Silviase/jgov_v1.4_full_ann huggingface dataset:
it with respect to $ n_{r} $ , we obtain the following:

$$ \frac{\partial f_{i}}{\partial n_{r}}=\frac{\partial h_{i}}{\partial n_{r}}-\frac{\partial X}{\partial n_{r}}\frac{\partial f_{i}}{\partial x} $$

This equation means that the presence of a child of type r affects adult expenditure i in two separate ways: through substitution effects (the first term) as well as through negative income effect (the second term). If we consider the addition of a child to the household, the income effect is the reduction in adult consumption that is required to feed the child, while the substitution effects are the rearrangements in adult consumption that are desired even if the adults were compensated for the negative income effects of the child.

By rearranging the equation (2) we define the $ \pi $ -ratios as follows:

$$ \pi_{_{ir}}\equiv\frac{\partial f_{_{i}}/\partial n_{_{r}}}{\partial f_{_{i}}/\partial x}\frac{n}{x}=\frac{\partial h_{_{i}}/\partial n_{_{r}}}{\partial f_{_{i}}/\partial x}\frac{n}{x}-\frac{\partial X/x}{\partial n_{_{r}}/n} $$

The $ \pi $ -ratios have an interesting property to accord with the negative income effect, for $ \forall i \in I $ , if we define adult goods (I) as the group of goods without substitution effects from child presences, i.e., without the first term in the right hand side of equation (3).

$$ \pi_{_{ir}}\equiv\frac{\partial f_{_{i}}/\partial n_{_{r}}}{\partial f_{_{i}}/\partial x}\frac{n}{x}=-\frac{\partial X/x}{\partial n_{_{r}}/n}=\pi_{_{r}}\quad for\quad\forall i\in I $$

Therefore, if we need to make some inferences about the effects of a child $ (r) $ presence, e.g., the effects of gender on household spending allocation, all we have to do is to identify at least one (or some) adult good(s) without substitution effects and to calculate the $ \pi $ -ratio(s), or “outlay equivalent ratio(s)” above to see the negative income effect of the addition to the household of one more person of type r.

In order to compute the $ \pi $ -ratios, we need to estimate the marginal propensity to consume and the effects of household demographic structure on spending. To obtain those
variables, we estimate the following empirical Engel curve specification to relate linearly the share of expenditure of each good and the logarithm of total outlay:

$$ w_{i}=\frac{p_{i}q_{i}}{x}=\alpha_{i}+\beta_{i}\ln(x/n)+\eta_{i}\ln n+\sum_{1}^{J-1}\gamma_{ij}(n_{j}/n)+\delta_{i}\bullet z+e_{i} $$

where $ w_{i} $ is the share of good i relative to total outlay. The explanatory variables include a constant term, logarithm of outlay per household member, logarithm of number of household members, shares of each demographic category (total j categories). The vector z contains dummy variables allowing for possible effects of other household characteristics such as multiple worker households, homeowner households, and household location (prefectures).

Given the parameters in the equation (4), the $ \pi $ -ratios can be calculated as:

$$ \pi_{_{ir}}\equiv\frac{\partial f_{_{i}}/\partial n_{_{r}}}{\partial f_{_{i}}/\partial x}\frac{n}{x}=\frac{(\eta_{_{i}}-\beta_{_{i}})+\gamma_{_{ir}}-\sum_{_{1}}^{J-1}\gamma_{_{ij}}(n_{_{j}}/n)}{\beta_{_{i}}+w_{_{i}}} $$

for $ r=1,\ldots,J-1 $ and without the $ \gamma $ term for r=J. The parameters are replaced with their OLS estimates and $ w_{i} $ and $ n_{i}/n $ are with their values at the sample mean of the data.

