MICRO-BASED ESTIMATES
OF HETEROGENEOUS PRICING
RULES: THE UNITED STATES
VS. THE EURO AREA
Luis J. Álvarez and Pablo Burriel
Documentos de Trabajo
N.º 1019
2010
MICRO-BASED ESTIMATES OF HETEROGENEOUS PRICING RULES:
THE UNITED STATES VS. THE EURO AREA
MICRO-BASED ESTIMATES OF HETEROGENEOUS PRICING
RULES: THE UNITED STATES VS. THE EURO AREA (*)
Luis J. Álvarez and Pablo Burriel (**)
BANCO DE ESPAÑA
(*) We are extremely grateful to the Instituto Nacional de Estadística for providing us with the Spanish micro price
data and to Josef Baumgartner, Emmanuel Dhyne, Johannes Hoffmann, Peter Klenow, Hervé Le Bihan, Patrick
Lünnemann and Giovanni Veronese for providing us with data on the distribution function of price durations for
their respective countries.The paper has also benefited from the comments of seminar participants at Banco de
España, Mark Bils (the editor) and 3 anonymous referees. The views expressed here are those of the authors and
do not necessarily reflect those of Banco de España. Correspondence address: Alcalá 48, 28014 Madrid, Spain.
Email address: [email protected]
Documentos de Trabajo. N.º 1019
2010
The Working Paper Series seeks to disseminate original research in economics and finance. All papers
have been anonymously refereed. By publishing these papers, the Banco de España aims to contribute
to economic analysis and, in particular, to knowledge of the Spanish economy and its international
environment.
The opinions and analyses in the Working Paper Series are the responsibility of the authors and, therefore,
do not necessarily coincide with those of the Banco de España or the Eurosystem.
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Reproduction for educational and non-commercial purposes is permitted provided that the source is
acknowledged.
© BANCO DE ESPAÑA, Madrid, 2010
ISSN: 0213-2710 (print)
ISSN: 1579-8666 (on line)
Depósito legal: M. 30123-2010
Unidad de Publicaciones, Banco de España
Abstract
This paper presents US and euro area estimates for a fully heterogeneous model, in which
there is a continuum of firms setting prices with a constant probability of adjustment,
which may differ from firm to firm. The estimated model accurately matches the empirical
distribution function of individual price durations for the US and the euro area. Incorporating
these micro based pricing rules into a DSGE model, we find that nominal shocks have a
greater real impact in the fully heterogeneous economy than in the standard Calvo model.
We also find that nominal and real shocks bring about a reallocation of resources among
sectors. Monetary policy is found to have a greater real impact in the euro area than in the
United States.
Keywords: price setting, heterogeneity, DSGE, Calvo model.
JEL classification: C40, D40, E30.
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DOCUMENTO DE TRABAJO N.º 1019
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DOCUMENTO DE TRABAJO N.º 1019
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DOCUMENTO DE TRABAJO N.º 1019
Table 1 presents parameter estimates for the models considered,18 as well as the Akaike Information
Criterion (AIC), Bayesian Information Criterion (BIC) and an statistic measuring the quadratic
distance between the empirical and the fitted probability mass funcion (qd):
qd =
max
k
k=1
fkempirical − fkfitted
fkempirical
2
Table 1: Estimation of price setting models
United States
Model
a
Fully Heterogeneous [FH]
Standard Calvo [C]
Sectoral Calvo [SC]
b
c
AIC
Euro area
BIC
qd
a
b
c
AIC
BIC
qd
0.46 0.47 0.00 2,723,646 2,723,669 0.008
(0.00) (0.00) (0.00)
0.49 0.33 0.00 439,707 439,735 0.019
(0.00) (0.00) (0.00)
theta
theta
0.71
(0.00)
---
AIC
BIC
qd
3,142,891 3,142,895 0.414
---
---
0.57
0.81
(0.00)
---
AIC
BIC
qd
507,032 507,035 0.588
---
---
0.81
Note: Standard errors of estimates are reported within parentheses.
Figure 2 shows that the fully heterogeneous model very accurately matches the distribution functions of price durations in the US and the euro area, which results in low qd statistics. Moreover,
it seen that the share of very flexible price setters is considerably higher in the US than in the
euro area. In contrast with the fully heterogeneous model, the standard Calvo model provides
a bad fit of the distribution in terms of qd and substantially underestimates the share of very
flexible price setters, particularly so in the US. Figure 3 presents the hazard rates of both models.
