Working Paper Series

Congressional Budget Office

Washington, DC

LABOR ADJUSTMENT, PRODUCTIVITY AND OUTPUT VOLATILITY:

AN EVALUATION OF JAPAN’S EMPLOYMENT ADJUSTMENT SUBSIDY

Naomi N. Griffin

Macroeconomic Analysis Division

Congressional Budget Office

Washington, DC

E-mail: naomi.griffin@cbo.gov

December 2005

2005-10

Working papers in this series are preliminary and are circulated to stimulate discussion

and critical comment. These papers are not subject to CBO’s formal review and editing

processes. The analysis and conclusions expressed in them are those of the authors and

should not be interpreted as those of the Congressional Budget Office. References in

publications should be cleared with the authors. Papers in this series can be obtained at

www.cbo.gov (select Publications and then Working and Technical Papers).
Abstract

This paper provides a theoretical examination of the impact of Japan’s Employment Adjustment Subsidy, a major employment insurance policy since 1975, on labor adjustment, productivity and output fluctuations in the iron and steel sector. A partial equilibrium industry model

with heterogeneous establishments and aggregate uncertainty shows that the EAS reduces

steady-state labor productivity by encouraging labor hoarding, while reducing job flows and

increasing average firm-level employment. While the directly measured impact on productivity is proportional to the fraction of subsidized workers, the indirect effects of the subsidy

on output and employment volatility can be substantially larger. First, the subsidy can lead to

a sizable increase in output fluctuations over business cycles by symmetrically increasing the

output response to shocks. This result is achieved through lower output via subsidy during

unfavorable aggregate shocks and higher output via less spending on hiring during favorable

aggregate shocks. Second, the subsidy meets its primary objective of reduced employment

volatility. The reduction can be considerable when hiring and firing costs are set equal to the

annual wage.

Journal of Economic Literature Classification Numbers: D21, E32, E37, L16.

Key Words: Employment policy, productivity, output volatility, business cycle, job

creation and destruction.

i
Table of Contents

1 Introduction 1

2 Background 8

2.1 Summary of the EAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Overview of the Iron and Steel Industry . . . . . . . . . . . . . . . . . . . . 13

3 An Industry Model 18

4 Results 33

4.1 Basic Setup and Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2 Stationary Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5 Conclusion 50

Appendix 53

A. Graphic Illustration of Subsidy Take-up State Spaces . . . . . . . . . . . . . . . 53

B. Strategy for Solving the Numerical Dynamic Optimization Problem . . . . . . . 55

ii
1 Introduction

This paper examines the Employment Adjustment Subsidy (EAS), a core Japanese

employment insurance policy since 1975.1 The EAS program allows firms to reduce output

during unfavorable business conditions without laying off workers by providing part of the

costs of sustaining excess workers.2 The EAS policy has not yet been formally analyzed

despite recent macroeconomic literature emphasizing job reallocation as a driving force behind

business cycles. Therefore, the primary objective of this paper is to point out some of the key

implications of the policy through the application of a theoretical framework of heterogeneous

establishments with aggregate uncertainty. In particular, this paper investigates the impact of

the EAS on average labor productivity, job flows and entry/exit rates at the steady-state. In

addition, it examines the implications of the policy for the volatility of employment, output

and productivity over business cycles.

Between 1990 and 2002, more than 360 billion yen (over 3.6 billion US dollars) was

spent on the EAS. On average between January 1991 and October 2001, about 170,000 establishments were eligible for the subsidy program.3 According to the 1996 Establishment

Census, there are about 6.5 million establishments in Japan (excluding public service) with

770,000 in manufacturing. Thus, the average number of targeted establishments corresponds

1

I wish to thank John Haltiwanger, John Shea, Michael Pries, Jeffery Smith, Katherine Abraham, Akie

Takeuchi, Ana Maria Oviedo, and Kazuhiko Odaki for their comments and invaluable suggestions, Kyoji Fukao

for providing the JIP database, and Employment Security Bureau of Japanese Ministry of Health, Labor and

Welfare for preparing the EAS information.

2Since 1975, the employment insurance programs had three central interrelated projects: (1) an employment

stabilization project that was carried out through the Employment Adjustment Subsidy, (2) a skill development

project providing assistance to the management and development of job training centers, and (3) a workers’

welfare project providing employment consultation. The employment stabilization project has been the most

predominant of the three.

3As described later in this paper, additional criteria set by the government in terms of past employment and

output trends must be satisfied in order to receive the subsidy.

1
to 2.6% of the total number of establishments, or approximately 20% of manufacturing establishments. The number of targeted establishments peaked at 411,000 units in February

2000.

The EAS recipients are heavily concentrated in the manufacturing sector, with the

largest beneficiary being the iron and steel industry. The manufacturing sector and the iron

and steel industry, respectively, received approximately 94% and 40% of the total subsidy bill

between 1990 and 2002.4 Although the program in principle involves the entire economy, to

illustrate the theoretical implications of the program, this paper focuses on the iron and steel

industry. The calibrated industry model developed later will attempt to match key moments

obtained from the data for this industry.

With respect to the empirical background, Davis and Haltiwanger (1990, 1992, 1999)

and Davis, Haltiwanger and Schuh (1996), using longitudinal data sets in the US manufacturing sector, expose the importance of idiosyncratic differences across establishments in explaining business cycle dynamics. Many theoretical frameworks analyzing industry dynamics, such as Jovanovic (1982), Hopenhayn (1992), Hopenhayn and Rogerson (1993), Ericson

and Pakes (1995) and Campbell and Fisher (2000), also stress the importance of heterogeneity

across firms when characterizing firm’s production and entry/exit decisions. To the extent that

the EAS interacts with such heterogeneity across establishments within an industry, the appro4

In October 2001, the Japanese government abolished industry selection completely in response to criticism

that the program was skewed toward particular industries: the current guidelines provide that any establishment

can receive the subsidy if specific and much stricter criteria are satisfied. Namely, the monthly average of the

last six months’ production has to drop by more than 10% and employment has to be less than or equal to,

in comparison with the same months of the previous year. Previously, the monthly average of the last three

months’ production had to be strictly less, while employment had to be equal or less than the previous year.

Furthermore, the subsidy cannot be given to establishments whose unfavorable business conditions are predicted

to last for more than two years, and establishments are no longer able to receive the subsidy continuously for more

than a year. Instead, they are required to take a year long hiatus, except during severe economic circumstances.

2
priate theoretical framework to analyze the effect of the policy must also encompass similar

features.

In addition, prior research concerning the implications of differing labor market institutions, particularly European employment policies, has shown that labor market policies have

an important effect on equilibrium job flows, unemployment and productivity. Hopenhayn

and Rogerson (1993), for instance, illustrate that high firing costs in Europe, which interfere

with the process of job reallocation, lead to a sizable reduction in employment and a drop

in average productivity. Others have stressed the interactions between a changing economic

environment and labor market policy. Ljungqvist and Sargent (1998) explain that generous

unemployment benefits increase unemployment rates when the skill mix demanded in the labor market is rapidly changing. Other studies have linked multiple labor market policies.

Bentola and Rogerson (1993), for example, demonstrate that wage compression in Europe

tends to generate more volatile employment flows, fostering a policy that restricts the firing of

workers. They argue that these institutional differences can account for the similarities in job

flows and differences in unemployment between Europe and the US. Even though this paper

will not examine the political economy of the origin of the EAS, one of the chief objectives of

the EAS has been to reduce the volatility of employment.

As wage compression can be considered as a precondition for firing restrictions, some

labor market institutions, namely labor adjustment costs and wage rigidities, are likely preconditions for the EAS, since the subsidy will not be used if labor adjustment is costless or

if wages can absorb shocks. Despite the fact that there are few quantitative studies that estimate the cost of firing workers in Japan, there is some legal evidence that suggests that firing

3
workers in Japan is generally very difficult, more similar to the European than the US case.5

Moreover, the post-war tradition of life-time employment has encouraged firms to invest in

building firm specific human capital.6 This evidence indicates that adjusting employment has

been quite costly in Japan. Correspondingly, the EAS was designed in order to “assist firms

in their efforts to maintain employment in times of temporary unfavorable business conditions

owing to economic recession or changes in the industrial structure of the Japanese economy,

as well as to promote employment stability and prevent unemployment.”7

While there has not been a formal empirical study on the effect of the subsidy program,

primarily due to the unavailability of data, some existing studies suggest that the EAS distorts

employment behavior. For instance, Hashimoto (1993) uses monthly aggregate manufacturing data and finds that, since the subsidy allows for adjustment through temporary business

closures, employment became less sensitive, while working hours became more sensitive, to

demand shocks after the subsidy program was enacted in 1975.8 While factors other than

the EAS may be part of his results, the estimated elasticity of employment with respect to

unanticipated demand shocks drops dramatically from .30 before (1967-74) to -.27 (1975-86)

after the initiation of the EAS policy. Likewise, the estimated elasticity of employment with

respect to anticipated demand shocks falls from .28 to -.27. These coefficients are significant

in all cases. He also points out that the treatment of temporarily laid off workers in Japanese

5Takashi Araki (2000) discusses the legal evidence of stringent firing restrictions in Japan from the perspective

of corporate governance.

6A detailed discussion of the relationship between intensive human capital investment and the low turnover

rate in Japan is provided by Mincer and Higuchi (1988).

7

Japanese Ministry of Health, Labor and Welfare. “Guidebook for Employment Adjustment Subsidy,” 2002.

8On the contrary, the unemployment insurance (UI) system in the US encourages temporary layoffs instead of

temporary business closures. Feldstein (1976, 1978) and Anderson and Meyer (1993) discuss the incentive for

firms to increase temporary layoffs when the experience rating of firms’ unemployment insurance is imperfect.

Feldstein (1976) explains why employment instead of hours is reduced in response to negative demand shocks

under the UI system in the US.

4
statistics as ‘employed’ explains part of the differences in unemployment rates between Japan

and the US.

Another related yet unexplored empirical issue is that the presence of subsidized workers reduces measured productivity, since hoarded workers are not properly taken into account

in employment statistics. This paper will attempt to estimate the number of unutilized workers through the subsidy program in the iron and steel industry, as well as the reduction in

productivity that can be accounted for by the inclusion of subsidized workers in employment

statistics. Then, these estimates will subsequently be used for the calibration of the model.

The model developed here offers insights beyond the direct effect of labor hoarding on productivity. The indirect effects of the EAS on the cyclical dynamics of output and employment

generate a wide set of empirical predictions, testable in future research as more data becomes

available.

The model exploits the theoretical framework of Hopenhayn (1992) and Hopenhayn

and Rogerson (1993). The main advantage of using their framework is is that, as previously

mentioned, their model allows for a heterogeneity across establishments and thus allows us

to evaluate the impact of the subsidy program on industry dynamics by explicitly modeling

the equilibrium response of heterogeneous establishments. Unlike Hopenhayn and Rogerson,

however, the consideration of labor supply decisions and hence the households’ problem will

be omitted to focus on the impact of the subsidy on establishment-level dynamics. Thus,

the analysis will be a partial equilibrium estimate of the change in overall industry dynamics

caused by the subsidy program. Moreover, two-state aggregate uncertainty is added to the

model, a feature that was not present in Hopenhayn and Rogerson (1993). Since the wage remains constant in the model, the aggregate uncertainty should be best interpreted as reflecting

5
the partial equilibrium real impact of shocks net of their impact on wages.

