Discussion Papers In Economics
And Business

A Welfare Cost of the Lost Decade in Japan

Tatsuyoshi Miyakoshi and Masakatsu Okubo

Discussion Paper 07-27

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANA Welfare Cost of the Lost Decade in Japan

Tatsuyoshi Miyakoshi and Masakatsu Okubo

Discussion Paper 07-27

June 2007
この研究は「大学院経済学研究科・経済学部記念事業」
基金より援助を受けた、記して感謝する。
Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANA Welfare Cost of the Lost Decade in Japan
by
Tatsuyoshi Miyakoshi a* and Masakatsu OkubobabOsaka School of International Public Policy,Osaka University

Graduate School of Systems and Information Engineering,University of Tsukuba
Abstract

This paper measures the welfare cost of the Japanese economy in a ‘lost decade’ from 1990
to 2002, by using panels of different consumer groups. This paper finds that the costs for
consumers in the lower and middle income quintiles and in urban districts are much higher,
while it is a benefit for consumer in rural districts. This paper suggests that such costdisparities express the defects related to districts and income quintile group with high costs.
Also, there exist consumers feeling this stagnation to be costless and the seriousness ofstagnation are not recognized unanimously.

Keywords: welfare cost; a lost decade of Japanese economy; Lucas model
JEL Classification Number:E32;E60;E20
Correspondence: Tatsuyoshi Miyakoshi

Osaka School of International Public Policy, Osaka University
1-31, Machikaneyama-machi, Toyonaka,Osaka, 560-0043, Japan.
tel:+81-6-6850-5638; fax:+81-6-6850-5656, E-mail: miyakoshi@osipp.osaka-u.ac.jp* Earlier versions of this paper were presented at Osaka University and Hitotsubashi University in
2003, City University of Hong Kong and Tokyo University in 2004, 2004 Western Regional Science
Association Conference (in Hawaii), 2004 Western Economic Association Conference (inVancouver), 2004 East Asian Economic Association Conference (in Hong Kong). We thankKenneth S. Chan, Makoto Saito, Yum K. Kwan, Yong Wang, Eiji Ogawa, Yoshiro Tsutsui, Yuzo
Honda, Shinsuke Ikeda, Soyoung Kim, and Joshua Aizenman for useful suggestions. The firstauthor’s research was supported by Grant-in-Aid 16530204 from the Ministry of Education, Culture,
Sport, Science, and Technology of Japan.

1. Introduction
The Japanese stagnation has continued for a long time and seems to have become worse
recently. Average annual real GDP growth rates were 10.4% in the 1960s, 5.0% in the
1970s, 3.8% in the 1980s, but only 1.7% in the 1990s and only 1.8% in the 2000s(2000–2004).1 These figures suggest that the stagnation of the 1990s and the 2000s is thelongest and deepest of the last fifty years.
Such a long stagnation is a big turmoil in academics as a “lost decade” of Japanese
economy. In general, the research for the cause of this stagnation has two strands. As a firststrand, Kwon (1998), Ogawa and Suzuki (1998),Bayoumi (1999) and Miyakoshi and
Tsukuda (2004), while different a little in a methodology, concluded that fluctuations inasset prices affected output through bank lending. Meltzer (2001) argued that a decline inmoney growth caused the recession in early past of the decade while a decline in exports
caused the recession in the later part of the decade. Motonishi and Yoshikawa (1999) foundthat real factors were principally responsible for sluggish investment in the period
1992-1994, but the credit crunch appeared after then and lowered the growth rate of GDP
by 1.6%. As a second strand, Hayashi and Prescott (2002) stressed that the problem is not abreakdown of the financial system, but a low productivity growth rate, and that research
efforts should be focused on what policy changes will allow productivity to again growrapidly. Morana (2004) and Jorgenson and Nomura (2005), while using different analyticalframeworks, find that the productivity shock explains the bulk of output fluctuation both in
the short- and the long-terms, supporting the Hayashi and Prescott’s hypothesis.
The Japanese economy is still in a long stagnation at around 1% growth rate. It isnecessary to add more fact findings on stagnation, in order to analyze the mechanism and to

1

See Annual Report on National Accounts of 2005, Cabinet Office, the Government of Japan.

1find appropriate policy for stagnation. Until now, the cost of stagnation has typically beenmeasured by reductions in GDP growth and other similar economic indicators. Whereas
producers and firm managers have strong concerns about such cost measures, consumers
generally do not. Since such measures are not directly related to welfare costs, consumers
are not strongly concerned about these costs. It is interesting to use welfare costs measure
to do fact findings. Most previous researches use aggregate data, while the disaggregate
data such as district and income quintile group show the influence of stagnation on different
people. Then, the detail information for stagnation will be obtained. However, to ourknowledge, there have been few attempts to calculate the welfare cost of stagnation and touse disaggregate data.
The purpose of this paper is to measure the welfare cost of the Japanese economy in a‘lost decade’ from 1990 to 2002, by deploying a Lucas-Obstfeld model with panels ofdifferent consumer groups (incorporating five income quintiles and nine districts groups).
This paper finds that the costs for consumers in the lower and middle income quintiles andthose in urban districts are much higher, while it is a benefit for consumer in Shikoku
district. This paper suggests that such cost disparities express the defects related to districts
and income quintile group with high costs: Kanto and Kinki districts and the group of about
less than 4 millions yen. Also, the paper suggests that there exist consumers feeling thisstagnation to be costless and the seriousness of stagnation are not recognized unanimously.
This welfare cost measure was provided by Lucas (1987) and developed by Obstfeld(1994), Saito (1996), Dolmars (1998), Storestetten,et.al. (2001),Beaudry and Pages (2001)
and Pallage and Robe(2003) to measure the cost of the economic instability.2 They
measured both compensations that would leave consumers indifferent to a decline in the2

A useful survey of this field is Lucas (2003).

