Frequency of Magazine Price Adjustments - Cecchetti 1986

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Joumal of Econometrics 31 (1986) 255-274. North-Holland

THE FREQUENCY OF PRICE ADJUSTMENTA Study of the Newsstand Prices of Magazines*

Stephen G. CECCHETIINew York University, New York, NY 10006, USA

Received March 1985, final version received November 1985

Data on the newsstand prices of American magazines is used to investigate the determinants of thefrequency of nominal price change. Magazine price changes, often coming after real prices havefallen by one quarter, provide strong evidence for monopolistic sticky price models. The data isexamined by applying a fixed effects logit specification to the price change rule implied by atarget-threshold model of a firm facing general price inftation, an uncertain future and costlynominal adjustment. The essay concludes that higher inftation leads to more frequent priceadjustment and that the real cost of price changes vares with the size of a real price change.

1. Introduction

The effect of price stickinesson aggregateoutput fluctuations has been thesubject of much recent macroeconomicresearch.1Models which assume thatindividual agents adjust their prices at discrete and overlapping intervalsconclude that longer periods between price changes lead to greater serialcorrelation of output in response to unanticipated shocks. The presence ofmonopolistic competition at the levelof the individual price setters is usuallyused to justify the price change technology imposed on the model. Thedescriptive power of these modelsdepends on the accuracyof their characteri-zation of the price change process. ConsequentIy,describing the evolution ofthe price change frequeI1cyand identifyingits determinants is importantto theunderstanding of macroeconomicfluctuations.

The frequency of price adjustment is almost certainIy dependent on theeconomic environment. In this context, two questions are of interest. First,what is the response of the frequency of adjustment to increases in general

*This paper is a revised version of the second essay of my Ph.D. dissertation completed inAugust 1982 at the University of California, Berkeley. Thanks are due especially to George Akerlofwithout whom this study would never have been started, to Bill Greene for providing help at everystage, and to Paul Ruud, Tom Rothenberg, Bob Cumby, George Sofianos, Peter Berck, PaulWachtel, Keith Johnson and anonyrnous referees for comments. AlI remaining errors are mine.

lThe work of Taylor (1980) on staggered contracts, of Blanchard (1984) on price asynchroniza-tion and of Rotemberg (1983a,b) on sticky prices are examples.

0304-4076j86j$3.50@1986, Elsevier Science Publishers B.V. (North-Holland)


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256 S. G. Cecchetti, The frequency of price adjustment

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price inflation? And second, what is the structure of the cost of price adjust-ment? Theoretical models of price determination in the presence of monopolis-tic competition, inc1uding those in Sheshinski and Weiss (1977,1983), Mussa(1981a, b) and Iwai (1981), offer no general answer to the first question.Regarding the second, they assume the cost of a nominal price change to beconstant in real terms. These costs are believed to take two forms: administra-tive, the cost of determining and implementing a new price; and informational,the cost imposed on the firm's customers and associated with a possible loss ofsales to competitors. Rotemberg (1982a, b) has suggested that in the presenceof monopolistic competition where substitute goods are readily available, thecosts may be proportional to the size of the real price change. He argues thatcustomers prefer stable price paths which exhibit small adjustments to thosewith large infrequent jumps. Alternatively, the hypothesis that the cost ofchanging a nominal price may bt: a decreasing function of the frequency withwhich the price is changed yields similar price adjustment behavior.2 Butwhether costs are invariant to the size or frequency of price change is anempirical question.

Studying price changes requires data of a type that is not normally available.Ideally one would like observations on the changes in the transactions price ofa consistent product over a period of time long enough for there to have beensubstantial variation in economic conditions. In addition, the product pricemust not be the outcome of a continuous auction market mechanism. Auctionprices change costlessly between each transaction.

Data on the newsstand or cover prices of magazines fit these requirementsquite well. The prices exhibit the desired property of discrete and infrequentadjustment, suggesting that they are .not the result of an auction mechanism.The data are readily available in libraries, and transactions actually occurred atthese prices.

This paper continues with a descriptive presentation of the data on thenewsstand prices of.thirty-eight American magazines over the period from1953 to 1979. Section 3 describes a target-threshold modelof a monopolisti-cally competitive firm facing general price inflation, an uncertain future andcostly nominal price adjustment. The model implies that the firm will developa rule for changing prices which states that the firm's fixed nominal price ischanged when it is far enough out of line with current conditions. A logisticspecification of the probability of observing a magazine price change duringa given time period is derived from the model. The estimation focuses onthe econometric problems associated with the possibility that magazines haveprice change rules that change over time. These difficulties are addressed by

employing a rarely used but very powerful fixed effects model developedby Chamberlain (1980,1984) to deal with discrete panel data sets where

2These hypotheses are all variants of the Okun (1975,1981) customer market hypothesis.


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S. G. Cecchetti, The Irequency 01price adjustment 257"

unobservable effects vary both across time and across groupS.3The fourthsection presents estimates of the model and a discussionof their properties.

The paper provides two conclusions.While in theoreticalmodelswhere the

relationsbip between aggregateinfiation and the frequencyof price change isambiguous, the results for these data indicate that prices have changed morefrequently during periods of bigher inflation.4 In addition, the data areinconsistent with a simplemodelwherethe cost of a prjte changeis constant inreal terms. The observedincreasesin frequencyof price changesare too rapidgiven the changes in aggregate inflation. The iinplication of this is that thecosts of changing prices decrease as either the frequency of adjustment .increases or the size of a real price change decreases. This provides anempirical basis for the cost technologiesassumed by Rotemberg (1982a,b) inbis studies of the aggregateconsequencesof stickyprices.

