

Department of Social Systems and Management
Discussion Paper Series

No.1290

Earnings Dynamics and Profile Heterogeneity:
Estimates from Japanese Panel Data
byMasakatsu OKUBO

March 2012

UNIVERSITY OF TSUKUBA
Tsukuba, Ibaraki 305-8573
JAPANEarnings Dynamics and Profile Heterogeneity: Estimates from JapanesePanel Data ∗Masakatsu Okubo †University of Tsukuba

Abstract
The recent empirical work on earnings processes by Guvenen (2009) using US panel data findsthat ignoring heterogeneity in earnings profiles among individuals leads to an upward bias in
the autoregressive parameter of earnings shocks. It then argues that the existing assumptions inincomplete markets, heterogeneous-agent models, almost all of which require highly persistentearnings shocks and no individual- and group-specific differences in earnings growth rates, may
be inappropriate. This paper investigates the applicability of this US data-based debate to otherdeveloped countries by using a panel of Japanese male earnings. The results indicate that it ispossible to corroborate Guvenen’s arguments, despite some differences in the estimates.

Keywords: Labor earnings risk, Heterogeneous earnings profiles, Incomplete markets models,Transitory shock, Persistent shock.
JEL Classification: C33, D31.

∗First draft, September 2009; Revised, March 2012. The author is grateful to seminar participants at theDevelopment Bank of Japan and Naohito Abe for helpful comments and discussions. Financial support from
the Ministry of Education, Culture, Sports, Science and Technology of Japan (Grant-in-Aid No. 21730171) isgratefully acknowledged.
†

Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba,

Ibaraki 305-8573, Japan; Tel.: +81-29-853-5369; Fax: +81-29-853-5070; E-mail: okubo@sk.tsukuba.ac.jp

1

Introduction

The modeling of an individual’s earnings dynamics is a longstanding issue that has been debatedover three decades in the field of labor economics, and it is more recently becoming an essential element of quantitative macroeconomic studies under incomplete markets environments.1
Among such recent studies on earnings dynamics, the most interesting and suggestive one fromthe viewpoint of macroeconomics is probably Guvenen (2009). His findings, which are based on
a US panel drawn from the Panel Study of Income Dynamics (PSID), are in sharp contrast to theassumptions about earnings processes in the existing incomplete markets, heterogeneous-agent
models (especially with a life-cycle dimension), almost all of which require that idiosyncratic
earnings shocks be highly persistent; in other words, that the autoregressive parameter be nearor exactly equal to one.2 A succinct justification for this highly persistent-shock assumption isthat some earlier papers (e.g., MaCurdy (1982), Abowd and Card (1989), Moffitt and Gottschalk(1995)) provide evidence in favor of the unit root model or its more flexible versions.3 Anotherone is, to borrow Lucas’ (2003, p.10) phrase, consistency with “the fanning out over time ofthe earnings and consumption distributions within a cohort” that Deaton and Paxson (1994)
1

See, e.g., Heathcote et al. (2009) and Meghir and Pistaferri (2010) for recent surveys from this perspective.

2

In this paper, we focus entirely on models with an exogenous and relatively simple univariate earnings process(specified as an AR(1) shock plus a transitory shock) to satisfy the objective of this paper described in thenext two paragraphs. However, previous studies have attempted to specify the conditional variance of shocks,
endogenize earnings dynamics, and incorporate multivariate processes or more flexible processes with many typesof heterogeneity. See, e.g., Meghir and Pistaferri (2004), Huggett et al. (2006), Altonji et al. (2009), and Browning
et al. (2009) for these extensions.
3

More recent studies (e.g., Blundell et al. (2008) and Attanasio et al. (2008)) still refer to the findings by

MaCurdy (1982) and Abowd and Card (1989) as justification when assuming the unit root model of earnings
shocks, despite subsequent contributions that report evidence in favor of moderate earnings shocks (e.g., Baker(1997) and Haider (2001)). Thus, this evidence in favor of the unit root model still has a great influence on theliterature. In light of these subsequent studies, Moffitt and Gottschalk (2002, 2009) extend their original sample
period up to 1996 or 2004 and report new estimation results to confirm their previous findings.

1

found.4
What makes Guvenen’s work interesting is not only that it documents that the observed
fanning-out effect can be explained even under moderate earnings shocks, but also that it includes
the new findings that ignoring heterogeneity in earnings profiles (i) leads to an upward bias in the
autoregressive parameter (consequently, a near unit-root model) and (ii) obscures a significant
difference in the dispersion of earnings growth rates between college-educated and high-schooleducated groups. The former finding explains why earlier studies such as MaCurdy (1982) and
Abowd and Card (1989) support the unit root model of earnings processes, invalidating the firstjustification for highly persistent shocks if it is robust.5 The latter finding, on the other hand,
explains why earlier studies such as Hubbard et al. (1994, 1995) and Carroll and Samwick (1997)
obtain similar estimation results for earnings processes among groups with different educational
backgrounds, contrary to predictions from human capital investment theory.6 Thus, Guvenen’sfindings force us to reconsider the modeling strategy of earnings processes that we wish to use
as an input in constructing incomplete markets, heterogeneous-agent models.
In this paper, we focus on the above-mentioned two points, (i) and (ii), and ask whether
they are PSID data-specific by studying a panel of Japanese individuals, partly because there
is a possibility that different conclusions may arise from the analysis of other panels, and partly
because of the first step of evaluating whether the US debate (and consequently, theory tailored
for the US data) is universally applicable to other developed countries. The data used in this4

For further analysis and discussions relating to this result, see, e.g., Storesletten et al. (2001, 2004a,b).

5

More recently, Hryshko (2009) reexamines the model with a dispersion of earnings growth rates and finds little

evidence in favor of profile heterogeneity using the PSID data. Therefore, this finding is not necessarily conclusive,
which also motivates the present paper. Beyond this controversy on earnings dynamics, a new literature has begun
to take an approach that distinguishes the model allowing for profile heterogeneity from the unit root model in amore structural way. See, e.g., Guvenen and Smith (2009).
6

See, e.g., Becker (1993), and a more recent paper, Guvenen and Kuruscu (2010), for a comprehensive discussion

about the relationship between human capital investment and earnings (or wage) profiles.

2paper are drawn from the Japanese Panel Survey of Consumers for the period 1993–2004. From
this survey, it is possible to create panel data sets of earnings and relevant variables for individuals and by education group, as does previous empirical work based on the PSID. We consider
both balanced and unbalanced panels, mainly because we examine the robustness of our results
under the sample selection criteria used in this paper, and because there exists no corresponding
previous work for Japan.7

Consequently, we include in our analysis a specification of earn-ings processes similar to that of Baker (1997) and Haider (2001) as well as Guvenen’s (2009)
specification.
The use of Japanese data is of particular interest for the purpose of this study, not only
because we can analyze earnings dynamics for individuals and by education group in a similar
way to the US studies, but also because Japan has been recognized as representative of countries
with relatively low income inequality compared with the United States or as a country withdifferent earnings profiles from the United States. Indeed, as Moriguchi and Saez (2008, SectionII) point out, there is a general belief that income inequality is much smaller in Japan than in
the United States (see Tachibanaki (2005, 2006) and Ohtake (2005) for this debate). On theother hand, the question of how and why earnings profiles for Japan are different from those for
the United States has attracted the interest of many researchers in the context of estimation of
Mincer-type earnings (or wage) regressions using cross-sectional data (see, e.g., Hashimoto andRaisian (1985, 1992), Mincer and Higuchi (1988), Clark and Ogawa (1992a,b), and Abe (2000)).
7

There are a few papers that have studied consumption and income inequality using cross-section data ofJapanese households from the National Survey of Family Income and Expenditure conducted by the Japanese
government. For example, on the basis of this cross-sectional data, Ohtake and Saito (1998) analyze consumption
inequality within a fixed cohort, following Deaton and Paxson’s (1994) method, and Abe and Yamada (2009)
estimate an income process of Japanese households, using a similar specification to that of Storesletten et al.
(2004b). The only study comparable to ours is Abe and Inakura (2007), who apply Abowd and Card’s (1989)
method to a Japanese panel drawn from the same survey as ours, but they also do not focus on heterogeneity inearnings profiles.

3

Nevertheless, nobody has attempted to estimate earnings dynamics, as we do in this paper.
We obtain both corroborating evidence and some different findings. First, an increase in thevariance of the earnings residual (defined as the deviation from a component of log real earnings
common to all individuals) over time can also be observed in our data on Japanese individuals, and when we try to explain this increase using the models, ignoring profile heterogeneity(especially, the dispersion of earnings growth rates) leads to a substantial upward bias in thepersistence of earnings shocks. Second, according to our estimation results by education groupbased on the unbalanced panel data, we cannot find a significant difference in the dispersion of
earnings growth rates between the college-educated and the noncollege-educated groups. Third,
the fixed effect (i.e., differences in the initial conditions at the time when individuals enter into
labor markets) also has a significant effect on the variance of the earnings residual even in themodel allowing for heterogeneous earnings profiles (hereafter called the profile heterogeneity
model).8 Although the second and third findings are different from Guvenen’s findings for theUnited States, we do find evidence supporting his finding of a moderate earnings shock and asignificant dispersion of earnings growth rates for each group. We also find that the estimatesof the dispersion parameter of earnings growth rates are similar to those reported in Guvenen(2009), Baker (1997), and Haider (2001).
To provide additional evidence on causes of the preceding second result, we examine whether
the result is sensitive to aggregation across diverse groups, and we also attempt estimation thatallows for the possibility of occupational differences in earnings profiles (pointed out by, e.g.,

8

In this paper, we use the term “profile heterogeneity model” as in Baker (1997). We shall not use the term

“heterogeneous income profile model” as in Guvenen (2009) and Hryshko (2009) because we focus on earnings andbecause income is usually used in a broader sense than earnings. See, e.g., Ehrenberg and Smith (2009, pp.34–35)
for the relationship between earnings and income. For the same reason, we use the simple term “restricted model”
instead of “restricted income profile model” later on.

4

Topel (1991)).9 We show that both aggregation and occupational differences can account forpart of the dispersion in earnings growth rates, so that the estimate of the dispersion parametercan have a slightly upward bias. We show that the second result holds as long as our data set isused, but the profile heterogeneity model still cannot be rejected. We argue that our findings as awhole indicate the importance of allowing for heterogeneity in earnings growth rates in modelingearnings dynamics, which agrees with the main message drawn from Guvenen’s findings for theUnited States, despite some differences in the details of the estimates.
The paper is organized as follows. In Section 2, we first summarize the findings and arguments by Guvenen on which we focus in this paper, for the sake of completeness. We thendescribe, in Section 3, the Japanese panel data and show the characteristics of the samples
derived from the data. In Section 4, we present some corroborating evidence and new findings
using the Japanese panel data. Section 5 concludes.

2

The Profile Heterogeneity Model

The hypothesis that we concentrate on in this paper is very simple: initial earnings and earnings
growth rates vary across individuals, so that each individual has a specific earnings profile overtheir life cycle. Despite various attempts since Lillard and Willis (1978), this hypothesis hasremained at the heart of empirical work on earnings dynamics in the labor economics literature(see, e.g., Baker (1997), Haider (2001), Baker and Solon (2003), and references therein), but
it has not explicitly been connected with recent work in modern quantitative macroeconomics,
until Guvenen (2007, 2009).
The specification of the earnings process used by Guvenen is standard in the literatureon labor economics rather than macroeconomics, which is composed of three components: a
9Carroll and Samwick (1997) estimate the unit root model of earnings processes with no profile heterogeneity

not only by education group but also by occupation group. Guvenen (2009) focuses on their estimation resultsby education group and argues point (ii) mentioned above.

