Title: Panel Data Models with Interactive Fixed Effects
Description: This thesis explores a Bayesian approach for four types of panel data models with interactive fixed effects: linear, dynamic tobit, probit, and linear with a nonhomogeneous block-wise factor structure. Monte Carlo simulation shows good estimation results for the linear dynamic panel data model with interactive fixed effects, even with the correlation between covariates and factor loadings and with multidimensional interactive fixed effects. This approach is applied to NLSY79 data with a balanced panel of 1831 individuals over 16 years (from 1984 to 2008) to study Mincer's human capital earnings function with unobserved skills and returns. The Mincer regression model is applied to the whole sample and to subgroups based on race and gender. This thesis also proposes estimation methods for tobit and probit models with interactive fixed effects. A data augmentation approach by Gibbs sampling is used to simulate latent dependent variable and latent factor structure, and I achieve good estimation results for both coefficient and factor structure.

This thesis also proposes a new type of model: the panel data model with a nonhomogeneous block-wise factor structure. Extensive literature exists in macroeconomics and finance on block-wise factor models; however, these block-wise factor structures are homogeneous, and the subjects do not change the blocks that they belong to. For example, in research about how business cycle variations are driven by different types of shocks related to regional or country-specific events, the macroeconomic variables of the United States will always belong to the North American block. However, we have a nonhomogeneous block-wise factor structure inside wage dynamics: as workers have different returns, or may be subjected to different productivity shocks for their unobserved skills in different regions (blocks), the regions where workers reside could also change over time. According to our balanced data set from NLSY79 for more than 20 years, 306 of 1831 (16.72%) workers moved across regions during the survey period, which cannot simply be ignored.

This thesis proposes a set of identification conditions and estimation methods for this new type of model, and the Monte Carlo simulation yields very good estimation results. I also apply this model to study the NLSY79 balanced panel data, and find that the Northeast and the South have similar regional value patterns, while the Midwest and the West share similar patterns. Two chapters using a frequentist approach are also included in the thesis. The commentary on Hu (Econometrica 2002) shows that certain alternative sets of moment conditions in that paper are invalid to estimate censored dynamic panel data models. The other chapter focuses on how model selection procedures prior to actual data analysis will affect the properties of post-model-selection inference. The calculation of conditional size indicates that this correlation would interact with the distance between two competing non-nested models and generate conditional size distortion even asymptotically. A new second stage statistic that is asymptotically independent of the first stage Vuong statistic is proposed, and it performs better than the normal t statistic.