2. Description of magazine price data

Data were collected on the newsstand prices of thirty-eight magazines overthe period from 1953 to 1979. s (The list of magazines included appears in theappendix.) For each magazine, the price of the first issue in each year wasnoted. If a magazine' s price at the beginning of 1975 differed lrom the price at

the beginning of 1976, then the magazine was assigned a price change during1975. As a consequence of this procedure, the frequency ol the data is annual.6Belore beginning the more rigorous statistical investigation of the properties

ol these data, it is useful to examine some simple summary statistics. These arepresented in table 1. From the first two columns ol the table it appears that amagazine is more likely to change its price when general price inflation is bigh.Closer examination gives the impression that increases in the ~umber ol pricechanges lag rises in infiation by roughly one year.

Table 1 also presents information on the experience ol magazines whose

price changed in a given year. As will be argued in the next section, it is theexperience of a firm since its last price change that determines if a price

3The choice of a logit model, as opposed to a duration model of the type studied in Kiefer(1985), provides substantial ftexibility in dea1ing with fixed elfects. In aItemative approaches theinc1usion of individual or group elfects can be extremely difficult except in the simplest of cases.

4 In a study of the price of noodles and instant colfee in Israel over the period from 1965 to 1978,Sheshinski, Tishler and Weiss (1979) aIso conc1ude that increases in inftation led to more frequentprice adjustments. B,ut the nature of government intervention in the Israel price system suggeststhat further research using market-determined prices is of interest.

s While most magazines are sold by subscription, nearly one-third are sold as single copies. Datafrom the Magazine Publishers Association covering the period of the sample show that an averageof 218 million copies of magazines are sold annually. Of these, an average of 69 million weresingle-copy sales.

6There are so few price changes that an increased observation frequency, say quarterly, wouldyield many time periods with no changes at aI1.


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changes. The three series reported are for the average time since the last changefor those magazines that change price (the length of spells completed in a givenyear),' the average fixed price change actually observed, and the cumulativeaggregate inftation during that periodo Several interesting conclusions emergefrom these data. First, over the entire sample period there was an increase inthe number of changes along with a decrease in the average length of acompleted spell. At the same time, the average size of the fixed price change

remained remarkably stable, while the cumulative aggregate inftation first

'To facilitale Ibis compulation. lor each magazine data was collected on the data of the pricechange prior to 1953.

/258 S. G. Cecchetti, TheIrequency 01price adjustment

Table1

Magazinepricechanges.1953-1979.a

Average AverageNumber numberof Average inftation

of magazines Current yearssince fixed sincechangingprice inftation last change pricechange last change

1953 1 0.2 6.0 14.3 15.71954 2 2.2 7.0 27.0 17.91955 4 2.8 6.5 21.9 16.41956 8 3.8 6.4 31.5 18.31957 12 2.3 8.3 22.9 22.61958 4 1.0 9.8 20.2 23.11959 2 2.4 3.0 22.5 5.71960 1 1.1 14.0 18.2 37.11961 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 14.31964 7 0.9 6.0 16.4 10.21965 5 1.7 7.4 26.4 10.81966 9 4.0 5.2 17.5 10.81967 11 2.8 4.6 28.2 9.81968 8 4.3 6.9 29.0 18.31969 9 4.9 5.8 21.7 17.21970 8 5.0 7.5 25.5 23.61971 4 3.4 6.3 28.0 22.21972 4 2.9 5.3 22.6 19.41973 8 5.2 5.9 27.3 22.91974 19 11.9 4.8 29.4 28.01975 11 7.5 3.6 25.2 24.31976 17 4.8 2.9 24.9 18.01977 13 5.4 3.5 26.3 20.31978 12 8.1 1.8 24.5 12.71979 12 8.1 3.1 19.1 22.2

aCalculationsusing newsstandpricesof magazineswhichchangedprice lrom first issue ol yearlo first issue ol lollowing year. 1be magazines used are listed in the appendix. Inftationcomputations use the deftator lor gross domestic non.farm product, exc1udinghousing services. Allchangesare measuredas percentages.


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S. G. Cecchetti, The Irequency 01price adjustment 259

decreased in the 1960's and then increased in the 1970's. The actual quantity ofgeneral price inftation between price changes is quite striking. As inftationincreased in the 1970's magazines allowed their real prices to erode by nearly

one-quarter. This is evidence of incredible price stickiness which can only'beassociated with high costs of fixed price changes. It is very unlikely that theadministrative costs of actually changing prices can explain this. The obviousexplanation is that each magazine fears that if it 'moves' first to adjust its pricefor inftation, it will raise its relative price above that of the competition, losingsales. The degree of magazine price stickiness provides strong support forsticky price theories based on monopolistic competition.

3. Specification of the model

Explicit modeling of the timing of a firm's price change is extremely difficult.The decision to change a price in the presence of adjustment costs and anuncertain future is the solution to a stochastic dynamic programming problem.The problem is complicated by the fact that-a firm knows that it can update itsexpectations in \ater periods, correcting any mistakes it may have previouslymade. While the repeated nature of the problem simplifies it considerably, itallows only a characterization of long-term average behavior.

