This dissertation contains two essays which examine the theory of model selection in econometrics and its applications. In the first essay, we utilize a model average approach to estimate a mixture copula. We average over the estimates of each individual copula and their composite and select their associated weights by minimizing a leave-one-group-out cross-validation criterion. We are able to prove that our model average estimator is asymptotically optimal in the sense of achieving the infeasible lowest possible squared estimation losses. Simulation results prove that our model average estimators for mixture copula exhibit smaller estimation loss than some benchmark methods. We empirically examine the dependence structures among the stock markets in U.S., United Kingdom, Japan and Hong Kong, and we show that our model average estimators give more reasonable estimations for the dependence structures among these markets. In the second essay, we implement a panel data approach to estimate the treatment effect of the justice reform in Virginia in 1995. The fundamental idea behind this method is to exploit the dependence among cross-sectional units to construct the counterfactual analysis. This panel data method uses the outcomes of the control units to simulate the path of the treated unit during the pre-treatment period and then predict the counterfactual path of the treated unit during the post-treatment period. In order to find the control units which simulate the pre-treatment path of the treated unit best, model selection criterion such as Akaike Information Criterion (AIC) and corrected Akaike Information Criterion (AICC) are used. We confirm that both violent and property crime rates declined in Virginia after the justice reform.