2

economic growth rate and to an increase of economic instability. However, their concern
was only with the latter compensation. On the other hand, Miyakoshi, Okubo and Shimada(2006) call both compensation as a ‘welfare cost of stagnation’ and their model as a
‘Lucas-Obstfeld model’, and have explored the practical use of meaning this cost. 3
This paper is organized as follows. In Section 2, we review Lucas- Obstfeld model. In
Section 3, we describe the data set and the statistical methodology used for estimating theparameters. In Section 4 and 5, we estimate the costs of stagnation, discuss the estimatesand implications of the results. In Section 6, we calibrate the model and check therobustness of the results. Section 7 concludes the paper.

2. Lucas-Obstfeld Model
We sketch the Lucas-Obstfeld model, while details of derivations are given in Miyakoshi,
Okubo and Shimada (2006). The representative agent lives infinitely and maximizes an
expected utility function V by choosing real consumption Ct at time t . The agent has apreferences specified by:⎤⎡∞
1
V = E ⎢∑ β t
Ct1−γ ⎥ ,1−γ⎦
⎣ t =03(1)Moreover, they propose an alternative measure to the Lucas–Obstfeld model to analyze
the welfare costs of stagnation. Compared with the Lucas–Obstfeld model, the alternativemodel can evaluate: (i) whether the policy was implemented in a timely fashion, (ii)whether the policy cost was expensive compared with the cost of stagnation, and (iii)
whether the policy implemented was effective or whether an additional policy is required.
These specific exercises cannot be carried out under the existing frameworks, including the3

where β∈(0,1) is a constant discount factor and γ>0 is the constant coefficient of relativerisk aversion. Here, we consider a pure exchange economy with no production, no storable
goods and no borrowing. Then, the optimal consumption Ct for an agent is subject toexogenous income It in each period and hence is equal to income: Ct = It for all t.
Lucas and Obstfeld assume a class of exogenous income. Hence, the optimal
consumption streams Ct with trend and cycle components, are given by:

Ct = λ (1+ µ ) e
t

1
− σ2
2

zt ,

1
i. e., ln Ct = ln λ - σ 2 + t ⋅ ln (1+ µ ) + ln zt : ln zt ~ N (0,σ 2 )2(2)where µ is the growth rate of consumption and ln zt ~ N(0, σ2). In addition, Lucas andObstfeld assume that an agent has rational expectations, which implies that an agent knows
those moments of the consumption distribution, and then maximizes an unconditional
expectation of utility (1): the subscript of time t is not attached on V in (1). Owing to theproperty of the log-normal distribution, E(zt•exp(–σ2/2)) = 1, the mean consumption is:

Et (Ct ) = λ (1+ µ )t ,(3)

where the mean consumption at t = 0 is λ.
Thus, Lucas and Obstfeld assumed that the stagnation process of exogenous income(consumption) can be expressed by constant moments over time of the distribution ofLucas–Obstfeld model.
4consumption, λ, µ, and σ2, and that an agent has rational expectations.
Under the above setup, we can calculate the indirect utility given the consumption
process described by (2) and denote it by V(λ, µ, σ2|γ,β). This is derived as follows:

V (λ, µ,σ 2 | γ , β ) =1γ⎧⎫exp⎨(1− γ )(ln λ − σ 2 )⎬ if φ < 1,
(1− γ )(1− φ )
2
⎩
⎭
(4)

φ = exp{ln β + (1− γ ) ln(1+ µ)}.

We consider two economies. One is called the stagnation economy, in which consumption
growth µ s and its variance σs2 are calculated based on the data in the stagnation period. We
denote the resulting indirect utility as V( λ S , µ S , σ S2 | γ , β ) . The other economy is called
the hypothetical economy (i.e., the economy without stagnation), which is based on
expected consumption under the assumption that the growth rate and the variance in theprestagnation period are maintained during the stagnation period. The resulting indirect
utility is V( λ H , µ H , σ H2 | γ , β ) . The intuition behind this comparison is shown in Figure 1.
Owing to (3), the λH is mean consumption at the beginning of the stagnation period for the
hypothetical economy. Thus, we compare both economies from the beginning of thestagnation period (denoted by t = 0 in Figure 1). Although γ and β may differ between theprestagnation and stagnation periods, we assume that they remain constant over time at(γ , β ) .

[INSERT Figure 1]

5Based on the indirect utilities under these economies, we define the cost of stagnation
as follows.

Definition 1. The cost of stagnation is given by λ*, which satisfies the following equation:

V (λS + λ*, µS , σ S2 | γ , β ) = V (λH , µ H ,σ H2 | γ , β ) ,(5)where the subscripts S and H denote the stagnation and hypothetical economy,
respectively.4 The cost implies the compensation from the beginning of stagnation to the
future.
Then, the cost of stagnation λ* is given by:

λ* = exp{Ψ} − λS ,
Ψ=⎫1 ⎧ 1 - φS
) + (1− γ )(ln λH − γσ H2 /2)⎬ + γσ S2 /2 , (6)⎨ln(
1 − γ ⎩ 1- φH
⎭

where

φS = exp{ln β + (1− γ ) ln(1+ µS )} and φH = exp{ln β + (1− γ ) ln(1+ µ H )}.

