TFP Growth Slowdown
and the Japanese Labor Market in the 1990s∗
Julen Esteban-Pretel†

Ryo Nakajima‡

Ryuichi Tanaka§

University of Tokyo

University of Tsukuba

Tokyo Institute of Technology

January 5, 2009

Abstract
Unemployment in Japan nearly tripled during the 1990s. Underlying this upsurge lie anincrease in the probability of workers to lose their jobs and a decrease in the probability thatthe unemployed find jobs. This paper analyzes the sources responsible for these labor market
changes in Japan in the decade of the 1990s. We build, calibrate and simulate a neo-classicalgrowth model with search frictions in the labor market. Using actual TFP data, the model isable to reproduce the path of unemployment and the job flows, as well as that of output. We
find it to be the decrease in productivity, coupled with the reduction in hours worked, whichcurtails the profits of firms, inducing a drop in employment and an increase in unemployment.
Keywords: Growth model, TFP, unemployment, search and matching, Japan, Lost Decade
JEL Classification: E2, E13, O4, J6∗

The authors wish to thank Toni Braun, Junichi Fujimoto, Fumio Hayashi, Hidehiko Ichimura, Daiji Kawaguchi,

Keisuke Otsu, Yasuyuki Sawada, Katsuya Takii and the seminar participants at RIETI and GRIPS for helpfulcomments and discussions. We are also grateful to Nao Sudou for his help in constructing part of the data used inthis paper, and to Sachiko Kuroda for sharing her data on worker flows. This project was partially financed by the
Grant-in-Aid for Young Researchers of the Japanese Ministry of Education. All remaining errors are our own.
†
Corresponding Author: Faculty of Economics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033,
Japan. Email: julen@e.u-tokyo.ac.jp; Tel: +81-3-5841-5526; Fax: +81-3-5841-8294.
‡
nakajima@dpipe.tsukuba.ac.jp§
tanaka@mei.titech.ac.jp1

1

Introduction

The 1990s in Japan have been labeled the Lost Decade. It was a time when output per capita grewat an average of 0.5%, far below the average of the previous decade, 3.2%, and that of the U.S.
during the same period, 2.6%. At the same time, the labor market suffered one of the worst periods
in recent Japanese history. Workers were fired in record numbers, and unemployment reached ahistorical high of 5.4% in 2002, more than 2.5 times the level in 1990. Underlying this substantial
increase in unemployment lie a decrease in the probability of unemployed workers to find jobs, andan increase in that of employed workers losing their jobs. This rise in unemployment has been amatter of great concern for economists and policy makers.
The aim of this paper is to explain the behavior of the Japanese labor market during the Lost
Decade by investigating the causes of the increase in unemployment and the pattern of the flowof workers during the 1990s. To do so, we build, calibrate and simulate, using actual data, a neoclassical growth model with search frictions in the labor market. We use a deterministic generalequilibrium framework based on the traditional growth model of Cass-Koopmans, with capital andlabor as inputs of production, and we impose a search and matching labor market, in the style ofMortensen and Pissarides (1994)1 . We also assume a government which taxes labor and capitalincome and spends its revenue in its own consumption. The calibration of the model parameters
is performed to match the empirical evidence from Japan prior to the Lost Decade. We solve andsimulate, using a two-boundary problem solution method, the transition path of the economy froman initial steady state, assumed to be 1990, to a new steady state far in the future. The driving
force behind the switch in steady state is the drop in TFP growth. We also impose the empiricallyobserved reduction in hours of work2 and the rise in government expenditure over the 1990s. To
the best of our knowledge, this is the first paper that uses actual TFP data fed into a model withlabor search frictions in order to account for the transition path of unemployment and other labormarket variables between two steady states: this is one of the contributions of this paper.
We find that our model is capable of reproducing the increase in the unemployment rate from1990 to 2002. The forces responsible for this increase, according to our simulations, are the drop in
TFP growth and the decrease in hours of work. Each of these two factors contributes equally to theincrease in unemployment by the year 2002, which implies that technology change alone explains
1
2This type of non-Walrasian labor market allows the model to display involuntary unemployment in equilibrium.
As is explained in the empirical evidence section, during the 1990s the Japanese government introduced changes

in regulations that effectively imposed a reduction of the length of the work week from 6 to 5 days.

2

around 50% of the movements in the labor market. The model not only accounts for the change inthe level of unemployment between 1990 and 2002, it closely tracks the path of this variable during
the transition. The model is also capable of reproducing the paths of the flows of workers in andout of unemployment, as well as the behavior of output observed in the data. Finally, we show that
our results are robust to alternative specifications for the future path of TFP.
The intuition why the model can replicate the empirical path of output and the labor market
variables is that the slowdown of TFP growth reduces the stationary level of productivity, which
together with the fact that firms cannot work their employees longer due to the exogenous decreasein hours lowers the profits of the firm. This makes it more difficult for firms to continue the current
matches, and increases the probability of job loss for the worker. At the same time, it discourages
the posting of new vacancies, which reduces the probability of finding new jobs for each unemployedworker. The overall reduction in employment and the decrease in productivity accounts for the dropin output.
Our research is related to the strand of literature that offers explanations of the poor performanceof the Japanese economy during the Lost Decade. One of the best known explanations is foundin Hayashi and Prescott (2002). They show that the slowdown of TFP can account for the drop
in detrended output and the behaviour of other macroeconomic variables, such as the capitaloutput ratio and the after-tax return. An alternative hypothesis which has attracted attention is
the so-called zombie lending explanation. Peek and Rosengren (2005) and Caballero, Hoshi, andKashyap (2008) show how the misallocation of resources to unproductive (zombie) firms, following
the financial bubble burst at the turn of the decade, could explain the downturn of the economy.
Another explanation, put forward by Krugman (1998) and used in Eggertsson and Woodford (2003),
is that the Japanese economy fell into a liquidity trap, which prevented the monetary authority fromacting in an effective manner against the recession which began with the financial crisis. Thesepapers have focused on explaining the performance of the Japanese economy measured by severalof the main macroeconomic variables, such as output or the capital-output ratio. However neither
these nor other papers have tried to theoretically explain the reasons behind the increase in theunemployment rate and the evolution of the labor market flows during the 1990s.
Of the previous papers, Hayashi and Prescott (2002) is the closest to ours, since we focus on
the TFP explanation to account for the Japanese labor market changes over the Lost Decade. We
use this hypothesis since we believe that a decade-long recession, such as the one analyzed here, isdeeply rooted in real factors. However, we do not discount the value of the other explanations, andin fact Fukao and Miyagawa (2008) show that the misallocation of resources between 1996 to 20023

can account for around 5% of the decline in Japanese TFP. Since the focus of this paper is not on
the causes underlying the decline in TFP but the effects of this decline on the economy, we follow
Hayashi and Prescott (2002) and assume exogenous TFP movements3 .
Our paper is also related to the growing literature which embeds a search and matching labormarket in a general equilibrium framework. Pioneering in this literature are the works by Merz
(1995) and Andolfatto (1996). Papers in this area have focused primarily on business cycle fluctuations, but have been under scrutiny following the criticisms raised by Shimer (2005) and Hall
(2005). The former study shows that the textbook search and matching model cannot replicate
the empirically observed volatility of unemployment using reasonable movements in productivity.
Recent work by Hagedorn and Manovskii (2008), however, has shown that under certain parameterizations of the model, wages become very insensitive to changes in productivity, and unemployment
becomes more responsive to such shocks. Although our paper focuses on medium-term changes inthe economy and not business cycle fluctuations, we provide a discussion on the reasons for the
success of our model in generating movements in unemployment. The two main reasons are the sizeof the productivity movements and the existence of capital in our model. The inclusion of capital,
which is essential in a growth model, makes wages more insensitive to productivity changes, as inHagedorn and Manovskii (2008), even though we do not use their calibration but rather that of
Shimer (2005). The intuition is that capital rents make firms’ profits smaller, and this implies thatthe difference between the after non-labor cost flow profits for the firm and the flow value of unemployment is very small4 . This makes wages more insensitive, and unemployment more responsive
to productivity movements.
The remainder of the paper is organized as follows. Section 2 briefly explains the experience of
the Japanese economy in the 1990s, putting emphasis on the behavior of the labor market variables.
Section 3 builds the theoretical model. Section 4 describes the calibration of the model parameters
and the exogenous variables. Section 5 displays the simulation results. It also presents a robustness
test of the results to alternative specifications of the future path of TFP. In Section 6, we discuss
how our results relate to the Shimer-Hall critique. Finally, Section 7 summarizes and concludes thepaper.
3

