Bayesian Aspects of Treatment Choice

This paper considers an individual making a treatment choice. The individual has access to data on other individuals, with values for a list of characteristics, treatment assignments, and outcomes. The individual knows his value for the list of characteristics. The goal is to use this data set to guide his treatment choice. The role of treatment assignment is developed, and how it affects the specification of prior distributions. The likelihood function is the same for random assignment and for selection on observables, but the prior distributions differ. A question here is whether there is a value in knowing the propensity score. The propensity score does not appear in the likelihood, but it does appear in the prior distribution. So there is a value to knowing the propensity score if the prior is not dominated by the data. In particular, the list of measured characteristics may be of high dimension, and the paper considers prior distributions that may be effective in this case. The paper also considers selection on unobservables and the use of instrumental variables. The prior distribution is not dominated by the data. We make a particular suggestion, in which the undominated part of the prior shows up in the choice of a functional form, which is then combined with a maximum-likelihood approximation to obtain a decision rule. We discuss the role of extrapolation in this decision rule by making a connection with compliers, always-takers, and never-takers in the local average treatment effect developed by Imbens and Angrist (1994). May 2009 Revised October 8, 2009 BAYESIAN ASPECTS OF TREATMENT CHOICE