Documentos de Trabajo - Banco de España€¦ · BANCO DE ESPAÑA 17 DOCUMENTO DE TRABAJO N.º 0508...

DO DECREASING HAZARD FUNCTIONS FOR PRICE CHANGES MAKE ANY SENSE?

Documentos de Trabajo N.º 0508

Luis J. Álvarez, Pablo Burrieland Ignacio Hernando

2005

DO DECREASING HAZARD FUNCTIONS FOR PRICE CHANGES MAKE ANY SENSE?

DO DECREASING HAZARD FUNCTIONS FOR PRICE CHANGES

MAKE ANY SENSE? (*)

Luis J. Álvarez, Pablo Burriel and Ignacio Hernando

BANCO DE ESPAÑA

(*) This study was conducted in the context of the Eurosystem Inflation Persistence Network. We are extremely gratefulto the Instituto Nacional de Estadística for providing us with the micro price data and, particularly, to Aránzazu García-Almuzara, Manuel Garrido, Ignacio González-Veiga and Alberta Ruiz del Campo for their help. In addition, we wish to thank all the other network members for discussions and suggestions, in particular Stephen Cecchetti, Daniel Dias, JordiGalí, Vitor Gaspar, Hervé Le Bihan, Pedro Neves, Patrick Sevestre, Frank Smets, Harald Stahl and Philip Vermeulen. Weare most grateful to Josef Baumgartner, Emmanuel Dhyne, Pete Klenow, Hervé Le Bihan and Giovanni Veronese forproviding us with data on the hazard function of their respective countries, and to Alex Wolman for providing the codes used in Dotsey, King and Wolman (1999).

Documentos de Trabajo. N.º 0508

2005

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. The Banco de España disseminates its main reports and most of its publications via the INTERNET at the following website: http://www.bde.es. Reproduction for educational and non-commercial purposes is permitted provided that the source is acknowledged. © BANCO DE ESPAÑA, Madrid, 2005 ISSN: 0213-2710 (print) ISSN: 1579-8666 (on line) Depósito legal: Imprenta del Banco de España

Abstract

A common finding in empirical studies using micro data on consumer and producer prices is

that hazard functions for price changes are decreasing. This means that a firm will have a

lower probability of changing its price the longer it has kept it unchanged. This result is at

odds with standard models of price setting. In this note a simple explanation is proposed:

decreasing hazards may result from aggregating heterogeneous price setters. We show

analytically the form of this heterogeneity effect for the most commonly used pricing rules and

find that the aggregate hazard is (nearly always) decreasing. Results are illustrated using

Spanish producer and consumer price data. We find that a very accurate representation of

individual data is obtained by considering just 4 groups of agents: one group of flexible Calvo

agents, one group of intermediate Calvo agents and one group of sticky Calvo agents plus an

annual Calvo process.

Key words: hazard function, price setting models, heterogeneous agents, mixture models.

JEL Codes: C40, D40, E30.

BANCO DE ESPAÑA 9 DOCUMENTO DE TRABAJO N.º 0508


Figure 1: International evidence on decreasing hazard functions for price changes

AUSTRIA - CPI BELGIUM - CPI

SPAIN - CPI US - CPI

ITALY - CPIFRANCE - CPI

SPAIN - PPI

0%

10%

20%

30%

40%

50%

60%

0 12 24 36months since the last price change

Prob

abili

ty o

f a p

rice

chan

ge

0%

10%

20%

30%

40%

50%

60%


Prob

abili

ty o

f a p

rice

chan

ge

0%

10%

20%

30%

40%

50%

60%


Prob

abili

ty o

f a p

rice

chan

ge

0%

10%

20%

30%

40%

50%

60%


Prob

abili

ty o

f a p

rice

chan

ge

0%

10%

20%

30%

40%

50%

60%


Prob

abili

ty o

f a p

rice

chan

ge0%

10%

20%

30%

40%

50%

60%


Prob

abili

ty o

f a p

rice

chan

ge

0%

10%

20%

30%

40%

50%

60%


Prob

abili

ty o

f a p

rice

chan

ge


Figure 2. Hazard of 2 groups with Calvo price setting and average price duration of 3 and 12 months,respectively

Hazard of 2 Calvo modelswith different

average durations

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

duration months 3duration in months 12

Population Hazard rate,50% of firms with Calvo average duration of 12 months50% of firms with Calvo average duration of 3 months

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


Figure 3. Hazard of 1 Calvo and 1 Taylor

Population Hazard rate,91.7% of firms with Calvo average duration of 12 months

5.5% of firms with Taylor contracts of 12 months3% of firms with Taylor contracts of 24 months

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Hazard of 1 Calvo and1 Taylor model

