Tsukuba Economics Working Papers
No. 2014-005

Neutrality Theorem Revisited:
An Empirical Examination of Household Public
Goods Provision∗by
Ken Yamadaand Hisahiro Naito

August 2014

UNIVERSITY OF TSUKUBA
Department of Economics
1-1-1 Tennodai
Tsukuba, Ibaraki 305-8571
JAPAN

Neutrality Theorem Revisited: An Empirical
Examination of Household Public Goods Provision
Ken Yamada∗ and Hisahiro Naito†‡§Current version July 2014

Abstract
Households have many economic roles in society. One of such roles is to sharehousehold-level public goods that are jointly consumed by members of the household.
Several theoretical models have been proposed in the literature: the unitary model,
the non-cooperative game theoretical model and the bargaining model. Using both theinformation on Japanese Tax reforms conducted in the 1990s as natural experiments
and Japanese panel data that has information on household expenditures in detail, we
examine the relevance of the unitary model and the non-cooperative game theoreticalmodel. We find that the neutrality result regarding income redistribution does nothold, which shows the failure of the unitary model. We also find evidences that the
non-cooperative game model does not hold either.

Keywords: public goods, household behavior, income distribution∗

School of Economics of Singapore Management University,90 Stanford Road, Singapore 178903
Corresponding author‡
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§
We are very grateful to the Institute for Research on Household Economics for giving us the permission
to use the Japanese Panel Survey of Consumers, data which has been collected by the Institute. We are also
thankful to the participants of the workshops held at the Institute for Research on Household Economics, theTCER Macro Conference, the University of Tsukuba and Hitotsubashi University for their helpful 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 begins to form a family, the family will start to have many functions in society and one of such functions is to share household public goods. Such household public
goods include basic housing service, children’s welfare and sharing household level chores.
For example, Becker (1981) pointed out that children have characteristics of classical public
goods within a family: both husband and wife obtain utility from their children’s happinessand it is difficult to exclude the husband’s (wife’s) enjoyment of their children’s happiness
when the wife (husband) is enjoying it too. In such a situation, the question of how the expenditures on such household public goods are 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. For example, when
the government increases a tax credit or income deduction for a family having children to
improve the welfare of children, one might wonder whether the government should give tax
preference to the husband, wife or both. Secondly, in order to design the basic principle ofboth the tax and the public expenditure system, information on how the household resource
allocation is determined is necessary. When many countries’ tax and public expendituresystems are compared, one would immediately notice that the basic unit of those systems isdifferent for different countries: some countries use individual income as the basic unit andother countries use household income (the sum of the incomes of the husband and the wife)as the basic unit. One might ask which system is more efficient and how the difference
between those two systems, household income base or individual income base, affects economic behavior such as labor supply, retirement, savings and the provision of household
public goods. Also, recently in Japan, the appropriate size of the non-working spouse’s
benefits such as the pension benefit and the tax allowance for a spouse are becoming important policy issues. Although the Japanese tax and the public pension system are basedon individual income, there are some exceptions. For example, in the Japanese public pension system, the spouse whose annual earning is less than 1.3 million yen (approximately
13 thousands US dollars) can receive the basic pension benefit without paying the pension
premium at all. Some critics argue that such a system is unfair and inefficient. To answer

1those questions, information regarding whether a household behaves as if it is a single unit
or whether each member of the household behaves individually is necessary.
There are three major hypotheses that could explain the resource allocation within ahousehold including household public goods. The first hypothesis is that a family will
behave as if it is a single agent. In this case, it is straightforward to show that the amount ofhousehold public goods is Pareto-efficient within the household and that income distribution
between husband and wife does not affect the allocation of public goods and private goods
once they are conditioned by the household income.
The second hypothesis is that the amount of public goods provided in the family is determined as the equilibrium of the non-cooperative game (the Nash equilibrium). In thiscase, each member of the household determines his/her contribution to household public
goods given the contribution of the other members of the household to public goods and thetotal amount of public goods is determined as the Nash equilibrium of this non-cooperative
game. As Samuelson (1954) demonstrated, it is well-known that in this non-cooperative
game, the total amount of public goods provided within a household is smaller than theefficient level because of the free-rider problem. In addition, in this non-cooperative game,
Warr (1982) and Bergstrom, Blume and Varian (1986) prove that when the government
redistributes income among public goods contributors, the total amount of public goods
provided is not affected by this government income redistribution. Bergstrom, Blume andVarian (1986) also show that when the government redistributes income from a public goods
contributor to a non-contributor of the public goods, the level of public goods is not neutral
regarding this government redistribution. Thus, whether the exogenous income redistribution affects the resource allocation or not depends on the initial condition. However,
applying a simple non-cooperative game theoretical model to the data has a problem; asimple non-cooperative game theoretical model implies that the consumption of the nonworking spouse is zero in single earner couples. To fix this obvious inconsistency of thetheoretical prediction of the simple non-cooperative game model with the empirical fact,
we introduce a small altruism in the non-cooperative game theoretical model. As we show
in the next section, a non-cooperative game theoretical model with a small altruism haverich implications for the effect of income restitution on the household resource allocation.
2

The third hypothesis is that the household allocation is chosen among Pareto-efficient
allocations, but the allocation among Pareto-efficient allocations is determined as the equilibrium of the bargaining game between the wife and the husband with appropriate threat
points. In this case, the neutrality of the allocation with respect to income distribution
depends on the threat point in the bargaining model. If the threat points are the non- cooperative Nash equilibrium, the neutral and non-neutral results of the non-cooperative gametheoretical model hold in the bargaining model. On the other hand, if the threats points
are different from the non-cooperative Nash equilibrium allocation, the neutrality of private
goods would not hold. The amount of public goods provision can be neutral with respect toincome distribution between wife and husband for another reason. Bergstrom and Cornes(1981) and Bergstrom (1983) find that when the preference of each member has the Gorman form, the Pareto-efficient level of public goods is independent of income distribution.
As Cox (1987) correctly points out, the bargaining model becomes the standard exchange
model when the bargaining power of the service provider becomes equal to zero.
Finding the relevant model among those three hypotheses is important since those threehypotheses have different implications for public policy. For example, if the unitary modelis true, the income tax system should be based on household income, not individual income
from the point of equity. In addition, since the level of public goods supplied within thehousehold is Pareto-efficient, no government intervention is needed to increase the level
household public goods. In the case of the non-cooperative game theoretical model it is notclear whether the fundamental unit of tax and public expenditure system should be based onfamily income. Also, since the level of public goods is under-supplied, some government
intervention can improve efficiency. Furthermore, the non-cooperative game theoreticalmodel suggests that different generations can be linked through public goods such as theutility of grand children.
In this paper, we use the Japanese panel data (the Japanese Panel of Survey of Consumers) and information on Japanese tax reforms conducted during the 1990s to examine the unitary model and non-cooperative bargaining model. Although the unitary modeland the non-cooperative Nash equilibrium model make similar predictions, there are somedifferences. In the non-cooperative Nash equilibrium model, if the redistribution occurs
3