Iwai (1981) has examined the firm's price adjustment problem using atarget-threshold model of the type developed by Miller and Orr (1966) in theirstudy of the demand for money.8 Faced with costs of charging a price differentfrom the short-term profit-maximizing price, and costs of changing its nominalprice, the firm develops a rule that governs its price changes. This rule statesthat when the fixed nominal price, P(t), is far enough away from theshort-term optimal price, P*(t), the price will be changed.9 The short-termoptimal price is the price that would be set if price change were costless and

continuous.The firm's price change rule can be characterized by the maximum distance

P*(t) will be allowed to deviate from P(t) before the price is changed. Definethe firm's measure of disequilibrium Zt = 10g(P*(t)/ P(t, he to be the maxi-mum value Zt can attain before the price is changed, the barrier, and ho to bethe distance from P *( t) at which P( t) is set when it is changed, the returnpoint.lO

To best understand how this works, take an example where the firm'senvironment is stable so that the price change rule is constant. Beginning with

KSheshinski and Weiss (1977,1983) derive a general set of conditions under which it is optimalfor a firm to adopt a target-threshold pricing policy, often referred to as (s, S).

9For a rigorous and complete treatment, the reader is referred to Iwai (1982), particularly ch. 6,along with its appendices and supplement.

10Depending on the firm's loss function and discount rate, ho may be set equal to zero.


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260 S. G. Cecchetti, The frequency of price adjustment

the observation of a price change at t = O, the fixed price is set so that Zo = ho,or log P(O) = log P*(O) - ho. Under the usual circumstances with a positiveaggregate inflation rate, the fixed price is set above p* so ho is negative. Astime proceeds, p* grows steadily until it exceeds the level prescribed by theroleo When the change in p* exceeds the distance from the return point to thebarrier, so log P*(t) -log P*(O) ~ (he - ho), the price is changed. The newprice log P(t) equals log p* - ho = log P(O) + (he - ho),u

It is c1ear from this exposition that the probability of observing a fixed pricechange corresponds to the probability that the measure of disequilibrium ZIexceeds the barrier he' or that log p* has traveled more than the distance(he - ho). In a stochastic steady state, Iwai has shown that the probability ofseeing a price change depends on the long-ron expected rate of change of the

short-term optimal price and the volatility of sales (the drift and variance inP *), as well as the cost of changing prices. But since an increase in inflation,for real adjustment costs fixed, leads to a change in the price change role whichis represented by a growth in the distance (he - ho), as well as an increase inthe speed at which P*(t) moves, one cannot determine whether higherinflationleads to an increase in the probability of observing a price change.But Iwai does show unambiguously that as the cost of price change declines,the distance (he - ho), from the return point to the barrier, falls as well.

An emprical specification of the probability of seeing a magazine price

change can be developed from this discussion. This can be done so as to yieldinformation not only about the effects of inflation, but also about the pricechange rule itself. There are two approaches that can be taken. The first derivesa specification directly from the theoretical work. The Iwai model is a char-acterization of behavior in a stochastic steady state. If one were in a stochasticsteady state where the transition probabilities are constant, the probability ofobserving a price change would depend only on the expected rate of change inthe short-term optimal price and the volatility of sales. The steady stateassumption would make the probability of a particular firm changing its priceindependent of tliat firm's history. One would be able to collect data that wasconsistent with the interpretation of the model as representing long-termaverage behavior. With data on individual firm prices, this would suggestestimation of a probability model with inflation and sales volatility as the onlyindependent variables.

If prices changed frequently relative to changes in the econonllc environ-ment, the data on price changes would come from a sequence of steady statesand this simple approach would be sensible. The reported results in section 4inc1ude such a specification. But since the amount of short-term inflation, as

(

llThe complete version of the model would include 'a ftoor barrier' in addition to the ceilingbarrier he' But since no downward adjustments are observed in the data, this has been omitted.


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S. G. Cecchetti, The frequency of price adjustment 261

reported in table 1, fluctuates dramatically relative to the time betweenmagazine price changes, it is unlikely that the steady state model is ap-propriate. To maleethe point more explicitly,notice from table 1 that in 1970

eight magazineschanged their prices after an averageperiod of sevenand onehalf years. During the seven years from 1963 to 1970, annual inflationfluctuated from 1% to 5%. This suggests that prices changed infrequentlyrelative to changes in the economicenvironment and leads to the conclusionthat the period under consideration is not made up of many different steadystates.

An altemative procedurebeginsby noting that a firm'sprice changedecisiondepends on the distance p* has moved since its last price change, and thedistance from the return point to the barrier as specifiedby the current rule.The probability of viewinga price change then depends on the rea1izedpathfollowedby p* during the time the nominal price is unchanged.The problemthat arises in this interpretation is that the rule may change over time. But asIwai has suggested,in the short run, the firm's rule is probably an artifact oflong-term expectationsheld some time in the pastoThe specificationdevelopedbelow is able to account for the type of gradual change this implies.

