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INTRA-HOUSEHOLD GENDER WAGE GAP IN CHINA: EVIDENCE FROM THE CHINA HEALTH & NUTRITION SURVEY

Article This paper analyzes the intra-household wage gap and wage determination of husbands and wives under the urban-rural dual economic structure in China. A two-step estimation procedure was used to determine the factors that are related to living in urban or rural areas by employing the probit model. Additionally, the effects of different factors affecting gender wage across regimes and between husbands and wives was examined using the seemingly unrelated regression estimation (SURE) model. It was found that the intra-household gender wage gap is larger in rural areas than in urban areas. At different percentiles, the gender wage gap is also different. There is a larger gender wage gap between low income earners than higher income earners. The largest gender wage gap is in the 10 th percentile in rural areas with a wife – husband wage ratio of 67%. The wage determination pattern between spouses is different in urban and rural areas. Except for human capital impact, urban-rural dual economic structure and family factors, spousal factors also effect the intra-household wage gap. study to the modeling and empirical investigation of the intra-household gender wage gap in China. This paper constructs a two-step econometric model to estimate the effects of different explanatory variables on the intra-household gender wage gap under the urban-rural dual economic structure,


INTRODUCTION
Households are the main basic units in society all around the world. The intra-household wage gap is an important aspect of the gender wage gap. A lot of studies have focused on gender wage gap, but few of them relate to income inequality between spouses in the same household. Due to the economic reform and marketization in China, researchers are paying more attention to China's gender-related income gap. Gustafsson & Li (2000) were the first to estimate the gender earning gap in China and they showed that the gap in urban China is relatively small compared to other countries while the gap tends to broaden in urban China. Shi, Jin, & Xiaochuan (2011) showed that gender wage gap increased significantly between 2002-2007 in urban China. A meta-analysis conducted by Iwasaki & Ma (2020) shows that in China, the gender wage gap has been increasing rapidly in recent years. Using the gaps between men and women regarding economic participation and opportunity, educational attainment, health and survival, and Asian Economic and Financial Review greater than the social gender income gap in China, and the unexplained proportion of the gender income gap between couples is larger than the social gender income gap. This leads to the consideration that there might be some factors that influence intra-household wages for couples, such as household maintenance and childcare related activities. Yu & Xie (2018) showed that a motherhood wage penalty exists among women, and each additional child lowers hourly wages by about 12%.
Literature on China's inequality almost universally shows that disparity between urban and rural household incomes in China is large and has increased over time (Binkai & Yifu, 2013;Chao & Shen, 2014;Teng, Yue, & Bjorn, 2007;Yang, 1999). According to China (2018), the ratio of urban individuals' disposable income over their rural counterparts was 2.71 in 2017, and with 58.5% of the population living in urban areas and 41.5% living in rural areas, this constitutes China's urban-rural dual economic structure. When analyzing the gender wage gap, researchers commonly use the Mincer earnings function and the Blinder-Oaxaca decomposition technique (Arulampalam, Booth, & Bryan, 2007;Blinder, 1973;Lo Sasso, Armstrong, Forte, & Gerber, 2020;Mincer, 1974;Oaxaca, 1973;Sax et al., 2017), and they mainly consider human capital factors that influence the pay gap. For the intra-household gender income gap, there might be some common factors (family factors) and some spousal factors influencing the pay gap.
This comes from the fact that most households make labor supply decisions collectively rather than a single household member deciding on their own, according to the collective model of labor supply (Chiappori, 1992;Donni, 2008;Gayle & Shephard, 2019;Michaud, Van Soest, & Bissonnette, 2020). As the study by Papps (2010) suggests, women's working hours are positively related to spousal education at the time of marriage and then fall over time after getting married, especially among women with educated husbands. As there is little research that has examined the effects of family and spousal factors on intra-household wages empirically, this has led to a research gap which this study aims to fill.
In this study, we extend the Mincer earnings function with a collective model under different regimes (the urbanrural dual structure) to measure China's intra-household gender wage gap, and the following questions are used: (i) Aside from the human capital factors, do family and spousal factors influence intra-household wages? (ii) If they do, what is the extent of the effects? (iii) Is there any difference between the effects on husband's and wife's wages? (iv) Are the effects different between urban and rural areas? This study classifies three types of factors: self, family, and spousal. By using the three types of factors, their effects can be measured in two steps: (i) determining the factors that relate to living in urban or rural areas, (ii) measuring the effects of different factors on gender wage across the regimes and between husbands and wives.