Heterogeneity in the frequency of price adjustment explains the declining population hazard rate:
the population hazard depends on the share of the different frequency of adjustment firms at each
horizon. As the price age increases, the composition of price adjusters shifts towards the low
18
As a robustness check, we considered a functional form that allowed for individual increasing hazard rates. We
did not find evidence in favour of upward sloping hazard functions.We also considered a beta distribution for the
distribution of the price adjustment parameter, which lead to a worse fit. Both sets of results are available from
the authors upon request.
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DOCUMENTO DE TRABAJO N.º 1019
frequency price adjusters, motivating the decline in the population hazard rate. Hazard rates corresponding to estimated fully hetereogeneous models closely match empirical ones both for price
spells with short and long durations and for both economies. As expected, the standard Calvo
model, which implies a flat hazard rate, has a disappointing performance. The Calvo parameter
is lower in the US than in the euro area, in line with the higher average frequency of adjustment.
Figure 2: Empirical and model based distributions of price durations
0.8
0.8
United States
0.7
0.6
0.6
Empirical
Empirical
Fully Heterogeneous
0.5
Euro Area
0.7
Fully Heterogeneous
0.5
Standard calvo
0.4
Standard calvo
0.4
Sectoral calvo
0.3
0.3
0.2
0.2
0.1
0.1
0.0
Sectoral calvo
0.0
1-3 months
4-12 months
13-24 months
>24 months
1-3 months
4-12 months
13-24 months
>24 months
Figure 3: Empirical versus fitted hazard
0.6
0.6
United States
Euro Area
0.5
0.5
Empirical
Fully Heterogenous
Standard Calvo
0.4
Hazard
Hazard
0.4
0.3
0.2
0.1
0.1
0.0
0
12
24
36
Months since the last price change
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Standard Calvo
0.3
0.2
0.0
Empirical
Fully Heterogenous
17
DOCUMENTO DE TRABAJO N.º 1019
48
0
12
24
36
Months since the last price change
48
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DOCUMENTO DE TRABAJO N.º 1019
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DOCUMENTO DE TRABAJO N.º 1019
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BANCO DE ESPAÑA
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DOCUMENTO DE TRABAJO N.º 1019
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BANCO DE ESPAÑA
22
DOCUMENTO DE TRABAJO N.º 1019
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BANCO DE ESPAÑA
23
DOCUMENTO DE TRABAJO N.º 1019
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BANCO DE ESPAÑA
24
DOCUMENTO DE TRABAJO N.º 1019
'G6C2== 6FC@ 2C62 >@?6E2CJ A@=:4J 92D 2 8C62E6C =6G6C286 @? E96 C62= 64@?@>J :? E96 D9@CE CF?
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$! $" !" " $#" # !# ""
88C682E6 AC@5F4E:G:EJ D9@4<
0.05
32D:D A@:?ED :?E6C6DE C:D6
0.05
0.00
0.00
-0.05
-0.05
-0.10
-0.10
-0.15
0.2
-0.25
Inflation
(Euro Area)
-0.20
-0.40
-0.45
d<3m
3m<d<12m
d>12m
Inflation
-0.40
-0.45
-0.50
3
5
7
9
11
0.7
Output
(United States)
0.6
0.5
-1.0
-1.4
-1.6
1
3
5
7
9
11
0.7
Output
(Euro Area)
0.6
d<3m
3m<d<12m
d>12m
Inflation
-1.2
-1.4
-1.6
1
3
5
7
9
11
0.5
0.5
0.4
-0.8
d<3m
3m<d<12m
