Learning about the across-regime correlation in switching regression models

Private Insurance, Selection, and Health Care Use

“…This model might be restrictive because the effects of all exogenous variables may not be the same for treated and untreated individuals and the treatment may create interaction effects with observed or unobserved personal characteristics. We develop a Markov chain Monte Carlo (MCMC) algorithm to estimate the parameters of this model, building on the recent research of Koop and Poirier (1997), Li (1998), McCulloch, Polson, andRossi (2000), and Geweke, Gowrisankaran, and Town (2003). The proposed algorithm is more efficient (with respect to computational time and convergence) than the existing MCMC algorithms dealing with Poisson-lognormal mixtures in studies by Chib, Greenberg, and Winkelmann (1998), Chib and Winkelmann (2001), and Munkin and Trivedi (2003).…”

“…In such cases, the identification of some parameters is often possible only under some strong assumptions. To address this issue, Vijverberg (1993), Koop and Poirier (1997), Chib and Hamilton (2000), Chib (2003), and Poirier and Tobias (2003) used different strategies. Various measures of treatment effects for the Roy model have been proposed; see, for example, Heckman, Tobias, and Vytlacil (2001), , and Poirier and Tobias (2003).…”

Bayesian inference in a correlated random coefficients model: Modeling causal effect heterogeneity with an application to heterogeneous returns to schooling

“…To be sure, our study is certainly not the first such effort, and, indeed, a sizeable Bayesian literature has evolved for the estimation of treatment-response models with observational data. 2 Early efforts in this regard primarily focused on the Markov chain Monte Carlo (MCMC) implementation (e.g., Poirier, 1997 andChib andHamilton, 2000) and included some discussion of recovering individual-level treatment impacts within a potential outcomes framework. 3 More recent work has focused on problems associated with weak instruments generally, has discussed priors that yield posteriors similar to sampling distributions for the two-stage least squares (2SLS) and limited information maximum likelihood (LIML) estimators (e.g., Kleibergen and Zivot, 2003), has introduced a non-parametric modeling of outcomes via a Dirichlet process prior (Conley et al, 2008), and has obtained new results associated with the seminal Angrist and Krueger (1991) study (e.g., Hoogerheide et al, 2007).…”

“…The novelty of our approach is that we directly model the process generating the individualspecific causal effect and thus can calculate any statistic of interest (such as return percentiles or the probability of a positive treatment impact) associated with the causal effect heterogeneity distribution. Of course, our ability to do this stems from particular parametric assumptions made regarding 2 Important examples of this work include Koop and Poirier (1997), Li (1998), Chib andHamilton (2000, 2002), Poirier and Tobias (2003), and Chib (2007). Li et al (2003), Munkin and Trivedi (2003), and Deb et al (2006) provide applications of these methods.…”

“…Chib and Hamilton (2002), for example, point out the possibility of learning about individual-level treatment effects, while Koop and Poirier (1997) and Poirier and Tobias (2003) discuss the potential for learning about outcome gain distributions and the cross-regime correlation parameter. In recent work, Chib (2007) argues in favor of avoiding explicit modeling of the counterfactual, owing to concerns associated with modeling the nonidentifiable cross-regime correlation parameter.…”