between contributors and non-contributors, the neutrality result does not hold. Thus, it ispossible that empirical findings of the non-neutrality of the household resource allocation
mainly occur through the redistribution between the contributors and the non-contributors.
The data we use in this paper is the Japanese Panel of Survey of Consumers (JPSC)
from 1993 to 1999. The JPSC has several advantages compared to the data used in theprevious research for testing the household resource allocations. First, the JPSC asks not
only about the expenditures on each family member (private goods) but about the common
expenditures used for all family members and the expenditures for children (household
public goods). Second, the JPSC asks about the amount of savings for different purposes,i.e., for the husband for the wife, for the children and for common expenditures. Thus we
can observe how the household income is used not only for current expenditure but also
for savings for different members of the household and public goods. Moreover, the JPSC
asks about a detailed use of time by the husband and the wife. For example, the JPSC
asks how much time the wife and the husband use for work, housework, their own sleeping
hours, and their leisure. Third, the years that the JPSC covers are also useful for identifying
different hypotheses in this paper. During the 1990s, the Japanese government conducted
several reforms of the income tax system. Those reforms changed the income distribution
between the husband and the wife since the income tax liability in the Japanese tax system iscalculated based on individual income rather than family income. Therefore, the Japanese
tax reforms provide us ideal exogenous changes of income distribution between the husband
and the wife.

2

Literature Review

Warr (1982) is the first paper that claims that voluntary provision of public goods is independent of income distribution. Bergstrom, Blume and Varian (1986) analyze this issue
fully and examine under what conditions this theorem is valid. More specifically, they showthat the neutrality holds as long as income redistribution is conducted among the contributors to public goods. In addition, they show that if the income redistribution is conductedfrom the contributors to the non-contributors to the public goods, the total level of public
4

goods will decrease. For the empirical analysis of the voluntary provision of public and theincome distribution. Brunner (1997) and Murdoch and Sandler (1997) are the first papers
to analyze this issue. Brunner analyzes the contribution on national level public goods andMurdoch and Sandler examine the voluntary provision of international public goods. To thebest of our knowledge, there is no paper that attempts to apply the non-cooperative model
to empirically examine the household public goods allocation.
There are many papers that study the relationship between income distribution andhousehold public goods provision. Among them are Thomas (1990), Hadda and Hoddinot(1995), Schultz (1990). Thomas (1990) finds that in Brazilian families, unearned incomeof the mother has a stronger positive effect on child welfare Hadda and Hoddinot (1995)
find that in Cote d’Ivoire children’s height for their age is positively related with the shareof family wealth controlled by mother. However, as Bergstrom (1995) points out in his
well-organized survey on economics of family, it is still possible that the non-cooperative
Nash equilibrium model applies. For example, in the studies by Thomas (1990), Hoddinotand Hadda (1995) and Schultz (1990), the non-neutrality of household public goods can be
explained by the redistribution from non-contributors to contributor.
Some researchers also examine the bargaining model regarding household resource allocation. The earlier theoretical works are Manser and Brown (1980) and McElory andHorney (1981). Several authors estimate those bargaining models (Browning and Chiappori 1998; Browning Bourguignon Chiappori Lechene 1994).
As for the neutrality of the private goods, many studies already exist in the literature.
Among them are Hayashi (1995), Altonji, Hayashi and Kotlikoff (1992), Browning, Bourguignon Chiappori and Valerie (1994), and Hoddinot and Haddad (1995). Hayashi (1995)
and Altonji, Hayashi and Kotlikoff (1992) examine the neutrality within the extended families while Browning, Chiappori and Valerie (1994) and Hoddinot and Haddad (1995) examine the neutrality within a household. The results in those papers consistently showed thatthe non-neutrality of private goods within extended families or within a family. However,note that those results do not necessarily imply the non-neutrality of public goods for two
reasons. First, it is possible that the non-neutrality results on private goods in the previous
research were caused by income redistribution from the non-contributors to the contribu5

tors of public goods the mechanism first demonstrated by Bergstrom, Blume and Varian(1986). Second, when the household resource allocation is determined as the cooperative
bargaining model with the utility functions that have the Gorman form, the allocation of private goods is not neutral with respect to income redistribution while the provision of public
goods is independent of income redistribution because the bargaining model assumes thatthe allocation of public goods is Pareto-efficient and because the Pareto-efficient level of
public goods is independent of income distribution.

3

Data and Exogenous Variations

The data set that we use in this paper is the Japanese Panel Study of Consumers (JPSC).
The Institute for Research on Household Economics has surveyed 1500 women aged twenty
four to thirty four since 1993. These individuals are national representatives of this demographic group. The institute added 500 women aged twenty four to thirty four in 1997 to
the original 1500 women to increase the sample size. Since then, the institute surveyed
them annually. The women interviewed by the JPSC were asked on many dimensions of
their economic and social lives. They are asked about labor market outcome, education,savings, housing, the relationship between their parents and husbands, and the household
expenditures.
The JPSC is an appropriate data for testing the neutrality theorem because it surveys
the composition of consumption expenditures and savings in September and husband’s andwife’s after tax incomes separately for the married. The JPSC also asks about the hours
of housework and childcare of the husband and the wife in addition to labor supply. In
the questionnaire, the consumption expenditures and savings are respectively divided into
the following five categories: common expenditures (savings) for family expenditures (savings) for wife, expenditures (savings) for husband expenditures (savings) for children and
expenditures (savings) for others. The availability of detailed information on consumption expenditures and savings for each family member and labor supply and the hours ofhousework and childcare has several advantages in testing the neutrality theorem. First,
it is possible to analyze the provision of public goods because common expenditures and6

