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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Paper provided by Iowa State University, Department of Economics in its series Staff General Research Papers with number
12429.
Length: Date of creation: 04 Oct 2005 Date of revision: Publication status: Published in Advances in Econometrics, Volume 21: Estimating and Evaluating Treatment Effects in Econometrics, 2008, Vol. 21. Handle: RePEc:isu:genres:12429
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