To calculate the costs of stagnation, we proceed as follows. First, we decide the4

The key concept relating to the cost of stagnation is the following. The consumption
parameters are different between the stagnation and the hypothetical economies. Consumer
preferences, given by ( γ , β ) , transform the difference in consumption parameters into a
difference in utility levels. The cost of stagnation is measured by the compensation required
to leave consumers indifferent between the two economies.

6

beginning of the stagnation period and then partition the whole period into two periods: thepre-stagnation and the stagnation periods. Second, the preference parameters (γ,β) of (1) are
decided based on the previous researches for the Japanese economy, the parameters (λ,µ,σ2)of (2) for both economies are estimated by the Maximum Likelihood (ML) and we computethe costs, which are reported in Tables 1 and Table 2. Third, we measure the costs ofstagnation in different income quintiles and districts, which are reported in Tables 3 and 4.
Fourth, we calculate these costs for varying values of the parameters (γ,β) to check therobustness of the results. These results are reported at the last panels of Table 3 and Table 4.

3. Data and Estimation Methods
Data
The data used in this paper are monthly data from January 1975 to August 2002 (i.e.,
1975:M1 to 2002:M8), which gives 332 observations. To estimate the parameters (λ, µ, σ2)
for consumption in the model, we use total consumption expenditure for workers’
households from the Monthly Report on Family Income and Expenditures Survey (FIES).
As the FIES reports nonseasonally adjusted data, we apply the census X-11 method to
obtain the seasonally adjusted series. The per capita series is constructed by dividing
consumption expenditure by the number of family members in the household. These data
are converted to real values by using the consumer price index (for general prices in 2000)
from the Monthly Report of the Consumer Price Index. All data are taken from the NIKKEINEEDS CD-ROM.
We partition the whole sample (1975:M1 to 2002:M8) into two subsamples. The
first subsample (a pre-stagnation period) is from 1975:M1 to 1989:M12 and the second (thestagnation period) is from 1990:M1 to 2002:M8. Our objective is to estimate the cost of
stagnation economy during the stagnation period by comparing it with the hypothetical7

economy. This partition of periods is supported by Miyakoshi, Okubo and Shimada (2006)
where some historical events are shown and a structural break is tested by using Perron(1989,pp.1380).5 They also reject the null hypothesis of unit root for consumption with abreak point, supporting the stationality of data.

Preference Parameters
A large empirical literature has been devoted to estimating the coefficient of relativerisk aversion and the discount factor. However, it seems fair to say that there is no complete
consensus on their values; in particular, it is difficult to specify what value of the relative
aversion coefficient is. (see, e.g., Nakano and Saito (1998) and Hamori (1998)). Following
convention, therefore, we adopt a strategy that sets the preference parameters exogenously
within some range. In this paper, as a base value, we use 0.996 for β and 2.5 for γ as in
Miyakoshi, Okubo, and Shimada (2006). To check robustness of the base result, we also
try γ = 0.5, 1.5, 3.5, 5.0, which encompass the range of parameter values used in previous
research. Since it is recognized that the estimates of the discount factor are relatively stable,
the discount factor is fixed at the base value for ease of comparison.

Estimated Consumption Parameters

5

They show that this partition of periods is consistent with previous research including
Hayashi and Prescott (2002). They suggest that stagnation began in 1990:M1 because the
NIKKEI 225 peaked at a stock price of 38,926 yen in 1989:M12. Since that date, it has fallen
gradually, as has the price of land. These events are said to define the collapse of the so-called
Japanese bubble economy. In line with previous research, we maintain the importance of these
events in defining the starting point of stagnation. Figure 2 plots consumption in logs, which shows
the behavior of the data in the model. It suggests a trend break in the log of consumption (which
reduces consumption growth) around 1990:M1. These figures suggest an obvious structural change.

8The parameters for consumption in a pre-stagnation period (1975:M1-1989:M12) and astagnation period (1990:M1-2002:M8) are estimated by applying a ML methodology to thewhole sample from 1975:M1 to 2002:M8:

1
lnCt = ln(λH (1− DUt ) + λS DUt ) − (σH2 (1− DUt ) +σS2DUt )2+ t ⋅ ln(1+ µH (1− DUt ) + µS DUt ) + lnzt :lnzt ~ N(0,σ (1− DUt ) +σ DUt )
2
H

(9)

2
S

where DUt=1 if t>TB (that is, TB=1989:M12) and 0 otherwise. All parameters can be
identified by being included in the variance of the distribution. Miyakoshi, Okubo andShimada (2006) have already supported the normality of ln zt. They have also showed thatthe parameters in both the prestagnation and the stagnation periods are estimated anddenoted as the estimated parameters for the hypothetical economy and the stagnation
economy. The exception is an estimate for λ in a hypothetical economy, which is replacedwith one for a stagnation economy. The values are shown in Panel (B) of Table 1 in thispaper. An agent perceives that the estimated parameters in both periods are the consumption
parameters for both economies. All parameter estimates for consumption are statisticallysignificant at the 1% level. The estimated monthly consumption growth rate falls from
0.1059% in the pre-stagnation period to –0.002018%. The variance (which represents
instability) of the error term in the log of consumption increases from 2.339E(-4) to
3.927E(-4). The difference in consumption growth and variance between both economies isalso statistically significant at 5 % level, as is shown in Panel (C) of Table 1. The λH for the
hypothetical economy, an estimated consumption for 1990:M1 (out-of-sample) by using theestimated parameters during the pre-stagnation periods, can be available. However, for thesake of simplicity, we reset the λH equal to λS.

