NOMINAL RIGIDITIES IN A DSGE MODEL: THE CANONICAL NEW KEYNESIAN MODEL OCTOBER 18, 2011 THE AGGREGATE SUPPLY BLOCK. Simplifying the NK Model
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1 NOMINAL RIGIDITIES IN A DSGE MODEL: THE CANONICAL NEW KEYNESIAN MODEL OCTOBER 8, 20 Simplifying he NK Model THE AGGREGATE SUPPLY BLOCK Opimal pricing and aggregae inflaion described by ε * * ε ε ε p i x = pi y + αe Ξ+ π+ x * + ε p i+ ε * 2 * ε + ε p i 2 x = pi ymc + αe Ξ+ π+ x * + p i+ 2 x = x = απ + ( α) p ε * ε Ocober 8, 20 2
2 Simplifying he NK Model THE AGGREGATE SUPPLY BLOCK Opimal pricing and aggregae inflaion described by ε * * ε ε ε p i x = pi y + αe Ξ+ π+ x * + ε p i+ ε * 2 * ε + ε p i 2 x = pi ymc + αe Ξ+ π+ x * + p i+ 2 x = x Noe DROPPED law of moion for price dispersion around a zero-inflaion seady-sae, average dispersion = 0 see Yun (2005 AER) for NK model wih LOM for s All measured in log (percen) deviaions from seady sae zˆ ln( z / z) = απ + ( α) p Ocober 8, 20 3 ε * ε ˆ π = βe ˆ π + κmcˆ + Condense and log-linearize around zero-inflaion (π = ) seady sae See Woodford ex (2003), Walsh ex (2003, Chaper 5) for deails Measures sensiiviy of inflaion o marginal cos ( α)( αβ ) κ = α Simplifying he NK Model THE AGGREGATE SUPPLY BLOCK If no oher marke fricions besides nominal price rigidiy, in which case wrie as ˆ π = βe ˆ π + κyˆ + mcˆ yˆ Reminiscen of old Keynesian Phillips curve Relaion beween curren inflaion and curren measure of aciviy Here couched in language of gaps: inflaion gap and oupu gap Differen from old Phillips curve because of presence of expeced fuure inflaion: expecaions-augmened Phillips Curve Trivial implicaion: moneary policy faces no radeoff beween sabilizing oupu gap and sabilizing inflaion gap Divine Coincidence (Blanchard and Gali 2007 JMCB) Ocober 8,
3 Simplifying he NK Model THE AGGREGATE SUPPLY BLOCK If no oher marke fricions besides nominal price rigidiy, in which case wrie as ˆ π = βe ˆ π + κyˆ + mcˆ Reminiscen of old Keynesian Phillips curve Relaion beween curren inflaion and curren measure of aciviy Here couched in language of gaps: inflaion gap and oupu gap Differen from old Phillips curve because of presence of expeced fuure inflaion: expecaions-augmened Phillips Curve Trivial implicaion: moneary policy faces no radeoff beween sabilizing oupu gap and sabilizing inflaion gap Divine Coincidence (Blanchard and Gali 2007 JMCB) yˆ THE NEW KEYNESIAN PHILLIPS CURVE Inroduce a cos-push shock: ˆ π ˆ ˆ = βeπ+ + κy + u Idea: capures variaion in mc due o facors oher han oupu gap (aka excess demand ) Some sources of u variaion: exogenous markup variaion; sicky nominal wages; pricing complemenariies; fin. fricions Ocober 8, 20 5 Simplifying he NK Model THE AGGREGATE DEMAND BLOCK Compleely ignore ransacions role of money No CIA, MIU, ec a cashless environmen Money plays only a uni-of-accoun role Jusificaion: cash balances a iny fracion of wealh Technical Aside: as long as money eners household preferences addiively-separably, could have money, bu wouldn affec he real equilibrium a all Criical household opimaliy condiion: consumpion-savings uc = β RE uc + π + Derived off a riskless one-period NOMINAL asse Gross nominal ineres rae In closed-economy equilibrium, same as invesmen Ocober 8,
