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 i