Analysis of Discrete Data Models with Endogeneity, Simultaneity, and Missing Outcomes

This thesis is concerned with specifying and estimating multivariate models in discrete data settings. The models are applied to several empirical applications with an emphasis in banking and monetary history. The approaches presented here are of central importance in model evaluation, policy analysis, and prediction.The first chapter develops a framework for estimating multivariate treatment effect models in the presence of sample selection. The methodology deals with several important issues prevalent in program evaluation, including non-random treatment assignment, endogeneity, and discrete outcomes. The framework is applied to evaluate the effectiveness of bank recapitalization programs and their ability to resuscitate the financial system. This paper presents a novel bank-level data set and employs the new methodology to jointly model a bank's decision to apply for assistance, the central bank's decision to approve or decline the assistance, and the bank's performance. The article offers practical estimation tools to unveil new answers to important regulatory and government intervention questions.The second chapter examines an important but often overlooked obstacle in multivariate discrete data models which is the proper specification of endogenous covariates. Endogeneity can be modeled as latent or observed, representing competing hypotheses about the outcomes of interest. This paper highlights the use of existing Bayesian model comparison techniques to understand the nature of endogeneity. Consideration of both observed and latent modeling approaches is emphasized in two empirical applications. The first application examines linkages for banking contagion and the second application evaluates the impact of education on socioeconomic outcomes.The third chapter, which is joint work with Professor Ivan Jeliazkov, studies the formulation of the likelihood function for simultaneous equation models for discrete data. The approach rests on casting the required distribution as the invariant distribution of a suitably defined Markov chain. The derivation resolves puzzling paradoxes highlighted in earlier work, shows that such models are theoretically coherent, and offers simple and intuitive linkages to the better understood analysis of continuous outcomes. The new methodology is employed in two applications involving simultaneous equation models of (i) female labor supply and family financial stability, and (ii) the interactions between health and wealth.