4 Simplifying he NK Model THE AGGREGATE DEMAND BLOCK Compleely ignore ransacions role of money No CIA, MIU, ec a cashless environmen Money plays only a uni-of-accoun role Jusificaion: cash balances a iny fracion of wealh Technical Aside: as long as money eners household preferences addiively-separably, could have money, bu wouldn affec he real equilibrium a all Criical household opimaliy condiion: consumpion-savings uc = β RE uc + π + Derived off a riskless one-period NOMINAL asse Gross nominal ineres rae In closed-economy equilibrium, same as invesmen Simplify by assuming zero invesmen and zero gov spending (simples NK models assume k is consan see Gali and Gerler (2007) for relaxing his) cˆ = R ˆ E ˆ π + Ecˆ Wih CRRA uiliy (risk-aversion σ), log-linearizaion yields + + Ex-ane real ineres rae Ocober 8, 20 7 Simplifying he NK Model THE AGGREGATE DEMAND BLOCK Compleely ignore ransacions role of money No CIA, MIU, ec a cashless environmen Money plays only a uni-of-accoun role Jusificaion: cash balances a iny fracion of wealh Technical Aside: as long as money eners household preferences addiively-separably, could have money, bu wouldn affec he real equilibrium a all Criical household opimaliy condiion: consumpion-savings uc = β RE uc + π + Derived off a riskless one-period NOMINAL asse Wih rivial resource consrain: y = c THE NEW KEYNESIAN IS CURVE aka AGGREGATE DEMAND CURVE Gross nominal ineres rae In closed-economy equilibrium, same as invesmen Simplify by assuming zero invesmen and zero gov spending (simples NK models assume k is consan see Gali and Gerler (2007) for relaxing his) yˆ = R ˆ E ˆ π + Eyˆ + g Wih CRRA uiliy (risk-aversion σ), log-linearizaion yields + + Ex-ane real ineres rae Force in aggregae demand shock (i.e., gov spending) Ocober 8,
5 The Baseline NK Model SOME SIMPLE ANALYSIS New Keynesian Phillips Curve/Aggregae Supply Curve ˆ π = βe ˆ π + κyˆ + u + AS slopes upwards ˆ π ˆ / y > 0 Higher expeced fuure inflaion shifs AS ouwards Inerpreaion: he expecaions of fuure inflaion ha policy-makers induce have an effec on he period- equilibrium Expecaions missing in old Phillips Curve/AS-AD frameworks Curren inflaion a funcion of all fuure oupu gaps and cos-push shocks (recursively subsiue for π ) Ocober 8, 20 9 The Baseline NK Model SOME SIMPLE ANALYSIS New Keynesian Phillips Curve/Aggregae Supply Curve ˆ π = βe ˆ π + κyˆ + u + AS slopes upwards ˆ π ˆ / y > 0 Higher expeced fuure inflaion shifs AS ouwards Inerpreaion: he expecaions of fuure inflaion ha policy-makers induce have an effec on he period- equilibrium Expecaions missing in old Phillips Curve/AS-AD frameworks Curren inflaion a funcion of all fuure oupu gaps and cos-push shocks (recursively subsiue for π ) Can even be < 0!!! Reference empirical value(s) of κ: anywhere from 0.05 (Sbordone 2002 JME) o 0.3 (Robers 995 JMCB) Sensiive o wheher mc y Sensiive o precise empirical measure of mc The oulier Uni labor cos (i.e., w/mpn) he correc heoreical measure bu wha does uni labor cos in he daa mean?... Ocober 8,
6 The Baseline NK Model SOME SIMPLE ANALYSIS New Keynesian IS Curve/Aggregae Demand Curve yˆ = R ˆ E ˆ π + Eyˆ + g + + AD slopes downwards wih respec o ex-ane real ineres rae Higher expeced fuure oupu shifs AD ouwards Consumpion-smoohing foundaion Ocober 8, 20 The Baseline NK Model SOME SIMPLE ANALYSIS New Keynesian IS Curve/Aggregae Demand Curve AD slopes downwards wih respec o ex-ane real ineres rae Higher expeced fuure oupu shifs AD ouwards Consumpion-smoohing foundaion Curren oupu (gap) a funcion of all fuure real ineres raes, which depend on expeced policy and expeced inflaion (recursively subsiue for y ) Reference value of σ: (borrowed from RBC models) Wha deermines policy? yˆ = R ˆ E ˆ π + Eyˆ + g + + Ocober 8,
