Menu costs, firm size and price rigidity

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1 Economics Letters 66 (2000) locte/ econbse Menu costs, firm size nd price rigidity Robert A. Buckle *, John A. Crlson, b School of Economics nd Finnce, Victori University of Wellington, P.O. Box 600, Wellington, New Zelnd b Krnnert School of Mngement, Purdue University, West Lfyette, USA Received 11 Mrch 1999; ccepted 13 July 1999 Abstrct If menu costs hve non-negligible lump-sum component nd with lrger firms hving greter benefits from price djustments, then lrger firms will chnge price more frequently thn smller firms. Dt from New Zelnd firms support this hypothesis. Price durtion decreses s firm size increses. Ordered probit nlysis indictes the effect comes primrily from lrger firms being more likely thn smller firms to rise price in response to demnd or cost increses Elsevier Science S.A. All rights reserved. Keywords: Menu costs; Firm size; Price durtion; Price rigidity JEL clssifiction: E3; D4 1. Introduction Menu costs of price djustment hve become populr explntion for price stickiness in mrkets chrcterised by monopolistic competition (See reviews by Andersen, 1994; Bll nd Mnkiw, 1994; Benssi et l., 1994, ch. 7). Menu costs include dministrtive, technicl nd informtionl costs of deciding on nd implementing price chnge. A significnt proportion of these costs is likely to be lump-sum nd independent of firm size. For exmple, n importnt cost of price djustment is the time nd ttention required by mngers to gther the relevnt informtion to mke nd implement pricing decisions (Levy et l., 1997). Similrly, lthough the totl cost of chnging price lists, tgs nd ctlogues nd dvertising price chnges my vry with firm size (for instnce, firms with lrge volume of output my need to distribute new price ctlogues to lrger number of distribution outlets), there will nevertheless be lump-sum set-up costs which re likely to be similr cross firms irrespective of their size. *Corresponding uthor. Tel.: ; fx: E-mil ddress: bob.buckle@vuw.c.nz (R.A. Buckle) / 00/ $ see front mtter 2000 Elsevier Science S.A. All rights reserved. PII: S (99)

2 60 R.A. Buckle, J.A. Crlson / Economics Letters 66 (2000) If menu costs involve common lump-sum component, the cost of price djustment per unit of output will fll systemticlly s firm size increses. It follows, therefore, tht in the presence of lump-sum menu costs nd common shocks to desired price, other things equl, smll firms will tend to exhibit greter price rigidity thn lrge firms. We present simple expression tht cptures the reltionship between firm size nd the benefit of price chnge following shock to desired price. Dt from survey of New Zelnd firms is then used to mesure price rigidity: (i) by n estimte of price durtion, defined s the verge length of time between successive price chnges nd (ii) by price responsiveness of firms to cost nd demnd chnges. 2. Hypotheses bout the effects of firm size on price rigidity Consider simplified version of n optiml Ss rule for price setting monopolist specified by Blnchrd nd Fischer (1989, pp ). Assume the following liner demnd nd cost functions: Y 5 2 bp 1 m;,b. 0 (1) C 5 (d 1h)Y; d. 0 (2) where Y5output, P5price, C5costs of producing output nd m nd h re shifts in demnd nd costs, respectively. There re two differences from the specifiction in Blnchrd nd Fischer. The first is tht we hve dropped their qudrtic term in the cost function. The second is the introduction of cost shifts. Suppose price hs been set to mximize profits when m 50 nd h50. As m nd h chnge over time, the firm could increse profits by chnging its price but my not do so when there re menu costs of mking price chnge. When m nd/or h re non-zero, the difference between profits with n optiml price nd profits with no chnge in price cn be shown to be: 2 2 m bh mh 2 B(m,h) 5] 1]] 1] 5(m 1 bh) /4b (3) 4b 4 2 Cll this benefit from chnging price the opportunity cost of not chnging price. Suppose tht the firm will chnge price whenever this opportunity cost exceeds criticl level tht represents the cost of mking price chnge. At tht point, price is reset optimlly, the nd d prmeters re redefined to include the m nd h chnges tht hve occurred since the prior price chnge, nd the process is repeted. We hve ssumed tht lrger firms hve lrger demnd. More explicitly, in this model lrger firm hs lrger vlues of both b nd the stndrd devition of m. However, ny upwrd shift in costs will tend to be the sme cross firms of different size. As result, exmintion of Eq. (3) revels tht B(m,h), the opportunity cost of not chnging price, rises in direct proportion to firm size. If the cost of chnging price hs non-negligible lump-sum component or rises less thn proportiontely to the increse in the size of the firm, then smller firms will tend to chnge price less frequently thn lrger firms. Consider, for exmple, distribution of cost chnges. Lrger firms, with lrger vlues for b, will hve more dispersed distribution of B(m,h). As result higher proportion