savings for family and expenditures and savings for children are classified as the provisions of public goods and expenditures and savings for husband or wife are classified as theconsumption of private goods. Second, it is possible to comprehensively examine the consumption of private goods because the exclusive goods are comprehensively included in theprivate goods and because savings and consumption for the husband (wife) can be included
in private goods of the husband (wife). Third, the availability of the hours of houseworkand childcare enables us to examine the non-separability of the expenditure for children
and family from the hours of housework and childcare. The share of the expenditure andsavings for others are very small. Thus, we ignore this category for our analysis.
We use the JPSC from 1993 to 1999 and focus mainly on two samples. The first sample
is 906 single-dual earner households with at least one child. The second sample is 376 dualearner households with at least one child. The 376 dual earner households sample is thesubset of the 906 single-dual earner households sample. Those two samples are unbalanced
panel data. We select those two samples based on the following selection rule; (i) they are
married; (ii) they have at least one child; (iii) two earners are salaried workers for at least
more than two years in the dual-earner sample and all earners (one or two) are salaried
workers in the single and dual earner sample; (iv) they have necessary information for atleast more than two years. We use the selection rule (ii) because the neutrality could be more
likely to be reached in the couples with children because they share more public goods thanthe couple with no children, the sample used by Browning, Bourguignon, Chiappori, andLechene (1994) and Browning and Chiappori (1998). In the case of dual-earner couples
with at least one child, the neutrality through the voluntary provision of public goods aswell as through income pooling can be reached. Moreover, Japanese couples share thefamily budget, and the wife typically manages it even in dual-earner households, as shownin Table 1.
The key exogenous variations that we utilize in this paper are the two major permanent
income tax reforms conducted in 1995 and 1999 and the characteristics of the Japaneseincome tax system itself. In the Japanese income tax system, the fundamental units ofincome tax are not family income, but individual income. In addition, the sum of the levelof basic allowance which is similar to the exemption in the US, and the allowance for7salaried worker which is similar to the standard deduction in the US, is quite high in theJapanese income tax system (1 million yen in 1993). As a result, there are many individuals
who do not have to pay the income tax. Even if they pay the amount of tax liability is quite
small and those whose tax liability is small are often the secondary earners in the family
because the basic unit of the Japanese income tax system is individual income, not family
income. Moreover, when the spouse income is less than a certain level, the primary earner,
not the spouse, can receive the spouse allowance and the special allowance for the spouse.
As for two tax reforms in Japan, in 1993 the tax brackets and the marginal rate of income
tax were changed and various types of allowance, such as the basic allowance, the allowance
for spouses, the allowance for salaried workers, the special allowance for spouses, and theallowance for dependents were expanded by thirty thousand yen respectively. In the 1999
tax reform, 20% of the tax payment was deducted regardless of the marginal tax rate and the
top marginal rate was also reduced. Thus, when the Japanese government introduced two
permanent tax reforms in the 1990s, many secondary earners who did not pay the income
tax did not receive the benefit from those tax reforms. In addition, the expansion of theallowance for the spouse and the special allowance for the spouse benefited the primaryearners, not the secondary earners, due to the nature of the Japanese income tax system.
Since the initial income distribution between the husband and the wife are different, those
two tax reforms in the 1990s changed income distribution between the husband and thewife differently for different households. We utilize two tax reforms on income distribution
among different households as the key exogenous variations.
We calculate the amount of income tax based on permanent income, that is the weighted
average of after tax income per month over time, in order to avoid the endogeniety of tax
brackets. By applying the permanent income to the table for the monthly amount of withholding income tax, we calculate the amount of income tax.

4

Analysis

Consider a family that is composed of a husband, a wife and their child. In this familyboth the husband and the spouse have non-labor income and labor income. We denote
8

husbands as h, wives as s and children as k. Let j be the index that shows a memberof the household where j=h, s, k. Let Kj, Lj, ljk ljj , wj be the non-labor income, timeendowment, housework, leisure and the market wage rate of the husband and the wife. By
definition, the labor supply of the member j is Lj−ljk −ljj . This family spends their income
for the husband, the wife and the child. We assume that the husband’s utility consists ofthe consumption of his own private goods and the utility from his wife and the utility of hischild as follows:uh (ch ) + f h (lhh ) + αhk uk (cks , lhk , lsk )We assume that the wife’s utility function is represented as follows:
us (cs ) + f s (lss ) + αsk uk (ck , lhk , lsk )and is the utility function of their child; f j (ljj ) is the utility from active leisure of member
j. For the utility of child, we assume that the husband and the wife’s time are imperfect
substitutes. In the unitary model, the household maximizes the weighted sum of the utilityof two persons subject to the household budget constraint. Let Ψj be the weight on themember j within the household. Then, the household solves the following maximization
problem:XΨj uj (cj ) + f j (ljj ) + αjk uk (ck , lhk , lsk )

(1)

j=h,s

s.t.

X
j=h,s

cj + ck =X{Kj + wj (Lj − ljj − ljk )}j=h,s

The above optimization program has several implications. First, it shows that the
lump-sum income transfer between the husband and the wife does not affect the allocation. Second, it shows that the optimal allocation can be solved in two steps. In the firststage, the household maximizes the objective function given ljj and ljk and obtains theconditional indirect utility function Γ(lhh , lhk , lss , lsk ). In the second stage, the household chooses ljj and ljk to maximize Γ(lhh , lhk , lss , lsk ). This implies that at the firststage, the conditional demand of ch , cs and ck are functions of ljj , ljk and the total income

9P

j=h,s {Kj + wj (Lj − ljj − ljk )}.

Thus, as long as ljk and lkk are being fixed, cj and ck

are independent from the income distribution between the husband and the wife. This is theempirical strategy that many previous studies have employed to test the unitary model.1

4.1

Non-cooperative game theoretical model

In the non-cooperative game theoretical model (hereafter we simply call the non-cooperativemodel to save the space), the husband chooses his private consumption, his contribution tohousehold public goods the cash-transfer to the wife, housework and labor supply given thewife’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,
the cash transfer from the husband and the housework by the husband. In this model, we
assume that husband is the primary earner and the wife is the secondary earner. The husband (primary earner) has some altruism to the wife (the secondary earner). We need thisassumption; otherwise the consumption of the spouse in the single earner couple becomes
zero, which is inconsistent with the empirical fact that the consumption of the spouse in
the single earner couple is not zero. Let gh , gs and m be the contribution of the household
public goods by the husband and the wife and the cash transfer from the husband to wife
respectively. Let τ be the lump tax imposed on the husband by the government and −τ isthe lump sum subsidy to the wife.
∗∗
The Nash equilibrium of this non-cooperative game {c∗j , gj∗ , m∗ , ljj, ljk; j = h, s} is1

In fact, in the above formulation, we assume that the time for active leisure,ljj , is additively separable.
In this case, we can drop the ljj from the conditional demand function.