For papers that build models of endogenous TFP for the Japanese economy, please refer to Braun, Okada andSudou (2006), and those found in the special volumes of the Journal of the Japanese and International Economies,
edited by Hoshi and Jorgenson (2005), and in the Japanese Economic Review, edited by Ariga, Hayashi and Horioka(2006). These two volumes focus on the Lost Decade.
4
The difference in these two variables is the crucial disagreement between the calibrations of Shimer (2005) andHagedorn and Manovskii (2008).

4

2

The Japanese Economy in the 1990s

During the 1990s, Japan experienced its worst economic times since World War II. Hayashi and
Prescott (2002) report the basic facts about the Japanese economy over this period. As they show,
detrended GNP decreased over the decade, and by 2000 its level was less than 90% of what it had
been in 1990. This drop in detrended output was accompanied by an increase in the capital output
ratio and a decrease in the after-tax return on capital. The focus of this paper is on unemployment
and the underlying movements in the labor market, hence we now explain the characteristics ofthese variables during this turbulent decade.
Figure 1 presents the evolution of the main labor market variables from 1990 to 20025 . As we
can see in panel (a), the unemployment rate almost tripled in this period, increasing from 2.1% toa maximum of 5.4% in 2002. This increase is even more striking when compared to the previous
unemployment rate maximum in the post-war era, which was 2.8% in 1988. Although not shown in
Figure 1, labor force participation was fairly stable, around 63%, between 1990 and 1996, decreasing
to around 61% by the turn of the decade. These numbers imply that during the 1990s, the total
number of workers, the employment to population ratio, and the employment rate all decreased.
In order to better understand the forces responsible for the changes in unemployment, it is usefulto analyze the flows of workers in the labor market6 . Figure 1 (b) shows that over the 1990s, thequarterly probability for a worker to leave unemployment7 (left axis) decreased from 41% to 27%.
At the same time, the probability of losing a job (right axis) increased from 0.8% to 1.9% from 1990
to 2002. However, it is interesting to note that, although the probability of finding a job decreased
and that of losing a job increased, the total number of workers who both found and lost jobs in thisperiod increased (Figure 1 (c)). That is, unemployment increased despite the fact that the number
5

We focus on the period between 1990 and 2002, since after 2002 the TFP stabilizes, and labor market variables

either stabilize, as for instance hours of work do, or reverse their trend, as is the case for unemployment. Hence, since
the focus of this paper is on the Lost Decade, 2002 seems the natural terminal point for the analysis.
6
Genda (1998) and Kuroda (2005) study these labor market flows in detail for the Japanese economy. We arethankful to Sachiko Kuroda for sharing with us the data on worker flows from her paper. This data is used to build
Figures 1 (b) and (c). The description and construction of the data can be found in Kuroda (2005).
7
The probability of a worker to leave unemployment in a given month is calculated as the number of workers
who move from unemployment to employment in that month divided by the number of unemployed workers at
the beginning of the month. The monthly probability is then compounded appropriately to obtain the quarterly
probability. Similarly, the probability of a worker to lose a job is calculated as the number of employees who movefrom employment to unemployment in a given month divided by the number of workers at the start of the month,and then compounded to find the quarterly probability.

5

of workers moving out of unemployment and into employment increased over time8 . The reason isthat the total number of workers losing their jobs was higher, therefore raising unemployment.
Simultaneous to the increase in unemployment, the government instituted several policies toreduce the number of hours worked. Some of these policies included the creation of new national
holidays and the closure of government offices on Saturdays, which effectively reduced the length of
the work week from 6 to 5 days for many workers. The evolution of hours is shown in panel (d) of
Figure 1, where we can see that weekly hours of work dropped from 43 to 38 in the course of thedecade.
The increase in unemployment and decrease in hours worked was not paralleled by a decrease in
detrended wages until the latter part of the decade. Figure 1 (e) shows how detrended real wages9
decreased to below 90% of the 1990 level by the end of the decade, and declined further with theturn of the century.
As stated in the introduction, the hypothesis of this paper is that the force behind the increase in
unemployment and the other labor market movements, as well as the decrease in detrended output,
is the slowdown in TFP growth, with the extra push provided by the government imposed decreasein hours worked. Figure 1 (f) shows the evolution of TFP since 1980. We can see that technology
grew at a healthy rate during the 1980s, 1.9%, but this growth slowed considerably during the Lost
Decade, when it averaged 0.3%. It seemed to recover after 2002, and averaged 1.5% from that year
until 2006.
In summary, the 1990s in Japan saw a decrease in detrended output, an increase in unemployment due to a greater increase in the number of workers losing their jobs than those finding a newone, although both series increased, a decrease in hours worked due to changes in regulations, anda drop in detrended wages after the first half of the decade. We now proceed to explain the model
used to try to account for these facts.

3

The Model

The model is a discrete time neo-classical growth model, in the style of Cass-Koopmans, withthree types of infinitely lived agents: Consumers/workers, firms, and government. There is only
8

During the 1990s, labor force participation remained constant at around 63% in the first half of the decade, anddecreased slightly to 61% by the turn of the century. It remained around that level thereafter.
9
Real wages, as well as output, are detrended at a 2% rate, which is the growth rate of the world’s leading economy,
the U.S., over the 20th century, and is the one used by Hayashi and Prescott (2002).

6

one good, which is produced using capital and labor and sold by the firms to the consumers.
The labor market is modeled in the style of the search and matching literature with endogenous job
destruction. The replacement of the traditional Walrasian labor market for one with search frictions
allows the model to display involuntary unemployment in equilibrium, essential to the focus of thispaper. Furthermore, by assuming endogenous job destruction, we analyze the ability of the model
to reproduce the increase in the rate of job destruction observed in the data over the Lost Decade.
We follow Hayashi and Prescott (2002) and assume that there is no uncertainty in terms of
the aggregate exogenous variables in the economy, although the model still displays uncertainty at
the firm and worker levels. We model individual uncertainty in terms of an idiosyncratic shockto the match, which is responsible for the heterogeneity across matches. However, this individual
uncertainty disappears when the model is aggregated before solving it. In the following, we explain
the decision problem faced by each of the agents and the definition of the equilibrium.