To proceed, define Yit to be.one if magazine i changed price at time t,L1logP*(i,t) to be the change in the short-term optimal price since the last

nominal price change, and [hc(i, t), ho(i, t)] to be the ith magazine's rule attime t. Then,

Pr(yit = 1) = pr{ L1logP*(i,t) > hc(i, t) - ho(i, i)}, (1)

where is the time of the last price change,so ho(i, i) is the return point fromthe rule in effectwhen the price was last changed. Eq. (1) states that when thedistance the short-term optimal price has traveled exceeds the distance fromthe previous retum point to the current barrier, the firm changesits priceP

An approach similar to Rotemberg (1982a,b) can be used to develop amodel for P*. Assume that each firm i is a monopolistic competitor withdemand and cost function of the followingform:

(2)and

C(Q(i, t =AeatQ(i, t)"w(t), (3)

where P is the aggregate ppce level, X(t) is total industry sales, eat representstechnologica1 change, w(t) is input prices, and a, b, A, and a are constants.

12This is exactly the same as stating that the proportional difference between P*(t) and P(t)exceeds he.


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262 S. G. Cecchetti,The Irequency 01price adjustment lSubstituting (2) into (3) allows formation of the firm's profit function. Takingthe derivative of profits with respect to the price, setting the result equal to zeroand solving for P(i, t), yields 10gP*(i, t). Then, assuming P and w(t) changeat the same constant rate '1T,and adding a stochastic error UiI to representcomponents of p* not directIy inc1uded in (2) and (3), .110gP*(i, t) can bewritten as

(4)

where TiI is the time since the last price change for magazine i, ('1TT)it iscumulative inftation since the last price change, and Xii is the cumulativechange in industry sales since the last price change for the ith magazineP

Inc1udedin the error term u iI are firm-and time-specificmeasuresof costs anddemand which are not readily observable.Specification of eq. (1) for the purposes of estimation can be carried out by

defining

Sil = .110gP*( i, t) - {hc(i, t) - ho(i,l)}(5)

11~, The quantity ail represents information about magazine i's price change ruleat time t. Assuming UiI has a cumulative logistic distribution, then

Pr( YiI = 1 ) = F( Sil ), (6)

where F signifies the logistic function and Sil = SiI- Uj('14 Obviously for ail tobe identified, it cannot be permitted to change for each magazine for everytime periodo In what follows identification is achieved by assuming that .theconstant associated with a magazine takes on the same value in non-overlap-

ping three-year periods.Substituting eq. (5) into (6) yields the model for estimation. It has the

characteristic that the probability of observing a magazine price change on agiven day depends on a firm's history, or path, prior to that day. The modeldecomposes the probability of observing a price change into a component thatcan be explained by rule changes and a component that can be explained bychanges in the movement of P*. Changes in the constan! term ail in eq. (5)represent changes in the distance (hc(i, t) - ho(i, 1) both across magazines

/13The term in eq. (4) for the time since the last price change, 11" may represent a trend in

demand as well as technological change. To see why, note that inclusion of an exponential timetrend in (2) leads to exactly the same expression.

14See Chamberlain (1980,1984) for a discussion of the use of the logistic distribution in discretedata analysis.


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S. G. Cecchetti, The frequency of price adjustment 263

and over time. And the b's are related to the short-run changesin theprobability of observing a price change, holding the price change role fixed.

The model specified in (5) can be modified to include the information

contained in the magazine's previous fixed price change, .1logP(i, i). Note that

.1logP(i, 1) = hc(i, 1) - ho(i, 1), (7)so

(8)

Then, defining a~ = ait + .1logP(i, i), and substituting the result into eq. (5), a

new specification can be derived with the previous fixed price change added tothe original set of right-hand-side variables. For tbis case (5) can be rewrittenas

Sit = a~ - .1logP(i, 1) + boTt + b1 ('TTT)t + b2Xit + Uit. (9)

The new constant term, a~, is a measure of the distance from the currentceiling barrier to the one implied by the previouspric.echange.

In order to allow both the ait's and the a~'s, and consequentlythe pricechange role, to vary both acrossmagazinesand over time, a particular form ofa logistic model is used. In bis study of the analysisof covariancein discretedata models, Chamberlain (1980,1984) describes a technique designed tohandle what he calls fixedindividualor group effects.Problemsoccur in paneldata sets where small groups of observationsare known to be related, havingspecial charateristicsthat cannot be directlyobserved.Tbis relationsbipis thefixed effect. Examples are readily apparent in applications using longitudinaldata where a group is an individual or a family.As Chamberlain points out,when personal characteristics are correlated with the explanatory variables,standard estimation techniquesfail to identify the coefficientsrelated to thesevariables. He then proposes a practical way to control for these fixed effectsthereby circumventingthe problem.

In the framework of the magazine price model a 'group' is a series ofadjacent years for a given magazine during wbich the price change rule isassumed not to change. One approach to dealing with this would be to allowthe constant term to vary from group to group, including a dummy variablefor each. When there are a large number of groups and on1ya smallnumber ofobservations in each, this involvesmassivecomputation. In the standard case,one would simply choose estimates of the a's and b's to maximizelog L =LLt 10gF(S;t). Chamberlainnotes that when F is a logisticfunction, the sumof the dependent variables within a group is a sufficientstatistic for the fixedeffect, or group-specificconstant termoTo see how this works, label a group ;)f


