RDP 9511: Superannuation and Saving Equation (10)

Δ ⌈ S n ⌉ ⌊ y ⌋ t =ϕ+ Σ b=0 k β b Δ ⌈ S s ⌉ ⌊ y ⌋ t−b + Σ c=1 k β c Δ ⌈ S n ⌉ ⌊ y ⌋ t−c + Σ d=0 k β d Δ ⌈ y ^ L ⌉ ⌊ y ⌋ t−d + Σ e=0 k β e Δ ⌈ A ⌉ ⌊ y ⌋ t−e + Σ f=1 k β f r t−f + Σ g=1 k β g Δ D t−g + Σ h=1 k β h Δ Y ˜ t−h + Σ i=1 k β i Δ Π t−i + Σ j=1 k β j Δ U t−j }short run + α 1 ⌈ A ⌉ ⌊ y ⌋ t−1 + α 2 ⌈ y ^ L ⌉ ⌊ y ⌋ t−1 + α 4 D t−1 + α 6 Π t−1 + α 7 U t−1 +( α 8 −1 ) ⌈ S s ⌉ ⌊ y ⌋ t−1 +γ ⌈ S n ⌉ ⌊ y ⌋ t−1 + ε t }Long run MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaadaGaca abaeqabaGaeuiLdq0aaSaaaeaadaWbdaqaaiaadofadaahaaWcbeqa aiaad6gaaaaakiaaw6o+caGL5JpaaeaadaGbdaqaaiaadMhaaiaawc p+caGL7JpaaaWaaSbaaSqaaiaadshaaeqaaOGaeyypa0Jaeqy1dyMa ey4kaSYaaabCaeaacqaHYoGydaWgaaWcbaGaamOyaaqabaGccqqHuo araSqaaiaadkgacqGH9aqpcaaIWaaabaGaam4AaaqdcqGHris5aOWa aSaaaeaadaWbdaqaaiaadofadaahaaWcbeqaaiaadohaaaaakiaaw6 o+caGL5JpaaeaadaGbdaqaaiaadMhaaiaawcp+caGL7JpaaaWaaSba aSqaaiaadshacqGHsislcaWGIbaabeaakiabgUcaRmaaqahabaGaeq OSdi2aaSbaaSqaaiaadogaaeqaaOGaeuiLdqealeaacaWGJbGaeyyp a0JaaGymaaqaaiaadUgaa0GaeyyeIuoakmaalaaabaWaaCWaaeaaca WGtbWaaWbaaSqabeaacaWGUbaaaaGccaGLUJVaayz+4daabaWaayWa aeaacaWG5baacaGLWJVaay5+4daaamaaBaaaleaacaWG0bGaeyOeI0 Iaam4yaaqabaGccqGHRaWkdaaeWbqaaiabek7aInaaBaaaleaacaWG Kbaabeaakiabfs5aebWcbaGaamizaiabg2da9iaaicdaaeaacaWGRb aaniabggHiLdGcdaWcaaqaamaahmaabaGabmyEayaajaWaaSbaaSqa aiaadYeaaeqaaaGccaGLUJVaayz+4daabaWaayWaaeaacaWG5baaca GLWJVaay5+4daaamaaBaaaleaacaWG0bGaeyOeI0IaamizaaqabaGc cqGHRaWkdaaeWbqaaiabek7aInaaBaaaleaacaWGLbaabeaakiabfs 5aebWcbaGaamyzaiabg2da9iaaicdaaeaacaWGRbaaniabggHiLdGc daWcaaqaamaahmaabaGaamyqaaGaayP74laawMp+aaqaamaagmaaba GaamyEaaGaayj84laawUp+aaaadaWgaaWcbaGaamiDaiabgkHiTiaa dwgaaeqaaaGcbaGaey4kaSYaaabCaeaacqaHYoGydaWgaaWcbaGaam OzaaqabaGccaWGYbWaaSbaaSqaaiaadshacqGHsislcaWGMbaabeaa kiabgUcaRmaaqahabaGaeqOSdi2aaSbaaSqaaiaadEgaaeqaaOGaeu