9[INSERT Figure 2 and Table 1]

Estimated Cost
What is the estimated cost of stagnation according to this model? As Table 2 shows,by using these parameters in equation (5), we obtain a utility level of -3.813E(-06) for the
hypothetical economy and one of -5.362E(-06) for the stagnation economy. This implies thatthe stagnation reduces utility. Our cost measure λ* enables us to convert the reduction in
the utility level into a level of compensation in Japanese yen. The cost of stagnation is25,390 yen. The cost ratio (cost/λH) is the ratio of the cost to the consumption of the
hypothetical economy at the starting period. It is 26%, which shows the relative amounts
and hence an actual impact.
To check the robustness of the results, we calibrate the preference parameters in (1).
Note here that γ>0 implies risk aversion. The costs and the ratios of costs range from
20,257 yen to 33,180 yen and from 20% to 33% as γ decreases. These findings werealready shown theoretically in Miyakoshi, Okubo and Shimada (2006) as follows:∂ λ∗ / ∂ β > 0, ∂ λ∗ / ∂ γ < 0if µ H > µ S ,∂λ∗ / ∂ β < 0, ∂λ∗ / ∂γ > 0 if µ H < µ S ,

(10)

and

∂λ∗ / ∂µ H > 0, ∂λ∗ / ∂µ S < 0, ∂λ∗ / ∂σ H < 0, ∂λ∗ / ∂σ S > 0.

(11)

Thus, the proposed welfare cost measure λ*, which is particularly relevant to
consumers, suggests that the cost of stagnation is large for Japanese consumers. As thisrepresents what people are willing to pay to prevent the outbreak of stagnation, it indicates
10that people were prepared to pay a great deal to avoid the stagnation.

[INSERT Table 2]

4. Welfare costs of workers’ households in different categories

Most of investigations for workers’ household in Section 3 are already implemented by
Miyakoshi, Okubo and Shimada (2006). However, in this section, by using these methods
and comparing with these results, we measure and evaluate the welfare costs of workers’
households in different categories. Considering the stationarity, the date of structuralchange, the normality of stochastic term of (9) for workers’ household consumption data,
we assume that consumption data in different categories satisfy these conditions.
Figure 3 plots the consumption series for workers’ households in five income quintile
groups. For example, the five income quintiles observed in 2002 are (in millions of yen peryear): less than 4.56; from 4.56 to 6.03; from 6.03 to 7.62; from 7.62 to 9.79; and greaterthan 9.79. The same household will belong to some income quintile in the current year andto another quintile in the subsequent year. We suppose that the household changes thepreference and consumption parameters from one year to the next, depending on the
different income quintile. We evaluate the changes in these consumption series.

[INSERT Figure 3]

Panels (A) and (B) of Table 3 report the estimated consumption parameters (λ, µ, σ2)and the base preference parameters (γ, β) for each income quintile. By using theseparameters, we evaluate the difference in consumption between the hypothetical and thestagnation economies. The larger the difference in consumption parameters between two
11

economies and the smaller the associated preference parameters γ, the higher the costs ofstagnation are, as theoretically suggested by (10) and (11).
There is substantial variation in the differences in (µ, σ2) between the five income
quintile groups. The differences in (µ, σ2) between the stagnation and the hypothetical
economies are (–0.00129, –0.00161) for the first group and (–0.00125, 0.00078) for the
fourth group, respectively. The negative difference of µ and the positive difference σ2enlarge the costs, as shown in (11). These differences are computed from the figures inTable 3. However, for the same preference parameters (0.996, 2.5) for the first and fifthgroups, the differences in consumption parameters are associated with higher costs ofstagnation (i.e., 20,637 yen and 28,721 yen). The cost, 20,637 yen, is less than that for
consumers in the upper income quintile. However, the costs of 20,637 yen and 28,721 yen
are 29% and 22% of the initial levels of consumption λH=71,427 yen andλH=133,232 yen,prevailing in 1990:M1. Hence, in percentage figures, the cost for the first group is higher
than the cost for the fifth group. Thus, there are large differences in the costs of stagnation
for consumers in different income quintile groups: the lower and middle group with larger
costs; the upper group with smaller costs. The cost 26% for an average worker seen in
Table 2 locates between second and third groups in Table 3, irrespective to the values of γ.
These findings are supported by Figure 3, which shows that consumption growth increases
and decreases more for the first and fifth groups in both sub-periods, respectively.

[INSERT Table 3 and Table 4]

Similar investigations are applied to the cost for consumers living in different districts.
As Panel (C) (γ=γ*, β=β*) of Table 4 shows, the costs for consumers living in rural districts
such as Hokkaido (8,180 yen, or 9% to initial consumption λH), Shikoku (–5,000 yen, or
12-7%) and Kyusyu (5,586 yen, or 6%) are low. In fact, consumers in the Shikoku district
benefited during the stagnation period. By contrast, the costs for consumers in urban
districts such as Kanto (47,772 yen, or 42%) and Kinki (28,642 yen, or 28%) are high. Thus,
there are large costs differences for consumers living in different districts.