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264 S. G. Cecchetti, The Irequency 01price a4justment

observations for magazine i over which the constant term is the same by j andits associated constant aij' Then the sum of the value of the dependentvariable over the group, call this t'Pij, is a sufticient statistic for aij' If, for

example, a set of observations is one magazine for three years, then aijrepresents the constant for that portion of the panel data set and the sum t'Pij isthe number of price changes that occurred over that periodo Chamberlainshows that maximizing 10gL is the same as maximizing the conditionallikelihood 10gU = 1:):, 10gG(S;,) where G(S;,) = Pr(YitI t'Pi) and the observa-tion at time t is in group j. Some thought reveals that formulation of 10gLwill entail throwing out any cells where all Yit's are the same, so .their sum iseither zero or the size of the cell. These cells are degenerate; the likelihood ofobserving a particular outcome at a given time is completely determined given

this sumoIt is important to understand the nature of the conditional likelihood

function that is used in the fixed effects estimation. First, it is only a functionof the slope parameters, the b's in eqs. (5) and (9), and not the fixed effectsthemselves. The a 's, which are treated as nuisance parameters, are integratedout. They are never estimated. The con~itional likelihood function and theunconditional likelihood function of the standard logit estimation are notcomparable. They need not be of the same order of magnitude. In fact,whenever degenerate cells exist, the probability of observing the sum, Pr( c;t)ij)'cannot be computed and calculation of the value of the unconditionallikeli-hood will not be possible.

4. Empirical results

The model developed in the last section was estimated using data on changesin the newsstand prices of magazines. Th Chamberlain fixed effects logisticformulation was used. The constant term was allowed to change for eachmagazine every three ')rears.15There are a total of 318 constant terms for the954 observations in the sample. This is equivalent to allowing each magazine torevise its price change rule at most once in each three-year period, or up tonine times over the twenty-seven years covered in the sample.

Table 2 presents the estimates for five specifications of the model. All utilizethe Chamberlain technique.16 The results for each model include the parameterestimates, the b's, with their asymptotic t-statistics in the left half of eachcolumn, and the estimated slope of the probability at the regressor means, they's, in the second half. An individual Yi is defined as the derivative of the

15The length of the period was chosen to be small enough to allow ftexibility in the specification,large enough so that the remaining parameters could be estimated with precision, and because it isan integer divisor of twenty-seven, the number of years in the sample. Experimentation with two-and four-year periods yielded similar results.

16Newton's method was used to obtain the estimates. See Greene (1983).


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,probability with respect to Xi' evaluated at the mean of the data set, andequals bP(I- P), where P is the average probability of observing a pricechange in the data set as a whole. The asymptotic (-statistics for the y's are

also reported.17The first column of table 2 presents results for the steady state model that

implies the probability of observing a price change should depend on inftationand sales volatility alone. This model was estimated using the fixed effectsformulation both for comparability with the path-dependent versions and toallow differences across magazines. The log likelihood value of -181.30 isbarely different from the value of - 182.37 computed when the parameters areconstrained to zero.18Along with the theoretical arguments in the previoussection, this is evidence that the steady state model is inappropriate for thestudy 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 ~logP(i, i) as aright-hand-side variable. The fourth and fifth columns of the table combine thesteady state and path-dependent models by adding current inftation and salesvolatility to the variables representing ~logP*. The combined models areattempts to include the determinants of the price change rule directly in thespecification to be estimated. They are a type of reduced form.19The values ofthe log likelihood function suggest that the four path-dependent models aresubstantially better at explaining the data than is the steady state model. 20Theestimates 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 timesince the last price change by one year increases the probability of a pricechange by a substantial amount, between 0.13 and 0.18. This increase holdsfixed the amount of cumulative inftation experienced over the period since thelast change, so it reftects technological change in production as well as seculardemand shifts.

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

1'Note that since P -F( Xb), computation of the standard errors is non-trivial.1HAnexperiment was performed where current inftation was replaced by a three-year lagged

moving average. The results were nearly identical.

19Asis discussed below, if the rule is truIy linear in current inftation and sales volatility, then theChamberlain technique would be unnecessary. The constant would not vary at least over time.Allowing the constant to vary allows the specification of the determinants of the rule to be morecomplex than a simple fixed linear function.

20Statistical comparison of the steady state model with the other models in table 2 would requiredevelopment of a test for non-nested limited dependent variable models. While it may be possibleto work out a test for the case under consideration, it is beyond the scope of this paper.


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s. G. Cecchetti, The Irequency 01price adjustment 267

ences higher inftation for any year since its last price change, tbe probability ofits price changing will increase unambiguously. In fact, a single year witb justfive percentage points more inftation will increase tbe probability by tbe y for'1fT of 1.95, times 0.05, or nearly 0.1. But tbe estimates of models (4) and (5) tella different story. Tbey predict tbat a five percentage point increase in inftationfor one year will initially lower tbe probability by 0.05 below where it wouldhave been. (Tbis is tbe sum of tbe y's for '1fT and '1f times 0.05.) Tben in tbefollowing year, tbe probability will rise 0.15 above where it would have been.According to tbe combined model, tbe time patb of tbe inftation increasesmatters.21

