Response of Inequality to a Growth Rate Slowdown inJapanese Economy during the Lost Decades∗
Nao Sudo†Bank of Japan, Tokyo
Michio Suzuki‡
Graduate School of Economics, University of Tokyo, Tokyo
Tomoaki Yamada§
School of Commerce, Meiji University, Tokyo
June 16, 2014∗

Very preliminary and incomplete. The latest version is available on request. We
thank the Statistics Bureau, the Ministry of Internal Aﬀairs and Communications in Japan forletting us use the Family Income and Expenditure Survey for this project. We are grateful to
Ichiro Muto, Takemasa Oda, Hiroshi Fujiki, Daisuke Ikeda, Michael Fabinger, Hidehiko Ichimura,Kozo Ueda, Mike Elsby, Tim Kehoe, R. Anton Braun, Selo İmrohoroğlu and seminar participantsat Bank of Japan, University of Tokyo, and CIGS for many comments. Yamada thanks financial
support from the Ministry of Education, Science, Sports, and Culture, Grant-in-Aid for Young
Scientists (B) 24730173. The views expressed in this paper are those of the authors and do notnecessarily reflect the oﬃcial views of the Bank of Japan.
†
E-mail: nao.sudou@boj.or.jp.
‡
E-mail: msuzuki@e.u-tokyo.ac.jp.
§
E-mail: tyamada@meiji.ac.jp.

Abstract
Japan has experienced a long-lasting slow down of the aggregate output growth over thetwo decades since the early 1990s, called the lost decades. In this study, we explore how
and why cross-sectional moments of Japanese households have changed during the lost
decades. We first construct monthly series of variance of log income and consumption
and income-consumption correlation from 1981 to 2008 using micro data set on Japanesehouseholds from the Family Income and Expenditure Survey (FIES). By making use ofstructural break test, we ask if these time series have statistically changed over time. We
show that the lost decades has come together with a slowdown of income and consumption inequality growth and weakening of income and consumption correlation. Next,
we theoretically ask why these changes have occurred. We construct a dynamic general equilibrium model with heterogeneous households with diﬀerent degree of skills andidiosyncratic income shocks. We show that two factors, a growth rate decline in aggregate TFP and skill biased technology, are the driving forces of changes in cross-sectional
moments and aggregate output growth during the lost decades.
Keywords: Income Inequality, Consumption Inequality, Structural Change
JEL Classification: E21, D12, D31

1Introduction

Japan has experienced a long-lasting slow down of the aggregate economic growth over
the two decades since the early 1990s. This period is often called as the lost decades.
Figure 1 displays how Japanese economy has changed from the 1980s to the 1990s andbeyond. It shows the time path of the key aggregate macroeconomic variables; aggregate
households’ consumption expenditure, aggregate GDP, aggregate labor compensation,
and aggregate TFP, from the 1980s to the current years.1 The dotted black line depicts
the actual growth rate of each macroeconomic variable. The red solid line depicts theestimated mean growth rate of each macroeconomic variable in each sample period. Herethe mean is estimated by structural break test that is discussed in later section. The
mean growth rates of the four macroeconomic variables have dropped in the early 1990s
and never reverted back to the original growth rates of the 1980s in the subsequent years.
In this paper, we explore how cross-sectional moments across Japanese households
have changed with the aggregate economic slowdown characterized by the downward
shifts in the mean growth rates of aggregate macroeconomic variables during the early
1990s. The cross-sectional moments include variance of log income and consumption as
well as income-consumption correlation across Japanese households. We first construct a
set of cross-sectional moments using the micro data survey on Japanese households, theFamily Income and Expenditure Survey. We then apply structural break test proposedby Bai and Perron (1998) to these constructed series. The test allows us to pin down thenumber, timing, and size of the breaks in these series by statistical inference. There arethree noteworthy observations: (i) The lost decades has come together with permanent
slowdown of income and consumption inequality growth rate. That is, income andconsumption inequality have grown at lower rates during the 1990s and beyond comparedwith the 1980s. (ii) Slowdown of income inequality growth during the early 1990 ismostly attributed to a disproportionately large slowdown of income growth rate of highincome households. (iii) The linkage between income and consumption has weakened
during the 1990s and beyond compared with the case during the 1980s.
In order to examine causes of the changes in observed cross-sectional moments, aswell as aggregate economic slowdown, we develop a dynamic general equilibrium model.
In our model, households are subject to idiosyncratic income shocks and therefore diﬀer
from each other in terms of their income profiles. In addition, households are diﬀerent interms of degree of skills attached to their labor inputs. That is, one type of households
supply skilled labor inputs to firms and the other type of the households supply unskilledlabor inputs to firms. Firms produce output from the two types of labor inputs as wellas capital inputs supplied from households. We then examine the linkage between two
kinds of technology, aggregate technology and technology that enhances productivity
1

The four series are shown on a year-to-year growth rate basis.

1

of skilled labor inputs–skill biased technology–and the cross-sectional moment acrosshouseholds. We consider two cases, a case where aggregate technology growth slows
down and a case where skilled biased technology growth slows down and we study if thetwo growth rate slowdowns may account for the three observations discussed above.
Based on the model calibrated to the Japanese economy, we show that growth rate
slowdown of both technologies are needed to fully account for changes in the crosssectional moments observed in the data. Growth rate slowdown of aggregate technology is silent about income inequality but it lowers consumption inequality and incomeconsumption relationship across households. The latter eﬀect comes from decreases inhouseholds who are subject to borrowing constraints. Note that when its expected income growth falls, a household spends less and its borrowing constraint ceases to bite. In
the aggregate, therefore income-consumption correlation falls and consumption inequality shrinks. Growth rate slowdown of skilled biased technology trivially lowers growthrate of income and consumption inequality. It however, increases income-consumption
correlations as consumption of households with skilled labor inputs becomes more responsive to income profiles.
A good number of studies have already explored the linkage between aggregate
macroeconomic activity, such as recession or expansion, and developments of inequality.
For instance, Krueger et al. (2010) summarize common features of developments in inequality in nine countries and document that earning inequality appears to be strongly
counter-cyclical. Storesletten et al. (2004) conduct GMM using annual panel data ofPanel Study on Income Dynamics (PSID) to extract cyclicality of idiosyncratic labormarket risk and report that the risk is strongly countercyclical. In addition to thesestudies, our study is related to works that focus on the role of skill biased technology
in generating income inequality. For instance, Katz and Autor (1999) discusses that alarge part of the rising wage inequality observed in the U.S. is explained by the returns
to observed/unobserved skills and education attainment. Relatedly, Acemoglu (2002)
theoretically shows that rapid increase in skill biased technology may lead to wideningof income inequality.
In contrast to these existing studies, our study is novel in two aspects. First, ourstudy focuses on the eﬀects on inequality of a permanent slowdown of economy ordecades-long recession that has lasted longer than ordinary business cycle. In this aspect, our study is close to the work by Meyer and Sullivan (2013) that focus on theimpact of the current Great Recession on income and consumption inequality in the
U.S. Second, our monthly time series of inequality allows us to conduct structural break
test to the inequality data. We therefore able to pin down when and how changes ininequality have changed.
The structure of this paper is as follows. Section 2 explains our micro data set
and construction methodology of time series used in our analysis. It also empirically2

investigates when and how households income, consumption, and the correlation between
the two variables have evolved during the last three decades. Section 3 describes ourmodel settings. Section 4 describes our model calibration. Section 5 discusses our
simulation analysis. Section 6 concludes.