3.1

HouseholdWe follow the literature on models with labor market frictions in a general equilibrium framework
and assume that all of the individuals in the economy belong to a big family or household. This
assumption delivers perfect self-insurance for the individuals in the family, and simplifies the problem
by not requiring keeping track of employment and wealth distributions. The household owns thecapital, which it rents to firms, and also earns income from the wages collected by the members whoare employed and from the unemployment benefits or home production of the unemployed members.
Both capital and labor income are taxed by the government. The household decides every periodon the levels of consumption and savings, which maximizes its life-time utility.
Therefore, the household chooses {Ct+i , Kt+i+1 }∞t=0 to max∞!

β i u (Ct+i )

(1)

i=0

subject to

Ct+i + Kt+i+1 = (1 − τn ) Wt+i + Πt+i + (1 − δ) Kt+i + rt+i Kt+i − τk (rt+i − δ) Kt+i(2)

+ (1 − nt+i ) bt+i zt+i − Tt+i ,given K0 ,for i = {0, ..., ∞}, where β ∈ (0, 1) is the discount rate; Ct is the consumption level of the household;

Kt is the total capital in the economy; Wt is the total amount of wages paid to the employed workers;
7Πt are the total profits of the firms, which are distributed back to the household, since it ultimately
owns them; rt is the rental rate of capital, and δ is its depreciation rate; τn is the labor income tax;
τk is the capital income tax, where only the return net of depreciation is taxed; bt is the amount ofhome production or unemployment benefits collected by the unemployed workers; nt is the numberof employed workers, and since population is normalized to one, and there are no workers out of
the labor force, ut = 1 − nt is the number of unemployed workers; zt is a variable that grows
at the average growth rate of technology along the balance growth path, and it multiplies bt andother stationary parameters throughout the model so that their importance does not decay as the
economy grows; finally, Tt is the total amount of lump sum taxes collected by the government.
This problem yields the traditional consumption-Euler equation, which shows how the individual
is indifferent between saving or consuming and extra unit in equilibrium:

3.2

Labor Market"#u" (Ct ) = β (1 + (1 − τk ) (rt+1 − δ)) u" (Ct+1 ) .

(3)The labor market is modeled in the style of Mortensen and Pissarides (1994), where there exist
search frictions, and workers and firms try match and form employment relationships. Firms produce
using capital, labor and available technology, and matches are destroyed endogenously as an optimal
decision by the firm and worker.
Employment relationships are of one worker and one firm, and matching occurs randomly according to a constant returns to scale matching function, m(ut , vt ), where ut is total unemployment
and vt is the number of vacancies. We define the market tightness as the ratio of vacancies tounemployed workers, θt ≡ uvtt , and further define the probability that a firm meets a worker in any$%
given period as qt (θt ) ≡ m uvtt , 1 . Similarly, the probability that a worker matches with a firm isθt qt (θt ).

We model the endogenous destruction by assuming that productive firms need to pay, on topof the labor and capital costs, a non-productive intermediate input cost xt , which is idiosyncratic
to each match. The firm-specific intermediate input cost is independent and identically distributed
across firms and time, with distribution function G : [xmin , xmax ] → [0, 1]. A new idiosyncratic costis drawn every period by existing matches, and if the cost is too high it may be beneficial for thefirm and the worker to discontinue the employment relationship. The value of xt which dissolves
the match is denoted by x̄t . The probability of job destruction is therefore 1 − G (x̄t ).

In a productive employment relationship, the firm produces output according to a constant8

returns to scale production function which has hours and capital as inputs. While capital is achoice variable for the firm, hours are not, and they are assumed to be exogenous to the firm andthe worker10 . The production function of the individual firm is yt = At f (kt , ht ), where At is totalfactor productivity (TFP), and yt , kt and ht are respectively output, capital and hours per worker.
Hence, yt and kt are related to aggregate output and capital according to the following equations11 :Yt = nt yt and

Kt = nt kt .

(4)

The timing of the model is as follows. At the beginning of every period, the level of technologyof the economy is revealed, and every matched firm draws an idiosyncratic cost. These two variables
determine the number of productive and unproductive matches for the period. After destruction
takes place, the levels of employment and unemployment are determined. At that point production
starts at firms, and vacancies and unemployed workers try to meet in the labor market. At the endof the period, wages are paid and the firm’s profits are distributed to the household, which pays
taxes and decides how much to consume and how much to save.
3.2.1

The Firm’s Problem

Firms post vacancies in the labor market and, when matched with a worker, implement optimal
production plans in order to maximize their profits. Posting vacancies has a flow cost for the firmof φ, which is multiplied by the growing component of technology, zt , so that it does not disappear
in the long run. If the firm is matched, and the idiosyncratic cost is low enough, below x̄t+1 , thefirm obtains the value of being filled in the following period, otherwise it remains as a vacancy. Vt
and Jt (xt ) denote the values, measured in terms of consumption, of having a vacancy opened andof a match for a firm with the idiosyncratic cost xt which hires a worker. The value of a vacancy isx̄(t+1
Jt+1 (xt+1 ) dG (xt+1 ) + (1 − qt (θt ) G (x̄t+1 )) Vt+1  ,(5)Vt = −φzt + βt q (θt )
xmin

"

t+1 )
where βt = β uu(Cis the factor used by firms and workers to discount the future, since firms are" (C )
tultimately owned by the household.
10

We make this assumption to be consistent with the evidence explained in Section 2, which indicates that thedecrease in hours observed in Japan over the 1990s was mostly due to changes in regulations by the government,
rather than a voluntary reduction in hours on the part of firms or workers.
11
As is shown later, every firm chooses the same amount of capital, and hence produces the same quantity ofoutput.

9

Free entry of firms is assumed in equilibrium, which implies that firms enter the market up to
the point where the value of posting an extra vacancy is zero. Therefore, in equilibrium, we findthat the value of a vacancy is
0 = −φzt + βt q (θt )(x̄t

Jt+1 (xt+1 ) dG (xt+1 ) .

(6)

xmin

The value for the filled firm is
Jt (xt ) = At f (kt , ht ) − rt kt − xt zt − wt (xt ) ht + βtx̄(t+1

Jt+1 (xt+1 ) dG (xt+1 ) .

(7)

xmin

The interpretation of the previous equation is as follows. During the current period, given the firm’s
idiosyncratic cost, xt , the firm produces output and pays wages, the rental cost of capital and suchintermediate inputs, xt . In the following period, if the idiosyncratic cost is below the threshold,the match is still productive, with a value of Jt+1 (xt+1 ), otherwise the match is destroyed and it
becomes a vacancy, which has value zero.
The firm chooses capital kt to maximize the present discounted value of being filled, which
implies that it will rent capital to the point where its rental cost equals its marginal product,
rt = At fk (kt , ht ) .

(8)

The optimal condition for capital determination, equation (8), implies that in equilibrium, every
firm chooses the same amount of capital and therefore produces the same quantity of output.
We can now define the total profits of the firms, which are transferred to the household, asΠt = nt At f (kt , ht ) − rt nt kt − Wt − xTt zt − vt φzt ,where xTt is the total amount of intermediate input costs paid by the firms. Total wages paid to
the workers, Wt , are defined as the average wage, conditional on working, times the number of
employed workers:
1
W t = nt
G (x̄t )
3.2.2

(x̄t

wt (xt ) ht dG (xt )xmin

The Worker’s Problem

Consider now the problem for the worker. We denote by Ut and Nt (xt ), measured in terms of consumption, the values of being unemployed and of being matched with a firm with the idiosyncratic
cost xt .
10

An unemployed worker obtains bt units of consumption while unemployed. bt can be interpreted
as home production, unemployment benefits, or simply the value of leisure in units of consumption.
If the worker matches with a firm, which happens with probability θt q (θt ) , and the idiosyncratic
cost for the firm is below the threshold, x̄t+1 , he becomes a productive worker in the following
period. If he does not enter into an employment relationship with a firm, he remains unemployed.
Hence, the value of being unemployed at period t is:x̄(t+1
Ut = bt zt + βt θt q (θt )Nt+1 (xt+1 ) dG (xt+1 ) + (1 − θt q (θt ) G (x̄t+1 )) Ut+1  .

