Discussion Paper No. 663

DO BORROWING CONSTRAINTS MATTER?
AN ANALYSIS OF WHY
THE PERMANENT INCOME HYPOTHESISDOES NOT APPLY IN JAPAN*
Miki Kohara
andCharles Yuji Horioka

June 2006

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan*Forthcoming in Japan and the World Economy, Vol. 18, No. 4 (December 2006).

Do Borrowing Constraints Matter? An Analysisof Why the Permanent Income Hypothesis Does
Not Apply in Japan
Miki Koharaand Charles Yuji Horioka†,‡

Abstract
We use micro data on young married households from the Japanese Panel
Survey of Consumers in order to analyze the importance of borrowing constraints in Japan. We ﬁnd (1) that 8 to 15 percent of young married Japanesehouseholds are borrowing-constrained, (2) that household assets and the husband’s educational attainment are the most important determinants of whether
or not a household is borrowing-constrained, and (3) that the Euler equation
implication is rejected for both the full sample and for the subsample of unconstrained households. These results suggest that the life cycle/permanent
income hypothesis does not apply in Japan and that the presence of borrowing
constraints is not the main reason why it does not apply.
Key Words: Borrowing constraints; Liquidity constraints; Consumption;
Life Cycle/Permanent Income Hypothesis; Permanent Income
Hypothesis; Euler Equation; Households; JapanJEL Classiﬁcation Codes: D1, D9, E2, and G1Osaka School of International Public Policy, Osaka University; 1-31, Machikaneyama, Toyonaka, Osaka 560-0043, Japan. (Tel) 81-6-6851-5622 (E-mail) kohara@osipp.osaka-u.ac.jp†
Institute of Social and Economic Research, Osaka University, 6-1, Mihogaoka, Ibaraki, Osaka
567-0047, Japan‡The authors are grateful to Kenn Ariga, Anton Braun, Robert Dekle, Yasushi Hamao, Fumio
Hayashi, Yasushi Iwamoto, Shizuka Sekita, Toshiaki Tachibanaki, and seminar participants at
Osaka University and the University of Tokyo for their valuable comments and to the Ministry of
Education, Culture, Sports, Science and Technology of the Japanese Government for Grant-in-Aid
for Scientiﬁc Research number 12124207, which supported this research.

1

Introduction

If the life cycle/permanent income hypothesis (hereafter LCPIH) holds, changes
in consumption should not be sensitive to changes in expected income. On theother hand, if this hypothesis does not hold (for example, because households areborrowing-constrained), changes in consumption will be sensitive to changes in expected income. Thus, a commonly used test of the validity of the LCPIH is toestimate an Euler equation to see whether changes in consumption are sensitive tochanges in expected income.
If the LCPIH does not hold and the reason is the existence of borrowing constraints, we would expect changes in consumption to be sensitive to changes in
expected income in the case of borrowing-constrained households but not in thecase of unconstrained households. In this paper, we use micro data on young married households from the Japanese Panel Survey of Consumers, conducted by theInstitute for Research on Household Economics, to shed light on (1) the prevalenceof borrowing constraints in Japan, (2) what households are borrowing-constrainedin Japan, (3) whether the LCPIH holds in Japan, and (4) whether the presence ofborrowing constraints is the reason why the LCPIH does not hold in Japan.
To summarize our main ﬁndings, we ﬁnd (1) that 8-15 percent of young married
Japanese households are borrowing-constrained, (2) that household assets and thehusband’s educational attainment are the most important determinants of whether
or not a household is borrowing-constrained, and (3) that the Euler equation implication is rejected for both the full sample and for the subsample of unconstrained1households. These results suggest that the LCPIH does not apply in Japan and thatthe presence of borrowing constraints is not the main reason why it does not apply.
The paper is organized as follows: in Section 2, we present the theoretical model;
in Section 3, we describe the data and analyze what households are borrowingconstrained in Japan; in Section 4, we present the results of our Euler equation
tests; and Section 5 concludes.

2

The Model

2.1

Consumption Smoothing

Consumption smoothing behavior is characterized by the Euler equation. We summarize this, making the usual assumptions. An individual holds At of total assets atthe beginning of period t and purchases a total of Nt of assets at (the end of) t. The
individual earns a real wage of w, and spends it on the consumption of goods, c, andthe purchase of assets, N. We do not consider the individual’s leisure choice, andassume w is exogenous. The saving constraint faced by the consumer is described as
Nt  At = wt  ct . The asset accumulation constraint is At+1 = Nt (1 + rt+1 ) wherert+1 is the interest rate at the beginning of period t+1. All individuals face the sameinterest rate, live for a ﬁnite lifetime T , and leave no bequests at T +1. Suppose thatthe individual’s utility is stationary and additively separable over time and written
nP
o
T
1
as Et
u(c
)
,where Et is an expectation operator conditional on ink
k3t
k=t (1+4)
formation available at t, u is a function that is increasing and concave in ct and 4
is the rate of time preference, which is assumed to be homogeneous over individuals
2and time. The representative consumer’s maximization problem can be written as
1
a dynamic programming problem. Maximizing Vt = u(ct ) + 1+4
Et Vt+1 (At+1 , wt+1 ),no
1+rt+1 Yut+1t
we obtain the ﬁrst order condition for consumption: Et Yu

= 0.
Yct
1+4 Yct+1

This is the Euler equation, implying consumption at t should be chosen so that the
expected discounted gain of saving now for the future is equal to marginal utility inthis period. Further assume that utility is isoelastic, u(cit ) = c13
it /1  , where  isthe risk aversion parameter. Marginal utility is convex and allows for precautionarysaving as a special case. If it is assumed that lnci,t+1 and rt+1 have a joint normal
distribution, the Euler equation becomes1
Et { ln ci,t+1 =  31 (Et rt+1  4) + / 2i,t .
2(1)

In the last term, /2i,t is the conditional variance, which equals the variance of({ ln ci,t+1  rt+1 /) and partly reﬂects uncertainty and the precautionary motive
for saving.
There are at least two ways to test the validity of equation (1). The ﬁrst way is
to test a structural form, estimating utility function parameters using Generalized
Method of Moments (nonlinear instrumental variable) estimation. This is a direct
test using the Euler equation, whose error term should be orthogonal to information
before t (see, for example, Runkle (1991)). GMM estimation is beneﬁcial in the sensethat we can avoid the approximation of linear marginal utility in consumption, theassumption of distribution, and the assumption of income exogeneity.
However, many researchers have for a long time used another way to test the3Euler equation implication. This is a test of the reduced form Euler equation withadditional variables in past information sets. It tests the validity of this additional
information (for example, income changes) predicted by previous information. Additional variables should not explain consumption changes if the Euler equation holds.
For example, consumption changes should not react to predicted income changes.
That is, we test whether q = 0 in the equation1e{ ln ci,t+1 = k1 Ft + k2 {Xi,t+1 + k3 / 2i,t + q{ ln yi,t+1+ 0i,t+1 ,
2

