Asymmetric Adjustments of Price and Output

ASYMMETRIC ADJUSTMENTS OFPRICEANDOUTPUT P.A.TinsleyandRevaKrieger (cid:3) version: June1997 Abstract: Asymmetries in price adjustment can reconcile contrasts between rapid price movements in inflationary episodes, consistent with classical theories of flexible pricing, and sluggish price responses in contractions, consistent with Keynesian theories of sticky price adjustments. Nonparametric analysis of SIC two-digit industry data indicates that negative asymmetries are more pronounced for real outputs than for nominal outputs, suggesting reversed positive asymmetries in producer pricing. Pricing decision rulesareestimatedtodistinguishbetweenasymmetriesinconditioningshocksandasymmetriesinproducer responses. Tworationalmotivesforasymmetricpricingaresupported. Keywords: Asymmetrictrenddeviations, rationalerrorcorrection, producerpricing. (cid:3) Authors' addresses are: Federal Reserve Board, Washington, D.C. 20551, ptinsley@frb.gov; and International Monetary Fund, Washington, D.C. 20431, rkrieger@imf.org. Views presented are those of the authors and do not necessarily represent those of the Federal Reserve Board or the International Monetary Fund. Our thanks to R. Sweeneyandtworefereesforusefulsuggestions.ForthcominginEconomicInquiry.

1 I.INTRODUCTION A sharp difference persists in economics regarding the dynamic adjustments of prices. In classical theories, markets are continuously cleared by flexible prices with instantaneous adjustments of prices to agents' perceptions of monetary policy. In contrast, Keynesian theories suggest non-auction prices are slow to adjust to equilibrium with short-run clearing achieved by adjustments of transacted quantities. A sufficient reason for the continued split in descriptions is thatbothviewsaresupportedbyempiricalevidence. Thecaseforstickypricesisnoteasilysquared withtherapidmovementsofpricesininflationaryepisodes,asreviewedbySargent[1982]. Onthe otherhand,theassumptionofinstantaneouslyflexibleproducerpricesseemsinconsistentwiththe lengthy spells of rigid prices documented in Carlton [1986] and Blinder [1991] and the sluggish priceresponsesestimatedbySims[1992]andChristiano,Eichenbaum,andEvans[1994]. A third alternative is that both classical and Keynesian characterizations may be describing pricebehaviorindifferentstagesofbusinesscyclesifproducersrespondasymmetricallytopositive and negative deviations from trends. Prompt producer corrections of prices that are below trends can account for the essential classical feature of flexible price responses to expected inflation. Conversely, resistance to margin reductions for prices that are above trends can support the Keynesian description of sluggish adjustment that leaves prices at excessively high levels over extendedintervals.1 Thispaper examinesthecaseforasymmetricpricinginfoursteps: (cid:15) A recent literature, vid. Sichel [1993], indicates that manufacturing output exhibits various negative asymmetries, such as larger trend deviations (in absolute value) at cyclical troughs than at peaks. In section II, a search for similar asymmetries in the outputs of SIC two-digit industries finds that negative asymmetries in trend deviations are more pronounced in real outputs than in nominal outputs. This suggests an offsetting positive asymmetry in industry prices where below-trendprices are morereadilyraisedthanabove-trendprices arelowered. (cid:15) Although suggestive, reported measures of asymmetric data features are atheoretic so sources of asymmetric behavior are ambiguous. To help distinguish between the roles of exogenous shocks and endogenous responses in producer pricing, benchmark structural models of symmetric pricing are examined in section III. The standard frictions model of gradual price corrections based on costly adjustment of price levels, such as Rotemberg [1982; 1987], is rejected forprices ofmanufacturingindustries. Empiricalmodelsofindustrypricingappearto be consistent with an extended definition of frictions where producers aim to smooth moving averages ofprices andinflationrates. 1Although short-run inflexibility of nominal prices is a tenet of new-Keynesian theories of business cycle contractions,anawkwardimplicationofsymmetricallystickypricemodelsisthatpricesmaygetstuckalsoatlevels thataretoolowformarketclearing.

2 (cid:15) TheextendedfrictionsmodelofsymmetricpricingisthenusedinsectionIVtoidentifysources ofasymmetriesinproducerpricing. Empiricaltestsindicatethattheeffects oftrenddeviations in output on price adjustmentsare either statisticallyinsignificant or inconsistentwithpositive asymmetries in pricing, and that asymmetric pricing appears to be a structural decision that depends onwhethertheindustrypriceis beloworaboveitstrend. (cid:15) Section V reviews several interpretations of asymmetric pricing and suggests a representative indicator for each theory. Industry values of these indicators are compared with industry estimates of asymmetric pricing; the cross-industry correlations support two rational motives for positiveasymmetriesinproducerpricing. SectionVIconcludes. II. ASYMMETRIESININDUSTRYOUTPUT This section presents nonparametric measures of asymmetric behavior in output. In contrast to previous work on macroeconomic aggregates, discussion is aimed at outputs of SIC two-digit industries in manufacturing. A comparison between real and nominal outputs is also introduced whichsuggestsanasymmetryinindustrypricing. Descriptions of asymmetricbehavior were prominent in prewar business cycle literature, such as Mitchell [1927], Means [1935], and Haberler [1938]. The issue of cyclical asymmetries then fell into disfavor with the postwar emergence of models of agent behavior based on stochastic linear difference equations. However, over the last decade, several studies have resuscitated atheoretic measurement of cycle asymmetries, with mixed findings for asymmetry. Neftci [1984] presents evidence of asymmetry in the aggregate rate of unemployment, with unemployment faster to rise and slower to fall. Falk [1986] and DeLong and Summers [1986] confirm the positive asymmetry in the unemployment rate but find no evidence of matching asymmetries in the movements of detrended GNP. By contrast, Goodwin and Sweeney [1993] provide evidence of negative asymmetry in real GNP growth where positive growth rates are constrained by a real output ceiling, as suggested by Friedman [1993]. Because the amplitudes of cyclical fluctuations are larger in goods than in services, recent analyses of McNevin and Neftci [1991], McQueen and Thorley [1993], and Sichel [1993] examine cyclical movements in industrial production and indicatethat thebehaviorofgoodsoutputappears tobedifferentinrecessionsthaninexpansions. Thepatternsofasymmetricmovementsreportedforaggregateoutputvarybystudy,inpartdue todifferentdefinitionsofasymmetry. ThepremiseadvancedbyMitchell[1927]isthatoutputfalls fasterfromcyclicalpeaktotroughthanintheexpansionfromtroughtopeak. Termed“steepness” asymmetrybySichel[1993],apatternofslowascentsandrapiddescentswillbedescribedhereas negativegrowth rate asymmetry. Asymmetries in positiveand negativegrowth rates of detrended output are supported for production of durable goods in McNevin and Neftci [1991] but rejected fortotalindustrialproductionbySichel[1993].

3 A contrasting pattern of cyclical asymmetry was suggested by the nonlinear business cycle model of Hicks [1950] where output expansions are eventually constrained by capacity ceilings dueto shortages of laboror fixed capital. Because capacity ceilings placeupper boundson output growth in expansions that are not matched by comparable lower bounds on output contractions in recessions, the average squared negativedeviation from trend may exceed the average squared positivedeviationfromtrend.2 Sichel[1993]indicatesthattrenddeviationsattroughsarelarger(in absolute value) than trend deviations at peaks for industrial production, depending on the method ofdetrending. Dubbed“deepness”asymmetrybySichel,thispatternisdescribedhereas negative gap asymmetry, to emphasize that this is a pattern of trend deviations in log levels rather than in logdifferences. Theanalysisofindustryoutputsthatfollowsis directedatthreeunresolvedissues: (cid:15) First, are asymmetries reported for aggregate goods output also reproduced in industry disaggregations? Ifasymmetricmotionisonlyapparentintotalgoodsoutputthenitisunlikely tobeanintrinsiccharacteristicofproducerbehaviorbutaresultofaggregation,perhapsdueto cyclical shiftsinthecompositionofaggregatedemand. (cid:15) Second, are either of the asymmetric patterns catalogued by Sichel [1993] pervasive in industry behavior? As indicated later, if displacements away from a trend are due largely to unanticipated shocks then asymmetry in gaps on different sides of the trend, due to different producer responses to positive and negative shocks, is amenable to structural interpretations. By contrast, asymmetry in detrended growth rates is more difficult to rationalize in a typical shock/response model of behavior because the set of positive (negative) growth rates encompassesboththereturnfromatrough(peak)turningpointtothetrendandthesubsequent departure fromthetrendtothenextpeak(trough). (cid:15) Third, if systematic asymmetries are detected in industry outputs, are they also reproduced in nominaloutput? Ifthesame asymmetriesinreal outputare reproduced innominaloutputthen an intrinsic asymmetry in producer pricing, such as the “administered pricing” conjecture of Means [1935],is unlikelytobeanimportantcauseofcyclicalasymmetriesinoutput. SelectingtheTrendsof IndustryOutputsandPrices. Although the empirical literature cited above presents evidence of asymmetries in economic timeseries,theredoes not appear tobea consensusamongeconomiststhatasymmetricresponses are a fundamental characteristic of agent behavior. In the case of trending variables, a sufficient reason for scepticism is that empirical evidence of asymmetries appears to depend on the method 2Asymmetryinsquareddeviationsisnotinconsistentwithstandarddetrendingconstructionsthatyieldequalsums (inabsolutevalue)ofnegativeandpositivetrenddeviations.

