NBER WORKING PAPER SERIES RESET PRICE INFLATION AND THE IMPACT OF MONETARY POLICY SHOCKS. Mark Bils Peter J. Klenow Benjamin A.

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1 NBER WORKING PAPER SERIES RESET PRICE INFLATION AND THE IMPACT OF MONETARY POLICY SHOCKS Mark Bils Peer J. Klenow Benjamin A. Malin Working Paper hp:// NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachuses Avenue Cambridge, MA March 2009 This research was conduced wih resriced access o U.S. Bureau of Labor Saisics (BLS) daa. Rob McClelland provided us invaluable assisance and guidance in using BLS daa. We hank Jose Musre Del Rio for excellen research assisance. The views expressed here are hose of he auhors and do no necessarily reflec he views of he BLS or he Federal Reserve Sysem. We are graeful o Carlos Carvalho, Jon Seinsson, and numerous seminar paricipans for helpful commens. The views expressed herein are hose of he auhor(s) and do no necessarily reflec he views of he Naional Bureau of Economic Research. NBER working papers are circulaed for discussion and commen purposes. They have no been peerreviewed or been subjec o he review by he NBER Board of Direcors ha accompanies official NBER publicaions by Mark Bils, Peer J. Klenow, and Benjamin A. Malin. All righs reserved. Shor secions of ex, no o exceed wo paragraphs, may be quoed wihou explici permission provided ha full credi, including noice, is given o he source.

2 Rese Price Inflaion and he Impac of Moneary Policy Shocks Mark Bils, Peer J. Klenow, and Benjamin A. Malin NBER Working Paper No March 2009 JEL No. E31,E32,E52 ABSTRACT A sandard sae-dependen pricing model generaes lile moneary non-neuraliy. Two ways of generaing more meaningful real effecs are ime-dependen pricing and sraegic complemenariies. These mechanisms have ellale implicaions for he persisence and volailiy of "rese price inflaion." Rese price inflaion is he rae of change of all desired prices (including for goods ha have no changed price in he curren period). Using he micro daa underpinning he CPI, we consruc an empirical measure of rese price inflaion. We find ha ime-dependen models imply unrealisically high persisence and sabiliy of rese price inflaion. This discrepancy is exacerbaed by adding sraegic complemenariies, even under sae-dependen pricing. A sae-dependen model wih no sraegic complemenariies aligns mos closely wih he daa. Mark Bils Deparmen of Economics Universiy of Rocheser Rocheser, NY and NBER bils@roi.cc.rocheser.edu Benjamin A. Malin Federal Reserve Board of Governors Mail Sop 97 21s and C S., NW Washingon, D.C benjamin.a.malin@frb.gov Peer J. Klenow Deparmen of Economics 579 Serra Mall Sanford Universiy Sanford, CA and NBER Pee@Klenow.ne

3 1. Inroducion Consumer prices change every seven or eigh monhs in he U.S. 1 Ye he real effecs of moneary shocks have been esimaed o las around hiry monhs. 2 These figures sugges real effecs lasing roughly four imes longer han nominal price sickiness i.e., a conrac muliplier of around four in Taylor s (1980) erminology. In conras, research on calibraed DSGE models obains much lower conrac mulipliers, a leas in he absence of sraegic complemenariies and sicky informaion. Chari, Kehoe and McGraan (2000) repor conrac mulipliers around one in a variey of ime-dependen pricing models. Caballero and Engel (2007) and Golosov and Lucas (2007) arrive a conrac mulipliers well below one in heir sae-dependen pricing models. Dosey, King and Wolman (1999) and Midrigan (2008) obain inermediae conrac mulipliers in heir sae-dependen models. As has been well-known since Ball and Romer (1990) and Kimball (1995), sraegic complemenariies in he pricing decisions of individual sellers can produce large conrac mulipliers. 3 A saring poin for hese models is ha he nominal sickiness be saggered, o creae he possibiliy of coordinaion failure among price seers. 4 In response o an aggregae shock, sraegic complemenariies mue he size of price changes for hose changing prices, as price seers wai for he average price o respond. 1 Klenow and Krysov (2008) and Nakamura and Seinsson (2008a). This figure ignores price changes involving sale prices, oherwise he number would be abou four monhs. 2 Chrisiano, Eichenbaum, and Evans (1999), Romer and Romer (2004), and Bernanke, Boivin, and Eliasz (2005), each based on U.S. daa, are a few of he many examples. 3 Recen papers in his vein include Alig e al. (2005), Carvalho (2006), Blanchard and Gali (2007), Gerler and Leahy (2008) and Nakamura and Seinsson (2008b). 4 Saggered price seing appears o describe he U.S. daa well. Klenow and Kryvsov (2008) find ha he fracion of consumer prices changing does flucuae bu is no highly correlaed wih movemens in inflaion. They also find big individual price changes. Golosov and Lucas (2007) show hese facs can be explained by large idiosyncraic shocks ha govern boh he iming and size of price changes a he micro level. 1

