Modeling and inferential approaches for treatment response data in cross-section and panel settings with confounding on unobservables

This dissertation is concerned with isolating the effect of a binary treatment on some outcome of interest in settings when the treatment intake is non-random and depends on unobserved factors that are likely to be correlated with the outcome. In such cases it is not possible to find the treatment effect without auxiliary, un-testable assumptions about the unobserved confounders and a model of their effect on the intake and the outcome. The challenge therefore is to isolate defensible assumptions and models that are appropriate and meaningful. My dissertation addresses this challenge by developing Bayesian inferential approaches for two different settings with confounding on unobservables, thus contributing to a growing literature in statistics and econometrics. The proposed models are subjected to a full prior-posterior Bayesian analysis based on Markov Chain Monte Carlo (MCMC) methods and methods for the estimation of treatment effects based on the predictive approach are discussed. The performance of these methods is tested in extensive simulation studies. We also develop marginal likelihood/Bayes factor methods for model comparison.; The first chapter considers a setting where the treatment is taken once at baseline and we observe a balanced panel of outcomes. This set-up arises for example in the evaluation of job-market training problems and educational attainment on labor market outcomes, but to our knowledge has not been analyzed in the literature. Following the work by Chib (2004) in the cross-section context we propose a joint model for the panel of outcomes and the treatment intake that allows for a general form of dependence amongst the unobservables and also allows for subject-specific coefficients in the outcome model that are potentially correlated with the covariates. The second chapter focuses on settings where the treatment is assigned randomly but the actual treatment intake is not necessarily the same as the assignment for subjects in the treatment arm; subjects in the control arm, however, have no access to the treatment. Such designs (here referred to as eligibility designs) arise in the context of clinical trials and social science experiments. The existing approaches for the eligibility setting have mainly been developed under a frequentist perspective and without exception proceed by modeling the unobserved confounder in terms of a latent discrete compliance type variable (for example, Sommer and Zeger 1991, Frangakis and Rubin 1999, Yau and Little 2001, Albert 2003). Conditional on this discrete confounder the outcome and the intake are assumed to be uncorrelated. In contrast to this discrete confounder approach, the joint modeling of the outcome and the treatment intake, as discussed for example in the first chapter for a noneligibility setting, assumes a continuous confounding variable without reference to the compliance behavior. Here we extend the continuous confounder approach to the eligibility setting. We show that the non-stochastic treatment intake for subjects in the control arm has interesting implications for the modeling and the MCMC methods that are discussed in the chapter. (Abstract shortened by UMI.)...