10

determined as the solution of the following fixed point problem:∗∗(c∗h , gh∗ , m∗ , lhh, lhk) = argmax{ch ,lhh ,lhk ,g h ,m}∗uh (ch ) + f h (lhh ) + αhk uk (gh + gs∗ , lhk , lsk)(2)+ αhs {us (cs ) + f s (lss )}s.t. ch + g h + m = Kh + wh {Lh − lhh − lhk } − τwhere m ≥ 0 and g h ≥ 0∗∗(c∗s , gs∗ , lss, lsk) = argmax{cs ,lss ,lsk ,g s }∗us (cs ) + f s (lss ) + αsk uk (gh∗ + gs , lhk, lsk )

s.t. cs + g s = Kh + m + ws {Ls − lss − lsk } + τ
where g s ≥ 0Now, we can conduct comparative static analysis regarding τ . It is useful to consider
two cases where the first case is m∗ > 0 and the second case is m∗ = 0. First consider
the Nash equilibrium with m∗ > 0. Assume that the government redistributes income ex∗∗) fixed. In, ljk
ogenously between the husband and the wife and the government keeps (ljj

the first case, since the husband is making a transfer to the wife, it is obvious that suchexogenous income redistribution does not affect the equilibrium value. On the other hand,in the second case, the comparative static analysis shows the following results:∂(gh∗ + gs∗ )
∂g ∗
∂g ∗
∂c∗
∂c∗
= 0, h = −1, s = 1, h = 0 and s = 0
∂τ
∂τ
∂τ
∂τ
∂τ
∗
∗
; j = h, s}, ljk
as long as gh∗ > 0 and gs∗ > 0 for a fixed level of {ljj

In other words, the exogenous income redistribution does not affect either the level of
public goods nor the private goods. When the income of the husband increases by one
dollar and the 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 to one dollar.
Thus, the exogenous income redistribution is completely offset by the changes of voluntary
contribution to public goods by the husband and the wife.
Now what will happen if the government keeps redistributing income from the wife to11the husband? The above argument shows that as long as the contribution of the wife isstrictly positive, the husband increases his contribution and the wife decrease her contribution by the exact amount of the exogenous income redistribution and the neutrality of
public goods and the private goods keeps holding. However as the government keeps redistributing income, the contribution of the wife to public goods becomes smaller and smaller
and at some point it reaches zero. From that point, the neutrality does not hold any more.
But as the government keeps redistributing further, the amount of public goods would start
to increase. This is because the husband becomes the sole contributor to public goods andbecause the husband’s income increases as the government keeps redistribution. Since public goods is usually normal goods, the level of public goods will increase. On the other
hand, the wife spends her income only for her private consumption and her private consumption keeps decreasing as the government keeps redistributing income from the wife to
the husband. This process will continue as long as the marginal utility of the husband’s consumption is greater than the discounted marginal utility of the wife’s consumption. Whenthe marginal utility of the husband’s consumption becomes smaller than the wife’s marginalutility of the consumption, the husband starts to makes a transfer. From this point, further
income redistribution does not affect the equilibrium allocation since the transfer from thehusband to the wife offset the redistribution from the wife to the husband.
Figure 1(a) shows the case 1 and Figure 1(b) shows the case 2. G indicates the levelof public goods and θ indicates the share of the husband’s income. In the Figure 1(a),voluntary transfer occurs even when both husband and wife contribute to public goods In
this case, income redistribution does not affect the level of public goods provided in thishousehold.
In Figure 1(b), initially only the wife provides public goods (between A and B). As theincome share of the wife decreases, the level of public goods will decrease. As the income
redistribution from the wife to the husband continues, both the husband and the wife start
to contribute public goods (point B). While both the husband and the wife contribute public
goods income redistribution does not affect the level of public goods. As the government
keeps redistributing from the wife to the husband, the wife’s contribution becomes smaller
and the husband’s contribution becomes larger. At some point, the wife’s contribution
12

reaches zero (point C). Further redistribution from the wife to the husband increases thelevel of public goods in this household. At point D, the marginal utility of the husband’s
consumption becomes equal to the discounted marginal utility of the wife’s consumption.
From point D, the husband starts to make a positive cash transfer to the wife. Between
point D and E, income redistribution does not affect the level of public goods because acash transfer completely offsets income redistribution. Figure 1(c) shows the graph of theconsumption of the husband.
This result has several empirical implications for the data. First, this result suggeststhat income distribution between husband and wife does not affect the resource allocation
as long as both the husband and the wife contribute to household public goods. Second, it
provides the case that the effect of income redistribution in the non-cooperative model isdifferent from the effect in the unitary model. In the unitary model, income redistribution
does not matter whether both husband and the wife contribute to household public goods
or only one of them contributes to household public goods. On the other hand, in the noncooperative model, the neutrality result is valid only when both the husband and the wife
contribute. This is the strategy that we use in this paper to discriminate two models.

4.2

Empirical Strategy

Let i be the index to denote the household and n be the index to indicate the category of
the expenditure and savings, respectively. In this data, the expenditure and savings areclassified as for husband (h), wife (w), family (f) and children (k). For each category weuse subscript h, s, f and k. Let Eint Sint and Yint be the current expenditure, savings andthe sum of the current expenditure and saving for category n, at time t for household i. Let
Eit Sit and Yit be the total current expenditure, total savings, the sum of the total current
expenditure and the saving of the household i. By definition, Yint = Eint + Sint , Eit =PPn Eint , Sit =n Sint , Yit = Eit + Sit . Let θit , Ihit , Isit , Iit and Xit be the income share of
the husband, the total income of the husband, the total income of the wife, the total incomeSYof the household and the vector of demographic variables, respectively. Let hE
int , hint , hint

be the share of Eint in the total expenditure. In the unitary model, for given level of ljjit

13

and ljkit , we can consider the following Engel curve:
hbint = β1nb θit + β2nb ln bit + β3nb lhkit + β4nb lwkit + Xit δbn + aib + εinbt(3)

where b = E, Y ; n = h, s, f, k; t = 1993, 1994, ..., 1999
Several comments would be useful for (5). First, Xit includes the age of the husband,
the wife and the number of children of the household i at the period t. ainb represents timeinvariant preference shocks. Second, (5) is based on the conditional demand curve in whichlhkit and lwkit are conditioned. The first-order condition for given level of lhkit and lwkit in
the unitary model reveals that once the equation is conditioned by the total expenditure, theequation should not include the wage rates of the husband and the wife but should include
the housework of the husband and the wife due to possible non-weak separability between
housework and hb in (5). Third, we can derive (5) from the non-cooperative model given{ljj , ljk ; j = h, s}. Fourth, in the case of b = E, the model assumes additive separability between the current consumption and future consumption. If this additive separability
assumption fails, but if the unitary model is still true, (5) is valid only for b = Y
The parameter of our interest is β1nb and it measures how an increase of the husband’s
income will increase the level of household public goods (or the consumption of private
goods) when the total household income is held constant. In the unitary model, β1nb is equal
to zero. β3nb and β4nb indicate the degree of non-separability between the expenditure shareof category n with housework of the husband and the wife, respectively. For estimating theabove equation, previous studies use the total income for the instrumental variable of ln Eit
and ln Yit . However, there are still several problems. The first problem is the correlation
between the time-invariant preference shocks ainb and explanatory variables Because of
the definition of θit , θit is likely to be correlated with ainb . This is possible when the
spouse’s time-invariant preference shocks for public goods is correlated with the spouse’stime invariant preferences for housework.
The standard way to solve the correlation between the time-invariant preference shocks
and the income distribution between the husband and the wife is to rewrite (1) in terms of

