A Bayesian Semiparametric Approach to the Instrumental Variables Problem with a Binary Treatment or Outcome

• Activity Number: 652
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jessica Pruszynski*+ and Purushottan Laud and Rodney Sparapani and Robert E. McCulloch
• Companies: Medical College of Wisconsin and Medical College of Wisconsin and Medical College of Wisconsin and The University of Chicago Booth School of Business
• Keywords: Bayesian semiparametric ; comparative effectiveness research ; Markov chain Monte Carlo ; Probit regression

Abstract

Instrumental variable methods are used to estimate causal relationships when performing a randomized experiment is not possible. Traditional instrumental variable methods in econometrics do not account for the presence of a binary or categorical variable. In this paper, we consider two separate instrumental variables models in which either the outcome or the treatment is a binary variable. We compare the performance of a two stage least squares moment based approach to a model-based Bayesian approach under two scenarios. In the first scenario, we ignore the binary treatment and proceed with the analysis as if the treatment were continuous. In the second scenario, we apply the correct model with the knowledge that the treatment is binary. For the second scenario, we investigate the use of Bayesian semiparametric models in order to relax the parametric assumptions of the model. Under both scenarios, we compare, using repeated data simulation, the moment-based and Bayesian approaches using such quantities as power, bias, mean squared error, and confidence/credible interval length and coverage.