2

Time-series Properties of Inequalities before and during
the Lost Decades

In this section, we empirically explore when and how time series properties of inequalities have changed. We examine the mean value, the variance of logarithm, and covariance/correlation between variables of the monthly time series data by making use of an
econometric framework that allows for multiple structural breaks during the sample period and study the date and size of the breaks. In particular, we focus on the diﬀerenceof the mean value of the time series before and during the lost decades.

2.1

Data

To conduct the time-series analysis on economic inequalities, we construct a monthly
time series of variance of logarithm of earnings and consumption as well as mean of income and consumption of households that are categorized by their characteristics. The
time series is constructed from the micro data survey, the Family Income and Expenditures Survey (hereafter FIES), that is compiled and released by the Statistics Bureau,
Ministry of Internal Aﬀairs and Communications in Japan.2
The FIES is a monthly diary survey that collects earnings, income and expenditures of Japanese households and reports characteristics of sampled households including
household members’ ages, gender, occupation, industry of employment, marital status,
and region of residence. The survey reports monthly labor income of household head,
spouse and the sum of other household members Unfortunately, the FIES does notcollect information about education, which prohibits us to estimate college premium directly from the FIES. The consumption expenditures include food, services, nondurable,
semidurable and durable expenditures. The survey was first conducted in 1953. However, we have access only to data for the period from January 1981 to December 2008
for the purpose of the current research. We use data of multi-person households only
because the data of single-person households is available only after 2002. The survey contains approximately 8,000 households per month. Surveyed households reportsmonthly earnings and expenditures for a maximum of six consecutive months. The sampled households overlap, and one-sixth of the total sample is generally replaced by new
2

FIES is a source data of the households’ expenditures weighting used to construct Consumption
Price Index. FIES is also a primary source data of Private Consumption series in GDP that is compiled
and published from the Cabinet Oﬃce.

3

households each month.
We closely follow Lise, et al. (2014), in which they study the evolution of economic
inequality of Japanese economy from the boom time including the bubble period oflate 1980s to the lost decades, in constructing the time series of inequality measuresand means. The key diﬀerence between Lise, et al. (2014) and our study is that we
employ the monthly series instead of annual series. The monthly inequality series exhibit
seasonality reflecting seasonal variations in households’ income and consumption at the
micro level. In particular, the bonus payment, which is typically paid twice in a year, inJune (or July) and December, makes strong seasonality for labor income. To obtain theseasonally adjusted series, we first construct the seasonally unadjusted monthly series
and apply X12 ARIMA to these series.
We focus on the monthly series of before-tax equivalized household labor income
yL and nondurable expenditure cN D .3 The household labor income is calculated as
the sum of labor earnings of household head, spouse and other household members,
and it is equivalized using the OECD equivalent scale. We restrict the usage of data
set to households with employed household head aged 25–59, because it is diﬃcult tomeasure monthly income of self-employed workers. Both rising unemployment rates andincreasing number of non-standard workers such as contingent workers and part-timeworkers undoubtedly contribute recent trend of rising inequality of Japanese economy.
In regard to this point, our estimates may underestimate the true whole inequality.
However, even if we focus on the employed household, the trend in economic inequality
appears positive. We use nondurable expenditures as consumption to be consistent with
consumption smoothing.4 That is, housing, purchasing cars and durable expenses suchas furniture are excluded. Every variables are deflated to the 2005 price using the CPI.

2.2

Econometric Methodology for Identifying Breaks

Before documenting the time series properties of inequality, we briefly describe the econometric methodology. The analytical framework is borrowed from the early work by Bai
and Perron (1998). Following Bai and Perron (1998) (1998), for each of the monthly
time series which we analyze ξt for t = 1, ..., T , we consider the following multiple linear

3

We have also conducted the time series analysis on disposable income, and we confirmed that our
main results do not change even if we use disposable income.
4
For the detailed definition on nondurable expenditure, see Lise, et al. (2014).

4

law of motion with m number of breaks (m + 1 breaks).
ξt = xt β + ut , for t = 1, ..., T1 ,(1)ξt = xt β + z1 δ1 + ut , for t = T1 + 1, ..., T2 ,..
.
l∑zl δl + ut , for t = Tl + 1, ..., Tl+1 ,ξ t = xt β +j=1

ξ t = xt β +m∑zj δj + ut , for t = Tm + 1, ..., T,

j=1

where x = {xt } is a T × 1 vector whose elements are all unity and zj is a variable thattakes zero for t ≤ Tj and takes unity in the period beyond T . β and δj for j = 1, ..., m arecorresponding parameters. The indices (T1 , ..., Tm ) are break dates. They are unknown
and to be estimated as well. ut is the disturbance at period t.
Using the time series of ξt from January 1981 to December 2008, we estimate a period(T1 , ..., Tm ) and the break size δj . In determining the number of breaks, we follow Bai
and Perron (1998) and consider a test for the null hypothesis that there are no structural
breaks in the sampled period against an alternative hypothesis that there is a structural
break, or against the alternative hypothesis that there are j number of structural breaks
for j = 1, 2, ..., m. Throughout the paper, we assume that the maximum number ofbreaks m is equal to or less than 5.

2.3

Income and Consumption Inequality

We start with describing the developments of inequality before and during the lost
decades. Figure 2 displays the time path of income and consumption inequality acrosshouseholds. The inequalities are measured by the variance of log of equivalized disposable income and equivalized non-durable consumption expenditure which we denote by var (log (yi,t )) and var (log (ci,t )) respectively. The upper panel of the figure
displays the level of inequalities, that is var (log (yi,t )) and var (log (ci,t )), and thelower panel of the figure displays the year-on-year diﬀerence of inequalities, that isvar (log (yi,t )) − var (log (yi,t−12 )) and var (log (ci,t )) − var (log (ci,t−12 )). The dottedblack lines depict the actual time path ξt and the red solid lines depict the estimated∑mean, which is xt β + lj=1 zl δl , of the series in period t = Tl + 1, ...Tl+1 . In both ofthe level and growth specifications, it is seen that income and consumption inequality
have a positive trend over the sample period. In addition, the two inequalities grow at a
slower pace during the 1990s and beyond compared with the pace during the 1980s. For
instance, regarding the level of variance of log income, the inequality has risen from 0.26
in the early 1980s to 0.33 in 2008, the bulk of the diﬀerence in the number is attributed5

to the breaks that have occurred until the early 1990s. The similar picture is observed forthe comparable series for consumption. Clearly, the lost decades is accompanied by theslowdown of income inequality growth and such slowdown is to some extent transmitted
to the slowdown of consumption income growth.

