GSDE-新凯恩斯模型-ch3

Lectures on Monetary Policy,In‡ation and the Business Cycle

The Basic New Keynesian Model

by

Jordi Galí

February2007

Motivation and Outline

Evidence on Money,Output,and Prices:

The Long Run

Short Run E¤ects of Monetary Policy Shocks

(i)persistent e¤ects on real variables

(ii)slow adjustment of aggregate price level

(iii)liquidity e¤ect

Micro Evidence on Price-setting Behavior:signi…cant price and wage rigidities

Failure of Classical Monetary Models

A Baseline Model with Nominal Rigidities

monopolistic competition

sticky prices(staggered price setting)

competitive labor markets,closed economy,no capital accumulation

Households

Representative household solves

1X t=0 t U(C t;N t)

max E0

where

C t Z10C t(i)1 1 di 1 subject to Z10P t(i)C t(i)di+Q t B t B t 1+W t N t T t

for t=0;1;2;:::plus solvency constraint.

Optimality conditions

1.Optimal allocation of expenditures

C t(i)= P t(i)P t C t implying Z10P t(i)C t(i)di=P t C t where

P t Z10P t(i)1 di 11 2.Other optimality conditions

U n;t U

c;t =

W t

P t

Q t= E t U c;t+1U c;t P t P t+1

Speci…cation of utility:

U(C t;N t)=C1

t

1

N1+'

t

1+'

implied log-linear optimality conditions(aggregate variables)

w t p t= c t+'n t

c t=E t f c t+1g 1 (i t E t f t+1g )

where i t log Q t is the nominal interest rate and log is the discount rate.

Ad-hoc money demand

m t p t=y t i t

Firms

Continuum of…rms,indexed by i2[0;1]

Each…rm produces a di¤erentiated good

Identical technology

Y t(i)=A t N t(i)1

Probability of being able to reset price in any given period:1 , independent across…rms(Calvo(1983)).

2[0;1]:index of price stickiness

Implied average price duration11

Aggregate Price Dynamics

P t= (P t 1)1 +(1 )(P t)1 11

Dividing by P t 1:

= +(1 ) P t P t 1 1

1

t

Log-linearization around zero in‡ation steady state

t=(1 )(p t p t 1)(1) or,equivalently

p t= p t 1+(1 )p t

Optimal Price Setting

1X k=0 k E t Q t;t+k P t Y t+k j t t+k(Y t+k j t) max

P t

subject to

Y t+k j t=(P t=P t+k) C t+k

for k=0;1;2;:::where

Q t;t+k k C t+k C t P t P t+k

Optimality condition:

1X k=0 k E t Q t;t+k Y t+k j t P t M t+k j t =0 where t+k j t 0t+k(Y t+k j t)and M 1

Equivalently,

1X k=0 k E t Q t;t+k Y t+k j t P t P t 1 M MC t+k j t t 1;t+k =0 where MC t+k j t t+k j t=P t+k and t 1;t+k P t+k=P t 1

Perfect Foresight,Zero In‡ation Steady State:

P t P t 1=1; t 1;t+k=1;Y t+k j t=Y;Q t;t+k= k;MC=

1

M