources to estimate the mis-match by using the U–V analysis.

Fig. 3. Comparison of cyclical components of unemployment and job vacancy, 1980–2009. Note: Shaded areas indicate ESRI-dated recessions.

In Fig. 3, I present the cyclical components of unemployment and job vacancies simultaneously. The correlation between these two series during the sample period is 0.642. Since unemployment is countercyclical, while job vacancies are procyclical, the vacancy–unemployment ratio is strongly procyclical. The standard deviation of the cyclical component of the vacancy–unemployment ratio is 0.293. Now I turn to see the job finding rate and the separation rate. I construct job find and separation rates from the monthly LFS over the period 1980–2009.1112 The LFS is a rotating panel in which each household participates for 4 consecutive months, leaves the sample for the following 8 months, and joins the sample for 4 months in the following year. Half of the households are replaced every month, and thus half of the sample is surveyed over 2 consecutive months. In the LFS, an individual is classified into three categories: employed, unemployed, and not in the labor force. By matching workers across the 2 months, I can measure month-overmonth transitions by individual workers between employed, unemployed, and non-in-labor-force. Due to sample rotation, missing observations, and errors in responses, transition information of a substantial subset of the sample is not available.13 The failure to match individual workers across months is referred to as margin error. Because of the margin error, the calculated stocks using the flow data are not consistent with the officially reported stocks of workers. I correct the margin error using the adjustment method of Ministry of Labour (1985).14 I then seasonally adjust the series using the X12-filter.

11 The data for the period after 2000 are released from the website of the Japanese Ministry of Internal Affairs and Communications, http://www.stat.go.jp/. However, the data from the period before 2000 is not released through the website or other statistical books. We can obtain these data at the statistical library in the Ministry of Internal Affairs and Communications. 12 By using Labour Force Survey, Kuroda (2003); Ohta and Teruyama (2003a,b); Ohta (2005); Sakura (2006); Genda et al. (2008) also construct the worker flows. Abe and Ohta (2001) construct the worker flows from the Special Survey of the Labor Force, and study the industry-level causes of fluctuations in Japanese unemployment in the 1990’s. Sasaki (2008) calculates the inflow and outflow rates of unemployment by using administrative data. 13 The effect of missing observations and misclassification error has been studied by Abowd and Zellner (1985) and by Poterba and Summers (1986) using the Current Population Survey in the US. 14 In order to reduce the discrepancies between the officially reported stocks of workers and the stocks of workers constructed from the flow measures, first we replace the latter stock values by the former officially reported stocks of workers. Then, using an allocation pattern of flow measures in the uncorrected data, we calculate each component of gross flows. See Ministry of Labour (1985) for details of the adjustment method.

H. Miyamoto / Japan and the World Economy 23 (2011) 214–225

0.22

10

Job-Finding Rate Trend

Separation Rate Trend

9

Separation Rate (10-3)

0.2

Job-Finding Rate

217

0.18 0.16 0.14 0.12 0.1

8 7 6 5 4 3

0.08 1980

1985

1990

1995

2000

2005

2 1980

2010

1985

1990

From the adjusted series, I compute continuous-time transition rates, assuming that they are constant during the month. Let eu and ue denote the margin error adjusted gross flows from employment to unemployment and from unemployment to employment, respectively, and let e and u indicate the measured stocks of employed and unemployed workers, respectively. Then, the discrete-time monthly job finding rate fˆ and separation rate sˆ are determined by uet fˆt ¼ ut1

and

sˆt ¼

In order to remove excess volatility that may stem from measurement errors in the LFS, these monthly series are converted to quarterly frequency by simple averaging. I then detrend the quarterly data using an HP filter with smoothing parameter 105. Fig. 4 shows the quarterly average of the monthly job finding rate and its trend. The average of the job finding rate during the sample period is 14.2 percent. The difference between the log of the job finding rate and its trend has a standard deviation of 0.120. Thus, the job finding rate displayed considerable variations. The correlation between the cyclical components of the vacancy– unemployment ratio and that of the job finding rate is 0.655. This high correlation is consistent with a fairly stable matching function, as assumed by the standard search and matching model. Fig. 5 shows the quarterly average of the monthly separation rate and its trend. The separation rate is small, averaging 0.4 percent during the sample period. This implies that jobs last on average for 18 years. The trend of the separation rate moved upward in the 1990s and was roughly stable afterwards. The difference between the log of the separation rate and its trend has a standard deviation of 0.140, and is countercyclical. Now I study the relative contributions of job finding and separation rates to the cyclical fluctuations in the unemployment

2010

6 5 4 3 2 1

Let f and s denote the continuous-time job finding rate and the separation rate, respectively. Following Fujita and Ramey (2009), I can obtain these rates by using the following relationship between discrete- and continuous time transition rates: ft ½1  exp ð f t  st Þ; f t þ st st sˆt ¼ ½1  exp ð f t  st Þ: f t þ st

2005

7

eut : et1

fˆt ¼

2000

Fig. 5. Monthly separation rate for unemployed workers, 1980–2009. Note: The separation rate is computed using the gross worker flows constructed from the Labour Force Survey. It is expressed as a quarterly average of monthly data. The series are seasonal adjusted by using the Census’s X-12-ARIMA algorithm. The trend is an HP filter of the quarterly data with smoothing parameter 105. Shaded areas indicate ESRI-dated recessions. Sample covers 1980Q1–2009Q4.

Percent

Fig. 4. Monthly job-finding rate for unemployed workers, 1980–2009. Note: The job finding rate is computed using the gross worker flows constructed from the Labour Force Survey. It is expressed as a quarterly average of monthly data. The series are seasonal adjusted by using the Census’s X-12-ARIMA algorithm. The trend is an HP filter of the quarterly data with smoothing parameter 105. Shaded areas indicate ESRI-dated recessions. Sample covers 1980Q1–2009Q4.

