Tsukuba Economics Working Papers
No. 2015-004
Provision of Household Public Goods and theHousehold Income Distribution

By
Hisahiro Naito
Graduate School of Humanities and Social Sciences
University of Tsukuba
December 2015

UNIVERSITY OF TSUKUBA
Graduate School of Humanities and Social Sciences
1-1-1 Tennodai
Tsukuba, Ibaraki 305-8571
JAPAN

Provision of Household Public Goods and theHousehold Income Distribution
Hisahiro Naito ∗†Current version December 20, 2015

Abstract
Several theoretical models have been proposed to explain household behavior, such as the unitary model, non-cooperative model, and cooperative model.
These three models make different predictions about the provision of household
public goods. By using both the Japanese tax reforms conducted in the 1990s as
a quasi-natural experiment and Japanese panel data on household expenditure,
I study how the within-household income distribution affects household public
goods and discuss which model is most relevant. I find that the neutrality ofthe effect of the income distribution on household public goods does not hold,which shows the failure of the unitary model. I also find evidence that the
non-cooperative model does not hold either. Finally, I argue that the observed
data are consistent with the cooperative bargaining model.

Keywords: public goods, household behavior, income distribution∗

University of Tsukuba, Graduate School of Humanities and Social Sciences, Phone: 81-29853-7431; fax: 81-29-853-7440; address: Tennodai 1-1-1, Tsukuba City, Ibaraki, Japan 305-8573;
email:naito@dpipe.tsukuba.ac.jp†
I are grateful to the Institute for Research on Household Economics for granting us permission
to use the Japanese Panel Survey of Consumers. I are also thankful to the participants of the TCER
Macro Conference, CEA, IIPF, the University of Tsukuba, and Hitotsubashi University for theirhelpful comments. Hisahiro Naito appreciates the financial grant from the Ministry of Education,
Science, Sports and Culture and the faculty research fund.

1

Introduction

When a couple starts a family, one of the family’s functions in society is to share household public goods such as basic housing services, children’s welfare, and householdchores. For example, Becker (1981) pointed out that children have the characteristics
of classical public goods within a family in the sense that both the husband and thewife obtain utility from their children’s happiness and it is difficult to exclude thehusband’s (wife’s) enjoyment of their children’s happiness when the wife (husband) is
enjoying it, too.
Models that explain household behavior can be divided into three categories: theunitary model, non-cooperative model, and cooperative model. The unitary model isbased on the hypothesis that a family will behave as if it is a single agent (Samuelson,(1954; Becker, 1974, 1981). In this model, the within-household income distribution
does not affect the resource allocation.
In the non-cooperative model, each member of the household determines his/her
contribution to household public goods given the contribution of the other membersof the household, and the total amount of public goods is determined as the Nashequilibrium of this non-cooperative game. In the non-cooperative game literature,
Warr (1983) and Bergstrom, Blume, and Varian (1986) proved that an exogenous
income redistribution does not affect the resource allocation as long as income isredistributed among public goods contributors.
The cooperative model is based on the hypothesis that the household allocation ischosen among Pareto-efficient allocations. Several types of cooperative models exist.
The collective model developed by Chiappori (1988, 1992) assumes only Pareto efficiency for the household allocation and shows that the allocation implied by Pareto
efficiency must satisfy a certain sharing rule. Other types of cooperative models specify more detailed structures. For example, McElroy and Horney (1981) and Manser
and Brown (1980) assumed that the household allocation is determined as Nash bargaining where the threat point is the outcome when a couple become divorced. In theso-called separate spheres bargaining model, Lundberg and Pollak (1993) suggested1that the final household allocation is determined by Nash bargaining but the threat
point is the equilibrium of the non-cooperative game. In this case, how an exogenous income redistribution within household members affects the resource allocation
depends on how the non-cooperative bargaining solution is affected by the income
redistribution.
The question of how expenditure on household public goods is determined is important for several reasons. First, government policies are often targeted to household
public goods such as housing services, children’s health, nutrition, and human capital
accumulation. Second, to design the basic principle of both the tax and the public
expenditure systems, information on how the household resource allocation is determined is necessary. In the tax system, some countries use individual income as thebasic unit, while others use household income (the sum of the incomes of the husband and wife). One might ask which system is more efficient and how the difference
between these two systems, household income base or individual income base, affects
economic behavior such as labor supply, retirement, savings, and the provision ofhousehold public goods.
In this study, I first show theoretically how an exogenous variation in income
share affects the level of public goods in the unitary model, non-cooperative model,
and cooperative bargaining model with a non-cooperative threat point. Second, I empirically examine how an exogenous change in the income distribution affects the levelof household public goods and discuss which model is consistent with this observeddata.
The contribution of this study is twofold. First, it uses detailed household datataken from the Japanese Panel Survey of Consumers (JPSC). Using the JPSC has
several advantages. First, this dataset not only collects data on expenditure for thehusband, wife, and children, but also asks about how much is saved. For most couples,some income is saved. Focusing on only current expenditure can thus be misleading
for the analysis of the effect of the income distribution on the household allocation. In
this data, I can observe how household income is used not only for current expenditure
but also for savings for different members of the household and public goods. Thus,
2these data are more comprehensive than those used in previous studies.
Second, the JPSC asks about the detailed use of time by the husband and wife.
For example, it asks how much time each spends on child-rearing, work, housework,
leisure, and sleeping. When the wife’s income share increases because of an increase in
her hours of work, she is often forced to spend less time with the children; as a result,
expenditure on children rises. Thus, to assess the effect of the income distribution
between the husband and wife on expenditure on children, it is important to control
for the time spent child-rearing. In the JPSC, it is possible to control for such aneffect.
Third, the years that the JPSC covers includes the 1990s. During the 1990s, theJapanese government conducted several reforms of the income tax system and I use
those reforms for identification, as discussed below.
The second contribution of this study is offering an empirical strategy that generates a quasi-experimental exogenous income distribution between the husband andwife. To generate such a quasi-experimental exogenous income distribution, I use thechanges in Japanese tax policies. The Japanese tax system is based on individual income, not on family income, and the exemption level is quite high. This fact implies
that many secondary earners whose income is low are exempt from the tax system.
Thus, when the Japanese government introduced its income tax credit, few secondary
earners received it. As a result, the income distribution between the husband andwife changed substantially. I use this tax policy change to generate the exogenous
income distribution between the husband and wife. To use the tax policy change as
the instrumental variable (IV), I adopt the method initially used by Gruber and Saez
(2002) to analyze the effect of labor supply.
Several studies are related to this study. This work rests on the previous advancement of the theoretical description of household behavior including Becker, Horney,
and McElroy (1981), Manser and Brown (1980), Lundberg and Pollak (1993), andChiappori (1988, 1992). In terms of more recent work, Blundell, Chiappori, andMeghir (2005) analyzed the household labor supply with household public goods.
They proposed a responsiveness condition of the marginal rate of substitution (MRS)3between public and private goods. They showed that if this condition is satisfied, it
is possible to map the income distribution and level of household public goods in acooperative model. More specifically, they showed that if member i’s MRS between
public goods and private goods is more responsive than that of member j, the shift
in bargaining power from j to i will increase the provision of the public good in acooperative model. In this study, I use a similar responsive condition but formulate
it differently to Blundell, Chiappori, and Meghir (2005).
Empirically, Browning and Lechene (2001) and Cherchye, De Rock, and Vermeulen(2012) are the most closely related works to this study. Browning and Lechene (2001)
theoretically and empirically analyzed several models including the non-cooperativemodel and cooperative model with a non-cooperative threat point. Cherchye, De
Rock, and Vermeulen (2012) conducted a structural estimation of the model developed
by Blundell, Chiappori, and Meghir (2005). Interestingly, they found that a change inempowerment from the husband to wife has little effect on a child’s consumption andwelfare contrary to the results of previous studies. In this study, by contrast, I use
the reduced-form estimation of the effect of the income distribution on the provisionof public goods and pay more attention to the exogeneity of the income distribution
between the husband and wife. Although conducting the structural estimation isuseful for ex-ante policy simulation, assumptions on the functional form and error
terms are quite strong. In addition, implementing the IV or GMM estimation in the
structural model is difficult. In a non-linear model, the moment conditions do nothold even if the explanatory variable is exogenous. In contrast, the reduced-form
estimation places less restriction on the functional form. Thus, I believe that thisempirical strategy complements the structural estimation approach.1
I employ the reduced-form estimation for two reasons. First, I have an exogenous
tax policy change that could generate an exogenous variation in the income distribution. By employing the method proposed by Gruber and Saez (2002), I apply the1

