Cecchetti - Frequency of Price Adjustments

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Jo u rn a l o f E co n o m e t r i c s 3 1 (19 8 6) 2 5 5 -2 7 4 . N o r t h -H o l l an d

T H E F R E Q U EN C Y O F P R IC E A D J U S T M E N T

A S tudy of the New sstand Prices of M agazines*

Stephen G. CECCHETTI

New Yor k Universi ty , New Y ork , N Y 10006 , USA

Received M arch 1985, f ina l vers ion rece ived No vem ber 1985

D ata on the new sstand pr ices of Am erican magazines i s used to invest iga te the de terminan ts o f thefrequency of nominal p r ice change . Magazine pr ice changes , o f ten coming af te r rea l p r ices havefa l len by one quarter , p rovide s t rong ev idence for monopol i s t ic s t icky pr ice models . The da ta i sexam ined by apply ing a f ixed effec ts log i t spec if ica tion to the pr ice change ru le im pl ied by atarge t - th reshold model o f a f i rm fac ing genera l p r ice in f la t ion , an uncerta in fu ture and cost lynominal ad jus tment . The essay concludes tha t h igher in f la t ion leads to more frequent p r iceadjustment and that the real cost of price changes varies with the size of a real price change.

1. Introduction

Th e e f f ec t o f p r i ce s t i ck iness o n ag g r eg ate o u tp u t f l u c tu a t io n s h as b een th es u b j e c t o f m u c h r e c e n t m a c r o e c o n o m i c r e se a rc h .1 M o d e l s wh ich a s su m e th a t

in d iv id u a l ag en t s ad ju s t t h e i r p r i ce s a t d i sc r e t e an d o v e r l ap p in g in t e r v a l s

co n c lu d e th a t l o n g e r p e r io d s b e tween p r i ce ch an g es l ead to g r ea t e r se r i a l

co r r e l a t io n o f o u tp u t i n r e sp o n se to u n an t i c ip a t ed sh o ck s . Th e p r e sen ce o f

m o n o p o l i s t i c co m p e t i t i o n a t t h e l eve l o f t h e in d iv id u a l p r ice se t t e rs i s u su a l ly

u sed to ju s t i f y th e p r ice ch an g e t ech n o lo g y im p o sed o n th e m o d e l . Th e

d esc r ip t iv e p o w er o f t h e se m o d e l s d ep en d s o n th e accu r ac y o f t h e i r ch a r ac te r i -

za t io n o f t h e p r i ce ch an g e p r o cess . Co n seq u en t ly , d e sc rib in g th e ev o lu t io n o f

th e p r i ce ch a n g e f r eq u e r l cy an d id en t i f y in g i ts d e t e r m in a n t s is im p o r t an t t o t h eu n d e r s t a n d i n g o f m a c r o e c o n o m i c f lu c tu a ti o ns .

T h e f r e q u e n c y o f p r i ce a d j u s t m e n t is a l m o s t c e r t a in l y d e p e n d e n t o n t h e

eco n o m ic en v i r o n m en t . I n t h i s co n tex t , two q u es t io n s a r e o f i n t e r e s t . F i r s t ,

wh a t i s t h e r e sp o n se o f t h e f r eq u en cy o f ad ju s tm en t t o i n c r ea se s i n g en e r a l

*This paper i s a rev ised vers ion of the second essay of my Ph .D. d i sser ta t ion comple ted inAu gus t 1982 a t the U nivers i ty of Cal i forn ia , Berkeley . Thanks are due especia l ly to Georg e Akerlo fwi t h o u t wh o m t h is s t u d y w o u l d n ev e r h av e b een s t a r ted , t o B il l Green e fo r p ro v i d in g h e lp a t ev e rystage , and to Paul Ruud, Tom Rothenberg , Bob Cumby, George Sofianos , Pe ter Berck , Paul

W ach t e l , K e i t h Jo h n so n an d an o n y mo u s re fe rees fo r co mmen t s . Al l r ema i n i n g er ro rs a re mi ne .1Th e w ork o f Tay lor (1980) on s taggered cont rac ts , o f Blanchard (1984) on pr ice asynchroniza-

t ion and of R otem ber g (1983a ,b) on s t icky pr ices are examples .

030 4-4 076 /86/$ 3 .50 © 1986, Elsev ier Sc ience Publi shers B.V. (N orth-H ol land)



256 S.G. Cecchetti , The frequency o f price adjustm ent

pr ice in f l a t ion? And second , what i s the s t ruc tu re o f the cos t o f p r i ce ad jus t -

m en t ? T h eo re t i ca l mo d e l s o f p r i ce d e te rm i n a t i o n i n t h e p r e s en ce o f mo n o p o l i s -

t i c compet i t ion , inc lud ing those in Shesh insk i and Weiss (1977 ,1983) , Mussa

(1981a , b ) an d Iwai (1981), o f fe r no genera l answ er to the f i r st ques t ion .

Reg a rd i n g t h e s eco n d , t h ey a s s u me t h e co s t o f a n o mi n a l p r i ce ch an g e t o b e

co n s t an t i n r ea l t e rms . T h es e co st s a re b e l i ev ed t o t ak e t w o fo rms : ad m i n i st r a -

t iv e , t h e co s t o f d e t e rmi n i n g a n d i mp l emen t in g a n ew p r ice ; a n d i n fo rma t io n a l ,

t h e co s t i m p o s e d o n t h e f irm ' s cu s t o m er s an d a s s o c i a t ed w i t h a p o s s i b l e l o ss o f

s a le s t o co m p e t i t o r s . R o t em b erg (1 9 82 a , b ) h a s s u g g es ted t h a t i n t h e p r e s en ce

o f mo n o p o l i s t i c co mp e t i t i o n w h e re s u b s t i t u t e g o o d s a r e r ead i l y av a i l ab l e , t h e

co s t s may b e p ro p o r t i o n a l t o t h e s i ze o f t h e r ea l p r i ce ch an g e . H e a rg u es t h a t

cu s t o mer s p r e f e r s t ab l e p r i ce p a t h s w h i ch ex h i b i t s ma l l ad j u s t men t s t o t h o s e

w i t h l a rg e i n f r eq u e n t j u m p s . A l t e rn a t iv e l y , t h e h y p o t h es i s t h a t t h e co s t o f

ch an g i n g a n o mi n a l p r i ce may b e a d ec rea s i n g fu n c t i o n o f t h e f r eq u en cy w i t hw h i ch t h e p r i ce i s ch an g ed y i e ld s s i mi la r p r i ce a d j u s t m en t b eh av i o r . 2 Bu t

w h e t h e r co s t s a r e i n v a r i an t t o t h e s i ze o r f r eq u en cy o f p r i ce ch an g e i s an

emp i r i ca l q u es t i o n .

S t u d y i n g p r i ce ch an g es r eq u ir e s d a t a o f a t y p e t h a t i s n o t n o rm a l l y av a il ab le .

Id ea l l y o n e w o u l d l ik e o b s e rv a t io n s o n t h e ch an g es in t h e t r an s ac t io n s p r i ce o f

a co n s i s t en t p ro d u c t o v e r a p e r i o d o f t i me l o n g en o u g h fo r t h e r e t o h av e b een

s u b s t an t i a l v a r i a t i o n i n eco n o m i c co n d i t io n s . I n ad d i t i o n , t h e p ro d u c t p r i ce

m u s t n o t b e t h e o u t c o m e o f a c o n t in u o u s a u c t io n m a r k e t m e c h a n is m . A u c t io n

p r i ce s c h an g e co s t le s s ly b e t w e en each t r an sac t io n .D a t a o n t h e n ew s s t an d o r co v e r p r ice s o f mag az i n es f it th e s e req u i r emen t s

q u i t e w e l l . T h e p r i ce s ex h i b i t t h e d es i r ed p ro p e r t y o f d i s c r e t e an d i n f r eq u en t

ad j u s t men t , s u g g es t i n g t h a t t h ey a r e n o t t h e r e s u l t o f an au c t i o n mech an i s m.

T he da ta a re read i ly ava i l ab le in l ib ra r ies , and t ran sac t ions ac tua l ly occ ur red a t

these p r i ces .

T h i s p ap e r co n t i n u es w i t h a d e s c r i p t i v e p r e s en t a t i o n o f t h e d a t a o n t h e

n ew s s t an d p r i ce s o f t h ir t y- e ig h t A mer i can mag az i n es o v e r th e p e r i o d f ro m

1 9 5 3 t o 1 9 7 9. Sec t i o n 3 d es c r i b e s a t a rg e t - t h r e s h o l d m o d e l o f a mo n o p o l i st i -

ca l ly compet i t ive f i rm fac ing genera l p r i ce in f l a t ion , an uncer t a in fu tu re andco s t l y n o m i n a l p r i ce ad j u s tmen t . T h e m o d e l i mp l ie s t h a t t h e f i rm w i ll d ev e l o p

a ru le fo r chang ing p r i ces which s t a t es tha t the f i rm' s f ixed nominal p r i ce i s

ch an g ed w h en i t i s f a r en o u g h o u t o f l i n e w i t h cu r r en t co n d i t i o n s . A l o g i s t i c

s p ec i f i ca t i o n o f t h e p ro b ab i l i t y o f o b s e rv i n g a mag az i n e p r i ce ch an g e d u r i n g

a g i v en t i me p e r i o d i s d e r i v ed f ro m t h e mo d e l . T h e e s t i ma t i o n fo cu s es o n

t h e eco n o me t r i c p ro b l ems a s s o c i a t ed w i t h t h e p o s s i b i l i t y t h a t mag az i n es h av e

pr ice change ru les tha t change over t ime. These d i f f i cu l t i es a re addressed by

emp l o y i n g a r a r e l y u s ed b u t v e ry p o w er fu l f i x ed e f f ec t s mo d e l d ev e l o p ed

b y Ch amb er l a i n (1 9 8 0 ,1 9 8 4 ) t o d ea l w i t h d i s c r e t e p an e l d a t a s e t s w h e re

2These hypothesesare all variants of the Ok un (1975,1981) custom er market hypothesis.



S.G. Cecchet ti , The frequency o f pr ice adjus tment 257

u n o b se r v ab le e f f ec t s v a r y b o th ac r oss t im e an d across groups . 3 T h e f o u r t h

sec t io n p r e se n t s e s t im a te s o f t h e m o d e l an d a d i scu ss io n o f th e i r p ro p e r t ie s .

Th e p ap e r p r o v id es two co n c lu s io n s . W h i l e i n t h eo r e t i ca l m o d e l s wh e r e th e

r e l a t io n sh ip b e tw een ag g r eg a te i n f la t io n an d th e f r eq u en cy o f p r i ce ch an g e i s

am b ig u o u s , t h e r e su l t s f o r t h e se d a t a i n d ica t e t h a t p r i ce s h av e ch an g ed m o r e

f r eq u en t ly d u r in g p e r io d s o f h ig h e r i n fl a tio n . 4 I n ad d i t io n , t h e d a t a a r e

in co n s i s t en t w i th a s im p le m o d e l wh e r e th e co s t o f a p r i ce ch an g e is co n s t an t i n

r ea l t e r m s . T h e o b se r v ed in c r ea se s i n f r eq u en cy o f p r i ce ch an g es a r e t o o r ap id

g iven the changes in aggrega te in f la t ion . The i inp l ica t ion o f th is i s tha t the

co s t s o f ch a n g in g p r i ces d ec r ease a s e i th e r th e f r eq u en cy o f ad ju s tm e n t

increases o r the s ize o f a rea l p r ice change decreases . Th is p rov ides an

em p i r i ca l b a s i s f o r t h e co s t t e ch n o lo g ie s a s su m e d b y Ro tem b er g ( 19 82 a, b ) i n

h is s tud ies o f the aggrega te conseq uences o f s t icky pr ices .