3 R.A. Buckle, J.A. Crlson / Economics Letters 66 (2000) of lrger firms with cost increses will decide to rise price nd higher proportion with cost decreses will decide to lower price compred to smller firms. A similr prediction holds for demnd chnges if lrger firms tend to hve more dispersed distribution of demnd shifts. If, s suggested by the foregoing rgument, lrger firms chnge prices more frequently thn smller firms do, then we predict tht mesure of price durtion, the verge time between price chnges, will be longer for smller firms. 3. Micro firm dt Informtion bout firm price, cost nd demnd chnges nd firm size ws obtined from the New Zelnd Institute of Economic Reserch s Qurterly Survey of Business Opinion. This survey involves the distribution to business executives of stndrd questionnire tht identifies the firm, its principl ctivity, loction, size, nd series of questions sking bout the firm s operting environment. It lso contins stndrd question sking executives to report their perceptions of the ctul chnge during the immedite pst 3 months for severl ctivity vribles including verge selling prices, verge costs, nd new orders. Firms do not indicte the mgnitude of chnge, only the direction of chnge, whether up, sme or down. Firms were llocted to size ctegory ccording to their response to the following question: How mny employees re covered by this return? There re six size ctegories: (1) Employees#20; (2) 20,Employees#50; (3) 50,Employees#100; (4) 100,Employees#200; (5) 200,Employees# 500; (6) 500,Employees. 4. Tests of reltive price rigidity 4.1. Durtion of prices The following procedure ws used to obtin sttistics for price durtion. Let p 5percent of firms d reporting price increses in the lst n months nd p 5percent of firms reporting price decreses in the lst n months. An verge time T in months between price chnges is then given by the following: u d T 5 n/(p 1 p ) (4) For exmple, if in qurterly survey 75% of the firms report they did not mke price chnge in the lst 3 months nd 25% did, then representtive firm will go 3/ months before chnging price. There re potentil bises in this mesure. On the one hnd, if firms tend to chnge prices on u d only some items during the qurter but their verge prices re up or down, then ( p 1p ) overestimtes the extent of price chnging ctivity nd T is bised downwrd. On the other hnd, if firms chnge prices more frequently thn once qurter, then T overestimtes the verge durtion between price chnges. Tble 1 shows price durtion estimtes for New Zelnd mnufcturing nd building firms by firm size using this procedure. From Tble 1 it is cler tht the length of time firms hold prices constnt does in fct vry by firm size. The smllest firms in our smple chnged prices on verge every 8.1 u

