Essays on non-normality, nonparametrics and cross-sectional dependence in panel data

Panel data has recently become one of the active research fields in econometrics. By pooling together of the observations of different individuals time, panel data provides some advantages for econometric modeling over a pure cross-section or time series method. This dissertation focuses on finite sample properties of panel data estimators under non-normality and the estimation in the presence of cross sectional dependence in panel data.; In Chapter 1, I study the finite sample properties of the feasible generalized least square (FGLS) estimator for the random-effects model with non-normal errors. By using the asymptotic expansion of the FGLS estimator, we obtain the analytic second-order Bias and MSE of FGLS. The numerical evaluation shows that asymptotic Bias and mean square error may give inaccurate results in finite samples. In Chapter 2, I study the fully modified (FM) estimation in panel vector autoregression (PVAR) under cross sectional dependence when the time dimension of the panel is large. The time series properties of the model variables are allowed to be an unknown mixture of stationary and unit root processes with possible cointegrating relations. The cross sectional shocks are modeled with a factor structure. FM method is used for estimating the parameters in panel VAR and we also give the asymptotic distribution of the FM-VAR estimator under cross sectional dependence. It is found in simulation that the estimates from the factor-augmented method give better finite sample properties when the signal from cross sectional shock is strong. Chapter 3 proposes a nonparametric method for estimation in static panel under cross sectional dependence. The unobserved cross sectional shocks can be expressed in terms of observed variables by averaging over a local constant regression across different cross sectional units. I derive the asymptotic distribution of the estimators and simulation results show that there can be substantial efficiency gain by incorporating cross sectional dependence into estimation.