Three Essays on Econometrics

The dissertation includes three chapters on econometrics. In the first chapter, we study the estimation and inference of the quantile treatment effect under covariate-adaptive randomization. We Show that, when the treatment assignment rule does not achieve strong balance, the inverse propensity score weighted estimator has a smaller asymptotic variance than the simple quantile regression estimator. We also show that, for both methods, the asymptotic size of the Wald test using a covariate-adaptive bootstrap standard error equals the nominal level. In the second chapter, we propose a novel consistent model specification test based on the martingale difference divergence (MDD) of the error term given the covariates. Our MDD test does not require any nonparametric estimation under the null or alternative and it is applicable even if we have many covariates in the regression model. It’s the only test that has well controlled size in the presence of many covariates and reasonable power against high frequent alternatives as well. It has great performance to test for the correct specification of functional forms in gravity equations for four datasets. In the third chapter, we consider the Nickell bias problem in dynamic fixed effects multi-level panel data models with various kinds of multi-way error components. For some specifications of error components, there exist many different forms of within estimators which are shown to be of possibly different asymptotic properties. We also apply the split-sample jackknife approach to eliminate the bias.