2.4

Breakdown of Income Inequality Growth

In order to see the background behind the slowdown of income and consumption inequality, we compare the income and consumption profile of households with diﬀerent
characteristics. Our measure of characteristics includes household’s head’s income level
quantile, occupation of household’s head, industry of household’s head job, and household’s head age. For each of the measures, we divide households into subgroups according
to their profiles and construct the time path of the mean of the income and consumption
by taking average across households. We then apply the structural break tests to theyear-on-year growth rate of the mean series of each subgroup household.
Table 1 and 2 display the estimation results of the structural break tests for themean income and mean consumption, respectively. The first three columns stand forthe first, second, and third break dates that have taken place in the mean series of eachsubgroup.5 The fourth column stands for the average growth rate, which corresponds
to β in equation (1). The last three columns stand for the size of the first, second,
and third structural break in terms of year-on-year growth rate. The two observations
are noteworthy related to the mean income growth. First, mean income growth grows
at diﬀerent rate across households that have distinct profiles. For instance, regarding
occupation, mean income growth of temporary worker is strictly lower than that ofother subgroups. Second, most of the subgroups have witnessed downward structural
break around the period of the bubble burst and beyond and size of the break diﬀers
across subgroups. At least the analysis regarding income quantile is concerned, the two
observations provide possible explanations as to why growth rate of income inequality has
slowed down after the early 1990s. Among subgroups categorized by income quantiles,
the subgroup of upper-quantile-households witnesses higher mean income growth thanthose of lower-quantile-households throughout the period. During the early 1990s, only
the two highest subgroups see the downward structural break in their mean income
growth rate while the rest of the households do not see the breaks. In particular the breaksize is larger for the highest subgroup. Clearly, such asymmetric breaks soften income
inequality growth. During the late 1990s, lower-quantile-household see the downward
break as well but their quantitative size is minor.

5Note that though we set that the maximum number of the breaks is five throughout the estimations,the number of breaks detected in these series are two at the largest.

6

2.5

Transmission from Income Inequality to Consumption Inequality

We show in Figure 2 that breaks in income inequality are to some extent translated
to consumption inequality. Here we further analyze the transmission by computing
correlation between income and consumption. Figure ?? displays the time path of contemporaneous covariance between income and consumption var (log (yi,t ) , log (ci,t )) , corresponding correlation between income and consumption, contemporaneous covariance
between income growth and consumption var (log (yi,t /yi,t−1 ) , log (ci,t /ci,t−1 )) , corresponding contemporaneous correlation between income growth and consumption, andvariance of consumption growth var (log (ci,t ) / log (ci,t−1 )). The structural break tests
are applied to all of the series and estimated means are depicted in red solid line. There
are signs for the weakening of transmission from income to consumption over the sample
period. For instance, the correlation between level of income and consumption is positive
but has lowered by about 0.1 from the 1980s to the 1990s and beyond.

3

Model

We provide a quantitative models that account for the empirical findings documented
in Section 2. To this end, we develop an incomplete-market overlapping-generations
model so as to identify the transmission mechanism from the slowdown of the aggregate
economy to the inequality across households. In particular, we focus on the following
empirical observations: (i) simultaneous slowdown of mean growth rate of aggregate
GDP and that of inequality growth rate and (ii) weakening of the transmission fromincome variations to consumption variations.
Demographics: There is a continuum of households that faces survival risk sj+1 ,which denote the conditional survival probability from the age j to j + 1. Denote thepopulation size of age j as µj . Then the population size transits from the following
equation:sj+1µj+1 =µj ,1+nwhere n is a population growth rate. We normalize the total population to be one,∑i.e., Jj=1 µj = 1. We assume that the population distribution is constant over time.
Household: There is a continuum of households who retire at the age of j ret , and lives
at most J. Denote calender time t. There are two types of households, those with skilledlabor input s and those with unskilled labor input u. Households face idiosyncratic laborproductivity risks in their working age. The labor income consists of the macroeconomic
wage level wte , which diﬀers by skill type e ∈ {s, u}, the age-specific eﬃciency κej , thepersistent component of labor productivity shock η and the purely transitory shock ε:7before-tax labor income is determined by yj,t = wte κej ηε. The government imposes labor
income tax τ y on the labor income, and it also collects social security benefit from thelabor income as a payroll tax τ ss . After retirement, households receive public pension
ss from the government. We assume that the public pension benefit is constant acrossthe same type of households, although they may have diﬀerent realizations of past labor
income and, as a result, diﬀerent public pension contribution. We also assume thatthe public pension benefit is a constant fraction of the average earnings at period t,∑j retret , by skill type. Denoting the replacement rate as ϕ, the pensionL̄e =j=1 yj,t /jbenefit is written as ss = ϕwte L̄et .
The household problem is defined as follows:
[ e
]
e
Vj,t
(aj,t , η, ε) = max u(cj,t ) + sj+1 βE Vj+1,t+1(aj+1 , η ′ , ε′ ) ,cj ,aj+1(2)

subject to
cj,t + aj+1,t+1 = ỹj,t + (1 + (1 − τ k )rt )(aj,t + bt ),{(1 − τ y − τ ss )wte κej ηε if j ≤ j ret ,ỹj,t =
ϕwte L̄et
if j > j ret ,(3)

aj+1,t+1 ≥ 0.
where cj,t is consumption at age j and time t, aj,t and aj+1,t+1 are current and next
period’s savings, and bt is an accidental bequest. The accidental bequests are collectedby the government and redistributed by the lump-sum manner. The financial asset yields
return rt although the capital income tax τ k is imposed on the asset income rt (aj,t + bt ).
We assume that households face the borrowing constraint, aj+1,t+1 ≥ 0.
Aggregation: Aggregate labor inputs of both types of workers are defined as populationweighted sum of heterogeneous households:
∫

ret

Let =

j
∑

µj

κej ηεdΨej,t (a, η, ε),e ∈ {s, u},

(4)

j=1

where Ψej,t (a, η, ε) is the density function of age j over the state variables (a, η, ε).
Skilled and unskilled labor inputs are combined using the following aggregator function:6
1
Lt = [(Ast Lst )ρ + (Aut Lut )ρ ] ρ , ρ ≤ 1,
(5)
where Ast and Aut are factor augmenting technologies for skilled and unskilled aggregate1labor inputs, respectively. The parameter 1−ρdetermines the elasticity of substitution
between two types of labor input.
6

For details, see Heckman et al. (1998), Acemoglu (2002), and Heathcote et al. (2010).

8Aggregate capital is defined as population-weighted sum of household savings:
Kt =

J
∑

∫
adΨej,t (a, η, ε).

µj

(6)

j=1

A representative firm combines the aggregate capital and labor for production using thestandard Cobb-Douglas type technology:
Yt = At Ktα L1−α,t1/(1−α)where the TFP factor grows with 1 + gt =At+1

1/(1−α)At. As will be discussed in Section 4,

we allow both the TFP factor growth rate gt and the demand for skilled and unskiled
labor {As , Au } varies over time.
Equilibrium wages are determined from the first order conditions:()
Kt α 1−ρ s ρ s ρ−1
Lt (At ) (Lt ) ,
Lt
( )α
Kt
= (1 − α)At
L1−ρ(Aut )ρ (Lut )ρ−1 .
t
Lt

wts = (1 − α)At

(7)

wtu

(8)

As both equations suggest, the skilled/unskilled wages are aﬀected by the skill demandand labor supply of skilled and unskilled workers.
Government: The government collect taxes through labor income τ y and capital income τ k , and the tax revenues are used for the government expenditure which yields noutility for households.
∫

ret

Gt = τ

j
∑ ∑

y

µj

wte κej ηεdΨej,t (a, η, ε) + τ ke∈{s,u} j=1

J
∑ ∑

∫
µj

rt adΨej,t (a, η, ε). (9)e∈{s,u} j=1

The accidental bequests are distributed to survived households as lump-sum transfer:
bt =