5

common factor across all individuals, individual-specific factors, and stochastic shocks. Moreprecisely, it is given by:
yit = f (Xit , ψt ) + (αi + βi Xit ) + zit + $it ,(1)
zit = ρzit−1 + ηit , zi0 = 0,
where yit is the natural logarithm of real earnings of individual i in year t, and Xit is a measureof individual i’s labor market experience in year t.10

The first term on the right-hand sideof the first equation captures the variation that is common to all individuals (called the meanearnings profile or common life-cycle component in the literature), and f (·) is assumed to be apolynomial function of Xit with a parameter vector ψt . The second term (αi + βi Xit ) capturesindividual-specific factors, in which αi and βi allow individuals to have different initial earnings
and earnings growth rates, relative to the mean earnings profile. Transitory shocks, $it andηit , are independent of each other and over time, with zero mean and variances σ!2 and ση2 .11
Individual-specific parameters αi and βi are assumed to be independent of the transitory shocks$it and ηit , and have zero mean, variances σα2 and σβ2 , and a covariance σαβ .
To focus on the last two factors, define the earnings residual as ŷit ≡ yit − f (Xit , ψt ).
10

In the literature, there are subtle variations in the definition of the subscript t. One definition is the year asis the case here, which is adopted by, e.g., MaCurdy (1982), Abowd and Card (1989), Baker (1997), and Haider(2001). Guvenen (2009) further distinguishes notation between the year and the number of years of labor market
experience. A second definition is age, which is adopted by, e.g., Moffitt and Gottschalk (1995, 2002, 2009),
Storesletten et al. (2004a), and Guvenen (2007). All of these studies are based on the US PSID. However, if
a very rich data set is available, as in the Canadian case of Baker and Solon (2003), then it would be ideal tofollow their paper and define yit as the log real earnings in year t of individual i born in year b. In other words,
the definition of the subscript t (and consequently yit ) depends on the richness of data used in the analysis. As
described in Section 3, our data sets are rather close to those of the previous studies using the year t definition,cited above, in terms of sample sizes and lengths of time periods. For this reason, here we define subscript t
as the year. In our empirical analysis, however, we allow for differences in earnings variances among cohorts byconsidering three types of data sets.
11

It is possible to allow these variances to vary with time. For simplicity of discussion, here we do not consider

time-varying variances, but we deal with one such case in our empirical analysis.

6Specification (1) then becomes:ŷit = αi + βi Xit + zit + $it .

(2)

One difference from a typical specification in the labor economics literature (e.g., Baker (1997)
and Haider (2001)) is that equation (2) includes the transitory shock $it , which can be regarded
as one characteristic of Guvenen’s specification.12

In contrast to this, a typical specification

used widely in the macroeconomics literature (see, e.g., Storesletten et al. (2004a,b)) is givenby:ŷit = αi + zit + $it .

(3)

By comparison with (2), this specification can be interpreted as excluding, by assumption, thepossibility of heterogeneity in earnings growth rates. The following is a short list of the main
discussions and findings (on which we concentrate in this paper) associated with these two
specifications:13• The variance of ŷit under the restricted specification (3) is calculated as:
Var(ŷit ) = σα2 + σ!2 + ση2

t−1
!

j=0

= σα2 + σ!2 + tση2ρ2j if ρ #= 1,(4)

if ρ = 1.

Therefore, a highly persistent shock is the only factor that leads to a rise in the varianceof log earnings. The restricted specification with ρ ≈ 1 is consistent with Deaton and12

If the transitory component !it is interpreted as capturing measurement error, then ignoring it may lead toa downward bias in the persistence parameter ρ. In fact, a comparison between his findings and Baker’s suggeststhat this possibility may be true for the US data-based analysis. Thus, this modification is important, although
it may appear minor at first glance.
13

As mentioned previously, this section does not intend to provide a comprehensive survey of recent contribu-

tions. For such surveys from a macroeconomic perspective, see Heathcote et al. (2009) and Meghir and Pistaferri(2010). In particular, Section 3.1.5 and Table 2 of Meghir and Pistaferri (2010) summarize the main results inthe extensive literature tersely.

7

Paxson’s (1994) finding, a significant rise in the variance of log earnings within a cohort
over the life cycle, which has been one reason for its acceptance in the macroeconomics
literature (see, e.g., Storesletten et al. (2004a)).
• The unrestricted specification (2), which we call the profile heterogeneity model, is consistent with some compelling hypotheses based on the theory of human capital investment, such as heterogeneity in growth rates of earnings dependent on individuals’ ability
differences,14 while the restricted specification with ρ ≈ 1 is not so, and its theoreticalinterpretation is not necessarily clear. In this respect, the restricted specification withρ ≈ 1 has not been preferred in the labor economics literature, even though it was not
rejected (see, e.g., Baker (1997) and Haider (2001) for discussions).
• In a discussion that bridges these different views, Guvenen (2007, 2009) argues that it
is possible to explain a rise in the variance of log earnings even under the unrestricted
specification (2). The variance of ŷit calculated from (2) is:
Var(ŷit ) = σα2 + σ!2 + ση2t−1!

ρ2j + (2σαβ Xit + σβ2 Xit2 )j=0

if ρ #= 1.

(5)This equation implies that, even if there are no highly persistent shocks (i.e., ρ is not close
to one), differences in labor market experiences that will be accumulated as individuals getolder, which appear as the last two terms, can lead to a rise in the variance of log earnings.
Guvenen (2009) also notes that estimation of the earnings process (especially focused on
the autoregressive parameter ρ) in the context of the unrestricted specification (2) withthe transitory shock $it has not been done so far. According to his empirical work basedon a US panel of earnings drawn from the PSID data, the unrestricted specification (2) isestimated to yield a moderate persistence (about ρ = 0.8) and a significant heterogeneityin earnings growth rates (i.e., σβ2 > 0) (see Table 1 of Guvenen (2009)). Given these14

For a list of other theoretical justifications, see, e.g., footnote 7 of Haider (2001).

8

estimates, the last two terms can account for about 0.3 percent at age 30 and about 80
percent at age 65 (i.e., retirement age) of the variance Var (ŷit ) (see Table 2 of Guvenen(2007)).
• Conversely, ignoring profile heterogeneity (i.e., assuming the restricted specification (3))
leads to an upward bias in the autoregressive parameter ρ. In the US case, for example, theestimate of ρ rises from 0.821 to 0.988 for all individuals (see Table 1 of Guvenen (2009)),
which is close to the values that were extensively used in calibration studies that assumed
the restricted specification (see, e.g., Huggett (1996) and Storesletten et al. (2004a)).
• Guvenen (2009) further notes that there exists no corresponding analysis that investigates
the differences across education groups in the context of the unrestricted specification (2).
His findings reveal that there are few differences in the estimate of ρ across education groups(ρ = 0.805 for the college-educated group and ρ = 0.829 for the high-school-educatedgroup); however, the dispersion of the earnings profiles captured by σβ2 is significantly
larger for the college-educated group, which is about 2.5 times as high as that of the highschool-educated group (σβ2 = 0.00049 for the college-educated group and σβ2 = 0.00020
for the high-school-educated group) (see Table 1 of Guvenen (2009)). This is inconsistent
with studies such as Hubbard et al. (1994, 1995) and Carroll and Samwick (1997), whichassume that there is no profile heterogeneity for all education groups (i.e., βi = 0, andconsequently, σβ2 = σαβ = 0).
Of the above-mentioned points, the empirical findings by Guvenen (2009) suggest that (i)we do not need to rely on the restricted specification assuming a highly persistent shock to develop incomplete markets, heterogeneous-agent models; and (ii) the assumption of no individualspecific or no education-group-specific differences in earnings growth rates may be inappropriate.
Given this sharp contrast to the existing assumptions, corroborating his findings, and asking
9whether they are PSID data-specific—in other words, asking whether the debate tailored for US
data is universally applicable—is an important and necessary task, which also obviously affects
the premise when one considers as the next step the microfoundations for earnings dynamics.15
In this paper, we use a panel of Japanese individuals, described in the next section, and as astarting point for this paper we first examine whether Guvenen’s (2009) new empirical findings
for the United States summarized above hold up on the basis of that data, and thus for Japaneseindividuals.

3

The Data

3.1

The Japanese Panel Survey of Consumers

The data used in this paper are drawn from the Japanese Panel Survey of Consumers (hereafter
JPSC) compiled by the Institute for Research on Household Economics (a public corporation
duly approved by the Prime Minister and established in 1986 in cooperation with the Economic
Planning Agency, currently the Cabinet Office of the Japanese government). The JPSC has
been conducted in October every year since 1993, and it follows the same individuals, as does
the PSID. Respondents to the survey are 1500 women in the age range 24–34 as of 1993. They
were selected from the entire area of Japan on the basis of a two-stage stratified random sampling method.16 To administer the survey, survey conductors visit and distribute survey sheets
to every household, and then collect them in person after one month. Questionnaire items in
the JPSC include questions about, e.g., family composition changes, employment, consumption
expenditure, income, savings, financial assets, loans, housing, consumer durables, time management, and satisfaction of life, some of which ask about not only the respondent but also her

15See, e.g., Heathcote et al. (2009) for a survey of recent research on the microfoundations.

16

The 1995 Annual Report of the JPSC (Institute for Research on Household Economics (1995)) compares thissample with the results of other representative surveys including the census of Japan conducted in 1990, andconcludes that the JPSC sample reflects the characteristics of the population quite well.

10

family members. Thus, adequate information about individuals and households is available fromthe JPSC, and it allows us to construct variables necessary for estimating the earnings processesof males, as in empirical work based on the PSID.17
In the JPSC, information about labor market experience is elicited by the following questions:“How long has your husband worked since his graduation from school? (Please respond in years
and months.)” and “Does your husband currently work?” By combining these, it is possible
to calculate the labor market experience of an individual with reasonable accuracy.18

The

measure of labor earnings that we use in this paper is earnings before tax from employment anddoes not include labor portions of other types of income such as farm income, business income,market gardening income, and roomers and boarders income. Therefore, it is slightly narrow
relative to the typical measure (total labor income) in previous studies using the PSID (e.g.,
Baker (1997), Haider (2001), and Guvenen (2009)); however, we do not attempt to reconcile thisdifference because there is no detailed information on the above items of income in the JPSC.
Labor earnings in the year t survey refer to annual earnings in calendar year t − 1; therefore, to
17

A slightly inconvenient feature of the JPSC data, compared with the PSID data, is that the submission of an

application form is required for use of the data, and after obtaining permission from the Institute the applicant
receives a CD-ROM. The application form is downloadable from the Web site of the Institute for Research on
Household Economics (http://www.kakeiken.or.jp/en/).
18

In the US literature, labor market experience is calculated from information on education using formulas

such as (age − education − 6) and (age − max(years of schooling, 12) − 6). In the JPSC, there is no questionthat asks years of schooling directly. Instead, the respondent provides information on her own and her husband’s
educational background by selecting from various categories. It may be possible to calculate the labor market
experience by inferring years of schooling from this answer in a similar way to the US literature. However, we did
not adopt this method because of at least two difficulties. First, we cannot identify years of schooling for those
who dropped out and repeated a grade. Second, it is difficult to pin down years of schooling for categories such as“both vocational school and high school” and “junior college or specialized vocational high school”. To deal withthese, we need to make some assumptions about the relation between the educational background reported andyears of schooling, but doing so may introduce measurement error. Although the use of retrospective questions
also may introduce measurement error, it has the advantage that the calculation is simple and does not dependon additional assumptions.

11

convert nominal values into real ones, they are deflated by the consumer price index (using 2005
as the base year) in the corresponding calendar year. We follow convention in the literature andrefer to the survey year as the observed year to avoid needless confusion. Appendix A contains
details on our use of the data and the definitions of the variables used for analysis.
A common problem with panel data is that there is attrition for various reasons every year.
The JPSC is no exception. In response to this problem, 500 women in the age range 24–27 asof 1997 have been added since 1997, and 836 women in the age range 24–29 as of 2003 havebeen added since 2003 as new respondents. In this paper, we use 12 waves covering the period
from 1993 to 2004 (the latest survey available at the time of writing). Therefore, three samples(called in turn cohort A, cohort B, and cohort C by the Institute for Research on Household
Economics) are available for that period; however, the last sample covered since 2003 (cohortC) is excluded from our analysis because of a scarcity of time periods.
Using 12 waves of the JPSC, we create three panel data sets. The first panel covers the survey
years 1993–2004 and includes only the original JPSC sample (cohort A). This choice maximizes
the number of years used for analysis but reduces the number of households considerably. The
second panel covers the survey years 1997–2004 and includes both the original JPSC sample
and the sample since 1997 (cohort A and cohort B). These two panels are balanced ones, so
the second panel maximizes the number of households in the context of balanced panels. The
third panel is, on the other hand, unbalanced and covers the survey years 1993–2004, which
maximizes the number of households as well as the number of years. The samples used foranalysis are selected from the raw data using the following criteria. (i) The respondent and her
spouse are a continuously married couple. Further, the spouse (i.e., husband of the respondent)(ii) is classified as an employee using the definition of the JPSC (i.e., a wage or salary earner,
excluding self-employed workers, family workers, and freelance professionals; see Appendix A for
details), (iii) reports positive labor earnings, and (iv) reports annual hours of work between 728
12and 5096 hours (i.e., weekly hours of work between 14 and 98 hours). For the balanced panels,
these requirements need to be satisfied over the entire sample period. For the unbalanced panel,these requirements need to be satisfied for at least five (not necessarily consecutive) years.19
We adopt requirement (i) in addition to focusing on male earnings, so that an individualin the samples forms a household. Hence, we use the term “households” interchangeably inreference to individuals (husbands) in the following description, hopefully without confusion
to readers.20

By construction of the JPSC questionnaire items, requirements (ii) and (iii)exclude student part-time workers and retirees. For this reason, unlike the US literature, we
do not further impose an age restriction for the husband. The first wave of the JPSC (i.e.,the 1993 survey) does not include questionnaire items about hours worked. We therefore do
not impose requirement (iv) on the year 1993. In addition to elimination of households using
these requirements, we remove households for which data needed in the calculations are missing,households for which the husband’s age either increases more than a year or remains the sameover two years,21 households with no information on the husband’s education, and householdswith extreme values of the husband’s real labor earnings (specifically, a growth rate above 250
percent, below −80 percent, or a level below one million yen in any given year, which were19

We discuss later on in Section 4.2 how this restriction on the number of observed years can affect estimation

results through a comparison of estimates from the balanced and unbalanced panels.
20

The JPSC questionnaire uses the term “husband” throughout rather than “head of household” or “malehousehold head”. To maintain consistency with the questionnaire, we follow this terminology and do not use theterm “head of household” or “male household head” by conscious choice.
21

These errors in information on age have been discovered by the author. The response to the author’s inquiries

about these errors from the Institute for Research on Household Economics was that they may be modified afterreconfirming by further interview. Note that a newly released JPSC CD-ROM (probably after January 2011)
may include such corrections. Hence, readers who are interested in replicating our results should pay attention
to this point when using the replication programs for this paper, and if the corrections were made, then suchreaders should modify the programs appropriately. However, we do not expect that it would substantially affectour results because the number of households with these errors in age is small, as described in Appendix B.