(9)

xmin

As in the case of the firm, the value of a match for a worker is a function of the idiosyncratic shock

xt . The value of employment for a worker is composed by the after-tax wage and the continuation
value, which is the value of being employed if the match is not destroyed, or the value of being
unemployment if the idiosyncratic cost is too high.
 x̄t+1(Nt (xt ) = (1 − τn ) wt (xt ) ht + βt 
Nt+1 (xt+1 ) dG (xt+1 ) + (1 − G (x̄t+1 )) Ut+1  .

(10)

xmin

3.2.3

Surplus, Bargaining, Wages and Destruction Threshold

When an employment relationship takes place, it creates a surplus which is shared between the firm
and the worker. The surplus of the match is defined as the sum of the values of a filled job fora firm and a worker minus their outside options, which are the value of a vacancy and the valueof unemployment, respectively. Since there is free entry of firms, the expression for the surplus is
St (xt ) = Jt (xt ) + Nt (xt ) − Ut .

Wages are chosen as the Nash solution to the following bargaining problem, where η is thebargaining power of the worker:
max (Nt (xt ) − Ut )η (Jt (xt ) − Vt )1−η .

wt (xt )The previous problem delivers the sharing rule for the surplus, and it implies that both firm andworker receive a constant fraction of the surplus. Due to the existence of labor taxes, the fraction
differs from the bargaining power, and the optimal sharing rules are:Nt (xt ) − Ut = η

1
1 − τnSt (xt ) and Jt (xt ) = (1 − η)St (xt ) .
1 − ητn1 − ητn
11(11)

Combining the previous two expressions with equations (7) to (10), the surplus for a match canbe expressed as:
St (xt ) = At f (kt , ht )−rt kt −xt zt −τn wt (xt ) ht −bt zt +βt+

1 − τn1 − θt q (θt ) η
1 − ητn, x̄(t+1
xmin

St+1 (xt+1 ) dG (xt+1 ) .
(12)The division of the surplus between firm and worker yields the wage paid to the employee. The
expression for the wage is:
wt (xt ) ht = η [At f (kt , ht ) − rt kt − xt zt + θt φzt ] + (1 − η)b t zt.
1 − τn(13)

The worker is compensated for a proportion η of the production of the firm, and for a measureof the saved cost of searching for new matches. He is also compensated for a fraction (1 − η) of theforgone home production, adjusted by taxes.

An employment relationship is terminated when the idiosyncratic intermediate input cost to thefirm is so high that it drives the surplus to zero. This determines the threshold cost above which
both worker and firm agree to dissolve the match and search for better options. Using equation(12) and equating it to zero, we obtain the expression for the threshold:x̄t zt = At f (kt , ht ) − rt kt − τn wt (x̄t ) ht − bzt + βt

3.2.4

+

1 − τn1 − θt q (θt ) η
1 − ητn, x̄(t+1
xmin

St+1 (xt+1 ) dG (xt+1 ) .
(14)

Evolution of Unemployment

Finally, given this timing explained earlier and normalizing the labor force to unity, the evolutionof unemployment is characterized by the following equations:
ut = [1 − θt−1 q (θt−1 ) G (x̄t )] ut−1 + [1 − G (x̄t )] nt−1

nt = 1 − u t ,

(15)
(16)

where θt−1 q (θt−1 ) G (x̄t ) is the fraction of workers who found a successful match the previous periodand [1 − G (x̄t )] is the proportion of employed workers who lost their jobs.

3.3

Government

The government taxes the household and uses the revenues to finance its expenditures on goods andservices, which are assumed to have no productive or utility use. We express government spending12

as a fraction of aggregate output, where ψt is the share of these expenditures in output. The
government budget constraint, which is balanced every period, is:ψt Yt = τn Wt + τk (rt − δ) Kt + Tt

3.4

(17)

Equilibrium

A perfect foresight competitive equilibrium, given the path of TFP and hours {At , ht }∞t=0 , a gov∞
ernment policy {τn , τk , ψt , Tt }∞t=0 and K0 , is a set of prices {rt , wt (xt )}t=0 and allocations{Yt , Kt+1 , Ct , kt , nt , ut , vt , θt , x̄t }∞t=0 which satisfy that (i) agents optimize, i.e. the household’s op-

timal condition (3), the value functions in the labor market (6) to (10), the capital rental optimal
condition (8), and the optimal surplus sharing rule (11) are satisfied; (ii) markets clear for consumption goods, (1 − ψt ) Yt = Ct + Kt+1 − (1 − δ) Kt − (1 − nt ) bzt + φzt vt + nzt xTt ; capital, equation(4); and labor, equations (15) and (16); (iii) the government has a balanced budget, as in equation(17).
In order to solve the model, we rewrite the equilibrium conditions in terms of stationary variables.
γ̄, theThese non-growing variables are obtained by dividing each by zt , which grows at the rate 1−α1average growth rate of the TFP factor, At1−α , in the balance growth path12 . The steady state ofthis economy is a perfect foresight stationary equilibrium in which all detrended variables remain
constant across time. The definition of this perfect foresight stationary equilibrium can be found in
Appendix A.

4Parametrization and Exogenous Variables

We now proceed to explain the method used to parametrize the model, and we later explain thesimulation technique, along with the assumptions related to the exogenous variables of the model.

4.1

Calibration

We choose functional forms which are standard in the literature and then calibrate the parametersof the model to match the empirical evidence for Japan in 1990, which is assumed to be the initialsteady state in our simulations. We set the length of the period to one quarter.
12γ̄ is the average growth rate of TFP, At , along the balance growth path.

13

The utility function is assumed to be logarithmic, u (Ct ) = log (Ct ). The discount factor, β, iscalibrated using the stationary Euler equation (19), shown in Appendix A, to match the quarterly
capital-output ratio of Japan in 1990, 7.82, and set to β = 0.9957.
Labor and capital income tax rates, τn and τk , fluctuated slightly over the 1990s. We set these
rates to the average from 1990 to 1996 using Mendoza et al. (1994) extended data from EnriqueMendoza’s website13 . These tax rates are set to τn = 0.28 and τk = 0.44.
The production function of the firms is assumed to have a standard Cobb-Douglas form, f (kt , ht ) =α
kt h1−α. We set the share of capital rents in output, α, to 0.383. The depreciation rate of capital, δ,tis set to 0.028. These two numbers are estimated extending the data used in Braun, Esteban-Pretel,
Okada, and Sudou (2006) and they are used to calculate the TFP of the economy. The initial levelof technology, A0 , is normalized to unity, and the average and long-run growth rate of TFP, γ̄, isassumed to be 1.5%, which is the average in the data from 2002 to 2006.
In the labor market, we assume that the bargaining power of the worker, η, is 0.5, as has
become standard in the literature. The matching function in the labor market is Cobb-Douglass,m (ut , vt ) = µuξt vt1−ξ . We follow what is standard in these types of models and set the elasticity
of matching with respect to unemployment, ξ, to 0.5. The idiosyncratic cost to the firm is drawn
1 −x
from an exponential distribution, x ∼ e χ , which only requires to calibrate one parameter, theχmean of the distribution, χ. Hence, xmin = 0 and xmax = ∞. χ is jointly calibrated with thescaling parameter in the matching function, µ, and the cost of posting a vacancy, φ, to matchthe unemployment rate and probability of leaving unemployment in Japan in 1990, 0.021 and 0.42
respectively, and a market tightness of unity14 . We set these parameters to χ = 0.0407, µ = 0.42,
and φ = 0.037.
We assume that the value of leisure, home production, or unemployment benefit, bt , is a fraction
λ of the output that the average worker would produce in the firm, or what is the same in standard
search and matching models, the marginal product of one worker. We set λ = 0.4, which is thevalue used in Shimer (2005). This value of λ implies a replacement ratio in terms of the average
wage in the model of 0.68, which is consistent with the replacement ratio in Japan of between 60
to 80 percent of the last wage received15 .
13Theextended

data

only

reports

taxes

up

to

1996.