4 of detrending, vid. Canova [1993]. If the true trend is overstated then the average of negative deviationsfromtrendwilltendtoexceedtheaverageofpositivedeviations,biasingresultstowards a finding of negative asymmetry, and vice versa for underestimates of the trend. The analytical focus of theliterature onasymmetrictrend deviationsis further blurred bythe wideassortment of availabledetrendingmethods.3 In the case of manufacturingindustries,postwartimeseries on industryoutputsand prices are consistent with difference-stationary behavior so it appears appropriate to select I(1) trends that arecointegratedwiththerelevantindustrypricesandoutputs. Forlogindustryoutput, q t ,thetrend measuresusedhereare basedonFRB staffestimatesofcapacityutilization,Raddock[1985]. The industrylogutilizationrates are stationary,sothesamplemeanof an industryutilizationratemay be interpreted as the long-run preferred utilization rate of producers. Trend output or the log of preferred output, q (cid:3) t , is constructed by subtracting the log of the industry utilization rate from log output, q (cid:3) t (cid:17) q t (cid:0) u t . The log of the preferred utilization rate is normalized to zero by removing thesamplemeantoensurethatthesumofsampletrenddeviationsis zero, P t u t = 0 . The log of industry nominal output, n t , is the sum of log output plus log price, n t = q t + p t . Under imperfect competition by identical producers, the optimal industry price can be expressed as a markup over marginal cost.4 Under the assumption that gross production is Cobb-Douglas, the log price trend, p (cid:3) , of each industry is constructed by cointegration regressions on weighted indexes of the log prices of raw and intermediate materials inputs and unit labor costs, where the index weights reflect the input requirements of the relevant industry. As one would hope for exogenous trend constructions, vid. Gonzalo and Granger [1995], systematic reductions in the trenddeviationsofbothindustryprice andoutputare dominatedbytheerror correction responses of industry price, (cid:1) p t , and output, (cid:1) q t , whereas error correction responses of trend price, (cid:1) p (cid:3) t , andtrendoutput, (cid:1) q (cid:3) t ,are negligible.5 Contrastsofreal andnominaloutputtrenddeviations. Asymmetries in trend deviations by industry real and nominal output are displayed in table I. The basic measure of asymmetry in table I is the ratio of the positive semi-variance (the mean of squaredpositivedeviationsfromtrend)tothenegativesemi-variance(themeanofsquarednegative 3Cautions against indiscriminate use of detrending methods include those of Nelson and Kang [1981] on deterministic trends, Osborn [1993] on detrending by moving average filters, and Harvey and Jaeger [1993] on detrendingbytheHodrick-Prescottfilter. 4Instandardformulations,suchasWaterson[1984],thelogmarginis l o g [1 (cid:0) ( s (cid:17) ) (cid:0) 1 (cid:0) ] 1 where (cid:17) denotestheprice elasticityofindustrydemandand s isthenumberofproducers,illustratingmonoplyorcompetitivesolutionsas s ! 1 or s ! 1 5Anappendixontheintegrationorders,cointegratingtrends,anderrorcorrectionresponsesofindustrypricesand outputsisavailablefromtheauthors.

5 deviations from trend). The entries in table I will be one if the distribution of trend deviations is symmetricalbut lessthanoneifthedistributionisnegativelyskewed.6 Negative asymmetry in growth rates is rejected for detrended real GNP by DeLong and Summers [1986] and Sichel [1993]. The first two columns of table I indicate the extent of asymmetry in the growth rates of detrended industry outputs, (cid:1) q t (cid:0) (cid:1) q (cid:3) t . Trend output, q (cid:3) t , is measuredinthefirstcolumnbyasimplelineartrend,labeledOLStrend,andinthesecondcolumn by the cointegrating construction based on FRB capacity utilization rates, labeled I(1) trend. Negative asymmetry in growth rates appears to be reasonably widespread among manufacturing industries,andthedegreeofasymmetryisrelativelyinsensitivetothechoiceoftrend. Theratioof positive to negative semi-variances for the growth rates of real output is less than unity at a 9 0 % significancelevelorbetterforsevenindustriesandconsiderablylessthanunityforallbutthreeor fourindustries. The third column in table I displays the ratio of semi-variances in the growth rates of trend deviations in industry nominal outputs. Here, there appears to be much less evidence of negative asymmetry in growth rates. The semi-variance ratios for nominal output are generally larger than those for real output and about a third of the ratios are greater than one, indicating that the positivegrowthratesofdetrendednominaloutputarelargerthanthenegativegrowthratesinthose industries. TherighthalfoftableIdisplaysasymmetriesinthelevelsoftrenddeviationswheretherelevant measure is the gap deviation, q t (cid:0) q (cid:3) t . As with the growth rate measures, the first two columns in the right half of table I measure the asymmetry in squared output gaps for two measures of trend in output. In the case of the linear OLS trend, there is no clear tendency towards negative gap asymmetrywithabouthalfoftheindustriesaboveoneandtheremainderbelow. However,because OLS regressions minimize the sum of squared deviations, the linear trend is biased against gap asymmetry. Even if negative gap asymmetry exists, the OLS estimator pulls down the estimated trendinordertoreducethesquaredoutliereffects ofthelargernegativegaps. A different picture emerges in the next column of table I, labeled I(1) trend, which uses the cointegrating trends based on preferred utilization of capacity output. This measure suggests negative gap asymmetry in output is even more pervasive across industries than the asymmetry ofgrowthratesshowninthefirsthalfofthetable. Theratioofthesemi-variancesofpositivetrend gapstonegativetrendgapsis lessthanoneforall butoneindustry. Morestrikingthanthegeneral incidence of negativegap asymmetry is the severityof the average shortfall from trend utilization 6Let (cid:15) t denoteadeviationfromtrendinperiod t . Asnotedearlier,themeantrenddeviationiszerobyconstruction, P t (cid:15) t = 0 . Asymmetryin“gaps”ismeasuredbytheratioofthemeanofsquaredpositivedeviationstothemeanof squared negativedeviations, ( P t [(cid:15) + t 2 ] = n + ) = ( P t [(cid:15) (cid:0) t 2 ] = n (cid:0) ) , wherethere are n + positive trend deviations, (cid:15) + t > 0 , and n (cid:0) negativetrenddeviations, (cid:15) (cid:0) t < 0 . Asymmetryingrowthratesissimilarlymeasuredbytheratioofthemean ofsquaredpositivefirst-differencesinthetrenddeviationstothemeanofsquarednegativefirst-differences.

6 of capacity production that occurs in many industries. In about half of the industries, the average squared negative output gap is more than double the size of the average squared positive output gap. The last column in table I shows asymmetry gap measures for industry nominal output. The incidence of negative asymmetry is much less evident for nominal output. By contrast with the measureforrealoutputintheprecedingcolumn,themeasureofgapasymmetryfornominaloutput moves toward or past unity for most industries, and negative gap asymmetry remains statistically significantforonlythreeindustries. The finding that negative gap asymmetry is more pervasive and marked for real output than for nominal output also suggests a reverse positive asymmetry in pricing. If industry price is symmetricallysluggish about its own trend, we might expect the gap asymmetry in real output to be more-or-less reproduced in nominal output. The fact that negative gap asymmetry in nominal output is generally much closer to unity or even replaced by positive asymmetry suggests that negativeasymmetriesin real outputare often matchedby positiveasymmetries inprices, yielding moresymmetricdistributionsfornominaloutputgaps. Although results in table I indicate sizable asymmetries in the production and pricing of manufacturingproducers,itisimportanttonotoverinterpretwhatcanbeestablishedbyatheoretic measurement. Negative gap asymmetry for output may indicate that the average negative shock to output is larger than the average positive shock or that production is slower to recover from adverseshocks. Indeed,intheabsenceofanarticulatedmodelofproducerbehavior,itisnotclear whether motion away from trends represent unforeseen displacements due to shocks or planned overshootingoftrendsbyproducers. To reduce such ambiguities associated with atheoretic analysis, the remainder of the paper explores possible sources of asymmetries using structural models of producer behavior. Specific dynamic optimalityconditions will be discussedin some detail later. However, a brief preview of thisstructuralframeworkisprovidedbyarepresentativeEulerconditionforoptimaladjustmentof aproducerdecisionvariablesuchas outputorprice E t f f ( y (cid:0)t i ; y t ; y +t i j (cid:18) ) (cid:0) y (cid:3) t g = 0 ; ( 1 ) where f ( : ) is a two-sided function of leads and lags in the decision variable, y ; (cid:18) denotes the parameters of f ( : ) that are shaped largely by the nature of the frictions or “adjustment costs” that confront producers; and the forcing term of the Euler equation, y (cid:3) t , is the effective trend or long-run target of the decision variable. In the absence of adjustment costs, f ( : ) (cid:17) y t , and the expected gap or trend deviation, E t f y t (cid:0) y (cid:3) t g , is zero. This simple structural model of producer behaviorsuggeststwosources ofasymmetriesinrealized gaps. Oneis exogenousandstemsfrom