In this study, I do not examine the relevance of the bargaining model where the threat point isthe divorce. In the long run, such a model might be relevant. However, in this data, the exogenous
income redistribution is a tax reform. Given the change in income implied by the tax reform, it
is unclear how each individual negotiates the resource allocation using the divorce as the potential
threat point.

4IV estimation. To use the IV estimation, employing the reduced-form estimation isquite natural. In contrast, in a structural estimation, the model becomes non-linear
regarding the error term. In such a case, conducting the IV estimation is challenging.

2

Literature Review

Since the literature on household behavior is large, this literature review is restricted
to static analyses. Even in static analysis, the literature is nevertheless large. In
this static analysis literature, several works have studied the relationship between theincome distribution and household public goods provision.2
Warr (1983) was the first study to claim that the income distribution is neutral
regarding the resource allocation when public goods are voluntarily provided in the
non-cooperative model. Bergstrom, Blume, and Varian (1986) analyzed this issue
fully and examined the conditions under which this theorem is valid. More specifically,
they showed that neutrality holds as long as the income redistribution is conductedamong the contributors to public goods. In addition, they showed that if the income
redistribution is conducted from the contributors to the non-contributors to public
goods, total public goods will decrease.3 In the context of household behavior, noncooperative models have been presented by Ulph (1988) and Konrad and Lommerud(1995). These models have been applied to the division of housework (Bragstad, 1989),
domestic violence (Tauchen et al., 1991), and expenditure on children by divorced
parents (Del Boca and Flinn, 1994; Welling, 2000).4
The cooperative household model was developed Manser and Brown (1980) andMcElroy and Horney (1981). Lundberg and Pollak (1993) developed a separate
spheres model where the threat point is the equilibrium allocation of the non-cooperative
2

Among them are Thomas (1990), Hoddinott and Haddad (1995), and Schultz (1990). Thomas(1990) found that in Brazilian families, the unearned income of the mother has a stronger positiveeffect on child welfare. Haddad and Hoddinott (1995) found that in Cote d’Ivoire, children’s height
for their age is positively related to the share of family wealth controlled by the mother.
3
For the empirical analysis of the voluntary provision of public goods and income distribution,
Brunner (1997) and Murdoch and Sandler (1997) were the first studies to analyze this issue. Brunner(1997) analyzed the contribution to national public goods and Murdoch and Sandler (1997) examinedthe voluntary provision of international public goods.
4
Naito and Yamada (2004) examine the household public goods in a non-cooperative model.

5equilibrium. Haddad and Kanbur (1994), Konrad and Lommerud (2000), Chen andWoolley (2001), and Browning, Chiappori, and Lechene (2011) are also along this lineof research.
For collective models, as discussed in the Introduction, seminal works are Chiappori (1988, 1992) and subsequent extensions (Bourguignon, Browning, Chiappori,and Lechene, 1993, 1994; Chiappori, 1997). Recently, collective models have included
both labor supply and household public goods (Blundell, Chiappori, and Meghir,
2005; Cherchye, De Rock, and Vermeulen, 2012).
Finally, many studies have examined the neutrality of the effect of the income
distribution on private goods consumption, such as Hayashi (1995), Altonji, Hayashi,
and Kotlikoff (1992), Bourguignon, Browning, Chiappori, and Lechene (1994), andHoddinott and Haddad (1995). Hayashi (1995) and Altonji, Hayashi, and Kotlikoff(1992) examined neutrality within extended families, while Bourguignon, Browning,
Chiappori, and Lechene (1994) and Hoddinott and Haddad (1995) investigated neutrality within a household. The results of those studies consistently showed the nonneutrality of private goods within extended families or within a family.

3

DatasetThe dataset that I use in this study is the JPSC. Since 1993, the Institute for Researchon Household Economics has surveyed 1500 women aged 24 to 34. These individuals
are national representatives of this demographic group. The institute added another
500 women aged 24 to 34 in 1997 to increase the sample size. Since then, the institute has surveyed them annually. The women interviewed by the JPSC are asked
about their economic and social lives, such as labor market outcomes, education, savings, housing, the relationship between their parents and husbands, and household
expenditure.
The JPSC is an appropriate dataset for testing the neutrality of the effect of theincome distribution on the provision of household public goods because it surveys thecomposition of consumption expenditure and savings in September and assesses the6husband’s and wife’s after tax incomes separately for married couples. The JPSC alsoasks about hours of housework, leisure, sleeping, and child-rearing for the husband
and wife in addition to labor supply. In the questionnaire, consumption expenditureis divided into the following five categories: common expenditure, family expenditure(savings), expenditure on wife, expenditure on husband, expenditure on children, andexpenditure on others. Savings are divided similarly. However, the JPSC has several
disadvantages. First, the sample size is small compared with other panel datasets
such as PSID. Although the JPSC initially includes approximately 2000 households,
after cleaning the dataset, the number of households that have at least one childis approximately 1000. Second, for expenditure on each item, the JPSC only asks
women. This implies that the information of the consumption of the husband could
have a lot of noise.5 Hence, for the estimation, I need to take special account of thosevariables. To solve this issue, I thus use the IV estimation.
I use the JPSC from 1993 to 1999 and focus on two samples for the reasons
explained in the section on empirical strategies. The first sample comprises 906 singleand dual-earner households with at least one child. The second sample is composed of
376 dual-earner households with at least one child. The dual-earner households sample
is a subset of the 906 single- and dual-earner households sample. These two samples
are unbalanced panel data. I select participants based on the following selection rules:(i) they are married; (ii) they have at least one child; (iii) the two earners have beensalaried workers for at least two years in the dual-earner sample and all earners (oneor both) are salaried workers in the single- and dual-earner sample; and (iv) they
have the necessary information for more than two years. I use selection rule (ii)because neutrality is more likely to be reached in the couples with children because
they share more public goods than those with no children (see the samples used by
Bourguignon, Browning, Chiappori, and Lechene, 1994; Browning and Chiappori,1998). In the case of dual-earner couples with at least one child, neutrality throughthe voluntary provision of public goods as well as through income pooling can be5

For the single- and dual-earner sample, among the 4225 observations, the wife manages thehome budget in 3855 observations. In the 2780 dual-earner observations, the wife manages the homebudget in 1505 observations.