In interpreting the impact of the subsidy on average labor productivity, a word of caution is in order: while firms are heterogeneous in the model, workers are homogeneous in the

sense that productivity does not increase with tenure. The subsidy could increase average

productivity if this feature were added to the model. This feature was not added in the model

because of the high concentration of the subsidy in sectors where the value of workers’ skills

seems to be depreciating faster in comparison to other sectors.9In my model, the difference

between old and new workers is solely reflected in the hiring cost, which reduces output during

the first period; the productivity of new and old workers is equalized afterwards.

I show that the subsidy program reduces steady-state average productivity primarily

by increasing the number of unutilized workers (labor hoarding effect). Roughly speaking,

the reduction in average productivity is more or less proportional to the fraction of subsidized

workers: when the fraction of subsidized workers is about 1%, average productivity also falls

by roughly the same amount. At the same time, average firm-level employment increases and

the job turnover rate falls with the subsidy. When the cost of the subsidy and the gains of reduced adjustment costs are included in the calculation of average productivity, productivity is

further reduced for reasonably sized labor adjustment costs, as the cost of the subsidy exceeds

the savings on labor adjustment costs.10

The estimated direct impact of the subsidy on productivity is small, as the estimated

average fraction of subsidized workers in the iron and steel sector between 1990 and 2002 is

9For example, the subsidy seemed to have concentrated in those sectors with comparative disadvantage in the

international market. The government often cites as reason for industry selection into the EAS as “unfavorable

business conditions arising from the competition with cheaper imports from China” etc.

10However, with high enough labor adjustment costs, it is possible that the savings on adjustment costs could

exceed the cost of the subsidy.

6
about 2.1%. Novertheless, the second moment features generated by my simulation exercises

reveal that with realistic parameters, the subsidy program has a disproportionately large impact

on output and employment dynamics over the business cycle. In particular, output volatility

can increase by 3.5% even when the steady-state fraction of subsidized workers is around

1.6%. The intuitive reason for this result is that the subsidy increases the sensitivity of output

to aggregate shocks symmetrically: following unfavorable shocks, the subsidy allows firms

to reduce production without laying off workers, while following favorable shocks, firms are

able to increase output without hiring new workers.

On the other hand, the subsidy reduces employment volatility. In some cases, the drop

in employment volatility can be substantial, even when the fraction of subsidized workers is

small. Below, I show that hiring and firing costs set equal to the annual wage of workers can

reduce the volatility of employment by about 12% even if the fraction of subsidized workers

is less than 2%. The reduction in employment volatility is achieved by the reduced sensitivity

of job creation and destruction to aggregate shocks over the business cycle. The EAS also increases the average size of the firm while reducing average firm level output at the steady-state.

Finally, the steady-state exit/entry rate as well as the steady-state job creation/destruction rate

drop with the subsidy.

This paper proceeds as follows: section (2) provides a brief background of the EAS

as well as an overview of the employment and output trends obtained from the aggregate iron

and steel industry data. I then calculate the direct impact of the EAS on TFP induced by

labor hoarding, which later will be used for the calibration of the model. Section (3) lays

out the theoretical framework of the industry model and provides analytical results. Section

(4) shows results from solving a stochastic version of the model through numerical dynamic

7
programming. I present key statistical features obtained from the stationary distribution of

the model as well as simulation exercises, and compare the subsidy case with the benchmark

case that sets the subsidy to zero. Section (5) concludes.

2 Background

2.1 Summary of the EAS

The Employment Adjustment Subsidy program was initiated in 1975 as a preemptive

measure against unemployment. More specifically, it was initiated in response to policymakers’ concern that the unemployment rate would rise following the first oil shock and the

resulting changes in the industrial structure of the Japanese economy.11 In principle, however,

the subsidy was designed to help sustain employment during “temporary unfavorable business

conditions” without incurring the loss associated with labor adjustment costs.12 This objective was mainly achieved by reimbursing a fraction of wages for establishments closing

part or all of its operations, or a fraction of the cost of sending workers to other (unrelated)

establishments. The subsidy was expected to lower unemployment as well as the cost of

unemployment insurance by reducing the unemployment rate.

Prior to 2001, the government selected eligible industries, either entire four-digit sectors or subsectors, based on recent trends in industrial output and employment, or changes in

11The Japanese Ministry of Labor reports that the EAS was originally designed in response to a recommendation by the OECD that the Japanese government prepare for higher unemployment arising from the transition

from a growing to a mature economy. [Japanese Ministry of Labor, Employment Security Bureau (1999), p. 14.]

Another justification often provided was to assist firms, which had been the primary provider of job security often

in the form of life-time employment, to sustain employment during difficult times.

12While the government preferred to consider the subsidy as a “temporary” assistance measure designed to

reduce the severe negative impact of sectoral shocks on unemployment, in practice, some industries facing longterm structural changes were often able to maintain eligibility for an extended period of time.

8
the industrial structure, such as rising competition from foreign imports. The official selection criteria in terms of output and employment were: i) the average of the past three months’

industrial production dropped more than 5% compared to the same months of the previous

year, and ii) the average of the past three months’ employment had not increased compared

to the same months of the previous year.13 Furthermore, additional special selection criteria

were set in 1995 for more generous subsidy coverage: “as a result of an appreciation of the

yen or economic globalization, the monthly average of the past six months’ industrial production and employment fell or is predicted to fall more than 10% compared to the same season

in one of the three previous years.” The selection was not completely deterministic as explained by the government: the “selection is not solely based on figures but also determined

in accordance with our objective of the prevention of unemployment.”14 The Japanese government abolished industry selection criteria in October 2001, replacing them with tougher

establishment-level eligibility criteria.

Under the standard selection rules, industries were selected for one year with the possibility of an extension for an extra year if needed. Once selected, industries could be reselected after a six-month break. For the special selection rules between 1995 and 2001, the

selection period was set to two years with the possibility of an extension. Between 1990 and

2001, the unweighted average length of eligibility for a selected industry was 2.6 years with

a maximum of 7 years. During the same period, about 96% of the selected four-digit industries or subcategories belonged to the manufacturing sector, of which about 14% belonged to

ceramic and clay products, 13% to general machinery, 10% to metal products, 10% to textiles

13As for the employment criteria, it became ‘a drop of 5% or more’ between March 2000 and October 2001.

14Japanese Ministry Labor, Employment Security Bureau (1999), p. 191.

9
Figure 1: Annual Total Subsidy Bill (in billions of yen) for 1975−2001

0

10

20

30

40

50

60

76 78 80 82 84 86 88 90 92 94 96 98 00

Temporary business closures

Temp. business closures w/ training

Sending workers to other establishments

Source: Employment Security Bureau of Japanese Ministry of Health, Labor and Welfare.

and 9% to the iron and steel industry.

Once an industry was selected, establishments in this industry, as well as their upstream

suppliers, could take up the subsidy if the average of their last three months’ production (employment) was less (equal or less) than the monthly average for the same season a year before.

Small- and medium-size establishments meeting these criteria could receive 2/3 of their labor

costs (3/4 under special selection) and large establishments could receive 1/2 of their labor

costs (2/3 under special selection) while they implemented temporary closures of their business operations.15 Additional allowances of three thousand yen per worker per day were

15Note that establishments do not have to pay full wages while they implement temporary business closures.

Moreover, the maximum coverage for the establishments in an industry selected under standard selection criteria

(shitei-gyosyu) was 100 days × the total number of employees, and the maximum coverage for firms in a industry

selected under the special selection criteria (tokutei koyo chosei gyosyu) was 200 days × the total number of

employees. Between July 1995 and October 2000, about 44% of the targeted establishments could apply under

the special selection criteria.

10
given if establishments provided job training to workers while they temporarily closed their

businesses.16 Instead of business closures, establishments could also send workers to other

unrelated establishments for more than three months. In this case, the receiving establishment

was required to pay for the labor service provided by the subsidized workers, and the sending

establishment paid the difference between the workers’ original wage and the amount paid

by the receiving establishment. The subsidy covered a fraction of the cost borne by sending

establishments.

Although the subsidy program started in 1975, its effect was probably largest during

the 1990s, the decade of sluggish growth. Figure 1 shows the subsidy bill for each of the three

options available to establishments. The total subsidy bill dramatically increased after 1992.

Furthermore, among the three options, temporary business closure had the highest share of

the total subsidy bill, especially during the 1990s. Subsequently, the analysis of this paper

focuses on the 1990s for the following reasons: i) more establishments were made eligible

during the 1990s, ii) the subsidy rules stabilized by 1990, and iii) data on the subsidy bill by

two-digit sector is available only after 1990. In the theoretical section, I will model the policy

using the criteria prior to the October 2001 revision.

The share of the total subsidy bill between 1990 and 2002 as well as the annual average share by two-digit sector is provided in Table 1.17 The iron and steel industry has

the largest annual average share (47.03%), followed by general machinery (10.49%), transportation equipment (8.15%), and textiles (4.93%).18 As mentioned previously, the high

16In October 2001, however, the allowance for training was reduced to 1200 yen.

17This data was made available upon request from Employment Stability Bureau of Ministry of Health, Labor

and Welfare.

18The share calculated is in terms of annual average. The results for the total subsidy bill between 1990 and

2002 are similar.

11
Table 1: Share of Subsidy Bill by Industries for 1990−2002

Total Bill Annual Average

Manufacturing Total 93.96% 93.45%

Food 0.09% 0.13%

Beverage, feed and tobacco 0.04% 0.03%

Textiles 5.31% 4.93%

Apparel and other textiles 1.74% 1.53%

Lumber and wood products 0.63% 0.59%

Furniture and fixtures 0.64% 0.59%

Pulp and paper products 0.44% 0.26%

Printing and publishing 0.03% 0.03%

Chemical and allied products 1.54% 1.28%

Petroleum and coal products 0.15% 0.15%

Plastics 0.54% 0.38%

Rubber products 1.40% 1.13%

Leather, tanning, fur products 0.19% 0.17%

Ceramic, stone and clay products 3.98% 3.52%

Iron and steel 40.70% 47.03%

Non-ferrous metals 1.61% 1.42%

Fabricated metals 3.36% 2.78%

General machinery 12.75% 10.49%

Electrical machinery 6.24% 7.21%

Transportation equipment 10.69% 8.15%

Precision instruments 1.06% 0.96%

Ordinance 0.03% 0.02%

Other manufacturing 0.80% 0.67%

Other Sector Total 6.04% 6.55%

Source: Employment Security Bureau of Japanese Ministry of Health, Labor

and Welfare.

concentration in the iron and steel industry motivates my modeling the effects of the subsidy

program on this industry.19

19A strong union presence, which generates wage rigidity and high labor adjustment costs, may be one of

the reasons why the iron and steel industry has a high take-up rate. Yet, since eligible industries are given

by four-digit industries or subcategories within four-digit industries while the estimated number of subsidized

workers are available by two-digit industries, the investigation of the take-up rates across sectors requires the

size of eligible workers to be estimated by two-digit industries. This estimation was not done in this paper and

remains an area for future research.