J
∑

∫
µj

(1 − sj+1 )gta (a, z, j)dΨj,t (a, z, ξ),

(10)

j=1

where aj+1,t+1 = gta (a, z, j) is a policy function for each household. Given the payroll
tax rate τ ss , the government set the replacement rate ϕ endogenously to satisfy thefollowing budget constraint:
∫

ret

j
∑ ∑
e∈{s,u} j=1

µj

τ

ss

wte κej ηεdΨej,t (a, η, ε) =∑J∑e∈{s,u} j=j ret +1

9

∫
µj

ϕwte L̄et dΨej,t (a, η, ε). (11)Equilibrium: The economy is initially in a steady state with high TFP factor growthrate and a set of skill demand {As , Au } that match Japanese economy in 1980s. Unexpectedly, households find that the TFP factor growth and/or skill demands changes atperiod 0, and it continues forever. In the benchmark case, we assume that all households understand that the growth rate drop happened at period 0. Thus, we computetransition paths between the initial steady state with high growth and the final steadystate with low TFP growth.
Definition (Recursive Competitive Equilibrium): Given the exogenous paths of
TFP factor growth rate gt , and factor augmenting technologies for skills {Ast , Aut },a }, aggrethe recursive competitive equilibrium is a set of the policy functions {gj,tgate capital {Kt }, factor prices {rt , wts , wtu }, replacement rate ϕ, and accidental
bequests {bt } that satisfy the following conditions:• Household optimality: Given factor prices {rt , wts , wtu } and tax rates {τ y , τ k , τ ss }, aa } is the associatedhousehold maximizes its expected utility, and the functions {gj,tpolicy functions.
• Firm optimality: Factor prices are competitively determined using equation (7)and (8).
• Market clearing: The market clearing conditions expressed in equation (6) and (5)are satisfied.
• Government budget: The government budget constraints expressed in equations(9) and (11) are satisfied.
• Accidental bequests: Accidental bequests are redistributed in accordance withequation (10).
• Transition law of motion: The distribution function Ψej,t (a, z, ξ) transits consistently with the policy functions.
Following Conesa and Krueger (1999), we first compute the initial and final steadystates, and then compute the transition path between them.

4

Calibration

4.1

Demographics

We calibrate the demographics of the model to match the actual population distribution
in Japan in 2010. The survival probabilities {sj }Jj=1 are taken from the estimates by
the National Institute for Population and Social Security Research, and the population
growth rate n is set to 0 to match the actual population distribution.
10

4.2

TFP Factor Growth Rate

The TFP factor growth rates are the key in our setup. As is well known from theresearch by Hayashi and Prescott (2002), the TFP factor growth rate sharply declined
after 1990s, which is a main cause of long stagnation in 1990s called the lost decade.
Muto, et al. (2013) also estimate the TFP growth rate from SNA. In the estimatesby Muto et al. (2013), although the average TFP growth rate in 1980s was 1.84%, it
declined to 0.42% in 1990s. Facing with the huge decline of the TFP growth rate in the
period of the great recession in 2009, the average TFP growth rate has further dropped
to 0.16% in 2000s. We assume that, in the initial steady state with high growth rate,
the TFP growth rate is set at 1.89%, but it drop to 0.16% from period 0 to period 1.
The low TFP growth rate continues from period 1 to the final steady state.

4.3

Preferences and Production Function

Preference parameters are determined as follows. The subjective discount factor β is set
at 0.99, and inverse of intertemporal elasticity of substitution parameter γ is set at 2.
These values are standard in the literature. As will be shown later, capital-to-output
ratio, K/Y , ranges between 2 and 2.5 in the benchmark model using these parameters.
We use estimates by İmrohoroğlu and Sudo (2011) to set capital share parameter α anddepreciation rate δ: α = 0.377 and δ = 0.08 respectively.

4.4

Idiosyncratic Income Risks

We set idiosyncratic income risks parameters following on Lise et al. (2014). Log of thepersistent component of the labor income follows AR(1) process as follows:ln ηj+1 = λ ln ηj + ωj ,

ω ∼ N (0, σω2 ),where λ determines persistence of the shock and σω2 is the shock size. The transitory
shock is purely i.i.d. shock and follows log-normal distribution:ln ε ∼ N (−σε2 /2, σε2 ).
Hayashi and Prescott (2002)) estimate the sizes of permanent and temporary shocks
from Japanese Panel Survey of Consumers. In their estimation, both the permanent andtransitory shocks are time-varying parameters and the persistence of permanent shockis one. Since Yamada (2012) shows that the persistence parameter λ is very close to
1, we set λ at 0.97. From Figure 6.1 in Lise et al. (2014), the average of variancesof permanent shock in Japan is approximately 0.01 from 1993 to 2005. Thus, we set
σω2 at 0.01. From the same figure, the variance of transitory shock σε2 is about 0.03.

11

The AR(1) process is approximated by finite Markov chain using Rouwenhorst (1995)’s
approximation method.7
ret
The age-eﬃciency profiles {κej }jj=1 are estimated from the Basic Survey on Wage
Structure.8 For each of the age-eﬃciency profile of skilled and unskilled workers, we use
wage of college graduate and high school graduate workers respectively.

4.5

Skill Premium

The factor augmenting technologies that determines the skill prices are calibrated tomatch the data following the approach by Acemoglu (2002). In particular, using the
Basic Survey on Wage Structure, we computeζ/(ζ−1)SAs= Hs u ,
u
A
L /L
s

s

where SH = wwu L
Lu is the ratio of the wage bill. Following Heathcote et al. (2010),1
ζ ≡ 1−ρ , which is the elasticity of substitution, is set at 1.4. We use total hours worked,
which is the product of the number of employees and the monthly actual number ofscheduled hours worked, to compute Ls and Lu respectively.
Calibrated parameters are summarized in Table 3.

5

Simulations

5.1

Simulation Exercise

Based on our model calibrated to Japanese economy, we conduct two experiments andexamine eﬀects of the technology growth slowdown on income and consumption inequality and the correlation of log income and consumption. In the first experiment, westudy a case where TFP growth rate unexpectedly drops from gH to gL in period T1 andbeyond. That is,
At+1
=
At

{

gH
gL

for t < T1 ,for t ≥ T1 .

In preceding studies that explore causes of the lost decades, including Hayashi and
Prescott (2002) and Muto et al. (2013), growth rate decline in TFP is considered as the
key source of output stagnation. In conducting the first exercise, we aim to investigate
its impact on cross-sectional moments of households as well as aggregate variables.

7

For details, Kopecky and Suen (2010). We choose the number of state for z at 9. The transitory
shock is approximated based on Gaussian quadrature points, and the number of approximated point is
5.
8
For details, see Braun et al. (2009).