7reached. Moreover, Japanese couples share the family budget, and the wife typicallymanages it even in dual-earner households, as shown in Table 1.

4

Tax Reforms

In the Japanese income tax system, the fundamental units of income tax are not family
income, but individual income. The amount of the tax is calculated by subtracting
the basic allowance, which is similar to the exemption in the United States, andthe allowance for salaried workers, which is similar to the standard deduction in the
United States, from gross income. The sum of the basic allowance and the allowance
for salaried workers is quite high in the Japanese income tax system (1 million yen
in 1993). As a result, many individuals do not have to pay income tax. Even if theypay, the amount of tax liability is quite small and those whose tax liability is small
are often the secondary earners in the family. Moreover, when the wife’s income isbelow a certain level, the primary earner can receive a spouse allowance and a special
allowance for the spouse.
The key exogenous variations that I use in this study are the two major income tax
reforms conducted in 1995 and 1999 and the characteristics of the Japanese income
tax system itself.6 In 1993, the tax brackets and marginal rate of income tax changed
and various types of allowances, such as the basic allowance, the allowance for wives,
the allowance for salaried workers, the special allowance for wives, and the allowancefor dependents, were expanded by 30,000 yen. In the 1999 tax reform effective in
1999, 20% of the tax payment was deducted regardless of the marginal tax rate. The
top marginal rate was also reduced. Thus, when the Japanese government introduced
two tax reforms in the 1990s, many secondary earners who did not pay income tax
did not receive the benefit from those tax reforms. In addition, the expansion of theallowance for the wife and the special allowance for the wife benefited primary earners,
not secondary earners, because of the nature of the Japanese income tax system. Since
the initial income distribution between the husband and wife is different, those two
6

The tax reform 1999 was planned in 1998 and implemented in 1999. Thus, using the 1999 data
does not cause a problem.

8

tax reforms in the 1990s changed the income distribution between the husband andwife differently for different households. I thus use the two tax reforms on the income
distribution among different households as the key exogenous variations.
I calculate the amount of income tax based on permanent income, which is theweighted average of after tax income per month over time, in order to avoid theendogeneity of tax brackets. By applying permanent income to the table for themonthly amount of withholding income tax, I calculate the amount of income tax.

5

Analysis5.1

Preferences

Consider a family composed of a husband, a wife, and their child. In this family, boththe husband (primary earner) and the wife (secondary earner) have non-labor income
and labor income. I denote the husband as h, the wife as w, and the child as k. Let
j be the index denoting the husband, j = h, and the wife, j = w. Let K j , Lj , Lj , ljk
ljj , and wj be the non-labor income, time endowment, labor supply, housework/time
spent child-rearing, leisure (including hours for sleeping), and market wage rate of
the husband and wife. By definition, the labor supply of member j, Lj , is equal to
Lj − ljk − ljj . This family spends its income on the husband, wife, and child. Letuh (ck , lhk , lwk ) be the utility of the child. I assume that the husband’s utility consistsof the consumption of his own private goods and the utility of his child as follows:
Vh = uh (ch ) + fh (lhh ) + αhk uk (ck , lhk , lwk )I assume that the wife’s utility function is represented as follows:
Vw = uw (cw ) + fw (lww ) + αwk uk (ck , lhk , lwk )where αhk and αwk are the degrees of altruism. fj (ljj ) is the utility from the active
leisure of member j. For the utility of the child, I assume that the husband and wife’s

9

time are imperfect substitutes.7

5.2

Unitary modelLet Ψj be the weight of member j in the household. Then, the household solves thefollowing maximization problem:
X

Ψj Vj

(1)

j=h,w

s.t.

X

cj + ck =

j=h,w

X 

K j + wj (Lj − ljj − ljk )j=h,w

The above optimization problem has several implications. First, it shows thatthe lump-sum income transfer between the husband and wife does not affect theallocation. Second, it shows that the optimal allocation can be solved in two steps. In
the first stage, the household maximizes the objective function given ljj and ljk andobtains the conditional indirect utility function Γ(lhh , lhk , lww , lwk ). In the second
stage, the household chooses ljj and ljk to maximize Γ(lhh , lhk , lww , and lwk ). Thisimplies that in the first stage, the conditional demand of ch , cw , and ck are functionsPof ljj , ljk , and total income
j=h,w K j + w j (Lj − ljj − ljk ) . Thus, as long as ljk
and lkk are fixed, cj and ck are independent of the income distribution between thehusband and wife. Many previous studies have employed this empirical strategy totest the unitary model.8

5.3

Non-cooperative model and cooperative model with a
non-cooperative threat point

Characterizing the Threat Point
7

In this formula, I do not include caring preferences, where the husband also cares about theutility of the wife. Conducting an empirical study that includes public goods, labor supply, andcaring preferences in a cooperative model is challenging. To the best of my knowledge, no such
empirical study has yet been conducted. This is left to future work.
8
In fact, in the above formulation, I assume that the time for active leisure, ljj , is additively
separable. In this case, I can drop ljj from the conditional demand function.

10

The separate spheres bargaining model is a cooperative model where the threat
point is the non-cooperative Nash equilibrium. In this model, how the income redistribution affects the resource allocation critically depends on the non-cooperativeequilibrium. Thus, I first characterize the non-cooperative equilibrium. In the noncooperative game theoretical model (I simply call this the non-cooperative model
hereafter to save space), the husband chooses his private consumption, contribution
to household public goods, cash transfer to the wife, housework, and labor supply
given the wife’s private consumption, her contribution to household public goods,
and her housework. Similarly, the wife determines her private goods consumption,
contribution to public goods, housework, and labor supply given the husband’s contribution to household public goods, cash transfer from the husband, and housework by
the husband. In this model, I assume that the husband is the primary earner and wifeis the secondary earner. Let gh and gw be the contribution of household public goods
by the husband and wife. To conduct the comparative statics needed for empiricalstudies, let τ be the exogenous transfer from the wife to the husband.
∗∗
The Nash equilibrium of this non-cooperative game {c∗j , gj∗ , ljj, ljk; j = h, w} isdetermined as the solution of the following fixed point problem:∗∗(c∗h , gh∗ , m∗ , lhh, lhk) = argmax{ch ,lhh ,lhk ,g h }∗uh (ch ) + fh (lhh ) + αhk uk (gh + gw∗ , lhk , lwk)

s.t. ch + gh + m = K h + wh {Lh − lhh − lhk } + τ
where g h ≥ 0∗∗) = arg, lwk(c∗w , gw∗ , lww

(2)
max

{cw ,lww ,lwk ,g w }∗uw (cw ) + fw (lww ) + αwk uk (gh∗ + gw , lhk, lwk )

s.t. cw + gw = K w + m + ww {Lw − lww − lwk } − τwhere gw ≥ 0(3)Now, I can conduct a comparative static analysis by increasing τ . Consider in∗∗creasing τ, holding (ljj
, ljk
) fixed. The comparative static analysis shows the following