12
2.2 Overview of the Iron and Steel Industry

This section provides an overview of output, employment and productivity behavior

in the iron and steel industry between 1973 and 2001. The data set used to study output is

the Japan Industry Productivity Database (JIP database).20 This data set was compiled as

a part of the Japanese government’s project to calculate annual TFP for 84 sectors in Japan

between 1973 and 1998.21 Since the database is based on the 1968 SNA (System of National Account), currently data is available only through 1998. Figure 2 shows real gross

output between 1973 and 1998. There is a considerable increase in output in the late 1980s

and early 1990s, followed by a large drop in the mid- and late-1990s. Figure 3 shows the

employment trend, taken from the Employment Trend Survey, which includes both permanent

and temporary workers for all establishments with more than five employees.22 Except in the

mid-1980s, employment exhibits a steady decline since 1973. This fact, combined with the

positive trend in real gross output implies increased capital intensity or TFP during this period.

If subsidized workers are included in employment, then standard productivity measures will be distorted since labor input will be systematically overstated.23 The data provides

the annual subsidy bill by two-digit sector between 1990 and 2002, but does not provide the

total number of subsidized work days in each sector. Consequently, we need to estimate the

number of unutilized workers for each year using the annual subsidy bill. This estimation

was accomplished as follows: first, the average subsidy cost per work day (i.e., per worker

20The JIP database is made available in English by Kyoji Fukao on his website: http://www.ier.hitu.ac.jp/ ̃fukao/english/data/index.html.

21See Fukao et al. (2003) for the TFP analysis of the 84 sectors from 1973 to 1998 using the JIP database.

22The beginning-of-year (January 1) figure was used to represent the employment of the previous year.

23Note that average work hours may capture part of labor hoarding through the EAS, but it is unlikely to

entirely capture the total number of subsidized workers. For the discussion of variable factor utilization in

affecting cyclicality of productivity, see Basu and Kimball (1997), Basu and Fernald (2000) and Basu, Fernald

and Shapiro (2001).

13
Figure 2: Real Gross Output in the Iron and Steel Industry (in billions of yen)

19000

20000

21000

22000

23000

24000

25000

26000

27000

28000

72 74 76 78 80 82 84 86 88 90 92 94 96 98

Real gross output

Source: JIP database.

Figure 3: Annual Employment in the Iron and Steel Industry (in thousands)

240

280

320

360

400

440

480

520

72 74 76 78 80 82 84 86 88 90 92 94 96 98

Employment

Source: Employment Trend Survey.

Note: The figure includes both permanent and temporary workers for all establishments with

more than five employees.

14
per day) was calculated by dividing the total subsidy bill covering the entire economy by the

total number of subsidized work days covered each year.24 Then, the annual subsidy bill for

the iron and steel industry was divided by the annual average subsidy cost per work day in

order to calculate the total number of subsidized days in this industry. Finally, this number

was divided by the annual average work days for workers in the iron and steel industry to get

an estimate of the number of subsidized workers for each year.25 Figure 4 shows the result

of this calculation. On average, 2.1% of iron and steel workers were subsidized during this

period. In 1995, the highest take-up year, 4.6% of iron and steel workers were subsidized.26

Since the JIP dataset ends in 1998, an alternative source of output data must be used

to calculate productivity between 1990 and 2001. I use measures of real value added as well

as capital stock, both based on the 1993 SNA standard, from the Annual Report on National

Account.

27 An annual growth accounting exercise, as in Hayashi and Prescott (2000), was

performed to estimate the level as well as the growth rate of TFP both before and after adjusting labor inputs for the number of subsidized workers. More specifically, I adopt the

following Cobb-Douglas specification:

Y = AKθ(h ·(E −S))1−θ, (1)

24Since there are three subsidy options (i.e., temporary closures, temporary closures with training, and sending

workers to other establishments), the weighted average of these three was taken to estimate the average cost per

work day. Since the workday cost for sending workers to other establishments cannot be estimated, this cost was

replaced by the work day cost of temporary closures.

25The average work days for workers in the iron and steel industry was taken from Monthly Labor Statistics

by the Japanese Ministry of Health, Labor and Welfare. Since the figure provided here is the monthly average,

it was multiplied by 12 to get an approximate annual figure. The data is available at the following website in

Japanese: http://stat.jil.go.jp.

26However, since the subsidy bill includes the third option, namely ‘sending workers to other establishments,’

if we focus only on temporary business closures given by the first two options, the estimated average fraction of

workers should be somewhat smaller than 2.1%.

27Capital stock is at completion basis. The data can be found at the following website in Japanese:

http://www.esri.cao.go.jp/jp/sna/toukei.html.

15
Figure 4: Estimated Hoarded Workers via EAS in the Iron and Steel Industry

0

2000

4000

6000

8000

10000

12000

14000

90 91 92 93 94 95 96 97 98 99 00 01 02

Estimated number of hoarded workers via EAS

Source: Subsidy information was provided by Employment Security Bureau of Japanese Ministry

of Health, Labor and Welfare. Other data used for the estimation is provided in the text.

where Y is real value added, A is the measure of TFP, K is the real capital stock, h is average

work hours, E is employment and S is the number of subsidized workers.28 The cost share of

capital θ is set equal to 0.464, which corresponds to the average cost share of capital excluding

material inputs between 1973 and 1998 given by the JIP database.29

Figure 5 shows the level of TFP in the iron and steel industry with and without adjustments for the subsidy, using the National Accounts data. The level of TFP is higher when

employment is adjusted for the subsidy for obvious reasons. The adjustment is the highest in

1995 in which adjusted TFP is higher than unadjusted TFP by 2.53%. On average, adjusted

TFP is higher by 1.15% between 1990 and 2001.

28The average work hours was taken from Monthly Labor Statistics by the Japanese Ministry of Health, Labor

and Welfare, and employment data is taken from the Employment Trend Survey. Note that the employment figure

is based on establishments with more than 5 employees, while the work hour figure is based on establishments

with more than 30 employees, due to the lack of series since 1975.

29In aggregating the cost share at the two-digit level with the JIP dataset, nominal gross output was used as a

weight because the dataset does not provide the total cost for each sector.

16
Figure 5: TFP (1990−2001) in the Iron and Steel Industry

.035

.036

.037

.038

.039

.040

.041

.042

.043

.044

90 91 92 93 94 95 96 97 98 99 00 01 02

TFP TFP (with subsidy adjustment)

Source: Annual Report on National Account for the output and capital

stock, Employment Trend Survey for annual employment, and Monthly Labor Statistics for average work hours. See the text for the estimated annual

number of subsidized workers.

The same exercise was done using the JIP database, in order to evaluate how much

this adjustment reduces the procyclicality of TFP. Note that since the subsidy bill by industry

is not available before 1990, the number of subsidized workers prior to 1990 is estimated by

applying iron and steel’s average annual share of 47% between 1990 and 2002 to the total

subsidy bill. While not shown here, the two measures of TFP are almost identical except

during the 1990s. The correlation between the log of TFP and the log real gross output falls

from 0.7916 to 0.7843 when the subsidy adjustment is made, and the correlation between the

log of TFP and the log real value added falls from 0.9921 to 0.9906. The correlation between

the log real gross output and the log subsidy bill is -0.645. The result is consistent with the

argument that labor hoarding via EAS increases the procyclicality of productivity, although

17
only a small part is accounted for by the subsidy.30

The exercise in this section reveals that the subsidy, due to the small fraction of subsidized workers, has a trivial impact on the level and procyclicality of TFP. The calibrated

model in the next section will attempt to match these moments to investigate the impact of the

subsidy program. I will show later that even when the direct impact is small, the EAS can

have a significant impact on output and employment volatility.

3 An Industry Model

In this section, I build a simple industry model to capture the effect of the employment

subsidy. Let nt denote the total number of employees in the firm and et ≤ ntthe number

of workers who are utilized for production at period t. The firm needs to pay a wage equal

to w to each of the et workers who actually work and produce, and a fraction γ of w to the

nt − et workers who are unutilized for production. Firms are eligible for the subsidy with

probability π. If eligible, they can receive payments for their nt −et unutilized workers. Let

s denote the fraction of the labor cost of unutilized workers that the government subsidizes.

That is, for each unutilized worker, the government pays a fraction s of the discounted wage

γw that unutilized workers receive, and the remaining (1− s)γw is paid by the firm. Hence,

the total subsidy received by a firm at time t when subsidized is given by (nt −et)γws.

31 Total

employment nt will be the state variable that firms carry to the next period, unless they decide

30In terms of growth rate, the correlation between the TFP growth rate and the growth rate of value added falls

from 0.9929 to 0.9879. The same exercise using National Accounts data shows that the correlation between the

log of TFP and the log real value added falls from 0.435 to 0.396, and the correlation between the log real value

added and the log subsidy bill is -0.244. Nonetheless, with this data, significance levels are low due to a small

number of observations.

31Note that the government provides a guideline on γ, but the consent of the workers is required (typically

through an agreement with their labor union) for them to miss work at a discounted wage γw.

18
to exit the market.

Firms have a stochastic production function f(et, εt), use labor as the only input of

production and receive a profitability shock, denoted as εt, that has an idiosyncratic component

as well as an aggregate component common to all firms. The production function is assumed

to be strictly concave in labor and satisfies fe > 0 and fee < 0. Moreover, the wage and price

are both assumed to be exogenously determined and invariant over time. For a given price

p, the expected profits for a firm that employs nt workers, utilizes et workers for production,

takes up the subsidy if available, and receives a shock εt at period t are as follows:

p f(et, εt)−wet −γw(nt −et) +χt(nt −et)γws− pc f −ψ(nt,nt−1)−φ(nt,nt−1). (2)

The first term is revenue from output. The second and third represent wage payments to

utilized and unutilized workers respectively. The fourth captures the subsidy receipts. Here,

χtis a random variable that takes a value of 1 with probability π and 0 with probability 1−π.

The term pc f reflects the fixed costs of production each period and can be interpreted as the

opportunity cost of the entrepreneur. This fixed cost provides firms incentives to exit the

market when their prospects look sufficiently unfavorable, instead of simply waiting for their

future prospects to turn around. As described in Hopenhayn and Rogerson (1993), this term

is necessary for some positive amount of exit to exist in equilibrium. In what follows, p will

be set as a numeraire so that it will not show for the rest of the analysis.

The terms ψ(nt,nt−1) and φ(nt,nt−1) represent linear hiring and firing costs respec19
tively, and are specified as:

ψ(nt,nt−1) = τh ·max(0,nt −nt−1) (3)

φ(nt,nt−1) = τ f·max(0,nt−1 −nt) (4)

where τh and τ f are the fixed costs of hiring and firing a worker. Either τh or τ f must be positive in order to provide firms incentives to take up the subsidy, since without labor adjustment

costs, labor adjustment is always instantaneous and there is no need to keep excess workers

when firms receive unfavorable shocks.

The timing of decisions is given as follows. An incumbent starts t with previous

period’s shock εt−1 and previous period’s employment nt−1. Before observing its current

profitability shock and subsidy eligibility, a firm must decide whether to shut down or stay in

business based on its expected profitability. If the firm decides to exit its business, the workers

will be dismissed entirely and the firm must pay the firing cost to each of its workers, while

avoiding the fixed cost of operation c f.

