# Bayesian Analysis of Treatment Effects in an Ordered Potential Outcomes Model

## Author Info

• Li, Mingliang
• Tobias, Justin

## Abstract

We describe a new Bayesian estimation algorithm for fitting a binary treatment, ordered outcome selection model in a potential outcomes framework. We show how recent advances in simulation methods, namely {\it data augmentation}, the {\it Gibbs sampler} and the {\it Metropolis-Hastings algorithm}, can be used to fit this model efficiently, and also introduce a reparameterization to help accelerate the convergence of our posterior simulator. Several computational strategies which allow for non-Normality are also discussed. Conventional treatment effects'' such as the Average Treatment Effect (ATE), the effect of treatment on the treated (TT) and the Local Average Treatment Effect (LATE) are derived for this specific model, and Bayesian strategies for calculating these treatment effects are introduced. Finally, we review how one can potentially learn (or at least bound) the non-identified cross-regime correlation parameter and use this learning to calculate (or bound) parameters of interest beyond mean treatment effects.

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## Bibliographic Info

Paper provided by Iowa State University, Department of Economics in its series Staff General Research Papers Archive with number 12429.

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 Length: Date of creation: 01 Jan 2008 Date of revision: Publication status: Published in Advances in Econometrics 2008, vol. 21 Handle: RePEc:isu:genres:12429 Contact details of provider: Postal: Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070Phone: +1 515.294.6741Fax: +1 515.294.0221Web page: http://www.econ.iastate.eduEmail: More information through EDIRC

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