5. Implications of the Results

High costs are attributable to a large decrease in the growth rate µ and the associatedsmall γ and large β preference parameters, as suggested by (10) and (11). Why does theconsumption growth rate µ for these groups decrease more than it does for those in theupper income quintile and those in rural districts? This is an interesting question for future
research.
However, we briefly consider the implication of the results. (i) The higher costsuggests the serious defect of work situation around these consumers. Miyakoshi and
Tsukuda (2004) find that regional disparities in banking performance made a substantial
contribution of regional disparities of economic growth: the bad (good) performance inurban (rural) districts caused to its low (high) economic growth. We provide the same
results for economic growth, though we did not investigate the causes in this paper. On theother hand, the Gini coefficient provides one of measures for inequality. However, even
without any significant Gini change, there is a statistical reason to worry. If individuals are
re-binned by income every month, then should not one expect to see people in the lower
income quintile to do worse, consumption-wise, than people who are doing relatively better,
income-wise? The welfare cost for consumer in lower income quintile express consumer to
do worse. In fact, the Japanese Gini coefficient for redistributed income is every three years
0.3455 in 1975, 0.3381 in 1978, (0.3143, 0.3426, 0.3382), 0.3643 in 1990, (0.3645, 0.3606),13

0.3814 in 1999, 0.3812 in 2002. The data source is called “Shyotoku Saibunpai Chyosa
Houkoku-shyo (in Japanese)”at
http://wwwdbtk.mhlw.go.jp/toukei/kouhyo/indexkk_6_3.html., in the Statistical Database,
The Ministry of Health, Labor and Welfare of Japan. In particular, the coefficient increases
from 1990, while it does not show the great increase. However, the consumers in the lowest
income group do worse and pay the cost ratio of 29%, compared with the 22% in thehighest income group. (ii) The regional and income quintile disparities for the welfare costs
suggest that there exist consumers feeling this stagnation to be costless and the seriousnessof stagnation are not recognized unanimously.

6. Robustness of Costs in Different Categories

We calibrate the model by using γ = 0.5, 1.5, 3.5, 5.0 and the estimates of β for consumers
in different categories, as in the previous section. We check the robustness of the effects byusing different values of γ. We focus on this cost ratio. The results are shown in Tables 3
and 4. The smaller the value of γ, the larger the cost ratio for the first group (lower income
group) is. The cost ratio in the first group account for 29% when γ = 2.5, while those in thefifth groups account for less than 27% for all γ. Thus, higher cost ratios appear in lower or
middle income groups, while lower cost ratios appear in the upper income quintiles,
approximately independently of the value of γ.
Similarly, we check the robustness of the costs in different districts when the value of
γ is the same for consumers in each district. For almost values of γ, Kanto, Kinki and
Hokuriku remain the highest cost districts, while Hokkaido, Kyusyu and Shikoku remain
the lowest cost districts, since the order of magnitude for cost does not change for all γ.
Moreover, the highest cost -5% (for γ = 5) of the low-cost districts exceeds the lowest cost
35% (for γ = 5.0) of the high-cost districts. Hence, costs for consumers living in the urban
14districts are high, and are low for those in the rural districts, approximately independentlyof the value of γ.
When the economic prospects of a locality permanently worsen, one expects that atleast some people who live there will try to relocate. If so, are those who stay the ones who
are at least able to move- and thus are likely to fare the worst? Or, to the contrary, are those
who move those who need it the most –in which case, those saving are likely to be left
relatively unscathed? Thus, if it turns out that these groups’ compositions did not remain
constant during or across the sample periods, such an analysis is flawed. The same problem
remains for the income quintiles. Due to the data ability, we focus on the regional disparityof welfare costs and have to confirm the population to be low mobile among regions during
the pre-stagnation and the stagnation periods. As Figure 5A shows, the ratios of the internalmigration for a whole Japan decreases gradually from 1975 when we start to investigate
compared with the previous years, suggesting the low mobility of population which support
the groups’ compositions remain constant. Also, as Figure 5B shows, the net internalmigration for Tokyo, Nagoya and Osaka Area which mostly correspond to the Kanto, Tokaiand Kink districts, decrease gradually to zero from 1975. Though the numbers of
in-migrants and out-migrants are not so small, the net migrant do not increases and then it
will not change the composition of people with large costs. As Figure 5C shows, the netinternal migration for each prefecture in Shikoku district increases from 1990, while mostof the in-migrants from other prefectures and out-migrants to other prefectures indicate themobile within the Shikoku district. We may consider that the groups’ compositions did
remain constant during or across the sample periods.

7. Concluding Remarks

This paper has calculated the cost of the Japanese long stagnation (so-called the lost decade15