11results:∂(gh∗ + gw∗ )
∂g ∗
∂g ∗
∂c∗
∂c∗
= 0, h = −1, w = 1, h = 0 and w = 0
∂τ
∂τ
∂τ
∂τ
∂τ
∗
∗
as long as gh∗ > 0 and gw∗ > 0 for a fixed level of {ljj, ljk
; j = h, w}

In other words, the exogenous income redistribution does not affect the level of
public or private goods. When the income of the husband increases by one dollar andthe income of the wife decreases by one dollar, the husband increases his contribution
to public goods by one dollar and the wife decreases her contribution by one dollar.
Thus, the exogenous income redistribution is completely offset by the changes involuntary contribution to public goods by the husband and wife.
Now, what would happen if I keep increasing τ ? The above argument shows thatas long as the contribution of the wife is strictly positive, the husband increases his
contribution and the wife decreases her contribution by the same amount of the exogenous income redistribution and the neutrality of public and private goods continues
to hold. However, as I keep increasing τ , the contribution of the wife to public goods
becomes smaller and at some point reaches zero. From that point, neutrality no longer
holds. However, as τ increases further, the amount of public goods starts to increase
because the husband becomes the sole contributor to public goods. Since public goods
are usually normal goods, the level of public goods will increase. On the contrary, thewife spends her income only on her private consumption, which keeps decreasing as
τ increases.
Characterizing Nash Bargaining
Let V

h

and V

w

be the utility level determined in the non-cooperative equilibria.

Then, the cooperative Nash equilibrium ishwmax(V h − V )(V w − V )X
X cj + ck =K j + wj (Lj − ljj − ljk )
j=h,w

(4)

j=h,w

To solve the above problem and conduct the comparative statics, it is useful to12

consider the following two steps. First, for the given ljj , ljk , and ck , I choose ch andcw . In the next step, I choose ck to maximize the objective function holding ljj and ljk
constant. Moreover, I fix ljj and ljk in this thought experiment since I always control
ljj and ljk to run the regression.
Comparative Statics
Now, I increase τ and conduct the comparative statics for a given level of ljj andljk . First, it becomes clear that a change in τ does not affect the final resource allocation when both the husband and the wife provide public goods at the corresponding
threat point. This is because in (4), the threat point does not move when both thehusband and the wife provide public goods. In contrast, as τ grows, at one point
only the husband provides public goods. Thus, from that point, an increase in τ willhw

increase V and decrease V . As I show in the Appendix, this finding implies that theconsumption of the husband increases and the consumption of the wife decreases. A
natural question in this case is what would happen to the public goods provision whenVhincreases and Vw

decreases. Here, I modify the responsiveness condition initiallyused by Blundell, Chiappori, and Meghir (2005) and introduce ck -constant responsiveness condition. Define MRSj as the MRS of private goods and the household
public goods of member j as follows:

M RSj ≡kαjk ∂u
∂ck

∂uj
∂cj

,

j = h, w

The optimal amount of public goods is determined at the point where the MRS of thehusband and wife is equal to the marginal cost of providing one unit of public goods,
which is one in this case:X

M RSj = 1

j=h,w

The ck -constant responsiveness condition can be summarized as follows:

13

(5)

ck -constant responsiveness condition:(6)∂M RSh∂M RSw<∂ch ck ,lhk ,lwk =constant∂cw ck ,lhk ,lwk =constant(7)

Note that in the above ck -constant responsiveness condition, ck is held fixed. Thus,
this condition is much easier to check than the responsiveness condition that is definedby Blundell, Chiappori and Meghir(2005).
Proposition 1
Consider a cooperative equilibrium where its threat point is the outcome of the
non-cooperative game. Assume that for the given τ,only the husband supplies household public goods at the corresponding threat point. If the ck -constant responsivenesscondition holds, then an increase in τ will decrease ck at the cooperative equilibria
holding lww , lhh , lhk , lwk constant. (Proof is in Naito (2015))
The usefulness of the ck -constant responsiveness condition can be seen as follows:
Proposition 2
The ck -constant responsiveness condition is satisfied whenu00 (ch )u00 (cw )∂uk∂uk< −  w 2 αwk−  h 2 αhk
∂ck
∂ck
∂uh
∂uw
∂ch

∂cw

where u00h (ch ) and u00w (cw ) are the second derivative of uh (ch ) and uw (cw ).
One obvious case that the above condition is satisfied is u00h (ch ) = 0 and u00w (cw ) < 0.
Thus, we have the following proposition.
Proposition 3
If the utility functions of the husband is quasi linear with respect to private goods
and if the marginal utility of the consumption of the wife is diminishing, then thec k -constant responsiveness condition is satisfied.
Combining Proposition 1-3, we have the following useful result.
Proposition 4
Consider a cooperative equilibrium where its threat point is the outcome of the14

non-cooperative game. Assume that for the given τ,only the husband supplies household public goods at the corresponding threat point. If the utility functions of thehusband is quasi linear with respect to private goods and if the marginal utility of theconsumption of the wife is diminishing, then an increase in τ will decrease ck at thecooperative equilibria holding lww , lhh , lhk , lwk constant.
In many empirical studies, it is observed that when the bargaining power of thehusband increases, the expenditure for children decreases. The Proposition 4 implies
that, assuming that the household resource allocation is Pareto-efficient, this observation is explained when the utility function of the husband’s consumption is linear
and the marginal utility of the wife’s consumption is diminishing.

5.4

Empirical strategy

The above theoretical analysis has an important implication. First, in the noncooperative model, as long as both the husband and the wife provide public goods,
the income distribution does not affect the resource allocation. If only the husband
provides public goods, then an increase in the income share of the husband will increase the level of public goods since he will become the only contributor of public
goods and the free rider problem does not exist. In a cooperative model with a noncooperative threat point, if both parties provide public goods at the non-cooperative
threat point, then the income distribution is neutral regarding the resource allocation.
If only the husband provides public goods at the non-cooperative threat point and if
the responsiveness condition is satisfied, then the level of public goods will increase.
This finding suggests that if I select only dual earners, it is likely that the neutralityof the resource allocation would hold in both the non-cooperative and the cooperativemodels. If I select both dual- and single-earner couples, then an increase in thehusband’s income distribution would increase the level of public goods in a noncooperative model and decrease the level of public goods in a cooperative model. In
the unitary model, the resource allocation would be neutral regarding the income
distribution.
Let i be the index denoting the household and n the index indicating the category15

of expenditure and savings, respectively. t is the index of time. In this dataset,
expenditure and savings are classified as husband (h), wife (w), family (f), and children(k). For each category, I use the subscripts h, w, f , and k. Let Eint , Sint , and Yint
be expenditure, savings, and the sum of expenditure and savings for category n attime t for household i. Let Eit , Sit , and Yit be total expenditure, total savings,
and the sum of total expenditure and total savings for household i. By definition,
P
P
Eit =
n=h,w,f,k Eint , Sit =n=h,w,f,k Sint , Yit = Eit + Sit and Yint = Eint + Sint .
Let θit , Ihit , Iwit , Iit , and Xit be the income share of the husband, total income of thehusband, total income of the wife, total income of the household, and vector of theSEYdemographic variables, respectively. Let qint
, qint, qintbe the share of Eint in total