13

decided after examining the empirical distribution of real earnings).
Our sample selection procedure yields 201 households (201 × 12 = 2412 observations) for
the 1993–2004 balanced panel, 384 households (384 × 8 = 3072 observations) for the 1997–2004 balanced panel, and 908 households in total (8162 observations) for the 1993–2004 unbalanced panel.22 We further divide each sample into two education groups: college-educatedand noncollege-educated groups. We adopt a slightly broad definition of education groups—the“college-educated group” consists of individuals with at least a four-year college degree, and the“noncollege-educated group” consists of individuals without a four-year college degree—in order
to avoid a reduction in the sample size for each group in the balanced panels (see Appendix A
for details of the definition). Appendix B contains details of the sample selection procedure aswell as the number of removed households or observations at each stage.

3.2

Summary Statistics

Table 1 reports summary statistics of our key variables for each of the three types of panel data
sets. Panels A, B, and C of Table 1 correspond to those of all individuals, the college-educatedgroup, and the noncollege-educated group, respectively. Here information on pooled data rather
than its time series is provided to make it easier to compare the characteristics of the three typesof panels and differences between the groups.

22

The length of the time periods in our panels may appear to be short, but it is not necessarily so, comparedwith those in previous studies. For example, MaCurdy (1982) uses a 10-year panel of earnings. Abowd and Card(1989) use an 11-year panel of earnings and hours worked. Baker (1997) examines a 10-year panel of earnings
as well as a 20-year panel. As for the sample size, MaCurdy (1982), for example, studies a balanced panel of
513 continuously married males, and Baker (1997) studies a balanced panel of 534 male household heads, bothof which are drawn from the US PSID. Given the difference in the total population between the United States
and Japan, it seems fair to state that our sample size of 201 or 384 households is not small. Using Swedish data,
Hause (1980), which is one of the early studies supporting profile heterogeneity, examines a panel of 279 males
for a period of six years. Thus, the length of our time periods and sample sizes of the balanced panels represent
an acceptable lower bound.

14

The following can be seen from Table 1. First, the husbands of the respondents used foranalysis are between 21 and 65 years old and have a mean age that falls into the range of 36
to 39 years old. As mentioned previously, although we have not imposed an age requirement,
this age range seems reasonable compared to previous studies. However, we need to note that
our samples are slightly weighted toward young age groups. Second, annual labor earnings arehigher for the college-educated group than for the noncollege-educated group. On the one hand,
annual hours worked (and weekly hours worked) are longer for the noncollege-educated groupthan for the college-educated group. These facts imply that higher educational attainment
results in higher wages (average hourly earnings). Third, labor market experience is longer forthe noncollege-educated group than for the college-educated group, which is consistent with thefact that noncollege graduates enter into labor markets earlier. These contrasts suggest that thecharacteristics of earnings dynamics are different across education groups.

3.3

The Covariance Structures of Earnings

The parameters of interest in this study are ρ, σα2 , σ!2 , ση2 , σβ2 , and σαβ . They are estimatedusing information on the variances and autocovariances of the earnings residual. The empirical
autocovariance matrix is constructed from the residuals of year-by-year regressions of log realearnings on the common factor f (Xit , ψt ), in which the function f (·) is assumed to be a cubic
polynomial in labor market experience.23
As noted by Guvenen (2009), the coefficients of this polynomial are time varying as a consequence of the year-by-year regression; therefore, the intercept of the function f (·) can beinterpreted as capturing time effects (i.e., aggregate shocks common to all individuals). In this23

In the US case, Baker (1997) uses a quadratic polynomial in experience, while Haider (2001) uses a quartic

polynomial in experience; however, these alternative specifications had no significant effect on the results reported
in this paper. In view of this result, it seems that including up to the quadratic term of experience is important2
3
at least for analysis based on our data. In the estimation, Xit
and Xitare divided by 102 and 103 , respectively,

as usual.

15

respect, there is no opportunity to add year dummy variables into our specification. On theother hand, it is possible to add other dummy variables such as cohort, education, and family
size into the function f (·), in principle. However, following Guvenen (2009), we do not pursue
these alternative specifications with many dummy variables, partly because later we estimate
the models after separating the sample into different education groups, and partly because it isdifficult to judge which dummy should be added except for the year dummy variables.24
Table 2 presents the variances and autocovariances of the earnings residual calculated using
all individuals for each of the three types of panels,25 and Figure 1 plots changes in the variances
over the sample period. First, looking at the first column of each panel in Table 2, the variances
are significantly different from zero, and as is clear from Figure 1, there is a strong increasein the variances over time. In balanced panels in particular, this increase can be interpreted
as indicating that the variation in earnings increases as individuals get older or increase theirlabor market experience. Second, comparing the magnitude of the variance and its changeover time between the balanced and unbalanced panels, the variance as a whole is larger for
the unbalanced panel, which implies that this sample contains more heterogeneous individuals.
Third, the autocovariances are positive and significantly different from zero. Looking at each row
of Table 2 from left to right, it appears that they tend to decline at the first and second orders
and then become relatively smooth (although higher-order autocovariances are not reported
24

However, it may be worth including a cohort dummy in the first-stage regression because our two panels (the1997–2004 balanced panel and the 1993–2004 unbalanced panel) include by construction the two cohorts (cohort
A and cohort B). We tried the regression with the cohort dummy, but it did not have a significant effect on the
results reported in the next section. On the other hand, we did not try a family size dummy because according to
the JPSC questionnaire, our measure of labor earnings does not include child allowance (i.e., it does not dependon the number of children). Consequently, we follow the same specification as Guvenen’s.
25

We estimate cross-sectional variances and autocovariances. See Arellano (2003, p.58) for the definition. There

are several ways to obtain the standard errors of the variances and autocovariances in the literature. Here wefollow Blundell et al. (2008) and report the estimates and standard errors obtained from regressing ŷit ŷit+j (j ≥ 0)
on a constant term by year.

16

in the table to save space). Although our data sets are targeted toward Japanese men, thesecharacteristics of autocovariances (excluding their magnitudes) seem similar to those identified
in the US literature (e.g., Baker (1997) for balanced panels, Haider (2001) for unbalanced panels)
to some extent.

4

Results

In this section, we first present estimation results based on the two balanced panels, and thenexamine estimates from the unbalanced panel. At the estimation stage, we allow the varianceof the transitory shock, σ!2 , to vary with time, which is attempted by Guvenen (2009).26 We
also attempt to estimate another specification without $it (i.e., that imposes σ!2 = 0). This
specification is close to the case attempted by Baker (1997) and Haider (2001), which enables
us to evaluate the effect on the autoregressive parameter of excluding $it .
The parameters of interest are estimated using minimum distance techniques (proposed by
Chamberlain (1984)), which minimize the distance between the empirical autocovariance matrix
and its counterpart implied by the two models. This approach is widely used in the literature,
but as emphasized by MaCurdy (2007, Section 6.6), there is a possibility that the familiar
procedures calculate incorrect values of the consistent estimate of the asymptotic variance when
unbalanced panel data are used. To avoid this pitfall, we incorporate MaCurdy’s suggestions
into our estimation procedure based on unbalanced panel data. Details of the estimation method
are provided in Appendix C.

26

More correctly, Guvenen (2009) considers the case in which the variance of the transitory component in theAR(1) process, ση2 , as well as the variance σ"2 , varies with time. We also tried this case, but it made almost allof the parameter estimates of interest insignificant. Hence, we adopt only the specification with the time-varying
σ"2 .

17

4.1

Preliminary Analysis: Estimates from the Balanced Panels

Table 3 reports the results for all individuals based on the two balanced panels. The results ofthe profile heterogeneity model are provided in panel A of Table 3. For the 1993–2004 panel,
the estimate of the autoregressive parameter ρ is 0.595 with a standard error of 0.348 whenσ!2 is allowed to vary with time; on the other hand, it is 0.384 with a standard error of 0.157
when the specification without $it is used. For the 1997–2004 panel, the estimates of ρ are 0.629
with a standard error of 0.284, and 0.331 with a standard error of 0.136, respectively. Thus,
the first finding is that ρ is estimated to be below one in the profile heterogeneity model. If thetransitory component $it captures measurement error, then the difference in ρ between the two
specifications suggests that the true persistence of earnings shocks will be underestimated byignoring it.
The estimates of σβ2 , which capture heterogeneity in earnings growth rates, are 0.00033 and
0.00044 for the 1993–2004 panel, and 0.00057 and 0.00076 for the 1997–2004 panel. They are all
significantly different from zero. Using a balanced panel from the PSID, Baker (1997) obtains
estimates of σβ2 ranging between 0.00039 and 0.00082. Haider (2001) uses a revolving panel fromthe PSID and reports an estimate of σβ2 = 0.00041. Guvenen (2009) uses unbalanced panelsfrom the PSID and obtains estimates of σβ2 = 0.00038, 0.00043, and 0.00055 for the case of all
individuals. Thus, our result reveals not only that there is statistically significant heterogeneityin earnings growth rates for Japanese men, but also that the magnitude of the estimates is very
similar to those obtained from the US data.
The estimates of σαβ are −0.00339 and −0.00525 for the 1993–2004 panel, and −0.00764 and−0.01093 for the 1997–2004 panel. They are significantly different from zero at conventionalsignificance levels. The negative value of σαβ implies that the intercept and slope of the earnings
profiles are negatively correlated, which is also consistent with the previous work cited above.27
27

Whether σαβ is negative is of economic interest because it has an important implication that human capital

18

The estimates of the variance of the fixed effect σα2 are 0.090 and 0.120 for the 1993–2004 panel,and 0.164 and 0.217 for the 1997–2004 panel. Again, they are all estimated to be significantly
different from zero. Thus, from the results stated so far, the profile heterogeneity component,
σα2 + σβ2 Xit2 + 2σαβ Xit , has a significant effect on earnings dynamics. On the other hand, theestimates of ση2 are 0.011 and 0.016 for the 1993–2004 panel, and 0.010 and 0.017 for the 1997–2004 panel. Except for one case, they are significantly different from zero. However, given that
we have obtained a low estimate of ρ, this result indicates that the AR(1) component (i.e., ση2× the cumulative sum of ρ) as a whole has only a relatively small effect on earnings dynamics.
Another concern here is about how the autoregressive parameter ρ is biased by imposing
βi = 0. The results of the restricted model are provided in panel B of Table 3. The estimatesof ρ are 1.049 with a standard error of 0.057, and 1.026 with a standard error of 0.043, for the
1993–2004 panel. Compared with the corresponding estimates from the profile heterogeneity
model (columns (1) and (2)), the estimated persistence rises significantly under the restricted
model. This rise is also true for the estimates of ρ from the 1997–2004 panel.
We next turn to the estimation results for the college-educated and noncollege-educatedgroups. The results are reported in Table 4. Estimation is implemented by applying the sameprocedure as that for all individuals to each education group separately. As already shown in
Table 3, there is a possibility that ignoring the transitory shock $it leads to a bias in the estimateof the autoregressive parameter. Hence, here we focus on the specification that allows σ!2 to varywith time.
Panel A of Table 4 reports the results of the profile heterogeneity model. This panel showsthat the estimation results differ considerably between the two groups. For the college-educatedgroup, the estimate of ρ is 0.286 for the 1993–2004 panel and 0.493 for the 1997–2004 panel, butinvestment (e.g., job training) involves a trade-off between initial earnings and the growth rate of earnings. See
Lillard and Weiss (1979) and Hause (1980) for detailed discussions of this interpretation.