(2)

e
where { ln yi,t+1
is income predicted by individuals using the information available

to them. This is calculated as predicted values from the ﬁrst stage estimation of{ ln yi,t+1 . Ft is a time-varying variable including  31 (Et rt+1  4). Preference shifts,
described as {Xi,t , could aect the consumption plan at any point in time. The
third term is the conditional variance of the uncertain components. One of ourmain focuses is to review past studies using proper data on consumption smoothing.
Thus, we conduct this reduced form exclusion test. Since our data are panel data on
households, we conduct IV estimation controlling for household-speciﬁc dierencesby applying ﬁxed eects estimation and random eects estimation. The null hypothesis is that the Euler equation holds and that individuals smooth consumptionchanges against predicted income changes. That is, q = 0: consumption does notreact to predicted income changes.
Most past studies drop the conditional variance term, 12 /2i,t , simply assumingthat it is the same across individuals. It is often necessary to make this assumption

4

because information is seldom available on precautionary motives, but Jappelli andPistaerri (2000) emphasize the importance of including this term; if we ignore thiseterm and if { ln yi,t+1
is related to uncertainty or precautionary saving motives, qmeasures not the sensitivity of consumption to income but the eect of uncertainty
on consumption. Jappelli and Pistaferri (2000) regard nominal (observable) income
variance as a proxy for the uncertainty term / 2i,t and include it as one of the
explanatory variables.
This method could, however, be problematic for the following reasons: First,
income uncertainty is only one of many uncertainties individuals face and is not a
su!cient indicator of general uncertainty. Second, even if uncertainty consists onlyof income uncertainty, using actual income uncertainty as a proxy for / 2i,t as welleas { ln yi,t+1
may raise a problem due to the correlation between the two. Thus, we

calculate consumption variances for each household, and conduct an additional testof the Euler equation implication controlling for this term.

2.2

Violation of Consumption Smoothing

If markets are complete and there exist appropriate securities against any futurestate, each household’s consumption is fully insured against any idiosyncratic shock.
Households can smooth consumption changes completely over expected and unexpected income ﬂuctuations, sharing risks with each other. Previous studies havetested this implication of consumption full insurance and most have rejected it. Although it is important to ﬁnd a situation (if any) where full insurance holds, therejection of the implication is not surprising. A more interesting issue is what can5and what cannot explain the violation of the implication.
For example, the existence of borrowing constraints may cause the Euler equation implication to be rejected. Many studies have, for a long time, inquired into
the existence of borrowing constraints and the dierences in consumption behavior
between borrowing-constrained and unconstrained households. Households should
fail to smooth consumption if they encountered an unexpected shock and could notborrow to carry out their original plans. Thus, unconstrained households should notreact to income shocks, while constrained households should react strongly. Basedon this analogy, many researchers have tested the Euler equation (e.g., Eq. (2)) andhave interpreted q as the proportion of borrowing-constrained households.
Once we have rejected the Euler equation implication, we should seek the reason
for it, checking each possible explanation one by one. The following parts focus on
the existence of borrowing constraints, which is the most frequently used explanation
for the violation of the Euler equation implication. Speciﬁcally, we identify unconstrained households using unique information on households’ borrowing constraints
and test the Euler equation implication using this subsample. If the existence ofborrowing constraints is the primary explanation for the violation of the Euler equation implication, we should ﬁnd evidence of the Euler equation implication for thissample but not for the full sample. However, if other explanations for the violation of the Euler equation implication matter, we should not ﬁnd support for this
implication even for the unconstrained sample. We will discuss other possible explanations for the violation of the Euler equation implication later after we haveexamined the empirical results for borrowing constraints.
6

3

The Data

3.1

JPSC Data

This paper uses micro data from the Japanese Panel Survey of Consumers, (hereafter the JPSC) (in Japanese, Shouhi Seikatsu ni kansuru Paneru Chousa), a panel
survey conducted by the Institute for Research on Household Economics (in Japanese,
Kakei Keizai Kenkyuusho). This survey has surveyed young married and unmarried
women (those between the ages of 24 and 34 in 1993) once a year since 1993, andthis paper uses the 1993-2004 waves from this survey. Because JPSC is a panel
survey, we can calculate changes in consumption from year to year, which is precisely the variable we need to test our theoretical model. We conﬁne our analysis tothe subsample of married women because most young single Japanese women livewith their parents and rely on their parents’ income but precise information is notavailable on their parents’ income and consumption. Note that married women are
asked not only about themselves but also about other household members.
Borrowing constraints. The ﬁrst and most important variable used in our analysis is the one pertaining to borrowing constraints. The JPSC asks three uniquequestions about borrowing constraints: (1) Have you (or your spouse) ever had aloan application turned down? (2) Have you (or your spouse) ever had the loan
amount reduced when you applied for a loan? (3) Have you (or your spouse) everdecided against applying for a loan because you expected your loan application to beturned down? Following Jappelli (1990), we refer to households answering "yes" tothese questions as "rejected," "reduced," and "discouraged" borrowers, respectively.
7

Households that replied "yes" to one or more of these questions were regarded as being borrowing-constrained. Unfortunately, this information is available only in the1993 wave and the 1998 and later waves1 . Thus, we had no choice but to assume
that borrowing constraints remained unchanged during years for which information
is not available. This is exactly what Jappelli (1990) and Jappelli, Pischke, andSouleles (1998) assume, even though it may be too strong an assumption. We will
return to this point in the last part of this section.
Consumption. The JPSC collects data on consumption (living expenses) by all
household members during the month of September. In the regression analysis, we
use the growth rate of monthly consumption. The data on monthly consumption
have at least two advantages: ﬁrst, they include all consumption goods and services,
unlike in the case of PSID, which collects data only on food consumption. Thus,
we need not make any assumptions about the separability of consumption. Second,using the change in consumption between two non-sequential months has the advantage of avoiding, to some extent, potentially serious problems raised by consumption
durability and habit formation2 .
Income. The JPSC collects data on several measures of income, including annual
1More speciﬁcally, the wording of the question about borrowing constraints was changed slightly
starting in 2003, and it now asks only about the respondent’s experience during the previous year.
For 2003 and later, we have created a new variable that indicates whether the respondent wasborrowing constrained at any point in the past.
2
The change in monthly consumption could be biased if the household engages in purchasesof big-ticket items such as homes and cars. The JPSC asks about spending on ‘living expenses’
during the previous month excluding spending on most big-ticket items. The survey asks separately
about purchases ﬁnanced by loans. Thus, we can exclude the possibility that consumption growthis overestimated as a result of purchases of big-ticket items. Unfortunately, the JPSC does not ask
for a breakdown of living expenses into durables, non-durables, and services so we cannot be surethat it excludes durables completely, but for the reason given above, we can be reasonably surethat it consists mostly of non-durables and services, which is what we want.