7 The Baseline NK Model MONETARY POLICY To close he model, need o specify how policy is se Taylor Rule (or varians of) he mos common Rˆ = δ ˆ π + δ yˆ π y Firs described by Taylor (993) as boh a posiive and normaive rule Wih appropriae coefficiens, describes reasonably well he behavior of U.S. (and oher counries ) moneary policy Taylor s coefficiens: δ π =.5, δ y = 0.5 Ocober 8, 20 3 The Baseline NK Model MONETARY POLICY To close he model, need o specify how policy is se Taylor Rule (or varians of) he mos common Rˆ = δ ˆ π + δ yˆ π y Firs described by Taylor (993) as boh a posiive and normaive rule Wih appropriae coefficiens, describes reasonably well he behavior of U.S. (and oher counries ) moneary policy Taylor s coefficiens: δ π =.5, δ y = 0.5 The subjec of MUCH heoreical and empirical ineres See Davig and Leeper (2006 AER) for an overview Taylor Principle: δ π > required for good policy Basic idea: δ π > ensures real ineres rae rises more han one-for-one wih a rise in inflaion he dampening effec on AD lowers inflaion Empirical evidence: δ π < pre-volcker, δ π > Volcker/Greenspan Ocober 8,
8 The Baseline NK Model MONETARY POLICY Why an ineres rae rule and no a money-supply rule? Hisorical/Pracical Reasons Experience wih monearism (in U.S. and U.K.) no very successful Fed s original mandae was o smooh ou he seasonaliy of ineres raes and hence (explicily or implicily...) likely operaed in erms of ineres raes Hard o communicae: We are going o increase he base money supply, M0, by 0.72 percen his week Theoreical Reasons Money demand shifs no well undersood Are money-search-based models helpful in his regard? Ineres raes govern basic decision margins Ineremporal margin (Cash-credi margin in a non-cashless model) Remarks by Bernanke on Taylor s conribuions o moneary heory and policy (Ocober 2, 2007): hp:// Ocober 8, 20 5 The Baseline NK Model THE THREE-EQUATION MODEL The basic framework Phillips Curve/Aggregae Supply ˆ π = βe ˆ π + κyˆ + u + IS Curve/Aggregae Demand yˆ = R ˆ E ˆ π + Eyˆ + g + + Moneary Policy (ineres rae) Rule Rˆ = δ ˆ π + δ yˆ π y (A couple of ) criical quesions How o define he arge variables (underneah he haed variables )? How o allow more flexibiliy in he moneary policy rule? A consan avalanche of analysis using his basic framework See Woodford ex (2003) for a sar on his lieraure Ocober 8,
9 NK Models of he Fuure? ONGOING/FUTURE RESEARCH Sae-dependen pricing Endogenize when firms re-se nominal price: Dosey, King, Wolman (999 QJE), Dosey and King (2005 JME), Golosov and Lucas (2007 JPE) Coordinaion fricions in key markes Labor marke fricions: already many papers: Krause and Lubik (2007 JME), Blanchard and Gali (200 AEJ:Macro), Ravenna and Walsh (200 AEJ:Macro), many ohers Capial marke fricions: financial acceleraor of Bernanke, Gerler, and Gilchris (999) Goods marke fricions: wheher o moivae money primiively (money search) or simply an ariculaion of he ime goods markes rades ake Heerogeneiy Redisribuional aspecs of (long-run and shor-run) moneary policy? Behavioral economics/norms Akerlof (2007 AER) Financial fricions Ocober 8,
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