7 potential asymmetries in unpredictableshocks to the forcing term; the other is endogenous due to asymmetricresponsesbyproducers,capturedbystate-conditionalmovementsintheparametersof theEulerequation, (cid:18) . Output,price,orbothmaybeviewedastheeffectiveinstrument(s)ofproducers. Theremainder of this paper focuses on friction models of pricing, y t (cid:17) p t . The reason for this is the evidence in table I that many industries exhibit both negative gap asymmetries in output and positive gap asymmetries in pricing. If output movements capture the original source of asymmetry then the negative asymmetry in output should be able to explain the positive asymmetry in pricing. An alternative conjecture is that resistance to downward adjustments of nominal prices, as in Means[1935]andTobin[1972],mayexacerbatecontractionsofindustryproductioninrecessions. This interpretation suggests an endogenous characterization of asymmetric pricing where the parameters of linear pricing rules, (cid:18) , exhibit asymmetric responses to positive and negative trend deviations in price. Tests of both interpretations of asymmetric pricing are discussed in a later section. III.STRUCTURAL MODELSOFSYMMETRICPRICE ADJUSTMENTS Although the final goal of this paper is to identify asymmetries in pricing, this section first develops a symmetric pricing model to be used as a testbed for asymmetric variations. Without a reasonable benchmark model, estimated asymmetries could plausibly be attributed to features of uninterestingadhocfixes,suchas autocorrelatederrors. The standard frictions model of gradual price responses, such as Rotemberg [1982; 1987], is based on costly adjustment of price levels. The initial subsection shows that the standard model is not supported by manufacturing prices, where empirical problems include substantial residual autocorrelation and rejection of the overidentifying restrictions associated with rational expectations. Thesecondsubsectiondevelopsamoregeneralmodeloffrictionsindynamicpricing thatappears tobeacceptedbyindustrydata. Rationalpricingunderquadraticcostsof adjustinglevels. By construction, a cointegrating target price path, p (cid:3) t , is an equilibrium objective for the industry price, p t , in the absence of stochastic shocks. However, once displaced from the target path, due to errors in estimating costs or demand, various frictions or dynamic market strategies mayimpedeanimmediatereturntothetarget path. A tractable description of gradual price adjustments is provided by Rotemberg [1982; 1987] whereasecond-orderexpansionofprofitsaboutanequilibriumprofit-maximizingpricerepresents producersasminimizingthediscountedsumofsquareddeviationsabouttheequilibriumpricepath

8 andthecost ofsquaredchanges intheleveloftheprice. p t = a r g m i n E t f 1 =i X 0 B i [ b 0 ( p +t i (cid:0) p (cid:3) +t i ) 2 + b 1 ( p +t i (cid:0) p +t (cid:0)i 1 ) 2 ] g ! ; ( 2 ) where E t f : g denotesproducerexpectationsgiveninformationthrough t (cid:0) 1 ,and B isa(quarterly) discountfactor.7 Theassociatedfirst-orderconditionforoptimalpriceadjustmentisdescribedbyasecond-order Euler equation, written here as a function of two first-order polynomials in lag, L , and lead F , operators where L x t = x (cid:0)t 1 and F x t = x +t 1 . E t f A ( B F ) A ( L ) p t (cid:0) A ( 1 ) A ( B ) p (cid:3) t g = 0 : ( 3 ) On the left-hand-side of 3 , A ( L ) denotes the first-order polynomial in the lag operator, ( 1 (cid:0) (cid:21) L ) A ( L ) (cid:17) ,and A ( B F ) isthematchingfactorpolynomialintheleadoperator. Thesepolynomialsare balancedontheothersideoftheminussignbythesumsofthepolynomialweights, A ( 1 ) (cid:17) 1 (cid:0) (cid:21) and A ( B ) (cid:17) 1 (cid:0) (cid:21) B .8 As is well-known,e.g., Tinsley[1970b],theoptimaldecisionruleunder quadraticadjustment costs can be written as a partial adjustment of the decision instrument towards a moving target. Multiplyingequation 3 bytheinverseoftheleadpolynomial, A ( B F ) (cid:0) 1 ,andrearranginggives (cid:1) p t = = = E A A t ( ( f 1 1 A ) ) A [ ( S 1 ) ( B ( t A (cid:21) ( ) E B B t ; ) f p A 1 =i X (cid:3) ) ( B ( 0 (cid:0) (cid:21) F B p (cid:0) ) ) (cid:0)t i 1 1 p ] (cid:3) p t (cid:3) +t ; + g i ( (cid:0) (cid:1) A p t ( 1 (cid:0) ) p A (cid:0)t ( L 1 ; ) p t ) g ; ( 4 ) where S t ( : ) denotesthemovingtarget ofdiscountedforwardtrendprices.9 In the case of I(1) difference-stationary variables, such as the industryprices considered here, thedecisionruleinequation 4 canbereformulatedalsoas a rationalerror correctionrule,Tinsley [1993]. Toshowthis,wefirstidentifytheunobservedexpectations, E t f : g ,byassumingthatagents' 7Bissetto :9 8 ,approximatingthepostwarannualrealreturntoequityofabout 8 percent. Noempiricalresultsin thispaperareoverturnedbymodestvariationsin B . 8Thecharacteristicrootsof3are (cid:21) and ( (cid:21) B ) (cid:0) 1 ,where (cid:21) isthefractionalrootoftheequation, 1 ) (cid:0) b 0 = b 1 = 0 ( 1 (cid:0) (cid:21) B ) ( (cid:21) (cid:0) 1 (cid:0) . Thissolutionwillalwaysexistfor b 0 = b 1 > 0 . 9AsnotedbyRotemberg[1987],theoptimalpriceresponseunderquadraticpricelevelfrictionisequivalenttothe staggeredpriceadjustmentmodelofCalvo[1983]whereproducersaresubjecttoaninvariantdistributionofrandom delaysinpricesignals.

9 forecasts are rationalandcapturedbytheVARmodel, z e t = H z (cid:0)t 1 ; ( 5 ) where the n (cid:2) 1 vector z (cid:0)t 1 defines the effective information set of the agents, H is the n n (cid:2) companion matrix of the relevant linearized forecast model,10 and the superscript “e” denotes forecasts conditionedonthelaggedinformationset, z (cid:0)t 1 . If p (cid:3) t is the (cid:3) th element of z t , multiperiodpricetrend predictionsof the forecast model in 5 are denotedby p (cid:3) e +t j = (cid:19) 0 (cid:3) H j + 1 z (cid:0)t 1 ; ( 6 ) wherethe n (cid:2) 1 selectorvector, (cid:19) (cid:3) ,has aoneinthe (cid:3) th elementandzeroes elsewhere. Next,forecasts from 6 aresubstitutedintothedecisionrule 4 togive (cid:1) p t = = = = (cid:0) (cid:0) A A A A ( ( 1 1 ( ( ) ) 1 1 [ [ ) ) A A ( (cid:15) ( B ( B (cid:0) p t (cid:0) 1 t ) ) 1 + 1 =i X 1 = j X (cid:0) S 0 (cid:19) (cid:3) 0 ( (cid:21) 0 (cid:3) p (cid:0)t 1 ( (cid:21) t ( (cid:21) B ) 1 B B H 0 j ) (cid:19) (cid:3) + A ; (cid:1) ( p i ) H (cid:0) z t ( 1 ) (cid:3) j H z 1 0 (cid:19) (cid:3) ) (cid:0)t + [ I : 1 (cid:0) 1 =i X (cid:0) 0 (cid:0) p t ( (cid:21) B (cid:21) B 1 ] ; H ) (cid:0) H ] i 1 [ H [ H (cid:0) (cid:0) I I ] z ] z (cid:0)t (cid:0)t 1 1 ) ; (cid:0) p (cid:0)t 1 ] ; ( 7 ) In the last line of 7 , the regressor in the first term on the right hand side of the equal sign is the standard notation for the error correction term in the trend deviation, (cid:15) (cid:0)t 1 = p (cid:0)t 1 (cid:0) p (cid:3) (cid:0)t 1 . The second term, S 1 t ( : j H ) , is a compact reference to the discounted forecasts of expected forward changesinthetarget path, (cid:1) p (cid:3) +t i ,thatare conditionedontheforecast modelin 5 .11 Another important way to interpret the second term in the last line of equation 7 is to rewrite it as the inner product of a restricted coefficient vector, h (cid:3) , and the producers' information set, S 1 t ( : ) = h 0 (cid:3) z (cid:0)t 1 . Note from the third line in 7 that the n (cid:2) 1 coefficient vector, h (cid:3) , is completely defined by the adjustment cost parameter, (cid:21) , the discount factor, B , and the H coefficients of the 10As illustrated in Swamy and Tinsley [1980] and Harvey [1989], companion matrices are a convenienttool for rewritingasystemofhigh-orderARMAequationsinafirst-orderformat.Inthecaseofamultivariatepth-orderVAR, x t = P p =i 1 A i x (cid:0)t i (wherethe A i are q (cid:2) q matrices),thecompanionmatrixis H = (cid:20) A 1 I A p q 2 (cid:0) q : : : A 0 p q (cid:21) : 11AssumingtherelevantVARforecastmodelisexpressedinlevels,thesecondandthirdlinesofequation7contain theterm [H (cid:0) I ] toobtainforecastsoftargetpricedifferences, (cid:1) p (cid:3) +t i .

10 forecast model in 5 . This is a very transparent way of showing the effect of the overidentifying restrictions that are imposed under rational expectations (RE) by the forecast model in 5 on the coefficientsoftherationalerrorcorrectionrulein 7 . Bycontrast,inaconventionalerrorcorrection regression, the coefficients associated with regressors in the agents' information set, z (cid:0)t 1 , are unrestricted.12 An estimate of the two-root decision rule 7 for the aggregate manufacturing price is shown in the first row of table II. Although this simple equation provides a respectable R 2 of .40, there are two problems with this equation. First, the estimated residual is heavily autocorrelated, as indicated by a p-value of .00 for the Breusch-Godfrey statistic in the column labeled BG(12). Second, the next column to the right in table II reports the p-value of a likelihood ratio test that adds the VAR model regressors of the price trend as unrestricted regressors; this test rejects the rational expectations (RE) restrictions imposed by the VAR forecast model at a p-value of .00. To save space, we do not show the results of applying the standard two-root adjustment model to everyindustrybut essentiallythe same problemsare encountered for all industries. In anycase, it is shown below that the standard two-root model is nested in the more general model of frictions presentedinthenextsubsection. Rationalpricingunderquadraticcostsof adjustingmovingaverages. Both of the empirical deficiencies noted for the first equation in table II can be eliminated by relaxing the restriction that agents are subject only to costs of adjusting the current levels of industry prices. While maintaining the quadratic expansion characteristic of symmetric cost functions,polynomialsinthelagoperatorcanprovidelessrestrictiveapproximationsofadjustment costfunctionsandleadtonatural interpretationsofhigher-orderEulerequations. One generalization of the quadratic adjustment cost terms in criterion 2 is to allow friction penalties to apply not only to changes in the price level but also to changes in any kth-orderdifferenceassociatedwithproducersmoothingofindustryinflationratesorhigher-order differences.13 p t = a r g m i n E t f 1 =i X 0 B i [ b 0 ( p +t i (cid:0) p (cid:3) +t i ) 2 + k X m = 1 b k ( ( 1 (cid:0) L ) k p +t i ) 2 ] g ! : ( 2 0 ) 12Intheempiricalestimatesshowninthetables,therelevantindustryVARforecastmodelcontainsfourquarterly lagsoftheinputpriceargumentsoftheindustrypricetrend, p (cid:3) t . Methodsofestimatingtherationalerrorcorrection decisionrulesdescribedinthissectionarediscussedinTinsley[1993]. 13Signallingconventionsin oligopolisticmarketsorinstrumentuncertaintyregardingcustomerresponsestoprice behaviormaymotivatesmoothingofbothlevelsandderivativesofprices. In asimilar vein,GreenwaldandStiglitz [1989]note “price rigidities appear to exist to a greater extent regardingpast rates of change(i.e. inflation inertia) ratherthanpastlevels(i.e. purepricelevelinertia)”(p.364).