8

(total) income, annual labor income, and monthly labor income. Annual (total)
income and annual labor income are inclusive of taxes so we need to estimate taxes
in order to calculate after-tax income. We use after-tax monthly labor income in
the main Euler equation for at least three reasons: ﬁrst, we wanted the period andtiming of consumption and income to match. If we use annual income, there isa danger of underestimating the degree of consumption smoothing simply because
annual income is more stable than monthly income or consumption. Another reason
for using monthly income is that using annual income would require us to waste thelast year of data since the survey asks about annual income in the previous year.
Finally, the use of monthly labor income helps to reduce the amount of household
heterogeneity because data on monthly labor income are not available for the selfemployed. We sum the monthly labor incomes of all household members and use
the growth rate of total monthly labor income in the regressions.
Household characteristics. Following the past literature on testing the LCPIH
and the existence of borrowing constraints by estimating an Euler equation, we
include the husband’s age, the household’s consumption needs, as proxied by the
number of family members, and year dummies. Although we tried including manyother time-variant and time-invariant variables that might possibly inﬂuence consumption, particularly that of young Japanese households such as those included inour sample, all of the variables we tried including had little eect and their inclusion
was not supported statistically3 . Time-invariant variables such as regional dummies3

For example, neither a dummy variable for those who had their ﬁrst baby during the current
year, which could make a big dierence in consumption patterns, nor a dummy variable for those
who starting living with their parents during the current year, which is often observed in Japan as

9are automatically dropped in the case of ﬁxed eects estimation. We estimate expected income change using income change in the previous year and the husband’s
educational attainment as instruments and include it in the explanatory variables
for consumption.
The total number of married women (households) was about 1000 in most years.
In order to estimate the Euler equation, we kept an observation if it contained
enough information for at least a one-year panel. Thus, the sample we used is an
unbalanced panel. We calculated consumption variances using consumption values
for the past four years, and information on borrowing constraints is available for1993 and for 1998 and later. Thus, data for 1998 to 2004 are used to test the Euler
equation implication. After eliminating observations with missing values for one ormore of the variables included in the regressions, we were left with 1006 households(4582 household-years) in the full sample and 956 households (4133 household-years)
in the unconstrained sample4 .

3.2

Who Is Constrained?

Before estimating the Euler equation, we summarize the characteristics of borrowingconstrained households. Table 1 summarizes the borrowing motives of households
that are currently in debt. Although housing and car purchases are the main reasonsfor borrowing, a few households do in fact borrow to ﬁnance living expenses. Morethe parents get older, changed the results below.
4
We did not drop outliers from our sample in the regression results shown in this paper. We
did try re-estimating the regressions after dropping observations whose monthly consumption anddisposable income lie outside of the "mean plus or minus three standard deviations" range, but
the results did not change qualitatively.

10than half of the sample is currently in debt, which suggests that borrowing plays animportant role in household planning.
Turning to data on the share of households that are borrowing-constrained, thisﬁgure was 7.61 percent in 1993, 9.29 percent in 1998, and 15.40 percent in 2003.
Thus, the share of borrowing constrained households was very low in 1993, andalthough it increased sharply during the 1990’s and early 2000’s, it was still lessthan one-sixth in 2003.
Many past studies have tried to distinguish borrowing-constrained households
from unconstrained households. Since direct data on borrowing constraints areusually not available, most previous studies have tried to predict who is borrowingconstrained using a variety of indicators. In our case as well as in the case of Jappelli(1990), however, direct information is available on whether or not a given householdis borrowing-constrained. Thus, following Jappelli (1990), we analyze what determines whether a given household is borrowing-constrained by regressing a dummy
variable that equals one if the household is borrowing-constrained and zero otherwise on various household characteristics using probit estimation. The household
characteristics we use include assets, income, the husband’s age and educational
attainment, household size, homeownership, debt, city size, and region. We use two
measures of assets: Asset1, which is deﬁned as holdings of bank and postal deposits,
bonds, and equities, and Asset2, which is deﬁned as Asset1 plus life and non-life
insurance, land, and housing. Only the results for Asset1 are shown in Table 3, but
the results for Asset2 were qualitatively similar. Debt is deﬁned as the amount ofoutstanding debt. The other variables are described in the previous section.
11

Table 2 shows the characteristics of borrowing-constrained and unconstrainedhouseholds separately. All borrowing-constrained households have lower assets andhusband’s educational attainment than unconstrained households and all borrowingconstrained households with the exception of "reduced" households have lower incomes and husband’s employment rate than unconstrained households. "Discouraged" borrowers have similar characteristics to "denied" and "reduced" households.
This ﬁnding underscores the importance of dierentiating "discouraged" households
from those completely free from borrowing constraints and grouping them together
with borrowing-constrained households.
Who is borrowing-constrained? Table 3 shows the estimation results of our probit analysis of who is borrowing-constrained for 1993, 1998, and 2003. Household
assets and income are two variables of interest since many past studies have used
the ratio of assets to income as an indicator of whether or not a given householdis borrowing-constrained, and as Table 3 shows, the marginal eects of the incomerelated variables are statistically signiﬁcant in only one of the 3 years (1998), but
the marginal eects of Asset and/or Asset-squared are statistically signiﬁcant in all
3 years, with the overall impact of assets being consistently negative, as can be seenfrom the partial eects on the last line of Table 35 . However, we found that thehusband’s educational attainment also has a statistically signiﬁcant impact on theprobability of being borrowing-constrained in the case of Japan, with college gradThe partial eect of Asset on the probability of being constrained is calculated as *(X) ·( 1 + 2 2 Asset+ +  3 Income+ +  4 HusAge+ ), where upper plus indicates the mean value and 1 ,  2 ,  3 ,and  4 are the coe!cients of Asset, Asset-squared, the cross-product of Asset and Income, and the cross-product of Asset and HusAge, respectively. *(·) is the standard normal density
function, and X is the linear prediction evaluated at the means.
512uates being signiﬁcantly less likely to be borrowing constrained than less educatedhouseholds. The results are unchanged even if we utilize the panel structure of thedata and do, say, a random eects logit estimation using 1993 and 1998-2004 data.
Jappelli (1990) found using U. S. data that income and assets have a signiﬁcant
impact on the probability of being borrowing constrained but that the husband’s
educational attainment does not, so our results for income and husband’s educational
attainment are dierent from those for the United States. Educational attainment
could be an indicator of current as well as future income, and a household in which
the educational attainment of the husband (usually the household head and mainincome earner) is relatively low might be regarded as having insu!cient ability to
repay loans.
Finally, we also tried including a number of other explanatory variables, but
their coe!cients were never signiﬁcant6 .
We turn now to a check of the accuracy of indicators used by previous studies
to identify borrowing-contrained and unconstrained households. Following previous
studies, we group the sample into ’hypothetically’ borrowing-constrained and unconstrained households using various indicators and then compare these households
to ’actually’ borrowing-constrained and unconstrained households. The results areshown in Table 4.
The ﬁrst three indicators, which were originally proposed by Zeldes (1989), are6

