RDP 2012-08: Estimation and Solution of Models with Expectations and Structural Changes Equation (21)

x t =   ( r − π ) − ( r t − I E t π t + 1 ) + I E t x t + 1 + ( 1 − ω ) ( 1 − ρ a ) a t MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBaaaleaacaWG0baabeaakiabg2da9iaabccacaGGOaGaamOCaiabgkHiTiabec8aWjaacMcacqGHsislcaGGOaGaamOCamaaBaaaleaacaWG0baabeaakiabgkHiTiaadMeacaWGfbWaaSbaaSqaaiaadshaaeqaaOGaeqiWda3aaSbaaSqaaiaadshacqGHRaWkcaaIXaaabeaakiaacMcacqGHRaWkcaWGjbGaamyramaaBaaaleaacaWG0baabeaakiaadIhadaWgaaWcbaGaamiDaiabgUcaRiaaigdaaeqaaOGaey4kaSIaaiikaiaaigdacqGHsislcqaHjpWDcaGGPaGaaiikaiaaigdacqGHsislcqaHbpGCdaWgaaWcbaGaamyyaaqabaGccaGGPaGaamyyamaaBaaaleaacaWG0baabeaaaaa@6076@

Equation (22)

π t  =  π  + β   ( I E t π t +1 − π ) + ψ x t − e t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiWda3aaS baaSqaaGqaciaa=rhaaeqaaOGaaeiiaiaab2dacaqGGaGaeqiWdaNa aeiiaiaabUcacqaHYoGycaaMc8UaaiikaiaadMeacaWGfbWaaSbaaS qaaiaa=rhaaeqaaOGaeqiWda3aaSbaaSqaaiaa=rhacaqGRaGaaeym aaqabaGccqGHsislcqaHapaCcaGGPaGaey4kaSIaeqiYdKNaamiEam aaBaaaleaacaWG0baabeaakiabgkHiTiaadwgadaWgaaWcbaGaamiD aaqabaaaaa@5411@

Equation (23)

r t =   r + ρ r ( r t − 1 − r ) + ρ π ( π t − π ) + ρ g ( g t − g ) + ρ x x t + ε r , t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCamaaBa aaleaacaWG0baabeaakiabg2da9iaabccacaWGYbGaey4kaSIaeqyW di3aaSbaaSqaaiaadkhaaeqaaOWaaeWaaeaacaWGYbWaaSbaaSqaai aadshacqGHsislcaaIXaaabeaakiabgkHiTiaadkhaaiaawIcacaGL PaaacqGHRaWkcqaHbpGCdaWgaaWcbaGaeqiWdahabeaakmaabmaaba GaeqiWda3aaSbaaSqaaiaadshaaeqaaOGaeyOeI0IaeqiWdahacaGL OaGaayzkaaGaey4kaSIaeqyWdi3aaSbaaSqaaiaadEgaaeqaaOWaae WaaeaacaWGNbWaaSbaaSqaaiaadshaaeqaaOGaeyOeI0Iaam4zaaGa ayjkaiaawMcaaiabgUcaRiabeg8aYnaaBaaaleaacaWG4baabeaaki aadIhadaWgaaWcbaGaamiDaaqabaGccqGHRaWkcqaH1oqzdaWgaaWc baGaamOCaiaacYcacaWG0baabeaaaaa@6611@

Equation (24)

x t =   y ^ t − ω a t MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBaaaleaacaWG0baabeaakiabg2da9iaabccaceWG5bGbaKaadaWgaaWcbaGaamiDaaqabaGccqGHsislcqaHjpWDcaWGHbWaaSbaaSqaaiaadshaaeqaaaaa@40CB@

Equation (25)

g t = g +   y ^ t − y ^ t − 1 + ε z , t MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4zamaaBaaaleaacaWG0baabeaakiabg2da9iaadEgacqGHRaWkcaqGGaGabmyEayaajaWaaSbaaSqaaiaadshaaeqaaOGaeyOeI0IabmyEayaajaWaaSbaaSqaaiaadshaaeqaaOWaaSbaaSqaaiabgkHiTiaaigdaaeqaaOGaey4kaSIaeqyTdu2aaSbaaSqaaiaadQhaaeqaaOWaaSbaaSqaaiaacYcaaeqaaOWaaSbaaSqaaiaadshaaeqaaaaa@4894@