2. Descr iption o f magaz ine pr ice data

D a ta we r e co l l ec ted o n th e n ew ss t an d p r ice s o f t h i r ty - e ig h t m ag az in es o v e r

th e p e r io d f r o m 1 9 5 3 to 1 9 7 9 ) ( Th e li s t o f m ag az in es in c lu d ed ap p ea r s i n t h e

ap p en d ix . ) Fo r each m ag az in e , t h e p r i ce o f t h e f i r s t i s su e in each y ea r was

n o te d . I f a m a g az in e ' s p r i ce a t t h e b eg in n in g o f 1 9 7 5 d i f fe r ed f r o m th e p r i ce a t

th e b eg in n in g o f 1 9 7 6 , t h en th e m ag az in e was a s s ig n ed a p r i ce ch an g e d u r in g

1 97 5. As a co n seq u en ce o f t h is p r o ced u r e , t h e f r eq u en c y o f t h e d a t a i s an n u a l . 6

Bef o r e b eg in n in g th e m o r e r ig o ro u s s t at is t ic a l i n v es t ig a t io n o f t h e p r o p e r t i e sof thes e da ta , i t is usefu l to exa m ine som e s imp le sum m ary stat is tics . The se a re

p r e s en te d in t ab l e 1 . F r o m th e fi rs t two co lu m n s o f t h e t ab le i t ap p ea r s t h a t a

m ag az in e i s m o r e l ik e ly to ch a n g e it s p r i ce wh en g en e r a l p r i ce in f l a tio n is h ig h .

Clo se r e x am in a t io n g iv es th e im p r ess io n th a t i n c r ea se s i n t h e n u m b er o f p r ice

ch an g es l ag r ise s i n i n f la t io n b y r o u g h ly o n e y ea r .

Tab le 1 a l so p r e sen t s i n f o r m a t io n o n th e ex p e r i en ce o f m ag az in es wh o se

pr ice changed in a g iven year . As wi l l be a rgued in the nex t sec t ion , i t i s the

ex p e r i en ce o f a f i r m s in ce i t s l a s t p r i ce ch an g e th a t d e t e r m in es i f a p r i ce

3T h e ch o ice o f a l o g l t model, a s o p p o s e d t o a d u r a t i o n m o d e l o f t h e t y p e s t u d i e d i n K i e f e r( 1 9 8 5 ), p r o v id es su b s t a n t i a l f l exib i li t y i n d ea l in g wi th f i xed e f fect s. I n a l t e r n a t iv e ap p r o ach es t h e

in c lu s io n o f i n d iv id u a l o r g r o u p e f fec t s c an b e ex t r em e ly d i ff i cu l t ex cep t i n t h e s im p le s t o f c ases .

4 I n a s tu d y o f t h e p r i ce o f n o o d le s an d in s t an t cof fee i n I s r ae l o v e r th e p e r io d f r o m 1 9 65 to 1 97 8 ,

Sh esh in sk i , T i sh l e r an d W ei ss ( 19 7 9 ) a lso co n c lu d e th a t i n c r ea se s i n i n f la t i o n l ed to m o r e f r eq u en tp r i ce a d ju s tm en t s . B u t t h e n a tu r e o f g o v e r n m en t i n t e r v en t io n in t h e I s r ae l i p r i ce sy s tem su g g es t s

th a t f u r th e r r e se a r ch u s in g m ar k e t - d e t e r m in ed p r i ce s is o f i n t e r e s t .

5 W h i l e m o s t m ag a z in es a r e so ld b y su b sc r ip t io n , n ea r ly o n e - th i r d a r e so ld a s s in g le co p ie s . D a taf r o m t h e M a g a z i n e P u b l i s h e r s A s s o c i a t io n c o v e ri n g t h e p e r io d o f t h e s a m p l e s h o w t h a t a n a v e r a g eo f 2 1 8 m i l l i o n co p ie s o f m ag az in es a r e so ld an n u a l ly . Of t h e se , an av e r ag e o f 6 9 m i l l i o n we r e

s in g le - co p y sa l e s.6 T h e r e a r e so f ew p r i ce ch an g es th a t a n in c r ea sed o b se r v a t io n f r eq u en cy , say q u a r t e r ly , wo u ld

y i e l d m a n y t i m e p e r i o d s w i t h n o c h a n g e s a t a ll.



258 S.G. Cecchetti, The frequenc y of price ad justment

Table 1

Magazine price changes, 1953-1979.a

Average AverageNumber number of Average inflation

of magazines Current years since fixed since

changing price inflation last change price change last change

1953 1 0.2 6.0 14.3 15.7

1954 2 2.2 7.0 27.0 17.9

1955 4 2.8 6.5 21.9 16.4

1956 8 3.8 6.4 31.5 18.31957 12 2.3 8.3 22.9 22.6

1958 4 1.0 9.8 20,2 23.1

1959 2 2.4 3.0 22.5 5.7

1960 1 1.1 14.0 18.2 37.1

1961 3 0.4 3.3 26.1 4.3

1962 5 1.9 9.0 29.1 17.81963 12 1.2 8.0 22.7 14.3

1964 7 0.9 6.0 16.4 10.2

1965 5 1.7 7.4 26.4 10,8

1966 9 4.0 5.2 17.5 10,8

1967 11 2.8 4.6 28.2 9.8

1968 8 4.3 6.9 29.0 18.31969 9 4.9 5.8 21.7 17,2

1970 8 5.0 7.5 25.5 23,6

1971 4 3.4 6.3 28.0 22.21972 4 2.9 5.3 22.6 19.4

1973 8 5.2 5.9 27.3 22.9

1974 19 11.9 4.8 29.4 28.01975 11 7.5 3.6 25.2 24.3

1976 17 4.8 2.9 24.9 18.0

1977 13 5.4 3.5 26.3 20.3

1978 12 8.1 1.8 24.5 12.7

1979 12 8.1 3.1 19.1 22.2

"Calcula tions using newsstand prices of magazines which changed price from first issue of year

to first issue of following year. The magazines used are listed in the appendix. Inflationcomputations use the deflator for gross domestic non-farm product, excluding housing services. Allchanges are measured as percentages.

cha nge s . T he three ser ies reported are for the average t ime s ince the las t chan ge

f o r t h o s e m a g a z i n e s t h a t c h a n g e p r i c e ( t h e le n g t h o f s p e l l s c o m p l e t e d i n a g i v en

year) , 7 the average f ixed pr ice change ac tual ly observed , and the cum ulat ive

aggregate in f la t ion dur ing that per iod . Severa l in t eres t ing conc lus ions emerge

from these data . F irs t , over the en t ire sample per iod there was an increase in

t h e n u m b e r o f c h a n g e s a l o n g w i t h a d e c r e a s e i n t h e a v e r a g e l e n g t h o f a

c o m p l e t e d s p e l l . A t t h e s a m e t i m e , t h e a v e r a g e s i z e o f t h e f i x e d p r i c e c h a n g e

rem aine d remarkab ly s tab le, w h i le the cum ulat ive aggregate in f la t ion fi rs t

7To facilitate this computation, for each magazine data was collected on the data of the price

change prior to 1953.



S.G. Cecchetti, The requency of price adjustment 259

d e c r e a s e d i n t h e 1 9 6 0 's a n d t h e n i n c r e a s e d in t h e 1 9 7 0's . T h e a c t u a l q u a n t i t y o f

g en e ra l p r i ce i n f l a t i o n b e t w een p r i ce ch an g e s is q u i t e s t r i k in g . As i n f l a t i o n

i n c r e a s e d i n t h e 1 9 7 0 ' s m a g a z i n e s a l l o w e d t h e i r r e a l p r i c e s t o e r o d e b y n e a r l y

o n e - q u a r t e r . T h i s i s e v i d e n c e o f i n c r e d i b l e p r i c e s t i c k i n e s s w h i c h c a n o n l y b e

as s o c i a t ed w i t h h i g h co s t s o f f i x ed p r i ce ch an g es . I t i s v e ry u n l i k e l y t h a t t h e

a d m i n i s t r a t i v e c o s t s o f a c t u a l l y c h a n g i n g p r i c e s c a n e x p l a i n t h i s . T h e o b v i o u s

e x p l a n a t i o n i s t h a t e a c h m a g a z i n e f e a r s t h a t i f i t ' m o v e s ' f i r st to a d j u s t i ts p r ic e

fo r i n f l a t i o n , i t w i ll ra i s e it s r e la t i v e p r i ce ab o v e t h a t o f t h e c o m p e t i t i o n , lo s i n g

s a l e s . T h e d e g r e e o f m a g a z i n e p r i c e s t i c k i n e s s p r o v i d e s s t r o n g s u p p o r t f o r

s t i c k y p r ic e t h e o r i e s b a s e d o n m o n o p o l i s t i c c o m p e t i t io n .

3 . S p e c i f i c a t i o n o f t h e m o d e l

E x p l i c i t m o d e l i n g o f t h e t i m i n g o f a f i rm ' s p r ic e c h a n g e i s e x t re m e l y d i ff ic u l t.

T h e d e c i s i o n t o c h a n g e a p r i c e i n t h e p r e s e n c e o f a d j u s t m e n t c o s t s a n d a n

u n c e r t a i n f u t u r e i s t he s o l u t io n t o a s to c h a s ti c d y n a m i c p r o g r a m m i n g p r o b le m .

T h e p r o b l e m i s c o m p l i c a t e d b y t h e f a c t t h a t a f i rm k n o w s t h a t i t c a n u p d a t e i t s

e x p e c t a t i o n s i n l a t e r p e r i o d s , c o r r e c t i n g a n y m i s t a k e s i t m a y h a v e p r e v i o u s l y

m a d e . W h i l e t h e r e p e a t e d n a t u r e o f t h e p r o b l e m s i m p l i f i e s i t c o n s i d e r a b l y , i t

a l l o w s o n l y a c h a r a c t e r i z a t i o n o f lo n g - t e r m a v e r a g e b e h a v i o r .

