This dissertation consists of three chapters on panel data models. The first chapter examines unconditional logit and conditional logit, and pooled correlated random effect (CRE) logit approaches in binary panel data models with highly dependent data. Simulation results show that, first, the conditional logit method is not robust to violation of the conditional independence (CI) assumption. The magnitude of bias for the model coefficient is greater for the data with smaller time dimensions and higher serial correlations. Second, we find no significant finite sample biases for average partial effects (APEs) and associated rejection frequency of CRE logit in the presence of high serial correlation under correct specification of unobserved heterogeneity. Finally, we quantify two sources of bias into the part due to unobserved heterogeneity and the part due to serial correlation by using unconditional logit and conditional logit methods. Finite sample biases by both sources are important in binary panel models with highly persistent outcome and correlated individual fixed effects. As an empirical example, we apply conditional logit and pooled CRE logit to the Survey of Income and Program Participation (SIPP) data where welfare participation exhibits high persistence. The results imply that it is important to account for both state dependence and unobserved heterogeneity simultaneously.The second chapter introduces two formal tests of the missing completely at random (MCAR) assumption in unbalanced panel data. In a Monte Carlo (MC) simulation, we provide the evidence of the substantial powers of tests. Inverse probability weighted (IPW) estimator and multiple imputation-based (MI) estimator under the missing at random (MAR) assumption are studied as methods for missing data when the MCAR assumption is violated. We suggest combining MI and IPW methods such that the MI method is applied to non-monotone missing data and the IPW method is applied to monotone missing data sequentially. Proposed tests and the MI-IPW method for missing data are applied to estimate the effect of class size reduction (CSR) on student scores for grades in K-3 using Project STAR. The result of empirical application shows the violation of the MCAR assumption and the MI-IPW estimates for the effects of CSR on student achievement scores in grades K-3 are about 4.5 to 6 percent while unweighted estimates are about 6 to 7.5 percent.In the last chapter, we extend the robust inference method with heterogenous variance and autocorrelation in Hansen (2007) to unbalanced panel data with large time dimension. With the homogeneity assumption and random attrition, we derive the robust inference result using weighted least squares (WLS) for unbalanced panel data. We show that, our inference method with WLS in unbalanced panel data provides conservative t-test results in Bakirov and Szekely (2006) in the presence of attrition or heteroskedastic variance. We study the size and the power of a proposed inference method in unbalanced panel data using the Monte Carlo simulation. A MC simulation reveals that a proposed WLS method reduces the size distortion and improves power over the methods of Ibragimov and Muller (2009) and Hansen (2007).
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