Model
The binary variable I indicates the urban-rural dual structure, = { 1, 0, .
Where I = 1 for households in urban areas and I = 0 for households in rural areas. The binary variable I signifies two different regimes for one couple's living area. Vector Z denotes socioeconomic variables that influence the wages of the husband and wife in a family. Then, given Z, the conditional probability of a household living in urban areas can be written as: Where F(•) is a known cumulative distribution function and is its parameter vector. This equation helps to determine the factors that relate to the area a family lives in (urban or rural).
Yj denotes the husband's or wife's wage in a family, j = h, w, which means that Yh is the husband's wage and Yw is the wife's wage. Given Z, an econometric model is used, which allows conditional expectation of Yh and Yw under the two different regimes denoted by the binary variable I. Also, given Z, the conditional expectations of a husband's and wife's wage can be written as, Given covariate Z and binary variable I, the conditional expectations of Yh and Yw are in linear form with different coefficients 1 and 0 with j = h,w as follows: Therefore, Equation 2 is equal to the weighted averages of the two in Equation 3.

Estimation
Given Equation 3, Equation 2 can be rewritten as: and Φ(•) is the cumulative distribution function of standard normal distribution. Now , 1 and 0 are parameter vectors that need to be estimated. Two steps were taken to achieve this goal. First, a probit model was used to estimate (Equation 5), and second, using the result of the first step, a seemingly unrelated regression estimation (SURE) model was used to estimate 1 and 0 (Equation 4). The selection of the SURE estimation method is based on the fact that the disturbance terms for the husband's and wife's wage equations are probably correlated within households (Srivastava & Dwivedi, 1979;Zellner, 1962). The use of SURE means that the estimation can be precisely compared to the usually used conventional ordinary least squares (OLS) estimation.

CHNS Data
The data used in this paper is from the 2011 China Health and Nutrition Survey (CHNS). The survey took place in 15 provinces and municipal cities that vary substantially in geography, economic development, public resources, and health indicators. The survey was first carried out in 1989 and the latest available data set is for 2011.

Sample and Variables
The original sample for 2011 includes 5812 households with 23,057 individuals and includes adults and children.
We selected a subsample of married working couples, which includes wives aged between 18-55 and husbands (household heads) aged between 18-60. In this dataset, it was found that married men who are under 22 years of age are all from rural areas, and married women who are under 20 years old are also from rural areas. This is in accordance with the phenomenon that in rural regions of China, young people tend to get married early, even if they are below the minimum legal age for marriage.
The variables investigated in this study are grouped by individual and family factors. Individual factors (for both husbands and wives) include annual wage (wage and bonus from one's main job), education, potential experience (we set potential experience, age -years of schooling -6 and others), and a control variable for occupation. Family factors include a dummy variable for region (urban or rural), number of young children (age 6 and younger; we calculated the number of children and their ages from the birth history of ever-married women and excluded children who died before the survey year), a dummy variable for house ownership, and province (classified as east, central, west, and northeast according to the economic regional divisions by the National Bureau of Statistics of China). The subsample selection and the exclusion of missing or incomplete information and merging with other data sets gave a final sample of 696 households.
The descriptive statistics of the sample are shown in Table 1. The mean annual wage for husbands is 33,892 Chinese Yuan (CNY), and 27,916 CNY for wives. The mean age for husbands is 42, and the wives' mean age is 40. In addition, husbands also hold a higher mean for education and work experience. This result shows that marriage gradient may exist in China's households. According to the marriage gradient, males tend to marry females who are younger and have a lower income and education (Kalmijn, 2013). Regarding domestic work, more than half of husbands do housework, whereas almost all wives do housework. To further investigate the wage differences related to education, children and region, the mean wages for wives and husbands by group are contained in Table 2. Several observations emerged from Table 2. Households in which the wife has a higher education tend to have a smaller intra-household wage gap. Under the Education section, when the husband has a higher education than his wife, the mean annual wage for the wife is 25,672 CHY, the mean annual wage for the husband is 33,022 CHY, and the ratio of mean wage between the wife and husband is 0.78. If a couple has an equal level of education, the mean wage for the wife is 27,294 CHY and the ratio of the mean wage between wife and husband is 0.81. If a wife has a higher education than her husband, the mean annual wage for the wife is 32,381 CNY and the ratio of the mean wage between wife and husband is 0.92. The Children panel shows that when couple has one young child, both the wife and husband earn more and the intra-household wage gap gets smaller compared to a couple who have no young children. Whereas if a couple has two young children, both the wife and husband earn less and the intra-household wage gap gets larger. The Region panel shows that the rural intrahousehold wage gap is larger than in urban areas. Table 3 summarizes the various percentiles of wage distribution for Regime 1 (urban) and Regime 0 (rural). It reveals that as wives' and husbands' wages increase, the intra-household wage gap gets smaller, but when the wage increases to a super high level (95 th percentile for urban areas, 90 th for rural areas), the intra-household wage gap gets larger. At the lower wage level, (e.g., the 10 th percentile), the rural intra-household wage gap is the largest across the distribution, while for urban areas, the intra-household wage gap is smaller at lower wage levels.