Use of tbe Chamberlain technique can be tested against several interesting

altematives. One might think tbat tbe structure of tbe constant term, andconsequently tbat of tbe price change role, might not be so complex. Twopossibilities are tbat tbe constant may vary only across magazines, or tbat itmight not vary at all. Tbis suggests several dummy variable specificationsagainst which to test tbe estimates from tbe more complex technique. Tbe firstcontaining one constant term, tbe same for all magazines and all time, and tbesecond including thirty-eight constant terms, one for each magazine. Undernormal circumstances, comparison of pairs of models is made possible byeither a likelihood ratio statistic based on the value of tbe two unconditional

likelihoods or a Wald statistic computed from tbe sets of parameter estimatesand tbeir estimated covariance matrices. But since tbe simpler models areestimated using tbe standard procedure which yields a value for tbe uncondi-tional likelihood, 10gL, in tbe previous discussion, and tbe Chamberlainmethod only allows computation of tbe non-comparable conditionallikelihood10gLC,tests of tbe first type cannot be performed. Furtbermore, direct estima-tion of all of tbe fixed effects, tbe a's in the Chamberlain model, is notpossible. But the various specifications of tbe constant can be compared using

a Hausman (1979) test to examine tbe parameters of interest, tbe b's in table2.22 Tbe test was run on tbe four patb-dependent specifications and tbe resultswere all tbe same. Tbe parameter vector from tbe estimation which utilized tbeChamberlain technique is always significantly different from that obtainedfrom either of the simpler constant term specifications. Test statistics witbchi-squared distributions witb 3, 4, or 5 degrees of freedom rise as high as 60and never fall below 40.

21Using tbe model discussed in Cecchetti (1985) it can be shown tbat tbese estimates imply tbat

an increase in inflation willlead to an increase in tbe dispersion of relative price inflation, eventbough tbe probability of seeing a price change increases. Hence an increase in inflation leads to adecrease in tbe informativeness of tbe price system.

22The Hausman test examines two nested models, one witb more parameters tban tbe otber.Under tbe hypotbesis tbat tbe model witb fewer parameters is not misspecified, tbe larger modelYields consistent but asymptotically inefficient estimates of tbe parameters of interest. Hausmandevelops a procedure based on tbe variance-covariance matrices of tbe two estimators for testingwhetber tbe parameter vectors are significantly different.


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268 S. G. Cecchetti, The Irequency 01price adjustment I

'..

The Hausman tests indicate that for models (2) and (3) the constant term,and consequently the price change rule, differs both across magazines and overtime. The interpretation of the constant term in specifications (4) and (5) is not

as clear-cut since it is the portion of the price change rule not adequatelycaptured by the current inftation and sales volatility variables. So the rejectionof the simple model based on the Hausman test is not as informative. Oneconclusion is that the inclusion of a linear function of current inftation andsales volatility to measure changes in the price change rule is inappropriate. Ifit were correct the test would fail to reject a simpler model. It can be arguedthat the variables as included in (4) and (5) are misspecified. A careful readingof the theory shows that it implies that the current distance {hc(i, t) - ho(i, t)}is determined by the long-run expectation of future inftation and volatility at

the time of the most recent rule revision. Modeling the price change rule usingcurrent levels of inftation and sales volatility presumes that the rule changesevery year.23 But in the path-dependent model prices change slowly and therule is an historical artifact. To specify the determinants of the rule correctlyone would have to formulate an explicit model of the timing of rule revisions.Only then, when one could specify the information available to agents at thetime of the revisions, would consideration of the determinants of (hc(i, t)-ho(i, t be possible. This argues for discounting (4) and (5) completely.24

To study the price change rule, estimates o the average value of the constantterm, call this at, were computed.25 Recall that the constant term is notestimated directly using the Chamberlain technique. Unfortunately, the tech-nique does not allow calculation of the actual value of the constant in everyone of the 318 cells for which it theoreticallyexists. In those cases where thesum of the Yit's over the three-year period is either zero or three, theprobability of any individual Yit being zero or one is completely determinedgiven this sumo In these degenerate cases, the constant is either positive ornegative infinity. What can be computed is the value of the constant at theJ..Ileanof the data for the nine non-overlapping three-year periods that comprisethe data seto These are measures of the constant for a representative averagemagazine.' Changes in at are changes in the probability of observing a pricechange, holding the distance P * has traveled fixed, and suggest changes in theprice change rule.

23Experimentation with lagged moving averages of inftation did not alter the results.24An altemative interpretation of the test results is that movements in the constant term in

models (4) and (5) are an indication of non-linearity in the relationship of the price change rule toits determinants. If the function is seriously non-linear in the range of the data, movements in theconstant term would reftect the differences between the correct relationsbip and the linear oneestimated. In tbis case as well, interpretation of the constant term is difficult.

2sIn light of the previous discussion, results are reported using only the pure path-dependentmodels (2) and (3). It is important to point out that the pattem of the estimated constant term forthe combined models (4) and (5) is exactly the same as that presented.