We first take a list of possible adult goods, calculate the $ \pi $ -ratios for each child and adult age and gender group, and test the hypothesis to discover whether the ratios for the children of type r are the same for all selected adult goods, i.e., $ H_{0}: \pi_{ir} = \pi_{jr} (= \pi_{r}) $ where all i and j refer to adult goods, to confirm the validity of our adult goods identification. Once we have identified the adult goods properly, we can make inferences about family relationships and gender bias (if any) in households by comparing $ \pi_{r} $ among family members of different characteristics, e.g., a school-aged boy vs. a school-aged girl.
In case that some adult goods are not properly identified, estimated $ \pi $ -ratios deviate from $ \pi_{r} $ for $ \forall k \notin I $ . For example, if a good k is consumed not only by adults but also by a child of type r, $ \pi_{kr} $ becomes smaller negative (in absolute term) than $ \pi_{r} $ or even positive, since the substitution effects are expected to turn to positive, i.e., $ \frac{\partial h_{k} / \partial n_{r}}{\partial f_{k} / \partial x} \frac{n}{x} > 0 $ . Even without direct consumptions by children, there may be some cases where presences of children affect adult expenditures directly. If presence of a child causes a certain change in the preference of parents that results in smaller adult expenditure on good k, i.e., $ \frac{\partial h_{k} / \partial n_{r}}{\partial f_{k} / \partial x} \frac{n}{x} < 0 $ , $ \pi_{kr} $ becomes larger negative (in absolute term) than the negative income effect, i.e., $ \pi_{r} $ . While we cannot interpret estimated $ \pi_{kr} $ for goods $ k \notin I $ as the negative income effect of child r's presence, we will report the estimates in the following section, since they still appear to contain rich information about family relationships in Japanese households.

### 4. Empirical results and discussions

### 4.1 Results for adult goods

Table 2 reports the estimated $ \pi $ -ratios by adult goods. $ ^{9} $ Engle curves were estimated for expenditures on each of our seven (potential) adult goods categories as well as for expenditures on adult goods as a whole. The first six rows of results for households surveyed in each year (1990, 2000, and 2010) in the table give the $ \pi $ -ratios for children. We expect coefficients in these rows to be negative (for all categories) and same size each
other if the adult goods are accurately defined. Most of the estimated coefficients are negative as expected, with notable exceptions being household head's spending money (column $ (g) $ ) for pre-school children of both sexes in 1990, men's clothing (column $ (c) $ ) for senior high school boys, and women's clothing (column $ (d) $ ) for senior high school girls. While the anomaly of the household head's spending money is hard to interpret as it turns negative in later years, the clothing effects probably reflect the fact that senior high school boys (girls) buy adult clothing for men (women). $ ^{10} $ For most of the other pairings of children and adult goods, expenditure falls when an additional child is added to the household. Finally, the negative $ \pi $ -ratios for all adult goods (column $ (h) $ ), the sum of $ (a) $ to $ (g) $ , indicate that adult consumption is reduced in households with children. The $ \pi $ -ratios in column $ (h') $ , which report the results for adult consumption excluding adult clothing, which may not be properly defined adult goods, confirm our finding.

The last four rows of results for each year (1990, 2000, and 2010) in Table 2 present the $ \pi $ -ratios for adults. For these coefficients, while the theory does not predict a specific sign pattern, the coefficients are expected to be positive if adults (in the category) have access to the specified adult goods. Obtained results look generally reasonable except tobacco and golf expenditures, which are not correctly estimated (probably because their shares are too small). For example, alcohol spending (column $ (a) $ ) increases when male adults are in the household, while it decreases in households with female adults. Spending for clothing for men (women) increases when male (female) adults are present and decreases when female (male) adults are present. The household head's spending money increases when male adults are present in the household.
The test statistics for the equality of the $ \pi $ -ratios are given in the last two rightmost columns of Table 2. Though there are some exceptions (especially in 1990), which are marginally significant, null hypotheses that all $ \pi $ -ratios are equal across adult goods categories aren’t significantly rejected in the rows for children of 15 years old or younger, suggesting that the choice of adult goods is acceptable. This holds true especially when we exclude adult clothing from our adult goods, i.e., the results reported in the last column. The Wald statistics for the four adult groups are also shown in the last four rows of each year’s results. As inferred from the fact that some adult good categories are classifiable into male or female adult goods, equalities of $ \pi $ -ratios are significantly rejected in the rows for adult categories, confirming that our procedure is capable of detecting adult and child effects.