of the Japanese economy) beginning in January 1990. We found that the cost of stagnation
for consumers is high at 25,390 yen, 26% of the consumption at the starting period ofstagnation (99,373 yen), per month. In particular, the cost ratio of stagnation for consumers
in lowest and middle income quintiles (Group1,3,4) and for consumers living in urban
districts (Kanto) are the highest: in detail, at different district category, Hokkaido(9%);Tohoku(12%);Kanto(42%);Hokuriku(22%); Tokai(18%); Kinki (28%);
Chugoku(25%);Shikoku(-7%);Kyushu(6%), at different income category; lowest
income(29%);second lower(23%);third (32%);fourth (30%);fifth(22%).
The higher cost suggests the serious defect of work situation around these consumers.
The high cost is due to the good economic condition in a pre-stagnation period or the bad
economic condition in a stagnation period. In general, the consumers in urban district andlow income quintiles are in this case. Also, the regional and income quintile disparities forthe welfare costs suggest that there exist consumers feeling this stagnation to be costlessand the seriousness of stagnation are not recognized unanimously. As the welfare costs ofstagnation equal to the costs that people are willing to pay to prevent the stagnation, theconsumers in low income quintiles and in urban district are easier to agree the high policy
cost, compared with their own welfare costs.
We did encounter at least one problem. We include the period of the Japanese bubble
economy (1985 to 1989) into the pre-stagnation period when we set up the hypothetical
economy (without the stagnation) as a base economy. However, the Japanese bubble
economy may not be a base economy. The problem is expected to be resolved in the future,but our approach is a first trial for understanding the costs of stagnation.

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18

Table 1. Estimated Parameters for Consumption.
(A) Utility Parameters(B)Consumption Parameters

H-ECO & S-ECO
λ
γ*
β*

2.5

µ

H-ECO

S-ECO

99373 yen

99373 yen(619.43)(619.43)1.059E(-3)–2.018E(-5)(101.91)(-3.33)2.339E(-4)

3.927E(-4)(10.95)(11.50)σ2

0.996(C) Test Hypotheses
Hypothesis

χ2(1)H1: µH=µS,8049.48

H2: σ2H=σ2S,

15.54

Notes: E(-0X) means 10-X . H-ECO and S-ECO denote the hypothetical and the stagnation
economies, respectively. The λ is consumption in yen in 1990:M1 for both economies. The criticalvalue of χ2(1) distribution is 3.84 at 5% level. See Miyakoshi, Okubo and Shimada (2006: Table
2B). The numbers in parentheses (..) denotes t-values.

Table 2. Costs of Stagnation (Aggregate) and Ratios of Cost
ModelsIndirect Utility
H-ECO

Costs of Stagnation

S-ECO
λ* (¥ yen) λ* /λH (%)γ=γ* β = β*–3.813E(–06)–5.362E(–06)

25,39026

γ= 0.5 〃181,567

157,237

33,18033

γ= 1.5 〃–1.401–1.59028,61029

γ= 3.5 〃–1.938E(–11)–3.256E(–11)

22,96823

γ= 5.0 〃–3.126E(–19)–6.557E(–19)

20,25720

Note: λ* /λH denotes the ratio (%) of cost λ* to consumption λH in yen in 1990:M1. See notes ofTable 1.

19

Table 3. Cost of Stagnation (Income Quintile Groups)
Economy Group 1

Group 2

Group 3

Group 4

Group 580,154

99,059109,051

133,232

71,42780,1540.00137 0.00112(24.01) (44.34)
0.00008 0.00012(7.43)(15.84)0.00277 0.00093(14.12) (10.08)

99,0590.00104(50.95)–0.00023(-22.64)0.00074(10.40)109,0510.00119(72.17)–0.00006(-5.02)0.00059(11.87)133,232
0.00088(15.40)–0.00003(-2.70)0.00275(14.33)0.00116 0.00069 0.00106(12.19) (8.13)(12.93)0.00137(9.17)

0.00120(10.72)496.871414.123101.673848.13244.28

54.95

3.90

8.82

24.42

48.59

γ*

2.5

2.5

2.5

2.5

2.5

β*

0.996

0.996

0.996

0.996

0.996

20,637[29]
30,319[42]
24,412[34]
17,963[25]
15,102[21]

18,092[23]
24,891[31]
20,867[26]
16,037[20]
13,765[17]

31,904[32]
39,303[40]
34,931[35]
29,689[30]
27,328[28]

32,564[30]
43,554[40]
36,983[34]
29,348[27]
25,852[24]

28,721[22]
36,047[27]
31,871[24]
26,228[20]
23,299[17](A) Consumption Parameters
Λ

H-ECO

Μ

S-ECO
H-ECO
S-ECO

σ2

H-ECO
S-ECO

H1: µH=µS

71,427

χ2(1)H2: σ2H=σ2S χ2(1)(B) Preference Parameters(C) Cost of Stagnation
γ = γ*

β = β*

γ = 0.5〃

γ = 1.5〃

γ = 3.5〃

γ = 5.0〃

Note: The β* and γ* are the base values of preference parameters for each income quintile group.
The numbers in parentheses [..] denote the λ* /λH (%) as seen in Table 2. See notes of Table 1.

20

Table 4. Cost of Stagnation (Districts)
EconomyHokkaido Tohoku(A) Consumption Parameters
λH-ECO
92,16890,731
S-ECO
92,16890,731
H-ECO
0.000650.00054μ(21.05)(15.84)
S-ECO
0.000260.00003(10.57)(1.62)
H-ECO
0.001960.00212σ2(8.27)(9.15)
S-ECO
0.003290.00268(9.24)(9.36)
H1: µB=µS
χ2(1)
79.35
187.462
2
2
H2: σ B=σ S χ (1)
9.57
2.33
(B) Utility Parameters
γ*
2.5
2.5
β*
0.996
0.996
(C) Cost of Stagnation
γ=γ*
β=β*
8,180
11,163
[9]
[12]
γ=0.5
〃
10,063
12,821
[11]
[14]
γ=1.5
〃
9,003
11,916
[10]
[13]
γ=3.5
〃
7,524
10,525
[8]
[12]
γ=5.0
〃
6,759
9,729
[7]
[11]
Notes: See notes of Table 1 and Table 3.