12

Figure 7 reports the transition paths of TFP growth rate, skill premium, after-tax
interest rate, and capital stock in the wake of unexpected change in TFP growth rate.
Note that we set T1 = 1. As shown in the panel (b), the skill premium is unaﬀectedby the TFP decline as wages of both skilled and unskilled labor inputs respond to thedecline symmetrically. As shown in the panel (c), the after-tax interest rate gradually
decreases after the decline of TFP growth rate. A lower growth rate of TFP drives
down the real return on capital investment. In addition to this direct eﬀect, an increasein capital stock due to higher saving of households help decrease interest rate. Figure
8 reports the transition path of variance of log income and that of log consumption.
Note that in this experiment, we only alter TFP growth rate g and maintain otherparameters, including the variance of log income σω2 and σε2 , constant. It is shown thatthe variance of log income does not respond to the change in TFP growth rate andevolves around the same level before and after the impact period T1 = 0. The varianceof log consumption drops at the period when TFP growth rate falls and remains stable
at the law level afterwards. Figure 9 displays the four measures of income-consumption
linkage, the covariance and correlation of log income and log consumption and those oflog diﬀerences of income and consumption. All of the four measures fall in response to
the decline in TFP growth rate.
In the second experiment, we study a case where growth rate of factor augmenting
technology for skilled labor inputs Ast increases from a growth rate gLs to a growth rate
s in period t = T and stays at the rate for a length or period until period t = T andgH12sreverts back to the original growth rate gL in period t = T2 + 1 and beyond. That is, gs
Ast+1  Ls
=
gH

Ast
 s
gL

for
t < T1 ,for T1 ≤ t ≤ T2
fort > T2As shown in Section 2, our data facts indicate that widening of income inequality during
the 1980s was attributed to a rapid income increase of upper-quantile households. Since
the early 1990s, the increase has been moderate compared with the previous years anddiﬀerential of income growth across households has been reduced. This exercise aims tocapture such movements of income growth diﬀerentials across households.
Figures 10–15 report simulation results for the second experiment.
Figure 10 reports the transition paths of TFP growth rate, skill premium, aftertax interest rate, and capital stock in the wake of unexpected change in skill biased
technology growth rate. Note that we set T1 = 1 and T2 = 10. As shown in thepanel (b), the skill premium widens permanently by the short-run acceleration of growthrate of skill biased technology. This reflects the fact that wage for skilled labor inputs
increases by a disproportionately large amount while wage for unskilled labor inputs
is little aﬀected by the changes in skilled biased technology. As shown in the panel

13

(c), the after-tax interest rate increases in the short-run and gradually reverts back to
the original level. Figure 11 reports the transition path of variance of log income andthat of log consumption. It is seen that the variances of log income and consumption
increase following the change in skilled biased TFP growth rate over the period from
T1 to T2 and remain at the high value in the subsequent period. Figure 15 displays thefour measures of income-consumption linkage. The changes in skilled biased technology
bring about diﬀerent impacts on income-consumption linkage in level and in growth rate.
That is, the covariance and correlation of log income and log consumption increase overthe period from T1 to T2 and remain at the high value in the subsequent period. By
contrast, the covariance and correlation of log diﬀerences of income and consumption isbarely aﬀected by the changes in skilled biased technology.

5.2

Model Mechanism

In this subsection, we discuss channels through which growth rate slowdowns of TFP At
or factor augmented technology for skilled labor inputs Ast aﬀects income and consumption inequality as well as income-consumption linkages.
Slowdown of growth rate of labor income inequality We first show that a decline
in the growth rate of TFP At does not aﬀect income inequality. To see this, we arrange
equations 7 and 8 into the following equation:var (ln (yt )) =

∑ (∫

 
)
dΨej,t (a, η, ε) ln  ∑

e=s,u

e=s,u

2
(∫

(Aet )ρ Let)dΨej,t (a, η, ε) (Aet )ρ (Let )
(12)

∫

where
e

Φ =

dΨej,t (a, η, ε) for e = s and u.

It is clear from equation (12) that the variance of log labor income is independent
from TFP as At does not appear in this equation.
By contrast, there is transmission mechanism from the growth rate of factor augmenting technology for skilled labor inputs Ast to the income inequality. Provided thatthe term (Ast )ρ Lst is greater than the term (Aut )ρ Lut , which is the case in our model,
the equation (12) indicates that the variance of log labor income increases with the gap
between the two terms (Ast )ρ Lst and (Aut )ρ Lut . These implications are consistent withwhat are shown in Figure 8 and Figure 11.
Slowdown of consumption inequality growth Next, we show the relationshipbetween the technology growth slowdown and consumption inequality. To this end, forillustrative purpose, we construct a stylized two-period model and discuss how changes

14

in aggregate TFP and technology for skilled labor inputs are translated to households’
consumption.9 In our two-period model, The utility maximization problem for household
j is written as follows.

u(cj,1 ) + βu(cj,2 )max

cj,1 ,cj,2 ,aj,2subject to

cj,1 + aj,2 = yj,1 + aj,1
cj,2 = yj,2 + (1 + r)aj,2
aj,1 given
aj,2 ≥ 0
cj,1 , cj,2 ≥ 0

Let yj,2 = gyj,1 . The coeﬃcient g represents a (gross) rate of income growth. When TFP
growth rate is considered, g is common to all households. When growth rate of skilledlabor inputs is considered, households with skilled labor inputs commonly witness thegrowth rate g s and those with unskilled labor inputs witness the growth rate g u . The(c )1−γ
utility function u(cj,t ) is defined by u(c) = j,t1−γ . Let xj,1 denote cash-on-hand inperiod 1, that is, xj,1 = yj,1 + aj,1 . The solution to the household problem is as follows.
{ (cj,1 =

1+r
1+r+Γ

)(

1
xj,1 + 1+r
yj,2

xj,1

)

if Γx1 ≥ gy1otherwise,1

where Γ = (β(1 + r)) σ .
We start with the analysis on how aggregate TFP growth At /At−1 is translated tothe consumption inequality. We show that though changes in aggregate TFP growth do
not aﬀect labor income inequality, they may aﬀect consumption inequality. To see this,we study a case when aj,1 = 0 for all households (case 1) and a case when aj,1 > 0 for
all j.
Case 1: Suppose that a1 = 0 for all households. In this case, x1 = y1 . Then,
{
c1 =

1+r+g
1+r+Γ y1if (Γ − g)y1 ≥ 0otherwisey1

1

If Γ ≥ g (or, (β(1 + r)) γ ≥ g), then the borrowing constraint does not bind for all
households, while if Γ < g, then the borrowing constraint binds for all households. But
the variance of ln c1 and the covariance of ln c1 and ln y1 do not depend on g. In fact,
9Here, we focus on a short-run eﬀect where the risk-free interest rate and the initial distribution ofincome and wealth are fixed.

15

for any value of g, we have V ar(ln c1 ) = V ar(ln y1 ) and Cov(ln c1 , ln y1 ) = V ar(ln y1 ).
Therefore, the correlation of log income and consumption is 1. Note that because of thisequality, changes in variance of log income is fully translated to changes in variance oflog consumption. When variance of log income increase due to changes in skill biased
technology Ast , the dynamics is reflected in variance of log consumption as shown in
Figure 11.
Case 2: Next, we suppose that the initial asset holdings a1 vary across households.
For simplicity, we further suppose that a1 takes on only two values, a1 ∈ {aL , aH }with aL = 0 and aH > 0. Let π denote the fraction of households with a1 = aH .
Furthermore, suppose that y1 = ȳ = 1 for all households. Consider the following twocases with diﬀerent growth rates of gL and gH .
(i) Γ < gH . For a1 = aL = 0, the borrowing constraint binds, because (Γ − gH )y1 < 0.
Suppose that aH is large enough so that Γ(y1 + (1 + r)aH ) > gH ȳ. Then, for
a1 = aH , the borrowing constraint does not bind for households with a1 = aH .
Note that with the non-degenerate wealth distribution, unlike Case 1, householdswith binding borrowing constraints and those without can coexist.
(ii) Γ ≥ gL . In this case, for all a1 , Γx1 ≥ gL ȳ. Thus, for all households, the borrowing
constraint does not bind.
Let cL (g) and cH (g) denote, given the growth rate of g, consumption when a1 = aL
and that when a1 = aH , respectively. First, let us examine the level diﬀerence betweencH and cL in the above two cases. For g = gH ,cH (gH ) − cL (gH ) =gH − Γ
1+r(xH − xL ) +
ȳ.
1+r+Γ
r + Γ}|1 + {z>0For g = gL ,cH (gL ) − cL (gL ) =1+r(xH − xL ).
1+r+Γ

Thus, cH (gH ) − cL (gH ) > cH (gL ) − cL (gL ).10 Next, let us examine the variance of log
consumption. Let V ar(ln c1 )|g denote the variance of log consumption when the growthrate is g. We can show that
V ar(ln c1 )|gL − V ar(ln c1 )|gH(
Γ − gH(1 + r)2(1 + r)2 )
⇔
ȳ +
−
aH
r + Γ}
1 + r + gL 1 + r + Γ|1 + {z
|
{z
}
<0

10

>0

The same result holds in Case 1.