11 Another generalization is to extend the quadratic adjustment costs in criterion 2 from one-period changes in the price level, ( 1 (cid:0) L ) p +t i , to changes in moving averages, L ) P k j (cid:0) = 1 0 p +t (cid:0)i j = ( 1 (cid:0) L k ) p +t i ( 1 (cid:0) ,suchas mightbeassociatedwithseasonalorterm contracts. p t = a r g m i n E t f 1 =i X 0 B i [ b 0 ( p +t i (cid:0) p (cid:3) +t i ) 2 + k X m = 1 b k ( ( 1 (cid:0) L k ) p +t i ) 2 ] g ! : ( 2 00 ) Under either of these extended criteria, the format of the associated Euler equation of the optimalpricepathisexactlythesameasthatshownearlierintheEulerequation 3 forthestandard criterion 2.14 However, the order of the factor polynomial, A ( L ) , may now exceed one, m (cid:21) 1 , where A ( L ) = ( 1 + a 1 L + a 2 L 2 + : : : + a m L m ) . Thus,insteadoftworoots, (cid:21) and ( (cid:21) B ) (cid:0) 1 ,theEuler equationnowcontains m pairsofrootswhereeachpairisreciprocalaboutthediscountfactor, B .15 The derivation of the optimal decision rule associated with either criterion 2 0 or criterion 2 00 proceeds similarly to the procedure shown earlier in equations 4 through 7 for the standard case where A ( : ) isafirst-orderpolynomial. Thegeneralizationoftherationalerrorcorrectionformatis (cid:1) p t = (cid:0) A ( 1 ) (cid:15) (cid:0)t 1 + A (cid:3) ( L ) (cid:1) p (cid:0)t 1 + S 1 t ( G ; (cid:1) p (cid:3) ) : ( 8 ) As in the two-root decision rule in 7 , the coefficient of the error correction term, (cid:15) (cid:0)t 1 , continues to be defined as the negative sum of coefficients in the factor polynomial, (cid:0) A ( 1 ) . However, the remainingterms are different and have two importantconsequences for the dynamicspecification oftheoptimalpricingrule. First, autoregressive lags of the industry price may now appear as regressors in the rational error correction decision rule 8 , with coefficients denoted by the A (cid:3) ( L ) component polynomial. The latter is the ( m (cid:0) 1 ) -order polynomial obtainedby rewriting the m -order lag polynomialin a levelanddifference format, A ( L ) (cid:17) A ( 1 ) L + ( 1 (cid:0) A (cid:3) ( L ) L ) ( 1 (cid:0) L ) .16 14TheEulerequationfor 2 0 is: E t f b 0 ( p t (cid:0) p (cid:3) t ) + P m k = 1 b k [( 1 (cid:0) L ) ( 1 (cid:0) B F ) k ] p t g = 0 andtheEulerequationfor 2 00 is: E t f b 0 ( p t (cid:0) p (cid:3) t ) + P m k = 1 b k [( 1 (cid:0) L k ) ( 1 (cid:0) B k F k ) ]p t g = 0 . BecausetheseEulerequationsaresymmetricin L and B F ,eachhasthefactorpolynomialrepresentationshowninequation3,vid.Tinsley[1993]. 15Another example of a higher-order Euler equation that is a special case of the moving-average smoothing in criterion 2 00 is the exampleof staggered contracts, Taylor [1980], where some agents negotiate a 1-periodcontract, some a 2-periodcontract, others a 3-periodcontract, and so on. Ignoringdiscounting, denotethe aggregateof new contractsformulatedinperiod t by x c t = E t f A ( 1 ) A ( F ) (cid:0) 1 x (cid:3) t g andtheassociatedaggregateofallexistingcontractsin t as x t = A ( 1 ) A ( L ) (cid:0) 1 x c t ,where A ( :) isanm-orderpolynomialthatapproximatestheexpirationscheduleofcontracts. SubstitutingoutthecontractpricesyieldstheEulerequation3for B = 1 : E t f A ( F ) A ( L ) x t (cid:0) A ( 1 ) 2 x (cid:3) t g = 0 . 16Thecoefficientsof A (cid:3) ( :) aresimplemovingsumsofthecoefficientsof A ( :) . Toillustrate,if a = [a 1 ; a 2 ; : : : ; a m 0 ] isthe m (cid:2) 1 vectoroftheunknownparametersinthe A ( :) polynomialand (cid:18) = [A ( 1 ) ; a (cid:3) 1 ; a (cid:3) 2 ; : : : ; a (cid:3) m (cid:0) 1 0 ] isthevector of transformedparameters, then (cid:18) = (cid:19) 1 + T a , where (cid:19) 1 is an m (cid:2) 1 vectorwith onein thetop elementand zeroes elsewhere,and T isan m (cid:2) m transformationmatrixwithallelementsonandabovethemaindiagonalequaltoone andzeroeselsewhere.

12 Second,forecasts offuturechanges inthetrendpricearenowdiscountedbymultiplediscount factors. As in the standard two-root case, the forward-looking term in the optimal decision rule can still be written as the inner product of a restricted coefficient vector, h (cid:3) , times the producers' information vector, S 1 t ( G ; (cid:1) p (cid:3) ) (cid:17) h 0 (cid:3) z t . As one might expect in the case of higher-order Euler equations,derivationofthevector, h (cid:3) ,ismorecomplicatedbuttheessentialroleofoveridentifying restrictionsimposedbytheparameters, H ,oftheVARforecastmodelremainsthesame. However, instead of discounting the forecasts of forward changes in the trend price by the single root, (cid:21) B , forecasts are now discountedby the m roots of the lead polynomial, A ( B F ) . As indicated by the notationin thelasttermofequation 8 ,these m rootsarecontainedinthematrix, G .17 An empirical exampleof the more general specification of dynamic adjustment in the rational errorcorrectiondecisionruleofequation 8 isshownforthemanufacturingpriceinthesecondline oftableII.Thecolumnheadedbylagindicatestheestimatedorderofthe A ( L ) polynomialfactor. In the case of the second line, the lag order is three ( m = 3 ) indicating that two autoregressive terms, (cid:1) p (cid:0)t 1 and (cid:1) p (cid:0)t 2 ,are significantas additionalregressors. Thethree rootsof A ( L ) areused also to compute the three discount factors used to weight the VAR forecasts of future target price changes in S 1 t ( : ) . In contrast to the statistical problems exhibited by the two-root decision rule in the first line of table II, the six-root decision rule in the second line does not exhibit residual autocorrelation (the p-value is .31) and the RE restrictions imposed on the decision rule by the VARtarget priceforecasts arenowaccepted. The remaining rows of table II show the results of applying the extended error correction decisionrulein 8 tothepricesofSICtwo-digitindustries. Generally,allindustriesshowsignificant errorcorrectiontothegapdeviationfromthetargetprice;theorderofthefactorpolynomial, A ( L ) , always exceedsone;18 andrationalexpectations(RE)restrictionsare acceptedforall industries. The last column in table II measures the change in the R 2 that is due to the presence of the forward-looking expectations term, S 1 t ( : ) . For the standard two-root pricing rule in the first line of table II, the entry is .36 indicating that removing forward-looking expectations, S 1 t ( : ) , lowers 17AsderivedinTinsley[1993],theclosed-formsolutionoftherestrictedcoefficientvectorisnow h (cid:3) = A ( 1 ) A ( B ) ( (cid:19) 0 m [I (cid:0) G (cid:0) ] 1 (cid:10) [H 0 (cid:0) I ]) [I (cid:0) G (cid:10) H 0 (cid:0) ] 1 ( (cid:19) m (cid:10) (cid:19) (cid:3) ) ; where (cid:19) m isan m (cid:2) 1 vectorwithaoneinthebottomelementandzeroeselsewhere; (cid:10) denotestheKroneckerproduct; andthe m (cid:2) m matrix G isacompanionmatrixoftheforwardpolynomial, A ( B F ) , G = (cid:20) (cid:0) a 0 m B m (cid:0) a m (cid:0) 1 B m (cid:0) 1 I m : (cid:0) : : 1 (cid:0) a 1 B (cid:21) : 18Although seasonal variations are small in most producer prices, Beaulieu and Miron [1990], and seasonal dummiesareincluded,thepolynomialorderforseveralindustriessuggestsseasonalresponses.