expenditure, the share of Sint in total savings, and the share of Yint in total income,E
S
Y
namely qint
= Eint /Eit , qint
= Sint /Sit , qint
= Yint /Yit . In the unitary model, for the

given level of ljjit and ljkit , I can consider the following Engel curve:bqint= β1nb θit + β2nb ln bit + β3nb lhkit + β4nb lwkit + Xit δbn + ainb + εinbt(8)where b = E, Y ; n = h, w, f, k; t = 1993, 1994, ..., 1999
Several comments would be useful for (8). First, Xit includes the age of thehusband, that of the wife, and the number of children in household i in period t. ainb
represents time-invariant preference shocks. Second, (8) is based on the conditional
demand curve on which lhkit and lwkit are conditioned. The first-order conditions of
all three models reveal the relationship between the consumption of each member forthe given level of lhkit and lwkit as well as total expenditure. Thus, I need to condition
on lhkit and lwkit . In addition, the IV, which is the change in the tax rate, affects
the amount of labor used for child-rearing since the change in the tax rate affects
the marginal price of housework. Thus, it is necessary to control for lhkit and lwkit .
Although lhkit and lwkit are endogenous, I do not apply the IVs on lhkit and lwkit since I
are not interested in the coefficient on lhkit and lwkit . In other words, I assume that the
IVs are independent given Xit ,lhkit , lwkit , and the other conditioning variables suchas labor supply. Third, in the case of b = E, the model assumes additive separability

16between current and future consumption. If this additive separability assumption
fails, but if the unitary model is still true, (8) is valid only for b = Y
The parameter of interest is β1nb , which measures how an increase in the husband’s
income share will increase the level of household public goods (or the consumption ofprivate goods) when total household income is held constant. In the unitary model,
β1nb is equal to zero. For the non-cooperative model, if both the husband and the wife
supply public goods, it is equal to zero. If only the husband provides public goods, it
is positive. For the cooperative model, if the responsiveness condition is satisfied, it
is negative. To estimate the above equation, previous studies use total income for the
IV of ln Eit and ln Yit . Using the IV of Eit and Yit is needed since the JPSC asks for
information on the husband’s income and expenditure on the wife, which may include
measurement errors.
Even if I use total income as the IV, however, several problems remain. The
first problem is the correlation between the time-invariant preference shocks ainb andexplanatory variables. Because of the definition of θit , θit is likely to be correlatedwith ainb . This is possible when the wife’s time-invariant preference shocks for public
goods are correlated with her preference for labor supply.
The standard way in which to solve the correlation between the time-invariant
preference shocks and income distribution between the husband and wife is to rewrite(1) in a time-demeaning form:
··

··

··

··

··

··

··

hb int = β1nb θit + β2nb lnbit + β3nb l hkit + β4nb l wkit + X hkit δbn + εhkit(9)where b = E, Y ; n = h, w, f, k; t = 1993, 1994, ..., 1999
In the above equation, ·· is an operator that calculates the time-demeaning mean.
····

For example, where θit is observed, in #(t) periods, θit is calculated as θit = θit −P(1/#(t)) t θit . Similarly, the other variables can be calculated in the same fashion.
The fixed effect estimation may aggravate the measurement error problem. To
alleviate this issue, I use the IV estimation. To construct the IVs, I use informationon the Japanese tax system and Japanese tax reforms in the 1990s. As noted earlier,17

during the 1990s, the Japanese government introduced two tax reforms and those tax
changes affected the income distribution between the husband and wife differently
for different households. This finding suggests that the cross-sectional variations in
the effect of the two tax reforms can be good instruments. Let τt (Ih , Iw , Dh ) andτt (Iw , Ih , Dw ) be the labor income tax function of the husband and wife in period t
when the husband and wife’s incomes are Ih and Ih and the number of dependentsof the husband and wife are Dh and Dw , respectively. For the function τt , there is a
subscript t because there were two tax reforms during the 1990s. τt is a function of thehusband’s (wife’s) labor income and the wife’s labor income as well as the number ofthe husband’s (wife’s) dependents. Although the Japanese income tax system is basedon individual income in principle, there are some exceptions such as the wife allowanceand the special wife allowance whose eligibility depends on the wife’s income. Thus,
the tax liability of the husband (wife) also depends on the wife’s income. Further, let
I p and I p be the permanent income of the husband and wife of household i. I calculate
the permanent income of I p and I p as the average of Ihit and Iwit for all the observed
periods. Then, I can calculateppt {τt (Ihi , Iwi , Dhit ) + τt (Iwi , Ihi , Dwit )}P

tax1it =pppp
τt (Ihi, Iwi, Dhit ) + τt (Iwi
, Ihi
, Dwit ) −tax2it =pp, Dhit )τt (Ihi
, Iwi
1 X
{
−
p
p
p
p
τt (Ihi, Iwi, Dhit ) + τt (Iwi
, Ihi
, Dwit ) #(t) t

#(t)
p
p
τt (Ihi, Iwi, Dhit )}pppp
τt (Ihi , Iwi , Dhit ) + τt (Iwi
, Ihi
, Dwit )(10)

where #(t) is the number of periods in which income is observed. tax1it is the timedemeaning mean of the sum of the tax liability of both the husband and wife. tax2itis the time-demeaning mean of the share of the tax liability of the husband. Notethat when calculating tax1it and tax2it , the tax liabilities are evaluated based on thepermanent income of the husband and wife. Further, Dhit and Dwit are the functionsof I p , I p , and the demographic variable Xit . Thus, tax 1it and tax 2it are the change
in the total tax liability and change in the share of the husband’s tax liability causedby the tax reform alone after being controlled by Xit . Therefore, by construction, it··