1995

Year

Year

0 Steady State Unemployment Rate Actual Unemployment Rate

1980

1985

1990

1995

2000

2005

2010

Fig. 6. Actual versus steady state unemployment rates, 1980Q1–2009Q4. Note: The solid line indicates the actual unemployment rate. The dashed line indicated the steady state unemployment rate. Shaded areas indicate ESRI-dated recessions. Sample covers 1980Q1–2009Q4.

rate. Recently, a number of studies quantify these contributions under the assumption that the actual unemployment rate is closely approximated by its steady state flow value (Elsby et al., 2009; Fujita and Ramey, 2009; Petrongolo and Pissarides, 2008; Shimer, 2007). Following the conventional unemployment decomposition method, I approximate the actual unemployment rate by the steady-state value associated with the contemporaneous job finding and separation rates. Thus,

ut ’

st  ut ; st þ f t

where ut is the steady-state unemployment rate. The correlation between the actual unemployment rate and the steady-state unemployment is 0.92. Fig. 6 shows the small discrepancy between the actual and steady state unemployment rates. There are two possible sources of the discrepancy between actual and steady state unemployment rates. First source of discrepancies comes from ignoring flows into and from ‘‘out-of-the labor force’’. The other source of discrepancies comes from the assumption that the actual unemployment is closely approximated by its steady state value. To see how large these two biases are, I calculate the

H. Miyamoto / Japan and the World Economy 23 (2011) 214–225

218

0.03

120

Labor Productivity (2000=100)

Cyclical Component of u t * Cyclical Component of u ft Cyclical Component of u st

0.025 0.02 0.015 0.01 0.005 0 -0.005 -0.01

Labor Productivity Trend

110 100 90 80 70

-0.015 -0.02 1980

60 1980 1985

1990

1995

2000

2005

1985

1990

1995

2000

2005

2010

Year

2010

Year

utf 

s¯ s¯ þ f t

and

ust 

st ; st þ f¯

where f¯ and s¯ are the average value of ft and st during the sample period. Fig. 7 compares the cyclical components of uf and us with the cyclical component of ut . Fig. 7 shows that both the job finding rate and the separation rate tend to move with the unemployment rate. In particular, the job finding rate accounts for 42 percent of the observed fluctuations in unemployment, while the separation rate accounts for 53 percent of those fluctuations.1516 The last variable examined is labor productivity that is measured as real output per employed workers. The output measure is based on the National Income and Product Accounts, while employment is constructed by Statistics Bureau and Statistics Center. Fig. 8 shows labor productivity, normalized to 100 for 2000, and its trend. Fig. 9 plots the cyclical components of the vacancy–unemployment ratio and labor productivity. The correlation between these two series is 0.81. The important message from this figure is that the vacancy–unemployment ratio fluctuates much more that labor productivity. The overall fluctuations in the vacancy–unemployment ratio are over ten times larger than those of labor productivity during the sample period. Table 1 summarizes the key statistical moments describing the Japanese labor market. Unemployment is about 6 times more volatile than labor productivity, while job vacancies are about 8 times more volatile than labor productivity. The vacancy– unemployment ratio is more than 13 times more volatile. Moreover, the vacancy–unemployment ratio is strongly pro15 ˜ . Since this is not an exact I obtain these numbers by regressing uf or us on u decomposition, these two numbers add up less than 1. See Shimer (2007) and Fujita and Ramey (2009) for a similar exercise. 16 Genda et al. (2008) also calculate contributions of inflows and outflows to the cyclical fluctuations of unemployment and find that the job separation rate is relatively important in Japan. My findings are consistent with their findings.

0.08

Productivity V-U Ratio

0.8

0.06

0.6

0.04

0.4

0.02

0.2

0

0

-0.02

-0.2

-0.04

-0.4

-0.06

-0.6

-0.08 1980

1985

1990

1995

2000

2005

% Change in Productivity

correlation between the cyclical component of the actual unemployment rate and the cyclical component of ut , and it is 0.74. Following Shimer (2007), the respective contribution of variation in the job finding rate and in the separation rate to the variation in the unemployment rate can be computed by

Fig. 8. Quarterly average labor productivity and trend, 1980Q1–2009Q4. Note: Labor productivity is measured as real output per employed workers, and is normalized to 100 for 2000. The series are seasonal adjusted by using the Census’s X-12-ARIMA algorithm. The trend is an HP filter of the quarterly data with smoothing parameter 105. Shaded areas indicate ESRI-dated recessions.

% Change in U-V Ratio

Fig. 7. Contribution of unemployment rate variability. Note: The solid line indicates the hypothetical unemployment rate u. The dashed line indicates the hypothetical unemployment rate if there were only fluctuations in the job finding rate uf. The solid dashed line indicates the hypothetical unemployment rate with only fluctuations in the separation rate us. Shaded areas indicate ESRI-dated recessions. See text for definitions of u, uf, and us.

-0.8 2010

Year Fig. 9. Cyclical components of the vacancy–unemployment ratio and labor productivity. Note: Both the vacancy–unemployment ratio and labor productivity are expressed in logs as deviations from HP filter with smoothing parameter 105. Shaded areas indicate ESRI-dated recessions.

cyclical. The job finding rate is about 5 times more volatile than labor productivity and is pro-cyclical. The separation rate is about 6 times more volatile than productivity and is counter-cyclical. It is also strongly autocorrelated. 3. The model Shimer (2005) demonstrates that the standard search and matching model cannot explain the cyclical volatility of unemployment and vacancies in the U.S. Now I examine whether this failure of the model can be observed in Japan as well. Shimer (2005) and Mortensen and Nagypa´l (2007) demonstrate that steady-state responses of the matching model are essentially equivalent to the dynamic response of the full stochastic version of it.17 Therefore, here I consider the non-stochastic version of the search and 17 In the model, the vacancy–unemployment ratio is a forward looking jump variable that responds immediately to an aggregate productivity shock. Thus, the dynamic response of this endogenous variable is very similar to the comparative static results as long as the productivity process is highly persistent. Since the job finding rate is determined by the vacancy–unemployment ratio, the job finding rate is also jump variable. The unemployment rate is the only endogenous variable that does not instantaneously adjust. However, due to the instantaneous adjustments of job finding, the transition dynamics of unemployment are very fast.