I w a i ( 1 9 81 ) h a s e x a m i n e d t h e f ir m ' s p r ic e a d j u s t m e n t p r o b l e m u s i n g a

t a r g e t - t h r e s h o l d m o d e l o f t h e t y p e d e v e l o p e d b y M i l l e r a n d O r r ( 19 6 6) i n th e i r

s t u d y o f t h e d e m a n d f o r m o n e y . 8 F a c e d w i t h c o s ts o f c h a r g i n g a p r ic e d i f f e r e n t

f r o m t h e s h o r t - t e r m p r o f i t -m a x i m i z i n g p r ic e , a n d c o s t s o f c h a n g i n g it s n o m i n a l

p r i ce , t h e f i rm d ev e l o p s a ru l e t h a t g o v e rn s i t s p r i ce ch an g es . Th i s ru l e s t a t e s

t h a t w h e n t h e f i x e d n o m i n a l p r i c e , P ( t ) , i s f a r e n o u g h a w a y f r o m t h e

s h o r t - t e r m o p t i m a l p r i ce , P * ( t ) , t h e p r ic e w i l l b e c h a n g e d . 9 T h e s h o r t - t e r m

o p t i m a l p r i c e i s t h e p r i c e t h a t w o u l d b e s e t i f p r i c e c h a n g e w e r e c o s t l e s s a n d

c o n t i n u o u s .

T h e f i r m ' s p r i c e c h a n g e r u l e c a n b e c h a r a c t e r i z e d b y t h e m a x i m u m d i s t a n c e

P * ( t ) w i l l b e a l l o w e d t o d e v i a t e f r o m P ( t ) b e f o r e t h e p r i c e is c h a n g e d . D e f i n e

t h e f i r m ' s m e a s u r e o f d i s e q u i l i b ri u m z t = l o g ( P * ( t ) / P ( t ) ) , h c t o b e t h e m a x i -m u m v alu e z t can a t t a i n b e fo re t h e p r i ce i s ch an g ed , t h e b a r r i e r , a n d h o to b e

t h e d i s t a n c e f r o m P * ( t ) a t w h i c h P ( t ) i s s e t wh en i t i s ch an g ed , t h e r e t u rnp o i n t . 1°

T o b e s t u n d e r s t a n d h o w t h i s w o r k s , t a k e a n e x a m p l e w h e r e t h e f i r m ' s

e n v i r o n m e n t i s s ta b l e s o t h a t t h e p r i c e c h a n g e r u l e is c o n s t a n t . B e g i n n i n g w i t h

~Sheshinski and W eiss (1977,1983) derive a gene ral set of con dition sunde r wh ich it is optimalfor a firm to adop t a target-thresholdpricing policy, often referred to as (s, S).

9For a rigorous and complete treatment, the reader is referred to lwa i (1982), particularlych. 6,along w ith its appendices and supplement.

1°Depending on the firm's oss function and discount rate, ho ma y be set equal to zero.



260 S.G. Cecchet ti , The frequency o f pr ice adjus tment

t h e o b s e rv a t i o n o f a p r i ce ch an g e a t t = 0 , t h e f i x ed p r i ce i s se t s o t h a t z 0 = h 0 ,

o r l o g P ( 0 ) = l o g P * ( 0 ) - h 0. U n d e r t h e u s u a l c i rc u m s t a n c e s w i t h a p o s i ti v e

ag g reg a t e i n f l a t i o n r a t e , t h e f i x ed p r i ce i s s e t ab o v e P * s o h 0 i s n eg a t iv e . As

t i m e p r o c e e d s , P * g r o w s s t e a d i ly u n t i l it e x c ee d s t h e le v el p r e s c r i b e d b y t h e

r u l e . W h e n t h e c h a n g e i n P * e x c e e d s t h e d i s t a n c e f r o m t h e r e t u r n p o i n t t o t h e

b a r ri e r, s o l o g P * ( t ) - l og P * ( 0 ) > ( h c - h 0 ) , t he p r ic e i s c ha n g ed . T h e n e w

p r i c e l o g P(t) eq u a l s l o g P* - h 0 = l o g P (0 ) + (h e - h o ) . 11

I t i s c l e a r f r o m t h is e x p o s i t i o n t h a t t h e p r o b a b i l i t y o f o b s e r v i n g a f ix e d p r i c e

c h a n g e c o r r e s p o n d s t o t h e p r o b a b i l i t y t h a t t h e m e a s u r e o f d i s e q u i l i b r iu m z t

e x c e e d s t h e b a r r i e r h e , o r t h a t l o g P * h a s t r a v e l e d m o r e t h a n t h e d i s t a n c e

( h e - h 0 ) . I n a s t o c h a s t i c s t e a d y st a te , I w a i h a s s h o w n t h a t t h e p r o b a b i l i t y o f

s e e i n g a p r i c e c h a n g e d e p e n d s o n t h e l o n g - r u n e x p e c t e d r a t e o f c h a n g e o f t h e

s h o r t - t e r m o p t i m a l p r i c e a n d t h e v o l a t i li t y o f s a le s ( t h e d r i f t a n d v a r i a n c e i n

P* ) , a s we l l a s t h e co s t o f ch an g i n g p r i ce s . B u t s i n ce an i n c rea s e i n i n f l a t i o n ,

f o r r e a l a d j u s t m e n t c o s t s f ix e d , l e a d s t o a c h a n g e i n t h e p r i c e c h a n g e r u l e w h i c h

i s r ep re s en t ed b y a g ro w t h i n t h e d i s t an ce (h c - h 0 ) , a s we l l a s an i n c rea s e i n

t h e s p e e d a t w h i c h P*(t) m o v e s , o n e c a n n o t d e t e r m i n e w h e t h e r h i g h e r

i n f l a t i o n l e a d s t o a n i n c re a s e i n t h e p r o b a b i l i t y o f o b s e r v i n g a p r ic e c h a n g e .

B u t I w a i d o e s s h o w u n a m b i g u o u s l y t h a t a s t h e c o s t o f p r ic e c h a n g e d e c l in e s ,

t h e d i s t a n ce (h c - h 0 ) , f ro m t h e r e t u rn p o i n t t o t h e b a r r i e r , f a l l s a s we ll .

A n e m p i r i c a l s p e c i fi c a ti o n o f t h e p r o b a b i l i t y o f s e e in g a m a g a z i n e p r i c e

c h a n g e c a n b e d e v e l o p e d f r o m t h is d is c u s si o n . T h i s c a n b e d o n e s o a s to y i e l d

i n f o r m a t i o n n o t o n l y a b o u t t h e e ff e c ts o f in f l a ti o n , b u t a l so a b o u t t h e p r ic ec h a n g e r u l e i ts e l f. T h e r e a r e t w o a p p r o a c h e s t h a t c a n b e t a k e n . T h e f ir st d e r i v e s

a s p e c i f i c a t i o n d i r e c t l y f r o m t h e t h e o r e t i c a l w o r k . T h e I w a i m o d e l is a c h a r -

a c t e r i z a t i o n o f b e h a v i o r i n a s t o c h a s t i c s te a d y s t a te . I f o n e w e r e i n a s t o c h a s t i c

s t e a d y s t a t e w h e r e t h e t r a n s i t i o n p r o b a b i l i t i e s a r e c o n s t a n t , t h e p r o b a b i l i t y o f

o b s e r v i n g a p r i c e c h a n g e w o u l d d e p e n d o n l y o n t h e e x p e c t e d r a te o f c h a n g e in

t h e s h o r t - t e r m o p t i m a l p r ic e a n d t h e v o l a t il i ty o f s al es . T h e s t e a d y s t a t e

a s s u m p t i o n w o u l d m a k e t h e p r o b a b i l i t y o f a p a r t i c u l a r f i r m c h a n g i n g i t s p r i c e

i n d e p e n d e n t o f t h a t f i r m ' s h i s t o r y . O n e w o u l d b e a b l e t o c o l l e c t d a t a t h a t w a s

c o n s i s t e n t w i t h t h e i n t e r p r e t a t i o n o f t h e m o d e l a s r e p r e s e n t i n g l o n g - t e r ma v e r a g e b e h a v i o r . W i t h d a t a o n i n d i v i d u a l f i r m p r i c e s , t h i s w o u l d s u g g e s t

e s t i m a t i o n o f a p r o b a b i l i ty m o d e l w i t h i n f l a t i o n a n d s a le s v o l a ti l it y a s t h e o n l y

i n d e p e n d e n t v a r ia b le s .

I f p r i c e s c h a n g e d f r e q u e n t l y r e l a ti v e to c h a n g e s i n t h e e c o n o m i c e n v i r o n -

m e n t , t h e d a t a o n p r ic e c h a n g e s w o u l d c o m e f r o m a s e q u e n c e o f s t e a d y s ta t es

a n d t h i s s i m p l e a p p r o a c h w o u l d b e s e n s i b l e . T h e r e p o r t e d r e s u l t s i n s e c t i o n 4

i n c l u d e s u c h a s p e c i f i c a t i o n . B u t s i n c e t h e a m o u n t o f s h o r t - t e r m i n f l a t i o n , a s

11 The complete version of the model would include 'a floor barri er' in addi tion to the ceiling

barr ier h c. But since no do wnward adjus tments are observed in the data, this has been omitted.



S.G. Cecchetti , The frequency o f price adjustment 261

r ep o r t ed i n t ab l e 1 , f l u c t u a t e s d rama t i ca l l y r e l a t i v e t o t h e t i me b e t w een

mag az i n e p r i ce ch an g es , i t i s u n l i k e l y t h a t t h e s t ead y s t a t e mo d e l i s ap -

p ro p r i a t e . T o m ak e t h e p o i n t m o re ex p l ic i tl y , n o t i ce f ro m t ab l e 1 t h a t i n 1 9 7 0

e i g h t mag az i n es ch an g ed t h e i r p r i ce s a f t e r an av e rag e p e r i o d o f s ev en an d o n e

hal f yea rs . D ur in g the seven years f rom 1963 to 1970, annual in f l a tion

f luc tua ted f rom 1% to 5%. Th is sugges t s tha t p r i ces changed in f requen t ly

re l a ti v e t o ch an g e s i n t h e eco n o mi c en v iro n m en t an d l ead s to t h e co n c l u s io n

t h a t t h e p e r i o d u n d e r co n s i d e ra t i o n i s n o t mad e u p o f man y d i f f e r en t s t ead y

s ta tes .

A n a l t e rn a t iv e p ro ced u re b eg in s b y n o t i n g t h a t a f irm ' s p r i ce ch an g e d ec i s io n

d ep en d s o n t h e d i s t an ce P* h as mo v ed s i n ce i t s l a s t p r i ce ch an g e , an d t h e

d i s t an ce f ro m t h e r e t u rn p o i n t t o t h e b a r r i e r a s s p ec i f i ed b y t h e cu r r en t ru l e .

T h e p ro b ab i l i t y o f v i ew i n g a p r i ce ch an g e t h en d ep en d s o n t h e r ea l i zed p a t h

fo l l o w e d b y P * d u r i n g t h e t ime t h e n o mi n a l p r i ce i s u n ch an g ed . T h e p ro b l em

tha t a r i ses in th i s in te rp re ta t ion i s tha t the ru le may change over t ime. But as

Iwai has sugges ted , in the shor t run , the f i rm' s ru le i s p robab ly an a r t i fac t o f

l o n g - t e rm ex p ec t a t i o n s h e l d s o m e t ime i n t h e p as t . T h e s p ec if ica t io n d ev e l o p ed

b e l o w i s ab l e t o acco u n t fo r t h e t y p e o f g r ad u a l ch an g e t h i s imp l ie s .

