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

## Author

Listed:
• 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.

## Suggested Citation

• Li, Mingliang & Tobias, Justin, 2008. "Bayesian Analysis of Treatment Effects in an Ordered Potential Outcomes Model," Staff General Research Papers Archive 12429, Iowa State University, Department of Economics.
• Handle: RePEc:isu:genres:12429
as

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## References listed on IDEAS

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8. Becker, Gary S & Grossman, Michael & Murphy, Kevin M, 1994. "An Empirical Analysis of Cigarette Addiction," American Economic Review, American Economic Association, pages 396-418.
9. Han, Aaron K & Park, Daekeun, 1989. "Testing for Structural Change in Panel Data: Application to a Study of U.S. Foreign Trade in Manufacturing Goods," The Review of Economics and Statistics, MIT Press, pages 135-142.
10. Dufour, Jean-Marie, 1982. "Recursive stability analysis of linear regression relationships: An exploratory methodology," Journal of Econometrics, Elsevier, pages 31-76.
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## Citations

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Cited by:

1. Munkin, Murat K. & Trivedi, Pravin K., 2008. "Bayesian analysis of the ordered probit model with endogenous selection," Journal of Econometrics, Elsevier, pages 334-348.
2. Klaus Moeltner & Richard Woodward, 2009. "Meta-Functional Benefit Transfer for Wetland Valuation: Making the Most of Small Samples," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 42(1), pages 89-108, January.
3. Li, Mingliang & Mumford, Kevin J. & Tobias, Justin L., 2012. "A Bayesian analysis of payday loans and their regulation," Journal of Econometrics, Elsevier, pages 205-216.

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