H. Miyamoto / Japan and the World Economy 23 (2011) 214–225

219

Table 1 Summary statistics, quarterly Japanese data, 1980–2009. u Standard deviation Autocorrelation

0.143 0.963

Correlation matrix u v v=u f s p

1 – – – – –

v

v=u

f

s

p

0.180 0.943

0.293 0.955

0.120 0.353

0.140 0.653

0.023 0.886

0.642 1 – – – –

0.882 0.927 1 – – –

0.548 0.632 0.655 1 – –

0.780 0.666 0.790 0.587 1 –

0.677 0.782 0.811 0.541 0.708 1

Note: Unemployment u is constructed from the Labour Force Survey (LFS). The job vacancies v are defined as the difference between the number of job openings and the number of job placements, and constructed from Employment Security Service Statistics. The job finding rate f and the separation rate s are constructed from the LFS. See the text for data construction details. u, v, f, and s are quarterly averages of monthly series. Labor productivity p is measured as real output per employed workers. I seasonally adjust all series using the Census’s X-12-ARIMA algorithm. All variables are reported in logs as deviations from an HP trend with smoothing parameter 105. Sample covers 1980Q1–2009Q4.

matching model of Pissarides (2000) with firm-specific training costs. An economy consists of a continuum of workers normalized to one and a large number of identical risk-neutral firms. Time is continuous. All agents are infinitely lived and maximize the present discounted value of their income with discount rate r. A firm has only one job that can be either filled or vacant. One job is filled by one worker.18 A firm can produce output p if its job is filled. If a firm does not employ a worker, it posts a vacant job at flow costs g and searches for a worker. Free entry drives the expected present value of an open vacancy to zero. A worker can be either employed or unemployed. If a worker is employed, he produces output and earns an endogenous wage but cannot search for other jobs. If he is not employed, he gets a flow utility z from non-market activity and searches for a job. Once a firm and a worker are paired, they separate with exogenous rate s at each time. After a matched firm–worker pair separates, the firm leaves the labor market or reposts a new vacant job. The worker enters the unemployment pool and looks for another job. In this study, I assume that a firm pays fixed firm-specific training costs c every moment of time until the training period is over, which occurs at rate l. The rate l governs how long the training cost needs to be paid. A worker remains ‘‘inexperienced’’ until a shock hits and changes its status to an ‘‘experienced worker’’. This specification has a natural link to the firm-specific human capital in the sense that the training cost c need to be paid every time the worker is hired by a different firm. Note that even if a worker becomes ‘‘experienced’’, he needs to be retrained once he separates from the firm. The wages are determined through the Nash bargaining between a firm and a worker over the share of expected future joint income, where the worker has bargaining power b 2(0, 1). When a shock hits the match and the worker becomes experienced, the firm and the worker renegotiate wages. Because of this, there is a difference between the wage for an inexperienced worker and the wage for an experienced worker, which are denoted by w and we , respectively. The number of successful job matches per unit time is given by the matching function Mðu; vÞ; where u is the number of unemployed workers and v is the number of vacancies. The matching function Mðu; vÞ is continuous, twice

differentiable, increasing in its arguments, and exhibits constant returns to scale. Define u  v=u; as the tightness of the labor market. The rate at which a firm with a vacancy is matched with a worker per unit of time is Mðu; vÞ=v ¼ Mð1=u; 1Þ  qðuÞ: Similarly, the rate at which an unemployed worker is matched per unit of time is Mðu; vÞ=u ¼ u qðuÞ  f ðuÞ: Because the matching function has constant-returns, q(u) is decreasing and f(u) is increasing in u. In the steady-state, the inverse of the transition rates, 1/q(u) and 1/f(u), are the expected duration of a vacancy and an unemployment, respectively. I also make the standard Inada-type assumptions on Mðu; vÞ; which ensure that lim u!1q(u) = 0, lim u!0q(u) = 1 , lim u!1f(u) = 0, and lim u!0f(u) = 1. Let the value of a vacant job be V, the value of a firm with an inexperienced worker be J, and the value of a firm with an experienced worker be Je. Then, they are characterized by the following Bellman equations: rV ¼ g þ qðuÞðJ  VÞ;

(1)

rJ ¼ p  w  c þ sðV  JÞ þ lðJ e  JÞ;

(2)

and rJe ¼ p  we þ sðV  J e Þ:

(3)

I now turn to the worker’s side. When an unemployed worker finds a job, he/she becomes to an inexperienced worker. Thus, the value of an unemployed worker U satisfies rU ¼ z þ f ðuÞðW  UÞ;

(4)

where W is the value of an inexperienced worker. The value of an inexperienced worker W and the value of an experienced worker We are given by rW ¼ w þ sðU  WÞ þ lðW e  WÞ;

(5)

and rW e ¼ w þ s½U  W e :

(6)

In equilibrium, all profit opportunities from new jobs are exploited, so that the following free entry condition holds: V ¼ 0:

(7)

18

In the standard search and matching model, each firm hires one worker and can post at most one vacancy (Mortensen and Pissarides, 1994; Pissarides, 2000). Pissarides (2000, Ch.3) considers a model of large firms in which each firm can employ many workers. He shows that a model with large firms has the same implications as the standard model, assuming that wages are determined through bargaining at the individual level.

The wages for an inexperienced worker and for an experienced workers are determined by the following equations w ¼ arg max ðW  UÞb ðJ  VÞ1b ;

220

H. Miyamoto / Japan and the World Economy 23 (2011) 214–225

and b e

e

e

w ¼ arg max ðW  UÞ ðJ  VÞ

1b

:

The solutions to this optimization problem, w and we , must satisfy the following first-order conditions, ð1  bÞðW  UÞ ¼ bðJ  VÞ;

(8)

and

u˙ ¼  e

e

ð1  bÞðW  UÞ ¼ bðJ  VÞ;

(9)

respectively. By using all the value functions (1)–(6), the free entry condition (7), and the wage sharing rules (8) and (9), I obtain the following equilibrium wages: w ¼ ð1  bÞz þ bð p  c þ ug Þ;

(10)

and we ¼ ð1  bÞz þ bð p þ ug Þ:

ð1  bÞð p  zÞ  bug : rþs

(12)

Similarly, substituting (10) into (2) and using (7) and (12), I obtain the value of a firm with an inexperienced worker, J¼

ð1  bÞð p  zÞ  bug ð1  bÞc  : rþsþl rþs

(13)

Making use of (1), (7), and (13), I obtain the equilibrium job creation condition   g p  z  bug =ð1  bÞ c ¼ ð1  bÞ  (14) : rþs rþsþl qðuÞ The job creation condition (14) states that the expected cost of posting a vacancy, the left-hand side of (14), is equal to the firm’s share of the expected net surplus from a new job match, the righthand side of (14). A steady-state equilibrium in this economy is a triplet of labor    market tightness and wage rates u ; w ; we that solves Eqs. (10), (11), and (14) for the steady-state productivity level p. The evolution of unemployment over time is given by

u˙ ¼ sð1  uÞ  f ðuÞu:

f ðu Þ ðu  u Þ; 1  u

where u is the steady-state unemployment rate. Since the job finding rate is large and there are a lot of persistent in productivity, the deviations of unemployment from steady-state are short-lived. Thus, steady-state responses to aggregate shocks are very good approximations to the true dynamic response of the model. From the job creation condition, I obtain the elasticity of the vacancy–unemployment ratio with respect to labor productivity,