13 the R 2 by an order of magnitude, from .40 to .04. However, in the second line of table II, after allowingforthemorecomplicatedfrictionssuggestedbythemanufacturingpriceautocorrelations, the incremental R 2 attributable to forward expectations is only .01 points or about 1 % of the total R 2 of .72. The remaining entries in the last column of table II indicate that the proportions of samplevariationexplainedbyforward-lookingexpectationsare oftenmodest after accountingfor higher-orderadjustmentcosts. Having discussed, in this section, the estimation of baseline models of rational symmetric pricing with reasonable statistical properties, we turn next to tests of possible sources of asymmetriesinproducerpricing. IV.SOURCES OFASYMMETRIESINPRODUCER PRICING This section first explores the possibilitythat asymmetric pricing may be largely attributed to asymmetric movements in output. The second subsection examines an alternative conjecture that pricingasymmetriesareduetostate-conditionalshiftsintheparameters oflinearpricingrules. Priceresponsestoindustryoutputgaps. Given the results in table I that there appear to be asymmetric movements in the output gaps of many industries, we first explore the obvious possibility that asymmetries in industry prices may reflect price responses to asymmetric industry output gaps. In the case of the industry target price, p (cid:3) , it seems plausible that either marginal cost or the desired price markup may vary with the rate of industry utilization. The sign of the price response may be either positive or negative, because marginal costs may increase or decrease with rising utilization rates. Also, margins may varyprocyclicallyorcountercyclically,dependingonboomorbustvariationsinthepriceelasticity ofdemandorintheperceivedreturntodefectionsfrom collusivepricingstrategies. A limitation of estimating the industry trend price, p (cid:3) t , by cointegration is that only I(1) argumentsofthepricetargetsareidentified. BecauseindustryutilizationratesareI(0)orstationary, as noted earlier, the influence of utilization rates on industry target prices cannot be captured by cointegrationandtheforcingterm oftheEulerequation 3 mustbedirectlyaltered: E t f A ( L ) A ( B F ) p t (cid:0) A ( 1 ) A ( B ) [ p (cid:3) t + D ( L ) u t ] g = 0 : ( 3 0 ) Here, we retain the notational convention that p (cid:3) denotes the portion of the target price that is capturedbycointegrationregressions. Theadditionalterm intherevisedEulerequation 3 0 applies alagpolynomial, D ( L ) ,totheindustryutilizationratetoallowforthepossibilitythattheindustry target pricemaybeinfluencedalsobyrecent trenddeviationsinoutput. Once again multiplying the Euler equation by the inverse of the lead polynomial, A ( B F ) (cid:0) 1 ,

14 andrearranginggivesthereviseddecisionrule (cid:1) p t = = (cid:0) (cid:0) A A ( ( 1 1 ) ) (cid:15) (cid:15) (cid:0)t (cid:0)t 1 1 + + A A (cid:3) (cid:3) ( ( L L ) ) (cid:1) (cid:1) p p (cid:0)t (cid:0)t 1 1 + + h h 0 (cid:3) 0 (cid:3) z z (cid:0)t (cid:0)t 1 1 + + E D f t ( L A ) ( [ 1 h ) 0 u A z ( (cid:0)t B 1 ) ] : A ( B F ) (cid:0) 1 D ( L ) u t g ; ( 9 ) Rational forecasts of forward industry utilization rates in the second line of 9 are obtained by applying a restricted coefficient vector, h u , to the information set contained in z (cid:0)t 1 .19 For the equations presented here, four-quarter autoregressions in the industry utilization rates are used to generate forward utilization forecasts. D ( L ) is arbitrarily set to a first-order polynomial, the minimum order that allows us to distinguish between transient price level responses to output gaps, D ( 1 ) = 0 ,andpersistentlevelresponses, D ( 1 ) 6= 0 . The first few columns intable III provideseveral of the keystatisticsreported in tableII, such as the level and difference decompositionof the factor polynomial, A ( L ) . The statistics mayvary slightly from those in table II because these are the final equations that include either estimated priceresponsestooutputgapsorasymmetricresponsestolaggedpricegaps(discussedinthenext subsection)orboth. Two statistics for utilization rate regressors are reported in table III in the columns headed by output gap effects. The first is the p-value of a likelihood ratio test for adding the industry outputgap regressors inthe RE format required by equation 9 . A p-valueless than.10 indicates a significantpriceresponsetoutilizationrates. Forexample,thefirstlineformanufacturingindicates that manufacturing utilizationis a significant determinant of manufacturing prices, with a p-value of.03. Asshownintheremainderofthiscolumn,utilizationrateforecasts aresignificantinabout athirdoftheindustries. Generally,thisoccursinindustrieswithrelativelyhomogeneousproducts, suchastextiles(SIC22)ormotorvehiclesSIC371),whereanaggregateindustrycapacityconcept maybemoreapplicable. The second statistic is the sum of the estimated weights, D ( 1 ) , on lags of the present-value of expected utilization rates. The sum of estimated weights for manufacturing is small (and statistically insignificant), indicating any persistent level effect on industry prices from higher or lowerutilizationrates is modest. The result most relevant for analysis of pricing asymmetries is that the weight sum is positive forallindustriesexceptmotorvehicles. Thisisthetraditionalsignexpectedforcapacitybottleneck pressure on industry pricing. However, positive price responses cannot transform negative gap 19Theclosed-formsolutionofthecoefficientvectorforREforecastsofutilizationratesis h u = A ( 1 ) A ( B ) [(cid:19) 0 m (cid:10) H 0 ][I n m (cid:0) G (cid:10) H 0 (cid:0) ] 1 ( (cid:19) m (cid:10) (cid:19) u ] where (cid:19) u denotestheselectorvectorfor u t in z t .

15 asymmetries in outputs into positive gap asymmetries for prices. Thus, output asymmetry is unlikelyto bethesourceofthepositivegapasymmetrynotedforindustryprices insectionII. Asymmetricpricingduetostate-conditionaladjustments. Having taken account of industry price responses to trend deviations in industry output, we nowturntothenatureofpriceresponsestothetrenddeviationsofprices. Thatis,incontrasttothe usualcyclicalanalysisofpricingwhichisgearedtooutputdeviationsfromtrend,itseemsplausible that price trend deviations themselves might be a promising indicator of potential asymmetries in adjustments to price trends. Given direct measurements of price trend deviations, a tractable analysisis todetermineiftheroots ofthefactor polynomialsare different whentheprice isabove trend, (cid:15) (cid:0)t 1 > 0 ,orbelow, (cid:15) (cid:0)t 1 < 0 . Initial experimentation with the estimated decision rules of all industries indicated that any detectableswitchingeffect wouldbeconfinedtoasignsplitonlyontheerrorcorrectionresponse, A ( 1 ) . The intuitionfor this attractivesimplificationcan be seen by examiningthe structure of the errorcorrectiondecisionruleforthetwo-rootcase,whichis restatedhereas (cid:1) p t = (cid:0) A ( 1 ) (cid:15) (cid:0)t 1 + A ( 1 ) A ( B ) (cid:0) 1 S t ( (cid:21) B ; (cid:1) p (cid:3) ) : ( 1 0 ) Incontrasttothenullhypothesisofsymmetricadjustment,thealternativesuggestedbytheresults in table I is that price adjustment speed is slower when the price is above trend. In other words, when the price gap is positive, the root of the factor polynomial moves towards unity, driving the error correction response, A ( 1 ) (cid:17) ( 1 (cid:0) (cid:21) ) , toward zero. However, the remaining term in equation 1 0 isrelativelyinsensitivetomoderateincreasesin (cid:21) . First,thepresent-valuesummation, S t ( : ) ,whoseweightssumtoone,isunlikelytovarymuchwithmoderateincreases intheeffective discount rate, (cid:21) B , which has an upper bound of B . Second, for discount factors, B , near unity, the effective coefficient, A ( 1 ) = A ( B ) , of the present-value sum is approximately one and also insensitivetovariationsin (cid:21) . The first two columns in table III under the heading asymmetric price gap effects list the p-valuesoftwotestsforasymmetricerrorcorrectionresponsesofindustrypricestosignedpatterns ofthepricegaps. Theestimatedpriceresponsetoapositivepricegap, (cid:15) + (cid:0)t 1 ,issignificantlydifferent from the estimated response to a negative price gap, (cid:15) (cid:0) (cid:0)t 1 , if the p-value in the column headed by L R ( (cid:15) + (cid:0)t 1 ; (cid:15) (cid:0) (cid:0)t 1 ) , is .10 or less. This test suggests asymmetric error correction responses are significantintotalmanufacturingandinabout 4 0 % oftheSICtwo-digitindustries. Inallcases,the coefficientofthepositivepricegapissignificantlysmallerthanthecoefficientofthenegativeprice gap, indicating a positive skew in price adjustments. In fact, the coefficient of the positive price gap in these industries, shown in the column headed by A + ( 1 ) , is also not significantly different