14

time-demeaning form:
··

··

··

··

··

··

··

hb int = β1nb θit + β2nb lnbit + β3nb l hkit + β4nb l skit + X hkit δbn + εhkit(4)where b = E, Y ; n = h, s, f, k; t = 1993, 1994, ..., 1999
In the above question, ·· is an operator that calculates the time-demeaning mean. For ex····ample, in a case where θit is observed, in #(t) periods, θit is calculated as θit = θit −P(1/#(t)) t θit . Similarly, other variables can be calculated in the same fashion.
On the other hand, the fixed effect estimation can have a problem, too. It is widely
recognized that the fixed effect estimation aggravates the measurement error problem. To
alleviate this measurement error problem, we use the instrumental variable estimation. For
constructing the instrumental variables, we use the information on the Japanese tax systemand the Japanese tax reforms in the 1990s. During the 1990s, the Japanese government
introduced two permanent tax reforms and those tax changes affected income distribution
between the husband and the wife differently for different household because of the nonlinearity of the income tax system and the tax reforms. This suggests that the cross-sectionalvariations of the effect of the two tax reforms can be good instruments. Let τt (Ih , Is , Dh )and τt (Is , Ih , Ds ) be the labor income tax function of the husband and the wife at periodt when the husband’s and the wife’s incomes are Ih and Ih and the number of dependentsof the husband and the wife are Dh and Ds , respectively. For a function τt , there is a
subscript t because there are two tax reforms during the 1990s. τt is a function of the husband’s (wife’s) labor income and the spouse’s labor income and the number of the husband’s(wife’s) dependents. Although the Japanese income tax system is based on individual income in principle there are some exceptions such as the spouse allowance and the special
spouse allowance whose eligibility depends on spouse’s income. Thus, the tax liability of
the husband (wife) also depends on the spouse’s income. Also let I p and I p be the permanent income of the husband and the wife of the household i. We calculate the permanent
income of I p and I p as the average of Ihit and Isit for all observed periods. Then, we can15

calculatePppt {τt (Ihi , Isi , Dhit ) + τt (Isi , Ihi , Dsit )}tax1it =p, Isip , Dhit ) + τt (I p I p Dsit ) −τt (Ihi

tax2it =p
1 X
τt (Ihi, Isip , Dhit )−{p, Isip , Dhit ) + τt (I p I p Dsit ) #(t) tτt (Ihi#(t)pτt (Ihi, Isip , Dhit )}p, Isip , Dhit ) + τt (I p I p Dsit )τt (Ihi

where #(t) is the number of periods that the income are observed. Note that when calculating tax1it and tax2it , the tax liabilities are evaluated at the permanent income of thehusband and the wife. Also notice that Dhit and Dsit are the function of I p , I p and thedemographic variable Xit . Thus, tax 1it and tax2it are the change of the total tax liability
and the change of the share of the husband’s tax liability caused by the tax reform alone····

after controlled by Xit . Therefore, by construction, it is uncorrelated with εhkit . As for l hkit··

and l skit , if they are correlated with time-variant preference shocks, we also need to use
the instrumental variable for them. However, we could not find good instrumental variables····

that are correlated with l hkit and l skit in the first stage. May variables including the wage····

rates and the marginal tax rates turn out to be uncorrelated with l hkit and l skit . Thus, we are····forced to assume that the l hkit and l skit are uncorrelated with the time-variant preference
shocks.
Up to this point, our discussion has been restricted to the examination of the unitarymodel. In this paper, we will also discriminate between the unitary model and the noncooperative model since the welfare implications of the two models are quite different.
The key observation to empirically distinguish the two models is that in the non-cooperativemodel, the effect of income redistribution is neutralized through the changes of contribution to public goods. In other words, when the government redistributes one dollar from thehusband to the wife, the husband decreases his voluntary contribution exactly by one dollar
and the wife increases her public goods contribution exactly by one dollar as long as boththe husband and the wife contribute to public goods. However, this mechanism of neutralization does not occur when either the contribution by the husband or the wife is equal tozero. This implies that the neutrality result is less likely to hold when the initial income
share between the husband and the wife is already extreme and, as a result, only one person
contributes to public goods. On the other hand, in the unitary model the neutrality theorem
16holds at any income share. This suggests the following identification strategy to distinguishthe unitary model and the non-cooperative Nash equilibrium model. If the non-cooperativemodel is true and if we estimate (6) for a sample that includes both the single earner couples
and the dual-earner couples, in which the single earner couple is headed by the husband,the neutrality result is not likely to hold and the coefficient of the husband’s income shareon the husband’s consumption and public goods should be positive. On the other hand, foranother sample with equitable income distribution between the husband and the wife, theneutrality result is likely to hold since both the husband and the wife are likely to contributeto public goods. Thus, in this paper, we make the two samples and test the demand neutrality. The first sample includes both single and dual earner couples in which the single earneris headed by the husband. The second sample includes only the dual earner couples. If the
non-cooperative model is true, we expect that the neutrality is more likely to hold in the
dual-earner sample while it does not in the single-dual earner sample. Also in this sample,
the coefficient of the husband’s income share on public goods and the consumption of thehusband (wife) should be positive (negative).

5

Results

Table 1 shows the number of households who share the budget with the spouse. As Table 1
shows more than 95 percent of the households (4055/4226=0.96) share the family budget
with the spouse to some degree This provides an indirect evidence that the household inour data lives in an environment in which the neutrality result is very likely to hold. Table
2 shows the descriptive statics of the variables that we use in this paper. In our data, wehave 907 household and 4226 observations for single and dual earner couples. Among 907
households, 376 households are the dual earner couples. In the 376 dual-earner sample, wehave 1505 observations. One noticeable feature in Table 2 is the similarity of the expenditure patterns between the single-dual earner sample (the first column) and the dual-earner
sample (the second column). Another noticeable characteristic in Table 2 is the fact that theshare of wife’s consumption is quite small (5%) and that 70% percent of the total expenditure is used for household public goods such as the expenditure for children and family.
17