is uncorrelated with εhkit .
18

6Results

Table 1 shows the number of households that share the budget with the wife. Morethan 95% of the households (4055/4226=0.96) share the family budget with the wife
to some degree. This finding provides indirect evidence that the neutrality result isvery likely to hold for the households in this dataset. Table 2 shows the descriptive
statistics of the variables used in this study. In this data, I have 907 households and4226 observations for single- and dual-earner couples. Among the 907 households, 376
households are dual-earner couples for which I have 1505 observations. One noticeablefeature in Table 2 is the similarity of the expenditure patterns between the singleearner sample (the first column) and the dual-earner sample (the second column).
Another noticeable characteristic in Table 2 is that the share of the wife’s consumption
is quite small (5%) and that 70% of total expenditure is used for household public
goods such as on children and family. This finding suggests that in the dual-earner
sample, both the husband and the wife are likely to contribute household public
goods. Because of these two facts, readers might conjecture that neutrality is likely
to hold in the dataset under all three models (unitary model, non-cooperative model,
cooperative model). However, the following regression analysis shows that such a
conjecture is not correct.
Columns (1), (2), (5), and (6) in Tables 3 and 4 show the estimates by the standard
IV estimation in equation (5), which have been used in many previous studies. In
Table 3, the dependent variables are the share of current expenditure on children,
family, husband, and wife in total current expenditure. In Table 4, the dependent
variables are the share of the sum of current expenditure and savings on children,
family, husband, and wife in the sum of total current expenditure and total savings.
The after tax income of the husband and wife is used as the IVs for the logarithm oftotal current expenditure (in Table 3) and the sum of total current expenditure andtotal savings (in Table 4). Table A1 presents the first stage regression, showing thatboth variables are good IVs. (The F-statistic is more than 10.) Columns (1) and (2)are the estimates from the single- and dual-earner sample and columns (5) and (6) are19the estimates from the dual-earner sample. All the numbers in Tables 3 and 4 show theeffect of the share of the husband’s income on the dependent variables. The common
explanatory variables other than the share of the husband’s income in Tables 3 and
4 are the hours spent on housework and child-rearing, the logarithm of total current
expenditure (in Table 3), the logarithm of the sum of total current expenditure andtotal savings (in Table 4), the age of the husband and wife, the number of children,
the number of family members, and year dummies. In some specifications, I add thelabor supply of the husband and wife in addition to the hours of housework of thehusband and wife as additional explanatory variables. The inclusion of the hours ofhousework and labor supply allows the possibility that labor supply and housework
are not weakly separable from the consumption of the wife, the husband, and public
goods.
In the standard IV estimates, the two tables show that neutrality is strongly denied
in both the single- and dual-earner sample and the dual-earner sample when demand
is not conditioned by the labor supply of the husband and the wife. When this isconditioned by labor supply, some coefficients become less significant and small, but
overall demand neutrality is denied. For example, column (1) of Table 4 shows that a
10 percentage point change in the income distribution from the wife to the husband
decreases the sum of expenditure and savings for children by 0.2 percentage points.
The standard IV estimation is subject to the bias caused by time-invariant preference shocks. The fixed effect estimation can solve this problem. Columns (3), (4), (7),and (8) in Tables 3 and 4 show the fixed effect estimation, which affects many of theestimates of the dual-earner sample. Except for the effect on expenditure on children(column (7) in Tables 3 and 4), the coefficients of the effect of the husband’s income
share become insignificant. For the single- and dual-earner sample, as long as they
are not conditioned by labor supply, many of the coefficients are still significant in
the fixed effect estimation and demand neutrality is denied. However, those estimates
are not robust to the inclusion of labor supply. Once they are conditioned by labor
supply, many become insignificant (columns (4) and (8)). Tables A3 and A4 present
the estimates of the other covariances in the fixed effect estimation, showing that the20housework of the wife is not weakly separable from the expenditure on children in the
single- and dual-earner sample, as one would predict. In contrast, I cannot find suchnon-separability in the dual-earner sample.
Tables 5 and 6 show the fixed effect IV estimation. As mentioned in the previous
section, the fixed effect estimation exacerbates the measurement error problem andIVs can fix this issue if appropriate variables are used. As the IVs, I used tax 1it andtax 2it defined in (10). Table A2 shows that both these IVs satisfy the rank condition
at a reasonably small and significant t level.
As predicted, the fixed effect IV estimation raises the absolute value of the coefficient, which suggests the existence of the measurement error problem. Again, Table 5
assumes additive separability between current and future consumption, while Table 6
does not. I also conduct the Hausman test against the null hypothesis that the error··

term in (6) is uncorrelated with θit . The numbers in the square brackets show theHausman statistic.
In Table 5, which does not assume additive separability between current and future
consumption, the effect of the husband’s income share on expenditure on children
becomes significant in all four specifications in the single- and dual-earner sample.
The Hausman statistic shows that the fixed effect IV estimation is better than the
fixed effect estimation. In contrast, as for the effect of the husband’s income shareon the wife’s consumption in the same sample, the fixed effect estimation shows
significant estimates, while the fixed effect IV estimation shows insignificant estimates.
Therefore, the Hausman statistic suggests the fixed effect estimation is preferable tothe fixed effect IV estimation.
In the dual-earner sample of Table 6, only the effect of the husband’s income shareon the husband’s consumption becomes significant. For the coefficients on the effect of
the husband’s income share on the sum of current expenditure and savings on children,which are significant in the single- and dual-earner sample, they become insignificant
for all specifications in the fixed effect IV estimation; however, the Hausman statistic
indicates that the fixed effect estimation is preferable to the fixed effect IV estimation.
In the fixed effect estimation, the coefficient on the effect of the husband’s income share21

on the sum of current expenditure and savings on children is not robust to adding
labor supply to the covariances. Once the labor supply of the husband and wife isadded, the coefficient becomes insignificant in the fixed effect estimation. In summaryin the single- and dual-earner sample, I can conclude that neutrality is denied in manyof the specifications. However, in the dual-earner sample, non-neutrality is supported
only marginally.
How can I reconcile these estimation results with the economic theory? Clearly,
the unitary model is denied. In addition, the non-cooperative model is rejected.
Although the evidence in the dual-earner sample is thin, the coefficient on the effectof the husband’s income share on public goods in the single- and dual-earner sample
is contrary to that predicted by the non-cooperative model. In contrast, the data areconsistent with those of the non-cooperative model. If the responsiveness conditionis satisfied, it is possible that as the husband’s income share increases, the level of
public goods decreases.

7

Implications and Conclusions

In this study, by using tax reforms as a quasi-experiment and Japanese panel data,
I studied the effect of the within-household income distribution on household public goods. I first examined this topic by using a conventional IV estimation. The
estimation results showed the non-neutrality of the income distribution in both thesingle- and dual-earner sample and the dual-earner sample. Next, I corrected thetime-invariant preference shocks by using a fixed effect estimation. With the fixed effect correction, the non-neutrality result was obtained for the single- and dual-earner
sample, while non-neutrality became marginal in the dual-earner sample. After applying the fixed effect IV estimation, the non-neutrality result was still valid in the
single- and dual-earner sample and it was marginal in the dual-earner sample. Thus,
the unitary model was clearly denied. The coefficient of the husband’s income shareon expenditure on public goods in the single- and dual-earner sample was opposite tothat predicted by the non-cooperative model. Thus, the non-cooperative model was

22

rejected. On the other hand, the result was consistent with the cooperative model aslong as the responsiveness condition holds.

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26

Table 1: Types of Family Budget Management
Single-Earner andDual-Earner
Dual-Earner
Couples
CouplesNumber of Observations
Yes
4054
1398
Do you share the family
No74
71
budget with your
NA.
97
36
spouse?
Total
4225
1505
Wife
3899
1278
Who manages the family
Husband155
120
budget?
Total
4054
1398
The husband gives over all his salary to his wife
3035
964
How much do you share The husband gives over some of his salary to his wife864
314
the family budeget with
The wife gives over all her salary to her husband
52
44
your spouse?
The wife gives over some of her salary to her husband
103
76
Total
4054
1398

Table 2: Summary Statistics
Single-Earner and DualEarner Couples

Dual-Earner Couples

Mean (Standard Deviation)
Husband's after tax income per month
28.7 (11.0)
26.8 (9.61)
Wife's after tax income
4.33 (7.11)
11.7 (7.26)
Husband's share of family income
0.89 (0.16)
0.73 (0.28)
Husband's hours of housework and child care per week
8.48 (8.77)
7.92 (9.07)
Wife's hours of housework and child care61.5 (27.3)
39.4 (16.3)
Number of children
1.89 (0.72)
1.92 (0.69)
Number of family members
4.58 (1.27)
4.85 (1.29)
Husband's age
35.2 (5.17)
36.2 (6.13)
Wife's age
32.2 (3.68)
33.3 (3.57)
Total consumption expenditures per month
21.2 (8.99)
22.6 (9.92)
Total consumption expenditures and savings per month
28.3 (11.5)
1.73 (3.63)
Share of consumption expenditures forchildren0.13 (0.10)
0.15 (0.10)
family0.60 (0.20)
0.56 (0.20)
husband0.15 (0.11)
0.16 (0.11)
wife
0.05 (0.08)
0.07 (0.08)
other family members per month0.05 (0.10)
0.06 (0.11)
Share of consumption expenditures and savings forchildren
0.15 (0.10)
0.16 (0.09)
family0.57 (0.19)
0.53 (0.19)
husband0.16 (0.10)
0.16 (0.10)
wife
0.07 (0.07)
0.09 (0.08)
other family members per month0.05 (0.09)
0.05 (0.09)
Number of Families
906
376
Number of Observations
4225
1505
Notes: The sample includes single-earner and dual-earner couples with at least one child in column 1 anddual-earner couples with at least one child in column 2. The amount of income, consumption, and saving
are measured in ten thousand yen.