4 62 R.A. Buckle, J.A. Crlson / Economics Letters 66 (2000) Tble 1 Durtion of prices by firm size (qurterly surveys: 1984:3 1996:1) Firm size: All firms Price durtion (months) (1.03) Stndrd error in prentheses. months during our 11.5-yer smple period. This is more thn 50% longer thn the verge 5.1 months durtion of prices for the lrgest firms. There is lso perfect rnk-order correltion between firm size nd the verge frequency of price chnges. These results strongly support our hypothesis tht lrge firms chnge price more frequently thn smll firms Price responsiveness to cost nd demnd chnges We next look more specificlly t the effect of firm size on price responsiveness to cost nd demnd chnges. To do tht, we use ordered probit regressions to estimte the influence of chnges in costs nd demnd on the probbility of chnge in price seprtely for smll firms (ctegories 1 nd 2) nd lrge firms (ctegories 5 nd 6). The ide of n ordered probit nlysis is to ssign vlue v to ech price chnge observtion. According to expression (3) the probbility of price chnge will be influenced by chnges in costs nd chnges in demnd. In our prticulr ppliction, for firm j t time t, let v 5 g c 1 g d (5) where c5chnge in costs (c51 if costs5 Up, c50 if costs5 Sme, c521 if costs5 Down ) nd where d5chnge in demnd (d51 if demnd5 Up, d50 if demnd5 Sme, d521 if demnd5 Down ) experienced by firm j in qurter t. Let u be stndrd norml vrible (with zero men nd vrince of one) nd define three price chnge probbilities: Pr[price 5 down u c,d] 5 Pr[v 1 u, k ] 5 Pr[u, k 2 v] (6) 1 1 Pr[price 5 sme u c,d] 5 Pr[k, v 1 u, k ] 5 Pr[k 2 v, u, k 2 v] (7) Pr[price 5 up uc,d] 5 Pr[k, v 1 u] 5 Pr[k 2 v, u] (8) 2 2 An ordered probit regression procedure estimtes the coefficients g1 nd g2 nd two cut-point prmeters k1 nd k2 tht mximize the likelihood of observing the ctul smple of reported price chnges (see Greene, 1993; nd Stt Corportion, 1995). Tble 2 reports the results of ordered probit estimtes. The coefficients on cost nd demnd chnges re highly significnt for both smll nd lrge firms. To ssess the reltive responsiveness of lrge nd smll firms to cost nd demnd chnges, we need to convert these estimtes into probbilities of price chnges in response to specific cost nd demnd chnges. For exmple, for smll firms tht report cost increse (c51) nd no demnd chnge (d50), the probbility of price increse is given by the Pr [0.781u.1.05]5Pr[u.0.27]50.39 where the

5 R.A. Buckle, J.A. Crlson / Economics Letters 66 (2000) Tble 2 Ordered probit estimtes of influences of cost nd demnd chnges on price chnges (qurterly observtions: 1984:3 1996:1) v 5 g c 1 g d Smll firms Lrge firms No. observtions g (19.10)* 0.59 (18.14)* g 0.37 (12.24)* 0.20 (7.33)* 2 k k z rtios re in prentheses; *denotes significnt t 1% level. Tble 3 Conditionl probbilities of price chnges Pr[price5up u c,d]5pr[k22v,u] Pr[price5down u c,d]5pr[u,k12v] Smll firms Pr[ p5up u c5up, d5sme] Pr[ p5up u c5sme, d5up] Pr[ p5down u c5down, d5sme] Pr[ p5down u c5sme, d5down] Lrge firms v 5 g c 1 g d. Probbilities re bsed on estimtes of the g nd k coefficients reported in Tble 2. lst equlity comes from tble of stndrd norml vribles. These probbilities for smll nd lrge firms re shown in Tble 3. In response to cost increse, lrge firms hve 50% probbility of rising price, wheres smll firms hve only 39% probbility. In the cse of demnd increse, lrge firms hve 35% probbility of rising price nd smll firms 25%. Thus, s predicted, lrge firms re more likely to increse price in response to cost increse or to demnd increse thn smll firms. When there re cost or demnd decreses, there is not much difference in the probbilities tht lrge firms will lower price thn smll firms. In fct, smll firms pper slightly more likely to decrese price in response to cost decrese or to demnd decrese thn lrge firms. We hd not expected tht result. The shorter price durtion for lrger firms rises primrily becuse lrger firms re quicker to respond to cost nd demnd increses thn re smller firms. References Andersen, T.M., In: Price Rigidity Cuses nd Implictions, Oxford University Press, Oxford. Bll, L., Mnkiw, N.G., 1994, A Sticky-Price Mnifesto, Crnegie-Rochester Conference Series on Public Policy, vol. 41, pp Benssi, C., Chirco, A., Colombo, C., In: The New Keynesin Economics, Blckwell, Oxford. Blnchrd, O.J., Fischer, S., In: Lectures on Mcroeconomics, MIT Press, Cmbridge. Greene, W.H., In: Econometric Anlysis, 2nd ed., McMilln, New York. Levy, D., Bergen, M., Dutt, S., Venble, R., The mgnitude of menu costs: direct evidence from lrge US supermrket chins. The Qurterly Journl of Economics 112, Stt Corportion, 1995, Stt Sttisticl Softwre: Relese 4.0, College Sttion, TX, USA.