T o p ro ceed , d e f i n e y , t o b e o n e i f mag az i n e i ch an g ed p r i ce a t t i me t ,

A l o g P* ( i , t ) t o b e t h e ch an g e i n t h e s h o r t - t e rm o p t i ma l p r i ce s i n ce t h e l a s t

n o mi n a l p r i ce ch an g e , an d [ h e ( i , t ) , h o ( i , t ) ] to be the i th magaz ine ' s ru le a t

t i me t . T h en ,

P r ( Y i t = 1 ) = P r{ A l o g P ' ( i , t ) > h e ( i , t ) - h o ( i , ? )} , ( 1 )

where ? i s the t ime o f the l as t p r i ce change , so ho( i , ? ) i s the re tu rn po in t f rom

the ru le in e f fec t wh en the p r i ce was l as t changed . Eq . (1 ) s t a t es tha t wh en the

d i s t an ce t h e s h o r t - t e rm o p t i ma l p r i ce h as t r av e l ed ex ceed s t h e d i s t an ce f ro m

the p re v iou s re tu rn po in t to the c ur ren t bar r i e r , the f irm chan ges i t s p ri ce . 12

A n ap p ro a ch s imi l a r to R o t em b erg (19 82 a, b ) can b e u s ed t o d ev e l o p a

m o d e l fo r P* . A s s u m e th a t e ach f irm i is a mo n o p o l i s t ic co m p e t i t o r w i t h

d e m an d an d co s t fu n c t io n o f th e fo ll o w i n g fo rm:

Q d ( i , t ) = [ P ( i , t ) / P ( t ) ] a X ( t ) b , (2 )

a n d

C ( Q ( i , t ) ) = A e a ' Q ( i , t ) ~ w ( t ) , (3 )

w he re P i s the aggrega te p r i ce l eve l, X ( t ) i s to tal indust ry sales , e 8 t represen t s

t ech n o l o g i ca l ch an g e , w ( t ) i s inpu t p r i ces, and a , b , A , and a a re cons tan t s .

12This is exactly the sam e as stating tha t the p roportional differencebetween P * ( t ) a n d P ( t )exceeds hc.



2 6 2 S.G. Cecch etti , Th e frequency of price adjustm ent

Subs t i tu t ing (2 ) in to (3 ) a l lows fo rmat ion o f the f i rm' s p ro f i t func t ion . Tak ing

the der iv a t ive o f p ro f i t s wi th respe c t to the p r i ce , se t t ing the resu l t equa l to zero

an d s o l v i n g fo r P ( i , t ) , y i e ld s l o g P* ( i , t ) . T h en , a s s u mi n g f f an d w ( t ) c h a n g e

a t the same cons tan t ra te ~r , and add ing a s tochas t i c e r ro r u it t o r ep re s en t

co m p o n en t s o f P * n o t d ir ec t ly i n c l u d ed i n (2 ) an d (3 ), A l o g P * ( i , t) c an b e

w r i t t en a s

A l o g P * ( i , t ) = b o T it + b l ( e r T ) i , + b z f ( i t + u it , ( 4 )

w her e T , i s the t ime s ince the l as t p r i ce change fo r magaz ine i , ( ¢ r T ) i t is

cumula t ive in f l a t ion s ince the l as t p r i ce change , and S(i t i s the cumula t ive

cha nge in in du s t ry sa les s ince the l as t p r ice change fo r the i th magaz ine . 13

In c l u d ed i n t h e e r ro r t e rm u it are f irm- and t ime-spec i f i c m easures o f cos t s and

d eman d w h i ch a r e n o t r ead i l y o b s e rv ab l e .Sp ec i f i ca t io n o f eq . (1 ) fo r th e p u rp o s es o f e s t ima t i o n can b e ca r r i ed o u t b y

def in ing

S i t = A l o g P * ( i , t ) - ( h c ( i , t ) - h 0 ( i , t ' ) )

= a i r + b o T i t + b l ( ' / / ' Z ) i t + b 2 f ( i t + u i t . ( 5 )

T h e q u a n t i t y a it r ep re s en t s i n fo rma t i o n ab o u t mag az i n e i ' s p r i ce ch an g e ru l e

a t t i me t . A s s u mi n g u it has a cumula t ive log i s t i c d i s t r ibu t ion , then

P r (y it = 1 ) = F ( ~ , ) , (6 )

w he re F s ign i f ies the log i s ti c func t ion and ~ t = S i t - u i t .1 4 O b v i o u s l y f o r a it to

b e i d en t i f i ed , i t c an n o t b e p e rmi t t ed t o ch an g e fo r each mag az i n e fo r ev e ry

t ime per iod . In wh at fo l lows iden t i f ica t ion i s ach ieved b y assum ing tha t " the

co n s t an t a s s o c i a t ed w i t h a mag az i n e t ak es o n t h e s ame v a l u e i n n o n -o v e r l ap -

p i n g t h r ee -y ea r p e r i o d s .

Subs t i tu t ing eq . (5 ) in to (6 ) y ie lds the model fo r es t imat ion . I t has thech a rac t e r i s t i c t h a t t h e p ro b ab i l i t y o f o b s e rv i n g a mag az i n e p r i ce ch an g e o n a

g i v en d ay d ep en d s o n a f i rm ' s h i s t o ry , o r p a t h , p r i o r t o t h a t d ay . T h e mo d e l

d e c o m p o s e s t h e p r o b a b i l it y o f o b se r v in g a p r i c e c h an g e i n t o a c o m p o n e n t t h at

can b e ex p l a i n ed b y ru l e ch an g es an d a co mp o n en t t h a t c an b e ex p l a i l f ed b y

ch an g es i n t h e mo v emen t o f P* . Ch an g es i n t h e co n s t an t t e rm a it in eq. (5)

r ep re s en t ch an g es i n t h e d i s t an ce (h c ( i , t ) - h o ( i , ?) ) bo th across magaz ines

13 T h e t e r m i n e q . ( 4) f o r t h e t i m e s i n c e t h e l a s t p r i c e c h a n g e , T it , m a y r e p r e s e n t a t r e n d i n

d e m a n d a s w e l l a s t e c h n o l o g ic a l c h a n g e . T o s e e w h y , n o t e t h a t i n c lu s i o n o f a n e x p o n e n t i a l t i m e

t r e n d i n ( 2 ) l e a d s t o e x a c t l y t h e s a m e e x p r e s s i o n .14 S e e C h a m b e r l a i n ( 1 9 8 0 ,1 9 8 4 ) f o r a d i s c u s s i o n o f t h e u s e o f t h e l o g i s ti c d i s t r i b u t i o n i n d i s c r e t e

d a t a a n a l y s i s .



S.G. Cecchetti, The frequen cy of price adjustmen t 263

a n d o v e r t i m e . A n d t h e b , ' s a r e r e l a t e d t o t h e s h o r t - r u n c h a n g e s i n t h e

p r o b a b i l i t y o f o b s e r v i n g a p r ic e c h a n g e , h o l d i n g t h e p r i c e c h a n g e r u l e f ix e d .

T h e m o d e l s p e c i f i e d i n ( 5 ) c a n b e m o d i f i e d t o i n c l u d e t h e i n f o r m a t i o n

c o n t a i n e d i n t h e m a g a z i n e ' s p r e v i o u s fi x ed p r i c e c h a n g e , A l o g P ( i , 1 ). N o t e t h a t

A l o g P ( i , t ' ) = h c ( i , i ) - h o ( i , ~ ) , (7 )

SO

a , + a l o g P ( i , t ' ) = h e ( i , i ) - h c ( i , t ) . ( 8 )

Th en , d e f i n i n g a~ t = a , + A l o g P( i , ? ), an d s u b s t i t u t i n g t h e r e s u lt i n t o eq . (5) , a

n e w s p e c i f i c a t io n c a n b e d e r i v e d w i t h t h e p r e v i o u s f ix e d p r i c e c h a n g e a d d e d t o

t h e o r i g i n a l s e t o f r i g h t -h an d - s i d e v a r iab l e s . Fo r t h i s c a s e (5 ) can b e r ew r i t t ena s

S i t = a ~ - A l o g P ( i , i ) + b o T i , + b l ( ~ r T ) , + b 2 f ( i t + u , . ( 9 )

T h e n e w c o n s t a n t t e r m , a i * , i s a m e a s u r e o f th e d i s t a n c e f r o m t h e c u r r e n t

c e i l i n g b a r r i e r t o t h e o n e i m p l i e d b y t h e p r e v i o u s p ri c e c h a n g e .

' * ' a n d c o n s e q u e n t l y t h e p r i c en o r d e r t o a ll o w b o t h t h e a , s a n d t h e a i r s,

c h a n g e r u le , t o v a r y b o t h a c r o ss m a g a z i n e s a n d o v e r t im e , a p a r t i c u l a r f o r m o f

a l o g i s t i c m o d e l i s u s ed . In h i s s t u d y o f t h e an a l y s i s o f co v a r i an ce i n d i s c re t ed a t a m o d e l s , C h a m b e r l a i n ( 1 9 8 0 , 1 9 8 4 ) d e s c r i b e s a t e c h n i q u e d e s i g n e d t o

h a n d l e w h a t h e c a l l s f ix e d i n d i v i d u a l o r g r o u p e ff e ct s. P r o b le m s o c c u r i n p a n e l

d a t a s e ts w h e r e s m a l l g r o u p s o f o b s e r v a t i o n s a r e k n o w n t o b e r e l a t e d , h a v i n g

s p e c i a l c h a r a c t e r i s t i c s t h a t c a n n o t b e d i r e c t ly o b se r v e d . T h i s r e l a t i o n s h i p is t h e

f i x e d e f f e c t . E x a m p l e s a r e r e a d i l y a p p a r e n t i n a p p l i c a t i o n s u s i n g l o n g i t u d i n a l

d a t a w h e r e a g r o u p i s a n i n d i v i d u a l o r a f a m i l y . A s C h a m b e r l a i n p o i n t s o u t ,

w h e n p e r s o n a l c h a r a c t e r i s t i c s a r e c o r r e l a t e d w i t h t h e e x p l a u a t o r y v a r i a b l e s ,

s t a n d a r d e s t i m a t i o n t e c h n i q u e s f a i l t o i d e n t i f y t h e c o e f f ic i e nt s r e l a t e d t o t h e s e

v a r i a b l e s . H e t h e n p r o p o s e s a p r a c t i c a l w a y t o c o n t r o l f o r t h e s e f i x e d e f f e c t st h e r e b y c i r c u m v e n t i n g t h e p ro b l e m .