16

⋛ 0
⋛ 0

Γ−gH
Recall that (cH (gL ) − cL (gL )) − (cH (gH ) − cL (gH )) = 1+r+Γ
. Thus, the first term
represents the eﬀect of the growth slowdown on the dispersion in the level consumption.
On the other hand, the second term represents a level eﬀect, as gL governs the level ofcL (gL ) and cH (gL ). When the first term dominates, the variance of log consumption
decreases as the aggregate growth rate declines.11
This examples show that changes in the aggregate growth rate can aﬀect the crosssectional distribution of consumption through changes in the fraction of households
facing binding borrowing constraints. The higher the aggregate growth rate, the morehouseholds tend to face binding borrowing constraints.
Based on the arguments above, we discuss how growth rate slowdown of aggregate
TFP and changes in skill biased technology aﬀect cross-sectional moments. For simplicity, we consider a case where a1 = 0 for all households and that there are householdswith high expected growth and low expected growth. Then consumption choice of thetwo households will be expressed as

1 + r + gH
1+r+Γ1
+ r + gL
= αyju where α ≡.
1+r+Γ

csj = γyjs where γ ≡cuj

We further assume that the population of the two types of households are expressed as
Φs and Φu respectively and mean income in each household group is expressed by y s
and y u . Then the covariance of log income and log consumption across all households is
given by
Φs

∑(

∑(
)(
)
)(
)
log cuj − log c log yju − log y ,log csj − log c log yjs − log y + (1 − Φs )
(13)

where
log c ≡ Φs log y s + (1 − Φs ) log y u + Φs log γ + (1 − Φs ) log α
log y ≡ Φs log y s + (1 − Φs ) log y u .
This equation reduces to∑()()
log yjs − log y + (1 − Φs ) log γ − (1 − Φs ) log α log yjs − log y∑()()+ (1 − Φs )log yju − log y − Φs log γ + Φs log α log yju − log yΦsConsidering that higher growth rate of skill biased technology increases γ, its impact on
covariance is obtained by taking the first derivative of the equation above with respect
11

Note that if the borrowing constraint does not bind with the high (and low) growth rate, the firstterm disappears and the variance of log consumption increases with growth rates.

17

to γ. Because on average skilledhouseholds )receive (higher labor income
than unskilled
)
∑(
∑
s
u
households, which implies
log yj − log y >log yj − log y , the increase in γ
implies a higher covariance as shown in Figure 15. In order to discuss eﬀects of aggregate
technology slowdown, we assume that γ is unity and consider a case that impact of
decrease in Φs in the following equation.
∑()()
log yjs − log y − (1 − Φs ) log α log yjs − log y∑()()+ (1 − Φs )log yju − log y + Φs log α log yju − log yΦs

The eﬀect is positive when Φs is suﬃciently small as is the case in our model.

6Conclusion

Japan’s economy has substantially changed from the early 1990s. That is, growth ratesof the aggregate macroeconomic variables have declined and the declines have persisted
more than two decades. In this paper, we study how the second moments across households, including income and consumption inequalities and income-consumption correlation, have responded to the changes in the aggregate economic circumstances.
To this end, we first conduct the econometric analysis and study how time series properties of the inequalities have statistically changed before and during the lost decades.
We construct monthly series of inequalities from 1981 to 2008 using micro data set on
Japanese households, the Family Income and Expenditure Survey (FIES). We conduct
structural break tests developed by Bai and Perron (1998) to these series and check thetiming and size of changes in the inequality series. We find that the lost decades hascome together with changes in the way that the time series of inequality evolve. That is,
growth rates of income and consumption inequality have slowed down and correlation
between income and consumption across households has declined during the lost decades.
The growth rate declines in inequalities and lower correlation have never reverted backto the growth rates and the level of the 1980s even in the current years.
Next, we ask theoretically if these observed changes in the inequalities and thechanges in the macroeconomic activities are accounted for by the common economic factors. To do this, we construct a dynamic general equilibrium model with heterogeneous
households with diﬀerent degree of skills and idiosyncratic income shocks. We study if
the growth rate slowdown of the aggregate TFP, skill biased technology, or both may
account for changes in income and consumption inequalities and income-consumption
correlation as well as the aggregate output growth. Our theoretical analysis shows thata growth rate decline in both of the technologies are needed to bring the model close to
the data.

18

In the current paper, we focus on documenting changes in cross-sectional moments
across Japaneses households and theoretically studying why they have occurred. Though
it is not discussed in the current study, our findings have important policy implications.
For instance, the slowdown of the inequality growth may have contributed to mitigating
the social welfare loss due to the slowdown of the aggregate output growth during the lost
decades.12 In addition, the decline in the correlation between income and consumption
may have influenced the transmission mechanism of macroeconomic stabilization policy,
such as monetary policy and government expenditure policy. Extending our frameworkin that direction remains a future goal of our continuing research.

References
Acemoglu, D. (2002). Technical change, inequality, and the labor market. Journal of
Economic Literature 40 (1), 7–72.
Bai, J. and P. Perron (1998). Estimating and testing linear models with multiple
structural changes. Econometrica 66 (1), 47–78.
Braun, R. A., D. Ikeda, and D. Joines (2009). The saving rate in Japan: Why it has
fallen and why it will remain low. International Economics Review 50 (1), 291–321.
Conesa, J. C. and D. Krueger (1999). Social security with heterogeneous agents. Review of Economic Dynamics 2 (4), 757–795.
Hayashi, F. and E. C. Prescott (2002). The 1990s in Japan: A lost decade. Review of
Economic Dyamics 5 (1), 206–235.
Heathcote, J., K. Storesletten, and G. L. Violante (2010). The macroeconomic implications of rising wage inequality in the United States. Journal of Political Economy 118 (4), 681–672.
Heathcote, J., K. Storesletten, and G. L. Violante (2012). From wages to welfare:Decomposing gains and losses from rising inequality. In D. Acemoglu, M. Arellano, and E. Dekel (Eds.), Advances in Economics and Econometrics: Theory& Applications, Tenth World Congress of the Econometric Society, pp. 235–282.
Cambridge: Cambridge University Press.
Heckman, J. J., L. Lochner, and C. Taber (1998). Explaining rising wage inequality:
Explorations with a dynamic general equilibrium model of labor earnings withheterogeneous agents. Review of Economic Dynamics 1 (1), 1–58.
İmrohoroğlu, S. and N. Sudo (2011). Will a growth miracle reduce debt in Japan.
IMES Discussion Paper Series, 11-E-01.
12

See for example Heathcote et al. (2012) where welfare implications of rising economic inequality in
the U.S. is analyzed.