Enrique

Mendoza’s

websiteis

http://www.econ.umd.edu/~mendoza
14
As explained in Shimer (2005), changing the value of the market tightness only rescales the value of µ, leaving
everything else unchanged.
15
Although not detailed in this paper for the sake of brevity, the results shown in the Section 5 are robust tochanges in η and ξ within standard values (0.4 to 0.6). They are also robust to reducing the replacement ratio, λ,14The values for the model parameters are summarized in Table 1.

4.2

Simulation Technique and Path of Exogenous Variables

The model presented above is simulated by assuming that the economy transitions from an initialsteady state in 1990 to a new steady state at a far enough point in the future16 . The length oftime in the model simulations is one quarter, but the data is later aggregated by year, since we areinterested in the long-run transition of the economy and not in its short-term fluctuations. The
simulation is deterministic, and the agents know the path of the variables that change exogenously
over time.
The data on TFP growth rate, hours per worker and government expenditure, is an extended
version of the data set of Braun, Esteban-Pretel, Okada, and Sudou (2006)17 .The path of these
exogenous variables in the data is as follows:• Growth rate of technology, γt : The path of TFP growth rates, γt , is calculated from the datat
, from 1990 to 2002 and then remains constantas the period by period change, i.e. eγt = AAt−1

at the long-run value, γ̄.
• Hours of work, ht : These decrease from the initial level of 44 to the final level of 38 over the
sample period, following the path shown in Figure 1 (d). They remain constant after the lastperiod at the final level.
• Government expenditure share in output, ψt : This variable fluctuates between 12 to 14 percent
over the studied period. The actual path of government purchases as a share of output is shownin Figure 5 of Hayashi and Prescott (2002). We assume that it remains constant at the final
level after the last period.
below the benchmark 0.4 to 0.3 and even 0.2. However, the model calibration does not allow us to increase the valueof λ much higher than the benchmark. The reason is the existence of capital and endogenous job destruction in themodel, which, given the other parameter values, implies that raising the outside option of the worker too greatly
prevents the existence of matches with surplus above zero.
16
The model is simulated using the equations shown in Appendix A, the parameters from Section 4.1 and the pathsof exogenous variables explained in this subsection. The simulations were performed using the Dynare package forMatlab, version 3.065.
17
We are thankful to Nao Sudou for his help on the extension of the data. The original and extended data sets canbe found in the research section of Julen Esteban-Pretel’s website <http://www.e.u-tokyo.ac.jp/~julen>.

15

5

Simulation Results

The results of the simulations are shown in Figures 2 and 3. These figures show that the model
is successful in replicating the path observed in the data from 1990 to 2002 for the labor market
variables, as well as that of output.
Figure 2 (a) shows that the decrease in TFP growth and the decline in hours are the maincauses of the sharp increase in the unemployment rate in Japan over the 1990s18 . The model canalso replicate well the actual path of unemployment over the decade. The intuition for the successof the model is as follows. The drop in productivity growth produces a decline in the detrended
productivity level, which along with the fact that firms cannot work their employees longer due
to the exogenous decrease in hours decreases the profits of the firm. Productive firms face higher
incentives to discontinue matches, which increases the probability for workers to lose their jobs, as
shown in Figure 3 (b). At the same time, potential entrants expect lower future profits, and therefore
fewer vacancies are posted, which with the increase in unemployment reduces the probability for
non-working individuals to find jobs, as shown in Figure 3 (a). The model is able to capture themovements of these two variables in the data, although the drop in the probability of finding a jobin the model is not as pronounced as in the data. When looking at the fraction of workers who findand lose jobs every period, the model tracks the increase in both variables well, as seen in Figures 3(c) and (d). Hence, as is the case in the data, the model produces an increase in unemployment due
to a greater increase in the number of workers losing their jobs than of those finding employment.
The behaviour of detrended output over the 1990s, which is already well explained by Hayashi
and Prescott (2002), is shown in Figure 2 (b). We can see that the inclusion of search frictions in
the labor market does not worsen the ability of the model to track the path of output, at which
it does a good job. However, it is worth noting one variable, the behavior of which our model is
not able to replicate although that of Hayashi and Prescott (2002) can, namely the capital-output
ratio. This variable is not shown in the figures, but increases in the data from 7.82 to 9.66, whilein the model it does not increase, since the long-run TFP growth remains constant throughtout thesimulation.
In the data, detrended wages decreased over the course of the decade by more than 15%. The
18

Despite the limited role of government expenditures in the simulation results, they are included in the modelfor two reasons. The first is for consistency between the model and the data variables, since output in the data is
the net of government purchases. The second is that Hayashi and Prescott (2002) use government expenditures intheir model, and therefore, by including them here we can make clear comparisons of our results with theirs for the
non-labor market variables.

16

model is able to reproduce the level drop in wages, but it initially decreases too quickly, whilein the data it took 5 to 6 years to begin dropping. The model’s immediate decrease in wages iscaused by the reduction in the value of the outside option for the workers due to the increase in
unemployment (the labor market becomes less tight), which lowers their bargaining position anddecreases the wages.
Although not shown in the figures, it is worth stating that each of the two sources of variation,
TFP growth decline and drop in hours worked, contribute about half of the change in unemployment
in our simulation. This implies that the drop in growth rate of TFP alone is not sufficient to generate
the observed changes in the data in our model. The decline in hours imposed by the government
also plays a crucial role.

5.1

Robustness to the Future Path of TFPThe simulation results shown above are obtained under the assumption that the level of the exogenous variables remains constant at the 2002 level after that year19 . While this assumption isconsistent with the data up to the year 2006, if Japan were to stay in the balance growth path
implied by the final TFP growth, there would be a permanent divergence between the Japaneseand the U.S. economies. Although there are studies which rationalize the existence of differences in
the levels of TFP across economies, such as Parente and Prescott (1994), the notion of these two
economies diverging permanently, although also maintained in Hayashi and Prescott (2002), can bethought of as unappealing.
In this section, we check the robustness of our results to an alternative specification of the future
path the TFP. Here we assume that TFP is as observed in the baseline simulation until 2006, andthen starts returning to the pre-1990s balance growth path. We assume that it takes 10 years toreach that path. In other words, TFP grows at a rate of 3.72% from 2006 to 2016 while transitioning
back to the original balance growth path, and then remains constant at 1.9% after reaching it in201620 .
Figure 4 shows the evolution of the unemployment rate in the data and in the simulation under
the two specifications for the future path of TFP, the benchmark and the alternative. The first thing
to note is that in both cases the model does a good job of replicating the path of unemployment in
19This assumption is standard in papers with this type of simulation technique, such as Hayashi and Prescott(2002, 2008) and Chen et al. (2008).
20
Under this specification, we could consider the period between 1990 and 2016 as a very long cycle, or a mediumterm cycle, rather than a change in the balance growth path.