The self-employed may need to borrow and may face borrowing constraints more frequently
than others. Also, employment conditions such as tenure and ﬁrm size often aect household
decisions in Japan. Thus, we conducted the estimation including variables relating to the husband’s
self-employement, tenure, and ﬁrm size, but none of their coe!cients were signiﬁcant.

13the most frequently used indicators in many countries and are constructed by taking
the ratio of asset holdings to income. Since households who have adequate amountsof assets relative to income can dissave their assets when necessary and protect
their consumption against unexpected income shocks, households with a high assetincome ratio are regarded as being unconstrained. The ﬁrst indicator is whether or
not the household’s holdings of ﬁnancial assets are more than twice as much as theirmonthly income, and the second one is whether or not the household’s holdings of
total assets (ﬁnancial assets plus housing equity) are more than twice their monthly
income. The third indicator classiﬁes households with no ﬁnancial assets as being
borrowing-constrained and households whose holdings of ﬁnancial assets are morethan twice their monthly income as being unconstrained.
The fourth indicator is whether or not the household owns one or more credit
cards. If it owns one ore more credit cards, it can ﬁnance its consumption evenwhen it experiences an unexpected income decline. This indicator is close to theone suggested by Shintani (1994), who classiﬁes households as being unconstrained
if they own one or more credit cards or one or more cards with a free-loan feature
because they need to pass a credit check in order to receive one or both kindsof cards. The ﬁfth indicator, proposed by Hayashi (1985b), classiﬁes households
as unconstrained if they consume less than 85 percent of their annual disposable
income (minus all debt outstanding plus 20 percent of their ﬁnancial assets).
Finally, since we found from Table 3 that educational attainment is a signiﬁcant
indicator of being unconstrained, we propose a new indicator that identiﬁes college
graduates as being unconstrained. In addition, we construct another new indicator
14that is the same as the ﬁrst indicator suggested by Zeldes (1989) except that ﬁnancial
assets are replaced by a broader concept of assets—namely, bank and postal deposits,
bonds, equities, life and non-life insurance, land, and housing.
Table 4 shows the results. The predicted-unconstrained/actually-unconstrained
and predicted-constrained/actually-constrained cells indicate the proportion of households identiﬁed properly. The results are summarized in Table 5. As expected, thehusband’s educational attainment identiﬁes unconstrained households well, as does
Hayashi’s indicator (his consumption-income ratio). By contrast, Zeldes’s assetincome ratio is better at identifying borrowing-constrained households, but even so,
about 50% are misclassiﬁed. This ﬁnding is similar to Jappelli’s (1990) ﬁnding for
U.S. households that using the asset-income ratio leads to serious misclassiﬁcation of
constrained and unconstrained households, and moreover, misclassiﬁcation is evenmore serious in the case of Japanese households.
Thus, we should identify unconstrained households using information on educational attainment or the consumption-income ratio, but we should identify borrowing
constrained households using Zeldes’s asset-income ratio despite its limitations.

4

The Results

4.1

Euler Equation Test

In this section, we present the results of our Euler equation tests, but we ﬁrst present
the descriptive statistics for the sample used in the estimation in Table 6.
Parts (a) and (b) of Table 7 are the results of IV estimations controlling for in15

dividual eects using a ﬁxed eects model and a random eects model, respectively(see Appendix (1) for the ﬁrst stage regression results). Although the Wu-Hausman
test shows that individual eects in the error terms are not correlated with the explanatory variables so that the random eects model is good enough to be estimated,the ﬁxed eects model estimator is still consistent (but ine!cient) and may still be
preferred if unobserved time-invariant individual eects relating to the household’s
consumption and income changes are omitted from the equation. The coe!cient of
expected income is about 0.094 and 0.093 in the ﬁxed eects and random eects
models, respectively. Both coe!cients are signiﬁcant at the 1 percent signiﬁcancelevel. Thus, we strongly reject the applicability of the Euler equation implication.
When we control for conditional variances additionally, the coe!cients of expected income changes are still 0.097 and 0.092, respectively, in the ﬁxed eects
model and the random eects model, and both are signiﬁcant at at least the 5%
signiﬁcance level. Thus, we again reject the Euler equation implication.
The coe!cient of expected income changes in (a) might be upward biased because
the process of taking the dierence from the mean (within-estimator) to remove ﬁxedeects makes income changes "transitory or surprising" rather than "expected or
permanent" whereas we want to see the reaction of consumption to the latter. A
larger coe!cient in the ﬁxed eects model relative to the random eects model may
reﬂect this possibility.
A coe!cient of 0.09 or higher is roughly consistent with the values suggested
by previous studies for many countries. According to the previous literature, about
9% of all households are rule-of-thumb consumers. However, we will show soon that16

comparing coe!cients in this way is not meaningful. Although there is variationin the magnitude of the coe!cients, the test implications are the same: the Euler
equation implication is rejected. Households do not smooth consumption changes
over even expected income changes.

4.2

Do Borrowing Constraints Matter?

