Graduation Year


Document Type




Degree Granting Department


Major Professor

Murat K. Munkin


Bridge Sampling, Dirichlet Process, DPM, MCMC, Roy-type Model


This dissertation explores the estimation of endogenous treatment effects in the presence of heterogeneous responses. A Bayesian Nonparametric approach is taken to model the heterogeneity in treatment effects. Specifically, I adopt the Dirichlet Process Mixture (DPM) model to capture the heterogeneity and show that DPM often outperforms Finite Mixture Model (FMM) in providing more flexible function forms and thus better model fit. Rather than fixing the number of components in a mixture model, DPM allows the data and prior knowledge to determine the number of components in the data, thus providing an automatic mechanism for model selection.

Two DPM models are presented in this dissertation. The first DPM model is based on a two-equation selection model. A Dirichlet Process (DP) prior is specified on some or all the parameters of the structural equation, and marginal likelihoods are calculated to select the best DPM model. This model is used to study the incentive and selection

effects of having prescription drug coverage on total drug expenditures among Medicare beneficiaries.

The second DPM model utilizes a three-equation Roy-type

framework to model the observed heterogeneity that arises due to the treatment status, while the unobserved heterogeneity is handled by separate DPM models for the treated and untreated outcomes. This Roy-type DPM model is applied to a data set consisting of 33,081 independent individuals from the Medical Expenditure Panel Survey (MEPS), and the treatment effects of having private medical insurance on the outpatient expenditures are estimated.

Key Words: Treatment Effects, Endogeneity, Heterogeneity, Finite Mixture Model, Dirichlet Process Prior, Dirichlet Process Mixture, Roy-type Modeling, Importance Sampling,

Bridge Sampling