I n t h e f r a m e w o r k o f t h e m a g a z i n e p ri c e m o d e l a ' g r o u p ' i s a se ri es o f

a d j a c e n t y e a r s f o r a g i v e n m a g a z i n e d u r i n g w h i c h t h e p r i c e c h a n g e r u l e i s

a s s u m e d n o t t o c h a n g e . O n e a p p r o a c h t o d e a l i n g w i t h t h i s w o u l d b e t o a l l o w

t h e c o n s t a n t t e r m t o v a r y f r o m g r o u p t o g r o u p, i n c l u d in g a d u m m y v a ri a bl e

f o r e a c h . W h e n t h e re a r e a la r ge n u m b e r o f g r o u p s a n d o n l y a sm a l l n u m b e r o f

o b s e r v a t i o n s i n e a c h , t h i s i n v o lv e s m a s s i v e c o m p u t a t i o n . I n t h e s t a n d a r d c a se ,

o n e w o u l d s i m p l y c ho o s e e st im a t e s o f th e a ' s a n d b ' s t o m a x i m i z e lo g L =

E i E t l o g F ( ~ / ) . C h a m b e r l a i n n o te s t h a t w h e n F i s a lo g is ti c f u n c t io n , th e s u m

o f t h e d e p e n d en t v a r i ab l e s w i t h i n a g ro u p i s a s u ff i c ien t s t a t i s ti c fo r t h e f ix ed

e f f e c t, o r g r o u p - s p e c i fi c c o n s t a n t t e r m . T o s ee h o w t h is w o r k s , la b e l a g r o u p o f



26 4 S.G. Cecchetti, The frequenc y of price adjustmen t

o b s e r v a t i o n s f o r m a g a z i n e i o v e r w h i c h t h e c o n s t a n t t e r m i s t h e s a m e b y j a n d

i t s a s s o c i a t e d c o n s t a n t a ~ j . T h e n t h e s u m o f t h e v a l u e o f t h e d e p e n d e n t

v a r i a b l e o v e r t h e g ro u p , c a l l t h i s ~ j , i s a s u f f ic i en t s t a t i s t ic fo r a i j . I f , f o r

e x a m p l e , a s e t o f o b s e r v a t i o n s i s o n e m a g a z i n e f o r t h r e e y e a r s , t h e n a , j

r e p r e s e n t s t h e c o n s t a n t f o r th a t p o r t i o n o f t h e p a n e l d a t a s e t a n d t h e s u m ~ i j i s

t h e n u m b e r o f p r i c e c h a n g e s t h a t o c c u r r e d o v e r t h a t p e r i o d . C h a m b e r l a i n

s h o w s t h a t m a x i m i z i n g l o g L is th e s a m e a s m a x i m i z i n g t h e c o n d i ti o n a l

l i k e li h o o d l o g L c = ~ ~ t l ° g G ( ~ t ) w h e r e G ( ~ , ) = P r ( y i, I ~ i j ) a n d t h e ob s e rv a -

t i o n a t t i m e t i s i n g r o u p j . S o m e t h o u g h t r e ve a ls t h a t f o r m u l a t i o n o f l o g L c

w i l l e n t a i l t h r o w i n g o u t a n y c e l l s w h e r e a l l y , ' s a re t h e s am e , s o .t h ei r s u m i s

e i t h e r ze ro o r t h e s i ze o f t h e ce l l . Th es e ce l l s a r e d eg en e ra t e ; t h e l i k e l i h o o d o f

o b s e r v i n g a p a r t i c u l a r o u t c o m e a t a g i v e n ti m e is c o m p l e t e l y d e t e r m i n e d g i v e n

t h i s s u m .

I t i s i m p o r t a n t t o u n d e r s t a n d t h e n a t u r e o f t h e c o n d i t i o n a l l i k e l i h o o d

fu n c t i o n t h a t i s u s ed i n t h e f i x ed e f f ec t s e s t i m a t i o n . F i r s t , i t i s o n l y a fu n c t i o n

o f t h e s l o p e p a ram e t e r s , t h e b ' s i n eq s . (5 ) an d (9) , an d n o t t h e f i x ed e f f ec ts

t h e m s e l v e s . T h e a 's , w h i c h a r e t r e a t e d a s n u i s a n c e p a r a m e t e r s , a r e i n t e g r a t e d

o u t . T h e y a r e n e v e r e s t i m a t e d . T h e c o n d i t i o n a l l i k e l i h o o d f u n c t i o n a n d t h e

u n c o n d i t i o n a l l i k e l i h o o d f u n c t i o n o f t h e s t a n d a r d l o g i t e s t i m a t i o n a r e n o t

c o m p a r a b l e . T h e y n e e d n o t b e o f t h e s a m e o r d e r o f m a g n i t u d e . I n f a c t ,

w h e n e v e r d e g e n e r a t e c e l l s e x i s t , t h e p r o b a b i l i t y o f o b s e r v i n g t h e s u m , P r ( ~ q ) ,

c a n n o t b e c o m p u t e d a n d c a l c u l a t i o n o f t h e v a l u e o f t h e u n c o n d i t i o n a l l i k e l i -

h o o d w i l l n o t b e p o s s i b l e .

4. Empirical results

T h e m o d e l d e v e l o p e d i n th e la s t s e c ti o n w a s e s t i m a t e d u s i n g d a t a o n c h a n g e s

i n t h e n e w s s t a n d p r i c e s o f m a g a z i n e s . T h e C h a m b e r l a i n f ix e d e f fe c ts l o g is t ic

f o r m u l a t i o n w a s u s e d . T h e c o n s t a n t t e r m w a s a l l o w e d t o c h a n g e f o r e a c h

m a g a z i n e e v e r y t h r e e y e a r s . 15 T h e r e a r e a t o t a l o f 3 18 c o n s t a n t t e r m s f o r t h e

9 5 4 o b s e r v a t i o n s i n t h e s a m p l e . T h i s is e q u i v a l e n t t o a l l o w i n g e a c h m a g a z i n e t o

r e v i s e i t s p r i c e c h a n g e r u l e a t m o s t o n c e i n e a c h t h r e e - y e a r p e r i o d , o r u p t on i n e t i m e s o v e r t h e t w e n t y - s e v e n y e a r s c o v e r ed i n t h e s a m p l e .

Ta b l e 2 p re s e n t s t h e e s t i m a t e s fo r f iv e s p ec i f i ca t io n s o f t h e m o d e l . A l l u t il i z e

t h e C h a m b e r l a i n t e c h n i q u e ) 6 T h e r e su l ts f o r e a c h m o d e l i n c lu d e t h e p a r a m e t e r

e s t i m a t e s , t h e b ' s , w i t h t h e i r a s y m p t o t i c t - s t a t i s t i c s i n t h e l e f t h a l f o f e a c h

c o l u m n , a n d t h e e s t i m a t e d s l o p e o f t h e p r o b a b i l i t y a t t h e r e g r e s s o r m e a n s , t h e

' s , i n t h e s ec o n d h a l f . An i n d i v i d u a l ~,~ i s d e f i n ed a s t h e d e r i v a t i v e o f t h e

~5 T h e l en g th o f t h e p e r io d w as ch o sen to b e sm a l l en o u g h to a l l o w f l ex ib if i ty i n t h e sp ec i f i c a tio n ,l a r g e e n o u g h s o t h a t t h e r e m a i n i n g p a r a m e t e r s c o u l d b e e s t i m a t e d w i t h p r e c is i o n, a n d b e c a u s e i t is

a n i n t e g e r d i v i s o r o f t w e n ty - s ev e n , t h e n u m b e r o f y e a r s i n t h e s a m p l e . E x p e r i m e n t a t i o n w i t h t w o -an d f o u r - y ea r p e r io d s y i e ld ed s im i l a r r e su l t s .

1 6 Newto n ' s m e th o d was u sed to o b ta in t h e e s t im a te s . See Gr een e ( 1 9 8 3 ) .



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2 6 6 S .G. Cecchett i, The f requency o f pr ice ad justm ent

probabil ity with respect to X , evaluated at the mean of the data set, and

equals b iP(1 - P) , where P is the average probability of observing a price

change in the data set as a whole. The asymptotic t-statistics for the $'s arealso reported. 17

The first column of table 2 presents results for the steady state model that

implies the probability of observing a price change should depend on inflation

and sales volatility alone. This model was estimated using the fixed effects

formulation both for comparability with the path-dependent versions and to

allow differences across magazines. The log likelihood value of -181.30 is

barely different from the value of - 182.37 computed when the parameters are

constrained to zero. 18 Along with the theoretical arguments in the previous

section, this is evidence that the steady state model is inappropriate for the

study of magazine price changes.

The second and third columns of table 2 report estimates based on the pathdependent model of eqs. (5) and (6). Column (3) includes AlogP(i, ~') as a

right-hand-side variable. The fourth and fifth columns of the table combine the

steady state and path-dependent models by adding current inflation and sales

volatility to the variables representing AlogP*. The combined models are

attempts to include the determinants of the price change rule directly in the

specification to be estimated. They are a type of reduced form. 19 The values of

the log likelihood function suggest that the four path-dependent models are

substantially better at explaining the data than is the steady state model. 2° The

estimates represent the short-run response of the probability to changes in thethree variables in the model. These are short-run changes since the computa-

tions presume that the price change rule is fixed.

Several conclusions are immediately apparent. First, an increase in the time

since the last price change by one year increases the probabili ty of a price

change by a substantial amount, between 0.13 and 0.18. This increase holds

fixed the amount of cumulative inflation experienced over the period since the

last change, so it reflects technological change in production as well as secular

demand shifts.

The evidence on the effect of inflation on the probability of observing a pricechange appears mixed. Models (2) and (3) predict that if a magazine experi-

1 7 N o t e t h a t s i n c e P = F ( X b ) , c o m p u t a t i o n o f t h e s t a n d a r d e r r o r s i s n o n - tr i v ia l .

1 8A n e x p e r i m e n t w a s p e r f o r m e d w h e r e c u r r e n t i n f la t io n w a s r e p l a c ed b y a t h r e e - y e a r l a g g e d

m o v i n g a v e r a g e . T h e r e s u l t s w e r e n e a r l y i d e n ti c a l.

L gA s i s d i s c u s s e d b e l o w , i f t h e r u l e i s t r u l y l i n e a r i n c u r r e n t i n f l a t io n a n d s a l e s v o la t i li t y , t h e n t h e

C h a m b e r l a i n t e c h n i q u e w o u l d b e u n n e c e s s a r y . T h e c o n s t a n t w o u l d n o t v a r y a t l e a st o v er t i m e .

A l l o w i n g t h e c o n s t a n t t o v a r y a l lo w s t h e s p e c if i ca t io n o f t h e d e t e r m i n a n t s o f t h e r u le t o b e m o r e

c o m p l e x t h a n a s i m p l e f ix e d l i n e a r fu n c t i o n .

2 ° S t a t is t i ca l c o m p a r i s o n o f t h e s t e a d y s t at e m o d e l w i t h t h e o t h e r m o d e l s in t a b l e 2 w o u l d r e q u i r ed e v e l o p m e n t o f a t e s t f o r n o n - n e s t e d li m i t e d d e p e n d e n t v a r i a b le m o d e l s . W h i l e it m a y b e p o s s i b l e

t o w o r k o u t a t e s t f o r t h e c a s e u n d e r c o n s i d e r a t i o n , it is b e y o n d t h e s c o p e o f t h i s p a p e r .



S.G. Cecchet ti , The frequency o f pr ice adjus tment 26 7

enc es h igher in f la t ion for any yea r s ince it s l as t p r ice change, the pro ba bi l i ty of

i t s p r ice cha nging wi l l increase unam biguo us ly . In fac t , a s ing le yea r wi th jus t

f ive pe rcen t age po i n t s m ore i n f la t ion wi l l i nc rease t he p roba b i l i t y by t he $ fo r

r rT of 1 .95 , t ime s 0 .05 , o r near ly 0 .1 . Bu t the es t imates o f mo dels (4) and (5) t e ll

a d i f feren t s tory . They pred ic t tha t a f ive percentage poin t increase in in f la t ion

fo r o ne yea r w i ll i n it ia l ly l ower t he p ro bab i l i t y by 0 .05 be l ow whe re i t wou l d

have been . (This i s the sum of the $ ' s for ~rT and r r t imes 0 .05 . ) Then in the

fo l lowing year , the probabi l i ty wi l l r i se 0 .15 above where i t would have been .