d>12m
Inflation
-1.2
-0.50
1
Inflation
(Euro Area)
-0.6
-1.0
-0.35
d<3m
3m<d<12m
d>12m
Inflation
-0.4
Inflation
(United States)
-0.8
-0.30
-0.35
-0.2
-0.6
-0.25
-0.30
0.0
-0.2
-0.4
-0.15
Inflation
(United States)
-0.20
0.2
0.0
1
3
5
7
9
11
0.5
0.0
0.0
-0.5
-0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0.0
-0.1
d<3m
3m<d<12m
d>12m
Output
-0.2
-0.3
-0.4
-1.5
-0.1
d<3m
3m<d<12m
d>12m
Output
-0.2
-0.3
-0.4
1
3
5
7
9
11
0.00
1
3
5
7
9
Nominal Interest rate
-1.5
-2.5
-2.5
1
3
5
7
9
11
United States
Euro Area
-0.04
1
3
5
7
9
11
0.50
0.45
Productivity shock
Nominal Interest rate
0.25
0.80
0.20
0.60
0.15
Taylor Rule shock
0.40
-0.02
-0.03
d<3m
3m<d<12m
d>12m
Output
-2.0
0.30
1.00
Output
(Euro Area)
-1.0
d<3m
3m<d<12m
d>12m
Output
-2.0
11
1.20
-0.01
Output
(United States)
-1.0
0.35
0.30
United States
-0.05
-0.06
0.40
0.10
Euro Area
0.20
Euro Area
0.20
0.15
United States
-0.07
United States
0.25
Euro Area
0.10
0.05
-0.08
0.05
-0.09
0.00
1
3
5
7
9
11
0.00
1
3
5
7
9
11
0.00
1
3
5
7
9
11
1
3
5
7
9
11
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BANCO DE ESPAÑA
25
DOCUMENTO DE TRABAJO N.º 1019
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:?4C62D6 E96:C AC:46D 2?5 :?4FC @FEAFE =@DD6D H96C62D H96? E96 D64E@C2= D9@4< 2S64ED E96 DE:4<:6DE
LC>D E96 M6I:3=6 AC:46 D6EE6CD 2C6 2=D@ 23=6 E@ 4FE 5@H? E96:C AC:46D ,96 C62D@? :D E92E M6I:3=6
LC>D 42? 25;FDE AC:46D ?@H D@ 2D E@ C65F46 @FEAFE =@DD6D 3642FD6 E96J <?@H E92E E96J H:== 36
23=6 E@ 492?86 E96> 282:? :? E96 ?62C 7FEFC6 !? 4@?EC2DE DE:4<J AC:46 D6EE6CD 2C6 >@C6 4@?DEC2:?65
@? E96 7C6BF6?4J H:E9 H9:49 E96J 42CCJ @FE AC:46 492?86D D@ H96? E96J 564:56 E@ 25;FDE AC:46D
E96 6IA64E65 82:? 92D E@ 36 =2C86 6?@F89 E@ 4@>A6?D2E6 E96> 7C@> E96 724E E92E E96J 2C6 =:<6=J
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$! $" !" " $#" # "#! !$#%#' ""
=6I:3=6 AC:46D 2G6C286 AC:46 5FC2E:@? >@?E9D +E:4<:6C AC:46D 2G6C286 AC:46 5FC2E:@? >@?E9D
0.05
0.05
0.002
0.00
0.00
0.000
0.000
-0.05
-0.05
-0.002
-0.002
-0.10
Inflation
(Euro Area)
-0.10
Inflation
(United States)
-0.15
-0.15
-0.20
-0.004
-0.25
d<3m
3m<d<12m
d>12m
inflation
-0.30
-0.35
d<3m
3m<d<12m
d>12m
Inflation
-0.30
-0.35
-0.40
3
5
7
9
11
0.80
d<3m
3m<d<12m
d>12m
Output
0.60
0.40
-0.008
-0.010
-0.010
d<3m
3m<d<12m
d>12m
Inflation
-0.014
3
5
7
9
11
d<3m
3m<d<12m
d>12m
Output
0.60
-0.016
1
0.08
d<3m
3m<d<12m
d>12m
Inflation
-0.014
3
5
7
9
11
0.10
0.80
Inflation
(Euro Area)
-0.012
-0.016
1
1
3
5
7
9
d<3m
3m<d<12m
d>12m
Output
Output
(United States)
0.06
Output
(Euro Area)
0.08
11
d<3m
3m<d<12m
d>12m
Output
0.10
0.40
0.20
-0.006
-0.008
-0.012
-0.40
1
-0.004
Inflation
(United States)
-0.006
-0.20
-0.25
0.002
0.06
0.04
0.04
0.02
0.02
0.20
0.00
0.00
Output
(United States)
-0.20
-0.40
Output
(Euro Area)
-0.20
3
5
7
9
11
0.00
-0.02
-0.02
-0.04
-0.40
1
0.00
1
3
5
7
9
11
-0.04
1
3
5
7
9
11
1
3
5
7
9
11
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BANCO DE ESPAÑA
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DOCUMENTO DE TRABAJO N.º 1019
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DOCUMENTO DE TRABAJO N.º 1019
Figure 6: Impulse response functions to a monetary shock:
Fully heterogeneous vs Calvo and sectoral Calvo models.
