Advanced Macroeconomics II. Monetary Models with Nominal Rigidities. Jordi Galí Universitat Pompeu Fabra April 2018

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1 Advanced Macroeconomics II Monetary Models with Nominal Rigidities Jordi Galí Universitat Pompeu Fabra April 208

2 Motivation Empirical Evidence Macro evidence on the e ects of monetary policy shocks (i) persistent real e ects (ii) sluggish adjustment of aggregate price level (iii) liquidity e ect Micro evidence on patterns of price setting

3 Figure. Estimated Dynamic Response to a Monetary Policy Shock Federal funds rate GDP GDP deflator M2 Source: Christiano, Eichenbaum and Evans (999)

4 Source: Dhyne et al. (JEP, 2006)

5 Source: Álvarez et al. (JEEA, 2006)

6 Models with Nominal Rigidities di erentiated goods and monopolistic competition in goods market sticky prices competitive labor market, closed economy, no capital accumulation Maintained assumptions households optimality conditions c t = E t fc t+ g w t (i t E t f t+ g ) p t = c t + 'n t m t p t = c t i t continuum of rms/di erentiated goods, indexed by i 2 [0; ] technology: Y t (i) = A t N t (i) implied marginal cost: t(i) = w t a t + n t (i) log( )

7 Monopolistic Competition with Flexible Prices Firm s problem subject to demand schedule: Optimality condition: max P t (i) P t (i)y t (i) Y t (i) = C t (Y t (i)) Pt (i) C t P t P t (i) = M t (i) where M ("optimal gross markup") and t(i) Ct(Y 0 t (i)) ("marginal cost"). In logs: p t (i) = + t (i) = + w t (a t n t (i) + log( )) where log M and t (i) log t (i).

8 Equilibrium Goods market Aggregate demand Labor market Price setting Asset market y t (i) = c t (i); i 2 [0; ] =) y t = c t y t = E t fy t+ g (i t E t f t+ g ) n t = (y t a t ) w t = p t + c t + 'n t p t = + w t (a t n t + log( )) b t = 0

9 Equilibrium values: n t = ( ) + ' + a t + log( ) ( ) + ' + + ' y t = c t = ( ) + ' + a ( )(log( ) ) t + ( ) + ' + + ' w t p t = ( ) + ' + a (( ) + ')(log( ) ) t + ( ) + ' + r t i t E t f t+ g = ( + ')( a ) ( ) + ' + a t =) role of market power () =) ine ciencies =) monetary policy neutrality =) role of monetary policy and optimal monetary policy as in the classical model

10 Monopolistic Competition with Constant Prices Assumptions: constant prices: p t = p = 0 (normalization), t = 0; ; 2; ::: non-negative markup: t = p t 0, t = 0; ; 2; ::: Equilibrium y t = c t y t = E t fy t+ g (i t ) n t = (y t a t ) w t = y t + 'n t t = w t (a t n t log( ))

11 Monetary policy (I): Interest rate rule i t = + y y t + v t where Equilibrium: n t = v t = v v t + " v t y t = v t ( v ) + y [( v ) + y ]( ) v t a t =) non-neutrality of monetary policy: two dimensions =) technology shocks lower employment, unless o set by policy response Exercise: derive an interest rate rule that will replicate the exible price equilibrium

12 Monetary policy (II): Exogenous money supply Combining money demand and aggregate demand: X k y t = E t fm t+kg + + k=0 Example: m t = m m t + " m t y t = + ( m ) m t n t = ( )[ + ( m )] m t a t =) non-neutrality of money supply changes (anticipated and unanticipated) =) technology shocks lower employment, unless o set by policy response

13 The Basic New Keynesian Model The New Keynesian Phillips Curve t = E t f t+ g + ey t where ey t y t yt n ("output gap"). Dynamic IS equation ey t = (i t E t f t+ g rt n ) + E t fey t+ g Interest rate rule i t = + t + y by t + v t

14 The New Keynesian Phillips Curve Assumption: probability of price adjustment: ) fraction of rms keeping price unchanged: ) 2 [0; ] : índex of price rigidity Price level evolution Optimal price setting Combining both equations p t = + ( p t = p t + ( )p t ) X () k E t f t+k g k=0 t = E t f t+ g ( t ) (independent across rms) where t p t t (average price markup) and ( )( )

15 Average markup (assumption: = 0) t = p t (w t a t ) Labor market equilibrium w t p t = c t + 'n t n t = y t Goods market equilibrium y t = c t Average price markup and the output gap a t With exible prices: t = ( + ')a t = ( + ')a t ( + ')y t ( + ')y n t ) y n t = + ' + + ' + ' a t

16 Combining both equations: t = ( + ') ey t New Keynesian Phillips curve t = E t f t+ g + ey t where ( + ')

17 Properties (i) "Forward-looking" t = ) past in ation is irrelevant X k E t fey t+k g (ii) No trade-o between stabilization of in ation and output gap. ) "Divine coincidence" (Blanchard-Galí) ) no costs of disin ations. (iii) Two "output gap" concepts: k=0 by t = y t f(t) ey t y t yt n ) complicates empirical evaluation (Galí-Gertler 998).

18 Dynamic IS Equation Intertemporal optimality condition + good market equilibrium y t = E t fy t+ g (i t E t f t+ g ) Combined with ey t y t y n t where Monetary Policy ey t = (i t E t f t+ g r n t ) + E t fey t+ g r n t + E t fyt+g n ( + ') = + + ' E tfa t+ g i t = + t + y by t + v t

19 The Basic New Keynesian Model The New Keynesian Phillips Curve t = E t f t+ g + ey t where ey t y t yt n ("output gap"). Dynamic IS equation ey t = (i t E t f t+ g rt n ) + E t fey t+ g Interest Rate Rule Exogenous variables i t = + t + y by t + v t v t = v v t + " v t a t = a a t + " a t

20 Solving for the Equilibrium Assumptions (for simplicity): (i) fv t g and fa t g white noise ( a = v = 0) (ii) i t = + t + v t (iii) = ) br n t = a t ) by n t = a t Conjecture ("method of undetermined coe cients"): ey t = ya a t + yv v t t = a a t + v v t

21 Solution Discussion ey t = a t v t + + t = a t v t + + by t = ey t + by t n = a t v t + + bn t = by t a t = i t = + a t + v t + a t + + v t m t = ( ( + ) ) + a t v t + p t

22 Simulations of Calibrated Model (Galí 2008/ rev205) Calibration = 0:99, = ; ' = 5, = 9 = =4 = :5, y = 0:5=4 = 3=4 = 4 v = 0:5, a = 0:9 E ects of monetary policy shock E ects of technology shock

23 Dynamic responses to a monetary policy shock: Interest rate rule

24 Dynamic responses to a technology shock: Interest rate rule