32 It then receives zero profits in all future periods.

If the firm decides to stay, the incumbent firm observes current profitability εt and subsidy

eligibility χt, and it decides whether to take up the subsidy or not if χt = 1. Subsequently, it

chooses employment nt and the number of utilized workers et, and produces with et < nt with

the subsidy or et ≤ nt without the subsidy, before moving to the next period with nt. Here, I

do not impose the constraint et = nt when firms are not subsidized, although this equality will

hold at an optimum for the set of parameter values provided in the next section.

The value function for firms under this policy scheme is given by the following equa32Alternatively, this sequence of timing implies that at the beginning of the period when the current state is

revealed to the firm, it decides whether or not it exits from the market at the end of the period.

20
tion:

V(nt−1, εt,χt) = max

et≤nt,nt

{ f(et, εt)−wet −γw(nt −et) +χt(nt −et)γws−c f

−ψ(nt,nt−1)−φ(nt,nt−1) +β{ max

stay, exit

[EV(nt, εt+1,χt+1),−φ(0,nt)]}},

(5)

where et = ntif the firm fully utilizes all its workers. The first order conditions of the value

function with respect to et and ntimply that the optimal level of etis driven by the current

shock εt and parameters such as s, w, and γ, while the optimal ntis affected by w, s, τh, τ f and

the expected marginal future benefit of the extra worker. This result implies that the decision

to take up the subsidy will depend not only on the size of the subsidy and labor adjustment

costs, but also on how unfavorable today’s shock looks relative to future prospects.

Two additional intuitive implications of the subsidy program are the following. The

first is that an increase in the volatility of aggregate and/or idiosyncratic shocks, as well as a

reduction in the persistence of shocks, increases subsidy take-up by reducing optimal utilization beneath the optimal level of employment when a firm receives a temporary unfavorable

shock.33 The second is that a subsidized firm keeps the level of employment higher, and output lower, in comparison with a non-eligible firm with the same previous level of employment

and current profitability conditions. An analytic explanation will be provided shortly.

For a given set of parameter values, the state variables nt−1, εt and χt affect firms’

decisions regarding employment, production and subsidy decisions. First, I will provide a

graphical explanation of the state spaces over nt−1 and εt for which subsidy take-up takes

place given eligibility. Then using the first order conditions, I will show the marginal change

33The results obtained from a numerical experiment is available upon request from the author.

21
that eligibility generates by comparing the behavior of eligible and non-eligible firms facing

the same state condition (i.e., nt−1 and εt), assuming that the eligible firm finds it optimal to

take up the subsidy.

Ignoring the constraint et ≤ nt, consider a case in which a firm receives a temporarily

favorable shock. Figure 6 illustrates the optimal employment and production decision rules

for this case. Regarding the optimal choice of nt, notice that it features a region of inaction

owing to the presence of labor adjustment costs. The dotted diagonal line represents the points

where nt = nt−1. The firm expands in employment size when nt−1 is such that the optimal

ntlays above the dotted line, and it contracts if ntlays below the dotted line. Where the two

lines overlap, the figure shows the region of inaction.

On the other hand, the optimal choice of etis independent of the state variable nt−1.

Since firms in this case are having a temporary favorable shock, the et dictated by the optimal

current production decision will be higher than nt driven by the future prospect of profitability.

As a consequence, we have an infeasible situation in which the unconstrained optimal etis

higher than nt, as illustrated by Figure 6. Obviously, no firm can take up the subsidy under

this scenario.

Note that smaller firms that are expanding are unlikely to take up the subsidy. This

intuition is given by the fact that labor hoarding is costly even when firms receive a subsidy.

Numerical exercises also show that, for the parameter values provided in the next section,

firms do not apply at an optimum when they are expanding. Thus, I simply assume here that

no subsidy take-up takes place when the state variable nt−1 is such that the optimal ntlays

above the dotted diagonal line.

Next, consider a case in which a firm experiences a temporarily unfavorable shock.

22
Figure 6: Employment and Production Decision Rule for an Unsubsidized Firm

0 5 10 15

0

5

10

15

Optimal n vs. Optimal e for an Unsubsidized Firm

nt, et

nt−1

nt

et

nt=nt−1

Note: Since etis constrained to be less than nt, this represents the circumstance in which the subsidy

take-up does not take place.

Figure 7 presents a situation in which etlays below nt for some region of nt−1. The optimal

subsidy coverage in this case is the difference between nt and et for nt < nt−1, which is presented by Figure 8. As we can see, the subsidy coverage increases with the state space nt−1

within the region of inaction, but stays constant above the region. The distance between the

optimal nt and et will increase as the current profitability shock either becomes more unfavorable relative to future prospects, or the current shock becomes highly transitory. The subsidy

take-up state spaces are further investigated in the appendix, in which the optimal nt and et are

plotted against both nt−1 and εt.

Now, I will illustrate two cases contrasting differences in the behavior of eligible and

non-eligible firms facing the same values for state variables. As mentioned previously, the

purpose of this comparison is to study the marginal change in firm behavior that subsidy eligibility induces. For that reason, I restrict attention to the portion of the state space of the

23
Figure 7: Employment and Production Decision Rule for a Subsidized Firm

0 5 10 15

0

5

10

15

Optimal n vs. Optimal e for a Subsidized Firm

nt, et

nt−1

nt

et

nt=nt−1

Note: Firms apply when the optimally chosen etis strictly below nt.

profitability shocks and the level of employment such that subsidy take-up is optimal contingent on eligibility.34 The behaviors of expanding firms are not discussed since they are

unlikely to take up the subsidy. Nor will I discuss the situation where the firm is optimally in

a region of inaction regarding employment. Furthermore, I will not focus on the reallocative

implications of the subsidy program for the sake of simplicity, and therefore exit decisions are

omitted from the analysis for now. Lastly, note that this exercise is not intended to compare

behavior with the subsidy program to behavior without the subsidy program. That comparison will be performed using simulations from numerical dynamic programming in the next

section.

The program requires that a firm not increase employment when receiving a subsidy,

34While subsidy take-up often takes place over the profitability and employment state space in which downsizing is a preferred option for the firms, this does not imply that all downsizing firms take up the subsidy. For

example, firms are less likely to apply, the more persistent the sequence of profitability shocks becomes.

24
Figure 8: Optimal Subsidy Coverage for a Subsidized Firm

0 5 10 15

0

5

10

15

nt−et

nt−1

Note: This graph shows the distance between nt and etin Figure 7 for nt

strictly greater than et.

but as previously mentioned, expanding firms are unlikely to take up subsidy at optimum.35

As a result, subsidized firms have nt−1 ≥ nt > et. Ignoring the region of inaction, the first

order conditions of equation 5 with respect to nt and et for downsizing firms are:

(1−s)γw = βEVn(nt, εt+1,χt+1) +τ f (6)

and

w−(1−s)γw = fe(et, εt), (7)

where EVn(nt, εt+1,χt+1) is the derivative of EV(nt, εt+1,χt+1) with respect to nt.

36

35This result may not hold if labor adjustment costs are nonlinear in the number of workers, thereby creating

a smoothing incentive for labor adjustment, or if adjustment costs are stochastic.

36Suppose we let λ1 and λ2 be the Lagrange multipliers of constraints nt−1 ≥ nt and nt > et

, respectively. By

complementary slackness, λ2 must be zero for firms receiving the subsidy. Similarly, λ1 must also be zero as we

are considering downsizing firms.

25
Equation 6 shows that the unsubsidized portion of the labor cost of keeping an extra

worker, given by the left side of the equation, must be equated with the marginal future benefit

of keeping the worker as well as the benefit from avoiding the firing cost today. This provides

the optimal condition for nt. Similarly, equation (7) shows that the cost of utilizing a worker,

given by the difference between the wage of a production worker and the cost a firm bears

to sustain a worker unutilized, must be equated with the marginal revenue product. This

characterizes the optimal condition for et.

Note that the concavity of EV implies that EVn is declining in nt.

37 Thus, holding

everything else constant, optimal nt will increase as s approaches one or as γ approaches zero.

In addition, decreases in γ and increases in s or in the probability of being eligible π increase

EV in the presence of labor adjustment costs. This result further increases the optimal nt. On

the other hand, the concavity of f implies that the optimal et will decrease with s and increase

with γ. As a result, a higher s or lower γ, by reducing the costs of unutilized workers, increases

the distance between the optimal nt and et, thereby resulting in higher subsidy coverage.38

Equation (6) also implies that, holding EV constant, a higher firing cost τ fincreases

nt. Nonetheless, this effect is muted since an increase in τ findirectly reduces optimal nt by

reducing EV. Hiring costs do not affect nt directly, as hiring costs already paid are sunk for

non-expanding firms. But hiring costs reduce the optimal ntindirectly by lowering EV. This

37Once exit decisions are included in the problem, EV is not always concave in nt

. EV is still concave over

the range of nt for which firms decide to stay in business.

38More formally, consider the case for a downsizing firm (i.e., λ1 = 0). The implicit differentiation of equation

(6) with respect to nt and s gives ∂nt/∂s = −[γw + β(∂EVn/∂s)]/βEVnn > 0 due to the concavity of EV and

∂EVn/∂s > 0, while the implicit differentiation of equation (7) with respect to et and s yields ∂et/∂s = γw/ fee < 0

due to the concavity of f . Similarly, the implicit differentiation of equation (6) with respect to nt and γ gives

∂nt/∂γ = [(1−s)w−β(∂EVn/∂γ)]/βEVnn < 0 due to the concavity of EV and ∂EVn/∂γ < 0, while the implicit

differentiation of equation (7) with respect to et and γ yields ∂et/∂γ = −(1−s)w/ fee > 0 due to the concavity of

f .

26
intuition is given by Hopenhayn and Rogerson (1993): while high firing costs may directly

prevent firing, equilibrium employment can still be smaller if high labor adjustment costs

substantially reduce profits.

Next, I will investigate the case in which the same downsizing firm is not eligible for

the subsidy to examine the marginal change generated by eligibility. As mentioned previously,

I still allow for the possibility of not utilizing some of their workers when firms are not eligible,

but firms are not required to underutilize their workers. As a result, we have nt−1 ≥ nt ≥ et.

The first order conditions for this case is given simply by setting s = 0 for equations (6) and

equation (7):

γw = βEVn(nt, εt+1,χt+1) +τ f (8)

and

w−γw = fe(et, εt). (9)

The intuitions here are similar to the previous ones.

Notice that the absence of s makes ntto fall and etto rise. Where these two intersect,

the constraint binds so that et does not exceed nt.

39 More specifically, nt given by equation (6)

(hereafter denoted by n

s

t

) is strictly higher than the nt given by equation (8) (denoted simply

by nt) due to the concavity of EV. In addition, et given by equation (7) (hereafter denoted

by e

s

t

) is strictly smaller than the et given by equation (9) (denoted simply by et) due to the

concavity of f . Consequently, for a given profitability shock εt, the following condition holds

39With the absence of s, we can see that the distance between nt and et shrinks faster as γ gets closer to

one. Therefore, higher γ reduces the likelihood of a firm idling some of its workers in the absence of a subsidy,

provided that τ fis low enough. Nevertheless, this is not to say that there is no labor hoarding without subsidy.

