Some aspects of prior elicitation problems in disequilibrium models (Q1075001)

A switching regression model of the form \[ y_ t=\delta_ tx'\!_{1t}\beta_ 1+(1-\delta_ t)x'\!_{2t}\beta_ 2+\epsilon_ t;\quad \epsilon_ t\sim N(0,\sigma^ 2), \] \[ \delta_ t=1\quad if\quad x'\!_{1t}\beta_ 1<x'\!_{2t}\beta_ 2,\quad and\quad =0\quad otherwise \] which arises in models of market disequilibrium is analyzed here through the introduction of prior information on the regime partition and on the structural parameters. The prior density is assumed to belong to the traditional inverted gamma normal family: \[ D'(\beta,\sigma^ 2)=D'(\beta | \sigma^ 2)D'(\sigma^ 2),\quad D'(\sigma^ 2)=f_{\gamma}(\sigma^ 2| s_ 0,\nu_ 0),\quad D'(\beta | \sigma^ 2)=b_ N(\beta | \beta_ 0,M_ 0^{- 1}\sigma^ 2) \] and a two-step process of prior elicitation is used. An empirical application is made of the US labor market between 1930 and 1973.