(11)

The wage equation for an inexperienced worker differs from that for an experienced worker. Because firm-specific training costs are shared between the worker and the firm, the wage for an inexperienced worker is reduced by the worker’s share of training costs bc. Substituting (11) into (3) and using (7), I obtain the value of a firm with an experienced worker, Je ¼

literature, it is well know that comparative static results are essentially equivalent to the dynamic response of the full stochastic version of the model (See Shimer, 2005; Mortensen and Nagypa´l, 2007). To see why, here I provide a brief explanation. By using (15), the evolution of unemployment over time can be rewritten as

eu ; p 

@ln u pðr þ s þ b f ðuÞÞ ¼ ; @ln p ðp  z ððr þ sÞ=ðrþ s þ lÞÞcÞ½ðr þ sÞð1  hÞþ b f ðuÞ (16) 0

where h(u)  u[f(u)] /f(u) is the elasticity of the matching function with respect to vacancies. This elasticity is increasing in the firm-specific training cost c and decreasing in the worker conversion rate l. If I set the parameter c to zero, my model reduces to the standard search and matching model and this elasticity becomes identical to that presented in Mortensen and Nagypa´l (2007). Mortensen and Nagypa´l (2007) demonstrate that the cyclical response of labor market tightness with respect to productivity is amplified in the standard matching model when the surplus of the match, p  z, is small. Intuitively, when the surplus of the match is small, it becomes more responsive to changes in productivity. This leads to higher variability of vacancy postings and stronger unemployment fluctuations. Eq. (16) shows that the incorporation of firm-specific training costs can potentially magnify the response of labor market tightness to changes in productivity. The incorporation of firmspecific training costs squeezes the flow surplus of the match and thereby yields amplification of labor market tightness to changes in productivity. Furthermore, the value of the worker conversion rate l also affects the cyclical amplitude of labor market tightness. Recall that in this model, the parameter l governs how long training cost needs to be paid. The lower l means that a firm needs to pay training costs longer. This leads to smaller surplus of the match which generates larger volatilities of labor market tightness. The elasticity of the job finding rate with respect to labor productivity is given by

In the steady-state, the unemployment rate is determined by u¼

s : s þ f ðuÞ

(15)

3.1. Steady-state elasticities The central question in this paper is whether the search and matching model can explain the observed cyclical amplitude of unemployment and vacancy fluctuations in Japan. To explore this issue, I compute the impact of productivity shocks on equilibrium outcomes by calculating the steady-state response to a 1% increase in labor productivity p. I examine the steady-state response as an approximation to dynamic response of the full stochastic version of my model. In the

e f; p 

@ln f ðuÞ @ f ðuÞ u @ln u ¼ : @ln p @u f ðuÞ @ln p

From (15), I obtain the elasticity of the unemployment rate with respect to labor productivity

eu; p 

@ln u hðuÞ f ðuÞ @ln u ¼ : s þ f ðuÞ @ln p @ln p

Finally, the elasticity of vacancies with respect to labor productivity is

ev; p 

@ln v @ln u @ln u ¼ þ : @ln p @ln p @ln p

H. Miyamoto / Japan and the World Economy 23 (2011) 214–225

4. Quantitative analysis

221

Table 2 Calibrated parameter values.

4.1. Basic calibration

Parameter

Description

Value

Source/target

In this section, I calibrate a simplified version of the previous model, where the training cost c and the worker conversion rate l are set to be zero, to match Japanese labor market facts. The purpose is, in the same setup as Shimer (2005), to gauge to what extent the standard search and matching model explains the observed volatilities in unemployment and vacancies in Japan. The following 8 parameters have to be determined: the discount rate r, the level of labor productivity p, the value of leisure z, the worker’s bargaining power b, two matching function parameters m0 and a, the separation rate s, and the vacancy cost g. I choose the model period to be one-month and set the discount rate r = 0.003 because the average annual interest rate during the sample is 3.6%. The labor productivity parameter p is normalized to be one. I assume that the matching function is Cobb–Douglas,

r s

Discount rate Exogenous rate of job separation Value of non-market activity Scale parameter of matching function Elasticity of matching function Worker’s bargaining power Cost of posting a vacancy Labor productivity

0.003 0.004

Data Data

0.6

Martin (1998)

0.157

Job finding rate

0.4 0.6

Kano and Ohta (2002) b = 1  a (efficiency)

0.313

See text

1.0

Normalized

z m0

a b g p

Table 3 A comparison of the model with the Japanese data.

1a a

Mðu; vÞ ¼ m0 u

v ;

where m0 is the matching constant and a is the matching elasticity a with respect to vacancies. Then, the job finding rate is f(u) = m0u a and the vacancy filling rate is q(u) = m0u 1. Kano and Ohta (2002) estimate the matching function in Japanese labor market by using aggregate data, and obtain the elasticity of the matching function a of about 0.4. Therefore, I set a = 0.4.19 This value lies in the plausible range of 0.3–0.5 reported by Petrongolo and Pissarides (2001). I use the Hosios (1990) condition to pin down the worker’s bargaining power, so b = 1  a. The sample mean for the vacancy–unemployment ratio (yuko kyujin bairitsu) from the Report on Employment Service in 1980– 2009 is 0.78. I set u = 0.78. In Section 2, I construct the job finding rate and the separation rate from the LFS. The mean values of job finding and separation rates over the period of 1980–2009 are 0.142 and 0.0048, respectively. I use the monthly job finding rate f = 0.142 and the vacancy–unemployment ratio to pin down the scale parameter m0. I set the monthly exogenous separation rate at s = 0.0048. I now determine the value of non-market activity z. In calibration of search and matching models, the choice of the parameter value z is controversial.20Martin (1998) computes the average replacement rates, the ratio of unemployment benefits to average wages, in the OECD countries. Martin (1998) reports that the replacement rate in Japan is about 0.6, so I set z = 0.6. Finally, following Shimer (2005), the vacancy cost g is obtained from the steady-state solutions of the model. The parameter values are summarized in Table 2.