Kanto

Hokuriku

Tokai

Kinki

Chugoku

Shikoku

Kyusyu113,904
113,904
0.00136(71.94)-0.00029(-35.20)0.00071(11.13)0.00068(9.94)
6402.75
0.07

91,157
91,1570.00139(30.00)0.00035(11.54)0.00301(10.22)0.00497(9.36)
366.7410.28

86,95886,9580.00121(45.69)0.00037(24.99)0.00140(10.92)0.00235(9.72)
771.11
12.18

101,421
101,4210.00100(59.42)-0.00014(-11.35)0.00068(12.13)0.00166(8.37)
2998.40
22.36

95,80095,8000.00101(30.53)-0.00003(-1.91)0.00269(9.40)
0.00325(9.15)
779.871.51

72,97572,9750.00064(14.36)0.00102(50.13)0.00348(9.01)
0.00416(9.07)
59.35
1.26

87209
87209
0.00046(14.70)0.00018(14.47)0.00209(8.72)
0.00166(9.44)
65.61
2.15

2.5
0.996

2.5
0.996

2.5
0.996

2.5
0.996

2.5
0.996

2.5
0.996

2.5
0.996

20,105[22]
30,867[34]
24,200[27]
17,313[19]
14,464[16]

15,452[18]
22,786[26]
18,346[21]
13,405[15]
11,248[13]

28,642[28]
35,622[35]
31,540[31]
26,467[26]
24,055[24]

23,780[25]
30,531[32]
26,593[28]
21,646[23]
19,243[20]

47,772[42]
63,342[56]
53,734[47]
43,726[38]
39,723[35]

21-5,000[-7]-7,274[-10]-5,935[-8]-4,307[-6]-3,544
[-5]

5,586
[6]
6,590
[8]
6,047
[7]
5,187
[6]
4,679
[5]

Figure 1. Hypothetical and Stagnation Economieslog (Ct)

H-ECO
log(λH)= log(λS)

●
S-ECO

PSP

0

SP

t

Note: PSP (H-ECO) and SP (S-ECO) denote the prestagnation and the stagnation periods(the hypothetical and the stagnation economies), respectively. Parts of the intercept, -(1/2)σ2H
and -(1/2)σ2S , are neglected because they are negligible.

Figure 2. Per capita total consumption in logarithm (Aggregate)
Workers' Households
11.7
11.6
11.5
11.4
11.3
11.2
11.1
11.0
01/75

01/79

01/83

01/87

22

01/91

01/95

01/99

2001.11

2000.09

1999.07

1998.05

1997.03

1996.01

1994.111993.09

1992.071991.05

1990.03

1989.01

1987.111986.09

1985.07

1984.05

1983.03

1975.01
1976.03
1977.05
1978.07
1979.09
1980.11
1982.01
1983.03
1984.05
1985.071986.09
1987.11
1989.01
1990.03
1991.05
1992.071993.09
1994.111996.01
1997.03
1998.05
1999.072000.09
2001.11

197 5.01
197 6.03
197 7.05
197 8.07
197 9.09
198 0.11
198 2.01
198 3.03
198 4.05
198 5.07
198 6.09
198 7.11
198 9.01
199 0.03
199 1.05
199 2.07
199 3.09
199 4.11
199 6.01
199 7.03
199 8.05
199 9.07
200 0.09
200 1.11

1 9 7 5 .0 1
1 9 7 6 .0 3
1 9 7 7 .0 5
1 9 7 8 .0 7
1 9 7 9 .0 9
1 9 8 0 .1 1
1 9 8 2 .0 1
1 9 8 3 .0 3
1 9 8 4 .0 5
1 9 8 5 .0 7
1 9 8 6 .0 9
1 9 8 7 .1 1
1 9 8 9 .0 1
1 9 9 0 .0 3
1 9 9 1 .0 5
1 9 9 2 .0 7
1 9 9 3 .0 9
1 9 9 4 .1 1
1 9 9 6 .0 1
1 9 9 7 .0 3
1 9 9 8 .0 5
1 9 9 9 .0 7
2 0 0 0 .0 9
2 0 0 1 .1 1

1975.01
1976.03
1977.05
1978.07
1979.09
1980.11
1982.01
1983.03
1984.05
1985.071986.09
1987.11
1989.01
1990.03
1991.05
1992.071993.09
1994.111996.01
1997.03
1998.05
1999.072000.09
2001.11

12

1982.01

1980.11

1979.09

1978.071977.05

1976.03

1975.01

Figure 3. Per capita total consumption in logarithm (Income Quintile Groups,

Workers’ Households)

Income Quintile Group 1
Income Quintile Group 2

11.8
12

11.6
11.8

11.4
11.6

11.2
11.4

11
11.2

10.8
11

Income Quintile Group 3

12
12Income Quintile Group 4

11.8
11.8

11.6
11.6

11.4
11.4

11.2
11.2

11
11

Income Quintile Group 5

12

11.8

11.6

11.4

11.2

11

Note: For the notation of the period, the 1975.01 means Jan,1975.