Most of the past literature attributes the violation of the Euler equation implication
to the existence of borrowing constraints. Using this analogy, the coe!cient of
expected income changes, such as the 0.09 value shown in Table 7, is sometimes
interpreted as the share of constrained households. The 0.09 value is consistent
with our earlier ﬁnding that 8 to 15 percent of our sample is actually constrained.
If the existence of borrowing constraints is the reason for the violation of the Euler
equation implication, we would expect to ﬁnd that the Euler equation implication isapplicable or close to applicable in the sample of unconstrained households. Table
8 shows the results for the sample of unconstrained households, and as this tableshows, the coe!cient of expected income changes stays at about the same magnitude
and signiﬁcance level. The dierence in the coe!cients of expected income changes
between the full and unconstrained samples is quite small and not signiﬁcant at a 1
percent signiﬁcance level (see the bottom row of Table 8). Thus, the Euler equation
does not hold even for unconstrained households, which suggests that the existenceof borrowing constraints is not the reason for the violation of the Euler equation
implication7 .
7

Ideally, we would have liked to estimate the Euler equation for the sample of borrowing con-17

Many past studies that identify unconstrained households using the level of theasset-income ratio make the conclusions even more ambiguous. In the previous section, we found that splitting the sample by the asset-income ratio itself is questionable, especially when we are interested in the behavior of unconstrained households.
In addition to this problem, the sensitivity of consumption to expected incomechanges as measured by the above type of Euler equation does not show what proportion of households are borrowing-constrained. Nonetheless, the results obtainedin this paper suggest that the existence of borrowing constraints is not the primarycause of the violation of Euler equation implication.

4.3

Other Possible Explanations

If borrowing constraints are not the explanation, what is the explanation for theviolation of the Euler equation implication? First of all, the existence of future
constraints may aect the results. Our deﬁnition of constrained households does
not include the possibility of future constraints. As Hayashi (1997) emphasizes,
the current consumption of households that predict that they will face borrowing
constraints in the future will be sensitive to income changes. Unfortunately, we
cannot identify households who expect to be constrained in the future from among
currently unconstrained households.
Other data problems are also possible explanations of the rejection of the Euler
strained households also in order to see if the implication of the Euler equation was violated morestrongly for this sample, as expected, but unfortunately, we were not able to do so because the sample of borrowing constrained households was too small. Wakabayashi and Horioka (2005) test the
implication of the Euler equation for the full sample and for the sample of borrowing-constrainedhouseholds and ﬁnd that it holds for the full sample but not for the sample of borrowing-constrainedhouseholds.

18

equation implication. If we did not have data on total consumption but only on consumption of a certain good, we would need to assume separability between goods. If
we could not obtain the appropriate micro data to test the Euler equation implication, we would have to assume that aggregation were possible. If we could not ﬁndvalid instruments in the limited information set, the stochastic structure of income
would be misspeciﬁed. The last problem is related to informational constraints onhouseholds. However, these problems are not so serious in the present analysis.
Our consumption data is total consumption expenditure, and moreover, our data
set contains data on a large number and variety of household attributes, making iteasier to ﬁnd appropriate instruments.
The existence of consumption durability is another possible explanation of the rejection of the Euler equation implication. If a commodity is durable and expenditureon that commodity is increased in the current period, expenditure will be depressedin the next period even though the household is still enjoying the consumption services from that commodity. Households can derive beneﬁts from consuming now
rather than later, thereby showing excess sensitivity of consumption8 . In this case,the error term in Eq. (2) will contain the eects of past consumption and will becorrelated with the explanatory variables (Mankiw (1982), Hayashi (1985b, 1999)).
However, this problem is less serious in our case partly because our consumption
measure consists primarily of non-durables and services and partly because the survey we use measures consumption in two 1-month time periods 1 year apart).
8

Habit formation is another example of nonseparable consumption over time. In this case,consumption must increase over time and households try to save now for future consumption,
showing excess smoothness of consumption.

19

The existence of precautionary saving or dierences in households’ level of uncertainty is another possible explanation of the violation of the Euler equation implication. Our basic estimation model excludes this possibility by assuming that timeand individual ﬁxed eects can control for it, which may be too strong an assumption. The JPSC does not have information on overall uncertainty, and although weestimate the implication including consumption variances, this may not be enoughto control for household’s risk-related behavior.
Finally, the misspeciﬁcation of the theoretical assumption that consumption andleisure are separable is another possible explanation for the violation of the Euler
equation implication. Unless this assumption is imposed, we cannot derive our Euler
equation test, which presupposes that the consumption decision is made independently of the leisure decision. The JPSC contains information on individual’s time
allocation, but it is inappropriate to examine the Euler equation implication using leisure time in the above type of income-added-test since changes in leisure areprobably correlated with changes in income.
Thus, the possibility of precautionary behavior in the face of uncertainty andthat of inseparability between consumption and leisure remain as topics for future
research.

5

Conclusion

In this paper, we used micro data on young married households from the JapanesePanel Survey of Consumers, conducted by the Institute of Research on Household

20Economics, to shed light on (1) the prevalence of borrowing constraints in Japan,(2) what households are borrowing-constrained in Japan, (3) whether the life cycle/permanent income hypothesis (LCPIH) holds in Japan, and (4) whether thepresence of borrowing constraints is the reason why the LCPIH does not hold inJapan. To summarize our main ﬁndings, we found (1) that 8-15 percent of young
married Japanese households are borrowing-constrained, (2) that household assets
and the husband’s educational attainment are the most important determinantsof whether or not a household is borrowing-constrained, and (3) that the Euler
equation implication is rejected for both the full sample and for the subsample ofunconstrained households. These results suggest that the LCPIH does not apply inJapan and that the presence of borrowing constraints is not the main reason why itdoes not apply.
We turn ﬁnally to the implications of our ﬁndings for the causes of the prolonged
slowdown of the Japanese economy in the 1990s (the so-called "lost decade"). Many
studies have found that the prolonged slowdown exacerbated the borrowing constraints of ﬁrms, which in turn caused them to cut back on their investment, hiring,and R&D (see, for example, Ogawa (2003), but the impact of the slowdown on households via borrowing constraints does not appear to have been as pronounced. We
did ﬁnd that there was a sharp increase in the proportion of borrowing-constrainedhouseholds during the 1990s, but even after the increase, the proportion of borrowing constrained households was less than one-sixth, and moreover, our estimation
results imply that the consumption behavior of borrowing constrained household
is not fundamentally any dierent from the consumption behavior of unconstrained
21

households. Thus, it does not appear that the exacerbation of borrowing constraints
on households was an important determinant of the stagnation of household consumption during the prolonged slowdown (see Horioka (2006) for a discussion ofwhat were the main causes of the stagnation of household consumption during thisperiod), and moreover, Horioka (2006) ﬁnds that the stagnation of household consumption contributed far less to the prolonged slowdown than the stagnation ofprivate ﬁxed investment.