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270 S.G. Cecchetti, 1e frequency ofprice adjustment

that an increase in the constant from - 9.8 to - 6.1 increases the probabilityby the satne amount as waiting an additional 2.2 years.27 Put differently, therise of 2.3 in a, decreases the time since the last change required to achieve a

given probability by 2.2 years.Increases in a, represent a decrease in the distance from the previous retumpoint to the corrent barrier.28Analogously, an increase in a can be interpret-ed as a lowering of the corrent ceiling, he(t), relative to the previous one,he(l). These estimates, together with direct information on the average correntfixed price change .!1logP(t) reported in the third column of table 3, yield aninteresting picture of the evolution of the price change role.29 The table showssome large ftuctuations in the a,'s, but only small changes in the .!1logP(t)'s.The decreases in the a,'s during the entire sample suggest first a chmge in the

symmetry of the price change rule, and then an actual decrease in the distancefrom the ceiling to the barrier. When a, grows, but the actual price changeremains the same, the new barrier and return point will both be below theprevious ones. The growth in a signifies downward revisions of the ceilingbarrier he. A higher a, means that P* is not allowed to travel as far above thefixed price before a change, and that the fixed price is reset further above P *than it was before. It is interesting to speculate about the causes of this changein symmetry. Changes in uncertainty and attitudes to:-vards it in recent yearsmay be responsible.30 When estimates of future inftation are imprecise and the

costs of changing prices are high, it is reasonable to expect a risk-averse priceseUer to choose a fixed price that overshoots the corrent short-run optimalprice by more than he or she would if future inftation were certain.

The series presented in table 3 can also be used to examine the adjustmentcost strocture. The theory described in section 3 predicts that when the realcost of a price change is constant, the distance from the return point to thebarrier of the price change rule should grow with inftation. This means that thee.stimates of .!1logP(t) should increase with inftation, and that the a,'s shoulddecrease (become more negative). This is c1early not the case. The evidence

shows that the distance o the rule in nominal terms shrunk slightly during the

27The additional waiting time is .:1T- .:1iir/(b + b2w).

28Under certain circumstances, problems can arise in the interpretation of the average values ofthe fixed effect, ar and a. To the extent that either systematic changes in the price change rule arecorrelated with variables included in the model of P* or components causing movements in P*have been omiued, the estimates may not accurately reftect changes in the distance from the retumpoint to the barrier. But given the specification of the model it is difficult to see how this could beso.

29.:1logP(t) = hc(t) - ho(t), the average current fixed price change, should not be confused with.:1logP(i, t), the previous fixed price change for an individual magazine.

30Since the estimates of the ar 's from models (4) and (5) which include sales volatility show thesame pattem as those in table 3, the uncertainty would have to arise from a source not specificaIlyconsidered.


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s. G. Cecchetti, The frequency of price adjustment 271

1970's, a time when general price inflation was increasing. This is consistentwith the fact that the average reai fixOOprice change (nominal change lessinflation since the last change) decreasOOsubstantially during the 1970's. Since

the theory states that the distance from the return point to the barrier shrinkswith adjustment costs, the results suggest that the cost of a nominal pricechange falls either when the size of a real price change decreases, as describedby Rotemberg, or as the frequency of adjustment increases.31

S. Conclusion

The newsstand prices of magazines provide strong emprical support forsticky price models basOOon monopolistic competition. The data show thatmagazine prices exhibit substantial stickiness allowing their real prices to erodeby as much as one-quarter before implementing a fixOOprice change. FurtheranaIysis demonstrates that the costs of nominal price changes decrease eitherwith increases in the frequency of adjustment, or with decreases in the size of areal price change. The evidence supports the contention thatcustomers facedwith ready substitutes prefer stable price paths to those with large infrequentJumps.

Changes in the economic environment since the Korean War, most notablyincreases in the level of general price inflation, have 100 to an increase in thefrequency of magazine price change. As average annual inflation rose fromnear 2% in the 1953-1965 period to almost 8% in the latter half of the 1970's,the average time between magazine price changes' fell from seven and a halfyears to three and a quarter years. While this evidence is for prices in only oneindustry, it is extremely likely that the frequency of adjustment for all prices inthe economy increased over this period.32 The shortening of the time periodbetween nominal price adjustments has been the result of two complementary

and related factors. First, there has been an increase in the rate of change inthe price a firm would charge in the absence of adjustment costs. Thisshort-term optimal price has been moving more rapidly asa consequence ofhigher general price inflation. Second, contrary to the results of models thathold real adjustment costs fixOO,the emprical results show that higher inflationwas accompaniOO by relative constancy in the distance the optimal price has tomove before the fixOOprice is changOO.This finding implies both that pricesetters opt for more frequent price adjustment when inflation is higher, andthat adjustment costs fall as changes become more frequent. There appears to

31The slight increase in the estimates of the a/s for the 1971-1973 period is consistentwith theexpectation that the Nixon wage-price controls raised adjustment costs.

32Evidence is provided in Cecchetti (1985) that the average frequency of price change in theeconomyas a whole increased first in 1967 and again following the Nixon incomes policy in 1974.


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272 s. G. Cecchetti, The Irequency 01price adjustment lbe justification for the c1aim that an int1.ationary environment breeds a lower-ing of buyer resistance to price changes.

It is c1ear from this exercise that the frequency of price adjustment is aquabtity determined endogenously in the economy. Any attempt to build amodel of the inflation process and macroeconomic adjustment must takeaccount of this endogeneity. Both the short-run and long-run effects ofincreases in inflation on the frequency of price adjustment appear to be sizable.The implication is that higher inflation leads to faster adjustment and less pricestickiness.33 Failure of staggered contracts models to take this into accountcould easily lead to false conclusions about the short-term impact and longev-ity of both government intervention and external shocks.