17

the 1990s. Therefore, the results are robust to changes in the assumed future path of TFP.
The second point of note is that under both specifications, the model predicts that the unemployment rate should have continued to increase beyond the level of 2002, whereas the data showsthat unemployment started to decrease after that year. Therefore, it seems that something took
place in the Japanese economy which reversed the increase in unemployment in 2002 and is not
explained by TFP changes. Ohtake (2004) and Yamakawa (2001) describe several measures takenby the Japanese government after 1998 in order to try to control the rise in unemployment. These
measures include economic package incentives to revitalize employment and changes in the labor law
to flexibilize the labor market. Among the labor law changes, the most important are the revisionof the Labor Standards Law, the Worker Dispatch Law, and the Employment Security Law. These
amended laws meant a structural change to the labor market, which allowed firms to hire workers inmore flexible circumstances, such as through employment placement services or as dispatched workers, and may have increased the incentive for firms to hire workers and eventually have contributed
to the reduction in unemployment21 . A detailed investigation is needed to conclude whether or not
the cause of the decrease in unemployment after 2002 was a structural change in the labor market;
given that the purpose of this paper is to account for the increase in the unemployment rate inJapan over the 1990s, we leave this issue for future research.

6

Discussion

As explained in the introduction, the search and matching models have been under recent scrutiny
following the critiques of Shimer (2005) and Hall (2005). In particular, Shimer (2005) shows that
under a calibration similar to ours, the basic search and matching model is not able to reproduce
the behavior of unemployment and vacancies over the business cycle for reasonable movements
in productivity. Specifically, it is the volatility of these variables that the model has difficulty
replicating. As shown in the previous section, our model is able to reproduce the movements inunemployment over the 1990s in Japan. Although our model does not consider business cycle
frequencies but medium-term changes, it is worth analyzing why it succeeds in replicating thechanges in unemployment.
The main reason that our model can replicate the increase in unemployment in Japan overthe 1990s is that there are two sources of fluctuations. Changes in TFP account for half of the21

Similar labor market changes have been argued as being responsible for the decrease in unemployment for Euro-pean countries with high unemployment rates (i.e. Siebert, 1997 and Blanchard and Wolfers, 2000).

18

increase in the unemployment rate, whereas the other half is due to the decrease in hours. In
this sense, our results also indicate the inability of the standard search and matching model tofully account for observed changes in unemployment only through TFP changes. However, in
our simulations, productivity movements explain 50% of the change in unemployment, whereas in
Shimer (2005), productivity shocks only explain around 5% of the volatility of unemployment. There
are two main reasons for this higher explanatory power in our model. The first is the size of thefluctuations in productivity. TFP growth declined in Japan for over a decade. This growth decline
had an effect of the path of TFP equivalent to a 11% decline in its stationary level. This drop in
detrended productivity is much larger than the fluctuations observed at business cycle frequencies,and especially than the 2% volatility of U.S. productivity reported by Shimer (2005). The second
reason is the existence of capital and labor taxes, which make wages less responsive to productivity
shocks through the same mechanism put forward by Hagedorn and Manovskii (2008), and in turnmakes unemployment more sensitive to productivity movements. Let us explain this mechanism
further.
Hagedorn and Manovskii (2008) show that if the difference between the productivity of theworker and the flow value of unemployment (p − z in their model) is very low, then wages become

very insensitive to productivity changes, and the vacancy posting behavior of firms becomes more
responsive to such movements. They claim that calibrating the flow value of unemployment to
be 40% of the productivity of the worker, as in Shimer (2005), is too low, and in their preferredcalibration they set that fraction to be 95.5%, i.e. zp = 0.955. Under their preferred calibration, theyshow that the basic search and matching model is capable of reproducing the observed volatilityof unemployment in the U.S. for reasonable movements in productivity22 . In our model, given theexistence of capital23 and taxes, the equivalent ratio to zp from the basic text-book model is different.
Here, firms need capital to produce output and must pay for its rental cost. These costs reduce theflow profits for the firm by a percentage equal to a share of capital rents in output, α = 38%. The
1−η
existence of labor taxes, τn , implies that the worker gets a fraction 1−τ
of the forgone flow valuenof unemployment, higher than 1 − η as in the basic search and matching model. Therefore, if we22

See Hagedorn and Manovskii (2008) for a more detailed explanation of the mechanism and the intuition behind

this result.
23
We also have an additive intermediate input cost, but it represents less than 3% of the flow profit of the average
firm.

19

look at our stationary wage equation, (25), the equivalent ratio to zp in our model isb1−τn.
Ãk̃ α h1−α − rk̃ − nxa(18)

Having capital rents and taxes in the model implies that even though we follow Shimer (2005) andset the stationary flow value of unemployment to be 40% of the productivity of the worker24 , theequivalent ratio to zp in our model, (18), is 94.75%. Hence, in our simulations, as in Hagedorn andManovskii (2008), unemployment is much more responsive to movements in productivity than in
Shimer (2005), which is why we can account for 50% of the movements in the unemployment rate25 .
Finally, although not shown in the figures for the sake of brevity, we have performed an alternative simulation of the model without capital and using the appropriate measure of productivity26 ,and have found that the model accounts only for 10% of the change in unemployment by the year
2002. This provides further evidence for the premise that it is the existence of capital which is
responsible for the better performance of our model compared to the basic textbook version.

7

Conclusions

During the 1990s, Japan suffered the biggest increase in unemployment of the post-war era. Underlying this rise in unemployment was an increase in the destruction of jobs relative to job creation.
24

As explained in the calibration, setting b = 0.4 · Ãf (k̃, h) implies a replacement ratio of 68%, which is consistent

with Japanese data.
25
Note that in our model the movement in productivity accounts for 50% of the change in unemployment, whereas inHagedorn and Manovskii (2008) productivity shocks produce slightly more unemployment volatility than in the U.S.
data. The reason that productivity changes only account for 50% of the unemployment changes is twofold. First, there
is no study that has analyzed whether the “Shimer-Hall” puzzle applies to the Japanese economy. Therefore, there
is no evidence of how much of the cyclical volatility of Japanese unemployment can be accounted for by technology
shocks using the standard search and matching model. Second, since we are looking at medium term changes in theeconomy, and not at fluctuations around a steady state, we assume that over time, the flow value of unemployment
also changes when productivity varies, as can be seen in equation (26). This assumption is consistent with theempirical evidence for Japan, where the replacement ratio decreased over the Lost Decade. This implies that in ourmodel, wages are not as insensitive as in Hagedorn and Manovskii (2008), where the flow value of unemployment isconstant. However they are much more insensitive than in Shimer (2005) for the reasons explained above; our model
therefore accounts for more than Shimer, but less than Hagedorn and Manovskii.
26
If capital is not present in the model, the empirically relevant measure of productivity is no longer TFP but
Youtput per unit of labor input, i.e. hN. The results of this alternative simulation are available from the authors uponrequest.

