Li, Mingliang; Tobias, Justin

Advances in Econometrics Vol. 21 (2008)

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.