27

Table 3: The Effects of Husband's Share of Family Income on
the Budeget Share of Consumption Expenditures for Each Family Member
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
The Budget Share of
Estimation Methods
Consumption
IV
FE
IV
FE
Expenditures for-0.053-0.064-0.047-0.0079-0.075-0.070-0.11-0.076
ChildrenPublic(0.016)(0.029)(0.020)(0.028)(0.027)(0.034)(0.042)(0.043)
Goods
0.11
0.069
0.10
0.010
0.075
0.035
0.045
0.011
Family(0.030)(0.055)(0.041)(0.056)(0.052)(0.065)(0.084)(0.086)0.026
0.015-0.012 -0.00061
0.074
0.054
0.054
0.038
HusbandPrivate(0.016)(0.027)(0.022)(0.031)(0.028)(0.039)(0.043)(0.044)Goods-0.056-0.058-0.063-0.030-0.062-0.064
0.035
0.045
Wife
(0.011)(0.021)(0.014)(0.018)(0.022)(0.026)(0.031)(0.032)
No
Yes
No
Yes
No
Yes
No
Yes
Hours of Work?
376
Number of Families
906
Number of Observation
4225
1505
Notes: Clustering robust standard errors on an individual basis are in parentheses. The sample includes couples
with at least one child in columns 1 through 4 and dual-earner couples with at least one child in columns 5through 8. Other covariates in the estimation models are the number of children, the number of family
members, husband's hours of housework and childcare, and wife's hours of housework and childcare. In
addition to these covariates, the logarithm of total consumption expenditures, husband's age, wife's age, andyear dummies are included in columns 1, 2, 5 and 6, the logarithm of deflated total consumption expenditures
are included in columns 3, 4, 7, and 8, and husband's hours of work and wife's hours of work are included in aneven number of columns. In columns 1, 2, 5, and 6, husband's after tax income and wife's after tax income areused as the instrumental variables for total consumption expenditures. This notes apply to Table 4.

Table 4: The Effects of Husband's Share of Family Income on
the Budeget Share of Consumption Expenditures and Savings for Each Family Member
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
The Budget Share of
Estimation Methods
Consumption
IV
FE
IV
FE
Expenditures and-0.026-0.017-0.0370.0083-0.048-0.032-0.086-0.049ChildrenPublic(0.016)(0.027)(0.019)(0.026)(0.026)(0.032)(0.037)(0.038)
Goods
0.15
0.10
0.098
0.021
0.13
0.098
0.074
0.041
Family(0.031)(0.055)(0.038)(0.052)(0.054)(0.050)(0.077)(0.079)0.0040-0.0028 -0.0076
0.0013
0.044
0.029
0.058
0.050
HusbandPrivate(0.016)(0.031)(0.021)(0.028)(0.03)(0.037)(0.041)(0.042)
Goods
-0.10
-0.12
-0.077-0.058-0.13-0.13-0.013-0.0089Wife(0.014)(0.023)(0.013)(0.017)(0.025)(0.029)(0.030)(0.031)
No
Yes
No
Yes
No
Yes
No
Yes
Hours of Work?
376
Number of Families
906
Number of Observation
4225
1505
Notes: The logarithm of total consumption expenditures and savings and the logarithm of deflated total
consumption expenditures and savings are included in the covariates in place of the logarithm of total
consumption expenditures and the logarithm of deflated total consumption expenditures, respectively.

28

Table 5: Fixed Effects Instrumental Variable Estimation:
The Effect of Husband's Share of Family Income on The Budeget Share of Consumption Expenditures for Each Family Member
The Budget Share of Consumption
Expenditures forChildrenPublic Goods
FamilyHusbandPrivate Goods
Wife
Hours of Work?
Number of Instrumental Variables
Number of Families
Number of Observations

(1)

(2)

(3)

(4)
(5)
(6)
(7)
(8)
Estimation Methods
Fixed Effects Instrumental Variable Estimation
-0.46
-0.58
-0.37
-0.51
-0.38
-0.37
-0.30
-0.30
(0.15)(0.20)(0.14)(0.21)(0.16)(0.17)(0.18)(0.18)[-2.77][-2.88][-2.33][-2.41][-1.74][-2.20][-1.09][-1.67]
0.41
0.47
0.49
0.60
0.22
0.20
0.10
0.096
(0.28)(0.38)(0.27)(0.39)(0.32)(0.33)(0.34)(0.30)[1.44][1.22][1.80][1.52][0.56][0.59][0.17][-0.29]-0.060-0.071-0.048-0.059
0.094
0.092
0.23
0.24
(0.15)(0.21)(0.15)(0.21)(0.16)(0.17)(0.18)(0.19)[-0.40][-0.34][-0.32][-0.28][0.26][0.33][1.01][1.10]
0.12
0.19
0.037
0.11
0.21
0.22
0.18
0.19
(0.096)(0.12)(0.095)(0.13)(0.12)(0.12)(0.13)(0.13)[-1.20][1.62][0.46][0.88][1.50][1.51][1.14][1.07]
No
Yes
No
Yes
No
Yes
No
Yes
2
1
2
1
906
376
4225
1505

Notes: Clustering robust standard errors on individual household basis are in parentheses, and Hausman statistics are in square
brackets. The Hausman t statistic has an asymptotic standard normal distribution. The sample includes couples with at least one
child in columns 1 through 4 and dual-earner couples with at least one child in columns 5 through 8. Other covariates in theestimation models are the number of children, the number of family members, husband's hours of housework and childcare, andwife's hours of housework and childcare, and the logarithm of deflated total consumption expenditures. Additionally, husband's
hours of work and wife's hours of work are included in an even number of columns. In columns 1, 2, 5, and 6, husband's share of
the amount of income tax in the family is used as the instrumental variable for husband's share of family income. In columns 3,
4, 7, and 8, husband's share of the amount of income tax in the family and the amount of family income tax are used as the
instrumental variables for husband's share of family income and the logarithm of deflated total consumption expenditures. This
notes apply to Table 6.