22

References[1] Arellano, M., Bond, S., 1991. Some Tests of Speciﬁcation for Panel Data: Monte
Carlo Evidence and an Application to Employment Equations. Review of Economic Studies 58, 277-297.
[2] Campbell, J. H., Mankiw, G. N., 1991. The Response of Consumption to Income: A Cross-Country Investigation. European Economics Review 35, 723756.
[3] Hayashi, F., 1985a. The Permanent Income Hypothesis and Consumption Durability: Analysis Based on Japanese Panel Data. Quarterly Journal of Economics
100, 1083-1113.
[4] Hayashi, F., 1986. An Extension of the Permanent Income Hypothesis and Its
Test. Keizai Bunseki (Economic Analysis) 101, 1-23, (in Japanese).
[5] Hayashi, F., 1997, Understanding Saving, The MIT Press, Cambridge, Massachusetts.
[6] Horioka, C. Y., 2006. Causes of Japan’s Lost Decade: The Role of Household
Consumption, Japan and the World Economy 18.
[7] Jappelli, T., 1990. Who Is Credit Constrained in the U.S. Economy? Quarterly
Journal of Economics 105, 219-234.

23[8] Jappelli. T., Pistaferri, L., 2000. Using Subjective Income Expectations to Test
for Excess Sensitivity of Consumption to Predicted Income Growth. European
Economic Review 44, 337-358.
[9] Jappelli, T., Pischke, J., Souleles, N. S., 1998. Testing for Liquidity Constraints
in Euler Equations with Complementary Data Sources. Review of Economics
and Statistics 80, 251-62.
[10] Mankiw, N. G., 1982. Hall’s Consumption Hypothesis and Durable Goods.
Journal of Monetary Economics 10, 417-25.
[11] Ogawa, K., 1990. Cyclical Variations in Liquidity-Constrained Consumers: Evidence from Macro Data in Japan. Journal of the Japanese and International
Economies 4, 173-193.
[12] Ogawa, K., 2003. Daifukyou no Keizaigaku: Nihon Keizai Chouki Teimei wo
Kaimei (The Economics of the Great Recession: Explaining the Prolonged
Slowdown of the Japanese Economy). Tokyo: Nihon Keizai Shinbunsha (inJapanese).
[13] Runkle, D. E., 1991. Liquidity Constraints and the Permanent-income Hypothesis. Journal of Monetary Economics 27, 73-98.
[14] Shibata, A., Shintani, M., 1998. Capital Mobility in the World Economy: An
Alternative Test. Journal of International Money and Finance 17, 741-756.

24

[15] Shintani, M., 1994. Nippon no Shouhisha to Ryuudousei Seiyaku (Japanese
Consumers and Liquidity Constraints: A Test Based on Credit Information).
Osaka Economic Papers 44, 41-56, (in Japanese).
[16] Wakabayashi, M., Horioka, C. Y., 2005. Borrowing Constraints and Consumption Behavior in Japan. Discussion Paper No. 640, Institute of Social and Economic Research, Osaka University.
[17] Zeldes, S. P., 1989. Consumption and Liquidity Constraints: An EmpiricalInvestigation. Journal of Political Economy 97, 305-346.

25



1993 784 households
47.59% / 52.41%
housing
45.9%
car
39.1%
durables10.1%
clothing
8.7%
leisure4.6%
children's education
3.6%
children's marriage
1.4%
payment for accidents
5.6%
living expenses
5.3%
repayment of debt
5.1%
new business
1.2%
other
4.3%

No / Yes

Notes
1. Households answering "yes" to "Borrowing?" are households that are currently in debt,
and the figures in the second line and below show the proportion of households currently
in debt that are borrowing for each motive. Since some households are borrowing for
more than one motive, the figures sum to more than 100.
2. These data are from the first wave of the Japanese Panel Survey of Consumers, 1993.
Similar tables are available for other years.

Borrowing?
If yes,to finance:

Table 1. Borrowing Motives



200.0

88.1

198.9

86.1

213.7

109.9

217.3

119.7

240.5

144.8

227.9

117.7

Unconstrained
Constrained
92.39%
7.61%
Rejected (58.82%) Reduced (11.76%) Discouraged (72.55%)
Mean
Std.Dev.
Mean
Std.Dev.
Mean
Std.Dev.
Mean
Std.Dev.
Mean
Std.Dev.
32.88
4.81
32.71
5.55
33.07
5.86
31.67
5.39
32.41
5.96
0.360
0.480
0.059
0.238
0.067
0.254
0.167
0.408
0.054
0.229
0.997
0.057
0.980
0.140
0.967
0.183
1.000
0.000
0.973
0.164
4.25
1.48
4.25
1.02
4.23
1.17
5.00
1.26
4.11
0.88
0.553
0.498
0.353
0.483
0.333
0.479
0.333
0.516
0.351
0.484
3.324
4.372
0.943
1.720
1.272
2.129
0.587
0.873
0.538
0.696
0.043
0.096
0.051
0.081
0.047
0.082
0.076
0.111
0.051
0.082
5.815
2.488
5.275
2.652
5.474
2.736
7.220
4.691
4.590
1.822

Notes
1. The data are from the first wave of the Japanese Panel Survey of Consumers, 1993. Similar tables are available for other years.
2. "Constrained" households include 'rejected, 'reduced' and 'discouraged' households. Since some households experienced
two or more of the three events, the totals sum to more than 100%.
3. HusAge, HusCollege and HusEmployed denote the husband's age, college graduation, and employment status, respectively.
4. NumFamily denotes the number of family (household) members.
5. Asset denotes the household's total holdings of bank and postal deposits, bonds, and equities (in units of millions of yen). Debt is thehousehold's total liabilities outstanding including housing and other loans (in units of millions of yen).
6. Income is the annual disposable income of all household members (in units of millions of yen).
7. Consumption is monthly expenditure (in units of 1,000 yen).

HusAgeHusCollege (in percent)
HusEmployed (in percent)
NumFamily
Homeown (in percent)
Asset (in millions of yen)
Debt (in millions of yen)
Income (in millions of yen)Consumption (in thousandsof yen)Full Sample
670 households
Mean
Std.Dev.
32.87
4.87
0.337
0.473
0.996
0.067
4.25
1.45
0.537
0.499
3.142
4.275
0.043
0.095
5.774
2.503