20

In this paper, we build, calibrate and simulate a neo-classical growth model with search frictionsin the labor market to try to account for the changes seen in the Japanese unemployment rate
and the flows of workers during the Lost Decade. In our simulations, we feed the path of actual
TFP, hours of work, and government expenditures from the data into the model, to not only assess
its ability to replicate the medium-run changes in the economy, but also the actual path of thevariables.
We find that the slowdown in TFP growth, together with the decrease in hours worked, canexplain the changes observed in the labor market. The reason for this is that the drop in TFP growth,which reduces detrended TFP, together with the fact that firms cannot work their employees formore hours, induces a reduction in firms’ profits in the model. This in turn makes it harder for firms
to keep workers and to hire new ones, increasing the probability for workers to lose their jobs andreducing the probability for unemployed workers to find jobs. In the model, these changes induceincreased unemployment and reduce output, as in the data.
Finally, we should note that while this paper studies the Japanese experience over the Lost
Decade, there is nothing specific to Japan or this period in our model and methodology. Hence, ourframework can be used to analyze other episodes of medium-run changes in the labor market andother macroeconomic variables.

21

References[1] Andolfatto, D. (1996), Business Cycles and Labor-Market Search, American Economic Review,86, 112-132.
[2] Ariga, K., F. Hayashi and C. Horioka (2006), Symposium on Macroeconomic Analyses ofJapan’s Lost Decade, Japanese Economic Review 57 (2), 157-359.
[3] Blanchard, O. and J. Wolfers (2000), The Role of Shocks and Institutions in the Rise ofEuropean Unemployment: the Aggregate Evidence, The Economic Journal 110, 1-33.
[4] Braun, R. A., T. Okada, N. Sudou (2006), U.S. R&D and Japanese Medium Term Cycles,
Bank of Japan Working Paper Series, 06-E6. Econometric Society 2007 North American WinterMeetings contributed paper.
[5] Braun, R. A., J. Esteban-Pretel, T. Okada, N. Sudou (2006), A comparison of the Japaneseand U.S. business cycles, Japan and the World Economy 18, 441–463.
[6] Caballero, R. J.; T. Hoshi, and A. K. Kashyap (2008), Zombie Lending and Depressed Restructuring in Japan, American Economic Review, forthcoming.
[7] Chen, K., A. Imrohoroglu, and S. Imrohoroglu (2006), The Japanese Saving Rate, American
Economic Review 96 (5), 1850-1858.
[8] Eggertsson, G.B. and M. Woodford (2003), The Zero Bound on Interest Rates and Optimal
Monetary Policy, Brookings Papers on Economic Activity 1:2003, George L. Perry and William
C. Brainard, eds., Brookings Institution Press 2003, 350pp.
[9] Fukao, K. and T. Miyagawa Eds. (2008), Seisansei to Nippon no Keizaiseichou (in Japanese:
Productivity and Japan’s Economic Growth), The University of Tokyo Press, Tokyo, 384 pages.
[10] Genda, Y. (1998), Job Creation and Destruction in Japan, 1991-1995, Journal of the Japaneseand International Economies, 12, 1-23.
[11] Hall, R. E. (2005), Employment Fluctuations with Equilibrium Wage Stickiness, American
Economic Review, 95 (1), 50-65.
[12] Hagedorn, M. and I. Manovskii (2008), The cyclical behavior of equilibrium Unemployment
and vacancies revisided, European Central Bank, Working Paper 853.
22

[13] Hayashi, F. and E. C. Prescott (2002), The 1990s in Japan: A Lost Decade. Review of Economic
Dynamics 5 (1), 206-235.
[14] Hayashi, Fumio and Edward C. Prescott. 2008. The Depressing Effect of Agricultural Institutions on the Prewar Japanese Economy. Journal of Political Economy 116 (4), 573–632.
[15] Hoshi, H. and D. W. Jorgenson Eds. (2005), Special Conference Issue: Enhancing Productivity,
Japanese and International Economies 19 (4), 457-654.
[16] Kuroda, S. (2005), Analysis of Changes in Japan’s Unemployment Rate Using Gross Flow
Data, Monetary and Economic Studies, 21 (1), 69-104.
[17] Krugman, P., (1998), It’s baaack: Japan’s slump and the return of the liquidity trap, Brookings
Papers on Economic Activity 2:1998, 137-205.
[18] Mendoza, E. G., A. Razin, and L. L. Tesar (1994), Effective Tax Rates in Macroeconomics:
Cross-Country Estimates of Tax Rates on Factor Incomes and Consumption. Journal of Monetary Economics 34, 297-323.
[19] Merz, M. (1995), Search in the Labor Market and the Real Business Cycle, Journal of Monetary
Economics, 36, 269-300.
[20] Mortensen, D. T. and C. A. Pissarides (1994), Job Creation and Job Destruction in the Theoryof Unemployment, Review of Economic Studies 61, 397-415.
[21] Ohtake, F. (2004), Structural Unemployment Measures in Japan, Japan Labor Review , 1 (2),26-53.
[22] Parente, S. L. and E. C. Prescott (1994), Barriers to Technology Adoption and Development,
Journal of Political Economy, vol. 102 (2), 298-321.
[23] Peek, J. and E. S. Rosengren (2005, )Perverse Incentives and the Misallocation of Credit inJapan, American Economic Review, 95 (4), 1144-1166.
[24] Shimer, R. (2005), The Cyclical Behavior of Equilibrium Unemployment and Vacancies, American Economic Review, 95 (1), 25-49.
[25] Siebert, H. (1997), Labor Market Rigidities: At the Root of Unemployment in Europe, Journalof Economic Perspectives, 11 (3), 37-54.
23

[26] Yamakawa, R. (2001), Labor Law Reform in Japan: A Response to Recent Socio-Economic
Changes, The American Journal of Comparative Law, 49 (4), 627-651.

24

A

Stationary Equilibrium
1tDefine γt as the growth rate of TFP, i.e. eγt = AAt−1, and the TFP factor as At1−α . To obtain thestationary equilibrium we use zt , which is a variable growing at the average growth rate of the TFPγ̄
factor along the balance growth path, 1−α. The growing variables in the economy can be rendered

stationary by deflating them by zt as follows:
Kt
Ct
kt
Tt
Yt
, K̃t ≡, C̃t ≡
, k̃t ≡ , T̃t ≡ .
zt
zt
zt
zt
zt
Since we assume that technology is labor augmenting, and given the functional form of the producỸt ≡Attion function, f (kt , ht ) = ktα h1−α
, we define detrended TFP as Ãt ≡ z 1−α= Ãt−1 e(γt −γ̄) . In thettsimulations, we normalize the initial value of technology to unity, i.e. A0 = Ã0 = 1. Finally, denote
1
1 x̄t
the average stationary wage, conditional on being productive, as w̃t ≡ G(x̄
wt (xt ) dG (xt ).
t ) zt xmin
We can define a perfect foresight stationary competitive equilibrium, for a given path of ex-∞
ogenous of TFP growth rate and hours {γt , ht }∞
t=0/, and government policy {τn , τk , ψt }t=0 , as a set.
∞
rt , w̃t , Ỹt , K̃t+1 , C̃t , k̃t , nt , ut , vt , θt , x̄t , xat , bt , βt , T̃twhich satisfy the following equations:t=0• Euler equation:

1=β

0

γ̄
C̃t − 1−αe
(1 + (1 − τk ) (rt+1 − δ))
C̃t+1

1

.

(19)

• Aggregate resource constraint:γ̄

(1 − ψt ) Ỹt = C̃t + K̃t+1 e 1−α − (1 − δ) K̃t − (1 − nt ) bt + φvt + nt xat .
• Aggregate output:(20).
Ỹt = Ãt−1 e(γt −γ̄) nt k̃tα h1−αt(21)K̃t = nt k̃t .

