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# 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 with number 12429.

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Date of creation: 01 Jan 2008
Date of revision:
Publication status: Published in Advances in Econometrics 2008, vol. 21
Handle: RePEc:isu:genres:12429

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Postal: Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070
Phone: +1 515.294.6741
Fax: +1 515.294.0221
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Web page: http://www.econ.iastate.edu
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## Citations

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Cited by:
1. Klaus Moeltner & James J. Murphy & John K. Stranlund & Maria Alejandra Velez, 2007. "Processing Data from Social Dilemma Experiments: A Bayesian Comparison of Parametric Estimators," Working Papers 07-013, University of Nevada, Reno, Department of Economics & University of Nevada, Reno , Department of Resource Economics.
2. Li, Mingliang & Mumford, Kevin J. & Tobias, Justin L., 2012. "A Bayesian analysis of payday loans and their regulation," Journal of Econometrics, Elsevier, vol. 171(2), pages 205-216.
3. Munkin, Murat K. & Trivedi, Pravin K., 2008. "Bayesian analysis of the ordered probit model with endogenous selection," Journal of Econometrics, Elsevier, vol. 143(2), pages 334-348, April.

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