19 Kano and Ohta (2005) estimate the matching function in the Japanese labor market by using annual panel data, and obtain the elasticity of matching function a of 0.3. Since search and matching models aim at describing macroeconomic behavior of labor market variables, for bench mark case, instead of using the result of Kano and Ohta (2005), I use their estimation result based on aggregate data as my calibration target. In Section 4.3, I study how my results vary with this parameter. 20 Shimer (2005) sets z/p equal to 0.4 in order to capture unemployment benefits. Hagedorn and Manovskii (2008) argue that Shimer’s choice of the value of opportunity cost of employment is too low because it does not allow for the value of leisure, home production, as well as unemployment benefits. They calibrate the opportunity cost of employment and the worker’s bargaining power to match the observed cyclical response of wages and average profit rate. Their results are z = 0.955 and b = 0.052. Mortensen and Nagypa´l (2007) criticize Hagedorn and Manovskii (2008) for using these parameters because these parameters yield workers a gain of 2.8% in flow utility by going from unemployment to employment. Hall and Milgrom (2008) use utility parameter values based on the empirical literature on household consumption and labor supply and reports the effective replacement rate of 0.71.

Elasticity

eu, p eu, p ev; p ef, p

Data Unconditional on p

Conditional on p

12.6 6.16 7.73 5.15

10.2 4.17 6.05 2.79

Benchmark (1)

Benchmark + separation shock (2)

2.59 1.00 1.59 1.03

2.82 5.26 2.44 1.13

4.2. Results Table 3 reports the elasticities of relevant labor market variables with respect to labor productivity. The vacancy– unemployment ratio, the job finding rate, and vacancies are procyclical, while the unemployment rate is counter-cyclical. Thus, the prediction of the model is consistent with basic Japanese labor market facts. Column (1) of Table 3 summarizes the main results from my model. To evaluate the performance of the model, I use two data moments: unconditional and conditional moments. The unconditional data moments are the ratios of standard deviations sx/sp, where sx is the standard deviation of the ln x. They are calculated from the cyclical components of labor market variables constructed in Section 2. The conditional moments are obtained by rxpsx/sp, where rxp is the correlation between ln x and ln p. As Mortensen and Nagypa´l (2007) argue, this conditional criterion allows for the evaluation of the performance of the MP model in predicting the response to productivity shocks without making the strong assumption that other shocks are not affecting labor market fluctuations.21 In any case, as Table 3 reports, the elasticities are far from those observed in the Japanese labor market, both conditional and unconditional. In the literature, the elasticity of the vacancy– unemployment ratio with respect to labor productivity is used to evaluate the performance of the model over the business cycle. In the unconditional data moment, the target value for this elasticity is 12.6. In the model, the elasticity is 2.59, which explains 21% of observed volatility of the vacancy–unemployment ratio. Even using the conditional criterion, the model can explain only 25% of

21 Mortensen and Nagypa´l (2007) argue that the empirical equivalent to the change in x relative to changes in y in the matching model in which adjustment of all endogenous variables takes place instantaneously or very fast, ex, y, is the OLS regression coefficient rxysx/sy.

H. Miyamoto / Japan and the World Economy 23 (2011) 214–225

222

it. Thus, we conclude that the standard MP model fails to explain key business cycle properties of the Japanese labor market. As seen in Section 2, job separation is also the important determinant of the fluctuations in unemployment. To capture this fact, I incorporate separation shocks into the model. In data, the correlation between the logs of the separation rate s and labor productivity p is 0.708. Given the standard deviations of ln s and ln p are 0.140 and 0.023, respectively, the implied estimate of the response elasticity of the separation rate to labor productivity is

@ln s ss 0:140 ¼ 4:31: ¼ rs p ¼ 0:708  0:023 sp @ln p By taking logs and differentiating of (14), I obtain dln u ¼ dln p * (

eu ; p 

+ )  c b f ðu Þ cr˜ dln s  2 r˜ þ l r˜ þ b f ðuÞ ðr˜ þ lÞ dln p  1 r˜ þ b f ðuÞ cr˜ pz ;  r˜ð1  hÞ þ b f ðuÞ r˜ þ l

ps

1



pzþ

a

where r˜ ¼ r þ s. Recalling that f(u) = m0u , the elasticity of the job finding rate with respect to labor productivity is given by ef, p = aeu, p. I can also obtain the elasticities of the unemployment and vacancies rate with respect to labor productivity

eu; p 

@ln u hðuÞ f ðuÞ @ln u f @ln s ¼ þ ; s þ f ðu Þ @ln p s þ f ðuÞ @ln p @ln p

and

ev; p 

@ln v @ln u @ln u ¼ þ ; @ln p @ln p @ln p

respectively. Column (2) of Table 3 reports elasticities of labor market variables with respect to labor productivity when exogenous separation shocks are added. The elasticity of the vacancy– unemployment ratio with respect to labor productivity slightly rises to 2.82. However, the model with separation shocks predicts a counter-cyclicality of vacancies. This can be understood by looking at the job creation condition (14). A lower separation rate raises the vacancy–unemployment ratio, since it encourages firms to post vacancies by increasing the value of job creation. The rise in u rotates the job creation line anti-clockwise. On the other hand, a lower separation rate shifts the Beveridge curve toward the origin. Equilibrium moves from point E to point E0 as seen in Fig. 10. While unemployment decreases unambiguously, the effect on vacancies is ambiguous. With a Cobb–Douglas matching function, the shift of the Beveridge curve may be large enough to make both unemployment and vacancies decrease, explaining why the model with separation shocks predict counter-cyclical vacancies. 4.3. Sensitivity analysis Here I discuss the sensitivity of my results to my choice of parameter values. I study how my results vary with the flow value of unemployment z and the elasticity parameter in the matching function a. When I change these parameters, I re-calibrate parameters b and g in order to maintain my calibration target values. In Table 4, I report the elasticities of relevant labor market variables with respect to labor productivity under the re-calibrated parameter values. First, I discuss the sensitivity of the results to my choice of the flow value of unemployment z. The value of z is an important determinant of the overall volatility of the model in response to changes in productivity. In the benchmark calibration, I set z equal

Fig. 10. The effect of a decrease in the separation rate.

