Menu Costs, Calvo Fairy, Inflation, and Micro Facts Etienne Gagnon Federal Reserve Board
The views expressed in this presentation and associated paper are solely the responsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System, or any other person associated with the Federal Reserve System.
Bridging the gap between data and macro models
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Several data bases of individual prices used to compute price indexes were made available to researchers in recent years;
There has been a massive effort to document basic facts about setting of individual prices;
While a consensus on basic facts is emerging, there still is wide disagreement about how to model price-setting decisions.
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Bridging the gap between data and macro models (cont’d)
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Many price setting mechanisms are used in macro models: Calvo, fixed-duration contracts, menu-costs, information frictions, consumer anger, search, stochastic demand, etc.
They often have conflicting implications for slope of Phillips curve, degree of exchange rate pass-through, persistence of shocks, optimal policies, etc.
There is hope that micro evidence will help to discriminate among these models.
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What this paper does
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Focuses on three micro facts pertaining to the impacts of inflation on consumer prices;
Compare ability of Calvo and menu-cost models with idiosyncratic technology shocks at matching these facts.
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Inflation and time coverage of CPI studies 45 Austria Belgium Finland France Luxemburg Portugal Spain United-States Mexico
40
Four-quarter change in official CPI (%)
35
30
25
20
15
10
5
0 1988 1989
1990 1991
1992 1993
1994 1995
1996 1997
1998 1999
2000 2002
2002 2003
2004
Period covered by country studies
5
Etienne Gagnon - FRB
Inflation and time coverage of CPI studies 45 Austria Belgium Finland France Luxemburg Portugal Spain United-States Mexico
40
Four-quarter change in official CPI (%)
35
30
25
20
15
10
5
0 1988 1989
1990 1991
1992 1993
1994 1995
1996 1997
1998 1999
2000 2002
2002 2003
2004
Period covered by country studies
6
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Data coverage Time period: Price quotes: Total Monthly Average
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January 1994 to June 2002
3,800,000 37,000
Items
51,000
CPI coverage
63.4%
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Economic environment
Discrete-time version of Golosov-Lucas.
Three type of agents:
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Representative household; Continuum of firms; Monetary authority sets gt=log(Mt+1/Mt).
I focus on stationary equilibrium with gt=g. Etienne Gagnon - FRB
Representative Household
The representative HH’s problem is:
maxC t ,N t
∑
t logC t t0
− N t
Subject to a budget constraint and a simple money demand equation:
PtCt WtNt Ptt PtCt Mt
Consumption is a basket of differentiated items:
Ct 9
c j,t
−1
dj
−1
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Firms
The demand curve of firm j is given by:
cj,t
p j,t Pt
−
Ct
The production function is linear in labor:
yj,t cj,t j,t n j,t
Technology evolves according to:
log j,t 1 − log ̄ log j,t−1 j,t
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Where
j,t N0, 2
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Firms (cont’d)
Firms maximize present discounted real profits.
They must incur a menu cost j,t to change their nominal price.
The Calvo and menu-cost models differ only in terms of distribution of menu costs:
Menu cost:
Calvo model
j,t
j,t
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0
with probability 1 −
with probability
The models are calibrated to distribution of price changes. Etienne Gagnon - FRB
Fact 1
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Inflation and the average frequency and magnitude of price changes.
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Inflation and the average frequency of price changes
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Inflation and the average magnitude of price changes
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Calvo fit of the average frequency and magnitude of price changes
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Menu cost model fit of the average frequency and magnitude of price changes
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Calvo model fit of the average frequency and magnitude of price changes (variable hazard)
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Fact 2
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Inflation and the distribution of nonzero price changes.
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Models’ fit of the distribution of price changes under low inflation
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Models’ fit of the distribution of price changes under medium inflation
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Models’ fit of the distribution of price changes under high inflation
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Fact 3
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Price spell duration and the average magnitude of price changes.
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Motivation
Calvo’s good fit of the distribution of price changes hinges on constant hazard assumption:
Most price changes occur at short durations many small price changes; Non-negligible mass of firms with no change in long time fat tails.
Constant hazard implies that, firms change their price by amount of cumulated inflation since last price change:
Edp i |duri ss duri 23
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Motivation
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In menu-cost model, the magnitude of price changes does not depend on duration per se, but rather on width of Ss band.
The average magnitude of price changes is therefore a way to discriminate between the two models.
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Spell duration and magnitude of price changes
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Spell duration and magnitude of price changes
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Spell duration and magnitude of price changes
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Ss band and elasticity of substitution
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Concluding remarks
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Menu Cost
Calvo
Fact 1 : Impact of inflation on frequency and magnitude
Very good
Very bad
Fact 2 : Impact of inflation on distribution of price changes
Very bad
Good
Fact 3 : Price spell duration and magnitude of changes
Good
Bad
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Concluding remarks (cont’d)
Ideally, we want to combine the strengths of both models:
This suggests a model with both idiosyncratic technology (and demand) and menu-cost shocks;
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Some endogeneity in timing of price-setting decision; But not too much, as there is much uncertainty about timing of price changes.
Raises major identification issues; Need for good stories. Etienne Gagnon - FRB