Acco rd i ng t o t he com bi ned m ode l , t he t i m e pa t h o f t he i n f l a t i on i nc reasesm at te rs . 21

Use o f t he C ham ber l a i n t echn i que can be t e s t ed aga i ns t s eve ra l i n t e res t i ng

a l t e rna t i ves . One m i gh t t h i nk t ha t t he s t ruc t u re o f t he cons t an t t e rm , and

consequen t l y t ha t o f t he p r i ce change ru l e , m i gh t no t be so com pl ex . Two

poss ib i l i t i es are tha t the cons tan t may vary only across magazines , o r tha t i tmight no t vary a t a l l . This sugges t s severa l dummy var iab le speci f i ca t ions

aga i ns t wh i ch t o t e s t t he e s ti m a t es f rom t he m ore c om p l ex t echn i que . The f i r st

con t a i n i ng one cons t an t t e rm , t he s am e fo r al l m agaz i nes and a ll ti m e , and t he

second i nc l ud i ng t h i r t y -e i gh t cons t an t t e rm s , one fo r each m agaz i ne . Under

no rm al c i r cum s t ances , com par i son o f pa i r s o f m ode l s i s m ade pos s i b l e by

ei ther a l ike l ihood ra t io s ta t i s t i c based on the value of the two uncondi t ional

l i ke l i hoods o r a Wal d s t a t i s t i c com pu t ed f rom t he s e t s o f pa ram et e r e s t i m a t es

and t he i r e s t i m a t ed covar i ance m a t r i ces . B u t s i nce t he s i m p l e r m ode l s a re

es t i m a t ed u s i ng t he s t andard p rocedure wh i ch y i e l d s a va l ue fo r t he uncond i -t i ona l l i ke l i hood , l ogL , i n t he p rev i ous d i s cus s i on , and t he C ham ber l a i n

m et hod on l y a l l ows com pu t a t i on o f t he non -com parab l e cond i t i ona l l i ke l i hood

l og L c, te s t s o f t he f i rs t t ype cann o t be pe r fo rm ed . F u r t he rm ore , d i r ec t e s ti m a-

t ion of a l l o f the f ixed ef fec ts , the a ' s in the Cham ber la in mod el , is no t

pos s i b l e . B u t t he va r i ous spec if ica t ions o f t he cons t an t can b e com pared us i ng

a Hausm an (1979) t e s t t o exam i ne t he pa ram et e r s o f i n t e res t , t he b / s i n t ab l e

2 . 22 Th e tes t was run on the fou r pa th -dep end ent speci f ica t ions and the resu l ts

we re a l l the s am e . The pa ram et e r vec t o r from t he e s t im a t i on w h i ch u ti li zed t he

C ham ber l a i n t echn i que i s a l ways s i gn i f i can t l y d i f f e ren t f rom t ha t ob t a i nedfrom ei ther of the s impler cons tan t t e rm speci f i ca t ions . Tes t s t a t i s t i cs wi th

chi -squared d i s t r ibu t ions wi th 3 , 4 , o r 5 degrees of f reedom r i se as h igh as 60and never f a ll be l ow 40 .

21 U s i n g t h e m o d e l d i s c u s s e d i n C e c c h e t t i (1 98 5) i t c a n b e s h o w n t h a t t h e s e e s t i m a t e s i m p l y t h a t

a n i n c r e a s e i n i n f l a t i o n w i l l l e a d t o a n i n c r e a s e i n t h e d i s p e r s i o n o f r e l a t i v e p r i c e i n f l a t i o n , e v e n

t h o u g h t h e p r o b a b i l i t y o f s e e i n g a p r i c e c h a n g e i n c re a s e s. H e n c e a n i n c r e a s e in i n f l a ti o n le a d s t o ad e c r e a s e i n t h e i n f o r m a t i v e n e s s o f t h e p r ic e s y s t em .

22 T h e H a u s m a n t e s t e x a m i n e s t w o n e s t e d m o d e l s , o n e w i t h m o r e p a r a m e t e r s t h a n t h e o t h e r.

U n d e r t h e h y p o t h e s i s t h a t t h e m o d e l w i t h f e w e r p a r a m e t e r s is n o t m i s sp e c i fi e d , t h e l a rg e r m o d e l

y i e l d s c o n s i s t e n t b u t a s y m p t o t i c a l l y i n e ff ic i e n t e s t i m a t e s o f t h e p a r a m e t e r s o f i n t e re s t . H a u s m a nd e v e l o p s a p r o c e d u r e b a s e d o n t h e v a r ia n c e - c o v a r i a n c e m a t r i c e s o f t h e t w o e s t i m a t o r s fo r t e s ti n gw h e t h e r t h e p a r a m e t e r v e c t o r s a re s i g ni fi c a n tl y d i ff e re n t .

J.Econ B



2 6 8 S.G. Cecchet ti , The frequency o f pr ice adjus tment

T h e H au s man t e s t s i n d i ca t e t h a t f o r mo d e l s (2 ) an d (3 ) t h e co n s t an t t e rm,

an d co n s eq u en t l y th e p r i ce ch an g e ru le , d if f er s b o t h ac ro s s mag az i n es an d o v e r

t ime. The in te rp re ta t ion o f the cons tan t t e rm in spec i f i ca t ions (4 ) and (5 ) i s no t

a s c l ea r - cu t s i n ce i t i s t h e p o r t i o n o f t h e p r i ce ch an g e ru l e n o t ad eq u a t e l y

cap tu red by the cur ren t in f l a t ion and sa les vo la t i l i ty var i ab les . So the re j ec t ion

o f t h e s i mp l e mo d e l b a s ed o n t h e H au s man t e s t i s n o t a s i n fo rma t i v e . O n e

conclus ion i s tha t the inc lus ion o f a l inear func t ion o f cur ren t in f l a t ion and

sa les vo la t i l i ty to measure changes in the p r i ce change ru le i s inappropr ia t e . I f

i t were cor rec t the t es t would fa l l t o re j ec t a s impler model . I t can be a rgued

tha t the var i ab les as inc luded in (4 ) and (5) a re misspec if i ed . A c arefu l read ing

o f t h e t h eo ry s h o w s t h a t i t i mp l ie s t h a t t h e cu r r en t d i s t an ce { h e ( i , t ) - h o ( i , t ) )

i s d e t e rmi n ed b y t h e l o n g - ru n ex p ec t a t i o n o f fu t u r e i n f l a t i o n an d v o l a t i l i t y a t

t h e t i me o f t h e m o s t r ecen t r u l e rev is io n . M o d e l i n g t h e p r i ce ch an g e ru l e u s in g

cur ren t l eve l s o f in f l a t ion and sa les vo la t i l i ty p resumes tha t the ru le changesev e ry y ea r . 23 Bu t i n t h e p a t h -d ep en d e n t m o d e l p r i ce s ch an g e s l o w l y an d t h e

ru le i s an h i s to r i ca l a r t i fac t . To spe c i fy the de te rm inan t s o f the ru le cor rec t ly

o n e w o u l d h av e t o fo rmu l a t e an ex p l i c i t mo d e l o f t h e t i mi n g o f ru l e r ev i s i o n s .

O n l y t h en , w h en o n e co u l d s p ec i fy t h e in fo rm a t i o n av a i lab l e to ag en t s a t t h e

t i me o f t h e r ev i si o n s, w o u l d co n s i d e ra ti o n o f t h e d e t e rm i n an t s o f ( h c ( i , t ) -

h o ( i , t ) ) be poss ib le . Th i s a rgues fo r d i scoun t ing (4 ) and (5 ) comple te ly . 24

T o s t u d y t h e p r i ce ch an g e ru le , e s t ima t e s o f t h e av e rag e v a lu e o f t h e co n s t an t

t e rm , ca l l t h i s ~ t , were com puted . 25 Reca l l tha t the co ns tan t t e rm i s no t

e s t i ma t ed d i r ec t l y u s i n g t h e Ch amb er l a i n t ech n i q u e . U n fo r t u n a t e l y , t h e t ech -n i q u e d o es n o t a l l o w ca l cu l a t i o n o f t h e ac t u a l v a l u e o f t h e co n s t an t i n ev e ry

one o f the 318 ce l l s fo r which i t t heore t i ca l ly ex i s t s . In those cases where the

s u m o f t h e Y i t ' s over the th ree-year per iod i s e i ther zero o r th ree , the

p r o b a b i l i t y o f a n y i n d i v i d u a l Y i t b e i n g ze ro o r o n e i s co mp l e t e l y d e t e rmi n ed

g iven th i s sum. In these degenera te cases , the cons tan t i s e i ther pos i t ive o r

n eg a t i v e i n f i n i t y . W h a t can b e co mp u t ed i s t h e v a l u e o f t h e co n s t an t a t t h e

m ean o f t h e d a t a fo r t h e n i n e n o n -o v e r l ap p i n g t h r ee -y ea r p e r i o d s t h a t co mp r i s e

t h e d a t a s e t . T h es e a r e meas u re s o f t h e co n s t an t f o r a r ep re s en t a t i v e av e rag e

mag az i n e . C h a n g es i n ~ t a r e ch an g es i n t h e p ro b ab i l i t y o f o b s e rv i n g a p ri cechan ge , h o ld ing the d i s t ance P * has t rave led fixed, and sugg es t change s in the

p r i ce ch an g e ru l e .

2 3 E x p e r i m e n t a t i o n w i t h l a g g e d m o v i n g a v e r a g e s o f i n fl a t io n d i d n o t a l t er t h e r e s u lt s .

2 4A n a l t e r n a t i v e i n t e r p r e t a t io n o f t h e t e s t re s u l ts i s th a t m o v e m e n t s i n t h e c o n s t a n t t e r m i n

m o d e l s ( 4 ) a n d ( 5 ) a r e a n i n d i c a t i o n o f n o n - li n e a r i ty i n t h e r e l a t i o n s h ip o f t h e p r i c e c h a n g e r u l e t o

i t s d e t e r m i n a n t s . I f t h e f u n c t i o n i s s e r io u s l y n o n - l i n e a r in t h e r a n g e o f t h e d a t a , m o v e m e n t s i n t h e

c o n s t a n t t e r m w o u l d r e f le c t t h e d i f fe r e n c e s b e t w e e n t h e c o r r e c t r e l a t io n s h i p a n d t h e l i n e a r o n e

e s t i m a t e d . I n t h i s c a s e a s w e l l, i n t e r p r e t a t i o n o f t h e c o n s t a n t t e r m i s d if fi c u lt .

