RDP 2011-01: Estimating Inflation Expectations with a Limited Number of Inflation-indexed Bonds Equation

E t ( exp ( ∫ s s + τ π u d u ) ) = E t ( E s ( exp ( − ∫ s s + τ − π u d u ) ) ) = E t ( exp ( − α ¯ τ − β ¯ ′ τ x s ) ) = exp ( − α ¯ τ − β ¯ ′ τ ( e − K ( s − t ) x t + ( I − e − K ( s − t ) ) μ ) + 1 2 β ¯ ′ τ Ω s − t β ¯ τ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaatuuDJX wAK1uy0HMmaeHbfv3ySLgzG0uy0HgiuD3BaGqbaiab=ri8fnaaBaaa leaacaWG0baabeaakmaabmaabaGaciyzaiaacIhacaGGWbWaaeWaae aadaWdXaqaaiabec8aWnaaBaaaleaacaWG1baabeaaieaakiaa+rga caWG1baaleaacaWGZbaabaGaam4CaiabgUcaRiabes8a0bqdcqGHRi I8aaGccaGLOaGaayzkaaaacaGLOaGaayzkaaGaeyypa0Jae8hHWx0a aSbaaSqaaiaadshaaeqaaOWaaeWaaeaacqWFecFrdaWgaaWcbaGaam 4CaaqabaGcdaqadaqaaiGacwgacaGG4bGaaiiCamaabmaabaGaeyOe I0Yaa8qmaeaacqGHsislcqaHapaCdaWgaaWcbaGaamyDaaqabaGcca GFKbGaamyDaaWcbaGaam4CaaqaaiaadohacqGHRaWkcqaHepaDa0Ga ey4kIipaaOGaayjkaiaawMcaaaGaayjkaiaawMcaaaGaayjkaiaawM caaaqaaiabg2da9iab=ri8fnaaBaaaleaacaWG0baabeaakmaabmaa baGaciyzaiaacIhacaGGWbWaaeWaaeaacqGHsislcuaHXoqygaqeam aaBaaaleaacqaHepaDaeqaaOGaeyOeI0IafqOSdiMbaeHbauaadaWg aaWcbaGaeqiXdqhabeaakiaadIhadaWgaaWcbaGaam4Caaqabaaaki aawIcacaGLPaaaaiaawIcacaGLPaaaaeaacqGH9aqpciGGLbGaaiiE aiaacchadaqadaqaaiabgkHiTiqbeg7aHzaaraWaaSbaaSqaaiabes 8a0bqabaGccqGHsislcuaHYoGygaqegaqbamaaBaaaleaacqaHepaD aeqaaOWaaeWaaeaacaWGLbWaaWbaaSqabeaacqGHsislcaWGlbWaae WaaeaacaWGZbGaeyOeI0IaamiDaaGaayjkaiaawMcaaaaakiaabIha daWgaaWcbaGaamiDaaqabaGccqGHRaWkdaqadaqaaiaadMeacqGHsi slcaWGLbWaaWbaaSqabeaacqGHsislcaWGlbWaaeWaaeaacaWGZbGa eyOeI0IaamiDaaGaayjkaiaawMcaaaaaaOGaayjkaiaawMcaaGGadi ab9X7aTbGaayjkaiaawMcaaiabgUcaRmaalaaabaGaaGymaaqaaiaa ikdaaaGafqOSdiMbaeHbauaadaWgaaWcbaGaeqiXdqhabeaakiabfM 6axnaaBaaaleaacaWGZbGaeyOeI0IaamiDaaqabaGccuaHYoGygaqe amaaBaaaleaacqaHepaDaeqaaaGccaGLOaGaayzkaaaaaaa@BC85@