16 from zero,suggestingtheabsenceofsystematicerror correctionwhenpriceis abovetrend. A statistically zero response to positive price gaps also appeared in several of the remaining industries. This asymmetric error correction response pattern is not reliably detected by the first likelihood ratio if the sampling error of the estimated coefficient of the positive price gap is sufficiently large to encompass both zero and the coefficient estimated for the negative price gap. Consequently, a second test is applied to specifically test for nominal ratcheting where there is no systematic price response by producers to positive price gaps. This pattern proved to be surprisinglypervasive;nominalratchetingisrejectedforonlyeightindustries(whenthep-valueis .10orless inthecolumnheadedby L R ( 0 ; (cid:15) (cid:0) (cid:0)t 1 ) ). ThelasttwocolumnsintableIIIprovideestimatesofmeanlagresponsestorandomshocksthat are indicated by the estimatedasymmetric responses, where M L (cid:0) denotes the mean lag response (in quarters) ifthe price gapis negative(industryprice belowtrend) and M L + is the approximate mean lag if the price is above trend. Only a single mean lag statistic is reported if the estimated industryprice responseissymmetric.20 As indicated in the first row of table III, the mean lag response to shocks in manufacturing is about two quarters if the aggregate price index is below trend, M L (cid:0) = 1 : 8 , and about six quarters if the price is above trend, M L + = 6 : 2 . The substantial disparity between the mean lag responses reported for many of the industries indicates that asymmetric pricing is not just an econometric curiosity but implies economically meaningful variations in the average response times of industry prices. Depending on whether prices are above or below trend, mean lags in industryprice responsescandifferbyas muchas anorderofmagnitude. In summary, the evidence presented in this section supports the conjecture of section II that producersaremorereluctanttoreducepositivetrenddeviationsinpricesthantoeliminatenegative deviations. However, it is unsatisfying, if not tautological, to conclude that the perceived costs of reducing prices are simply larger than the costs of price increases. Modelling intertemporal decisionrulesisausefulstrategytodistinguishdynamicresponsesofagentsfromthebackground motion of conditioning variables (such as predetermined forcing terms) but it does not provide insights into the market or institutional constraints on agents that lead to asymmetric responses. Thenextsectionexaminesseveraltheoriesofasymmetricpricingandattemptstomatchpredictions oftheseinterpretationsagainstcharacteristicsofproducers withasymmetricpricing. 20Meanlagsareestimatedby [1 (cid:0) A (cid:6) ( 1 ) (cid:0) A (cid:3) ( 1 ) ]= A (cid:6) ( 1 ) . AsnotedintableIII,meanlagsforpositivepricegaps areapproximateforindustrieswithnonpositiveestimatesof A + ( 1 ) . Ofcourse,giventheforward-lookingroleofthe polynomialleadoperator, A ( B F ) (cid:0) 1 ,the“meanlag”foranticipatedeventsapproacheszeroasthediscountfactor, B , approachesone.

17 V.THEORIES OFPOSITIVEASYMMETRIESINPRICING Fourtheoriesofasymmetricpricingarereviewedandacentralfeatureofeachtheoryisselected toprovideanindicatorofthepropensityforasymmetricpricing. Thesecondsubsectiondiscusses correlationsoftheseindicatorswiththeindustrypricingasymmetriespresentedinsectionIV.Two interpretationshavemoderateempiricalsupport. Fourindicatorsofalternativetheories (1)StrategicpricingandtheHerfindahl(HF)indicator.A keyfindingof tableIII is that many producers are relatively quick to raise prices that fall below trend but are slower to reduce prices that are above trend. The most venerable explanations of positive asymmetries in pricing are those based on implicit price collusions by oligopolistic competitors, even in protracted intervals of depressed demand. Early examples include the inverse association suggested by Means [1935] between industry concentration and the frequency and size of price adjustments. There are also several modern theoretical variations of oligopolistic pricing strategies which predict countercyclical movements in price margins over cost, such as Rotemberg and Saloner [1986]. Followingapopularconventioninempiricalindustrialorganizationliterature,theHerfindahlindex of the sum of squared market shares, HF, is used as an indicator of the competitive structure of an industry. The indexes for SIC two-digit industries are constructed from the 1982 Census of Manufactures. (2)Wageinertiaandthelaborcompensationshare(LS) indicator.Anotherearlyinterpretation of asymmetry links the cyclical behavior of prices to asymmetric movements of unit costs, principally nominal wages. A well-known example is the suggestion by Keynes [1936] that employees may resist reductions in nominal wages because it is difficult for atomistic agents to coordinatetheiractions. Although downward stickiness of nominal wages was originally suggested to motivate the countercyclical movements in real wages required by neoclassical production functions, postwar time series evidence suggests that industry real product wages are largely acyclical, Barsky and Solon[1989]. Acyclicalbehaviorinreal wagesisnotinconsistentwithnominalratchetinginboth wages and prices. To indicate the potential influence of resistance to downward movements in labor compensation costs, the labor share of gross output, LS, is used to indicate those industries where the purchase of labor inputs is a major component of operating costs. The labor share of gross industry output, adjusted to remove the effect of indirect taxes, is obtained from the U.S. Commerce1982input-outputsystem. (3)Instrumentuncertaintyandaliquidasset(LA) indicator. Greenwald and Stiglitz [1989] applytheanalysisbyBrainard[1967]ofinstrumentuncertaintytosuggestatendencyforproducers to rely more on quantity adjustments than price adjustments over the business cycle. The basic

18 elements are that producers are risk averse and that price adjustments are perceived to be more riskythanquantityadjustments. Originally advanced to interpret the (symmetric) inertia of producer prices, this theory can be modified to explain positive asymmetry in producer prices by adding an asymmetry due to costs of illiquidity. This altered conjecture has two essential ingredients: (i) the profit variance associated with price changes is significantly larger than the variance effects of output changes; and (ii) producer risk varies countercyclically due to imperfect credit markets. Under the first condition, costs associated with altered production, such as worker hires or layoffs, are relatively predictable but the profit implications of price changes are more uncertain due to unpredictable customerorcompetitorresponses. Underthesecondcondition,risk-neutralfirmsconfrontingimperfectcreditmarketswillprefer self-financing and seek to avoid the costs of bankruptcyor technical insolvencywhich can trigger restrictive covenants imposed by creditors. In boom periods with large accumulations of retained earnings, the probability of exhausting internal liquid asset reserves is small; little weight is placed on the risk exposure associated with price variations and both price and output are varied to maximize the discounted stream of expected profits. However, in bad times, self-financing protectionis inevitablyeroded bydrainsonliquidasset bufferstocks,andthereis greater concern abouttheuncertaintyofprojectedreceiptsandmaintenanceofcashflows. Producersbecomemore cautious about changing prices to alter expected sales and respond to reduced demand prospects byscalingbacktherate ofplannedproduction. Theratioofliquidassetstothecapitalizedvalueofearnings,LA,appears tobeanappropriate indicator of a preference for self-financing.21 Note that we are not interested in historical movements of industry liquid asset ratios but the cross-industry ranking as a guide to the average self-financing protection selected by industries. Liquid assets are defined as cash and securities plus inventories less short-term debt; industry data is obtained from the U.S. Department of Commerce's 1982QuarterlyFinancial Report formanufacturing. (4)Expectedinflationandatrendinflation(TI) indicator. The fourth interpretation of asymmetric pricing is based on the direct costs of changing nominal prices. As outlined in Tsiddon [1993] and Ball and Mankiw [1994], if menu costs are associated with price changes, a positive expected drift in the industry price trend will induce asymmetric price responses where producers are relatively quick to close negative price gaps but slower to reverse positive price 21AsinTinsley[1970a],usingasimplifyingassumptionthatearningsineachperiodareindependentlydistributed andaccumulatedoveraplanninghorizon,theprobabilityofexhaustingliquidassetreservesisexponentiallydeclining intheratioofinitialreservestoexpectedearningsdividedbythesquaredcoefficientofvariationofearnings. Given imperfectaccesstocreditmarkets,firmsinindustrieswithmorevolatileearningswillholdhigherliquidassetreserves, onaverage,tometagivenprobabilityoftechnicalinsolvency.Becauseequityearningsarehighlyvolatilefromperiod toperiod,expectedearningsarereplacedbythecapitalizedvalueofaverageearnings.

19 gaps. A consequence of fixed (or proportional) costs associated with price actions is that a zone of price inaction is placed about the current price. Duration in the inaction zone will depend on the motion of the trend price. The larger the variability of trend price changes, the shorter will be the interval of time before either the upper or lower boundary of the inaction zone is crossed by the price trend, triggeringa price response by theproducer. Higher expectedinflationof thetrend price will increase the probability that the trend price will first reach the upper boundary rather than the lower boundary. When price is above trend, passive reversal of the positive price gap by the motion of the trend price may be preferred to price adjustment due to the cost of direct price action. Thus, in a menu cost interpretation of positiveasymmetry in producer pricing, the probability of active price adjustment will vary directly with the variability of the trend price and inversely with the rate of expected inflation in the trend. The inverse of the coefficient of variation of trend price inflation is selected as the indicator of this theory, where the trend inflation, TI, indicator is the ratio of the mean to standard deviation of the four-quarter inflation rate of the industry price trend. Cross-industrycontrastsof alternativetheories Two empirical screening tests of the alternative interpretations of asymmetric pricing, as represented by the four selected indicators, are presented in table IV. Each test is based on the hypothesisthatasuccessfulindicatorwillbepositivelycorrelatedwiththeextentofasymmetryin industrypricing. Thefirsttestcontrastsgroupmeansofeachindicatorwheretheaveragevalueofeachindicator isexpectedtobelargerinthegroupofindustriesthatexhibitasymmetricpricingthaninthegroup of industrieswithsymmetricpricingbehavior. The first rowof tableIV liststhe average indicator values in the eight industries with symmetric pricing (as classified in table III). The indicator averages in the thirteen industries with asymmetric pricing are shown in the second row of table IV. The average indicator value is always larger for the asymmetric pricing industries, although barely sofortheHerfindahl indicator,HF. The statistical significance of differences in the group means of the indicators is evaluated by the p-values in the third and fourth rows of table IV. In the case of equal variances in the two industry groupings (the third row), the industry group means of the Herfindahl indicator are not significantly different but the means of the remaining indicators are significantly larger in the asymmetricpricinggroupatsignificancelevelsthatexceed 9 0 % (p-valuelessthan.10). Whenthe null hypothesis allows for differences in the variances of the two industry groupings (the fourth row), the statistical support of the labor share, LS, and liquidasset, LA, indicators is weaker with