19

they are not significant. For the noncollege-educated group, the estimate of ρ is 0.804 for the
1993–2004 panel and 0.896 for the 1997–2004 panel, both of which are significant. On the one
hand, the estimate of σβ2 is significant for the college-educated group, but it is not significant
for the noncollege-educated group. Similarly, another key parameter of the profile heterogeneity
component σαβ is also significant only for the college-educated group. On the other hand, ση2
is significant only for the noncollege-educated group. Thus, for the noncollege-educated group,
there is no evidence in favor of the profile heterogeneity model, in contrast with the collegeeducated group.
Panel B of Table 4 reports the results of the restricted model. In the restricted model, theparameter estimates are improved overall for the noncollege-educated group, that is, all estimatesof ρ, σα2 , and ση2 are significant. This result appears to explain the findings in panel A of Table
4 that failed to accept the profile heterogeneity model for that group. Our finding that the
restricted model fits well for the noncollege-educated group seems consistent with, e.g., Carroll
and Samwick (1997), who estimate the restricted model with the further restriction of ρ = 1 forall educational backgrounds using the US data. However, our result shows that the estimateof ρ is less than one, and the restriction of ρ = 1 is not accepted for our data sets. For thecollege-educated group, the estimate of ρ is significant, but the estimate of ση2 is not significant.
In other words, it is difficult to explain the earnings dynamics of the college-educated groupusing the stochastic component (AR(1) plus transitory shock component). Combined with thefinding in panel A of Table 4, this result suggests that profile heterogeneity is still important inmodeling the earnings dynamics of the college-educated group.
Our results for each group just reported show that the profile heterogeneity model fails to
explain the earnings dynamics of the noncollege-educated group, which is not consistent with
Guvenen’s US findings summarized in Section 2. However, it may be premature to draw sucha conclusion at this stage of the analysis because our analysis here has the limitation that only20

relatively small sample sizes are available for each group (see the last two rows of Table 4 for theirsample sizes); that is, information necessary for identifying earnings dynamics for each group
may have been eliminated by the loss of observations involving the requirement of balanced
panels. Next we turn to the unbalanced panel and examine the robustness of our results.

4.2

Estimates from the Unbalanced Panel

Table 5 reports the results based on the unbalanced panel. As before, we present the results
using the specification both with and without $it for all individuals only, to confirm the effect of
excluding the transitory shock.
Panel A of Table 5 reports the estimation results of the profile heterogeneity model. As
shown in columns (1) and (2) of Table 5, for all individuals the estimate of the autoregressive
parameter ρ is 0.688 with a standard error of 0.167 when σ!2 is allowed to vary with time, and
it is 0.470 with a standard error of 0.077 under the specification without $it . The estimates ofρ are similar to those in panel A of Table 3, but we see that the use of the unbalanced panel
yields estimates with sharper standard errors.
The estimates of σβ2 are 0.00035 and 0.00034, both of which are significantly different fromzero. Again, as in the case of balanced panels (panel A of Table 3), the magnitude of σβ2
is comparable to those obtained from the US data. The estimates of σαβ are −0.00167 and−0.00140, and the magnitude is reduced relative to those in panel A of Table 3. However,they are still significantly different from zero. The estimates of σα2 and ση2 are also significantly
different from zero. Thus, we find that the profile heterogeneity component, σα2 +σβ2 Xit2 +2σαβ Xit ,as a whole is significantly estimated, regardless of whether balanced or unbalanced panels areused.
A common problem with this type of empirical research (not unique to our work) is theextent to which the sample selection used for analysis has biased the results. The comparison

21

here between the balanced and the unbalanced panels may also be viewed as a sensitivity analysis
for evaluating selection bias caused by eliminating individuals observed for shorter time periods.
For example, under the profile heterogeneity model, the estimate of ρ based on the restricted
sample (the 1993–2004 balanced panel) is smaller than that of the unrestricted sample (the1993–2004 unbalanced panel). A possible interpretation of this is that the restricted sample
has eliminated individuals who suffer more persistent shocks. However, the difference in theestimates is not large. This is also true for the estimate of σβ2 . Given these results, althoughsome recent studies require fewer—two, three, or four—years than our requirement of five years
to obtain the unbalanced panel (see Haider (2001), Storesletten et al. (2004b), and Guvenen(2009, row (7) of Table 1)), it is unlikely that this slight difference in requirements concerning
the number of years observed significantly affects our results.
The difference in the results between the balanced and unbalanced panels appears in theestimation by education group. Columns (3) and (4) of Table 5 report the results for thecollege-educated and noncollege-educated groups. As we have confirmed that ρ may be underestimated when the transitory shock $it is not allowed for, we concentrate on the results from thespecification with $it . As shown in columns (3) and (4) of Table 5, unlike the case of balanced
panels (panel A of Table 4), the estimates of ρ are significant, and the estimated persistence ishigher for the college-educated group than for the noncollege-educated group: ρ is estimated tobe 0.856 with a standard error of 0.144 for the college-educated group and 0.604 with a standard
error of 0.259 for the noncollege-educated group.
For the college-educated group, the estimate of σβ2 is 0.00032 with a standard error of 0.00018,
which is insignificant at the 5% level but significant at the 10% level. For the noncollege-educatedgroup, it is 0.00028 with a standard error of 0.00005. Thus, in our case there seems not to bea significant difference in the dispersion of earnings growth rates between the two groups. This
point is reexamined from a slightly different perspective in Section 4.3. The estimates of σαβ are
22

−0.00232 and −0.00166 for the college-educated and noncollege-educated groups, respectively,
both of which are significantly different from zero. This finding that σαβ is more negative forhighly educated individuals is consistent with Guvenen (2009), whose interpretation is that theaccumulation of human capital may be more important for high-skilled occupations for raising
future earnings (wage growth) (also see Hause (1980)). We also see from the table that theparameter ση2 is significantly estimated for both education groups, unlike the case of balanced
panels.
An important point to note in panel A of Table 5 is that σα2 is significantly estimated evenunder the profile heterogeneity model, which is differ from Guvenen (2009). In our case, theestimate of σα2 is 0.030 with a standard error of 0.008, or 0.026 with a standard error of 0.009 for
all individuals, and it is 0.039 with a standard error of 0.013 for the college-educated group, and0.024 with a standard error of 0.009 for the noncollege-educated group. In contrast, Guvenen(2009) finds that the estimates of σα2 are 0.022, 0.023, and 0.038 for all individuals, the collegeeducated group, and the high-school-educated group, respectively, which are similar to ours interms of magnitude, but are not significantly different from zero. This contrast suggests thatin our case the fixed effect (i.e., initial conditions at the time when individuals enter into labormarkets) can also account for heterogeneity in earnings, in addition to the dispersion of earnings
growth rates.
Panel B of Table 5 reports the estimation results of the restricted model. Columns (5) and(6) of Table 5 report the results for all individuals, and columns (7) and (8) of Table 5 report
the results by education group. As expected, the estimates of ρ go up relative to those of the
profile heterogeneity model: from 0.688 to 0.900 or 0.470 to 0.860 for all individuals; from 0.856
to 0.904 for the college-educated group; and from 0.604 to 0.873 for the noncollege-educatedgroup. There are two points to note here. First, the rise in ρ under the restricted model forthe college-educated group is very small relative to those for all individuals and the noncollege23

educated group. Second, the magnitude of the estimated ρ as a whole seems lower than that in
the balanced panels (e.g., panel B of Table 3). To understand these points, it is necessary toallow for the magnitude of the estimate of ση2 simultaneously, because the effect of the stochastic
shock ηit on the variances and autocovariances of the earnings residual appears as ση2 × the
cumulative sum of ρ, as in equation (4). For example, if the estimate of ση2 is higher, then theestimate of ρ is expected to be lower, other things being equal.
Looking at panels A and B of Table 5 again with this point in mind, while the estimateof ση2 increases from 0.006 to 0.011 for the college-educated group (columns (3) and (7)), it
remains at almost the same magnitude for all individuals and the noncollege-educated group.
This difference probably accounts for the first point to some extent. On the other hand, looking
at panel B of Table 3 once again, while the estimate of ση2 under the restricted model falls into
the range of 0.003 to 0.011, it is between 0.011 and 0.020 in panel B of Table 5. That is, one
reason why we have obtained the lower estimates of ρ in the estimation of the restricted model
based on the unbalanced panel can be related to the higher magnitude of ση2 . However, it isnoteworthy that even in our case we have found that ignoring profile heterogeneity leads to an
upward bias in ρ.
Another noteworthy point in panel B of Table 5 is that, as seen from a comparison between
columns (7) and (8), overall, there is little difference in the estimated parameters between thetwo groups. In other words, it reveals that the use of the restricted model obscures the difference
between the two groups.
In summary, we obtain three main findings from the analysis so far. First, an increase in
the variance of the earnings residual over time can also be observed in our data on Japaneseindividuals, and when we attempt to explain this increase using the models, ignoring profile
heterogeneity (especially, the dispersion of earnings growth rates) by assuming the restricted
model leads to a substantial upward bias in the persistence of earnings shocks. Second, according24

to our estimation by education group based on the unbalanced panel, the profile heterogeneity
model fits well for both the college-educated and noncollege-educated groups as well as all
individuals. However, we cannot find a significant difference in the dispersion of earnings growth
rates between the two groups (although its estimate is very slightly larger for the college-educatedgroup than for the noncollege-educated group). This is inconsistent with Guvenen’s US findings.
Third, the individual fixed effect is significant not only in the restricted model but also in the
profile heterogeneity model. This also contrasts with Guvenen’s US findings.

4.3
4.3.1

Discussion
Alternative Grouping and Occupational Differences

Our second result is different from the corresponding US finding. Here we examine two factorsthat may cause a bias in the parameter σβ2 . The first factor is that our grouping “noncollegeeducated group” includes non-high school graduates (i.e., those who did not graduate from highschool). As mentioned previously, this grouping was adopted for the purpose of securing anadequate sample size for the balanced panel data. However, we can now relax this restriction ofgrouping by the use of the unbalanced panel.
Panel A of Table 6 reports the estimation result of the profile heterogeneity model for thehigh-school-educated group (defined by removing non-high school graduates from the noncollegeeducated group). As a reduction in the total sample size by this elimination of non-high school
graduates, which is confirmed in the last two rows, may change the estimates for all individuals
in column (1) of Table 5, we also implement estimation for all individuals of the new sample(composed of the college-educated group and the high-school-educated group). Initial earnings
and earnings growth rates of junior high school graduates are usually lower than those of highschool graduates. Therefore, the inclusion of non-high school graduates increases variation inearnings, and consequently, it may lead to an upward bias in the estimate of σβ2 (and σα2 ) for
the noncollege-educated group. The result in column (1) of Table 6 shows that this conjecture25

indeed holds for our data set: the estimate of σβ2 decreases from 0.00028 to 0.00025 when thehigh-school-educated group is used instead of the noncollege-educated group. As expected fromthis result, the estimate of σβ2 based on all individuals in column (2) of Table 6 also slightly
decreases from 0.00035 (in column (1) of Table 5) to 0.00030. Thus, the earlier finding that thedifference in σβ2 between the two education groups is very small is partly attributable to the
upward bias in σβ2 caused by the inclusion of non-high school graduates. However, the differencein σβ2 between the college-educated and high-school-educated groups (i.e., 0.00032 and 0.00025)
still remains small compared with Guvenen’s finding for the United States (i.e., 0.00049 and
0.00020).
The second factor is treatment of occupations. As Topel (1991, p.164) puts it, “It is not hard
to imagine technological or other differences across occupations that would generate corresponding differences in wage profiles.” It is possible to consider this in our context: even if individuals
have the same education background (or skill if education is its indicator), differences in occupations (e.g., clerical jobs and technical jobs) would cause variation in initial earnings (i.e., σα2 )and in earnings growth rates (i.e., σβ2 ) to be larger if they were not controlled for. To see how theearlier finding is related to the failure in allowing for occupational differences in earnings profiles, we further attempt to control for its effect by including occupation dummy variables in thefirst-stage regression (see Appendix A for details of categories of occupations). Panel B of Table
6 reports the estimation results of the profile heterogeneity model for five cases: all individualsof the original sample (the college-educated group plus the noncollege-educated group), all individuals of the new sample (the college-educated group plus the high-school-educated group),
the college-educated group, the noncollege-educated group, and the high-school-educated group.
We obtain two findings from this exercise. First, the magnitude of the estimate of σβ2 as a whole
becomes smaller. In other words, this result suggests that the magnitude of the estimate of σβ2that we previously obtained in Table 5 had partially reflected occupational differences in earn26

ings growth rates. However, more importantly, σβ2 is again estimated to be significantly different
from zero even in this case. Second, comparing the estimate of σβ2 between the college-educatedand noncollege-educated groups (column (5) and column (6)) or between the college-graduatedand high-school-educated groups (column (5) and column (7)), we see that the difference is still
small.28