This suggests that in the dual-earner sample, both husband and wife are likely to contributehousehold public goods. Because of those two facts, readers might conjecture that the neutrality is likely to hold in the data due to either unitary model or the non-cooperative gametheoretical model. However the following regression analysis shows that such a conjecture
is not correct.
The columns (1), (2), (5) and (6) of Table 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 the current expenditure for children family husband or wife in the total current expenditure and in Table 4 the dependent variables are theshare of the sum of the current expenditure and saving for children, family, husband or wifein the sum of the total current expenditure and the total savings. The after tax income ofthe husband and that of the wife are used as the instrumental variables for the logarithmof the total current expenditure (in Table 3) and for logarithm of the sum of the total current expenditure and savings (in Table 4). Table A1 shows the first stage regression and it
shows that both variables are good instrumental variables.(The F-statistic is more than 10.)
Column (1) and (2) are the estimates from the single and dual earner couple sample andcolumns (5) and (6) are the estimates from the dual earner couple sample. All numbers in
Table 3 and Table 4 show the effect of the share of husband income on dependent variables.
Common explanatory variables other than the share of husband’s income in Table 3 andTable 4 are the hours for housework and childcare, the logarithm of the total current expenditure (in Table 3), the logarithm of the sum of the total current expenditure and the totalsavings (in Table 4), the age of husband and the wife, the number of children the numberof family members and year dummies. In some specifications, we add labor supply of thehusband and the wife in addition to the hours of housework of the husband and the wife asadditional explanatory variables. The inclusion of the hours of housework and labor supply
allows a possibility that the labor supply and housework are not weakly separable from theconsumption of the wife, the husband and the public goods.
In the standard IV estimates, the two tables show that the demand neutrality is strongly
denied in both the single-dual earner sample and the dual earner sample when the demand is
not conditioned by the labor supply of the husband and the wife. When they are conditioned18

by the labor supply, some of the coefficients become less significant and small, but over all
the demand neutrality is denied. For example, column (1) of Table 4 shows that a ten
percentage point change of income distribution from the wife to the husband will decrease
the sum of the expenditure and saving for children by a 0.2 percentage point.
The standard IV estimation is subject to the bias caused by time-invariant preference
shocks. The fixed effect estimation can solve this problem and columns (3), (4), (7) and(8) in Table 3 and Table 4 show the fixed effect estimation. The fixed effect estimation
affects many estimates of the dual-earner sample. Except the effect on the expenditure on
children (column (7) Table 3 and Table 4), the coefficients of the effect of the husband’s
income share become insignificant. For the single-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 the demand neutrality is denied. However, those estimates are
not robust to the inclusion of the labor supply. Once they are conditioned by the labor
supply, many of them becomes insignificant (column (4) and column (8)). Table A3 andA4 show the estimates of the other covariates in the fixed effect estimation. It shows thatthe housework of the wife is not weakly separable from the expenditure for children in the
single-dual earner sample, as one would predict. On the other hand, we cannot find such a
non-separability in the dual-earner sample.
Table 5 and Table 6 show the fixed effect differenced estimation, an estimation strategy
suggested by Altonji, Hayashi, and Kotlikoff (1992). Again, Table 5 assumes the additive
separability between the current consumption and future consumption while Table 6 doesnot. When the dependent variable is the sum of the current expenditure and saving for thehusband wife, children, and family (i.e. not assuming additive separability of the current
consumption and the future consumption), the coefficients of the effect of the husband’s
income share are all significant at the 10 percent level.
Table 7 and Table 8 show the fixed effect instrumental variable estimation. As we mentioned in the previous section, the fixed effect estimation exacerbates the measurement error
problem and the instrumental variable can fix such a problem if appropriate instrumental
variables are used. As the instrumental variables we used tax1it and tax2it defined in (7).
Table A2 shows that both two instrumental variables satisfy the rank condition with a rea19

sonably small significant t level.
As predicted, the fixed effect instrumental variable estimation makes the absolute valueof the coefficient larger, which suggests the existence of the measurement error problem.
Again, Table 7 assumes that the additive separability between the current consumption andthe future consumption while Table 8 does not. We also conduct the Hausman test against··

the null hypothesis that the error term in (6) is uncorrelated with θit . The number in thesquared bracket show the Hausman statistic.
In Table 8, which does not assume the additive separability between the current consumption and the future consumption, the effect of the husband’s income share on the expenditure for children becomes significant at all 4 specifications in the single-dual earner
sample. The Hausman statistic shows that the fixed effect IV estimation is better than the
fixed effect estimation. On the other hand, as for the effect of the husband’s income share on
the wife’s consumption in the same sample, the fixed effect estimation shows the significant
estimates while the fixed effect IV estimation show insignificant estimates. The Hausman
statistic suggests the fixed effect estimation is preferable to the fixed effect IV estimation.
In the dual-earner sample of Table 8, 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 the current expenditure and saving for children
which are significant in the single-dual earner sample, for all specifications in the fixed
effect IV estimation they become insignificant but Hausman statistics indicates the fixed
effect estimation is preferable to the fixed effect IV estimation. However, in the fixed effectestimation, the coefficient on the effect of the husband’s income share on the sum of thecurrent expenditure and saving for children is not robust to adding the labor supply to thecovariates. Once the labor supply of the husband and the wife are added, the coefficient
becomes insignificant in the fixed effect estimation. In summary in the single-dual earner
sample, we can conclude that the neutrality is denied in many specifications. However, inthe dual earner sample, the non-neutrality is supported only marginally.
How can we reconcile those estimation results with the economic theory? The idea todistinguish the unitary model from the non-cooperative model is that in the unitary model
the neutrality is likely to hold in any sample but in the non-cooperative model the neutrality20

is likely to hold only in the dual-earner sample. From that point, the unitary model isstrongly rejected. Also, the non-cooperative model is rejected. Although the evidence inthe dual-earner sample is thin, the coefficient of the effect of the husband’s income share on
public goods in the single-dual earner sample is opposite to what the non-cooperative model
predicts. As Figure 1(b) shows, the effect of the husband’s income share on public goods
should be positive in the single-dual earner sample in which the single earner is headed by
the husband. However, the data shows the opposite sign.

6

Implications and Conclusions

In this paper, by using Japanese panel data, we test the neutrality theorem of public goods
and private goods, which is unconditionally implied by the unitary model or which is supported under some circumstances in the non-cooperative game theoretical model. The data
is suitable for our analysis since the data includes the expenditure and saving for eachfamily member, the expenditure and saving for household public goods, and the hours ofhousework and labor supply by the wife and the husband. We first checked the neutrality
by using the conventional IV estimation. The estimation results showed the non-neutrality
in both the single-dual earner sample and the dual-earner sample. Next, we corrected thetime-invariant preference shocks by using fixed effect estimation. With the fixed effect correction, the non-neutrality result was obtained for the single-dual earner sample while thenon-neutrality became marginal in the dual-earner sample. After applying the fixed effectinstrumental variable estimation, the non-neutrality result was still valid in the single-dual
earner sample and it was marginal in the dual-earner sample. However, the coefficient of
the husband’s income share on the expenditure on public goods in the single-dual earner
sample is opposite to what the non-cooperative game theoretical model predicts. Thus, boththe unitary model and the non-cooperative game theoretical model are rejected.
Apart from the relevancy of those models, the results in this paper have important implications for public policy. For example, in Japan various changes of the income tax systemand the public pension system such as the elimination of the allowance of the spouse andthe expansion of the basic allowance are currently proposed. Given the current Japanese tax
21system, those change of the tax law is likely to decrease the income share of the husband
and increase the income share of the wife. Suppose that such changes of policy affects theincome distribution between the husband and the wife by one percentage point. Then, theresult in Table 8 shows that, if the preference is additively separable between the current
consumption and the future consumption, a one percentage point increase of income shareof the wife will increase the expenditure and saving share for children by a 0.48 percentage
point other things being constant.