0.05

0.06

0.07

0.08

0.09

0.10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Taylor 12 monthsCalvo 12 months

1

Population Hazard rate,94% of firms with Calvo average duration of 12 months

6% of firms with Taylor contracts of 12 months

0.05

0.06

0.07

0.08

0.09

0.10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

0,211


Figure 4. Hazard of 1 Calvo and 1 Annual Calvo

Calvo and annual Calvo

0

0.2

0.4

0.6

0.8

1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Months since the last price change

Calvo Seasonal Calvo Aggregation of Calvo and annual Calvo

0

0.2

0.4

0.6

0.8

1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35



Figure 5. Hazard of 1 Calvo and 1 DKW model

Aggregation of Calvo and DKW

0

0.2

0.4

0.6

0.8

1

3 12 21 30 39 48 57 66 75


Individual hazard rates

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

3 12 21 30 39 48 57 66 75


Calvo INF=0, average duration 1 year

DKW INF=1, Markup=30


Figure 6. Hazard of two different DKW models

Aggregation of DKW

0

0.2

0.4

0.6

0.8

1

3 9 15 21 27 33 39 45 51 57 63 69 75 81


INF=1% and 5%,

Mark-up:30%DKW hazard rates

0

0.2

0.4

0.6

0.8

1

3 9 15 21 27 33 39 45 51 57 63 69 75 81


DKW INF=1, Markup=30 DKW INF=5, Markup=30


number ofmodels

AIC BIC AIC BIC AIC BIC AIC BIC

1 144469 144476 1203134 1203144 130709 130711 1153457 1153460

2 133104 133116 914830 914847 123544 123552 906843 906853

3 121257 121274 897292 897316 122468 122480 902244 902261

4 125501 125523 902373 902404 124889 124906 920091 920115

5 122716 122743 901480 901518 123852 123874 907579 907609

firms spells

standard Calvo

Producer prices

standard + 1 annual Calvo

Table 1. Producer Prices: selection of the number of differentCalvo agents

firms spells


Price setting models

WeightCalvo

ParameterMean

duration WeightCalvo

ParameterMean


ParameterMean


ParameterMean

duration

Flexible Calvo 16.5% 0.11 1.1 56.9% 0.11 1.1 15.4% 0.08 1.1 56.7% 0.11 1.1(0,38%) (0,01) (0,02) (0,14%) (0,00) (0,00) (0,37%) (0,01) (0,01) (0,14%) (0,00) (0,00)

Intermediate Calvo 48.2% 0.92 12.3 32.3% 0.89 9.2 60.8% 0.93 13.8 37.8% 0.90 10.5(1,60%) (0,00) (0,48) (0,28%) (0,00) (0,11) (1,77%) (0,00) (0,47) (0,31%) (0,00) (0,11)

9.2 6.9Sticky Calvo 26.9% 0.99 91.4 6.8% 0.98 50.1 23.8% 0.99 105.9 5.5% 0.98 56.0

(1,68%) (0,00) (8,86) (0,29%) (0,00) (2,12) (1,87%) (0,00) (13,82) (0,33%) (0,00) (3,28)

Annual Calvo 8.5% 0.28 16.8 4.0% 0.21 15.2(0,27%) (0,02) (0,03) (0,06%) (0,01) (0,01)

Log likelihood -60621 -448639 -61229 -451117Number of observations 26965 244864 26965 244864Joint significance Wald test 20.15 2479.23 68.98 2553.07p- value 0.00 0.00 0.00 0.00

Table 2. Producer Prices: estimation of price setting models

standard + 1 annual Calvo standard Calvospellsfirms firms spells


Figure 7. Producer Prices: Hazard and contribution to hazard

00.0

5.0

5.1.1

.15

.15

.2.2

00 1212 2424 3636 4848m o nths s ince las t p r ice chang em o nths s ince las t p r ice chang e

fit ted h aza rdf it ted h aza rd em p ir ica l h az ardem p ir ica l h az ard

3 C alvo & C alvo an nu a l3 C alvo & C alvo an nu a lP P I haza rd by firmP PI haza rd by firm

0.2

.4.6

0 1 2 2 4 3 6 4 8m o n th s s in c e la s t p r ic e c h a n g e

fitte d h a z a rd em p ir ica l h aza rd

3 C a lv o & C a lv o a n n u a lP P I h a za rd

0.2

.4.6

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748

3 Calvo & 1 annual CalvoContributions to the PPI hazard rate

flexible Calvo intermediate Calvosticky Calvo annual Calvo

0.0

5.1

.15

.2

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748

3 Calvo & 1 annual CalvoContributions to the PPI hazard rate by firm



non-durablesfood

non-durablesnon- food durables intermediate energy capital All groups

Price setting ModelFlexible Calvo 3.5% 1.3% 1.0% 8.8% 6.1% 1.3% 21.9%Intermediate Calvo 8.6% 7.0% 7.2% 17.6% 4.2% 5.9% 50.5%Sticky Calvo 3.0% 3.1% 3.7% 7.2% 0.4% 3.5% 20.9%Annual Calvo 1.0% 1.1% 1.1% 2.0% 0.3% 1.2% 6.8%

