RBA Annual Conference – 2015 Equation (3)

E i t * = β 1 H E i , t − 1 + γ x i , t − 1 + φ z i t + ε i t , ε i t ~ N ( 0 , σ 2 ) , E i t = { 1 ( Sole   trader ) if   μ 0 = − ∞ < E i t * ≤ μ 1 2 ( 2 − 19 ) if   μ 1 < E i t * ≤ μ 2 3 ( 20 + ) if μ 2 < E i t * ≤ μ 3 = ∞ , Pr ( E i t = j ) = Pr ( μ j − 1 < E i t * ≤ μ j ) . MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGfb Waa0baaSqaaiaadMgacaWG0baabaGaaiOkaaaakiabg2da9iabek7a InaaBaaaleaacaaIXaaabeaakiaadIeacaWGfbWaaSbaaSqaaiaadM gacaGGSaGaamiDaiabgkHiTiaaigdaaeqaaOGaey4kaSIaeq4SdCgc bmGaa8hEamaaBaaaleaacaWGPbGaaiilaiaadshacqGHsislcaaIXa aabeaakiabgUcaRiabeA8aQjaa=PhadaWgaaWcbaGaamyAaiaadsha aeqaaOGaey4kaSIaeqyTdu2aaSbaaSqaaiaadMgacaWG0baabeaaki aacYcacqaH1oqzdaWgaaWcbaGaamyAaiaadshaaeqaaOGaaiOFaiaa d6eadaqadaqaaiaaicdacaGGSaGaeq4Wdm3aaWbaaSqabeaacaaIYa aaaaGccaGLOaGaayzkaaGaaiilaaqaaiaadweadaWgaaWcbaGaamyA aiaadshaaeqaaOGaeyypa0ZaaiqaaeaafaqaaeWaeaaaaeaacaaIXa aabaWaaeWaaeaacaqGtbGaae4BaiaabYgacaqGLbGaaGPaVlaabsha caqGYbGaaeyyaiaabsgacaqGLbGaaeOCaaGaayjkaiaawMcaaaqaai aabMgacaqGMbaabaGaaGPaVlabeY7aTnaaBaaaleaacaaIWaaabeaa kiabg2da9iabgkHiTiabg6HiLkabgYda8iaadweadaqhaaWcbaGaam yAaiaadshaaeaacaGGQaaaaKaaGjabgsMiJkabeY7aTPWaaSbaaSqa aiaaigdaaeqaaaGcbaGaaGOmaaqaamaabmaabaGaaGOmaiabgkHiTi aaigdacaaI5aaacaGLOaGaayzkaaaabaGaaeyAaiaabAgaaeaacaaM c8UaeqiVd02aaSbaaSqaaiaaigdaaeqaaOGaeyipaWJaamyramaaDa aaleaacaWGPbGaamiDaaqaaiaacQcaaaqcaaMaeyizImQaeqiVd0Mc daWgaaWcbaGaaGOmaaqabaaakeaacaaIZaaabaWaaeWaaeaacaaIYa GaaGimaiabgUcaRaGaayjkaiaawMcaaaqaaiaabMgacaqGMbaabaGa eqiVd02aaSbaaSqaaiaaikdaaeqaaOGaeyipaWJaamyramaaDaaale aacaWGPbGaamiDaaqaaiaacQcaaaqcaaMaeyizImQaeqiVd0McdaWg aaWcbaGaaG4maaqabaGccqGH9aqpcqGHEisPaaaacaGL7baacaGGSa aabaGaciiuaiaackhadaqadaqaaiaadweadaWgaaWcbaGaamyAaiaa dshaaeqaaOGaeyypa0JaamOAaaGaayjkaiaawMcaaiabg2da9iGacc facaGGYbWaaeWaaeaacqaH8oqBdaWgaaWcbaGaamOAaiabgkHiTiaa igdaaeqaaOGaeyipaWJaamyramaaDaaaleaacaWGPbGaamiDaaqaai aacQcaaaGccqGHKjYOcqaH8oqBdaWgaaWcbaGaamOAaaqabaaakiaa wIcacaGLPaaacaGGUaaaaaa@CC87@