(22)• Aggregate capital:• Optimal capital rental choice for the firm:
rt = αÃt−1 e(γt −γ̄) k̃tα−1 h1−α
.
t

(23)

• Average intermediate input cost in productive matches:xat =1G (x̄t )
25

(x̄t

xmin

xt dG (xt )(24)• Optimal wages:

2
3− rt k̃t − nt xat + φθt + (1 − η)w̃t ht = η Ãt−1 e(γt −γ̄) k̃tα h1−αtbt
1 − τn(25)• Value of home production/leisure:bt = λÃt−1 e(γt −γ̄) k̃tα h1−αt(26)

• Creation condition:
0 = −φ + βt µθtξ
• Destruction condition:

54γ̄
1 − η 1−αeG (x̄t+1 ) x̄t+1 − xat+1 .
1 − ητn−rt k̃t −τn w̃t ht −bt +βtx̄t = Ãt−1 e(γt −γ̄) k̃tα h1−αt+

1 − τn1 − µθt1+ξ η
1 − ητn

,

(27)

5
4
γ̄
e 1−α G (x̄t+1 ) x̄t+1 − xat+1 .
(28)• Evolution of unemployment and employment:231+ξ
ut = 1 − µθt−1
G (x̄t ) ut−1 + [1 − G (x̄t )] nt−1 ,nt = 1 − u t .
• Market tightness:βt = β

(30)

vt
.
ut

(31)

γ̄
C̃t − 1−α
e
.
C̃t+1

(32)

θt =

• Stochastic Factor:(29)• Government budget constraint:ψt Ỹt = τn w̃t nt + τk (rt − δ) K̃t + T̃t

26

(33)

Table 1: Model Parameters
β = 0.9957

τn = 0.28

τk = 0.44

α = 0.383

δ = 0.028γ̄ = 0.015

η = 0.5

ξ = 0.5µ = 0.42

χ = 0.041

φ = 0.037

λ = 0.4

Figure 1: Japanese Labor Market Empirical Evidence during the 1990s(b) Quarterly Prob of Finding and Lossing Job!

(a) Unemployment Rate!

Percent!

4.5!

3.0!

1.5!
1990!

1992!

1994!

1996!

1998!

2000!

50!

2.0!

40!

1.6!

30!

1.2!

20!

0.8!

10!
1990!

2002!

Prob. of Lossing Job (percent)!

Prob. of Finding Job (percent)!

6.0!

1992!

1994!

1996!

1998!

Prob. of finding job!

(c) Total Number of Workers Finding and Lossing Job !

2000!

0.4!
2002!

Prob. of lossing job!

(d) Hours per Week!

(as Percentage of the Labor Force)!
2.0!

44!

Percent!

1.7!

42!

1.4!
40!
1.1!
38!

0.8!
0.5!
1990!

1992!

1994!

1996!

Workers finding job!

1998!

2000!

36!
1990!

2002!

1992!

1994!

1996!

1998!

2000!

2002!

Workers lossing job!

(e) Detrended Wages!

(f) Total Factor Productivity!

(1990 = 100)!

(1990 = 100)!

110!

120!

100!

110!
100!

90!
90!
80!
80!
70!
1990!

1992!

1994!

1996!

1998!

2000!

70!
1980!

2002!

27

1985!

1990!

1995!

2000!

2005!

Figure 2: Data and Simulation’s Output, Unemployment Rate and Wages(a) Unemployment Rate!
6.5!

Percent!

5.5!
4.5!
3.5!
2.5!
1.5!
1990!

1992!

1994!

1996!

Data!

1998!

2000!

2002!

Model!

(b) Detrended GNP per Person!

(c) Detrended Wages!

(1990 = 100)!

(1990 = 100)!

105!

110!

100!
100!
95!
90!
90!
80!

85!
80!
1990!

1992!

1994!

1996!
Data!

1998!

2000!

70!
1990!

2002!

Model!

1992!

1994!

1996!
Data!

28

1998!
Model!

2000!

2002!

Figure 3: Data and Simulation’s Flows In and Out of Unemployment(b) Quarterly Prob of Lossing Job!

(a) Quarterly Prob of Finding Job!

45!

35!
Percent!

Percent!

2.0!

25!

1.6!
1.2!
0.8!

15!
1990!

1992!

1994!

1996!

1998!

2000!

0.4!
1990!

2002!

Model!

1994!

1996!

1998!

2000!

(d) Total Number of Workers Losing Job !

(as Percentage of the Labor Force)!

(as Percentage of the Labor Force)!
2.0!

1.7!

1.7!

1.4!
1.1!
0.8!

2002!

Model!

(c) Total Number of Workers Finding Job !

2.0!

0.5!
1990!

1992!

Data!

Percent!

Percent!

Data!

1.4!
1.1!
0.8!

1992!

1994!
Data!

1996!

1998!

2000!

0.5!
1990!

2002!

1992!

1994!
Data!

Model!

29

1996!

1998!
Model!

2000!

2002!

Figure 4: Data and Simulation’s Unemployment Rate under Different Future Paths of TFP
Unemployment Rate!
10.0!

8.0!

Percent!

6.0!

4.0!

2.0!

.0!
1990!

1992!

1994!

1996!

1998!

2000!

2002!

2004!

2006!

2008!

2010!

2012!

Alternative simulation: 1.9% TFP growth in balance growth path!
Baseline Simulation: 1.5% TFP growth in balance growth path!
Data!

30

2014!

2016!

Supplemental Appendix(Not intended for publication)
We include this supplemental appendix to provide additional information on some of the statements made in the parametrization and discussion sections of the paper.

A

Alternative Values of η and ξ

Here we present the simulation results for the unemployment rate when we simultaneously vary thebargaining power of the worker, η, and the elasticity of matching with respect to unemployment, ξ.
Figure 5: Data and Simulation’s Unemployment Rate under Different Values of η and ξ
Unemployment Rate
6.0

Percent

5.0

4.0

3.0

2.0

1.0
1990

1992

1994
Data

1996

Baseline model

1998
eta = 0.4, xi = 0.4

31

2000
eta=0.6, xi=0.6

2002

B

Alternative Values of λWe now show the results when we vary the ratio of the flow value of unemployment to the marginal
product of labor, λ. Note that a value of λ = 0.11 is equivalent to setting the ratio of zp in Shimer(2005) to 0.4. We can see in Figure (6) that for the case of λ = 0.11 unemployment increases by less,as we would expect, given the arguments in Shimer (2005) and Hagedorn and Manovskii (2008).
Figure 6: Data and Simulation’s Unemployment Rate under Different Values of λUnemployment Rate
6.0

Percent

5.0

4.0

3.0

2.0

1.0
1990

1992

1994
Data

1996
Baseline model (lambda=0.4)

32

1998

2000
Lambda=0.11

2002

C

Model with no Capital and Simulations with Constant Hours

In the main text of the paper we state that TFP growth changes alone can account for 50% of thechanges in the unemployment rate from 1990 to 2002. Furthermore, we state that the model withno capital and only changes in TFP growth accounts for 10% of the changes in unemployment. Here
we show the results for those two alternative simulations of the model.
Figure 7: Data and Simulation’s Unemployment Rate under Different Model and Shocks Specifications

Unemployment Rate
6.0

Percent

5.0

4.0

3.0

2.0

1.0
1990

1992

1994

1996

1998

2000

Data

Baseline model

Model with capital and constant hours

Model with no capital and constant hours

33

2002