Share of PPI 16.1% 12.4% 13.1% 35.5% 11.1% 11.8% 100.0%

Table 3. Price setting models by PPI main industrial groupings (using PPI weights)


number ofmodels

AIC BIC AIC BIC AIC BIC AIC BIC

1 75704 75711 894119 894129 73253 73255 891611 891614

2 76654 76664 787640 787656 68925 68931 789456 789465

3 67275 67290 778891 778914 68132 68142 781875 781891

4 67810 67829 781125 781154 68177 68192 786004 786026

5 67825 67848 779982 780017 68203 68222 791049 791078

firms

Table 4. Consumer Prices: selection of the number of differentCalvo agents

Consumer prices

spells

standard + 1 annual Calvo standard Calvo

firmsspells


Price setting models

WeightCalvo

ParameterMean


ParameterMean


ParameterMean


ParameterMean

duration

Flexible Calvo 22.1% 0.20 1.3 47.5% 0.24 1.3 21.6% 0.19 1.2 48.3% 0.24 1.3(0,62%) (0,02) (0,03) (0,28%) (0,00) (0,01) (0,68%) (0,02) (0,03) (0,26%) (0,00) (0,00)

Intermediate Calvo 50.4% 0.90 10.3 39.5% 0.84 6.4 59.9% 0.92 11.8 41.9% 0.86 7.3(1,44%) (0,00) (0,41) (0,31%) (0,00) (0,08) (1,64%) (0,00) (0,43) (0,35%) (0,00) (0,09)

Sticky Calvo 20.1% 0.98 58.4 9.8% 0.96 27.9 18.5% 0.98 62.6 9.7% 0.96 28.2(1,52%) (0,00) (4,12) (0,30%) (0,00) (0,56) (1,75%) (0,00) (5,45) (0,37%) (0,00) (0,64)

Annual Calvo 7.4% 0.42 20.5 3.2% 0.30 17.2(0,34%) (0,02) (0,06) (0,06%) (0,01) (0,02)

Log likelihood -33630 -389439 -34061 -390932Number of observations 12494 179673 12494 179673Joint significance Wald test 65.75 2058.42 86.84 2792.25p- value 0.00 0.00 0.00 0.00

Table 5. Consumer Prices: estimation of price setting models

standard + 1 annual Calvo standard Calvospellsfirms firms spells


Figure 8. Consumer Prices: Hazard and contribution to hazard0

.05

.1.1

5.2

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748

3 Calvo & 1 annual CalvoContributions to the PPI hazard rate by firm


0.1

.2.3

.4

0 1 2 2 4 3 6 4 8m on ths s ince la s t p rice cha ng e

fitted h a zard e m p irica l h aza rd

3 C a lv o & C a lvo a n n u a lC P I h a za rd

0.0

5.1

.15

.2.2

5

0 1 2 2 4 3 6 4 8m onths s ince las t p rice change

fitte d h a zard e m p irica l h aza rd

3 C a lv o & C a lv o a n n u a lC P I h a za rd by firm

0.1

.2.3

.4

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748

3 Calvo & 1 annual CalvoContributions to the CPI hazard rate


0.0

5.1

.15

.2.2

5

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748

3 Calvo & 1 annual CalvoContributions to the CPI hazard rate by firm



unprocessedfood

processedfood non energy services all

components

Price setting ModelFlexible Calvo 6.8% 4.4% 1.4% 0.8% 13.4%Intermediate Calvo 5.7% 12.4% 22.0% 16.4% 56.6%Sticky Calvo 0.2% 1.5% 7.2% 9.0% 17.9%Annual Calvo 0.1% 0.5% 4.8% 6.8% 12.1%

Share of CPI 12.8% 18.8% 35.4% 33.0% 100.0%

Table 6. Price setting models by CPI main componentes (using CPI weights)


Figure A.1. Cases 1 and 2: Hazard of 2 groups with Truncated Calvo price setting

Population Hazard rate,50% Truncated Calvo ave 12 months, J=36 m50% Truncated Calvo ave 3 months, J=36 m

0.00

0.05

0.10

0.15

0.20

0.25

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37

Population Hazard rate,50% Truncated Calvo ave 12 months, J=36 m50% Truncated Calvo ave 3 months, J=12 m

0.00

0.05

0.10

0.15

0.20

0.25

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37

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