Table 6: Fixed Effects Instrumental Variable Estimation:
The Effect of Husband's Share of Family Income on The Budeget Share of Consumption Expenditures and Savings
The Budget Share of Consumption
Expenditures and Savings forChildrenPublic Goods
FamilyHusbandPrivate Goods
Wife
2

χ statistic(p-value)
Hours of Work?
Number of Instrumental Variables
Number of Families
Number of Observations

(1)

(2)

(3)

(4)
(5)
(6)
(7)
(8)
Estimation Methods
Fixed Effects Instrumental Variable Estimation
-0.34
-0.44
-0.36
-0.48
-0.15
-0.13
-0.12
-0.11
(0.14)(0.18)(0.13)(0.18)(0.14)(0.15)(0.14)(0.15)[-2.18][-2.00][-2.51][-2.22][-0.47][-0.56][-0.25][-0.42]
0.30
0.33
0.30
0.35
-0.037-0.069-0.21-0.23(0.26)(0.35)(0.24)(0.33)(0.29)(0.31)(0.31)(0.31)[-0.79][0.89][0.85][1.01][-0.40][-0.37][-0.95][-0.90]
0.048
0.074
0.11
0.15
0.20
0.21
0.35
0.36
(0.14)(0.19)(0.13)(0.19)(0.15)(0.16)(0.17)(0.18)[0.40][0.39][0.92][0.79][0.98][1.04][1.76][1.77]-0.0190.010
0.0099
0.050
0.060
0.071
0.14
0.14
(0.089)(0.12)(0.083)(0.12)(0.12)(0.12)(0.13)(0.12)[1.09][-0.40][1.06][-0.067][0.63][0.69][1.21][1.28]
8.10
6.82
10.63
9.08
3.05
2.77
6.25
6.39
(0.088)(0.15)(0.031)(0.059)(0.55)(0.60)(0.18)(0.17)
No
Yes
No
Yes
No
Yes
No
Yes
1
2
1
2
906
376
4225
1505

Note: The logarithm of deflated total consumption expenditures and savings are included in the covariates in place of thelogarithm of total deflated consumption expenditures.

29

Table A1: First Stage Regressions in the Instrumental Variable Estimation
(1)
(2)
(3)
(4)
ln(Total Consumptionln(Total Consumption
Instrumental Variables
Expenditures and Savings)
Expenditures)
0.011
0.00380.012
0.0042
Husband's After Tax(0.0021)(0.0035)(0.0024)(0.0044)
Income
0.023
0.036
0.027
0.041
Wife's After Tax(0.0039)(0.0066)(0.0040)(0.0078)
Income
61.6
61.7
76.8
71.2
F statistic[0.00][0.00][0.00][0.00]
Number of Families
906
376
906
376
Number of Observations
4225
1505
4225
1505
Notes: Huber-White standard errors are in parentheses, and p-values are in square
brackets. The sample includes couples with at least one child in columns 1 and 3 anddual-earner couples with at least one child in columns 2 and 4. F statistic is a test statistic
under the null hypothesis that the coefficients of the two instrumental variables are zero.
Other covariates in the estimation models are the number of children, the number offamily members, husband's hours of housework and childcare, wife's hours of houseworkand childcare, husband's hoursof work, wife's hours of work, husband's age, wife's age,and year dummies.

Table A2: First Stage Regressions in the Fixed Effects Instrumental Variable Estimation

Instrumental Variables
Husband's Share of theAmount of Family Income
Amount of Family IncomeTax
F statistic
Number of Families
Number of Observations(1)(2)
Husband's Share of Family
Income-0.078-0.14(0.0091)(0.016)-0.012-0.032(0.0037)(0.011)43.1
45.4[0.00][0.00]
906
376
4225
1505

(3)
(4)
ln(Consumption
Expenditures)
0.15
0.25
(0.055)(0.085)-0.062-0.19(0.022)(0.060)7.10
8.65[0.00][0.00]
906
376
4225
1505

(5)
(6)
ln(Consumption Expenditures
and Savings)
0.069
0.16
(0.046)(0.071)-0.044-0.15(0.019)(0.50)
3.72
6.24[0.02][0.00]
906
376
4225
1505

Notes: Standard errors are in parentheses, and p-values are in square brackets. The sample includes couples with at least one
child in an odd number of columns and dual-earner couples with at least one child in an even number of columns. F statistic
is a test statistic under the null hypothesis that the coefficients of two instrumental variables are zero. Other covariates in theestimation models are the number of children, the number of family members, husband's hours of housework and childcare,
wife's hours of housework and childcare, husband's hours of work, and wife's hours of work.

30

Table A3: Fixed Effects Estimation: The Effects of Husband's Share of Family Income on
Consumption Expenditures for Each Family Member
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Consumption
Consumption and Saving
Public Goods
Private Goods
Public Goods
Private Goods
Instrumental Variables

Children

FamilyHusband's Share of Family-0.047
Income(0.020)ln(Total Consumption-0.035
Expenditures)(0.0057)
Husband's hours of housework
0.33
and childcare(0.23)
Wife's hours of housework-0.28
and childcare(0.087)
Number of Families
Number of Observations

Husband0.10(0.041)0.011(0.011)0.27(0.45)
0.024(0.17)-0.012(0.022)-0.019(0.0062)-0.29(0.25)
0.23(0.094)
906
4225

Wife

Children

FamilyHusbandWife-0.063(0.014)0.0079(0.0037)-0.11(0.15)-0.050(0.057)-0.11(0.042)-0.041(0.0099)
0.76(0.42)
0.0017(0.22)

0.045(0.084)-0.0078(0.020)-0.068(0.83)-0.76(0.44)

0.054(0.043)-0.011(0.010)-0.88(0.43)
0.71(0.23)

0.035(0.031)
0.028(0.0074)
0.30(0.32)-0.12(0.17)

376
1506

Notes: Standard errors are in parentheses. The sample includes couples with at least one child in columns 1 through 4 anddual-earner couples with at least one child in columns 5 through 8. The specification of the estimation models is the same asthat in columns 3 and 7 in Table 3. The estimated coefficients of husband's and wife's hours of housework and childcare
multiplied by 1000 are reported. The standard errors of the estimated coefficients of husband's and wife's hours of houseworkand childcare are also mulplied by 1000. This notes apply to Table A5.

Table A4: Fixed Effects Estimation: The Effects of Husband's Share of Family Income on
Consumption Expenditures and Savings for Each Family Member
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Public Goods
Private Goods
Public Goods
Private Goods
Children

FamilyHusband's Share of Family-0.037
Income(0.019)ln(Total Consumption-0.036
Expenditures and Savings)(0.0052)
Husband's hours of housework 0.067
and childcare(0.21)
Wife's hours of housework-0.17
and childcare(0.080)
Number of Families
Number of Observations

Instrumental Variables

0.098(0.038)0.029(0.010)0.055(0.42)
0.037(0.16)

Husband-0.0076(0.021)-0.026(0.0056)
0.062(0.23)
0.11(0.086)
906
4225

Wife

Children

Family-0.077(0.013)0.0024(0.0036)0.068(0.14)-0.049(0.054)-0.086(0.037)-0.041(0.0087)
0.48(0.37)
0.042(0.20)

0.074
0.058(0.077)(0.041)-0.00032-0.012(0.018)(0.0095)
-0.40
-0.55
(0.77)(0.41)-0.40
0.39(0.40)(0.21)
376
1506

Notes: The specification of the estimation models is the same as that in columns 3 and 7 in Table 4.

31

HusbandWife-0.013(0.030)0.019(0.0072)0.47(0.31)-0.15(0.16)