Estimating labour supply and time allocation by married Japanese men and unmarried Japanese women

Abstract

In this article, I estimate the uncompensated and compensated wage elasticities and the income elasticity of time, for married men and unmarried women in Japan. For the purpose of the estimation, I control for the potential endogeneity of the wage and income variables.

Acknowledgement

I thank the Institute for Research on Household Economics for providing the data. Helpful comments from Daiji Kawaguchi are gratefully acknowledged.

Notes

¹ Throughout this paper, the term ‘unmarried’ includes both women who have never been married and those who are divorced or widowed.

² Few existing studies estimate models of time allocation with comparable specifications using Japanese data, as summarized by Yamada (2005).

³ The hourly wage rate is calculated by dividing annual labour income by annual hours of work in the same year, where annual hours of work are calculated by multiplying weekly hours of work by the number of weeks in a year. Virtual income is taken to be the intercept of the linearized budget constraint. Nonlabour income, which is the main component of virtual income, is calculated as the after-tax sum of the husband's labour income, property income, social security benefits and other family income. Moreover, taxes are computed following Yamada (2004). The after-tax wage rate and virtual income are deflated by the consumer price index.

⁴ The empirical model used in this analysis relies on fewer exclusion restrictions than does that of Biddle and Hamermesh (1990), who estimated sample selection models of labour supply and sleep demand after taking into account the endogeneity of wages and selection in employment.

⁵ ‘The marginal propensity to earn out of (linearized) nonwage income’ or ‘the total income elasticity’ can also be calculated by multiplying the estimated coefficient on virtual income by the sample mean of after-tax wage rate (Pencavel, 1986).

⁶ The test procedure was as follows. First, I obtained the residuals in the auxiliary equations via OLS regressions of the potentially endogenous variables on the instrumental variables, the control variables, and the inverse Mills ratio. Next, I regressed time allocation on the residuals, the potentially endogenous variables, the control variables, and the inverse Mills ratio using OLS. Then, under the null hypothesis that the coefficient of the residual term from the first-stage regression is equal to zero, the t-statistic is the Hausman statistic. Under this null hypothesis, the potentially endogenous variables for which the residuals are estimated in the first-stage regression are exogenous.

⁷ Furthermore, I also estimate time allocation using a sample of childless, unmarried women, without the covariates for the numbers of young children. For this alternative specification, the R-squared is much lower in the OLS estimation for hours of housework and childcare; this constitutes the main difference between the results presented in Tables 2 and A2. The effects of income on time are larger but not statistically significant for the 2SLS estimations.