19

Kopecky, K. and R. Suen (2010). Finite state markov-chain approximations to highly
persistent processes. Review of Economic Dynamics 13, 701–714.
Krueger, D., F. Perri, L. Pistaferri, and G. L. Violante (2010). Cross-sectional facts
for macroeconomists. Review of Economic Dynamics 13 (1), 1–14.
Lise, J., N. Sudo, M. Suzuki, K. Yamada, and T. Yamada (2014). Wage, income
and consumption inequality in Japan, 1981-2008: from boom to lost decades.
Forthcoming, Review of Economic Dynamics.
Meyer, B. D. and J. X. Sullivan (2013). Consumption and income inequality andthe great recession. American Economic Review: Papers & Proceedings 103 (3),178–183.
Muto, I., N. Sudo, and S. Yoneyama (2013). Productivity slowdown in Japan’s lost
decades: How much of it is attributed to financial factors? Dynare Working Paper
Series, No. 28.
Rouwenhorst, K. G. (1995). Asset pricing implications of equilibrium business cycle
models. In T. Cooley (Ed.), Frontiers of Business Cycle Researc, pp. 294–330. New
Jersey: Princeton University Press.
Storesletten, K., C. I. Telmer, and A. Yaron (2004). Cyclical dynamics in idiosyncraticlabor-market risk. Journal of Political Economy 112 (3), 695–717.
Yamada, T. (2012). Income risk, macroeconomic and demographic change and economic inequality in Japan. Journal of Economic Dynamics and Control 36, 63–84.

20

A

TablesTable 1: Period and Size of Break in Mean Income (yD ) Growth by Characteristics

0-20%
20-40%
40-60%
60-80%
80-100%Regular Labourers
Temporary Worker
Private Oﬃce Workers
Oﬃcials
MiningConstruction
Manufacturing
Electricity
Transportation
Wholesale and Resale
Financial Sector
Real Estate
ServicePublic
25-29
30-39
40-49
50-59

Break Period
Break Size (YoY Growth Rate)
Break I Break II Average Growth Break I Break II
Income Quintile
1998.11 2004.01
0.013764-0.03078 0.02364
1998.11NA
0.014942-0.01822
NA
1996.09NA
0.016629-0.01755
NA
1993.08NA
0.018337-0.01928
NA
1992.01NA
0.020773-0.02117NA
Occupation
1997.02 2004.01
0.016479-0.03321 0.01954
NANA-0.008304
NANA
1992.12NA
0.020025-0.02075
NA
2001.04NA
0.014046-0.02092
NA
IndustryNANA-0.004828
NANA
1987.02 1993.02
0.006478
0.03496 -0.04834
1998.11 2003.09
0.018161-0.03560 0.02391
NANA
0.008807
NA
NA
1997.08NA
0.016723-0.02071
NA
1992012NA
0.020473-0.02382
NANA
NA
0.006870
NA
NA
NA
NA
0.005945
NA
NA
1998.06 2004.01
0.011985-0.03254 0.02117
1999.06NA
0.018161-0.02511
NA
Age
1992.11NA
0.026653-0.03501
NA
1996.02NA
0.019430-0.02395
NA
1992.06NA
0.018501-0.01846
NA
1999.02 2003.12
0.010134-0.03375 0.03202

21

Table 2: Period and Size of Break in Mean Consumption (cN D ) Growth by Characteristics

0-20%
20-40%
40-60%
60-80%
80-100%Regular Labourers
Temporary Worker
Private Oﬃce Workers
Oﬃcials
MiningConstruction
Manufacturing
Electricity
Transportation
Wholesale and Resale
Financial Sector
Real Estate
ServicePublic
25-29
30-39
40-49
50-59

Break Period
Break Size (YoY Growth Rate)
Break I Break II Average Growth Break I Break II
Income Quintile
1992.06NA
0.011827-0.01576
NA
1993.01NA
0.011609-0.01632
NA
1991.02NA
0.014911-0.01665
NA
1993.06NA
0.012930-0.01644
NANA
NA
0.002869
NANA
Occupation
1991.04NA
0.013128-0.01792
NANA
NA-0.003117
NANA
1987.12 1992.04
0.004043
0.01768 -0.02425
NANA
0.002686
NA
NA
IndustryNANA-0.005176
NANA
1987.03 1991.04
0.002263
0.03486 -0.04128
1992.04NA
0.017000-0.02043
NANA
NA
0.001978
NA
NA
NA
NA
0.002975
NA
NA
1992.12NA
0.014507-0.01883
NANA
NA
0.001618
NA
NA
NA
NA
-0.003677
NA
NA
NA
NA
-0.000190
NA
NA
NA
NA
0.003495
NA
NA
Age
NA
NA
-0.001252
NANA
1994.08NA
0.009184-0.01373
NA
1991.02NA
0.012980-0.01640
NA
1992.12NA
0.009767-0.01430
NA

22

Table 3: Calibration
Parameter
β
γ
gt
α
δ
λ
σψ2
σξ2
ρ
As /Auj retJ{κej }
{sj }
n
τy
τk
τ ss

Value
0.98
2.0
{1.84%,0.16%}
0.377
0.08
0.97
0.01
0.03
0.29
0.3233
45
81
–
–
0.0
10.0%
39.8%
13.58%

Source/Target
K/Y ≈ 2 ∼ 2.5
IES=0.5
Muto, et al. (2013)
İmrohoroğlu and Sudo (2011)
İmrohoroğlu and Sudo (2011)
Yamada (2012)
Lise, et al. (2014)
Lise, et al. (2014)
Heathcote, et al. (2010)
Acemoglu (2002)
Retire at 65
Live at most 100
BSWS
IPSR (2012)
IPSR (2012)İmrohoroğlu and Sudo (2011)
Value in 2004

