Three essays on econometrics - ZHENG, Xin (Institutional Knowledge at Singapore Management University, 2020)
The dissertation includes three chapters on econometrics. The first chapter is about treatment effects and its application in randomized control trial. The second chapter is about specification test. The third chapter is about panel data model with fixed effects. In the first chapter, we study the estimation and inference of the quantile treatment effect under covariate-adaptive randomization. We propose two estimation methods: (1) the simple quantile regression and (2) the inverse propensity score weighted quantile regression. For the two estimators, we derive their asymptotic distributions uniformly over a compact set of quantile indexes, and 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. For the inference of method (1), we show that the Wald test using a weighted bootstrap standard error under-rejects. But for method (2), its asymptotic size equals the nominal level. 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. We illustrate the finite sample performance of the new estimation and inference methods using both simulated and real datasets. 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. The MDD equals zero if and only if error term is conditionally mean independent of 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. We have established the asymptotic distributions of our test statistic under the null and under a sequence of Pitman local alternatives converging to the null at the usual parametric rate. We have conducted simulations to evaluate the finite sample performance of our test and compare it with its competitors. We find that our MDD test has superb performance in terms of both size and power and it generally dominates its competitors. In particular, 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. We apply our test to test for the correct specification of functional forms in gravity equations for four datasets. For all the datasets, we reject the log and level model coherently at 10% significance level. However, its competitors show mixed testing results for different datasets. The findings reveal the advantages of our test. In the third chapter, we consider the Nickell bias problem in dynamic fixed effects multilevel 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. The forms of the estimators in our framework are given explicitly. We apply the split-sample jackknife approach to eliminate the bias. In practice, our results can be easily extended to multilevel panel data models with higher dimensions.