Thus, it is difficult to conclude that the failure of grouping or allowing for occupa-

tional differences in earnings dynamics has obscured the existence of a significant difference inthe parameter σβ2 across education groups, as long as our data set is used.
4.3.2

Identification Problem

A final concern is that the results reported in Table 3 and Table 5 do not appear to reject
either of the two models in terms of the significance of the estimates. One way to evaluate
our results from a different perspective, which was proposed in the literature (e.g., MaCurdy(1982) and Abowd and Card (1989)), will be to use an approach that examines the signs of the
autocovariances of the first difference of ŷit . In our models, the autocovariances between ∆ŷi2and ∆ŷis are given by:
Cov(∆ŷi2 , ∆ŷis ) = σβ2 + Cov(∆zi2 , ∆zis ),(6)

for s > 2. For example, ∆ŷi2 corresponds to ∆ŷi,1994 for the 1993–2004 panel. If ρ = 1, then thesecond term on the right-hand side is zero because the shock ηit follows a white noise process inthat case. Moreover, if one considers the restricted model, then the right-hand side as a wholeis zero because of σβ2 = 0 by assumption. Therefore, the basic idea of the alternative way is totest whether the autocovariances of the first difference of ŷit are zero or not. As discussed inGuvenen (2009), however, it is extremely difficult to distinguish a very small value of σβ2 such
28

Note that this result about the variance does not mean that there exists no wage premium associated with acollege education in Japan because as described in Section 3.2, the summary statistics for our data suggest thatthe average wage for a worker with a college-level education is higher than the average wage for a high school
graduate.

27

as 0.00032 from zero. As our estimate of σβ2 is quite similar to the US case, this issue also holds
for our case.
As mentioned in the Introduction, this difficulty of distinguishing one model from the othermodel has motivated a new literature that includes Guvenen and Smith (2009), who propose
using information from consumption data as well as labor earnings data. Thus, drawing only
the conclusion that the results in this paper support the profile heterogeneity model should
be avoided, but at the same time, it is also true for the near unit root and unit root models:an impartial view is that, similarly, it is difficult to justify the highly persistent assumption of
earnings shocks by the finding that the restricted model is not rejected.

5Conclusion

The recent empirical work on earnings processes by Guvenen (2009) argues that the existing
assumptions in incomplete markets models, which require highly persistent earnings shocks andno individual-specific differences in earnings growth rates, may be inappropriate. In this paper,
we estimated the profile heterogeneity model and the restricted model using Japanese panel data,
and we found empirical evidence in favor of this argument. However, we failed to find support foranother argument that there is a significant difference in the dispersion of earnings growth rates
between the college-educated and noncollege-educated groups, although our results indicate thatthe magnitude of the dispersion parameter seems slightly larger for the college-educated groupthan for the noncollege-educated group.
We also found that, together with evidence of a moderate earnings shock and a significant
dispersion of earnings growth rates for each education group, the fixed effect is significantly estimated even when the profile heterogeneity model is used, suggesting that the initial conditions
at the time when individuals enter into labor markets are also important for earnings dynamics.
Our results seem to be compatible with the observations (in Japanese labor markets) that initial28

salaries differ across educational backgrounds or kinds of occupation, and that salary increases
also differ depending on individual-specific factors, such as ability. These observations are difficult to explain using the restricted model that does not allow for profile heterogeneity; however,
we argued that the restricted model also could not be rejected, which is an impartial view of ourempirical results. There are some differences between our estimates and Guvenen’s. Nevertheless, the general message from our analysis in this paper is similar to that drawn from Guvenen’sfindings for the United States: the empirical evidence offers no support for the modeling strategy(of earnings processes) that excludes profile heterogeneity by assumption.

29

Appendix
This appendix contains three sections. Section A provides the definitions of the variables usedin the analysis. Section B describes in detail how we created the three panel data sets. Section
C explains the estimation procedure.

A. Definition of Variables
In October 2008 (i.e., the time we obtained permission to use the data), the JPSC CD-ROM
provided by the Institute for Research on Household Economics contains data for the period
from 1993 to 2004 (12 waves). When describing the source of the variables below, we follow thenumber assigned to the questionnaire items in the survey sheet of 2004, unless otherwise noted,
and denote it by “Item xx, Question yy”. In addition to this, we also report the associatedvariable name in 2004, which is not listed in the survey sheet but assigned in the JPSC CDROM, for ease of reference. If the questionnaire items were not included in the 2004 survey,
we follow the latest survey including them. The 2004 survey sheet is downloadable both inJapanese and in English from the Web site of the Institute for Research on Household Economics(http://www.kakeiken.or.jp/en/).
Survey sheets referred. As described in the text, respondents of the JPSC are women, andif they are married, they are then asked about their husband. For this reason, if we access theabove-mentioned Web site or open up the folder (named p12 for the 2004 survey) that contains
survey sheets in the JPSC CD-ROM, there are three types of survey sheets: for married women,
for women with no spouse, and for women who got married in the past year (i.e., women who
were married after the survey in the previous year).29 The survey sheet that we refer to below
is the one for married women, unless otherwise noted because we focus on male earnings.
Age. Husband’s age is available from Item 1, Question 2 (variable name q13) if the respondent is married.
29

Unfortunately, the JPSC CD-ROM (at least the version provided to the author) does not contain the survey

sheets translated into English. The English version of the survey sheets is available only from the Web site of theInstitute for Research on Household Economics at the time of writing.

30Annual labor earnings. Husband’s labor earnings are earnings before tax from employment, available from Item 6, Question 3 (variable name q296a), in which respondents are asked
the annual amount of earnings for the preceding calendar year.30 For example, labor earnings
in the 1994 survey correspond to those obtained from January 1993 to December 1993. To convert to real terms, the nominal values are divided by the consumer price index (calendar year
average of general index, 2005 constant price) compiled by the Statistics Bureau in the Ministryof Internal Affairs and Communication of the Japanese government.
Annual hours worked. The JPSC does not have a questionnaire item that asks directly
for the annual hours worked. Instead, respondents are asked their husband’s categorized hours
worked per week and daily living schedule, as well as their own. The husband’s annual hours
worked are calculated using these questionnaire items in the following way. The other calculation
methods and their potential issues are discussed in Section B.4.
Step 1: We calculate total hours worked per week as: total hours worked per week =hours worked on weekdays × (7 − the number of holidays per week), where “hours worked on
weekdays” is available from Item 15, Question 1 (variable name q495bh for hours and q495bm
for minutes) and “the number of holidays per week” is from Item 14, Question 2 (variable nameq498a in 2002). Although “hours worked on weekdays” are available in all years, “the number ofholidays per week” is not available in 2003 and 2004. We assume that the numbers of holidays
per week in 2003 and 2004 are the same as that in 2002.
Step 2: In Item 4, Question 8 (variable name q223), respondents report their husband’s
hours worked per week by selecting one of 10 categories (1. less than 15 hours, 2. 15 to 21
hours, 3. 22 to 34 hours, 4. 35 to 42 hours, 5. 43 to 45 hours, 6. 46 to 48 hours, 7. 49 to 54
hours, 8. 55 to 59 hours, 9. 60 to 64 hours, 10. over 64 hours). If the calculated hours worked
per week in Step 1 exceed the upper limit of the categorized hours worked per week that the30

Although this question in the JPSC does not necessarily provide detailed information about components ofearnings, judging from the form of the question it seems appropriate to assume that bonuses and overtime areincluded.

31respondent reported, then we set it to the value of the upper limit. Conversely, if it is below
the lower limit of the category, then we set it to the value of the lower limit. For example, if a
respondent reports category 6 (i.e., 46 to 48 hours), but the calculated hours worked per week
is 50 hours, then we set her husband’s total hours worked per week to 48 hours.
Step 3: Judging from the JPSC questionnaire, the problem with using “hours worked on
weekdays” and “categorized hours worked per week” is that they may include hours of unpaid
overtime or service overtime work. The JPSC has a question item that asks hours of unpaid
overtime or service overtime work per week (Item 4, Question 9(2), variable name q225). It
consists of eight categories (1. 0 hour, 2. 1 to 3 hours, 3. 4 to 5 hours, 4. 6 to 10 hours, 5. 11 to
15 hours, 6. 16 to 20 hours, 7. 21 hours or more, 8. no service overtime work), and respondents
select one category from them.31 Using this information, hours worked per week are calculated
as: hours worked per week = total hours worked per week − average hours of overtime work per
week, where “average hours of overtime work per week” are defined as (the lower limit + theupper limit in the reported category)/2. For category 7, which does not have the upper limit,
we assume that average hours of overtime work per week are 21.
Step 4: Using the hours worked per week calculated in the first three steps, annual hours
worked are calculated as: annual hours worked = hours worked per week × 52, where 52 is thenumber of weeks per year computed as 365 days/7 days.
Labor market experience. There is a question that asks how long the husband has worked
since graduation from school; however, this is only in the first survey for each cohort (i.e., in the1993 survey for cohort A and in the 1997 survey for cohort B) or in an additional survey sheet
for respondents who were married after the survey in the previous year. It is labeled as Item 8,
Question 1 in the 1993 survey sheet, Item 6, Question 1 in the 1997 survey sheet, and Item 2,
Question 1 in the survey sheet for those who were married after the survey in the previous year
(variable name q689a for years and q689b for months). The husband’s labor market experience
31

The eighth category (i.e., 8. no service overtime work) was added in the 2003 survey, so that until the 2002

survey this question item consists of only the first seven categories.

32

is calculated by adding one to the number of years worked (calculated as q689a + q689b/12) if
the respondent answers that her husband currently works in Item 4, Question 1 (variable nameq213).
Education. Husband’s educational background is based on the categorical data createdusing the relevant questionnaire items by the Institute for Research on Household Economics(variable name q61sr). It consists of eight categories (1. junior high school, 2. vocational
school, 3. high school, 4. both vocational school and high school, 5. junior college or specialized
vocational high school, 6. 4-year college, 7. graduate school, 8. no response). We define
the husband’s education group as “college-educated group” if this variable is 6 or 7 and as“noncollege-educated group” if it is 1, 2, 3, 4, or 5. We define categories 1 and 2 as “non-highschool graduate”.
Occupation. Husband’s occupation is provided in Item 4, Question 3 (variable name q860).
The definition of an employee in this question of the JPSC includes the following: 6. Management (on a higher level than a manager in a company or organization, or a head of section ina public agency), 7. Other professionals (hospital doctor, researcher, professor, assistant professor or tutor in university or college, judge, etc.), 8. Technical employee (engineer, technician,programmer, medical nurse, dietitian, etc.), 9. Teacher (in primary, junior high school, seniorhigh school, special or professional school, kindergarten or day nursery), 10. Clerical employee(general clerk, business employee, bank clerk, etc.), 11. Skilled employee (skilled worker, police,deliveryman, motorman, artisan, etc.), 12. Sales and service employee (shop employee, salesperson, barber or hairdresser, chef, waiter, home helper, etc.), where the numbers (6 to 12) assigned
to each category follow those of the survey sheet.

B. Derivation of Samples
This section describes in detail how we derived the three samples from the raw data. The
deletion of households based on requirements (i)–(iv) involves, e.g., elimination of householdswith missing values for relevant variables, so that a few preliminary steps are required at each33

stage. As the following includes detailed descriptions of such steps, Appendix Figure 1 provides
a brief summary to make it easier to understand the process of the derivation.
B.1

The 1993–2004 Balanced Panel

From the original 1500 respondents in the JPSC, we removed the following households:
Singles and not continuously married couples. We removed singles or couples withchanges in marital status during 1993–2004 and kept only continuously married couples for that
period. The marital status can be judged from the categorical data created using the relevant
questionnaire items by the Institute for Research on Household Economics (variable name q1).
This deletion leaves us with 592 households.
Households for which the husband is not employed. We removed 70 households withperiods in which the husband did not work or with missing data on the husband’s labor force
status. The information on the husband’s labor force status is available from Item 4, Question 1(variable name q213). We then removed 140 households for which the husband is a self-employedworker, a family worker, or a freelance and kept households for which the husband is classified as
an “employee” for every year of the sample period. The definition of “employee” follows that in
the JPSC, which corresponds to categories 6 to 12 in Item 4, Question 3 (variable name q860),
as described in Appendix A. This leaves us with 382 households.
Households for which the husband has nonpositive earnings. We removed 106
households for which the husband’s labor earnings are not positive or recorded as 9999 and kept
households with positive earnings for the husband for every year of the sample period. This
leaves us with 276 households.
Households with missing data on the husband’s hours worked and labor market
experience. We removed 53 households for which the variables needed to construct the husband’s annual hours worked and labor market experience are not available. In the JPSC, thosemissing cases are recorded as 11 for q223, 8 (9 in 2003 and 2004) for q225, 99 for q495bh, 9 for
q495bm, 99 for q498a, and 99 for q689a and q689b. This leaves us with 223 households.

