One of the very interesting demographic features in the US over the last three decades of the 20th century is the increase of the married women labor force participation rate. Over the same period, estimated labor supply elasticity varies substantially. This dissertation is to investigate the reasons behind them. I first study the determinants of the increase of the labor participation rate for married women with preschool-aged children over the last three decades of the 20th century. Using 5% samples of the Integrated Public Use Microdata Series (IPUMS) for 1980, 1990 and 2000, I find that the existing explanations proposed in the literature may only account for 9.6% increase in the 1980s and 70% decrease in the 1990s. In this paper, I find that the rising ratio of career type women can explain 30.33% of the growth in the labor force participation rate, and the change in the composition of career motivating career type women can at least explain 17.22% growth across cohorts. Women who have been working three years before their first childbearing are more likely to return to work after the childbearing period. The analyzing data is the National Longitudinal Survey of Young Women (NLSYW) from 1968 to 2003 and the National Longitudinal Survey of Youth 1979 (NLSY79) from 1979 to 2008. This dissertation sheds some insight about a puzzle on estimated married women's labor supply elasticity variation. This important puzzle (sometimes referred to as the Hausman puzzle) is that the estimated labor supply elasticity varies substantially even when similar frameworks and similar datasets are used. I study the role of budget sets in producing this wide range of estimates. In particular, I study the effect of the typical convexification approximation of the non-convex budgets, and the well-known Heckman critique of the lack of bunching at the kink points of budget sets in the Hausman model. I introduce measurement error in nonlabor income to create an uncertain budget constraint that no longer implies bunching at kink points. Using the Panel Study of Income Dynamics (PSID) of 1984 and 2001, I find that neither the convexification approximation nor using a model with random budget sets affects the estimates. These results demonstrate that variations in budget constraints alone do not explain the different estimates of labor supply elasticity. Changing the level of budget sets, for example by ignoring the state individual income tax, could affect the variation in elasticities.