25 I n l i g h t o f t h e p r e v i o u s d i sc u s s i o n , r e s u lt s a r e r e p o r t e d u s i n g o n l y t h e p u r e p a t h - d e p e n d e n tm o d e l s ( 2 ) a n d ( 3 ). I t i s i m p o r t a n t t o p o i n t o u t t h a t t h e p a t t e r n o f t h e e s t im a t e d c o n s t a n t t e r m f o r

t h e c o m b i n e d m o d e l s ( 4) a n d ( 5 ) is e x a c tl y th e s a m e a s t h a t p r e s e n t e d .



S . G . Ce c c h e t ti , T h e f r e q u e n c y o f p r i c e a d j u s t m e n t

Table 3

Estimates of the average fixed effect (~t and ~ , ) a

26 9

AverageA v e r a g e n um b er o f

Per iod a t ~* [z l logP( t ) × 1 0 0 ] inf la t i on pr ice changes

1953 -1955 - 11.87 - 9.83 21.1 1.7 2.3(8.16) (5.71)

1956 -1958 - 9.86 - 7.94 25.8 2.4 8.0(7.05) (4.83)

1959 -1961 - 9.83 - 8.08 23.6 1.3 2.0(6.80) (4.94)

1962-1964 -9 .6 2 -7 .8 4 22.2 1.3 8.0(5.39) (4.18)

1965 -1967 - 8.71 - 6.94 24.0 2.8 8.3(6.13) (4.33)

1968 -1970 - 7.81 - 5.97 25.3 4.7 8.3(7.69) (4.28)

1971-1973 -8. 21 -6 .4 0 26.3 3.8 5.3(8.23) (4.71)

1974-1976 -6 .1 2 -4 .18 26.8 8.0 15.7(5.82) (2.85)

197 7-197 9 - 4.51 - 2.77 23.4 7.2 12.3(6.00) (2.21)

aValues in parentheses are asym ptotic t-statistics. The first two colum ns are calculated using eq.(5) substituted into (6), and estimated parameters reported in co lumns (2) and (3) of table 2. Thevalue for the average fixed effect is the log o f the average odds during the period, less the sum o fthe average level of the independ ent variables weighted by the parameter estimates. The remainingcolumns are three-year averages from table 1,

T h e f ir st c o l u m n o f ta b l e 3 r e p o r t s t h e e s t im a t e s o f t h e a v e r a g e ~ , ' s u s in g

m o d e l ( 2) o f t a b le 2 , a n d t h e s e c o n d c o l u m n r e p o r t s a v e r a g e ~ * ' s u s i n g m o d e l

( 3) . A s y m p t o t i c t -s ta t is t i cs a r e a ls o r e p o r t e d . T o u n d e r s t a n d h o w t h e s e a r e

c o m p u t e d t a k e a n e x a m p l e. T h e e s t im a t e d ~ t f o r t h e 1 9 6 5 - 1 9 6 7 p e r io d i s t h e

l o g o f t h e a v e r a g e o d d s o v e r t h e p e r io d , l e ss th e s u m o f t h e a v e r a g e v a lu e o f

e a c h i n d e p e n d e n t v a r i a b le w e i g h t e d b y i ts co e f fi c ie n t e s ti m a t e s, a s r e p o r t e d i n

t h e c o l u m n ( 2 ) o f t a b l e 2 . 26

C h a n g e s i n ~ , a r e c h a n g e s i n t h e p r o b a b i l i ty o f o b s e r v i n g a p r i c e c h a n g e

g i v e n t h e l e v el o f th e r i g h t -h a n d - s i d e v a r ia b l e s i n th e m o d e l . O n e w a y t o

c a l i b r a t e t h e s e c h a n g e s i s t o c o m p u t e h o w l o n g a w a it ( y e a rs s in c e th e p r e v i o u s

p r i c e c h a n g e ) p r o d u c e s a n e q u i v a l e n t c h a n g e i n t h e p r o b a b i l i t y . U s i n g t h e

e s t i m a t e s f r o m m o d e l (2 ) a n d a s s u m i n g s t e a d y 5% in f la t io n , i t c a n b e s h o w n

2 6 5 0 a t = l og (PJ (1 - Pt)) - X~b, w he re P~ is the averag e proba bility ove r a three-year period.



270 S.G. Cecch etti , The frequency of price adjustm ent

t h a t a n in c r e a s e i n t h e c o n s t a n t f r o m - 9 . 8 t o - 6 . 1 i n c r ea s e s t h e p r o b a b i l i t y

b y t h e s a m e a m o u n t a s w a i t i n g a n a d d i t i o n a l 2 . 2 y e a r s . 27 P u t d i f f e re n t l y , th e

r i s e o f 2 . 3 i n 8 t d e c r e a s e s t h e t i m e s i n c e t h e l a s t c h a n g e r e q u i r e d t o a c h i e v e a

g i v e n p r o b a b i l i t y b y 2 . 2 y e a r s .

I n c r e a s e s i n 8 t r e p r e s e n t a d e c r e a s e in t h e d i s t a n c e f r o m t h e p r e v i o u s r e t u r n

p o i n t t o t h e c u r r e n t b a r r i e r . 2a A n a l o g o u s l y , a n i n c r e a s e in 8 " c a n b e i n t e r p r e t -

e d a s a l o w e r i n g o f t h e c u r r e n t c e i li n g, h c ( t ) , r e l a ti v e t o th e p r e v i o u s o n e ,

h c ( ?) . T h e s e e s t im a t e s , t o g e t h e r w i t h d i r e c t i n f o r m a t i o n o n t h e a v e r a g e c u r r e n t

f i x e d p r i c e c h a n g e A l o g P ( t ) r e p o r t e d i n t h e t h i r d c o l u m n o f t a b l e 3 , y i e l d a n

i n t e r e s t i n g p i c t u r e o f t h e e v o l u ti o n o f t h e p r i c e c h a n g e rule . 29 T h e t a b l e s h o w s

s o m e l a r g e f l u c tu a t i o n s i n th e a t ' s , b u t o n l y s m a l l c h a n g e s i n t h e Z l l o g P ( t ) ' s .

T h e d e c r e a s e s i n t h e a t ' s d u r i n g t h e e n t i r e s a m p l e s u g g e s t f i r s t a c h a n g e i n t h e

s y m m e t r y o f t h e p r i c e c h a n g e r u le , a n d t h e n a n a c t u al d e c r e a s e in t h e d i s t a n c e

f r o m t h e c e i l in g t o t h e b a r r i e r . W h e n 8 t g r o w s , b u t t h e a c t u a l p r i c e c h a n g e

r e m a i n s t h e s a m e , t h e n e w b a r r i e r a n d r e t u r n p o i n t w i l l b o t h b e b e l o w t h e

p r e v i o u s o n e s . T h e g r o w t h i n 8 " s ig n if ie s d o w n w a r d r e v i s io n s o f th e c ei l in g

b a r r i e r h c. A h i g h e r a t m e a n s t h a t P * i s n o t a l l o w e d t o t r a v e l as f a r a b o v e t h e

f i x e d p r i c e b e f o r e a c h a n g e , a n d t h a t t h e f i x e d p r i c e i s r e s e t f u r t h e r a b o v e P *

t h a n i t w a s b e f o r e . I t i s i n t e r e s t i n g t o s p e c u l a t e a b o u t t h e c a u s e s o f t h i s c h a n g e

i n s y m m e t r y . C h a n g e s i n u n c e r t a i n t y a n d a t t i t u d e s t o w a r d s i t i n r e c e n t y e a r s

m a y b e r e s p o n s i b l e , a° W h e n e s t i m a t e s o f f u tu r e i n f la t io n a r e i m p r e c i s e a n d t h e

c o s t s o f c h a n g i n g p r i c e s a r e h i g h , it i s r e a s o n a b l e t o e x p e c t a r is k - a v e r s e p r i c e

s e t t e r t o c h o o s e a f i x e d p r i c e t h a t o v e r s h o o t s t h e c u r r e n t s h o r t - r u n o p t i m a lp r i c e b y m o r e t h a n h e o r s h e w o u l d i f f u t u r e i n fl a ti o n w e r e c e rt a in .

T h e s e r i e s p r e s e n t e d i n t a b l e 3 c a n a l s o b e u s e d t o e x a m i n e t h e a d j u s t m e n t

c o s t s t r u c t u r e . T h e t h e o r y d e s c r i b e d i n s e c t i o n 3 p r e d i c t s t h a t w h e n t h e r e a l

c o s t o f a p r i c e c h a n g e i s c o n s t a n t , t h e d i s t an c e f r o m t h e r e t u r n p o i n t t o t h e

b a r r i e r o f t h e p r i c e c h a n g e r u le s h o u l d g r o w w i th i n f la ti o n . T h i s m e a n s t h a t t h e

e s t i m a t e s o f A l o g P ( t ) s h o u l d i n c r e a s e w i t h i n f l a t i o n , a n d t h a t t h e 8 t ' s s h o u l d

d e c r e a s e ( b e c o m e m o r e n e g a t i v e ) . T h i s i s c l e a r l y n o t t h e c a s e . T h e e v i d e n c e

s h o w s t h a t t h e d i s t a n c e o f th e r u le in n o m i n a l t e r m s s h r u n k s li g h tl y d u r i n g t h e

27The additional waiting time is A T = A St/ (b 1 + b2~).

2SUnder certain circumstances, problem s can arise in the interpretation of the avei'agevalues ofthe fixed effect, a t and ~*. T o the extent that either systematicchanges in the p rice change rule arecorrelated w ith variables included in the mo del of P* or components causing movem ents in P*have b een om itted, the estimates may no t accurately reflect changes in the distance from the returnpoint to the barrier. But g iven the specification of the m odel it is difficult to see how this could beSO.

29A og P (t) = h c(t) - h o(t), the a verage current fixed price chang e, should not be confused withA log P( i, 7), the previous fixed price change for an individual magazine.

3°Since the e stimates of the at 's from m odels (4) and (5) w hich include sales volatility show the

sam e pattern as those in table 3, the uncertainty would hav e to arise from a source not specificallyconsidered.



S.G. Cecchetti, The requency of price adjustment 27 1

1970 's , a t im e wh en gen era l p r ice in f la tion was increas ing . Th is i s consis ten t

wi th th e f ac t t h a t t h e av e r ag e r ea l f i x ed p r i ce ch an g e ( n o m in a l ch an g e l e s s

in f la t ion s in ce the las t change) decrease d substan t ia l ly dur in g the 1970 's . S ince

th e th eo r y s t a te s t h a t t h e d i s t an ce f r o m th e r e tu r n p o in t t o t h e b a r r i e r sh rin k s

wi th ad ju s tm en t co s t s , t h e r e su l t s su g g es t t h a t t h e co s t o f a n o m in a l p r i ce

ch an ge fa l l s e i ther when the s ize o f a rea l p r ice chan ge decreases , as desc r ibed

b y Ro tem b er g , o r a s t h e f r eq u en cy o f ad ju s tm en t in c r ea se s.31

5 . C o n c l u s i o n

Th e n ewss t an d p r i ce s o f m ag az in es p r o v id e s t r o n g em p i r i ca l su p p o r t f o r

s t i ck y p r i ce m o d e l s b a sed o n m o n o p o l i s t i c co m p e t i t i o n . Th e d a t a sh o w th a t

m aga z ine p r ice s exh ib i t subs tan t ia l s t ick iness a l lowing the i r rea l p r ices to e rod e

b y a s m u ch a s o n e - q u a r t e r b e f o r e im p lem en t in g a f ix ed p r i ce ch an g e . Fu r th e r

an a ly s i s d em o n s t r a t e s t h a t t h e co s t s o f n o m in a l p r i ce ch an g es d ec r ease e i th e r

w i th in c r ea se s i n t h e f r eq u en cy o f ad ju s tm en t , o r w i th d ec r ease s i n t h e s ize o f a

r ea l p r i ce ch an g e . Th e ev id en ce su p p o r t s t h e co n ten t io n th a t cu s to m er s f aced

w i th r ea d y su b s t i tu t e s p r e f e r s tab l e p ri ce p a th s t o t h o se w i th l a r g e in f r eq u en t

j u m p s .