References[1] Altonji, Joseph, Fumio Hayashi and Lawrence Kotlikoff, ”Is the Extended Family Altruistically Linked? : Direct Test using Micro Data,” American Economic Review 1992,
vol82, pp 1117-1198.
[2] Altonji, Joseph, Fumio Hayashi and Lawrence Kotlikoff, ”Parental Altruism and Inter Vivos Transfer: Theory and Evidence,” Journal of Political Economy 1997, vol 105,
pp1121-1166.
[3] Barro, Robert J., ”Are Government Bond Net Wealth?”, Journal of Political Economy
1974, vol 82, pp1095-117[4] Becker, Gary S. ” A Theory of Social Interactions”, Journal of Political Economy
1974,vol 82, pp1063-1094.
[5] Becker, Gary S. A treatise on the family, Cambridge, Mass Harvard University Press,
1981[6] Bergstrom, Theodore, Lawrence Blume and Hal Varian, ”On the Private Provision of
Public Goods,” Journal of Public Economics 29(1), February 1986, pages 25-49.
[7] Bergstrom, Theodore, “A Survey of Theories of the Family”, in Handbook of Population
and Family Economics vol 1a, 1997.
[8] Bergstrom, Theodore and Richard Cornes, “Gorman and Musgrave are Dual: An Antipodean Theorem on Public Goods”, Economic Letters 1981, pp371-378.
[9] Bergstrom, Theodore and Richard Cornes, “Independence of Allocative Efficiency from
Distribution in the Theory of Public Goods”, Econometrica 1983, vol51, pp1753-1766.
22

[10] Bound, J., D. Jaeger and R. Baker, “Problems with instrumental variables estimation
when the correlation between the instruments and the endogenous explanatory variable isweak”, Journal of the American Statistical Association, 1995, vol. 90, no. 430, pp. 443450.
[11] Brunner, Eric J., ”An Empirical Test of Neutrality and the Crowding-Out Hypothesis,”
Public Choice, September 1997, 92(3-4), pp 261-79.
[12] Bouguignon, F. M. Browning, P.A. Chiappori and V. Lechene ”Intra-Household Allocation of Consumption: a Model and some Evidence from French Data”, Annales d’Economie
et de Statistique,1993, 29, pp1067-1096.
[13] Bouguignon, F. M. Browning, P.A. Chiappori and V. Lechene, ”Incomes and Outcomes: A Structural Model of Intra-Household Allocation,” Journal of Political Economy
1994, vol 102, pp 1067-1096[14] Browning M. and P.A. Chiappori, “Efficient Intra-Household Allocations: A General
Characterization and Empirical Tests,” Econometrica, 1998, vol 66, pp 1241- 1278.
[15] Cox, Donald “Motives for Private Income Transfers”, Journal of Political Economy
1987, pp508-546[16] Haddad Lawrence and John Hoddinott “Household Expenditures, Child Anthropomorphic Status and the Intra-household Division of Income: Evidence from the Cote d’Ivoire,”Oxford Bulletin of Economics and Statistics”, 1995, 57(1): 77-96[17] Mansser M. and M. Brown “Marriage and Household Decisionmaking:A Bargaining
Analysis,” International Economic Review 1980, 21 pp31-44[18] McElroy,M.B. and MJ. Horney “Nash-Bargained Household Decisionis:Toward A
Generalization of the Theory of demand”, International Economic Review 1981, 22, pp333340[19] McElroy Marjorie B. “The Empirical Content of Nash Bargained Household Behavior”, Journal of Human Resources, 25, pp559-583[20] Murdoch,James, and Todd Sandler ”The Voluntary Provision of a Pure Public Good:The Case of Reduced CFC Emissions and the Montreal Protocol”, Journal of Public Economics February 1997, 63(3): 331-49.
[21] Samuelson Paul A., “The Pure Theory of Public Expenditure”, Review of Economics
Statistics November, 1954.
23

[22] Warr Peter G. ” The Private provision of a public good is independent from income
distribution”, Economic Letter, 1983.
[23] Schultz, T. Paul (1990), Testing the Neoclassical Model of Family Labor Supply andFertility,” Journal of Human Resources, 25, 599-634.
[24] Thomas, Duncan (1990) Intra-household Resource Allocation: An Inferential Approach,” Journal of Human Resources, 25, 635-696.

24

Table 1: Types of Family Budget Management

Yes
No
NA.
Total
Wife
Who manages the family
Husbandbudget?
Total
The husband gives over all his salary to his wife
How much do you share The husband gives over some of his salary to his wife
the family budeget with
The wife gives over all her salary to her husband
your spouse?
The wife gives over some of her salary to her husband
Total
Do you share the family
budget with your
spouse?

Single-Earner andDual-Earner
Dual-Earner
Couples
CouplesNumber of Observations
1398
4054
71
74
97
36
4225
1505
1278
3899
155
120
4054
1398
3035
964
864
314
52
44
103
76
1398
4054

Table 2: Summary Statistics
Single-Earner and DualDual-Earner Couples
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
1.73 (3.63)
28.3 (11.5)
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)
0.05 (0.10)
0.06 (0.11)
other family members per month
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.

25

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 Expenditures for
IV
FE
IV
FE
-0.053-0.064-0.047-0.0079-0.075-0.070-0.11-0.076
Children[0.0095] [0.024](0.020)(0.028)[0.022][0.028](0.042)(0.043){0.016} {0.029}{0.027} {0.034}
Public Goods
0.11
0.069
0.10
0.010
0.075
0.035
0.045
0.011
Family[0.024][0.019](0.041)(0.056)[0.042][0.053](0.084)(0.086){0.030} {0.055}{0.052} {0.065}
0.026
0.015
-0.012-0.00061
0.074
0.054
0.054
0.038
Husband[0.013][0.027](0.022)(0.031)[0.022][0.031](0.043)(0.044){0.016} {0.033}{0.028} {0.039}
Private Goods-0.056-0.058-0.063-0.030-0.062-0.064
0.035
0.045
Wife
[0.0089][0.0080] (0.014)(0.018)[0.018][0.022](0.031)(0.032){0.011} {0.021}{0.022} {0.026}
Hours of Work?
No
Yes
No
Yes
No
Yes
No
Yes
Number of Families
906
376
Number of Observations
4225
1505
Notes: Standard errors, Huber-White robust standard errors, and clustering robust standard errors on an individual basis arein parentheses, square brackets, and curly brackets, respectively. The sample includes couples with at least one child incolumns 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,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, and year 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 ofwork are included in an even number of columns. In columns 1, 2, 5, and 6, husband's after tax income and wife's after tax
income are used 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
The Budget Share of
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Consumption Expenditures andEstimation Methods
IV
FE
IV
FE
Savings for-0.026-0.017-0.0370.0083-0.048-0.032-0.086-0.049Children[0.012][0.022](0.019)(0.026)[0.020][0.026](0.037)(0.038){0.016} {0.027}{0.026} {0.032}
Public Goods
0.15
0.10
0.098
0.021
0.13
0.098
0.074
0.041
Family[0.023][0.044](0.038)(0.052)[0.041][0.050](0.077)(0.079){0.031} {0.055}{0.054} {0.065}
0.0040-0.0028-0.00760.0013
0.044
0.029
0.058
0.050
Husband[0.012][0.025](0.021)(0.028)[0.022][0.028](0.041)(0.042){0.016} {0.031}{0.030} {0.037}
Private Goods
-0.10
-0.12
-0.077-0.058-0.13-0.13-0.013-0.0089Wife[0.0096] [0.018](0.013)(0.017)[0.019][0.023](0.030)(0.031){0.014} {0.023}{0.025} {0.029}
Hours of Work?
No
Yes
No
Yes
No
Yes
No
Yes
Number of Families
906
376
Number of Observations
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 thelogarithm of deflated total consumption expenditures, respectively.