23

B

Figures
Real Consumption

Real GDP

0.08

0.1

0.06
0.04

0.05

0.02
0

0

−0.02
−0.04
1980

1990

2000

2010

−0.05
1980

1990

Labor Compensation

2000

2010

2000

2010

TFP

0.08

0.1

0.06
0.04

0.05

0.02
0

0

−0.02
−0.04
1980

1990

2000

2010

−0.05
1980

1990

Figure 1: Time Path of Macroeconomic Variables during the Lost Decades

24

Var. of Log Labor Income (L)Var. of Log Non−durable Consumption (L)
0.3

0.38
0.36
0.34

0.25

0.32
0.3
0.2

0.28
0.26
0.24
1980

1990

2000

2010

0.15
1980

1990

2000

2010

Var. of Log Labor Income (YoY)Var. of Log Non−durable Consumption (YoY)
0.06

0.04
0.03

0.04

0.02
0.02

0.01

0

0
−0.01

−0.02

−0.02
−0.04
−0.06
1980

−0.03
1990

2000

2010

−0.04
1980

1990

2000

Figure 2: Variance of Income and Consumption across Households

25

2010

0−20%

20−40%

0.05

0.05

0

0

−0.05
1980

1990

2000

2010

−0.05
1980

40−60%
0.05

0

0

1990

2000

2000

2010

−0.05
1980

1990

2000

80−100%
0.05

0

−0.05
1980

1990

2000

2010

60−80%

0.05

−0.05
1980

1990

2010

Figure 3: Income Growth of Households with Diﬀerent Income Quintiles

26

2010

Covariance of Level

Correlation of Level
0.65

0.17
0.16

0.6

0.15
0.55
0.14
0.13

0.5

0.12
0.45
0.11
0.1
1980

1990

2000

2010

0.4
1980

Covariance of Growth

1990

2000

2010

Correlation of Growth
0.5
0.4

0.1
0.3
0.2
0.05
0.1
0
1980

1990

2000

2010

0
1980

1990

2000

Figure 4: Transmission from Income Growth to Consumption Growth

27

2010

0−20%

20−40%

0.2

0.2

0.1

0.1

0
1980

1990

2000

2010

0
1980

40−60%

0.2

0.1

0.1

1990

2000

2000

2010

60−80%

0.2

0
1980

1990

2010

0
1980

1990

2000

2010

80−100%
0.3
0.2
0.1
0
1980

1990

2000

2010

Figure 5: Income-Consumption Growth Covariance of Households with Diﬀerent Income
Quintiles28

0−20%

20−40%

0.05

0.05

0

0

−0.05
1980

1990

2000

2010

−0.05
1980

40−60%
0.05

0

0

1990

2000

2000

2010

−0.05
1980

1990

2000

80−100%
0.05

0

−0.05
1980

1990

2000

2010

60−80%

0.05

−0.05
1980

1990

2010

Figure 6: Consumption Growth of Households with Diﬀerent Income Quintiles

29

2010

1.4

1.025

1.36
u

1.02
s

Skill Premium: w /w

TFP Factor Growth Rate

1.38

1.015

1.01

1.005

1.34
1.32
1.3
1.28
1.26
1.24
1.22

1
−10

0

10

20
30
Period

40

50

1.2
−10

60

0

7.5

3.4

7

3.2

6.5

3

6

2.8

5.5

4.5

2.2

10

20
30
Period

40

50

60

2.6
2.4

0

40

SkilledUnskilled

5

4
−10

20
30
Period(b) Skill Premium

Wage

Interest Rate (%)(a) TFP Factor Growth Rate

10

50

60

(c) After-tax Rate of Return

2
−10

0

10

20
30
Period(d) Wage

Figure 7: Equilibrium Paths with One-time TFP Shock

30

40

50

60

0.24

Variance of Logarithm

0.22
0.2
0.18
Earnings
Consumption
0.16
0.14
0.12
0.1
−10

0

10

20
30
Period40

50

60

Figure 8: Variance of Logarithm of Earnings and Consumption with One-time TFP
Shock

31

0.9280.926

0.16

Correlation between y and c

Covariance between y and c

0.162

0.158
0.156
0.154
0.152
0.15
0.148
0.146
−10

0.924
0.922
0.92
0.918
0.916
0.914
0.912
0.91

0

10

20
30
Period

40

50

60

0.908
−10

(a) Covariance between y and c

2030
Period

40

50

60

50

60

0.62
Correlation between ∆ y and ∆ c

Covariance between ∆ y and ∆ c10(b) Correlation between y and c

0.019
0.018
0.017
0.016
0.015
0.014
0.013
0.012
−10

0

0

10

20
30
Period405060(c) Covariance between ∆y and ∆c

0.61
0.6
0.59
0.58
0.57
0.56
0.55
0.54
−10

0

10

20
30
Period40(d) Correlation between ∆y and ∆cFigure 9: Covariances and Correlations with One-time TFP Shock

32

1.4

2.5

1.36
u

2
s

Skill Premium: w /w

TFP Factor Growth Rate

1.38

1.5

1

0.5

1.34
1.32
1.3
1.28
1.26
1.24
1.22

0
−10

0

10

20
30
Period

40

50

1.2
−10

60

0

(a) TFP Factor Growth Rate

10

20
30
Period405060(b) Skill Premium

7.25

3
2.9
2.8
2.7

7.15

2.6
Wage

Interest Rate (%)

7.2

7.1

SkilledUnskilled

2.5
2.4
2.3

7.05

2.2
2.1

7
−10

0

10

20
30
Period405060(c) After-tax Rate of Return

2
−10

0

10

20
30
Period(d) Wage

Figure 10: Equilibrium Paths with One-time Skill Shock

33

40

50

60

0.26

Variance of Logarithm

0.24
0.22
0.2
Earnings
Consumption
0.18
0.16
0.14
0.12
−10

0

10

20
30
Period40

50

60

Figure 11: Variance of Logarithm of Earnings and Consumption with One-time Skill
Shock

34

0.93

0.172

0.929

Correlation between y and c

Covariance between y and c

0.174

0.17
0.168
0.166
0.164
0.162
0.16
0.158

0.928
0.927
0.926
0.925
0.924
0.923
0.922

0.156
−10

0

10

20
30
Period

40

50

0.921
−10

60

(a) Covariance between y and c

0

10

20
30
Period

40

50

60

50

60

(b) Correlation between y and c

Correlation between ∆ y and ∆ c

Covariance between ∆ y and ∆ c

0.018

0.01750.017

0.01650.016

0.0155

0.015
−10

0

10

20
30
Period405060(c) Covariance between ∆y and ∆c

0.605
0.6
0.595
0.59
0.585
0.58
0.575
0.57
−10

0

10

20
30
Period40(d) Correlation between ∆y and ∆cFigure 12: Covariances and Correlations with One-time Skill Shock

35

1.4

1.025

1.36
u

1.02
s

Skill Premium: w /w

TFP Factor Growth Rate

1.38

1.015

1.01

1.005

1.34
1.32
1.3
1.28
1.26
1.24
1.22

1
−10

0

10

20
30
Period

40

50

1.2
−10

60

0

(a) TFP Factor Growth Rate

10

20
30
Period405060(b) Skill Premium

7.5

3.5

6.5
3
6
Wage

Interest Rate (%)

7

5.5

SkilledUnskilled
2.5

5
4.5
4
−10

0

10

20
30
Period405060(c) After-tax Rate of Return

2
−10

0

10

20
30
Period40(d) Wage

Figure 13: Equilibrium Paths with One-time TFP and Skill Shock

36

50

60

0.26

Variance of Logarithm

0.24
0.22
0.2
Earnings
Consumption
0.18
0.16
0.14
0.12
−10

0

10

20
30
Period40

50

60

Figure 14: Variance of Logarithm of Earnings and Consumption with One-time TFPand Skill Shock37

0.928

0.162

0.926

Correlation between y and c

Covariance between y and c

0.163

0.161
0.16
0.159
0.158
0.157
0.156
0.155
−10

0.924
0.922
0.92
0.918
0.916
0.914
0.912

0

10

20
30
Period

40

50

0.91
−10

60

(a) Covariance between y and c

2030
Period

40

50

60

50

60

0.62
Correlation between ∆ y and ∆ c

Covariance between ∆ y and ∆ c10(b) Correlation between y and c

0.02
0.019
0.018
0.017
0.016
0.015
0.014
0.013
0.012
0.011
0.01
−10

0

0

10

20
30
Period405060(c) Covariance between ∆y and ∆c

0.6

0.58

0.56

0.54

0.52
−10

0

10

20
30
Period40(d) Correlation between ∆y and ∆cFigure 15: Covariances and Correlations with One-time TFP and Skill Shock38