The first essay considers how the timing of government education spending influences the intergenerational persistence of income. We build a life-cycle model where human capital is accumulated in early and late childhood. Both families and the government can increase the human capital of young agents by investing in education at each stage of childhood. Ability in each dynasty follows a stochastic process. Different abilities and resultant spending histories generate a stochastic steady state distribution of income. We calibrate our model to match aggregate statistics in terms of education expenditures, income persistence and inequality. We show that increasing government spending in early childhood education is effective in lowering intergenerational earnings elasticity. An increase in government funding of early childhood education equivalent to 0.8 percent of GDP reduces income persistence by 8.4 percent. We find that this relatively large effect is due to the weakening relationship between family income and education investment. Since this link is already weak in late childhood, allocating more public resources to late childhood education does not improve the intergenerational mobility of economic status. Furthermore, focusing more on late childhood may raise intergenerational persistence by amplifying the gap in human capital developed in early childhood. The second essay considers parental time investment in early childhood as an education input and explores the impact of early education policies on labor supply and human capital. I develop a five-period overlapping generations model where human capital formation is a multi-stage process. An agent's human capital is accumulated through early and late childhood. Parents make income and time allocation decisions in response to government expenditures and parental leave policies. The model is calibrated to the U.S. economy so that the generated data matches the Gini index and parental participation in education expenditures. The general equilibrium environment shows that subsidizing private education spending and adopting paid parental leave are both effective at increasing human capital. These two policies give parents incentives to increase physical and time investment, respectively. Labor supply decreases due to the introduction of paid parental leave as intended. In addition, low-wage earners are most responsive to parental leave by working less and spending more time with children. The third essay is on the motherhood wage penalty. There is substantial evidence that women with children bear a wage penalty of 5 to 10 percent due to their motherhood status. This wage gap is usually estimated by comparing the wages of working mothers to childless women after controlling for human capital and individual characteristics. This method runs into the problem of selection bias by excluding non-working women. This paper addresses the issue in two ways. First, I develop a simple model of fertility and labor participation decisions to examine the relationships among fertility, employment, and wages. The model implies that mothers face different reservation wages due to variance in preference over child care, while non-mothers face the same reservation wage. Thus, a mother with a relatively high wage may choose not to work because of her strong preference for time with children. In contrast, a childless woman who is not working must face a relatively low wage. For this reason, empirical analysis that focuses only on employed women may result in a biased estimate of the motherhood wage penalty. Second, to test the predictions of the model, I use 2004-2009 data from the 1997 National Longitudinal Survey of Youth (NLSY97) and include non-working women in the two-stage Heckman selection model. The empirical results from OLS and the fixed effects model are consistent with the findings in previous studies. However, the child penalty becomes smaller and insignificant after non-working women are included. It implies that the observed wage gap in the labor market appears to overstate the child wage penalty due to the sample selection bias.