8. Barro Gordon Model

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1 8. Barro Gordo Modl, -.. mi s t L mi goals of motary poliy:. Miimiz dviatios of iflatio from its optimal rat π. Try to ahiv ffiit mploymt, > Stati Phillips urv: = + π π, Loss futio L = π π + Rspos of th tral ak o giv xptatios Barro Gordo Modl Ratioal xptatios: π = π disrtioary solutio disrtioary solutio is iffiit! Iflatio ias

2 Barro Gordo Modl Rspos of tral ak to iflatio xptatios ππ without ommitmt π Phillips urv for π =π π for π =π π Iso-loss urvs 3 Barro Gordo Modl quilirium with ratioal xptatios: Disrtioary solutio = quilirium Phillips urv for π = π quilirium π quilirium π Iso-loss urv 4

3 Barro Gordo Modl Commitmt solutio: tral ak ommits rdily to optimal iflatio π. Phillips urv for π = π ommitmt solutio π Iso-loss urv 5 Barro Gordo Modl How to avoid th iflatio ias?. Rputatio: Barro-Gordo 983. Dlgatio: Rogoff Ctral ak otrat 4. Ruls istad of disrtioary disios Prolm: trad-off tw lowrig iflatio ias ad optimal rspos to supply shoks. Modr Viw of CBs: W do ot try to ahiv ffiit mploymt, just to los th output gap. i.. = => π = π i disrtioary quilirium 6

4 Barro Gordo Modl For avoidig th iflatio ias ad stailizig th oomy i a ffiit way,. th CB must aim at losig th output gap, istad of tryig to ahiv ffiiy, =,. th CB must idpdt from short-ru politial goals of th govrmt. Othrwis, thr is always a itiv to iras mploymt i th short ru, >. With L = π π + ad π = π. w gt L = π π + = Varπ + Var. 7 Stailizig Dmad ad Supply Shoks Stohasti oomy: - Liquidity shoks a asord y motary poliy. - Shoks of ommodity dmad: if CB stailizs iflatio, output ad mploymt ar stailizd as wll. - Supply shoks afft produtivity. Thy ar oud to hav ral ffts. 8

5 8. Stailizig supply shoks What is th optimal rspos of motary poliy to shoks i produtivity? produtio futio y = a + θ Produtivity shok θ : θ = 0 Varθ = σ Laor dmad = + π w + θ a Wags w = π Phillips urv All varials may itrprtd as growth rats. 9 Stailizig supply shoks Phillips urv i fa of supply shoks π = + π π + θ Phillips urv für θ = 0 π / 0

6 Stailizig supply shoks stailizig iflatio π = + π π + θ Phillips urv for θ = 0 / Var = σ mploymt flutuatios Stailizig supply shoks Stailizig mploymt π = + π π + θ Phillips urv for θ = 0 flutuatios of iflatio / Var π = σ

7 Stailizig supply shoks Solvig th trad-off tw stailizig iflatio ad mploymt. Mi π π + = Mi π π + π π + θ Si =, th iflatio ias is zro, so that π = π. => π π + π π + θ = 0 => + π π = θ 3 Mi π π + Stailizig supply shoks π = + π π + θ Phillips urv for θ = 0 flutuatios of iflatio / L mploymt flutuatios 4

8 8. Ruls vrsus Disrtio What ar optimal ruls i th fa of dmad ad supply shoks? produtio futio y = a + θ Produtivity shok θ : θ = 0 Varθ = Laor dmad Wags = + π w + θ, w = π Dmad sid quatity thory μ + η = π + y a Phillips urv Dmad shok η : η = 0 Varη = Loss futio L = π π + 5 Ruls vrsus Disrtio Rul : ostat rat of iflatio, π = π => π = π => = + θ 6

9 7 Ruls vrsus Disrtio Rul : ostat moy growth rat, μ = μ = π + a y a a a a a a a a 8 Ruls vrsus Disrtio Rul : ostat moy growth rat Iflatio a xptd wlfar loss

10 9 Ruls vrsus Disrtio Comparig wlfar loss for rul vrsus rul loss for ostat μ > loss for ostat π Costat moy supply growth lads to highr xptd osts tha ostat iflatio, if i th wight o pristaility is suffiitly larg, or ii th varia of dmad shoks is larg ompard to th varia of supply shoks.

macro Road map to this lecture Objectives Aggregate Supply and the Phillips Curve Three models of aggregate supply W = ω P The sticky-wage model

macro Road map to this lecture Objectives Aggregate Supply and the Phillips Curve Three models of aggregate supply W = ω P The sticky-wage model Road map to this lctur macro Aggrgat Supply ad th Phillips Curv W rlax th assumptio that th aggrgat supply curv is vrtical A vrsio of th aggrgat supply i trms of iflatio (rathr tha th pric lvl is calld