Table 2. Characteristics of Constrained and Unconstrained Households

Table 3. Who Is Constrained?
Dependent Variable: "Constrained" =1 if either rejected, reduced, or discouraged.
1993
1998
Marginal Effects
Marginal Effects(standard error)(standard error)
HusAge0.00290.0061(0.0054)(0.0121)
HusAge*HusAge
0.00000.0000(0.0001)(0.0002)
Income0.00190.0331(0.0126)(0.0210)
Income-squared
0.00010.0005 *(0.0003)(0.0003)
Income*HusAge-0.0001-0.0011 *(0.0004)(0.0006)
Asset-0.0329 **-0.0038(0.0156)(0.0246)
Asset-squared
0.00000.0002 ***(0.0001)(0.0001)
Asset*Income
0.00000.0000(0.0000)(0.0000)
Asset*HusAge
0.0005-0.0003(0.0004)(0.0007)
HusCollege-0.0280 **-0.0404 ***(0.0121)(0.0155)
HusEmployed-0.1139-0.0100(0.1722)(0.0687)
NumFamily
0.00470.0001(0.0034)(0.0057)
Homeown-0.0233 *-0.0017(0.0133)(0.0187)
Debt
0.05200.1755 ***(0.0447)(0.0700)
AreaScale_med-0.0230 **-0.0024(0.0119)(0.0174)
AreaScale_small-0.0191 **-0.0215(0.0084)(0.0193)
Number of obs (households)
670
958
Log likelihood-140.29-259.07
Likelihood Ratio
80.12
74.30
McFadden's Adjusted Index
0.089
0.044
Normalized AIC
328.588566.13
Partial effect on the probability of being constrained (evaluated at the means)
Asset-0.0155-0.0172

2003
Marginal Effects(standard error)-0.0505 ***(0.0139)0.0006 ***(0.0002)0.0152(0.0260)
0.0002(0.0002)-0.0005(0.0006)-0.0773 ***(0.0240)0.0003 **(0.0002)0.0000(0.0000)
0.0012 ***(0.0006)-0.0388 *(0.0231)-0.0184(0.0785)-0.0026(0.0077)-0.0308(0.0300)-0.0346(0.1040)-0.0399(0.0268)-0.0544 **(0.0261)831-288.66
136.730.124
625.32-0.0225

Notes
1. The marginal effects evaluated at the means are shown.
2. For the definitions of the variables, see the text and the notes to Table 2.
3. AreaScale_med and AreaScale_small are dummy variables indicating that the household
lives in medium-sized and small-sized cities, respectively, rather than in a metropolitan
area. Metropolitan areas denote the thirteen ordinance-designated cities.
4. The equation also includes seven regional dummies.
5. We obtain similar results when we replace Asset with broader definitions of assets such as the sum of thepaid-in value of life and non-life insurance and the value of land and housing in addition to total holdings ofbank and postal deposits, bonds, and equities.
6. * indicates significant at the 10% level, ** indicates significant at the 5% level, and *** indicates significant at the 1%
level.



Actually
unconstrained constrained
79.21
3.61
(85.69)(47.73)13.23
3.95(14.31)(52.27)
Actually
unconstrained constrained
83.70
7.60
(91.07)(93.94)8.21
0.49(8.93)(6.06)
Actually
unconstrained constrained
84.85
6.88
(92.50)(83.33)6.88
1.38(7.50)(16.67)③Asset (Extreme Split)
582 observations
The indicator
unconstrained
predicts:
constrained④Credit Card Holders
816 observations
The indicator
unconstrained
predicts:
constrained⑤Consumption-Income Ratio
581 observations
The indicator
unconstrained
predicts:
constrained(64.41)

5.42

Actually
unconstrained constrained
75.54
2.81
(79.50)(56.52)19.48
2.16(20.50)(43.48)(28.19)25.82②Asset (Total Wealth Split)
462 observations
The indicator
unconstrained
predicts:
constrained

constrained

Panel A- appropriateness of previously used indicators
Actually①Asset (Basic Split)
701 observations
unconstrained constrained
The indicator
unconstrained
65.76
3.00
predicts:(71.81)(35.59)(9.94)(33.33)

2.62

Actually
unconstrained constrained
88.89
7.65
(96.90)(92.54)2.84
0.62(3.10)(7.46)

9.16

Notes
1. "Basic Split" (1) is based on saving accounts and time deposits.
2. "Basic Split using a broader definiton of assets" (6) is based on saving andtime deposits, life and non-life insurance, and land and housing.

⑦College Graduates (husband)
810 observations
The indicator
unconstrained
predicts:
constrained

constrained

Panel B- other possible indicators
Actually⑥Basic Split using a broader definition ofassets 535 observations
unconstrained constrained
The indicator
unconstrained
82.99
5.23
predicts:(90.06)(66.67)

Table 4. Indicators of Constrained Households used in the Past Literature



85.61
84.19
83.16
77.70
71.18

④Credit Card Holders③Asset (Extreme Split)②Asset (Total Wealth Split)①Asset (Basic Split)

4
5
6
7

②Asset (Total Wealth Split)⑥Basic Split using a broader definitionof assets*⑤Consumption-Income Ratio⑦College Graduates (husband)④Credit Card Holders④Credit Card Holders⑥Basic Split using a broader definitionof assets*③Asset (Extreme Split)②Asset (Total Wealth Split)①Asset (Basic Split)
90.06
85.69
79.50
71.81

91.07

identified constrained households
properly①Asset (Basic Split)③Asset (Extreme Split)

identified unconstrained households
properly
96.90⑦College Graduates (husband)
92.50⑤Consumption-Income Ratio

Note: The circled numbers refer to the indicators defined in Table 4.

3

1
2

89.51
86.23

identified constrained andunconstrained households properly⑦College Graduates (husband)⑤Consumption-Income Ratio⑥Basic Split using a broader definition ofassets*Table 5. A Comparison of the Performance of Indicators of Constrained Households

33.33
16.67
7.46
6.06

43.48

64.41
52.27



The unconstrained sample (number of observations (households)= 4133 (956) )Mean
Std. Dev.
Min
Max
0.03400.4004-3.06812.86220.02840.3195-3.21892.6231

Consumption change rates
Income change rates
Income change rates one
year earlier
0.03220.3177-3.2189
2.86220.03140.3118-3.2189
2.8622
Income change rates two
years earlier
0.02880.3154-3.21893.40120.02620.2986-3.2189
2.8622
HusAge39.0650
5.463825
65
38.9986
5.418925
61
Family size change rates
4.51001.39411
11
4.5236
1.4133
1
11
HusAge*HusCollege
14.4732
19.3565061
15.2640
19.5646061Consumption variances
4.85898.93810.004297.5640
4.87999.15270.004297.564Notes
1. HusCollege and HusAge are defined in the same way as in table 2. HusAge*HusCollege is the cross-product of HusAge and HusCollege. Family sizeis the number of family members. Consumption and income changes are changes in monthly values. All changes are expressed as growth rates.
2. Consumption variances are variances of monthly consumption expenditures divided by 1000.