Table 4 Predicted labor market responses to productivity under an alternative calibration strategy. Elasticity

Benchmark (1)

Without separation shock eu, p 2.59 eu, p 1.00 ev; p 1.59 ef, p 1.03 With separation shock eu, p 2.82 eu, p 5.26 ev; p 2.44 ef, p 1.13

z = 0.4 (2)

a = 0.3 (3)

a = 0.57 (4)

1.72 0.67 1.06 0.69

2.56 0.74 1.81 0.77

2.67 1.48 1.19 1.53

1.95 4.92 2.97 0.78

2.75 4.97 2.21 0.83

3.00 5.83 2.83 1.72

to the replacement rate of 0.6 based on the estimates reported in Martin (1998). However, unemployment benefits in reality does not last indefinitely, while in the model there is positive probability that z will be last for a long time. Furthermore, the value of 0.6 is higher than that used for Shimer (2005). Therefore, following Shimer (2005), I recalibrate z by targeting the replacement rate of 0.4. The result is reported in column (2) of Table 4. Varying the value of unemployment flow utility substantially affects the magnitude of the impact of productivity shock on labor market variables. The smaller value of z increases the firm’s steadystate profit and so implies that productivity shock has a smaller proportional impact on profits. The change of z from 0.6 to 0.4 reduces the elasticity of labor market tightness from 2.59 to 1.72. Second, I consider the impact of the elasticity parameter in the matching function a. In my benchmark calibration, I use the parameter value a = 0.4, based on the results of Kano and Ohta (2002). Now I consider two different values of a, 0.3 and 0.57. Former one is the value of Kano and Ohta (2005) and latter one is the value that is obtained by using the method of Mortensen and Nagypa´l (2007). Kano and Ohta (2005) estimate the matching function in Japanese labor market by using annual panel data, and obtain the elasticity of matching function a of 0.3. Mortensen and Nagypa´l (2007) propose the method to estimate the elasticity parameter in the matching function a.22 Following their method, I obtain a = 0.57, which is somewhat above the upper bound on the plausible range of Petrongolo and Pissarides (2001). The columns (3) and (4) report the results under these parameter values. The

22

This method is explained in Appendix A.

H. Miyamoto / Japan and the World Economy 23 (2011) 214–225

223

Table 5 Model results at different training costs.

l

c

g

Without separation shocks

With separation shocks

eu

eu

ev

eu

eu

ev

1/12 1/12 1/12 1/12

0 0.1 0.3 0.5

0.313 0.307 0.293 0.280

2.59 2.64 2.76 2.90

1.00 1.02 1.07 1.12

1.59 1.62 1.69 1.78

2.82 2.93 3.17 3.43

5.26 5.30 5.39 5.49

2.44 2.37 2.23 2.07

1/6 1/6 1/6

0.1 0.3 0.5

0.310 0.303 0.296

2.62 2.68 2.74

1.01 1.04 1.06

1.60 1.64 1.68

2.88 3.00 3.13

5.28 5.33 5.38

2.41 2.33 2.25

1/18 1/18 1/18

0.1 0.3 0.5

0.304 0.284 0.265

2.67 2.85 3.06

1.03 1.10 1.18

1.64 1.75 1.87

2.98 3.32 3.73

5.32 5.46 5.61

2.34 2.13 1.88

Table 6 Model results at different training costs with targeted hiring costs.

l

c

b

Without separation shocks

With separation shocks

eu

eu

ev

eu

eu

ev

1/12 1/12 1/12 1/12

0 0.1 0.3 0.5

0.679 0.691 0.720 0.758

2.58 2.63 2.75 2.88

1.00 1.02 1.06 1.11

1.58 1.61 1.69 1.76

2.78 2.89 3.11 3.36

5.25 5.29 5.37 5.47

2.46 2.40 2.26 2.11

1/6 1/6 1/6

0.1 0.3 0.5

0.692 0.725 0.768

2.60 2.66 2.72

1.01 1.03 1.05

1.60 1.63 1.67

2.84 2.94 3.06

5.27 5.31 5.35

2.43 2.36 2.29

1/18 1/18 1/18

0.1 0.3 0.5

0.689 0.714 0.749

2.66 2.84 3.04

1.03 1.10 1.18

1.63 1.74 1.86

2.94 3.27 3.66

5.30 5.44 5.58

2.37 2.16 1.93

change in a does not substantially alter the elasticities of relevant labor market variables with respect to labor productivity. 5. The role of training costs In this section, I study the role of training costs in the amplification mechanism of the matching model. As seen in Section 3, the incorporation of firm-specific training costs can potentially magnify the response of labor market variables to changes in productivity. I now evaluate the amplification mechanism of firm-specific training costs, and study whether the cyclical volatility is substantially magnified. Since there is no empirical counterpart of training costs, I use the same targets and parameter values as in previous section, and calibrate the model without training costs, c = 0. Since the worker conversion rate l becomes irrelevant when c = 0, I set l = 0. Then, I study whether the extended MP model with training costs can explain the observed fluctuations in unemployment and vacancies by changing the values of c and l. As seen in Section 3, the higher training cost and the lower l would generate larger volatilities since it implies smaller surplus. When I change the values of c and l, I adjust the cost of posting a vacancy g in order to maintain the same steady-state value for labor market tightness. For the benchmark case, I assume that an average duration of 1 year before an employed worker becomes experienced. Thus, l is set to be 1/12. Table 5 reports the elasticity of the vacancy–unemployment ratio with respect to labor productivity for different values of c and l. Changes in elasticity are small when training costs changes. Without separation shocks, the elasticity of the vacancy–unemployment ratio increases by 12 percent when training costs c increase from 0 to 0.5 with l = 1/12. With separation shocks, the elasticity increases by 22 percent. Although the extended model

generates larger cyclical fluctuations in the vacancy–unemployment ratio compared with what the standard model predicts, the extended model still falls short of what we observed in the Japanese data. One question one might want to ask is what values of c and l are empirically plausible. As mentioned before, there is no good empirical counterpart that could guide these values. Although we have several published statistics on training costs in Japan, these are persuasive reasons for believing that these training-related data underestimate the true costs of training.23 Japanese firms train their employees through both on and off-the-job training. Basic Survey on Human Resource Development (Noryoku Kaihatsu Kihon Chosa) by Ministry of Health, Labor and Welfare reports that roughly 70–80% of the surveyed firms conducted some form of the off-the job training between the 1980s and the 2000s. It also reports that roughly 70% of the surveyed firms conducted systematic on-the-job training in 1980s, but recently the percentage of firms that conduct both on and off-the-job training decreases. Expenses incurred with off-the-job training have been reported for a long period of time in General Survey on Working Conditions (Shuro Joken Sogo Chosa) by the Ministry of Health, Labor and Welfare. The share of training cost in the total labor cost, which includes regular wage and bonus payment, is the average of 0.37% between the 1970s and the 2000s. This implies that the share of training costs in monthly regular wage is the average of 0.46% during the periods.24 Since Japanese firms give greater emphasis to on-the-job rather than off-the-job training and the former type of 23 Hart and Kawasaki (1999) argue that published training related data seriously underestimate the ‘true’ costs of training. 24 It is important to note that the proportion of training cost within total cost in Japan is considerably larger than that of the U.S.

