JOURNAL OF Ekonometrics EISEWIER Journal of Econometrics 78 (1997) 217-227 Learning about the across-regime correlation in switching regression models Gary Koop, Dale J. Poirier* Deprrrtnwnt @Economics. Llnicersi!v ofToronto, I50 St. George St., Toronto, Out.. M5S 3G7, Canada Received February 1945; final version received March 1996 Abstract Vijverberg (1993) considers the extended Roy/switching regression model of selectivity, focusing attention on the nonidentified correlation between the regime disturbances and describing how the positive definiteness of the covariance matrix implies that it is possible to learn sbout this covariance. In this paper, we show that this learning derives from prior dependence between identified and nonidentified parameters. Even though beliefs about the nonidentified covariance are updated, we show under reasonable a priori independence assumptions that beliefs about the partial correlation between distur- bances, control of the switching index, are not updated. Empirical illustrations show how an exact Bayesian analysis can be carried out using Gibbs sampling and related tech- niques. Key 1rord.s: Bayesian; Gibbs; identification; Roy model zyxwvutsrqponmlkjihgfedcbaZYXW JEL hw’jiiccttiott: Cl 1 1. Bayesian analysis of the Roy model The extended Roy/switching regression model involves two continuous de- pendent variables determined by fixed explanatory variables in two sectors (regimes). Individuals choose between the sectors. References to numerous applications are given in Poirier and Ruud (1981) and in Vijverberg (1993). Omitting observation subscripts, the basic model is I* = zy + U, 1’7 = x*/I* + El, Y; = x2/92 + 82, (1) *Correspondence address: 2746 Gough Street, Unit # 3, San Francisco, CA 94123-4405,USA Both authors acknowledge the generous research support of the Social Science Research Council of Canada. 0304-4076/97/S17.00 ,(:j 1997 Elscvier Science S.A. All rights reserved PI? SO304-4076(96)00009-7 \