The full sample (number of observations (households) =4582 (1006) )Mean
Std. Dev.
Min
Max
0.03390.4021-3.06812.86220.02730.3251-3.2189
2.8622

Table 6. Descriptive Statistics for the Euler Equation Estimation



Table 7. Euler Equation Estimation

1.0759(0.9544)4582
0.44
53.20 ***--0.426
0.014
13.38
0.29
1.01
142.31 ***0.0939 ***(0.0386)-0.0296(0.0231)0.0111(0.0076)
0.0086(0.0076)

0.0968 ***(0.0401)-0.0143 ***(0.0055)
0.0160(0.0200)
0.0094(0.0082)0.0045 ***(0.0015)0.3844(0.2061)3864
0.43
61.36 ***--0.415
0.020
6.92
0.31
1.06
130.44 ***-0.0191(0.1165)4582--28.77 ***
0.488
0.426
--13.38----1584.00 ***0.0929 ***(0.0359)-0.0003(0.0028)0.0112(0.0091)
0.0009(0.0008)

0.0918 **(0.0448)-0.0019(0.0012)0.0040(0.0047)0.0005(0.0003)0.0014 **(0.0007)0.0898(0.0532)3864--26.12 ***
0.000
0.415
--6.92----898.00 ***(b) IV with random effects

Number of observations
Test for indiv.effects: Ui=0
Test for all coefficients=0ıuiıvit
R-squared (for within-estimator)
Wu-Hausman Test for RE
First stage: R-squared
Test for indiv.effects: Ui=0
Test for all coefficients=0
Notes
1. For the first stage estimations to calculate expected income change, see Appendix Table 1.
2. The squares of ıu and ıv are variances of ui and vit, where the error terms are written as eit=ui+vit.
3. Wu-Hausman test statistics suggest that individual effects are not correlated with the explanatory variables
and that the random effect model is good enough to be estimated. However, the results of the fixed effects model arereported as well since they are consistent (but not efficient) even in this case.
4. The fixed effect model here takes a difference from the mean of time for each individual and adds the meanof the total number of observations (both over individuals and time). Since the last term is backed into a"usual" mean difference, a constant remains in the estimation.
5. Time and area dummies are included in all equations.
6. Also see the notes to Table 6.

constant

Consumption variance

HusAge*HusCollege

Family size change

HusAgeExpected income change*

For Full Sample
Dependent variable: Change in log consumption(a) IV with fixed effects

0.1254 ***(0.0422)-0.0359(0.0244)0.0158(0.0174)
0.0093(0.0080)(b) IV with random effects

0.1311 ***0.1147 ***0.1273 ***(0.0444)(0.0460)(0.0486)
HusAge-0.0143 **-0.0005-0.0021 *(0.0059)(0.0012)(0.0013)
Family size change
0.01480.0087 **0.0032(0.0209)(0.0045)(0.0049)
Husage*HusCollege
0.01080.00050.0005(0.0087)(0.0003)(0.0003)
Consumption variance0.0033 **0.0009(0.0016)(0.0007)
Constant
1.29510.3636 *0.00600.1006 *(1.0071)(0.2181)(0.0508)(0.0558)
Number of observations
4133
3463
4133
3463
Test for indiv.effects: Ui=0
0.45
0.44
----Test for all coefficients=052.52 ***
56.11 ***
27.23 ***
25.58 ***
ıui
0.321
0.292
0.000
0.000
ıvit
0.425
0.413
0.426
0.413
R-squared
0.015
0.020
----Wu-Hausman Test for RE
3.59
8.44
3.59
8.44
1st stage: R-squared
0.28
0.30
----Test for indiv.effects: Ui=0
1.04
1.08 **----Test for all coefficients=0123.50 ***110.88 ***920.00 ***787.00 ***The difference in the reaction of consumption to expected income between the full sample and the unconstrained sample
Difference (standard error)-0.032 (0.057)-0.034 (0.060)-0.022 (0.058)-0.036 (0.066)
Notes
1. There are no significant differences in the reaction of consumption to expected income between the full sample and the unconstrained sample.
2. Also see the notes to Table 7.

Expected Income change*

For Unconstrained Sample
Dependent Variable: Change in log consumption(a) IV with fixed effects

Table 8. Do Constraints Matter?

Appendix. (1) Prediction of Income Changes for Table 7
Dependent Variable: Change in log income(a) IV with fixed effects
Income change(t-1)
Income change(t-2)
HusAgeFamily size change
HusAge*HusCollege-0.6004 ***(0.0161)-0.3255 ***(0.0167)-0.0161(0.0159)
0.0251 **(0.0115)-0.0064(0.0052)

Consumption variance
Constant
Number of observations
Test for indiv.effects: U i=0
Test for all coefficients=0
R-squared
σui
σvit

0.7181(0.6573)4582
1.01
142.31 ***0.2852--0.294-0.6192 ***(0.0174)-0.3329 ***(0.0178)0.0028(0.0038)
0.0385 ***(0.0139)-0.0088(0.0057)0.0014(0.0010)-0.0921(0.1433)3864
1.06
130.44 ***0.3064--0.289(b) IV with random effects-0.5637 ***(0.0143)-0.2931 ***0.0146-0.0027(0.0020)0.0172 ***(0.0064)0.0003(0.0006)

0.1007(0.0817)4582--1584.00 ***--0.4880.426-0.4538 ***(0.0154)-0.2030 ***(0.0155)-0.0029 ***(0.0009)
0.0077 **(0.0035)0.0002(0.0002)0.0013 **(0.0005)0.1364(0.0399)3864--898.00 ***--0.000
0.415

Note: See the notes to Table 7.

(2) Prediction of Income Changes for Table 8
Dependent Variable: Change in log income.
(a) IV with fixed effects
Income change(t-1)
Income change(t-2)
HusAgeFamily size change
HusAge*HusCollege-0.5954 ***(0.0171)-0.3301 ***(0.0179)-0.0159(0.0165)0.0272 **(0.0117)-0.0073(0.0054)

Consumption variance
Constant
Number of observations
Test for indiv.effects: U i=0
Test for all coefficients=0
R-squared
σui
σvit

0.8725(0.6609)4133
1.04
123.50 ***0.281--0.289-0.6075 ***(0.0185)-0.3343(0.0192)0.0012(0.0040)0.0434 ***(0.0142)-0.0087(0.0059)0.0015(0.0011)-0.0484(0.1487)3463
1.08
110.88 ***0.299--0.282

Note: See the notes to Table 8.

(b) IV with random effects-0.4592 ***(0.0155)-0.2236 ***(0.0162)-0.0022 ***(0.0009)
0.0117 ***(0.0033)
0.0005 **(0.0002)0.0867 **(0.0369)4133--920.00 ***--0.006
0.424-0.4517 ***(0.0163)-0.2145 ***(0.0173)-0.0028 ***(0.0010)0.0098 ***(0.0036)0.0003(0.0002)0.0014 ***(0.0005)
0.1150 ***(0.0413)3463--803.00 ***--0.000
0.415