C h a n g e s i n t h e e c o n o m i c e n v i r o n m e n t s in c e th e K o r e a n W a r, m o s t n o t a b l y

increases in the leve l o f genera l p r ice in f la t ion , have led to an increase in the

f r eq u en cy o f m ag az in e p r i ce ch an g e . As av e r ag e an n u a l i n f l a t io n r o se f r o m

ne ar 2% in the 1953-1965 per iod to a lm ost 8% in the la t te r ha l f o f the 1970 's ,

t h e av e r ag e t im e b e tween m ag az in e p r i ce ch an g es f e l l f r o m sev en an d a h a l f

y ea r s t o t h r ee a n d a q u a r t e r y ea rs . W h i l e th i s ev id en ce is f o r p r i ce s i n o n ly o n e

in d u s t r y , i t i s ex t r em e ly l ik e ly th a t t h e f r eq u en cy o f ad ju s tm en t f o r a l l p r ice s i n

t h e e c o n o m y i n c re a s e d o v e r th is p e r i o d . 32 Th e sh o r t en in g o f t h e t im e p e r io d

b e t w e e n n o m i n a l p r ic e a d j u s tm e n t s h a s b e e n t h e r e su l t o f tw o c o m p l e m e n t a r y

an d r e l a t ed f ac to r s . F ir s t, t h e r e h as b een a n in c r ea se in t h e r a t e o f ch a n g e in

th e p r i ce a f i r m wo u ld ch a r g e in t h e ab sen ce o f ad ju s tm en t co s t s . Th i s

sh o r t - t e r m o p t im a l p r i ce h as b een m o v in g m o r e r ap id ly a s a co n seq u en ce o f

h ig h e r g en e r a l p r i ce in f l a t io n . Seco n d , co n t r a r y to t h e r e su l t s o f m o d e l s t h a tho ld re a l ad jus tm en t cos ts fixed , the emp ir ica l resu l ts show th a t h igh er in f la t ion

was acc o m p an ied b y r e l a tiv e co n s t an cy in th e d i s t an ce th e o p t im a l p r i ce h as to

m o v e b e f o r e th e f ix ed p r i ce i s ch an g ed . Th i s f i n d in g im p l i e s b o th th a t p r i ce

se t t e r s o p t f o r m o r e f r eq u en t p r i ce ad ju s tm en t wh en in f l a t io n i s h ig h e r , an d

th a t ad ju s tm en t co s t s fa l l a s ch an g es b eco m e m o r e f r eq u en t. Th e r e ap p ea r s t o

3 1 T h e s l i g h t in c r ea se in t h e e s t im a te s o f t h e a t ' s f o r t h e 1 9 7 1 - 1 9 7 3 p e r io d i s co n s i s t en t w i th t h ee x p e c t a t i o n t h a t t h e N i x o n w a g e - p r i c e c o n t r o ls r ai s e d a d j u s t m e n t c os ts .

3 2 E v id en ce i s p r o v id ed in Cecch e t t i ( 1 9 8 5 ) t h a t t h e av e r ag e f r eq u en cy o f p r i ce ch an g e in t h eeco n o m y a s a w h o le i n c r ea sed f i rs t i n 1 9 67 a n d a g a in f o l lo win g th e N ix o n in co m es p o l i cy in 1 97 4 .



272 S.G. Cecchetti, The frequency o f price ad justment

b e j u s t i f i c a t io n fo r t h e c l a im t h a t a n i n f l a t io n a ry en v i ro n m en t b r e ed s a l o w er -

i n g o f b u y e r r e s i s tan ce t o p r i ce ch ang es .

I t i s c l ear f rom th i s exerc i se tha t the f requency o f p r i ce ad jus tment i s a

q u a n t i t y d e t e r m i n e d e n d o g e n o u s ly i n t h e e co n o m y . A n y a t t e m p t t o b u il d a

m o d e l o f t h e i n f l a t i o n p r o c e s s a n d m a c r o e c o n o m i c a d j u s t m e n t m u s t t a k e

acc o u n t o f t h is en d o g en e i t y . Bo t h t h e s h o r t- ru n an d l o n g - ru n e f f ec ts o f

i n c rea s e s i n i n f l a ti o n o n t h e f r eq u en cy o f p r i ce ad j u s t men t ap p ea r t o b e s izab le .

The impl ica t ion i s tha t h igher in f l a t ion l eads to fas t e r ad jus tment and l es s p r i ce

s t i ck iness . 33 Fa i lu re o f s t aggered co n t rac t s m ode l s to t ak e th i s in to acc oun t

co u l d ea s i l y l e ad t o f a l s e co n c l u s i o n s ab o u t t h e s h o r t - t e rm i mp ac t an d l o n g ev -

i t y o f b o t h g o v e rn men t i n t e rv en t i o n an d ex t e rn a l s h o ck s .

Append ix

A.1. Magazines

T h e d a t a s e t is c o m p o s e d o f m a g a z in e s c o n t in u o u s l y p u b li s h e d f r o m J a n u a r y

1 9 5 0 t o J an u a r y 1 9 8 0 an d av a i l ab le o n a n ew s s t an d i n t h e w i n t e r o f 1 98 2. D u e

t o a l a ck o f i n fo rma t i o n o n t h e s i ze o f t h e p r ev i o u s n o mi n a l p r i ce ch an g e ,

A l o g P( ? ) , d a t a u s ed i n t h e e s ti ma t i o n o f sec t io n 4 d o es n o t b eg i n in 1 95 3 fo r

t h i r t een o f t h e t h i r t y - e i g h t mag az i n es . Fo r fo u r mag az i n es , d a t a w as l o s t f o r

th ree years , fo r e igh t i t was los t fo r s ix years , and fo r one , da ta was los t fo r

t w e l v e y ea r s . T h i s l e f t a t o ta l o f 9 5 4 o b s e rv a t io n s . T h e d a t a w as co l l ec t ed a t t h eBerk e l ey P u b l i c L i b ra ry an d a t v a r i o u s l ib r a r ie s o f t h e U n i v e r s i ty o f Ca l i fo rn ia .

T h e m a g a z i n e s u s e d w e r e : Antiques, Architectural Review , Atlantic, A udio,

Better Homes and Gardens, Business .Week, Commentary, Consumer Reports,

Current History, Ebony, Es qu ire , Films in Review, Fo reig n Affairs, G oodHousekeeping, H arper's Bazaar, Ha rper's Magazine, High Fidelity , Houseand Ga rden , House Beautiful, Interiors, Mod ern Photography, Motor Trend,

Nation, The N ew Leader, The Ne w Republic, N ew Yorker, New sweek, Parents ' ,Popular Mechanics, Popular Scien ce, Road and Track, Scien ce Digest, S cien-

tif ic Am erican, Sunset, Time, U.S. News and World Report, Vo gu e, andYachting.

A.2. The sales volatility index

The sa les vo la t i l i ty index used in the es t imat ion repor ted in sec t ion 3 , t ab le

2 , w as g en e ra t ed a s t h e t h r ee -y ea r cen t e r ed mo v i n g av e rag e o f t h e s q u a red

res idua l s f rom a regress ion o f the s ing le-copy sa les o f a l l magaz ines on th ree

p as t l ag s an d t h e t o t a l n u m b er o f mag az i n es av a i lab l e i n a g i v en y ea r.

3 3As i s n o te d ab o v e , t h e i n f o r m a t io n co n te n t o f t h e p r i ce sy s t em m ay d ec r ea se w i th i n f l a t io n a sr e l a t i v e p r ice v a r i a t i o n ap p ea r s t o i n c rea se . W h i l e ad ju s tm en t i s f a s te r , k n o wled g e ab o u t t h ecu r r en t en v i r o n m en t an d P* i s l e s s p r ec ise . T h i s c r ea t e s a t y p e o f in e f f ic i en cy th a t i s v e r y d i ff e r en t

f r o m th a t u su a l ly s tu d ied wi th s t i ck y p r i ce m o d e l s .



s .c . Cecchetti, The frequency ofprice adjustment 273

T h e r e g r e s s i o n r e s u l t s a r e

S c S ( t ) = - 9 , 7 5 8 . 2 8 0 + 1 . 1 2 3 S c S ( t - 1 ) - 0 . 5 3 7 S c S ( t - 2 )

( 1 . 7 9 ) ( 6 . 9 6 ) ( 1 . 9 2 )

+ 0 . 2 5 5 S c S ( t - 3 ) + 1 , 5 9 1 . 6 T M ( t ) ,

( 1 . 2 9 ) ( 2 . 1 8 )

~ 2 = 0 . 9 4 , D . W . = 1 . 9 4 , S . E . R . = 2 , 5 2 2 . 0 0 0 ,

w h e r e S c S ( t ) a r e t h e s i n g l e - c o p y s a le s i n y e a r t a n d T M ( t ) a r e t h e t o t a l

m a g a z i n e s a v a i l a b l e in y e a r t . T h e s o u r c e o f t h e s e d a t a i s t h e M a g a z i n e

P u b l i s h e r s A s s o c i a t i o n .

T h e s a l e s v o l a t i l i t y i n d e x u s e d i n t h e r e p o r t e d w o r k w a s s c a l e d b y a f a c t o r o f

1012 . T h e i n d e x r e p r e s e n t s t h e o n e - p e r i o d - a h e a d u n c e r t a i n t y i n i n d u s t r y s a le s

c o n d i t i o n a l o n s a l es d u r i n g t h e p a s t t h r e e y e a r s . T h e u s e o f s a l e s f ig u r e s ,

i n d i r e c t l y t o c o m p u t e t h e v o l a t i l i ty m e a s u r e a n d d i r e c t l y in f o r m i n g t h e p a s t

s a l es v a l u e , i n a n e s t im a t i o n b a s e d o n p r i c e s m a y p r o d u c e i n c o n s i s te n c y . B u t

g i v e n t h a t i t i s i n d u s t r y - w i d e s a le s b a s e d o n e i g h t y to h u n d r e d m a g a z i n e s t h a t

a r e u s e d , a n d t h a t t h e re a r e o n l y t h i r t y - e ig h t m a g a z i n e s i n th e s a m p l e , e a c h

m a g a z i n e ' s s a l e s a r e s m a l l re l a t i v e t o th e t o t a l , s o t h is i s u n l i k e l y t o b e a

s e r i o u s p r o b l e m .

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274 S.G. Cecchetti, The requen cy of price adjustment

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Cecchetti - Frequency of Price Adjustments