34

Households with extreme hours worked for the husband. We removed 14 householdswith the husband’s annual hours worked > 5096 (98 hours per week) or < 728 (14 hours perweek), which leaves us with 209 households.
Households with inconsistency between the husband’s age and labor market
experience. We removed three households for which the husband’s age increases more than ayear or remains the same over two years, which leaves us with 206 households.
Households with missing data on the husband’s education. There were no households
removed by this criterion.
Households with outliers. We removed five households with an extreme growth rate ofreal earnings (above 250 percent or below −80 percent) or with an extreme value of real earnings
that is one digit smaller in any given year (the latter case was deleted by imposing real earnings< one million yen).
The sample selection procedure stated so far leaves us with a sample of 201 households. The
total number of observations is 201 × 12 = 2412.
B.2

The 1997–2004 Balanced Panel

To construct a panel for the period 1997–2004, we need to note the following: (i) if respondents
are married as of the first survey of 1993 for cohort A and 1997 for cohort B, then they are asked
how long the husband has worked since graduation from school; (ii) after that survey, the samequestion is asked using an additional survey sheet only when they are newly married. Thus, byconstruction, the variables needed to calculate the husband’s labor market experience appear
only once for each respondent (unless they get divorced and remarry in the sample period). As
a result, the sample selection procedure needs to include the calculation of the husband’s labormarket experience before deleting the period 1993–1996. From 2000 respondents, composed of1500 from cohort A and 500 from cohort B, we removed the following households:
Singles. We removed singles and kept only married couples. This leaves us with 1550
households.

35

Households with missing data on the husband’s labor market experience. We
removed 43 households for which the variables needed to calculate the husband’s labor market
experience are recorded as 99 or missing.
Households with inconsistency between the husband’s age and labor market
experience. We removed 12 households for which the husband’s age increases more than ayear or remains the same over two years, which leaves us with 1495 households.
Period 1993–1996. After calculating the husband’s labor market experience, we removed
observations of the period 1993–1996.
After the above preparation, the sample selection proceeds as in the case of the 1993–2004
panel.
Not continuously married couples. We kept only continuously married couples for theperiod 1997–2004, leaving us with 804 households.
Households for which the husband is not employed. We removed 74 households withperiods in which the husband did not work or with missing data on the husband’s labor force
status. We then removed 156 households and kept households for which the husband is classified
as an “employee” in the definition of the JPSC for every year of the period 1997–2004. This
leaves us with 574 households.
Households for which the husband has nonpositive earnings. We removed 112
households for which the husband’s earnings are not positive or recorded as 9999 and kept
households with positive earnings for the husband for every year of the sample period. This
leaves us with 462 households.
Households with missing data or extreme values for the husband’s hours worked.
We removed 55 households for which the variables needed to calculate the husband’s annual
hours worked are not available. We then removed 18 households with the husband’s annual
hours worked > 5096 or < 728. This leaves us with 389 households.
Households with missing data on the husband’s education. We removed one household with no information about the husband’s education, which leaves us with 388 households.
36

Households with outliers. We removed four households with an extreme growth rate ofreal earnings (above 250 percent or below −80 percent) or with an extreme value of real earnings
below one million yen.
This sample selection procedure leaves us with a sample of 384 households (384 × 8 = 3072
observations).
B.3

The 1993–2004 Unbalanced Panel

For the same reason as that mentioned in the first paragraph of Section B.2, we need to calculate
the husband’s labor market experience and then implement the sample selection. From thesample of 2000 respondents, we first removed the following households:
Singles. We removed singles and kept only married couples. This leaves us with 1550
households.
Households with missing data on the husband’s labor market experience. We
removed 43 households for which the variables needed to calculate the husband’s labor market
experience are recorded as 99 or missing.
Households with inconsistency between the husband’s age and labor market
experience. We removed 12 households for which the husband’s age increases more than ayear or remains the same over two years, leaving us with 1495 households.
After calculating the husband’s labor market experience for this sample, we remove households that do not satisfy the conditions as in the previous procedures. However, note that, unlike
the case of the balanced panels, removing a household in any given year does not necessarilymean that the household is completely deleted from the final sample because we do not requirethat the conditions are satisfied over the entire sample period. Allowing for this difference between balanced and unbalanced panels, we report the number of observations removed or kept at
each stage of the sample selection procedure and finally provide the total number of households
included in the analysis.
Households for which the husband is not employed. We removed 5824 observations

37

of households with periods in which the husband did not work or with missing data on thehusband’s labor force status. We then removed 1870 observations and kept observations ofhouseholds for which the husband is classified as an “employee”. This leaves us with 10246
observations.
Households for which the husband has nonpositive earnings. We removed 633
observations of households for which the husband’s earnings are not positive or recorded as 9999
and kept observations of households with positive earnings for the husband. This leaves us with
9613 observations.
Households with missing data or extreme values for the husband’s hours worked.
We removed 438 observations of households for which the variables needed to calculate thehusband’s annual hours worked are not available. We then removed 52 observations of householdswith the husband’s annual hours worked > 5096 or < 728. This leaves us with 9123 observations.
Households with missing data on the husband’s education. We removed two observations of households with no information about the husband’s education, leaving us with 9121
observations.
Households with outliers. We removed 41 observations of households with an extreme
growth rate of real earnings (above 250 percent or below −80 percent) or with an extreme valueof real earnings below one million yen, which leaves us with 9080 observations.
Households for which the observed number of years is less than five. From thesample obtained thus far, we finally removed 918 observations of households for which theobserved number of years is less than five and kept households satisfying the requirements forat least five years, which leaves us with 8162 observations.
This sample selection procedure leaves us with 908 households in total.
B.4 Sample Selection Using Different Calculation Methods of Annual Hours Worked
The calculation of annual hours worked in this paper is not the only feasible approach. Perhaps
the simplest way is to use only the categorized hours worked per week and, e.g., to calculate38

(the lower limit + the upper limit)/2 for each of the 10 categories. However, as is readily
understood, this approach appears to smooth changes in hours worked per week (and hence
annual hours worked) excessively over time. In addition, as shown in step 2 of our calculationof hours worked, the range of hours is different among the 10 categories, which also appears to
introduce a measurement error in the calculated hours worked per week (and hence annual hours
worked). Another possible way may be to use Item 4, Question 10, in which respondents report
how many days the husband worked in the previous year by selecting one of 10 categories (1. lessthan 50 days, 2. 50 to 99 days, 3. 100 to 149 days, 4. 150 to 174 days, 5. 175 to 199 days, 6. 200
to 224 days, 7. 225 to 249 days, 8. 250 to 274 days, 9. 275 to 299 days, 10. 300 days or more),and to calculate annual hours worked as hours worked on weekdays × this number of days,
under additional assumptions such as (the lower limit + the upper limit)/2. Obviously, thisapproach will also introduce a measurement error because the ranges of days are large and differ
among the 10 categories. Unfortunately, it is difficult to judge what is the best method. For
this reason, we adopted an approach that uses as much information as possible to obtain annual
hours worked, and thereby eliminates the respondents with inconsistencies between the different
questionnaire items about the husband’s hours worked, unlike the two approaches above.

C. The Estimation Method
In this section, we first review the familiar approach to balanced panel data, and then describe
how it should be modified to carry out MaCurdy’s (2007) recommendation.32

32

In this paper, we follow a common practice in recent work, especially Haider (2001) and Guvenen (2009).

Unfortunately, they do not provide enough information about the calculation method of the consistent estimatorof the asymptotic variance exploited when computing standard errors of parameter estimates. For example,
it is difficult to judge whether the statements that “Both expectations are replaced by sample averages when
implemented” (Guvenen 2009, p.78) and “Finally, we estimate Φ and D with their simple empirical analogs”" ∗, S"∗ , and D∗ S"∗ D∗ described below.
(Haider 2001, p.830) mean the same calculation as those of the matrices G
Therefore, although some of descriptions in this appendix (in particular, Appendix C.1) are expected to be familiar
enough, it is still worth repeating them for clarification of MaCurdy’s points.

39C.1 Balanced PanelLet ŷit be the earnings residual of individual i in year t, obtained by regressing yit on thepolynomial function f (Xit , ψt ). Suppose that the covariance matrix of a T × 1 time seriesŷi = (ŷi1 , ŷi2 , . . . , ŷiT )# is a function of a p × 1 parameter vector θ, given by:E(ŷi ŷi# ) = Ωi (θ)(i = 1, 2, . . . , n),where the diagonal elements are:Var(ŷit ) = σα2 + σ!2 + ση2t−1!

ρ2j + (σβ2 Xit2 + 2σαβ Xit ),j=0

and the off-diagonal elements are:Cov(ŷit , ŷis ) = σα2 + ση2 ρ|t−s|

t−1
!

j=0

ρ2j + [σβ2 Xit Xis + σαβ (Xit + Xis )] (s #= t),so that the parameter vector to be estimated is θ = (ρ, σα2 , σ!2 , ση2 , σβ2 , σαβ )# for the profile heterogeneity model; on the other hand, it is θ = (ρ, σα2 , σ!2 , ση2 )# for the restricted model becauseof σβ2 = 0 and σαβ = 0. When σ!2 is allowed to vary with time, it is replaced with the parameter2 , σ 2 , . . . , σ 2 )# , whose dimension depends on the length of the sample period.
vector (σ!,1!,2!,T

Now let ci be an L(≡ T (T + 1)/2) × 1 vector of unique elements of ŷi ŷi# . Using the vech
operator that stacks by row the lower triangle elements of a square matrix, we define the L × 1
vector as:ci ≡ vech ŷi ŷi#
2 , ŷ ŷ , ŷ 2 , . . . , ŷ ŷ , ŷ ŷ , . . . , ŷ 2 )# .
= (ŷi1
i1 i2
iT i1
iT i2
i2
iT

Similarly, we define an L × 1 vector of unique elements of the covariance matrix Ωi (θ) as:
ω i (θ) ≡ vech Ωi (θ).
Letting gi (θ) ≡ ci − ω i (θ) and denoting the l-th element of gi (θ) by gil (θ), we consider thefollowing moment conditions:
E[gi (θ 0 )] = 0,
where θ 0 is the true parameter value of θ.
40The generalized method of moments (GMM) estimator θ̂ is a solution that minimizes theobjective function:

#

$#

#

$

n
n
!
1!
% 1
gi (θ) W
gi (θ) ,
n i=1
n i=1

&

and under a set of appropriate regularity conditions including √1n ni=1 gi (θ 0 ) →d N (0, S), it is√asymptotically normal: n(θ̂ − θ 0 ) →d N (0, V). An optimal choice of the weighting matrix% is S" −1 , the inverse of the sample counterpart of S ≡ E[gi (θ 0 )gi (θ 0 )# ] (under iid assumptionWof the data vector). However, it is known that the GMM estimator with this optimal weight
exhibits poor small-sample properties in the context of estimating covariance structures (Altonji% byand Segal (1996)). Therefore, we follow the practice of papers in this area and replace W

the identity matrix.33

In this case, the expression for the asymptotic variance reduces to

V = (G# G)−1 G# SG(G# G)−1 , which is consistently estimated by:
" ≡
G

n
n
!
1!
∂gi (θ̂)"≡ 1andSgi (θ̂)gi (θ̂)# .
n i=1 ∂θ #n i=1

The approximate distribution for θ̂ is:

1 " " " −1 " " " " " " " −1θ̂ ∼ N (θ 0 , (GG) G SG(G G) ).
n

"

"

"

" G)
" −1 G
" S
" G(
" G
" G)
" −1 .
Standard errors are calculated as the square root of the diagonal elements of n1 (GC.2 Unbalanced Panel

We allow the panel to be unbalanced in that individuals may not be observed every year (i.e.,some rows of ci and ω i (θ) may not be available). To handle missing observations, we define anindicator variable, dil , as:
dil =
33

'

1
0

if individual i contributes to the l-th moment,
otherwise,

As discussed by Newey and McFadden (1994), GMM is a special case of minimum distance (MD) estimation;%=S"−1 is often referred to as the optimal
therefore, the GMM estimator with the optimal weighting matrix W
minimum distance (OMD) estimator, especially in the literature on covariance structures (see, e.g., Altonji and
Segal (1996)). Furthermore, this approach, which uses the identity matrix as the weighting matrix, is often called
equally weighted minimum distance (EWMD) estimation. Following Newey and McFadden (1994), we use theterm GMM because the objective function is defined using a sample mean.