26

Table 5: Fixed Effects Estimation: The Effects of One's Income on Consumption Expenditures
(1)

(2)

(3)

(4)
(5)
(6)
(7)
(8)
Estimation Methods
FE
FD FE
FE
FD FE
0.042
0.037
0.021
0.019
0.045
0.042
0.017
0.015
After Tax Income(0.0032) (0.0037) (0.0056) (0.0056) (0.0072) (0.0079) (0.011)(0.011)
Hours of Work?
No
Yes
No
Yes
No
Yes
No
Yes
Number of Individuals
1812
1720
752
692
Number of Observations
8450
5988
3010
1956
Notes: Standard errors are in parentheses. The sample includes couples with at least one child in columns 1 through4 and dual-earner couples with at least one child in columns 5 through 8. In addition to this sample selection, thesample includes only the observations that have information for at least two years in a row in columns 3, 4, 7, and 8.
Other covariates in the estimation models are hours of housework and childcare and year dummies. In addition tothese covariates, one's hours of work is included in an even number of columns. This notes apply to Table 6.

Table 6: Fixed Effects Estimation: The Effects of One's Income on Consumption Expenditures and Savings(1)

After Tax Income
Hours of Work?
Number of Individuals
Number of Observations

(2)

FE
0.048
0.041
(0.0037) (0.0044)
No
Yes
1812
8450

(3)

(4)
(5)
(6)
Estimation Methods
FD FE
FE
0.027
0.025
0.064
0.060
(0.0066) (0.0066) (0.0085) (0.0092)
No
Yes
No
Yes
1720
752
5988
3010

27

(7)

(8)

FD FE
0.025
0.023
(0.013)(0.013)
No
Yes
692
1956

Table 7: Fixed Effects Instrumental Variable Estimation:
The Budeget Share of Consumption Expenditures for Each Family Member
(1)
(2)
(3)
(4)
(5)
(6)
The Budget Share of Consumption
Expenditures forChildrenPublic Goods
FamilyHusbandPrivate Goods
Wife
Hours of Work?
Number of Instrumental Variables
Number of Families
Number of Observations

(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
1
2
1
2
906
376
4225
1505

Notes: Standard errors are in parentheses, and Hausman statistics are in square brackets. Hausman statistic can be computed as
∧

∧

∧

2

∧

2

(βFEIV -βFE ) / {[se(βFEIV)] -[se(βFE)] }1/2. 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 the estimation models are the number of children, the number of family members, husband's hours ofhousework and childcare, and wife'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 forhusband'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 theamount of family income tax are used as the instrumental variables for husband's share of family income and the logarithm ofdeflated total consumption expenditures. This notes apply to Table 8.

Table 8: Fixed Effects Instrumental Variable Estimation:
The Budeget Share of Consumption Expenditures and Savings
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
The Budget Share of Consumption
Estimation Methods
Expenditures and Savings for
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)
Children[-0.56][-0.25][-0.42][-2.18][-2.00][-2.51][-2.22][-0.47]
Public Goods-0.069
-0.21
-0.23
0.30
0.33
0.30
0.35
-0.037(0.26)(0.35)(0.24)(0.33)(0.29)(0.31)(0.31)(0.31)
Family[-0.37][-0.95][-0.90][-0.79][0.89][0.85][1.01][-0.40]
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)
Husband[0.40][0.39][0.92][0.79][0.98][1.04][1.76][1.77]
Private Goods-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)
Wife[1.09][-0.40][1.06][-0.067][0.63][0.69][1.21][1.28]
Hours of Work?
No
Yes
No
Yes
No
Yes
No
Yes
Number of Instrumental Variables
12
12
Number of Families
906
376
Number of Observations
4225
1505
Notes: The logarithm of deflated total consumption expenditures and savings are included in the covariates in place of thelogarithm of total deflated consumption expenditures.

28

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 Income(0.0024)(0.0044)(0.0021)(0.0035)
0.023
0.036
0.027
0.041
Wife's After Tax Income(0.0040)(0.0078)(0.0039)(0.0066)
61.6
61.7
76.8
71.2
F statistic[0.00][0.00][0.00][0.00]
906
376
906
376
Number of Families
4225
1505
4225
1505
Number of Observations
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 and dual-earner couples
with at least one child in columns 2 and 4. F statistic is a test statistic under the null hypothesisthat the coefficients of the 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,
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.

29

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

Wife

Children

FamilyHusband

Wife

Husband's Share of Family
Incomeln(Total Consumption
Expenditures)
Husband's hours of houseworkand childcare
Wife's hours of houseworkand childcare
Number of Families
Number of Observations-0.047(0.020)-0.035(0.0057)
0.33(0.23)-0.28(0.087)0.10(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
4225-0.063(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
Instrumental Variables

Children

FamilyHusband

Wife

Children

FamilyHusband

Wife

Husband's Share of Family
Incomeln(Total Consumption
Expenditures and Savings)
Husband's hours of houseworkand childcare
Wife's hours of houseworkand childcare
Number of Families
Number of Observations-0.037(0.019)-0.036(0.0052)
0.067(0.21)-0.17(0.080)0.098(0.038)0.029(0.010)0.055(0.42)
0.037(0.16)-0.0076(0.021)-0.026(0.0056)
0.062(0.23)
0.11(0.086)906
4225-0.077(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
1506-0.013(0.030)0.019(0.0072)0.47(0.31)-0.15(0.16)

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

30

Figure 1(a)
G

θ

1

0

Figure 1(b)

G
A
D
B

E

C

θ
1
0

Figure 1(c)

C_h

1
0

31

θ