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Imperfect Common Knowledge, Price Stickiness, and Inflation Inertia
Porntawee Nantamanasikarn
University of Hawai’i at ManoaNovember 27, 2006
2
Introduction
The standard New Keynesian (NK) model does a poor job explaining observed inflation inertia (e.g. Mankiw, 2001)
Inflation response jumps immediately at the time of monetary shocks, because price, but not inflation, is sticky, and the representative agent is purely forward looking
3
Other Studies’ Proposed Solutions
Backward looking behavior Fuhrer and Moore (1995), Gali and Gertler (1999)
Limited or bounded rationality Roberts (1997), Ball (2000)
Automatic indexation to past inflation Yun (1996), Christiano et al. (2005)
4
Other Studies’ Proposed Solutions
Information stickiness Mankiw and Reis (2002, 2003)
Implementation lags Cochrane (1998), Bernanke and Woodford (1997)
Habit persistence Fuhrer (2000), Smets and Wouters (2003)
5
The Noisy Information (NI) Model
Woodford (2003) assumes monopolistic competitive market in Lucas’s (1973) island model to generate inflation inertia
Firms have heterogeneous subjective perceptions of current conditions (imperfect common knowledge)
Inflation responds sluggishly to monetary shock because higher-order expectations are slow to adjust
6
The NI Model’s Problems
Prices are fully flexible Implication: credible future policy change does not
affect current decisions
Can generate inflation persistence only if the monetary shock is persistent Implication: inflation inertia is the result of external
drivers, not internal propagation mechanism
7
The NI Model’s Problems
Firms have (noisy) information only on exogenous nominal spending, not on the endogenous aggregate price level
Agents’ perceptions are not affected by others’ current decisions
8
Research Objective
Develop models that credible future policy can affect current decisions can generate inflation inertia, even if monetary
shock is not very persistent others’ decisions simultaneously affect perceptions
How: assume imperfect CK and price stickiness
Challenge: the infinite regress problem
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The Infinite Regress Problem
Dating back to Pigou (1929), Muth (1960)
The recursive representation of the system requires infinite number of state variables
When agents must forecast the forecasts of others (which is unobserved), it is necessary for them to keep track of infinite history of observable variables
10
The Infinite Regress Problem
Some proposed “solutions”: Townsend (1983), Lucas (1975)
The NI model avoids this problem because there is no feedback from pricing decisions to the source of signals
I propose two alternative models for how expectations are formed: The Rational Believer (RB) Model The Limited Depth of Reasoning (LDR) Model
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Summary of Model Comparisons
Lucas (1973)
NK NI RB/
LDR
Perfectly competitive market? yes no no no
Flexible price? yes no yes no
Perfect (common) information? no yes no no
Infinite regress problem? no no no yes
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Adding Price Stickiness
Firms have a constant probability of (1-to adjust price in each period (Calvo 1983)
If able to adjust price, a forward looking firm will set the new price, according to
The aggregate price is
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Firms’ Signal Equation
Each firm receives idiosyncratic signal of the state variables according to
is mean-zero Gaussian white noise error terms, distributed independently both of the history of fundamental disturbance and of the observation errors of all other agents
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The Kalman Filter Updating Algorithm
Firms form minimum MSE estimates of the state variables, according to
where K is a matrix of Kalman gain
The equilibrium objects are L,M,N, which result in a fixed point of mapping from the perceived law of motion to the actual one when firms’ updating algorithm is the above equation
20
The Rational Believer Model
In a special case that A,B,D are known a priori, and C=0 and Q2=0, the equilibrium matrices L,M,N are exactly identified. Otherwise, there are more unknown variables than the number of equilibrium conditions
C=0 means that firms (mistakenly) believe that the actual aggregate price and nominal spending do not depend on their higher-order expectations
Q2=0 means that firms receive signals on the actual price and nominal spending, but not on their higher-order expectations
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The Rational Believer Model
The RB model assumes that firms believe and know that others also believe the economy evolves according to the full-info NK model
But they are unaware that their own decisions affect the aggregate outcome
Misperception persists because firms’ information set consists of only a history of contaminated signals, which cannot be used to prove that the NK model is actually wrong
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The Limited Depth of Reasoning Model
Firms are aware that their own decisions affect the aggregate outcome
But they can form expectations of others’ forecasts only for a finite (k) number of iterations (see the price eq.)
This is supported by the experimental evidence in Nagel (1995)
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The Limited Depth of Reasoning Model
Suppose that k=3, that is, firms assume that the 4th order expectation is the same as the 3rd
The state vector is
Limited depth of reasoning means
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The Impulse Response Functions
Assume that firms receive signals on contemporaneous nominal spending and aggregate price level (Q2=0)
Using the baseline parameter values from Woodford (2003)
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Inflation Response of the LDR Model, for varying k
0 5 10 150
0.1
0.2
0.3
0.4
0.5
0.6
0.7
k=1k=3k=6k=10NI
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Real Output Response of the LDR Model, for varying k
0 5 10 150
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
k=1k=3k=6k=10NI
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Inflation Response of the NI Model, for varying
0 5 10 150
0.1
0.2
0.3
0.4
0.5
0.6
0.7=0=0.3=0.6=0.9LDR (=0.3)
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Real Output Response of the NI Models,
for varying
0 5 10 15-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9=0=0.3=0.6=0.9LDR (=0.3)
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Response of all Models, for varying
0 5 10 15
0
0.2
0.4
0.6
2q(i)=2
p(i)= 0.0001
Inflation
0 5 10 15
0
0.2
0.4
0.6
0.8
1
Real Output
0 5 10 15
0
0.2
0.4
0.6
2q(i)=2
p(i)= 100
NKNIRBLDR
0 5 10 15
0
0.2
0.4
0.6
0.8
1
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Response of all Models, for varying
0 5 10 15
0
0.2
0.4
0.6
0.8
1
= 0.01
Inflation
0 5 10 15
0
0.2
0.4
0.6
0.8
1
Real Output
0 5 10 15
0
0.2
0.4
0.6
0.8
1
= 0.9
NKNIRBLDR
0 5 10 15
0
0.2
0.4
0.6
0.8
1