41

and let:









∗ (θ)
di1 gi1 (θ)
gi1

  ∗

 di2 gi2 (θ)   gi2 (θ) 
∗



.
gi (θ) ≡ 
..
..
=

.
.

 

∗ (θ)
giL

diL giL (θ)

Therefore, if individual i does not contribute to the l-th moment, then the l-th row of gi∗ (θ) is
filled with zero. The moment conditions that we consider are modified as:
E[gi∗ (θ 0 )] = 0.
The important difference from the balanced panel case is that the number of individuals who
contribute to each moment can be different. Inevitably, as described below, the asymptotic
distribution, the approximate distribution, and the standard errors that were presented for thebalanced panel case need to be modified.
Let nl (≤ n) be the number of individuals available to calculate the l-th sample moment.
First, the asymptotic distribution of the GMM estimator θ̂ for the unbalanced panel case depends
on, instead of the above-mentioned assumption √1n&ni=1 gi (θ 0 ) →d N (0, S), the assumption thatthe unequally normalized sample counterpart of E[gi∗ (θ 0 )] possesses an asymptotic distribution:




1 ! ∗
g (θ 0 ) √
n1 i∈{1} i1






.
..

 →d N (0, S∗ ),


!
 1

∗
 √
giL (θ 0 ) 
nL i∈{L}where {i ∈ {l}} is the set of individuals who contribute to the l-th moment, and&i∈{l} denotes

summation over the individuals in this set. Hence, the matrix S in the asymptotic variance V" ∗ whose (r, s)
is replaced with the matrix S∗ , which is consistently estimated by the matrix S

element takes the form:"∗ =(r, s) element of S

1 ! ∗∗g (θ̂)gis(θ̂),
nrs i∈{r,s} irwhere {i ∈ {r, s}} is the set of individuals who contribute to both the r-th moment and s-th
moment, and nrs denotes the number of individuals in this set. Second, the matrix G in the42asymptotic variance V is replaced with the matrix G∗ , which is consistently estimated by:∗ (θ̂)
1 ! ∂gi1


 n1
∂θ #

i∈{1}




.
∗
"

.
..
G =



 1 ! ∂g ∗ (θ̂) iLnL i∈{L} ∂θ #Third, and importantly, the approximate distribution for the GMM estimator is modified as:
"

"

"

"∗ G
" ∗ )−1 G" ∗ (D∗ S" ∗ D∗ )G" ∗ (G"∗ G" ∗ )−1 ),θ̂ ∼ N (θ 0 , (G√√where D∗ = diag(1/ n1 , . . . , 1/ nL ), and:" ∗ D∗ =(r, s) element of D∗ S

√

=

√

1
"∗
√ × (r, s) element of S
nr ns
1
√

nr ns

×

1 ! ∗
∗
g (θ̂)gis(θ̂).
nrs i∈{r,s} ir

To understand this last equation, which corresponds to equation (6.32) of MaCurdy (2007),
consider again the case of balanced panels. In this case, n = n1 = · · · = nL and n = nrs ;" ∗ = G," S
" ∗ = S," 1/√nr √ns = 1/n, and 1/nrs = 1/n. That is, the matrix D∗ S
" ∗ D∗
therefore, G"""" so that (G"∗ G" ∗ )−1 G" ∗ (D∗ S" ∗ D∗ )G" ∗ (G"∗ G" ∗ )−1 =for the balanced panel case reduces to n1 S,
1 " " " −1 " " " " " " " −1∗ "∗ ∗n (G G) G SG(G G) . Thus, the matrix D S D merely indicates that each element of the" ∗ is normalized by the unequal sample sizes, instead of 1/n, when unbalanced panel data
matrix S

are used. Finally, the standard errors of the parameter estimates in the unbalanced panel case are
"

"

"

"∗ G
" ∗ )−1 G" ∗ (D∗ S" ∗ D∗ ) G" ∗ (G"∗ G" ∗ )−1 .
calculated as the square root of the diagonal elements of (G" ∗ in practice, it is convenient
To program the sample counterpart of E[gi∗ (θ)] and the matrix S

to use notations similar to those of Blundell et al. (2008, Appendix D). That is, conformably

with the vector ŷi , we define the T × 1 vector dyi = (dyi1 , dyi2 , . . . , dyiT )# , where dyit is 1 if ŷit is
not missing and zero otherwise. Note that the variable dyit is related to the indicator variable"

introduced previously as follows: Di ≡ vech dyi dyi = (di1 , di2 , . . . , diL )# . The sample counterpartof E[gi∗ (θ)] is then calculated as:
vech

'. n
!
i=1

ŷi ŷi#

/

+

. n
!
i=1

"
dyi dyi/0− vech
43

'. n
!
i=1

/

Ωi (θ) +

. n
!
i=1

"
dyi dyi/0,where + denotes the element-by-element division. In the case of balanced panels, the first andsecond terms correspond to n1

&n

1 &n
i=1 ci and ni=1 ω i (θ), respectively; therefore, it turns out inthis case that this equation represents n1&ni=1 gi (θ) as a whole.

" ∗ is calculated as:
vector Di , the matrix S
"∗

S =

# n
!1
i=1

gi (θ̂)gi (θ̂)

#

2

,

3

$

4
Di D#i

+

. n
!
i=1

where the symbol , denotes the element-by-element product.

44

On the other hand, using the

Di D#i/,References
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49

50

38.55
592.712417.34
46.49
18.17

113
1356

5.99
164.27504.14
9.69
6.29

88
1056

24
119.28
728
14
1.67

26
129.61
728
14
3.5

24
119.28
728
14
1.67

57
1196.41
5070
97.5
39

54
3012.96
4576
88
31.5

57
3012.96
5070
97.5
39

37.80
494.902442.62
46.97
19.16

39.09
671.252363.02
45.44
16.59

38.32
565.162410.91
46.36
18.14

231
1848

6.32
163.60522.43
10.05
6.67

153
1224

4.89
225.14455.06
8.75
4.96

384
3072

5.83
209.14498.13
9.58
6.17

24
119.28
728
14
3.5

26
129.61728
14
3

24
119.28728
143

651196.41
5070
97.5
50

54
3012.96
4836
93
31.5

65
3012.96
5070
97.5
50

1997–2004 Balanced Panel
Mean Std.dev.
Min
Max

36.48
467.912467.28
47.45
17.91

37.39
634.752366.18
45.50
14.74

36.82
530.212429.53
46.72
16.73

577
5114

6.18
163.80532.14
10.23
6.54

331
3048

5.12
228.87456.50
8.78
5.20

908
8162

5.83
207.08507.56
9.76
6.26

21
101.11
728
14
1.08

24
129.61
728
14
1.42

21
101.11
728
14
1.08

65
1643.84
5096
98
50

54
3180.92
4836
93
31.5

65
3180.92
5096
98
50

1993–2004 Unbalanced Panel
Mean Std.dev.
MinMax

on the period 1994–2004 because there are no questionnaire items about hours worked in the 1993 survey.

experience is in years. Annual hours worked and weekly hours worked for the 1993–2004 balanced panel and the 1993–2004 unbalanced panel are based

Note: Annual labor earnings are in tens of thousands of yen and are measured in 2005 yen, adjusted using the consumer price index. Labor market

Number of households
Number of observations

Panel C: Noncollege-educated group
Age
38.36
Annual labor earnings
519.74
Annual hours worked
2468.88
Weekly hours worked
47.48
Labor market experience
19.66

Number of households
Number of observations

4.98
223.44426.63
8.20
5.04

201
2412

5.57
209.41475.27
9.14
6.01

1993–2004 Balanced Panel
Mean Std.dev.
Min
Max

Panel B: College-educated group
Age
38.80
Annual labor earnings
686.41
Annual hours worked
2351.16
Weekly hours worked
45.21
Labor market experience
16.26

Number of households
Number of observations

Panel A: All individuals
Age
Annual labor earnings
Annual hours worked
Weekly hours worked
Labor market experience

Variable

Table 1: Summary Statistics

51

0.0882(0.0095)
0.0868(0.0119)0.0803(0.0084)
0.0916(0.0102)0.0994(0.0120)0.0972(0.0112)0.1018(0.0111)0.1107(0.0129)0.1220(0.0137)
0.1229(0.0146)
0.1473(0.0207)0.1552(0.0213)Var(ŷit )(1)

0.0727(0.0098)
0.0726(0.0089)0.0741(0.0085)0.0841(0.0101)
0.0845(0.0105)
0.0902(0.0107)0.0975(0.0113)0.1095(0.0130)
0.1147(0.0136)0.1183(0.0145)0.1329(0.0173)——

0.0688(0.0082)
0.0735(0.0103)
0.0736(0.0088)0.0804(0.0094)
0.0887(0.0107)0.0894(0.0101)0.1009(0.0115)0.1053(0.0128)0.1157(0.0143)
0.1142(0.0153)———

0.0720(0.0088)
0.0738(0.0103)
0.0715(0.0082)
0.0819(0.0096)0.0851(0.0104)
0.0914(0.0106)
0.0963(0.0110)0.1056(0.0133)
0.1104(0.0148)—0.1026(0.0079)
0.1082(0.0085)0.1024(0.0077)
0.1090(0.0085)
0.1221(0.0092)
0.1178(0.0090)0.1397(0.0123)
0.1425(0.0129)

—

—

—

—

Var(ŷit )(5)

0.0879(0.0073)
0.0917(0.0075)
0.0927(0.0072)
0.1034(0.0084)
0.1105(0.0086)
0.1153(0.0093)0.1255(0.0109)
—

—

—

—

—

—

0.0858(0.0070)0.0919(0.0074)
0.0959(0.0076)
0.0988(0.0081)0.1136(0.0092)
0.1124(0.0098)
—

—

—

—

—

—

—

0.0841(0.0070)
0.0932(0.0077)
0.0919(0.0073)0.1017(0.0085)
0.1092(0.0095)
—

—

—

—

—

1997–2004 Balanced Panel
Autocovariances(ŷit , ŷit+1 ) (ŷit , ŷit+2 ) (ŷit , ŷit+3 )
(6)
(7)
(8)
0.1171(0.0085)
0.1095(0.0089)
0.1154(0.0078)
0.1120(0.0073)
0.1129(0.0064)
0.1172(0.0066)
0.1348(0.0077)
0.1310(0.0077)0.1402(0.0079)
0.1480(0.0091)
0.1669(0.0111)0.1652(0.0103)

0.0913(0.0070)
0.0925(0.0071)
0.0972(0.0067)
0.1008(0.0068)
0.0977(0.0058)
0.1048(0.0063)
0.1137(0.0071)
0.1175(0.0074)
0.1245(0.0075)0.1367(0.0080)0.1464(0.0098)——

0.0910(0.0067)
0.0916(0.0072)
0.0950(0.0066)
0.0990(0.0067)
0.0931(0.0058)
0.1004(0.0062)0.1125(0.0071)
0.1136(0.0072)
0.1219(0.0077)0.1297(0.0088)—

report Cov(ŷit , ŷit+1 ), Cov(ŷit , ŷit+2 ), and Cov(ŷit , ŷit+3 ), respectively.