The change in the intensity of the labor inputs’ use is a common practice, but this feature is not modeled in this

paper for a simpler exposition of the effects of the policy.

27
for a downsizing firm that applies for a subsidy when eligible40:

n

s

t > nt ≥ et > e

s

t

. (10)

That is, an eligible firm keeps the level of employment higher, and output lower, in comparison

with a non-eligible firm.

Finally, combining equation (6) and equation (7) (or equation (8) and equation (9)),

we obtain the following:

w−τ f = βEVn(nt, εt+1,χt+1) + fe(et, εt). (11)

This result implies that when firms are downsizing, they set the expected marginal future

benefit of an employed worker, combined with the marginal revenue product of a utilized

worker, equal to the difference between the wage and firing cost. The firing cost is subtracted

from wage as it represents the benefit from avoiding a payment that would otherwise be due

to the marginal fired worker.41

Next, using the first order conditions given above, we can examine each of the components which affects subsidy take-up. LetV

s

(nt−1, εt| χt = 1) denote the value function satisfy40Keep in mind that the condition given by equation (10) characterizes the employment and production behavior of subsidized and unsubsidized firms under the same subsidy program with the same s and π. If we wish to

compare the behavior of a firm under the regime without the subsidy program (s = 0, π = 0) and a firm under the

regime with the subsidy program (s > 0, π > 0), we also need to take into account the effect of subsidy on EV.

EV will be higher under the subsidy regime, so that the associated optimal nt will rise even further compared to

the optimal nt under the regime without subsidy.

41On the other hand, the first order condition for an expanding firm is:

w+τh = βEVn(nt, εt+1,χt+1) + fe(nt, εt+1). (12)

In this case, hiring costs show up as a cost of having an extra worker. Moreover, nt = et holds at an optimum for

expanding firms.

28
ing first order conditions given by equations (6) and (7) (i.e., n

s

t

and e

s

t

) and V(nt−1, εt| χt = 0)

denote the value function with the first order conditions given by equations (8) and (9) (i.e., nt

and et.) Firms are better off with the subsidy when V

s

(nt−1, εt|χt = 1) > V(nt−1, εt|χt = 0).

That is, the following condition must hold for a subsidy take-up to take place:

(n

s

t −e

s

t

)sγw

total subsidy receipt

+ τ f(n

s

t −nt)

savings on firing costs

+{β[EV(n

s

t

, εt+1,χt+1)−EV(nt, εt+1,χt+1)]}

change in future value

+ (1−γ)w(et −e

s

t

)

reduced wage payments

> { f(et, εt)− f(e

s

t

, εt)}

reduction in revenue

+ γw(n

s

t −nt)

increased employment costs

.

(13)

The first term on the left represents the total subsidy received by the firm, the second

term shows savings on firing costs with the subsidy, while the third term captures the change

in the expected marginal future benefit arising from the different choices of nt, and the fourth

term represents the savings on labor costs arising from increasing the number of unutilized

workers (i.e., firms pay γw instead of w so that the reduction in payment is w−γw or (1−γ)w

for each unutilized worker). In contrast, the first term on the right represents the reduction in

revenue associated with reduced production and the second term represents the increase in the

cost to the firm for sustaining excess workers through the subsidy program. Notice that with

the subsidy, firms benefit from the reduced wage payments at the production worker margin,

while firms lose from higher labor costs at the employment margin.

Obviously, the first and the second terms on the left and the last term on the right are

positive when a firm applies for the subsidy, according to equation (10). Comparing “savings

on firing costs” and “increased employment costs,” the benefit of applying rises relative to the

cost as the size of the firing cost, τ f, increases relative to the cost of sustaining a worker, γw,

and vice versa. Here, I call this a direct effect of τ f. The relative sizes of τ f and γw also

29
indirectly affects the benefit of the subsidy through the third term on the left. Equation (6) and

equation (8) show that if (1−s)γw > τ f, then EVn > 0 for both equations, and in particular,

EV(n

s

t

, εt+1,χt+1) > EV(nt, εt+1,χt+1). On the contrary, if γw < τ f, then EVn < 0 for both

equations and EV(n

s

t

, εt+1,χt+1) < EV(nt, εt+1,χt+1).

42 That is, when firing costs are very

high, the optimal level of ntis already so high that increasing ntthrough the subsidy reduces

the expected future value. In the later exercise, we will see that higher firing costs in general

increase subsidy take-up even when γw < τ f, suggesting that the direct effect dominates.43

I now investigate the exit decisions of firms. Firms will decide to exit from the market when the expected loss of staying in the market is greater than the cost of firing its entire

workforce (i.e., EV(nt, εt+1,χt+1) is smaller than −φ(0,nt)). Since EV(nt, εt+1,χt+1) considered here is concave and −φ(0,nt) is linearly declining in nt

, the threshold level of the exit

decision will be given by the intersection of EV(nt, εt+1,χt+1) and −φ(0,nt) when they are

plotted against nt while holding everything else constant. That is, the intersection gives the

upper bound of nt below which firms decide to exit for a given εt. EV and firing costs are

plotted against ntin Figure 9. Here, EV(2) corresponds to a higher level of profitability shock

compared to EV(1). As the figure shows, no firms with a profitability shock corresponding to

EV(2) will exit from the market, while some small firms with a profitability shock corresponding to EV(1) will exit. The subsidy shifts EV up slightly for all nt−1, thereby reducing the

upper bound of nt−1 for exiting. This result, combined with the higher employment induced

by the subsidy program, reduces the equilibrium amount of exit at the steady-state.

The strategy used in order to solve the numerical dynamic optimization problem is

42Furthermore, the slope of EV given by equation (6) is negative and the slope given by equation (8) is positive

if γw > τ f > (1−s)γw. In this case EV(n

s

t

, εt+1,χt+1)−EV(nt, εt+1,χt+1) can be either positive or negative.

43The size of hiring costs τh, on the other hand, only has an indirect effect through the third term on the left by

affecting EV.

30
Figure 9: The Threshold Level of Exit Decision, EV vs. Firing Costs

0 5 10 15

−12

−10

−8

−6

−4

−2

0

2

4

EV and Firing Costs

n

EV (1)

EV (2)

− firing costs

Note: Firms decide to exit from the market when the expected loss of staying in the

market is greater than the cost of firing its entire workforce. EV(2) corresponds to a

higher level of profitability shock compared to EV(1).

provided in the appendix. Using the solutions to problem given by equation (5), we obtain

a stationary distribution over the employment and profitability shock pairs for a given level

of entry M. This stationary distribution, in turn, will provide us the rates of entry, exit, job

reallocation, average employment, average output and average productivity in a stationary

equilibrium. Furthermore, a mass of size M new entrants are added each period in obtaining

a stationary distribution through contraction mapping. Following Hopenhayn and Rogerson

(1993), the starting level of profitability shock (or put differently, initial luck of the draw) for

an entrant is taken from the uniform distribution, and all entrants start at zero employment.

The boundaries of this uniform distribution are set by the condition of the discretization of the

AR(1) idiosyncratic profitability shock process explained in the following section.44 After

44As explained in the next section, the upper bound and the lower bound are set at three standard deviations

away from the mean, and the state space of idiosyncratic profitability shock is discretized into forty states.

The use of an uniform distribution was preferred over that of a stationary or normal distribution, since these

31
the initial profitability shock, entrants evolve just as incumbents. Furthermore, entering firms

are assumed not to receive a subsidy with their first production, and they must produce at least

once before exiting from the market.

Denoting λt as a vector which describes the distribution over the entire set of employment levels and profitability shocks at period t, and T(λt

,M) as the transition matrix that maps

the state at time t to the next state period given firms’ decision rules, the state transition equation is given by λt+1 = T(λt

,M). Accordingly, the time stationary distribution is described as

a vector bλ such that bλ = T(

bλ,M). This distribution provides us with steady-state average employment in the economy. Moreover, the stationary distribution over production-profitability

shock pair can be constructed from bλ, by moving the corresponding fraction of subsidized

firms to the optimally chosen level of production given by the first order condition of e, obtained from equation (7) for each level of shock. This distribution, in turn, provides us with

the steady-state level of average production in the economy.

Because the growth rate of the industry is held constant in equilibrium, the number

of firms that exit the market must be offset by the number of firms that enter the market M.

Thus, the analysis is one in which there is no net entry, as exit and entry rates are identical in

the steady-state. This simplification also follows Hopenhayn and Rogerson (1993). Since

total employment is held constant in equilibrium, the number of jobs destroyed by incumbents

and exiting firms have to be matched by the amount of jobs created by the incumbents and

entering firms.

Finally, the operator T is homogeneous of degree one in bλ and M. Consequently, the

distributions would reduce the steady-state rate of exit (and hence entry) by reducing the number of firms that

start off poorly.

32
rate of entry (and therefore the rate of exit) remains constant regardless of the size of M, as

doubling M also doubles the total number of firms in a stationary equilibrium. Likewise,

choosing a particular level of M corresponds to choosing a particular measure of firms and

the total amount of employment in a stationary equilibrium, while statistics such as average

employment, average output and productivity and the rates of job creation and destruction are

unaffected by the choice of M. Even though a positive subsidy can potentially affect the total

number of firms through M by raising the expected value of starting a business, M has not yet

been endogenized in this model. In the following section, the equilibrium amount of entry M

is simply set so that the total number of firms in equilibrium are the same for the subsidy case

with s > 0 and the benchmark case with s = 0.

4 Results

4.1 Basic Setup and Calibration

To find an equilibrium via numerical dynamic programming, I begin by specifying the

production function as:

f(et, εt) = εt· e

θ

t where 0 < θ < 1. (14)

The path for the profitability shocks εtis given as follows:

εt = αt +ut, (15)

33
and

αt =







αg with prob. δ if αt−1 = αg

αb with prob. 1−δ if αt−1 = αg

αg with prob. 1−δ if αt−1 = αb

αb with prob. δ if αt−1 = αb







where αg > αb > 0 (16)

and

ut = ρut−1 +vt where 0 < ρ < 1 and vt ∼ i.i.d. with E[vt] = 0. (17)

Here, αt represents the aggregate state. It follows a two-state Markov process with symmetric

transition probability δ. Whereas actual business cycles arguably display asymmetric transition probabilities with the good state being longer than the bad state, a symmetric probability

was used to reflect the longer than usual downturn experienced by the Japanese economy during the 1990s.45 Meanwhile, ut captures the idiosyncratic profitability shock, which follows

an AR(1) process. The parameter ρ is the persistence of idiosyncratic shocks that firms receive each period, and vt

is a Gaussian white noise process with the standard deviation σv.

For a given level of persistence ρ and the standard deviation σv, a corresponding forty-state

Markov transition matrix and state vector for idiosyncratic shocks were created to approximate the AR(1) process for each level of α. Further, for each aggregate state, the upper and

lower bounds of the shock are set at three standard deviations of ut away from αg and αb.

Note that forty idiosyncratic states combined with two aggregate states yields a total of eighty

profitability states.

The profitability shocks can be interpreted as technology shocks or as demand shocks

45The asymmetric transition probability reduces the steady-state fraction of subsidized workers and makes it

more difficult to match with the description of the data during the 1990s.

