Combined Estimation and Forecasting for Panel Data Models: Parametric and Semi-Parametric

This dissertation covers several topics in estimation and forecasting in panel data models.Chapter one considers the panel data model with correlated individual effects and regressors. We form a combined estimator from combining the fixed effects (FE) and random effects (RE) estimators. We derive the asymptotic distribution and the asymptotic risk of our estimator using a local asymptotic framework. We show that if the regressor dimension exceeds two, the asymptotic risk of the combined estimator is strictly less than that of FE estimator. Our simulation result shows that thecombined estimator can reduce finite sample MSE relative to the FE estimator for all degrees of endogeneity and heterogeneity, as well as relative to the RE estimator for moderate to large degrees of endogeneity and heterogeneity. We also apply the combined estimator to revisit the relationship between public capital infrastructure and private economic performance.Chapter two extends chapter one into the semi-parametric (SP) framework, and proposes a combined SP-FE and SP-RE estimator.Chapter three considers the panel data model with correlated residuals and regressors. In the presence of such correlation, both FE and RE estimators yield biased and inconsistent estimates of the parameter. We propose a combined FE and FE-2SLS estimator, and a combined RE and RE-2SLS estimator.Chapter four considers regression models for panel data that exhibit cross-section dependence due to common shocks. Model with factor structures for errors and regressors are considered. In this case, the FE estimator is inconsistent. To solve this problem, Pesaran (2006) introduced the common correlated effects pooled (CCEP) estimator. We propose a combined FE and CCEP estimator, and show that under certain conditions, the combined estimator has strictly smaller risk than the CCEP estimator. Finally, we use Holly et al. (2010) state-level housing data to show the applicability of the combined estimator.Chapter five proposes a combined approach to econometric forecasting. Monte-Carlo simulations are conducted to evaluate the performance of the combined forecast in finite samples. We contrast the out-of-sample forecast performance of the FE, RE and the combined approaches using the electricity and natural gas data sets