——

0.0906(0.0069)
0.0921(0.0078)
0.0936(0.0067)
0.0958(0.0069)
0.0906(0.0058)
0.0984(0.0061)
0.1113(0.0075)
0.1106(0.0075)
0.1176(0.0084)—

1993–2004 Unbalanced Panel
Autocovariances
Var(ŷit ) (ŷit , ŷit+1 ) (ŷit , ŷit+2 ) (ŷit , ŷit+3 )
(9)
(10)
(11)
(12)

Note: Standard errors are in parentheses. Variance and autocovariances are cross-sectional ones. Three columns labeled Autocovariances in each panel

2004

2003

2002

2001

2000

1999

1998

1997

1996

1995

1994

1993

Year

1993–2004 Balanced Panel
Autocovariances(ŷit , ŷit+1 ) (ŷit , ŷit+2 ) (ŷit , ŷit+3 )
(2)
(3)
(4)

Table 2: Autocovariance Matrix of Earnings Residual Calculated Using All Individuals

Table 3: Estimates of the Profile Heterogeneity and Restricted Models Using All
Individuals (Balanced Panel)Parameterρ
σβ2 × 100σαβ × 100
σα2
ση2
σ$2
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
Panel used#households#observations

Model
Panel A: Profile Heterogeneity
Panel B: Restricted
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
0.595
0.384
0.629
0.331
1.049
1.026
1.012
0.922
(0.348) (0.157) (0.284) (0.136)(0.057) (0.043) (0.059) (0.039)
0.033
0.044
0.057
0.076
—
—
—
—
(0.012) (0.012) (0.020) (0.022)-0.339-0.525-0.764-1.093————(0.174) (0.191) (0.296) (0.369)
0.090
0.120
0.164
0.217
0.066
0.064
0.080
0.077
(0.029) (0.032) (0.044) (0.060)(0.009) (0.009) (0.007) (0.007)
0.011
0.016
0.010
0.017
0.003
0.004
0.005
0.011
(0.008) (0.002) (0.004) (0.001)(0.002) (0.002) (0.002) (0.002)
0.012(0.010)0.005(0.007)-0.005(0.008)0.002(0.009)0.006(0.011)-0.000(0.011)-0.001(0.009)0.002(0.008)0.007(0.008)0.001(0.008)0.018(0.013)0.017(0.014)
93–04
201
2412

—

—

—

—

—

—

—

—

—

—

—

—

—

0.012
(0.005)0.012(0.006)0.001(0.005)0.003(0.006)0.011(0.005)-0.000(0.005)0.014(0.006)0.008(0.008)
97–04
384
3072

—

—
—
—
—
—
—
—
93–04
201
2412

—
—
—
—
—
—
—
97–04
384
3072

0.019
(0.005)0.015(0.006)0.004(0.005)0.012(0.006)0.015(0.006)0.008(0.006)0.008(0.004)0.011(0.007)0.016(0.006)0.010(0.007)0.027(0.013)0.026(0.014)
93–04
201
2412

—

—

—

—

—

—

—

—

—

—

—

—

—

0.018
(0.004)0.018(0.005)0.006(0.004)0.007(0.004)0.014(0.004)0.004(0.004)0.020(0.007)0.016(0.007)
97–04
384
3072

—

—
—
—
—
—
—
—
93–04
201
2412

—
—
—
—
—
—
—
97–04
384
3072

Note: Standard errors are in parentheses. 93–04 and 97–04 in the third row from the bottom (Panel used)
denote that the 1993–2004 balanced panel and the 1997–2004 balanced panel are used for estimation,
respectively.

52

Table 4: Estimates of the Profile Heterogeneity and Restricted Models by Education
Group (Balanced Panel)Parameterρ
σβ2 × 100σαβ × 100
σα2
ση2
σ$2
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
Panel used#households#observations

Model
Panel A: Profile Heterogeneity
College Noncollege College Noncollege
College
(1)
(2)
(3)
(4)
(5)
0.286
0.804
0.493
0.896
1.168
(0.818)(0.188)(0.668)(0.203)(0.119)
0.030
0.020
0.059
0.020
—
(0.011)(0.018)(0.026)(0.074)-0.343-0.262-0.693-0.414—(0.153)(0.252)(0.349)(1.066)
0.080
0.080
0.121
0.134
0.044
(0.023)(0.040)(0.047)(0.127)(0.010)
0.012
0.011
0.007
0.010
0.000
(0.035)(0.004)(0.008)(0.002)(0.001)0.000(0.034)0.015(0.027)-0.005(0.037)0.003(0.034)-0.003(0.036)0.010(0.040)-0.005(0.037)-0.002(0.035)-0.007(0.035)-0.012(0.033)-0.005(0.031)0.040(0.032)
93–04
88
1056

0.022
(0.008)-0.002(0.004)-0.009(0.006)0.001(0.007)0.007(0.009)-0.000(0.009)0.001(0.006)0.006(0.007)0.019(0.007)0.006(0.008)0.030(0.018)0.004(0.010)
93–04
113
1356

—

—

—

—

—

—

—

—

0.008
(0.009)0.015(0.012)0.008(0.009)0.004(0.008)0.008(0.010)-0.003(0.008)0.001(0.008)0.021(0.015)
97–04
153
1224

0.011
(0.004)0.015(0.005)0.002(0.004)0.004(0.005)0.012(0.004)0.002(0.005)0.023(0.008)0.005(0.006)
97–04
231
1848

0.013
(0.008)0.028(0.009)0.007(0.007)0.016(0.006)0.011(0.005)0.024(0.012)0.009(0.005)0.012(0.005)0.006(0.005)-0.000(0.006)0.004(0.006)0.042(0.026)
93–04
88
1056

Panel B: Restricted
Noncollege College Noncollege
(6)
(7)
(8)
0.930
1.114
0.857
(0.057)(0.093)(0.072)
—
—
—
—

—

—

0.048
(0.008)0.008(0.003)0.052(0.008)0.002(0.002)0.056(0.007)0.012(0.004)0.027(0.008)0.003(0.007)-0.005(0.008)0.004(0.006)0.009(0.008)0.001(0.008)0.002(0.005)0.007(0.008)0.021(0.007)0.010(0.009)0.035(0.020)0.013(0.012)
93–04
113
1356

—

—

—

—

—

—

—

—

0.012
(0.005)0.020(0.008)0.013(0.005)0.009(0.004)0.013(0.007)0.001(0.004)0.005(0.004)0.024(0.014)
97–04
153
1224

0.014
(0.006)0.014(0.006)0.000(0.005)0.002(0.005)0.010(0.005)0.000(0.005)0.022(0.010)0.005(0.006)
97–04
231
1848

Note: Standard errors are in parentheses. 93–04 and 97–04 in the third row from the bottom (Panel used)
denote that the 1993–2004 balanced panel and the 1997–2004 balanced panel are used for estimation, respectively.

53

Table 5: Estimates of the Profile Heterogeneity and Restricted Models(Unbalanced Panel)Parameterρ
σβ2 × 100σαβ × 100
σα2
ση2
σ$2
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
#households#observations

Model
Panel A: Profile Heterogeneity
All
All
College Noncollege
All
(1)
(2)
(3)
(4)
(5)
0.688
0.470
0.856
0.604
0.900
(0.167) (0.077) (0.144)(0.259)(0.016)
0.035
0.034
0.032
0.028
—
(0.005) (0.004) (0.018)(0.005)-0.167-0.140-0.232-0.166—(0.047) (0.058) (0.100)(0.051)
0.030
0.026
0.039
0.024
0.032
(0.008) (0.009) (0.013)(0.009)(0.003)
0.010
0.020
0.006
0.009
0.013
(0.002) (0.002) (0.003)(0.004)(0.001)0.018(0.004)0.006(0.004)0.008(0.005)0.005(0.004)0.013(0.004)0.012(0.005)0.024(0.005)0.012(0.006)0.010(0.005)0.008(0.005)0.011(0.005)0.000(0.004)
908
8162

—
—
—
—
—
—
—
—
—
—
—
—
908
8162

0.012
(0.003)0.013(0.005)0.005(0.004)0.006(0.004)0.012(0.004)0.023(0.006)0.017(0.006)0.015(0.007)0.009(0.007)0.002(0.007)0.003(0.006)0.012(0.010)
331
3048

0.019
(0.006)0.003(0.006)0.006(0.006)0.005(0.006)0.009(0.006)0.007(0.006)0.023(0.007)0.011(0.006)0.014(0.006)0.011(0.006)0.015(0.006)-0.002(0.005)577
5114

Note: Standard errors are in parentheses.

54

0.028
(0.004)0.011(0.004)0.012(0.003)0.008(0.003)0.017(0.003)0.018(0.003)0.031(0.005)0.020(0.004)0.020(0.004)0.023(0.005)0.026(0.006)0.018(0.005)908
8162

Panel B: Restricted
All
College Noncollege
(6)
(7)
(8)
0.860
0.904
0.873
(0.013) (0.028)(0.024)
—
—
—
—

—

—

0.031
(0.003)0.020(0.001)

0.022(0.004)0.011(0.002)0.022(0.003)0.012(0.002)—0.012(0.004)0.017(0.006)0.007(0.002)0.006(0.004)0.012(0.006)0.022(0.007)0.017(0.006)0.016(0.006)0.012(0.006)0.009(0.006)0.012(0.008)0.025(0.011)
331
3048

0.029
(0.005)0.008(0.005)0.009(0.004)0.009(0.003)0.012(0.003)0.012(0.004)0.030(0.006)0.019(0.005)0.024(0.005)0.025(0.006)0.030(0.007)0.015(0.005)
577
5114

—
—
—
—
—
—
—
—
—
—
—
908
8162

Table 6: Estimates of the Profile Heterogeneity Model Based on Alternative Grouping
and Specification (Unbalanced Panel)Parameterρ
σβ2 × 100σαβ × 100
σα2
ση2
σ$2
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
#households#observations

Profile Heterogeneity Model
Panel A
Panel B
Without non-high school graduates
With occupation dummy variables
High school
All
All
All
College Noncollege High school(new)(original) (new)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
0.697
0.749
0.780
0.806
0.847
0.722
0.764
(0.183)(0.128)(0.078)(0.065) (0.121)(0.149)(0.115)
0.025
0.030
0.019
0.015
0.022
0.019
0.014
(0.006)(0.007)(0.006)(0.007) (0.013)(0.005)(0.006)-0.114-0.116-0.155-0.120-0.237-0.129-0.077(0.056)(0.049)(0.044)(0.049) (0.078)(0.046)(0.052)
0.014
0.022
0.032
0.029
0.042
0.024
0.016
(0.010)(0.009)(0.008)(0.009) (0.012)(0.009)(0.011)
0.009
0.010
0.011
0.012
0.007
0.010
0.011
(0.003)(0.002)(0.001)(0.002) (0.002)(0.003)(0.002)0.019(0.006)0.004(0.006)0.009(0.006)0.008(0.005)0.011(0.005)0.005(0.005)0.021(0.006)0.013(0.007)0.011(0.005)0.014(0.007)0.015(0.006)-0.003(0.005)
493
4382

0.019
(0.004)0.007(0.004)0.010(0.005)0.006(0.004)0.015(0.004)0.012(0.004)0.022(0.005)0.014(0.006)0.009(0.005)0.010(0.006)0.009(0.005)0.001(0.005)
824
7430

0.019
(0.003)0.008(0.004)0.011(0.004)0.005(0.003)0.019(0.004)0.015(0.003)0.026(0.004)0.019(0.005)0.015(0.004)0.015(0.004)0.016(0.005)0.009(0.004)
908
8162

0.018
(0.003)0.008(0.004)0.012(0.004)0.006(0.003)0.019(0.004)0.013(0.003)0.024(0.004)0.020(0.005)0.015(0.004)0.017(0.005)0.016(0.006)0.008(0.005)
824
7430

0.011
(0.003)0.012(0.004)0.008(0.003)0.007(0.003)0.017(0.004)0.022(0.005)0.018(0.005)0.010(0.005)0.010(0.005)0.010(0.006)0.012(0.007)0.014(0.009)
331
3048

0.021
(0.005)0.004(0.005)0.009(0.005)0.006(0.004)0.014(0.004)0.010(0.005)0.026(0.006)0.018(0.006)0.017(0.005)0.014(0.006)0.018(0.006)0.004(0.005)
577
5114

0.019
(0.005)0.005(0.005)0.010(0.006)0.008(0.004)0.014(0.005)0.007(0.004)0.024(0.006)0.019(0.007)0.015(0.005)0.016(0.006)0.018(0.006)0.003(0.005)493
4382

Note: Standard errors are in parentheses. All (original) denotes the original sample composed of the collegeeducated group and the noncollege-educated group, and All (new) denotes the sample excluding non-high school
graduates from the original one.

55

Figure 1: Cross-Sectional Variance of Earnings Residual, 1993ʋ2004

Cross-Sectional Variance of Earnings Residual

0.18
0.16
0.14
0.12
0.1
0.08
1993䋭2004 Balanced Panel

0.06

1997䋭2004 Balanced Panel

0.04

1993䋭2004 Unbalanced Panel

0.02
0
1993

1994

1995

1996

1997

1998

1999

2000

2001

Year

Note: Data for this figure are from columns (1), (5), and (9) of Table 2.

56

2002

2003

2004

Appendix Figure 1: Derivation of Sample

Original sample

Singles

Married couples

Requirements (i)–(iv) (including deletionof cases with no information needed)

Remove extreme cases

Sample used for analysis(All individuals)

College-educatedNoncollege-educatedNote: The samples used for analysis are selected from the original sample using the following criteria.
(i) The respondent and her spouse are a continuously married couple. Further, the spouse (i.e., husbandof the respondent) (ii) is classified as an employee using the definition of the JPSC, (iii) reports positive
labor earnings, and (iv) reports annual hours of work between 728 and 5096 hours. After this selection,some cases with extreme values of real earnings (a growth rate above 250 percent or below 80 percent,or a level below one billion yen) are removed. The college-educated group consists of individuals with afour-year college degree, and the noncollege-educated group consists of individuals without a four-yearcollege degree.

57