The gender differences for both children and adults can be tested by comparing the $ \pi $ -ratios by gender as well as by commodity. Table 3 presents the differences in the estimated $ \pi $ -ratios by gender (male's ratio minus female's ratio) and their standard errors in parentheses for the seven adult good categories (column $ (a) $ to $ (g) $ ) as well as for the total adult expenditures (column $ (h) $ ) and adult expenditures excluding adult clothing (column $ (h') $ ). The last two columns for the total adult expenditures (with and without adult clothing) show that none of the coefficients is significantly different between boys and girls (see the first three rows of Table in each survey year), indicating that there is no evidence of significant favoritism toward boys in the reaction of expenditure on total adult goods to the presence of an additional child. By contrast, the $ \pi $ -ratios for adult males are often significantly larger than those for adult females (see the last two rows), implying that adult males have better access to the adult goods examined here.

While the total expenditure results above, which are based on the comparison of
negative income effects obtained from properly defined adult goods, confirm that there is no gender discrimination in Japanese households, we find more nuanced and interesting facts about family relations when we turn to the coefficients for our individual adult goods categories (column $ (a) $ to $ (g) $ ) in Table 3. In contrast to the adult good categories such as alcohol, tobacco, etc., for which the estimated boy-girl differences are insignificant, we see statistically significant differences in the $ \pi $ -ratios for school children by gender for the categories of clothing for men (column $ (c) $ ) and clothing for women (column $ (d) $ ). The positive and significant coefficients for men's clothing mean that the absolute values of the $ \pi $ -ratios are smaller for boys than those for girls, as reconfirmed by the estimates in Table 2. Since properly identified adult goods are expected to produce a constant $ \pi $ -ratio, this finding means that the condition $ \partial h_{k} / \partial n_{r}=0 $ does not hold for adult clothing. Larger and statistically significant negative $ \pi $ -ratios for school girls mean that expenditures on clothing for adult men are sacrificed more for school-age girls (than for school-age boys), probably due to a certain change in father's preferences to reduce his spending on clothing after the birth of a daughter. On the contrary, the negative and significant coefficients for women's clothing (column $ (d) $ of Table 3) mean that expenditures on clothing for adult women are sacrificed more for school-age boys (than for school-age girls), probably also due to a change in mother's preferences to reduce her spending on clothing. Moreover, the absolute sizes of the $ \pi $ -ratios increase as boys age, meaning that spending on clothing for adult women is reduced to a greater extent when older boys are present in households.

The pattern that expenditures by parents are reduced when a child of the opposite sex is present in the family may hold not only for adult clothing expenditures but also for some other adult expenditure categories, as long as they are the types of goods consumed by a specific gender. While their differences are not significantly detected in Table 3,
expenditures on alcohol and golf, which are likely to be consumed more by adult males, are reduced more when a girl is present, while expenditures on cosmetics, probably by adult females, is reduced more when a boy is present (Table 2). Therefore, in sum, there appears to be a favoritism toward children of the opposite sex (i.e., a father favors a daughter and a mother favors a son) in the reaction of expenditures to the presence of an additional child, though gender discrimination in total adult expenditures is not significantly detected through negative income effect estimated from the conventional Engle curve approach. $ ^{11} $

