Doctor of Philosophy / Department of Economics / Dong Li / This dissertation is a combination of three essays on spatial econometrics and labor economics. Essays 1 and 2 developed double length regression (DLR) tests for testing functional form and spatial dependence, which includes spatial error dependence and spatial lag dependence. More specifically, these essays derive the DLR joint, DLR one-direction, and DLR conditional tests for testing functional forms and spatial dependence. The essays also provide empirical examples and Monte Carlo simulations to examine how the DLR tests perform in the empirical work and how the power of the DLR test depends on changes in functional form and spatial dependence. The results suggested that DLR tests work similarly to its Lagrangian Multiplier (LM) counterpart for testing functional form and spatial dependence in the empirical example and simulations. The DLR tests do not require the second-order derivatives of the log-likelihood function, so they provide practitioners an easy-to-use method to test for functional forms and spatial dependence. Essay 3 investigates the effects of fertility on parental labor force participation and labor supply in Vietnam. The essay uses instrumental variable (IV) probit models to estimate the effects of fertility on parental labor force participation and the IV models to estimate the effects of fertility on parental labor supply. Using the gender of the first child and the same gender of the first two children as two instrumental variables, this essay found negative effects of fertility on maternal labor force participation and labor supply. It also found positive effects of fertility on paternal labor force participation and labor supply. The results suggest that fertility had the specialization effect on parental labor force participation and labor supply in Vietnam. The homogeneity test results indicate that the magnitude of the effects of fertility on parental labor force participation and labor supply is different among parents and locations.