iLdqKaamiramaaBaaaleaacaWG0bGaeyOeI0Iaam4zaaqabaaabaGa am4zaiabg2da9iaaigdaaeaacaWGRbaaniabggHiLdaaleaacaWGMb Gaeyypa0JaaGymaaqaaiaadUgaa0GaeyyeIuoakiabgUcaRmaaqaha baGaeqOSdi2aaSbaaSqaaiaadIgaaeqaaOGaeuiLdqKabmywayaaia WaaSbaaSqaaiaadshacqGHsislcaWGObaabeaakiabgUcaRmaaqaha baGaeqOSdi2aaSbaaSqaaiaadMgaaeqaaOGaeuiLdqKaeuiOda1aaS baaSqaaiaadshacqGHsislcaWGPbaabeaaaeaacaWGPbGaeyypa0Ja aGymaaqaaiaadUgaa0GaeyyeIuoaaSqaaiaadIgacqGH9aqpcaaIXa aabaGaam4AaaqdcqGHris5aOGaey4kaSYaaabCaeaacqaHYoGydaWg aaWcbaGaamOAaaqabaGccqqHuoaraSqaaiaadQgacqGH9aqpcaaIXa aabaGaam4AaaqdcqGHris5aOGaamyvamaaBaaaleaacaWG0bGaeyOe I0IaamOAaaqabaaaaOGaayzFaaGaam4CaiaadIgacaWGVbGaamOCai aadshacaaMc8UaamOCaiaadwhacaWGUbaabaWaaiGaaqaabeqaaiab gUcaRiabeg7aHnaaBaaaleaacaaIXaaabeaakmaalaaabaWaaCWaae aacaWGbbaacaGLUJVaayz+4daabaWaayWaaeaacaWG5baacaGLWJVa ay5+4daaamaaBaaaleaacaWG0bGaeyOeI0IaaGymaaqabaGccqGHRa WkcqaHXoqydaWgaaWcbaGaaGOmaaqabaGcdaWcaaqaamaahmaabaGa bmyEayaajaWaaSbaaSqaaiaadYeaaeqaaaGccaGLUJVaayz+4daaba WaayWaaeaacaWG5baacaGLWJVaay5+4daaamaaBaaaleaacaWG0bGa eyOeI0IaaGymaaqabaGccqGHRaWkcqaHXoqydaWgaaWcbaGaaGinaa qabaGccaWGebWaaSbaaSqaaiaadshacqGHsislcaaIXaaabeaakiab gUcaRiabeg7aHnaaBaaaleaacaaI2aaabeaakiabfc6aqnaaBaaale aacaWG0bGaeyOeI0IaaGymaaqabaGccqGHRaWkcqaHXoqydaWgaaWc baGaaG4naaqabaGccaWGvbWaaSbaaSqaaiaadshacqGHsislcaaIXa aabeaaaOqaaiabgUcaRmaabmaabaGaeqySde2aaSbaaSqaaiaaiIda aeqaaOGaeyOeI0IaaGymaaGaayjkaiaawMcaamaalaaabaWaaCWaae aacaWGtbWaaWbaaSqabeaacaWGZbaaaaGccaGLUJVaayz+4daabaWa ayWaaeaacaWG5baacaGLWJVaay5+4daaamaaBaaaleaacaWG0bGaey OeI0IaaGymaaqabaGccqGHRaWkcqaHZoWzdaWcaaqaamaahmaabaGa am4uamaaCaaaleqabaGaamOBaaaaaOGaayP74laawMp+aaqaamaagm aabaGaamyEaaGaayj84laawUp+aaaadaWgaaWcbaGaamiDaiabgkHi TiaaigdaaeqaaOGaey4kaSIaeqyTdu2aaSbaaSqaaiaadshaaeqaaa aakiaaw2haaiaadYeacaWGVbGaamOBaiaadEgacaaMc8UaamOCaiaa dwhacaWGUbaaaaa@7A25@