Bayesian analysis of switching regression models (Q1075000)

A class of switching linear regression models of the form: \[ y_ t=\min (x'\!_{1t}\beta_ 1,x'\!_{2t}\beta_ 2)+u_ t,\quad u_ t\sim N(0,\sigma^ 2), \] is considered, where the change of two or more regimes is represented by the min-operator. Such models are relevant for disequilibrium market models in econometrics. Classical methods of maximum likelihood are compared with the Bayesian methods for deriving the posterior density of the parameters \((\beta,\sigma^ 2)\). A Monte Carlo procedure is proposed to compute the posterior moments and the numerical results confirm that the Bayesian estimator has a smaller mean square error than the maximum likelihood estimator.