### 4.2 Results for child goods

So far, we have discussed the results on $ \pi $ -ratios for adult goods expenditure categories. Given diary-based high quality spending data from the Family Income and Expenditure Survey, it is also possible to perform the same exercise to compute $ \pi $ -ratios for “child consumption” which may enable us to directly observe gender bias in the consumption of specified expenditure categories (clothing for children and education, here), if any; if a household favors either sex, child consumption would be larger for the favored sex than for the other. $ ^{12} $ Table 4 reports the results. Note that the expected sign of the $ \pi $ -ratios is reverse in this case, i.e., the sign is expected to be positive for children and negative for adults.
First, the $ \pi $ -ratios of clothing for children age 12 or under (column (a) of Table 4) are positive and significant for pre-school and compulsory school-aged children. $ ^{13} $ This is the case both for boys and girls. The estimated $ \pi $ -ratios also show that household spending on child clothing stemming from additional children is larger for younger boys and girls. The $ \pi $ -ratios are negative and mostly significant for high school children, who are 15 years old and older, and adults. Second, the $ \pi $ -ratios of education for children (column (b)) are positive and significant for all children groups and the size of the ratio increases with the age of the children, i.e., the ratio is smallest for pre-school children and largest for high school children. These patterns are observed irrespective of the gender of children, showing that household spending on education becomes larger as either boys or girls get older. Third, the $ \pi $ -ratios of the sum of those two expenses (column (c)) have the same pattern seen in column (b). The last column presents the test statistics of equality of $ \pi $ -ratio across child goods for each age and gender. The null hypothesis that two child goods have the same $ \pi $ -ratios is rejected for most of the age-gender combinations, implying that the effect of additional children significantly differs between expenditure for clothing for children and education.

Table 5 presents the test statistics of equality of $ \pi $ -ratio by gender in each age group. For our two child expenditure categories as well as total child expenditures, the differences in the estimated $ \pi $ -ratios (males' ratio minus females' ratio) and the standard errors are reported. The null hypothesis is that the difference between males and females is zero (i.e., there is no gender bias in household spending on the specified child goods). First, looking at clothing for children under age 12 (column (a)), we see the difference is
negative and significant for compulsory school children in all years and for pre-school children in 1990, implying that those $ \pi $ -ratios are larger for girls (or spending on clothing for children is larger when a girl is present than when a boy is present).

Turning to education (column (b)), we observe that the differences are small and insignificant for preschool and compulsory school children, implying that there is no gender bias in spending on education for younger children. However, as for high school age children, the difference is positive and significant in 1990, i.e., households were spending more money on high school education for boys than for girls at that time. Interestingly, the pattern now appears to be reversed, i.e., the difference turns to negative and significant in 2000 and 2010, implying that households are spending more money on high school education for girls.

Finally, we observe a similar pattern for the sum of the two spending categories in the last column (column (c)): the differences in $ \pi $ -ratios are small and insignificant for compulsory school or younger children, and those for high school children switched from positive to negative beginning the 2000s. So, overall, the observed pattern here suggests that there is no sizable gender discrimination in household expenditures for younger children, but high school girls are receiving a larger share of expenditures than high school boys, as in educational expenditures these days.

### 5. Discussion

The previous section provided the first evidence on intra-household resource allocation in household spending patterns in Japan, which are summarized as follows. First, adult consumption is significantly reduced in households with children. Second, while there is no evidence of significant favoritism toward boys in the reaction of
expenditure on total adult goods to the presence of an additional child, we found a pattern that expenditures by parents are reduced when a child of the opposite sex is present: more specifically, a father's spending on clothing is reduced when the child is a school-age daughter, while a mother's spending on clothing decreases when a school-age son is in the home. Third, spending on clothing for a child is generally greater for girls of compulsory school age or younger than it is for boys of the same age. Fourth, spending on education for high school age children is greater for boys in 1990 but less in 2000 and 2010.

In this section, to expand on our results, we try to put our findings in this paper in a broader strand of the literature. One strand of the literature is a large volume of studies on altruism. Our first evidence on lower adult consumption when children are in the household probably closely relates to the configuration of parental altruism toward children (or inter-generational transfer), and the second evidence suggests that gender may matter in altruism. These findings are consistent with Fujii and Ishikawa (2013) which provided quantitative evidence on intra-household reallocation to show that one additional child is associated with a reduction in the share of the mother's private expenditure by at least two percentage points in Japan.