34
since εt will be multiplied by the price level p which is normalized to one. Here, I do not

consider the distinction between supply and demand shocks, and simply regard εt as profitability shocks. Furthermore, note that the steady-state statistics in section (4.2), computed

analytically by the stationary distributions, refer to the average figures of both aggregate states.

Alternatively, the steady-state statistics for a good aggregate state and a bad state can be computed separately. Nonetheless, the average statistics were used in order to measure the longrun impact of the subsidy. The second moment properties of the subsidy in terms of the

volatility of employment, productivity and output (i.e., fluctuation around the long-run mean)

are examined via simulation in section (4.3), instead of using an analytical computation.

Table 2: Parameter Values used to obtain Stationary Distributions

w = 1 wage

τh = 0.8 hiring costs

τ f = 0.8 firing costs

cf = 2 fixed cost of operation

r = 0.04 interest rate

β = (1/(1+r)) = 0.96 discount rate

γ = 0.8 fraction of wage paid to unutilized workers

π = 0.5 prob. of being eligible for the subsidy

s = 2/3 subsidy coverage

θ = 0.55 labor share of total cost

ρ = 0.75 persistence of idiosyncratic shocks

σv = 0.5 standard deviation of vt

αg = 3.13 mean profitability of good state

αb = 2.27 mean profitability of bad state

δ = 0.6 aggregate state transition probability

Key parameters used to solve the model are summarized in Table 2. Since subsidy

data is only available annually, the time interval is set to one year. Moreover, the focus of the

exercise will be the 1990s, during which the subsidy bill increased and data by two-digit sector

is available. The wage is normalized to one, and both hiring and firing costs are set equal to

35
80% of the annual wage.46 Later, we will examine the impact of higher adjustment costs by

setting both hiring and firing costs equal to the annual wage. The fixed cost of operation (or

entrepreneur’s opportunity cost) is set to twice the wage. The annual interest rate is set equal

to 4%. This figure corresponds to the government financial institutions’ key lending rate to

small- and medium- size enterprizes averaged in the 1990s.47

The EAS provides a guideline on the fraction of wages that firms should pay to subsidized workers, and it does not require that subsidized workers be paid the full amount. Accordingly, payment to unutilized workers is set equal to 80% of the wage. This number was

estimated by combining three figures: the annual salary of manufacturing workers, taken from

the Basic Survey on Wage Structure; the average work days of the manufacturing sector, provided by the Monthly Labor Statistics; and the average subsidy cost per worker per day as

described in section (2.2).

48 The estimated subsidy cost per person per day is about 42% of

the average basic wage between 1985 and 2001. This result implies that if s = 1/2, γ = 0.94

(or γ = 0.84 if instead of the basic wage, the actual wage which includes overtime is used)

and if s = 2/3, γ = 0.71 (or γ = 0.63 if the actual wage is used).49 The parameter value is set

around the midpoint at γ = 0.8.

The probability of being eligible for the subsidy program each year is set equal to 50%.

This seems reasonable given the high concentration of subsidies in the iron and steel industry

46Although the price is also normalized to one in the model, it is allowed to fluctuate relative to the wage as it

is multiplied by a profitability shock.

47The interest rate data used in this paper is made available at the Bank of Japan’s website in Japanese:

http://www.boj.or.jp/stat/dlong f.htm.

48Both the Basic Survey on Wage Structure and the Monthly Labor Statistics are published by the Ministry of

Labor (current Ministry of Health, Labor and Welfare). The data used in the paper is posted on the website of

the Japan Institute of Labor Policy and Training in Japanese: http://stat.jil.go.jp.

49Since the estimated subsidy cost per work day is not available by two-digit sectors, these estimates are for

the entire manufacturing sector.

36
during the 1990s.50 The subsidy coverage is set equal to 2/3 of the wage paid to unutilized

workers. The parameter θ, which equals the labor’s share of total cost, is set to 0.55; this

figure corresponds to the average cost share of labor (excluding intermediate inputs) between

1973 and 1998 given by the JIP database.

The persistence of the shock is set equal to 0.75, and the standard deviation of vtis

set equal to 0.5.51 The mean profitability shock in the bad state (αb) is set at 2.27, so that

the lowest shock in a bad state takes a positive value, and the distance between αg and αb is

set slightly above one standard deviation of idiosyncratic shocks.52 Here, αg is set at 3.13.

The probability that the aggregate state persists (δ) is equal to 0.6. These parameter values

are assigned to generate realistic statistical properties of key variables such as the fraction of

subsidized workers, job creation and destruction rates, and entry and exit rates. Employment

was discretized in 301 grid points ranging from zero to fifteen; the upper bound was set to

guarantee that it exceeds equilibrium employment with the highest value of the profitability

shock.

Average productivity is defined as total output divided by total employment. More

specifically, let N and S denote the number of employment grid points and the total number of

profitability states, respectively. Now, using bλ(ni, ε j) and bλ(ei, ε j) to represent the proportion

of firms over each (ni, ε j) and (ei, ε j) pairs in a stationary equilibrium, the average productivity

50Unfortunately, information on the fraction of firms covered by the subsidy is not currently available.

51These two combined implies that the standard deviation of the idiosyncratic shock is about 0.756 since

σu =

p

σ2

v/(1−ρ

2).

52This specification implies that idiosyncratic shocks play a larger role in controlling firm’s fortune than aggregate shocks do. Also, note that the lowest value of εt

is 0.002 when we set αb = 2.27.

37
is defined as:

Average productivity =

Total Output

Total Employment

=

N

∑

i=1

S

∑

j=1

Ã

ei·

bλ(ei

, ε j)

∑

N

i=1 ∑

S

j=1

ni·

bλ(ni

, ε j)

!μ

f(ei, ε j)

ei

¶

. (18)

The term in the first bracket shows the relative share of utilized workers in each (ei,ε j) pair

of the stationary distribution, and the second term reflects output per utilized worker. Notice

that this definition includes subsidized workers, who produce zero output, in calculating the

productivity.

I also present a productivity measure adjusted for hiring and firing costs and the subsidy cost per worker. This measure controls for the gain associated with having to spend less

resources in hiring and firing with the subsidy, as well as the associated loss in the form of a

higher government deficit and/or higher tax. The calculation is done simply by subtracting

the hiring and firing costs per worker as well as the cost of the subsidy per worker from average productivity as defined by equation (18). Yet, this should not be interpreted as a welfare

measure, as I have not modeled the utility benefit of the subsidy for workers nor the gains

associated with sustaining better job-worker matches for experienced workers.

Average productivity is alternatively defined as total output divided by the total number

of utilized workers:

Average productivity

(based on utilized workers)

=

Total Output

Total Number of Utilized Workers

=

N

∑

i=1

S

∑

j=1

Ã

ei·

bλ(ei

, ε j)

∑

N

i=1 ∑

S

j=1

ei·

bλ(ei

, ε j)

!μ

f(ei, ε j)

ei

¶

. (19)

38
Obviously, this definition excludes unutilized workers. Hence, comparing equation (18) and

equation (19) for the same level of subsidy coverage s captures the direct effect of hoarding

on average productivity. More specifically, the ratio of productivity based on employment to

productivity based on utilized workers (both when s = 2/3) shows a reduction in productivity

as a direct result of labor hoarding (i.e., the ratio of productivity calculated using equation

(18) to that given by equation (19)). Since this figure is equivalent to the ratio of the total

number of utilized workers to total employment, one minus this ratio matches the fraction of

subsidized workers.

Finally, the steady-state rate of job turnover is the ratio of the total number of jobs

destroyed by incumbents and exiting firms to total employment at the steady-state. Since

total employment stays constant in a stationary equilibrium, this figure obviously equals the

steady-state rate of job creation, which is the ratio of the jobs created by both incumbents and

entrants to total employment at the steady-state. These measures allow us to evaluate the

magnitude of total job reallocation occurring in the economy.

4.2 Stationary Distribution

This section examines the properties of stationary distribution. In order to examine

the effects of subsidies on productivity, the benchmark model sets s = 0 while the subsidy case

sets s = 2/3. First, I investigate a case without volatility in aggregate shocks. The value of α

in this exercise is set equal to 2.7. Then I will add volatility in α, while preserving the mean, as

specified in the previous section. Finally, I will increase the hiring and firing costs from 80%

of the wage to 100% to investigate the impact of this change. As mentioned previously, the

39
profitability shocks are parameterized to generate realistic values for the fraction of subsidized

workers, the rates of entry and exit, and the rates of job creation and destruction.

Despite the fact that studies on annual rates of entry, exit, job creation, and destruction

in Japan are not extensive, due to a lack of data comparable to the LRD for American manufacturing establishments, Motonishi and Tachibanaki (1999) attempt to estimate these figures

by using the establishment level data for 1988, 1990 and 1993 from Census of Manufacturers

compiled by the Japanese Ministry of Economy, Trade and Industry. The rate of entry (exit)

on an annualized basis is 8.74% (7.91%) for the iron and steel industry for 1988−1990, and

5.68% (8.15%) for 1990−1993.53 Motonishi and Tachibanaki also provide the rate of job

creation and destruction (adjusted on an annualized basis) during these periods.54 The rate of

job creation (destruction) on an annualized basis provided by this study is 4.55% (4.81%) for

the iron and steel industry for 1988−1990, and 2.91% (4.83%) for 1990−1993.

In this exercise, the number of entrants M is set so that the total number of firms is equal

to one in both cases. As mentioned before, increasing M increases the total number of firms,

and hence total employment and output proportionally, but average size as well as average

firm output remains the same. Here, I assume that the impact of the subsidy on M is trivial.

Moreover, the values for the average size of firms (or total employment), average output by

firm (or total output) and average productivity obtained for the subsidy case are normalized

53While this data includes all manufacturing establishments with more than 4 employees, it does not include

firms that have entered and exited between census years. As a result, the figures on entry and exit rates presented

in this study (which are adjusted on an annualized basis) may underestimate the true magnitude of entry and exit.

54Again, the annual rates of job flows may be underestimated since firms that enter and exit between the

census years are not included. Furthermore, employment volatility during the census years could potentially

generate smaller figures for both job creation and destruction rates when calculated on an annualized basis than

the actual annual job creation and destruction rates (i.e., if a firm hires 100 new employees in 1990 and fires 100

in 1993, this firm’s employment stays constant over the 1990 and 1993 census). GDP growth rates fluctuate

slightly between 1988−1990, but follow a steady decline for 1990−1993, so that the underestimation arising

from employment volatility is potentially less for the latter interval.

40
by the corresponding benchmark values to facilitate comparison, and for this reason these

benchmark values are set equal to one.

Table 3: Summary Statistics of Stationary Distributions without Aggregate Volatility

α = 2.7 s = 0 s = 2/3

Fraction of workers covered by the subsidy 0.0000 0.0036

Exit rate 0.0496 0.0486

Job turnover rate 0.0383 0.0378

Total number of firms 1.0000 1.0000

Average firm level employment 1.0000 1.0014

Average firm level output 1.0000 0.9985

Average productivity based on employment 1.0000 0.9971

— adjusted for hiring and firing costs 1.0000 0.9974

— adjusted for hiring, firing and subsidy costs 1.0000 0.9961

Average productivity based on utilized workers 1.0000 1.0007

The key statistics given by the stationary distributions without aggregate volatility are

summarized in Table 3. Overall the changes are small. The fraction of subsidized workers

generated by the stationary distribution is 0.36%. The exit rate drops from 4.96% to 4.86%

with the subsidy, while the job turnover rate falls from 3.83% to 3.78%. Average firm size is

0.14% higher and average firm level output is 0.15% lower. The reduction in output in spite

of higher employment is caused by the presence of unutilized workers.