RESULTS
To investigate the determinants of wage for husbands and wives in different regimes, the probit model and the seemingly unrelated regression estimation (SURE) model were used to estimate the parameters with the paired couple data from the CHNS. show that for husbands, higher education and potential experience will increase the probability of living in an urban area. The average number of years of schooling for husbands in urban areas is 14.6 years and 12.2 years for husbands in rural areas. The Wife panel shows that their higher education also increases the probability of living in an urban area, although the effect is smaller compared to husbands. The average years of schooling for wives in urban areas is 14.4 years and 11.4 years for wives in rural areas. The Family panel shows that owning a house will decrease the likelihood of Regime 1, which suggests that rural couples tend to have their own house compared to urban couples. Note: (***), (**) and (*) denote that the parameter is statistically significant at the 1%, 5% and 10% levels, respectively. for Regimes 1 and 0 are grouped into Self, Family and Spouse, and are reported respectively. Note: (***), (**) and (*) denote that the parameter is statistically significant at the 1%, 5% and 10% levels, respectively.

"Self" Factors
The Self panels show that education plays different roles in both regimes. In Regime 1, it reveals that husbands benefit more from education than wives in urban areas. While in Regime 0, it reveals that wives benefit more from education than husbands in rural areas. This is a little different from previous studies which state that a return to education is always more beneficial for women than for men (Carnoy & Marenbach, 1975;Dougherty, 2005;Gwartney & Long, 1978;Psacharopoulos, 1985). Across both regimes, it reveals that education impacts husbands' and wives' wages more in urban areas than in rural areas.
The firm type variable also impacts husbands' and wives' wages differently among regimes. In Regime 1, a husband's wage is statistically significantly impacted by firm type. Working in a state-owned or private enterprises decreases a husband's wage with -49.6 or -60.5 log points, respectively, compared to foreign-related companies and others (the default firm type variable) in urban areas. While firm type does not significantly impact wives' wages in urban areas, in rural areas, husbands' wages are significantly and positively related to firm type. Working in stateowned or private enterprises increase husbands' wages, with 74.7 or 50.6 log points, respectively, compared to foreign-related companies and others in rural areas. Working in a private enterprise decreases a wife's wage with -54 log points compared to foreign-related companies and others in rural areas. Across regimes, it was revealed that working in state-owned or private enterprises has a negative effect on husbands' wages in urban areas, while it has positive effect on husbands' wages in rural areas. This might be because, in urban areas, enterprise types and economic units are diverse, thus people have more opportunity to choose higher paid jobs rather than conventional jobs. In rural areas, enterprise types and economic units are relatively lacking in diversity so people tend to choose conventional jobs, such as working in state-owned enterprises that guarantee job security, which is referred to as "iron rice bowl".

Family Factors
In both regimes, the province variable significantly impacts husbands' and wives' wages, and the impact is larger for husbands than for wives. Across both regimes, it was found that husbands' and wives' wages tend to be lower in the northeast compared to the east, central and west urban areas, while it is the opposite in rural areas. In rural areas, husbands' and wives' wages tend to be higher in the northeast compared to other regions. It was also revealed that the intra-household wage gap may have different characteristics among the different economic regions in China.

Spousal Factors
The Spouse panels show that spousal factors have different impacts on husbands' and wives' wages, and across regimes, spousal factors have different impacts on wives' wages. In both regimes, a wife's education or housework have no significant impact on a husband's wage, while for a wife in Regime 1, her spouse's education positively affects her wage with 5.4 log points. This confirms the educational classification in marriage (Schwartz, Robert, Schwartz, & Mare, 2005). In Regime 0, a husband's education negatively affects a wife's wage with -4.9 log points, which implies that as a husband becomes more educated, his wife tends to have reduced labor participation and a lower wage. This is in accordance with Papps (2010), who found that women's working hours are positively related to spousal education at the time of marriage and then fall over time among those with the most educated husbands. This study revealed that this pattern emerges in rural rather than urban areas in China.

CONCLUSION
In this research, the intra-household wage gap and wage determination of husbands and wives were analyzed under the urban-rural dual economic structure in China, and the effects of socioeconomic factors related to living in urban or rural areas was examined. As revealed in the probit model results, a husband's education, potential experience, and a wife's education are positively related to the likelihood of living in urban areas. The effect of education is larger for husbands than for wives, with coefficients of 0.078 versus 0.045, suggesting that husbands have an education premium. Owning a house has a negative effect on the probability of living in urban areas, suggesting that rural couples are more likely to have their own house. The wage determination pattern of husbands and wives is different between urban and rural areas. In urban areas, education has a positive effect on both husbands' and wives' wages, but the effect is higher for husbands. The return to education for husbands is 0.093, and 0.071 for wives. In rural areas, the effect of education on wages is higher for wives than for husbands. In urban areas, firm type significantly affects husbands' wages, while it is not significant for wives. In rural areas, firm type has more of an