Appendix

A.l. Magazines

The data set is composed of magazines continuously published from January1950 to January 1980 and available on a newsstand in the winter of 1982. Dueto a lack of information on the size of the previous nominal price change,.:11ogP(i), data used in the estimation of section 4 does not begin in 1953 forthirteen of the thirty-eight magazines. For four magazines, data was lost forthree years, for eight it was lost for six years, and for one, data was lost fortwelve years. This left a total of 954 observations. The data was collected at theBerkeley Public Library and at various libraries of the University of California.

~I The magazines used were: Antiques, ArchitecturalReview, Atlantic, Audio,Better Homes and Gardens, Business .Week, Commentary, Consumer Reports,Current History, Ebony, Esquire, Films in Review, Foreign Affairs, GoodHousekeeping, Harper's Bazaar, Harper's Magazine, High Fidelity, Houseand Garden, House Beautiful, Interiors, Modern Photography, Motor Trend,Nation, The New Leader, The New Republic, New Yorker, Newsweek, Parents',

Popular Mechanics, Popular Science, Road and Track, Science Digest, Scien-tific American, Sunset, Time, U.S. News and World Report, Vogue, andYachting.

A.2. The sales volatility index

The sales volatility index used in the estimation reported in section 3, table2, was generated as the three-year centered moving average of the squaredresiduals from a regression of the single-copy sales of all magazines on three

past lags and the total number of magazines available in a given year.33As is noted above, the inforrnation content of the price system may decrease with inftation as

relative price variation appears to increase. While adjustment is faster, knowledge about thecurrent environment and P* is less precise. This creates a type of inefficiency that is very differentfrom that usually studied with sticky price models.


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S.G. Cecchetti, The Irequency 01price adjustment 273

The regression results are

ScS(t) = -9,758.280+ 1.123 ScS(t -1) - 0.537 ScS(t - 2)(1.79) (6.96) (1.92)

+ 0.255 ScS(t- 3) + 1,591.6 TM(t),(1.29) (2.18)

lP = 0.94, D.W. = 1.94, S.E.R. = 2,522.000,

where ScS(t) are the single-copy sales in year t and TM(t) are the totalmagazines available in year t. The source of these data is the MagazinePublishers Association.

The sales volatilityindexused in the reported workwas scaledby a factor of1012.The index represents the one-period-aheaduncertainty in industry salesconditional on sales during the past three years. The use of sales figures,indirectly to compute the volatility measure and directly in forming the pastsales value, in an estimation based on prices may produce inconsistency.Butgiven that it is industry-widesalesbased on eightyto hundred magazinesthatare used, and that there are only thirty-eight magazinesin the sample, each

magazine's sales are small relative to the total, so this is unlikely to be aserious problem.

References

Blanchard, O.J., 1983, Price asynchronization and price level inertia, in: R. Dombusch and M.H.Simonsen, eds. Inftation, debt and indexation (M.I.T. Press, Cambridge, MA).

Cecchetti, S.G., 1985, Staggered oontracts and the requency o price adjustment, QuarterlyJoumal o Economics 100, 925-959.

Chamberlain, G., 1980, AnaIysis o oovariance with qualitative data, Review o Economic Studies

47, 225-238.Chamberlain, G., 1984, Panel data, in: A. Gri\iches and M.D. Intriligator, OOs.,Handbook o

econometrics, Vol. 2 (North-Holland, Amsterdam) 1247-1318.Greene, W.H., 1983, LIMDEP, American Statistician 37,170.Hausman, J.A., 1978, Specification tests in econometrics, Econometrica 46,1251-1271.Iwai, K., 1982, Disequilibrium dynamics (Yale University Press, New Haven, CI).Kieer, N.M., OO., 1985, Econometric anaIysis o duration data, Annals 1985-1, Journal o

Econometrics 28,1-169.Miller, M.H. and D. Ore, 1966, A model o the demand or money by firms, Quarterly Joumal o

Economics 80, 413-415.Mussa, M., 1981a, Sticky individual prices and the dynamics o the general price level, in: K.

Brunner and A.H. Meltzer, 008., The oosts and oonsequences o inftation, Camegie-RochesterConerence Series on Public Policy, Vol. 15 (North-Holland, Amsterdam).Mussa, M., 1981b, Sticky prices and disequilibrium adjustment in a rationa! model o the

inftationary process, American Economic Review 71, 1020-1027.Okun, A.M., 1975, Inftation: Its mechanics and welfare oosts, Brookings Papers on Economic

Activity 2, 351-399.Okun, A.M., 1981, Prices and quantities (The Brookings Institution, Washington, DC).Rotemberg, J.J., 1982a, Monopolistic price adjustment and aggregate output, Review o Economic

Studies 49, 517-531.


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274 S. G. Cecchetti, The frequency 01price adjustment

Rotemberg, U., 1982b, Sticky prices in the United States, Journal of Political Economy 90,1187-1121.

Sheshinski, E., A. TishIer and Y. Weiss, 1979, Inftation, costs of adjustment and the amplitude ofreal price changes: An empirica1 analysis, Working paper 35-79 (Foerder Institute for Eco-nomic Research, Te1-AvivUniversity, TeJ-Aviv).

Sheshinski, E. and Y. Weiss, 1977, Inftation and costs of adjustment, Review of Economic Studies44, 281-303.Sh.shinski E. and Y. Weiss, 1983, Optimal pricing policy under stochastic inftation, Review of

Economic Studies 51, 513-529.TayJor, J.B., 1980, Aggregate dynamics and staggered contracts, Journal of Politica1 Economy 88,

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