Average productivity falls by about 0.29% with the subsidy program. When average

productivity is calculated based on utilized workers, it increases slightly by 0.07%. This

gain is generated by the increased flexibility of production decisions via the subsidy program:

under the benchmark case without subsidy, firms hold some excess workers who are used for

production due to the presence of labor adjustment costs. Whereas firms hold even more

excess workers with the subsidy program, these workers are not used for production, thereby

41
increasing productivity when calculated only in terms of utilized workers.

Here, the drop in productivity due to labor hoarding, which corresponds to the size of

subsidized workers, is 0.36%. In addition, when average productivity is adjusted for labor

adjustment costs, the negative impact of the subsidy on productivity shrinks, reflecting the

fact that the subsidy helps firms avoid labor adjustment costs. In spite of this gain, when

we further control for the cost of the subsidy, average productivity falls slightly further in

comparison with the benchmark value, indicating that the cost of the subsidy is higher than

savings on labor adjustment costs.

Now we add aggregate volatility without changing the mean α, while keeping hiring

and firing costs at 0.8. The results are presented in Table 4. The fraction of subsidized

workers generated by the stationary distribution now increases to 1.28%. As expected, this

result implies that volatility increases subsidy take-up. Since the estimated annual average

fraction of subsidized workers in the iron and steel industry is 2.1%, the model does not

exaggerate the extent of subsidy coverage. The model’s exit rate is 4.89% when the subsidy

is set equal to zero, and it drops to 4.73% when the subsidy is set equal to two-thirds of

payments to unutilized workers. The job turnover rate falls from 4.05% to 3.91% when the

subsidy program is in place. Compared with the “no aggregate volatility” case, the drop in

both the exit rate and the job turnover rate is slightly bigger with volatility. This result may

be due to the fact that the subsidy’s benefit increases with higher aggregate volatility, thereby

raising EV.

Similar to the “no aggregate volatility” case, average firm level employment goes up

with the subsidy while average firm level output drops. Again, higher average employment

does not lead to higher average output at the firm level, due to the presence of subsidized

42
Table 4: Summary Statistics of Stationary Distributions with Aggregate Volatility

Low adj. costs High adj. costs

αg = 3.13, αb = 2.27 τh = 1 = τf = 0.8 τh = 1 = τf = 1

s = 0 s = 2/3 s = 0 s = 2/3

Fraction of workers covered by the subsidy 0.0000 0.0128 0.0000 0.0157

Exit rate 0.0489 0.0473 0.0508 0.0484

Job turnover rate 0.0405 0.0391 0.0369 0.0343

Total number of firms 1.0000 1.0000 1.0000 1.0000

Average firm level employment 1.0000 1.0096 1.0000 1.0187

Average firm level output 1.0000 0.9982 1.0000 1.0015

Average productivity based on employment 1.0000 0.9887 1.0000 0.9831

— adjusted for hiring and firing costs 1.0000 0.9895 1.0000 0.9851

— adjusted for hiring, firing and subsidy costs 1.0000 0.9850 1.0000 0.9796

Average productivity based on utilized workers 1.0000 1.0016 1.0000 0.9988

workers. Average productivity based on employment, given by equation (18), falls about

1.13% with the subsidy. As before, average productivity based on utilized workers goes

up by 0.16% due to the flexibility of production decisions with the subsidy. The sum of

these two measures approximately corresponds to the drop in productivity as a direct result of

labor hoarding. As before, average productivity falls even further after controlling for labor

adjustment and subsidy costs.

The drop in productivity due to labor hoarding generated by this model is quite successful in approximating the impact of labor hoarding in the data as described in section (2.2).

Namely, the adjusted TFP (i.e., average productivity based on utilized workers) is higher than

unadjusted TFP (average productivity based on employment) by about 1.2% in the data between 1990 and 2001. Nonetheless, in the growth accounting exercise, the drop in TFP is

smaller than the fraction of subsidized workers, as only the labor share of total cost applies to

43
Figure 10: Cumulative Distribution Functions of Three Stationary Distributions

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

n (s = 0)

n (s = 2/3)

e (s = 2/3)

nt

Note: The solid line shows the cdf of firm level employment when the subsidy is set equal to zero.

The dashed line shows the cdf of employment when the subsidy is set equal to 2/3 of wage. The

dotted line shows the stationary distribution in terms of utilized workers when subsidy is set equal

to 2/3 of wage.

the overall reduction in productivity.55

Figure 10 provides cumulative distribution functions of three stationary distributions:

a stationary distribution over employment for all levels of idiosyncratic and aggregate shocks

when s = 0; a stationary distribution over employment for all levels of idiosyncratic and aggregate shocks when s = 2/3; and finally a stationary distribution over utilized workers for

all levels of idiosyncratic and aggregate shocks when s = 2/3. Note that the distributions are

bumpy since the state spaces (employment and profitability) are discontinuous. The figure

confirms that the average firm level employment is higher when the subsidy program is in

place, while we cannot tell whether or not the average firm level production is larger with the

55Although the iron and steel sector has gone through a process of substitution from labor towards capital over

the last couple of decades, the intensity of capital usage and labor are likely to be complementary over a much

shorter horizon (i.e., a year or less). The short-run complementarity assures that the correlation between capital

usage and labor is high at the high frequency, and hence introducing capital into the model should not undermine

the main results.

44
subsidy program.56

The final case investigates the impact of higher adjustment costs. Here, hiring and

firing costs are set equivalent to the annual wage. The results are also provided by Table

4. The fraction of subsidized workers rises further to 1.57%. The rate of reallocation in

terms of exit and job turnover falls again with the subsidy: the exit rate drops from 5.08% to

4.84%, while the job turnover rate falls from 3.69% to 3.43%. A comparison with the “low

adjustment costs” case reveals that the exit rate rises while the job turnover rate drops with

the increase in adjustment costs. Note that high labor adjustment costs have two competing

effects on exit behavior: while high firing costs increase the cost of exiting and therefore

prevent exit, high labor adjustment costs (both hiring and firing) reduce the expected value and

encourage exit. In our example, the exit rate rises with higher adjustment costs, indicating

that the “encouragement” effect of high firing costs outweighs the “prevention” effect of high

firing costs. Nonetheless, higher adjustment costs still seem to reduce the job turnover rate.

Furthermore, the impact on the average size of firms is greater with higher adjustment costs,

as average employment rises by 1.87% compared to the benchmark.

Average productivity based on employment falls by 1.7%, while unlike the first two

cases, average productivity based on utilized workers falls by 0.12%. The drop in the second

productivity measure implies that the distortion that the subsidy generates in the reallocation

measures is greater with the “higher adjustment costs,” and this offsets the productivity gain

generated by the flexible production adjustment provided by the subsidy. When productivity

is adjusted for hiring/firing costs, the drop in productivity is not as severe, as a result of the

56The ambiguity is observed since the cdf for e(s = 2/3) and the cdf for n(s = 0) intersect (around the employment level equals to 2.3).

45
gains accrued from smaller adjustment costs. Despite this gain, productivity falls again below

the baseline employment productivity, by 2.04%, when it is adjusted for both labor adjustment

and subsidy costs.

Even though the direct effect of the subsidy on productivity observed in this section

are small in all three cases, the indirect effect of the subsidy over the business cycle can be

substantially larger. I will examine these results in the next section.

4.3 Simulation Results

In the previous section, we saw that the direct effect of the subsidy on steady-state

productivity is more or less proportional to the number of subsidized workers. However,

the simulation exercises reveal that even when the productivity effect is small, the effects

of the subsidy on output and employment dynamics over business cycles are quite striking.

Accordingly, in this section, cyclical implications of the subsidy program are highlighted via

simulation.

For each simulation, a sequence of profitability shocks is generated for 150 periods

from the Markov-process described above for 5000 firms. The idiosyncratic component of the

profitability shock varies across firms, while the aggregate component is shared by all firms.

Furthermore, using the steady-state condition, I replace an exiting firm with an entering firm

so that the total number of firms remains constant.57 When a new firm enters, a new sequence

of the idiosyncratic component of profitability shocks is drawn from the distribution, and the

57Though exits would likely exceed entries during downturns, this simulation abstracts from the variations in

net entries over the business cycle. As long as the effect of the subsidy program on the variations in net entries is

small, normalization with the benchmark case insures that this simplification does not pose a significant problem

in assessing the policy impact. If the subsidy reduces the variation in net entries, both employment and output

should be less volatile than suggested by the results here. In this case, the employment volatility results will be

enhanced, while the output volatility results will be mitigated.

46
firm starts with zero employment.

Table 5: Summary Statistics given by Simulation Exercises with Low Adjustment Costs

τh = 0.8, τ f = 0.8 s = 0 s = 2/3 Ratio

Correlations between

— total output and average productivity (n) 0.9870 0.9895 1.0025

(0.0007) (0.0006)

— total output and average productivity (e) 0.9891

(0.0006)

Standard deviations of

— total output 0.1670 0.1717 1.0284

(0.0006) (0.0006)

— total employment 0.0424 0.0399 0.9409

(0.0007) (0.0007)

— average productivity 0.1320 0.1387 1.0512

(0.0003) (0.0003)

— job creation rate 0.0205 0.0198 0.9680

(0.0003) (0.0002)

— job destruction rate 0.0200 0.0186 0.9304

(0.0002) (0.0002)

In addition to profitability shocks, a sequence of eligibility is also generated for all

firms based on the unconditional probability π. After generating employment, output, entry

and exit behavior for 5000 firms for 150 periods, the first 50 periods are deleted in order to

eliminate the effects of the initial distribution. This entire exercise, in turn, was repeated 100

times to obtain the mean and the standard deviation of each statistic. Note that given the

procedure described above, ‘total output’ and ‘total employment’ in this exercise refer to the

total sample of 5000 firms.

First, I examine the “low adjustment costs” case that sets both hiring and firing costs

to 80% of the annual wage. Then, I investigate the “high adjustment costs” case where

both hiring and firing costs are increased to 100% of the annual wage to investigate its impact.

Table 5 reports statistics obtained from simulating the “low adjustment costs” case. It provides

47
statistics for s = 0 and s = 2/3, as well as their ratio, with the benchmark figure set as a

denominator. Standard deviations of each statistics are reported in parentheses. Note that

output, employment and productivity are now measured in natural logarithms. As the ‘ratio’

column shows, the correlation between total output and average productivity rises by 0.25%

with the subsidy indicating that the procyclicality of productivity is stronger with the subsidy

program. However, the predicted increase is very small.

The JIP database presented in section (2.2) showed that the correlation between TFP

and real gross output falls from 0.7916 to 0.7843 when the subsidy adjustment is made, and

the correlation between TFP and real value added falls from 0.9921 to 0.9906. In this theoretical exercise, the correlation between total output and average productivity falls slightly,

from 0.9895 to 0.9891, when subsidized workers are taken into account in calculating average

productivity (i.e., when I use equation (19) instead of (18)).