224

H. Miyamoto / Japan and the World Economy 23 (2011) 214–225

training cost is not reflected in these statistics, these measures of training costs underestimate true training expenditures. Although more evidence is necessary to pin down the values of training costs c, one may conclude from the above mentioned empirical evidence that lower values of c are empirically plausible. In the benchmark case, i.e., l = 1/12, with c = 0.1, 0.3, and 0.5, the share of training costs in monthly wage is about 10%, 38%, and 74%, respectively. Although the published data underestimate the true costs of training, these values are far from the data of 0.46%. As seen in Table 5, when I change c, I have different values of hiring costs g. One might want to ask whether these calibrated values of g are empirically plausible. Hart and Kawasaki (1999) report that hiring costs represent 10.5% of the annual cash earnings of a new hired worker. In the benchmark calibration without training costs, hiring costs represent about 14.5% of the annual wage. In Table 6, I report the simulated results when the vacancy cost g is calibrated so that it represents 10.5% of the annual cash earnings of a new hired worker.25 This exercise requires adjusting a different parameter to maintain my calibration target values. I choose the worker’s bargaining power b. The simulated elasticities are similar to the ones in Table 5. Thus, the conclusions I draw from these exercises are basically the same.

and suggestions. I also would like to thank to an anonymous referee for his/her suggestions. All remaining errors are mine. Appendix A A.1. The elasticity of the matching function I estimate the elasticity of the matching function a by using the method of Mortensen and Nagypa´l (2007). The steady-state unemployment rate is determined by equating the flow into unemployment with the flow out of it. Thus, I have Mðu; vÞ ¼ sð1  uÞ By using a Cobb–Douglas specification of the matching function and taking logarithms on both sides of the above equation, I obtain ln m0 þ aln v þ ð1  aÞln u ¼ ln s þ ln ð1  uÞ: Then, the regression coefficient implied by (15) is

6. Conclusions This paper studies whether the Mortensen–Pissarides search and matching can explain the business cycle fluctuations observed in the Japanese labor market. To do this, I first establish a number of key facts about the cyclical properties of the Japanese labor market. I find that the dynamics of the Japanese labor market are similar to that in the U.S. Qualitatively the standard MP model succeeds to predict the observed cyclical pattern in labor market variables. However, the model cannot explain the observed fluctuations in unemployment and job vacancies in response to productivity shocks of plausible magnitude. The calibrated model explains about 25 percent of the observed fluctuations in the vacancy– unemployment ratio. Since a number of studies emphasize the role of firm-specific training in the Japanese labor market, I extend the standard search and matching model by incorporating firm-specific training costs. The incorporation of firm-specific training costs can potentially amplify the response of labor market variables to productivity shocks, since it squeezes the flow surplus of the match. Although, relative to the standard MP model, the extended model with firmspecific training costs generates larger cyclical fluctuations in unemployment and vacancies, the extended model still falls short of what we observed in the Japanese data. Another important issue is to consider the role of worker flows in and out of the labor force. Shimer (2005) argues that the inclusion of such flows into the standard search and matching model would worsen the problem, and safely ignores this to make his points. Furthermore, often researchers assume that the flows in and out of the labor force tend to reduce the volatility of unemployment in the U.S. However, the use of female workers as a buffer in Japan, as discussed in papers such as Abraham and Houseman (1993), indicates that some of the movements in and out of the labor force increase the volatility of unemployment. To study the role of such worker flows is a fruitful avenue for future research. Acknowledgements I am grateful to Kyota Eguchi, Ryoichi Imai, Ryo Kambayashi, Ching-Yang Lin, and Yoshimasa Shirai for their invaluable comments 25 I want to equate the per worker hiring cost g/q(u) to 10.5% of the annual wage, 0:15  12w, since there are 12 months in year. Then, the implied monthly job filling a probability is given by q = m0u = 0.18. This implies that g ¼ 0:15  0:18  12w.

 @ln v 1 u ¼ þ1a : a 1u @ln u The data moments documented in Table 1 implies

@ln v sv 0:180 ¼ 0:808 ¼r ¼ 0:642  0:143 su @ln u Since the average monthly unemployment rates over the period of 1980–2009 is 3.40 percent, I obtain the estimated value of a = 0.573. References Abe, M., Ohta, S., 2001. Fluctuations in unemployment and industry labor markets. Journal of the Japanese and International Economics 15, 437–464. Abowd, J., Zellner, A., 1985. Estimating gross labor-force flows. Journal of Business and Economics Statistics 3, 254–293. Abraham, K., Houseman, S., 1993. Female workers as a buffer in Japanese economy. American Economic Review 83 (2), 45–51. Burgess, S., Turon, H., 2005. Worker flows, job flows and unemployment in a matching model. Bristol Economics Discussion Papers 05/572, Department of Economics, University of Bristol, UK. Costain, J., Reiter, M., 2008. Business cycles. Unemployment insurance, and the calibration of matching models. Journal of Economic Dynamics and Control 32, 1120–1155. Elsby, M., Michaels, R., Solon, G., 2009. The ins and outs of cyclical unemployment. American Economic Journal: Macroeconomics 1 (1), 84–110. Esteban-Pretel, J., Nakajima, R., Tanaka, R., 2010. Japan’s Labor Market Cyclicality and the Volatility Puzzle. Graduate Institute for Policy Studies, Mimeo. Fujita, S., Ramey, G., 2009. The cyclicality of separation and job finding rates. International Economic Review 50 (2), 415–430. Genda, Y., Ohta, S., Teruyama, H., 2008. 1990 Nendai Iko no Nihon no Shitsugyo: Tenbo (Japanese Unemployment after the 1990s: A Survey). Bank of Japan Working Paper No. 08-J-4 (in Japanese). Genda, Y., Pazienza, M.G., Signorelli, M., 2001. Labour Market Performance and Job Creation, Comparing Economic Systems. Hampshire and Palgrave, Italy and Japan. Hagedorn, M., Manovskii, I., 2008. The cyclical behavior of equilibrium unemployment and vacancies revisited. American Economic Review 98 (4), 1692–1706. Hall, R.E., 2005. Employment fluctuations with equilibrium wage stickiness. American Economic Review 95, 50–65. Hall, R.E., Milgrom, P., 2008. The limited influence of unemployment on the wage bargain. American Economic Review 98 (4), 1653–1674. Hart, R., Kawasaki, S., 1999. Work and Pay in Japan. Cambridge University Press, Cambridge, UK. Hashimoto, M., Raisian, J., 1985. Employment tenure and earnings profiles in Japan and the United States. American Economic Review 75 (4), 721–735. Hashimoto, M., Raisian, J., 1992. Employment tenure and earnings profile in Japan and the United States: Reply. American Economic Review 82 (1), 346–354. Hosios, A., 1990. On the efficiency of matching and related models of search and unemployment. Review of Economic Studies 57, 279–298.