20 p-valuesabove.10. The second set of screening tests in table IV uses regression analysis to estimate the degree of positive association between indicator values and a measure of the extent of asymmetry in industrypricing. Thesamplefor theregressionsis thecross-sectionof industriesinthegroupthat exhibitedasymmetricpricing. Thedependentvariableofeachcross-sectionregressionisanindex of asymmetric pricing, M L + = M L (cid:0) , defined as the ratio of the industry mean lag responses to positiveandnegativepricegapsshownintableIII. The fifth row of table IV displays the bivariate correlations of the asymmetric pricing index with the relevant industryindicator. The significance of the correlations is indicated by t-ratios in parentheses. The asymmetric pricing index is most strongly correlated with the liquid asset ratio, LA, and the trend inflation indicator, TI, where both correlations are moderately strong and have significancelevelswell above 9 0 % . The approach in the next row of table IV is to provide an adjustment for possible sampling errors in the cross-industry indicators. All indicators, except for the trend inflation indicator, TI, are based on industry values in a given year (1982). On the assumption that the cross-industry ranks of these indicators are more likely to be invariant to any sampling errors associated with cardinal measurements drawn from a single year, the industry ranks of the indicators are used as the relevant regressors in the sixth row of table IV. The major casualty of this adjustment is the Herfindahl indicator,HF. Becauseitisunlikelythatthereisonlyasingleexplanationofasymmetriesinindustrypricing, the last two rows of table IV employ multivariateregressions in an attempt to parse the explained variation in the asymmetric index among competing indicators. The explanatory power of the multiple indicator regressions is little affected by retaining only the liquid asset indicator, LA, and the trend inflation indicator, TI, as regressors, as shown in the last row of table IV. The liquid asset indicator remains statistically significant with a p-value less than .10, whereas the p-value of the coefficient of the trend inflation indicator is about .15. Bounds on the explanatory contributionsoftheindicatorscanbeestablishedbycomparingthe R 2 ofthelastequationintable IVwiththesquaresofthesimplecorrelationsinthefifthrow. Thiscontrastsuggeststhattheliquid asset indicator, LA, may be explaining from 2 0 % to 3 6 % of the total cross-industry variation in asymmetric pricing, and the trend inflation indicator, TI, may contribute from 1 2 % to 2 8 % of the cross-industryvariation.

21 VI.CONCLUDINGCOMMENTS Thispaperprovidesevidencetosupporttwostylizedfacts: Productioninmanymanufacturing industries exhibits negative asymmetry, where shortfalls from trend output are larger, on average, than positive trend deviations. By contrast, positive asymmetry is more common in producer pricing where positive trend deviations are more persistent than the deviations of prices below unitcosttrends. Reasons for these asymmetries in producer responses and the nature of causal interactions betweenoutputandpriceasymmetriesarenotresolvedinthispaper. Althoughtwointerpretations, menu costs and instrument uncertainty, are supported by the simple cross-industry regressions in the preceding section, this is only suggestiveevidence at best. These two candidate theories have very different implications for interpreting producer behavior and for the design of stabilization polices. Under menu costs, expected inflation is a source of asymmetric pricing responses to shocks. The deadweight loss of inefficient sectoral allocations due to asymmetric price adjustments will diminish at lower rates of expected inflation. Indeed, if menu costs are symmetric and aggregate inflation is the sole source of expected drift in industry target prices, this source of asymmetry in producerpricingwillvanishiftheexpectedrate ofaggregateinflationiszero. However,thecomplicationraisedintheprecedingsectionisthatexpectedinflationisprobably not thesolecauseof asymmetricpricing. Anotherplausibledeterminantis instrumentuncertainty where the preferred producer response to unfavorable shocks may be output contraction rather thanpriceadjustment. Ifthechoicebetweenoutputorpriceresponsesisinfluencedbytheinternal liquidityoffirmsthenthesacrificeratiosofdisinflationpoliciesmaydependonthecyclicaltiming of policy.22 Asymmetric reliance by producers on output responses to reduced demand is also consistent with concave industry supply functions, where negative output gaps are accompanied bylittleornochangeinpricebutoutputexpansionsabovepreferredoperatingratesmaybepaired with large changes in prices. Stabilization polices will increase average output if the supply of outputisaconcavefunctionofprice.23 Any source of positiveprice asymmetry may induce negativeasymmetries in output, not only in the same industry through downward sloping demand schedules but also in other industries through aggregate demand spillovereffects of reduced expenditures on material and labor inputs. However,theinstrumentuncertaintyinterpretationsuggeststhatproducersrespondtounfavorable 22State-conditional aggregate effects of monetary policy are not always cleanly linked with the existence of state-dependentproducerpricingrules;comparetheflexibleaggregatepriceresponsesinCaplinandSpulber[1987] withthestate-dependentrealoutputeffectsinCaplinandLeahy[1991]. 23Denotingthesupplyofoutputatagivenpriceby Q ( P ) ,supplyisconcavein P if Q ( :) liesonorbelowatangent attheaverageprice, E f P g . Itfollows,byJensen'sinequality,that Q ( E f P g ) (cid:21) E f Q ( P ) g .

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25 TableI AsymmetriesinIndustryOutputandPriceTrendDeviations a ratioofsemi-variances b growthratesoftrenddeviations levelsoftrenddeviations industry SIC realoutput realoutput nominaloutput realoutput realoutput nominaloutput [OLStrend] [I(1)trend] [I(1)trend] [OLStrend] [I(1)trend] [I(1)trend] manufacturing 20-39 .47** .50** .67 1.45 .77 .91 food 20 .54*** .55*** 1.19 1.68 .92 3.45 tobacco 21 1.18 .78 1.00 .70* .71 1.24 textiles 22 .82 .95 .76 1.49 .50 .61 apparel 23 .70 .64 .77 .73 .21* .52 lumber 24 .54** .62 .44* .45* .21*** .41* furniture 25 .54* .48* .44* 1.32 .69 .52* paper 26 .70 .64 .85 1.49 .41 .77 printingand 27 .76 .72 1.06 1.02 .37* .66 publishing chemicals 28 .63 .55 1.48 1.48 .51* .75 petroleum 29 .66 .70 1.44 1.70 .36* .55 refining rubberand 30 .78 .72 .60 2.20 .53* .60 plastics leather 31 1.33 1.38 .90 .86 .31*** 1.13 stone,clay 32 .86 .73 .92 1.38 .81 .70 andglass primary 33 .48* .67* .60** .93 .41 .48 metals fabricated 34 .54** .50** .65** 1.66 .74 .85 metals nonelectrical 35 .42** .59** .70 .68 .77 1.16 machinery electrical 36 .70 .57** .74 1.28 .64 .75 machinery motorvehicles 371 1.07 1.04 1.11 .60* .36** .34*** other 37x .79 .70 .92 1.85 1.13 2.06 transportation instruments 38 .61* .63* 1.66 .80 .76 2.44 miscellaneous 39 .89 1.10 1.21 1.06 .67 .72 a Thetrendinindustrylogoutputisrepresented,alternatively,bythelineartrendoflogoutput[OLStrend]andbya cointegratingtrendbasedonFRButilizationrates[I(1)trend]. Trenddeviationsinindustrynominaloutputarethesum oflogtrenddeviationsinindustryoutputandprice,seetext. Samplespansare1967Q1-1991Q4forSIC21,23,24,25, 27,31,and39,and1954Q1-1991Q4forremainingindustries. b Ratio of squared positive mean deviationsover squared negative mean deviations. The relevantratio is less than unityat90%(*), 95%(**),and99%(***)confidencelevels; standarderrorsarecorrectedforserialcorrelationusinga Newey-Westcovarianceconstructionwithabandwidthof (cid:6) fivequarters.

26 TableII ErrorCorrectionDecisionRulesforIndustryProducerPriceIndexes (cid:1) p t = (cid:0) A ( 1 ) (cid:15) (cid:0)t 1 + A (cid:3) ( L ) (cid:1) p (cid:0)t 1 + S 1 t ( G ; (cid:1) p (cid:3) ) + a t : a adjustmentcost pricetrend ( (cid:1) p (cid:3) ) parameters expectations industry SIC lag A ( 1 ) A (cid:3) ( 1 ) R 2 S E E B G ( 1 2 ) b L R ( (cid:1) p (cid:3) e ) c (cid:1) R 2 d manufacturing 20-39 1 .10 .40 .0106 .00 .00 .36(90%) (2.6) 3 .07 .63 .72 .0068 .31 .96 .01(1%) (2.7) (13.2) food 20 7 .25 .58 .30 .0311 .61 .13 .00(0%) (4.6) (3.8) tobacco 21 2 .18 -.12 .31 .0193 .35 .96 .14(45%) (3.5) (1.7) textiles 22 3 .11 .50 .60 .0108 .25 .27 .00(0%) (4.1) (8.4) apparel 23 2 .06 .60 .59 .0049 .45 .12 .05(8%) (1.8) (8.6) lumber 24 4 .07 .48 .25 .0288 .87 .27 .00(0%) (1.6) (3.5) furniture 25 2 .08 .21 .62 .0058 .47 .59 .07(11%) (2.6) (3.8) paper 26 2 .13 .60 .62 .0104 .39 .20 .03(5%) (4.6) (11.2) printingand 27 2 .11 .50 .65 .0109 .69 .51 .03(5%) publishing (5.1) (9.4) chemicals 28 3 .06 .73 .75 .0107 .62 .28 .01(1%) (3.2) (15.8) petroleum 29 7 .30 .80 .43 .0552 .11 .24 .05(12%) refining (5.5) (5.8) rubberand 30 2 .19 .51 .65 .0090 .56 .20 .08(12%) plastics (4.9) (9.9) (Footnotesatendoftable)