Perhaps the most significant finding of this exercise is that the standard deviation of

output increases on average by 2.84% when s = 2/3 compared to when s = 0. This is a

substantial increase in volatility given that the fraction of subsidized workers is only 1.3% of

total employment at the steady-state. Intuitively, this results from a symmetric increase in

output sensitivity to aggregate shocks: when the bad aggregate shock hits the economy, total

output is lower than otherwise as the subsidy allows for a reduction in output while sustaining

employment. When the good aggregate shock hits the economy, total output is higher with

the subsidy program as firms spend less on hiring. Since the subsidy program keeps average

employment higher, firms can more readily raise production in times of favorable shocks.

The higher responses of output to both good and bad shocks generate more volatility over the

business cycle.

48
Table 6: Summary Statistics given by Simulation Exercises with High Adjustment Costs

τh = 1, τf = 1 s = 0 s = 2/3 Ratio

Correlations between

— total output and average productivity (n) 0.9896 0.9927 1.0032

(0.0007) (0.0007)

— total output and average productivity (e) 0.9921

(0.0007)

Standard deviations of

— total output 0.1630 0.1687 1.0348

(0.0007) (0.0007)

— total employment 0.0373 0.0327 0.8759

(0.0008) (0.0009)

— average productivity 0.1322 0.1418 1.0722

(0.0003) (0.0004)

— job creation rate 0.0177 0.0159 0.9008

(0.0002) (0.0003)

— job destruction rate 0.0182 0.0149 0.8225

(0.0002) (0.0002)

On the contrary, the volatility of employment falls by about 6% with the subsidy program in place. This reduced volatility matches the objective of the government to reduce

undesired fluctuation in employment due to business cycles. The reduction comes from reduced job destruction during unfavorable aggregate conditions as well as stunted job creation

during favorable times. The standard deviation of job creation falls by about 3.2% with the

subsidy, whereas the standard deviation of job destruction falls by about 7%. Finally, the

standard deviation of average productivity rises by 5.12%.58

Table 6 highlights the results of the “high adjustment costs” case. The fraction of

58Since labor productivity is now expressed in logs (i.e., ln(Y/N)), the following formula applies:

var(ln(Y/N)) = var(lnY) +var(lnN)−2cov(lnY,lnN). (20)

Note that since the variance of output is much larger than the variance of employment, the increase in the variance

of output results in the higher variance of productivity, even with the reduction in the variance of employment.

Furthermore, the covariance between output and employment falls with the subsidy as expected, thereby further

increasing the variance of productivity under the subsidy case relative to the benchmark case.

49
subsidized workers given by the stationary distribution in this case is 1.59%. The results

for correlations are similar to the “low adjustment costs” case except that the correlations

are slightly higher due to higher adjustment costs. The volatility of output increases by

about 3.5%, but the volatility of employment falls substantially by about 12%. This result is

generated by a reduction in the volatility of job creation by 10% and job destruction by 18%.

In addition, the standard deviation of average productivity rises by 7.2%.

The comparison between the “high adjustment costs” and “low adjustment costs” cases

reveals that even when the effect of the subsidy on the steady-state employment and job reallocation rate is trivial, the effect on the volatility of employment over the business cycle is

substantial. This result is mainly driven by the reduced sensitivity of job creation and destruction to aggregate shocks. For this reason, the policy leads to a substantial reduction in

the volatility of job churning over the business cycles. Finally, although it is not reported in

this paper, the volatility of output increases by 4.2% and the volatility of employment falls by

10% when the size of adjustment costs are further increased to τh = τ f = 1.5, for the fraction

of subsidized workers equal to 2%.59

5 Conclusion

This paper has examined the effects of the EAS, Japan’s major employment insurance

program, on average productivity, employment, and the volatility of output and employment

over the business cycle, through the examination of the iron and steel industry. The partial

equilibrium model described in this paper shows that the subsidy reduces average productivity

59Note that the effectiveness of the subsidy in reducing employment volatility is not linear in the size of

adjustment costs because high adjustment costs are already associated with low employment volatility.

50
primarily by increasing the number of unutilized workers. Nevertheless, the direct impact

of the subsidy on productivity is predicted to be small due to a small fraction of subsidized

workers. On the contrary, simulation exercises reveal that the subsidy may have a substantial

impact on the volatility of output and employment. In particular, when hiring and firing

costs are set equal to 80% of the annual wage, the subsidy increases output volatility by 2.8%

and reduces employment volatility by 6% over the business cycles, even when the fraction of

subsidized workers is about 1.3%. When hiring and firing costs are increased equivalent to

the annual wage, the volatility of employment drops by 12% while that of output increases by

3.5%.

While measures such as productivity, employment and output volatility are often used

to evaluate welfare, I do not intend to draw a normative conclusion on the welfare effect of the

subsidy program. Nevertheless, I believe that the implications highlighted in this theoretical

exercise are important ones, providing policymakers a better understanding of the program,

thereby allowing them to more successfully target their policy objectives. Here, I raise a

couple of issues for a more complete welfare assessment. First, the paper predicts that the

subsidy increases output volatility while reducing employment volatility. Consequently, an

assessment of the policy requires an analysis of the cost of output volatility and the benefits

of employment stability.60 Second, while some labor market imperfections are assumed for

subsidy take-up to take place (i.e., firing restrictions and rigid wage), I have not investigated

how the subsidy program may enhance or reduce labor market imperfections.61 Neither have

I conducted a hypothetical comparison with a benchmark without labor market imperfections.

60For example, the subsidy program could bring a substantial benefit by promoting long-term employment if

the skill/productivity of workers increases with tenure.

61For example, the subsidy could potentially enhance the downward rigidity of wage. Similarly, it may create

less incentive to legislate reductions to firing restrictions and promote labor mobility.

51
The analysis presented here raises several additional issues for further investigation.

First, since the quantitative impact of the subsidy on the volatility of output and employment

is sensitive to the magnitude of labor adjustment costs, it will be important to quantify these

costs accurately to evaluate the potential impact of the subsidy program. Second, the analysis treated the iron and steel industry as an independent economy with no interaction with

other industries. New policy implications may arise if inter-industry interactions between

high productivity sectors and low productivity sectors are present in the model.62 Third, it

seems worthwhile to investigate why the subsidy was so heavily concentrated in the iron and

steel sector. Finally, employment volatility during the severe recession of the 1990s was

surprisingly mild in Japan compared to other industrial nations, despite the fact that EAS coverage was highly concentrated in certain sectors of the economy.63 It would be interesting to

empirically investigate what factors contributed to the stabilization of employment.

62The subsidy program may have an inter-industry reallocation effect as some industries are more heavily subsidized than others. This feature could potentially add another dimension to the analysis of overall productivity

dynamics.

63According to Labor Force Survey, the unemployment rate during the 1990s followed a steady increase rather

than being cyclical. The highest unemployment rate at the trough from 1998-1999 was still below 5%.

52
Appendix

A. Graphic Illustration of Subsidy Take-up State Spaces

In this section, I graphically illustrate the state spaces over profitability shock and

previous employment, in which firms decide to take up the subsidy. Figure 11 plots the unconstrained optimal choice of employment against previous level of employment and current

profitability shock. Note that the optimal nt here takes into account firms’ exit decisions.

Holding the previous level of employment constant, we see that the optimally chosen level

of employment, nt, increases as the level of idiosyncratic shock, εt, becomes higher. Also,

notice that the optimal ntjumps at the threshold level of shock below which firms decide to

exit. Furthermore, holding the level of current profitability shock constant, the optimal nt has

a region of inaction in which employment stays constant, as explained in the main text.

Figure 12 plots the unconstrained optimal choice of utilized workers. Note that the

unconstrained optimal etis affected neither by labor adjustment costs nor the expected future

value. Accordingly, the decision rules are independent of the previous level of employment,

and the figure exhibits a smooth curve.

The optimally chosen nt must exceed the unconstrained optimal et for firms to take

advantage of the subsidy program. By comparing these two figures, we see that at a high

level of idiosyncratic shocks, the optimal et exceeds the optimal nt, and therefore, firms do not

take-up the subsidy. However, as the level of idiosyncratic shocks becomes lower (i.e. around

20 in this case), nt starts to exceed et and firms take up the subsidy. Furthermore, at even

lower level of shocks (i.e. less than 13 in this case), firms do not take-up the subsidy as they

exit from the market. Finally, expanding firms, whose optimal choices of nt are observed at

53
Figure 11: The Unconstrained Optimal Level of Employment

0

100

200

300

0

10 20 30 40

0

5

10

15

Idiosyncratic shock nt−1

nt

Note: It plots the optimal choice of employment against the previous level of employment, nt−1, and current profitability shock, εt

.

Figure 12: The Unconstrained Optimal Level of Utilized Workers

0

100

200

300

0

10 20 30 40

0

5

10

15

Idiosyncratic shock nt−1

et

Note: It plots the optimal choice of utilized workers against the previous level of

employment, nt−1, and current profitability shock, εt.

54
the bottom of the region of inaction for each idiosyncratic shock, do not take advantage of the

subsidy program.

B. Strategy for Solving the Numerical Dynamic Optimization Problem

In this section, I explain the strategy used to solve the numerical dynamic optimization

problem given by equation (5). The first method is to use a brute force and solve the problem

using two choice variables, nt and et. This method is straightforward, but computationally

more time-consuming as it involves all combinations of nt and et. The computational burden

is doubled when we include limited eligibility since some firms now face a different profit

maximization problem when χ = 1.

The second method is to use the first order condition for et given by equation (7) and

reduce the problem for the subsidy application case into one which involves only one choice

variable, nt. Note that this nt does not take into account the current production decision, and

therefore it is not an appropriate one when firms decide not to use the subsidy. To overcome

this problem, two hypothetical value functions, V

s

(nt−1, εt| χt = 1) and V(nt−1, εt| χt = 0) as

described in the text, are created. By comparing these two, we can generate firm’s decision

rules regarding the subsidy take-up, Z(nt−1, εt,χt), where Z = 1 corresponds to taking up a

subsidy and Z = 0 corresponds to not taking up. When firms are not eligible, they follow

V(nt−1, εt| χt = 0) regardless of their subsidy decisions. This second method was used since

it is computationally less time-consuming.

We also obtain the following decision rules: X(nt−1, εt,χt), where X = 1 corresponds

to exiting from the market and X = 0 corresponds to staying; N(nt−1, εt,χt) and E(nt−1, εt,χt),

55
which give the optimal choices of employment and utilized workers, respectively, at time t.

Furthermore, whenever Z = 1, a fraction π of firms follow the decision rules which correspond

to V

s

(nt−1, εt| χt = 1) while the remaining fraction 1 − π of firms follow the decision rules

implied by V(nt−1, εt| χt = 0). On the other hand, when Z = 0, all firms follow the decision

rules obtained from V(nt−1, εt| χt = 0).

64

64Strictly speaking, χt = 1 for the fraction π of firms, but since they do not take-up the subsidy, their decision

rules are the same as the case for χt = 0.

56
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