4 We show ha models wih high conrac mulipliers a he macro level display slowmoving rese prices a he micro level. A rese price for an individual seller is ha price i would choose if i implemened a price change in he curren period. Acual prices ofen differ from rese prices, of course, because of nominal price sickiness. We define heoreical rese price inflaion as he weighed average change of all rese prices, including hose of curren price changers and non-changers alike. We denoe rese price inflaion as he weighed average change of rese prices for price changers only. In he Calvo (1983) ime-dependen pricing model, he probabiliy of changing price is independen of he desired rese price change, so rese price inflaion is a pure reflecion of heoreical rese price inflaion. In sae-dependen models, sellers weigh he benefis of moving o he rese price agains he (menu) coss of doing so. For hese models rese price inflaion can depar imporanly from heoreical rese price inflaion. Sraegic complemenariies should dampen he volailiy of rese price inflaion and boos is persisence. An individual seller will move by smaller amouns, requiring muliple price changes o fully respond o a shock. We confirm his inuiion by simulaing DSGE models feauring ime-dependen pricing (TDP) or sae-dependen pricing (SDP), wih or wihou sraegic complemenariies. The models feaure a single aggregae shock (o money or produciviy) plus idiosyncraic shocks o each seller s produciviy. The complemenariies ake he form of inermediae goods, as in Basu (1995). Inermediaes can slow down moneary pass-hrough because price changers have no seen heir inermediae coss fully adjus due o he sicky prices of heir suppliers. Sellers are grouped ino one of wo secors: he flexible price secor (low menu cos, bigger idiosyncraic shocks) or he sicky price secor (high menu cos, smaller shocks). 2

5 Using he micro daa on prices colleced by he U.S. Bureau of Labor Saisics for he Consumer Price Index, we consruc an empirical index of rese price inflaion for he monhs January 1989 hrough May We impue o all iems, boh hose changing and no, he rese price changes exhibied by price changers. To arrive a he rese price change for an iem changing price, we compare he iem s new price o is esimaed rese price he previous monh no he iem s las new price, se perhaps monhs earlier. A useful analogy is o home price indices consruced from repea sales (e.g., Shiller 1991 and Zillow.com). These indices esimae he value of residenial homes even when hey are no sold. Once a home is sold, he difference beween he ransaced price and he previous period s esimaed value is used o updae he esimaed value of oher homes ha were no sold. Our rese price index is he analogue for all consumer iems o hese home price indices. We compare he behavior of our empirical measure of rese price inflaion o ha of an idenically-consruced measure from simulaed TDP and SDP models. As menioned previously, rese price inflaion is he exac counerpar o heoreical rese price inflaion in he Calvo model. Even hough our consruced rese price inflaion is no he same as heoreical rese price inflaion for SDP models, we find ha simulaed SDP models yield clear predicions for our consruced rese price inflaion. To delve furher ino he role played by price rigidiy, we pariion he CPI goods ino flexible and sicky groups. The former reflecs 30 percen of consumer spending and displays an average monhly frequency of price changes of 1/3. The laer consiues 70 percen of spending and displays an average monhly frequency of around 1/10. Our simulaed models feaure flexible and sicky-price secors, wih each secor s frequency and absolue size of price changes maching hose saisics in he CPI daa. 3

6 We find he models wih big conrac mulipliers fundamenally a odds wih he daa. TDP models, wih or wihou sraegic complemenariies, and he SDP models wih sraegic complemenariies, generae unrealisically high persisence and low volailiy of rese price inflaion. These models predic ha he impac of a nominal shock on rese prices will build over ime. Bu in he daa we see he opposie. An increase in rese price inflaion predics lower, no higher, rese price inflaion in subsequen monhs, so ha an index of rese prices responds more on impac han over ime. Anoher model predicion is ha goods wih infrequen price changes (he sicky-price goods) will display relaively more persisen inflaion (overall, no rese). Bu we do no see his in he daa. The SDP model wih no complemenariies comes closes o maching he empirical paerns. I feaures broadly realisic volailiy and persisence of rese and acual price inflaion for all goods, flexible goods, and sicky goods. Relaed, a way o rescue sraegic complemenariies migh be o incorporae endogenous moneary policy. If moneary policy quickly offses he aggregae shock (o money iself or o aggregae produciviy), hen models wih complemenariies no longer imply ousized persisence of rese and acual inflaion. This soluion creaes wo problems, however. Firs, endogenous moneary policy essenially ges rid of he conrac muliplier. Second, his soluion reduces rese inflaion volailiy o around one-fifh of he observed level, and he variance of acual inflaion o less han oneenh he observed level. If moneary policy offses shocks, price seers respond lile o hese shocks and inflaion becomes much oo smooh. The lieraure on moneary policy has coalesced on sraegic complemenariies in order o raionalize a large conrac muliplier. Bu our resuls srongly rejec he predicions 4