23

Tokai

11.8

11.7

11.6

24
1996.01
1997.03
1998.05
1999.072000.09
2001.11

1998.05
1999.072000.09
2001.11

1989.01

1994.1111
1997.0311.1

111996.01

11.2

11.1

1994.11

11.3

11.2

1993.09

11.4

11.3

1992.07

11.5

11.4

1993.09

11.6

1991.05

11.7

1992.07

11.8

1990.03

Kinki

1991.05

11.9

1990.03

11.5

1989.01

11.9

1987.1111
1986.09

11.1

10.9

1999.072000.09
2001.11

1992.071993.09
1994.111996.01
1997.03
1998.05

1986.09
1987.11
1989.01
1990.03
1991.05

1979.09
1980.11
1982.01
1983.03
1984.05
1985.07

Hokkaido

1987.11

11

1985.07

Kanto

1986.09

11.1

1984.05

11.2

1985.07

11.6

1983.03

11.7

11.6

1984.05

11.8

11.7

1983.03

11.8

1982.0111

1980.1111.1

111979.09

11.2

11.1

1982.01

11.3

11.2

1978.07

11.4

11.3

1980.11

11.5

11.4

1979.09

11.6

11.5

1977.05

11.7

11.6

1978.07

11.8

11.7

1977.05

11.4

1975.01
1976.03
1977.05
1978.07

11.9

11.8

1976.03

11.5

1975.01

2000.09
2001.111994.111996.01
1997.03
1998.05
1999.071990.03
1991.05
1992.071993.09

1984.05
1985.071986.09
1987.11
1989.01

1979.09
1980.11
1982.01
1983.03

1975.01
1976.03
1977.05
1978.07

11.9

1976.03

2001.112000.09

1999.07

1998.05

1997.03

1996.01

1994.111993.09

1992.071991.05

1990.03

1989.01

1987.111986.09

1985.07

1984.05

1983.03

1982.01

1980.11

1979.09

1978.071977.05

1976.03

1975.01

11.9

1975.01

2001.112000.09

1999.07

1998.05

1997.03

1996.01

1994.111993.09

1992.071991.05

1990.03

1989.01

1987.111986.09

1985.07

1984.05

1983.03

1982.01

1980.11

1979.09

1978.071977.05

1976.03

1975.01

Figure 4. Per capita total consumption in logarithm (Districts, Workers’ Households)

TohokuHokuriku

11.9

11.5

11.3

11.4

11.3

11.2

11.5

11.4

11.3

11.2

11.1

11

1984.05
1985.071986.09
1987.11
1989.01

1979.09
1980.11
1982.01
1983.03

1975.01
1976.03
1977.05
1978.072001.111999.07

1998.05

1997.03

1996.01

1993.09

1992.071991.05

11.9

1975.01
1976.03
1977.05
1978.07
1979.09
1980.11
1982.01
1983.03
1984.05
1985.071986.09
1987.11
1989.01
1990.03
1991.05
1992.071993.09
1994.111996.01
1997.03
1998.05
1999.072000.09
2001.112000.09
2001.11

11.6

2000.09

11.7

1994.111996.01
1997.03
1998.05
1999.07

11.8

1994.11

Kyushu1990.03
1991.05
1992.071993.09

11.9

1990.03

1989.01

1987.111986.09

1985.07

1984.05

1983.03

1982.01

1980.11

1979.09

1978.071977.05

1976.03

1975.01

Chugoku

Shikoku

11.9

11.8

11.8

11.7

11.7

11.6

11.6

11.5

11.5

11.4

11.4

11.3

11.3

11.2

11.2

11.1

11.1

11

11

25

Figure 5A.

Rate of internal migration from 1954 to 2003 :

(%)

2002

1999

1996

1993

1990

1987

1984

1981

1978

1975

1972

1969

1966

1963

1960

1957

1954

9 .0 0
8 .0 0
7 .0 0
6 .0 0
5 .0 0
4 .0 0
3 .0 0
2 .0 0
1 .0 00 .0 0Note: Rate of internal migration for a whole Japan refers to the ratio of the
migrants to the Japanese population.

Figure 5B. Net internal migration for Tokyo, Nagoya and Osaka Area:
1954-2003:(people)⎯ Tokyo , ⎯ Nagoya, --- - Osaka
4 5 0 ,0 0 0
4 0 0 ,0 0 0
3 5 0 ,0 0 0
3 0 0 ,0 0 0
2 5 0 ,0 0 0
2 0 0 ,0 0 0
1 5 0 ,0 0 0

2002

1999

1996

1993

1990

1987

1984

1981

1978

1975

1972

1969

1966

1963

1960

1957

0
- 5 0 ,0 0 0

1954

1 0 0 ,0 0 0
5 0 ,0 0 0

Note: The minus means the net loss. Prefectures included each area are as follows.
Tokyo area:Tokyo,Saitama,Kanagawa,Chiba; Nagoya area: Aichi, Gifu, Mie;
Osaka area:Osaka,Hyogo,Kyoto,Nara.

Figure 5C. Net internal migration for Shikoku district:
1982-2003:(people)

2002

Kou c h i

2000

1998

1996

Eh ime1994

1992

Kagawa

1990

1988

1986

1984

2 ,0 0 0
1 ,0 0 00- 1 ,0 0 0- 2 ,0 0 0- 3 ,0 0 0- 4 ,0 0 0- 5 ,0 0 0- 6 ,0 0 0- 7 ,0 0 0- 8 ,0 0 0

1982

Toku sh ima

Note: Shikoku district consists of four prefectures: Tokushima, Kagawa, Ehime
and Kouchi.
Data source: Statistics Bureau of Japan (http://www.stat.go.jp/data/idou/3.htm)

26