27 TableIICont. ErrorCorrectionDecisionRulesforIndustryProducerPriceIndexes (cid:1) p t = (cid:0) A ( 1 ) (cid:15) (cid:0)t 1 + A (cid:3) ( L ) (cid:1) p (cid:0)t 1 + S 1 t ( G ; (cid:1) p (cid:3) ) + a t : a adjustmentcost pricetrend ( (cid:1) p (cid:3) ) parameters expectations industry SIC lag A ( 1 ) A (cid:3) ( 1 ) R 2 S E E B G ( 1 2 ) b L R ( (cid:1) p (cid:3) e ) c (cid:1) R 2 d leather 31 5 .08 .29 .38 .0445 .76 .26 .00(0%) (1.7) (1.6) stone,clay 32 5 .07 .62 .67 .0081 .31 .70 .03(4%) andglass (3.4) (9.7) primary 33 2 .11 .56 .41 .0201 .94 .60 .05(12%) metals (2.7) (6.3) fabricated 34 2 .10 .71 .68 .0099 .63 .14 .05(7%) metals (4.7) (13.9) nonelectrical 35 5 .08 .61 .83 .0046 .64 .20 .03(4%) machinery (3.1) (12.4) electrical 36 4 .08 .27 .75 .0052 .51 .18 .02(3%) machinery (5.8) (3.6) motor 371 5 .15 .13 .73 .0089 .90 .37 .00(0%) vehicles (4.9) (1.2) other 37x 5 .08 .42 .67 .0076 .60 .24 .06(9%) transportation (3.9) (4.9) instruments 38 2 .12 .22 .26 .0181 .98 .56 .03(12%) (4.0) (2.9) miscellaneous 39 2 .15 .26 .39 .0138 .18 .96 .07(18%) (3.6) (3.7) a Sample span 1954Q1 - 1991Q4; t-ratios in parentheses. As in the text, p denotes the log producer price; p (cid:3) is thecointegratedpricetrend; (cid:15) t isthecointegratingdiscrepancy, p t (cid:0) p (cid:3) t ; and S 1 t ( G ; (cid:1) p (cid:3) ) isthepresent-valueeffectof anticipatedpricetrendchanges. b Breusch-Godfreytest(p-value)ofresidualautocorrelation(12lags). c Likelihoodratiotest(p-value)ofRErestrictionsonpredictionsofpricetrendchanges, (cid:1) p (cid:3) e . d Changein R 2 duetopresent-valueeffectofanticipatedpricetrendchanges, S 1 t ( G ; (cid:1) p (cid:3) ) .

28 TableIII AdjustmentsofIndustryPricestoOuput( u )GapsandPrice( (cid:15) )Gaps (cid:1) p t = (cid:0) A ( 1 ) (cid:15) (cid:0)t 1 + A (cid:3) ( L ) (cid:1) p (cid:0)t 1 + S 1 t ( G ; (cid:1) p (cid:3) ) + D ( L ) h[ 0 u z (cid:0)t 1 ] (cid:0) A[ + ( 1 ) (cid:0) A ( a 1 ) (cid:15)] + (cid:0)t 1 + a t : adjustment output b asymmetricprice c mean d costs gapeffects gapeffects lags SIC A ( 1 ) A (cid:3) ( 1 ) R 2 LR(u) D(1) L R ( (cid:15) + ; (cid:15) (cid:0) ) L R ( 0 ; (cid:15) (cid:0) ) A + ( 1 ) M L (cid:0) M L + 20-39 .13 .63 .75 .03 .19 .04 .91 .00 1.8 6.2 (2.9) (12.8) (1.5) (0.0) 20 .24 .52 .33 .07 1.61 .14 .00 1.0 (4.4) (3.4) (2.3) 21 .27 -.20 .33 .90 .48 .62 .04 3.4 29.8 (3.0) (2.5) (0.4) 22 .19 .44 .64 .00 .42 .31 .21 .07 2.1 6.7 (3.5) (7.1) (2.3) (1.2) 23 .18 .45 .62 .17 .03 .19 -.06 1.9 12.8 (2.8) (6.5) (-1.1) 24 .07 .48 .25 .44 1.00 .27 6.7 (1.6) (3.5) 25 .12 .16 .61 .48 .21 .84 .02 6.0 41.0 (1.8) (2.7) (0.3) 26 .17 .56 .66 .00 .96 .08 .89 .00 1.6 6.3 (3.7) (10.5) (3.5) (0.1) 27 .16 .45 .66 .21 .07 .32 .05 2.4 9.9 (4.4) (8.4) (1.4) 28 .09 .69 .78 .02 1.33 .02 .77 .02 2.4 14.5 (3.0) (12.2) (2.3) (0.6) 29 .30 .80 .43 .79 .52 .00 -0.3 (5.5) (5.8) 30 .19 .51 .65 .27 .24 .10 1.6 (4.9) (9.9) 31 .08 .30 .41 .07 3.57 .15 .03 7.6 (1.8) (1.7) (1.0) (Footnotesatendoftable.)

29 TableIIICont. AdjustmentsofIndustryPricestoOuput( u )GapsandPrice( (cid:15) )Gaps (cid:1) p t = (cid:0) A ( 1 ) (cid:15) (cid:0)t 1 + A (cid:3) ( L ) (cid:1) p (cid:0)t 1 + S 1 t ( G ; (cid:1) p (cid:3) ) + D ( L ) h[ 0 u z (cid:0)t 1 ] (cid:0) A[ + ( 1 ) (cid:0) A ( a 1 ) (cid:15)] + (cid:0)t 1 + a t : adjustment output b asymmetricprice c mean d costs gapeffects gapeffects lags SIC A ( 1 ) A (cid:3) ( 1 ) R 2 LR(u) D(1) L R ( (cid:15) + ; (cid:15) (cid:0) ) L R ( 0 ; (cid:15) (cid:0) ) A + ( 1 ) M L (cid:0) M L + 32 .11 .62 .72 .00 .70 .07 .35 .04 2.4 9.3 (3.8) (10.2) (3.0) (1.0) 33 .18 .48 .44 .08 .30 .42 .32 .09 1.9 4.9 (1.8) (5.1) (1.7) (1.0) 34 .23 .53 .67 .40 .00 .86 .00 1.0 9.6 (4.6) (8.9) (0.0) 35 .15 .57 .85 .61 .00 .07 -.06 1.9 11.9 (3.5) (12.3) (-1.6) 36 .08 .27 .75 .86 .30 .06 7.7 (5.8) (3.6) 371 .16 .01 .75 .02 -.17 .74 .03 5.0 (5.3) (0.1) (-2.1) 37x .19 .25 .69 .82 .00 .51 -.00 3.0 29.1 (3.9) (2.8) (-0.2) 38 .26 .14 .29 .96 .01 .91 -.01 2.3 15.5 (4.0) (1.9) (-0.2) 39 .15 .26 .39 .47 .27 .01 3.9 (3.6) (3.7) a Samplespan1954Q1-1991Q4;t-ratiosinparentheses. Asinthetext, p denotesthelogproducerprice; p (cid:3) isthe cointegratedpricetrend; (cid:15) t isthepricegap, p t (cid:0) p (cid:3) t ; (cid:15) + t and (cid:15) (cid:0) t denotethepositiveandnegativepricegaps. S 1 t ( G ; (cid:1) p (cid:3) ) isthepresent-valueeffectofanticipatedpricetrendchanges;and D ( L ) h[ 0 u z (cid:0)t 1 ] isthepresent-valueeffectofanticipated outputgaps. b L R ( u ) isthep-valuetoacceptindustryoutputgapterms, D ( L ) h[ 0 u z (cid:0)t 1 ] ,assignificantregressors. c L R ( (cid:15) + ; (cid:15) (cid:0) ) isthep-valuetoacceptdifferenterror-correctionresponsestothesplitpricegaps, (cid:15) + and (cid:15) (cid:0) ; L R ( 0 ; (cid:15) (cid:0) ) isthep-valuetorejectazeroerror-correctionresponsetopositivepricegaps, (cid:15) + . d Mean lag in quarters, conditional on the sign of the price gap. For several industries, the mean lag estimate for positivepricegaps, M L + ,isconstructedbyaddingoneortwostandarderrorstononpositiveestimatesof A + ( 1 ) .

30 TableIV Proximate CausesofAsymmetricPricing industry characteristics a herfindahl labor liquid asset trend inflation index(HF) share(LS) ratio (LA) variation (TI) industry meancontrasts b meanofsymmetric 754 .24 .21 .59 pricing industries meanofasymmetric 758 .30 .29 .88 pricing industries p-values for meandifference: -equalvariances .50 .08 .08 .02 -unequal variances .50 .21 .18 .04 regressions toexplain asymmetric pricing index c bivariate correlations: withindustry .45 .14 .60 .53 characteristic (1.7) (0.5) (2.5) (2.1) withrank ofindustry .23 .22 .54 .53 characteristic (0.8) (0.7) (2.1) (2.1) multivariate regressions: ( R 2 = : 5 3 ) .85x10 (cid:0) 3 -.15 9.4 2.7 (0.8) (-0.0) (1.4) (1.3) ( R 2 = : 4 8 ) 11.2 2.9 (1.9) (1.5) a HF - Herfindahl concentration index; LS - employee compensation share of gross output; LA - ratio of net liquid assetstoequity;TI-ratioofmeantostandarddeviationoffour-quarterinflationinindustrypricetrend. b IndustriesexhibitingsymmetricorasymmetricpricingasindicatedintableIII.Thep-valuesareforaone-tailtestthat themeanofasymmetricindustriesexceedsthemeanofsymmetricindustries;p-valuesforunequalvariancesarebasedon Cochran'stest,LauerandHan[1974]. c Dependent variable, defined only for industries exhibiting asymmetric pricing responses, is the ratio of mean lags shownintableIIIforpositiveandnegativepricegaps, M L + = M L (cid:0) . Parenthesescontaint-ratios.