H. Miyamoto / Japan and the World Economy 23 (2011) 214–225 Kano, S., Ohta, M., 2002. An empirical matching function with regime switching: the Japanese case. Discussion Paper No. 967, Institute of Policy and Planning Sciences, University of Tsukuba, Tsukuba, Japan. Kano, S., Ohta, M., 2005. Estimating a matching function and regional matching efficiencies. Japan and the World Economy 17 (1), 25–41. Kennan, J., 2010. Private information, wage bargaining and employment fluctuations. Review of Economic Studies 77 (2), 633–664. Koike, K., 1984. Skill Formation System in the U.S. and Japan: A Comparative Study The Economic Analysis of the Japanese Firm. North-Holland, Amsterdam. Koike, K., 1988. Understanding Industrial Relations in Modern Japan. St. Martin’s Press, New York. Krause, M.U., Lubik, T.A., 2007. On-the-job search and the cyclical dynamics of the labor market. Discussion Paper Series 1: Economic Studies 2007, 15, Deutsche Bundesbank, Research Centre. Kuroda, S., 2003. Analysis of changes in Japan’s unemployment rate using gross flow data. Monetary and Economics Studies 69–104. Ohta, S., 2005. Furo kara Kangaeru (studying from flow data). In: Otake, F. (Ed.), Ouyokeizaigakyu heno Sasoi. Nihonhyoronsha, pp. 55–89 (in Japanese). Ohta, S., Teruyama, H., 2003a. Rodoryoku Flow Data ni yoru Shugyo oyobi Shitsugyo no Bunseki (Analysis on employment and unemployment based on workforce flow data), Keizai Bunseki (The Economic Analysis) 168, 125– 189 (in Japanese). Ohta, S., Teruyama, H., 2003b. Flow Data karamita Nihon no Shitsugyo—1980–2000 (Japanese unemployment by using flow data—1980–2000). Nihon Rodo Kenkyu Zasshi (The Monthly Journal of the Japan Institute of Labour) 516, 24–41. Poterba, J.M., Summers, L.H., 1986. Reporting errors and labor market dynamics. Econometrica 54 (6), 1319–1338. Martin, J.P., 1998. What works among active labour market policies: evidence from OECD countries’ experiences. OECD Labour Market and Social Policy-Occasional Papers No.35. Mincer, J., Higuchi, Y., 1988. Wage structure and labor turnover, in the United States and Japan. Journal of the Japanese and International Economics 2, 97–133. Ministry of Labour, 1985. Rodo Hakusho (White Paper on Labour). Ministry of Labour (in Japanese). Miyamoto, H., Shirai, Y., 2006. Job flows and unemployment in an equilibrium unemployment model with firm-specific skill training. The Japanese Economic Review 57 (4), 547–561.

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Mortensen, D.T., Pissarides, C.A., 1994. Job creation and job destruction in the theory of unemployment. Review of Economic Studies 61, 397–415. Mortensen, D.T., Nagypa´l, E., 2007. More on unemployment and vacancy fluctuations. Review of Economic Dynamics 10 (3), 327–347. Nagypa´l, E., 2007. Labor–Market Fluctuations and On-the-job Search. Northwestern University, Mimeo. Petrongolo, B., Pissarides, C.A., 2001. Looking into the black box: a survey of the matching function. Journal of Economic Literature 39, 390–431. Petrongolo, B., Pissarides, C.A., 2008. The ins and outs of European unemployment. American Economic Review 98 (2), 256–262. Pissarides, C.A., 2000. Equilibrium Unemployment Theory, 2nd ed. MIT Press, Cambridge, MA. Pissarides, C.A., 2009. The unemployment volatility puzzle: is wage stickiness the answer? Econometrica 77 (5), 1339–1369. Sakura, K., (2006). Flow Data ni yoru Wagakoku Rodoshijo no Bunseki (Analysis of the Japanese labor market by using flow data). Bank of Japan Working Paper Series No. 06-J-20. Sakurai, K., Tachibanaki, T., 1992. Estimation of mis-match and U–V analysis in Japan. Japan and the World Economy 4 (4), 319–332. Sasaki, M., 2008. Matching function for the Japanese labour market: random or stock-flow? Bulletin of Economic Research 60 (2), 209–230. Shimada, H., 1981. Earnings structure and human investment: a comparison between the United States and Japan. Keio Economic Observatory Monograph, No. 4, Kogakucha, Tokyo. Shimer, R., 2005. The cyclical behavior of unemployment and vacancies: evidence and theory. American Economic Review 95, 25–49. Shimer, R., 2007. Reassessing the ins and outs of unemployment. Manuscript. University of Chicago. Silva, J.I., Toledo, M., 2009a. Labor turnover costs and the cyclical behavior of vacancies and unemployment. Macroeconomic Dynamics 13, 76–96. Silva, J.I., Toledo, M., 2009b. The unemployment volatility puzzle: the role of matching costs revisited. MPRA Paper No. 15695. Tasci, M., 2006. On-the-Job Search and Labor Market Reallocation. University of Texas at Austin, Mimeo. Zhang, M., 2008. Cyclical behavior of unemployment and job vacancies: a comparison between Canada and the United States. The B.E. Journal of Macroeconomics: 8 (1 (Topics)) (Article 27).