0.0
0.0
-0.2
-0.2
Inflation
(United States)
-0.4
-0.6
-0.4
Inflation
(Euro Area)
-0.6
-0.8
-0.8
-1.0
-1.0
Standard Calvo
Standard Calvo
-1.2
-1.2
Fully heterogeneous
Fully Heterogenous
-1.4
Sectoral Calvo
-1.4
Sectoral Calvo
-1.6
-1.6
1
3
5
7
9
11
13
15
17
19
21
23
1
3
5
7
9
11
13
15
17
19
21
23
21
23
0.0
0.0
-0.2
-0.2
-0.4
-0.4
Output gap
(United States)
-0.6
-0.8
Output
(Euro Area)
-0.6
-0.8
-1.0
-1.0
-1.2
-1.2
-1.4
Standard Calvo
-1.4
-1.6
Fully Heterogenous
-1.6
-1.8
Sectoral Calvo
-1.8
Standard Calvo
Fully heterogeneous
Sectoral Calvo
-2.0
-2.0
1
3
5
7
9
11
13
15
17
19
21
1
23
0.30
3
5
7
9
11
13
15
17
19
0.30
0.25
Nominal interest rate
(Euro Area)
0.25
0.20
Nominal interest rate
(United States)
0.20
0.15
Standard Calvo
0.15
Standard Calvo
Fully heterogeneous
Fully Heterogenous
0.10
Sectoral Calvo
0.10
Sectoral Calvo
0.05
0.05
0.00
0.00
1
3
5
7
9
11
13
15
17
19
21
23
1
3
5
7
9
11
13
15
17
19
21
23
Table 2: Comparison of impulse response functions across price setting models
25 bp interest rate rise
Output
United States
Initial
Accumulated
Initial
Accumulated
Standard Calvo [C]
-1.8
-3.7
-1.4
-2.8
1.3
1.3
-1.8
-5.4
-1.5
-2.6
1.2
2.1
Sectoral Calvo [SC]
-1.8
-10.3
-0.4
-0.9
4.2
12.1
Initial
Accumulated
Initial
Accumulated
Initial
Accumulated
-1.8
-5.0
-0.7
-1.9
2.6
2.6
Standard Calvo [C]
28
Accumulated
Sacrifice ratio
Fully heterogeneous [FH]
Euro Area
BANCO DE ESPAÑA
Initial
Inflation
Fully heterogeneous [FH]
-1.8
-7.5
-0.9
-1.7
2.0
4.3
Sectoral Calvo [SC]
-1.8
-9.8
-0.2
-0.7
8.3
13.7
DOCUMENTO DE TRABAJO N.º 1019
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DOCUMENTO DE TRABAJO N.º 1019
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0.00
0.00
-0.10
-0.10
Core Inflation
(United States)
-0.20
-0.30
Core Inflation
(Euro Area)
-0.20
core inflation = headline
-0.30
core inflation = headline
core inflation = durations > 3 months
core inflation = durations > 3 months
core inflation = durations > 12 months
core inflation = durations > 12 months
-0.40
-0.40
1
3
5
7
9
11
13
15
17
0.4
1
3
5
0.40
7
9
11
13
15
17
core inflation = headline
core inflation = durations > 3 months
Output gap
(United States)
0.3
core inflation = durations > 12 months
0.30
0.2
0.20
core inflation = headline
0.1
0.10
Output gap
(Euro Area)
core inflation = durations > 3 months
core inflation = durations > 12 months
0.0
0.00
1
3
5
7
9
11
13
15
17
core inflation = headline
0.00
1
3
7
9
11
13
15
17
core inflation = durations > 3 months
core inflation = durations > 3 months
-0.01
5
core inflation = headline
0.00
-0.01
core inflation = durations > 12 months
core inflation = durations > 12 months
-0.01
-0.02
-0.02
-0.03
-0.02
-0.03
-0.04
Nominal interest rate
(United States)
-0.05
-0.03
Nominal interest rate
(Euro Area)
-0.04
-0.06
-0.04
1
3
5
7
9
11
13
15
17
1
3
5
7
9
11
13
15
17
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BANCO DE ESPAÑA
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DOCUMENTO DE TRABAJO N.º 1019
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DOCUMENTO DE TRABAJO N.º 1019
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DOCUMENTO DE TRABAJO N.º 1019
BANCO DE ESPAÑA PUBLICATIONS
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