Our findings as well as those by Fujii and Ishikawa (2013) probably echo other studies on gender difference in altruistic behavior in a more general setting. For example, Andreoni and Vesterlund (2001) performed an experimental dictator game and showed that women are kinder when altruism is expensive and men are more altruistic when it is less expensive. Eswaran and Kotwal (2004) theoretically examined gender difference in parental altruism and showed greater altruism in females.

While those studies showed gender difference in (parental) altruism between males
and females as givers, there is little research on whether or not the gender of recipients of altruism matters. A related study of the latter in Japan is Ono (2004), showing that the number of brothers in the household lowers women's likelihood for university advancement. While it may be partially offset by our finding that households spend more on educational expenses for high school girls, Ono's finding potentially implies that the gender of recipients of altruistic benefits matters.

Our finding that parents reduce their own personal spending for children of the opposite sex implies that the combination of genders of parents and children matters, too. To the best of our knowledge, there has been no empirical evidence on parental altruism in terms of the combination of genders of parents and children excepting a series of Engel curve based studies on gender bias, which is new in Japan. $ ^{14} $ We believe that our finding provides a new insight on a collective model of the household that deals with the heterogeneity of preferences among household members and describes the reality of household decision making better than a traditional unitary model.

While scarce literature in economics exists, there is some evidence in the psychology on whether the parent-child relationship depends on combination of gender (e.g., Collins and Russell (1991), Starrels (1994) and Russell and Saebel (1997)). However, it does not seem to reach a consensus that combination of gender matters or that a parent prefers a child of the opposite sex to a child of the same sex. The inconclusiveness may be attributed to possibility that parental preference may not be
innate but depend on other factors.

One such factor is the timing to measure parental preference. It is possible that parental preference may change after the individuals become fathers/mothers. For example, Moriizumi (2008) found that son preference got weak and mixed preference emerged over the recent two decades among Japanese before becoming parents. In contrast, Dahl and Moretti (2008) found that fathers are much more likely to obtain custody of sons compared to daughters after a divorce in the U.S. Another factor is the family’s economic status. There is a growing literature on gender difference in altruism toward members of the family in sociobiology and evolutionary psychology. Cox (2007) argued that educational attainment is higher for daughters in families with poor circumstances while it is higher for sons in families with better conditions and claimed that the finding is consistent with a variant of the Trivers-Willard hypothesis which originally reported a biased sex ratio in mammals. Indeed, Cox (2003) found that poor people are more likely to educate their daughters than their sons and rich people are more likely to educate their sons in the U.S., though Freese and Powell (1999) found that there is no significant difference in the association between educational investment and a child’s sex. $ ^{15} $

### 6. Conclusion

This paper provides new evidence on intra-household allocation of resources,
especially in terms of gender bias, in household spending patterns in Japan. As the research method, we employed the Engel curve approach developed by Deaton (1989, 1997) for the data from the Family Income and Expenditure Survey compiled by the Japanese government. We found that adult consumption is indeed significantly reduced in households with children and that there is no evidence of gender discrimination between boys and girls in terms of the outlay equivalent ratios ( $ \pi $ -ratio) representing a reduction of the total amount of expenditure for adult goods.

However, when we turn to the $ \pi $ -ratios for the individual adult goods categories, we found a gender bias in that expenditures by parents are reduced when a child of the opposite sex is present; specifically, a father's spending on clothing is reduced when school-age daughters are present and a mother's spending on clothing is reduced when school-age sons are present in the household. Our additional analysis on expenditures for children's goods shows that girls' clothing consumption is larger than that of boys. Even for educational spending, girls appear to be receiving more than boys in recent years.

Observed patterns of the intra-household resource allocation in this paper appear to indicate that further research on the subject may reveal incentives behind intra-household decision making. Whether a larger child expense in favor of girls is a result of altruism for daughters or of self-interest related to the expectation of receiving care later in life is an example of the issues to be explored. We need to accumulate more empirical evidence on the patterns of intra-household resource allocation as well as their determining factors, for example, in health-related matters, to explore the long lasting effect, if any, on human capital accumulation.