7 of hose sicky-price models we examine ha feaure sufficien complemenariies o produce an imporan conrac muliplier. The res of he paper proceeds as follows. Secion 2 describes he daase and he empirical properies of rese price inflaion. Secion 3 lays ou he models and compares saisics from he simulaed models o heir empirical counerpars. Secion 4 concludes. 2. An empirical measure of rese price inflaion The CPI Research Daabase We use he micro daa underlying he non-sheler porion of he CPI o consruc our measure of rese price inflaion. The BLS surveys abou 85,000 iems a monh in is Commodiies and Services Survey. Individual prices are colleced a around 20,000 reail oules across 45 large urban areas. 5 The survey covers all goods and services oher han sheler, or abou 70 percen of he CPI based on BLS consumer expendiure weighs. The CPI Research Daabase (hereafer CPI-RDB) mainained by he BLS Division of Price and Index Number Research conains all prices in he Commodiies and Services Survey since January We use he CPI-RDB hrough May 2008, for a sample of The BLS collecs consumer prices monhly for food and fuel iems in all areas. The BLS also collecs prices monhly for all iems in he hree larges meropolian areas (New York, Los Angeles, and Chicago). The BLS collecs prices for iems in oher caegories and oher urban areas only bimonhly. For our compeing models, he impulse responses for rese price inflaion differ markedly in he iniial periods afer a shock, making i valuable o have 5 The BLS selecs oules and iems based on household poin-of-purchase surveys, which furnish daa on where consumers purchase commodiies and services. The price collecors have deailed checkliss describing each 5

8 an empirical counerpar ha capures he daa a high frequency. For his reason, we resric our analysis o he op hree areas ha have monhly daa on all goods. The BLS defines 300 or so caegories of consumpion as Enry Level Iems (ELIs). Wihin hese caegories are prices for paricular iems (we call a longiudinal series of individual price quoes a he micro level a quoe-line ). The BLS provided us wih unpublished ELI weighs for each year from and based on Consumer Expendiure Surveys in each of hose years. We normalize he nonsheler porion of he weighs o sum o 1 in each year. We se he 1996 and 1997 ELI weighs o he 1995 weighs, and he 1998 weighs o heir 1999 level. We se he 2005 and onward weighs o heir 2004 level. The CPI-RDB also conains weighs for each price wihin an ELI. We allocae each ELI s weigh o individual prices in each monh in proporion o hese iem weighs o arrive a weighs i ha sum o 1 across iems (i s) in each monh. The BLS labels each price as eiher a sale price or a regular price. Sale prices are emporarily low prices (including clearance prices). Golosov and Lucas (2007), Nakamura and Seinsson (2008a), and ohers filer ou such sale prices on he grounds ha hey are idiosyncraic deviaions from sickier regular prices. Relaed, in classifying goods as flexible or sicky and in calibraing he model economies, we do so based on he frequency of regular price changes. We adop his reamen because i yields more conservaive resuls wih respec o our conclusions. If, alernaively, we encompass he higher rae of price changes involving prices labeled by he BLS as sales prices, we would obain an average frequency of price change of a lile over 25 percen monhly raher han 22 percen. In urn, his would require even larger conrac mulipliers for our model economies iem o be priced is oule and unique idenifying characerisics. They price each iem for up o five years, afer which he iem is roaed ou of he sample. 6

9 o generae he same persisence in he impac of moneary shocks. Bu we find ha he daa do no suppor large conrac mulipliers. We use all prices, including sale prices, when consrucing our inflaion and rese price inflaion series. To he exen sales are ruly idiosyncraic heir impac on he ime series for price inflaion, given he large samples of price quoes in each secor, will average close o zero. To he exen sales do affec aggregae price inflaion, hey are no idiosyncraic and so should no be excluded. Tha said, we will show ha our resuls are robus o excluding sales prices from he series for price inflaion. Forced iem subsiuions occur when an iem in he sample has been disconinued from is oule and he price collecor idenifies a similar replacemen iem (e.g., new model) in he oule o price going forward. The monhly rae of forced iem subsiuions is consisenly abou 3 percen in he sample. Essenially all iem subsiuions involve price changes. We include hese price changes a subsiuions in our saisics. 6 Bu our resuls are exremely robus o reaing all price changes as zero a forced subsiuions. Abou 12 percen of he prices he BLS aemps o collec are unavailable in a given monh. The BLS classifies roughly 5 percen of iems as ou-of-season. We pu zero weigh on ou-of-season iems when calculaing boh inflaion and he frequency of price changes. The BLS classifies he oher 7 percen as emporarily unavailable. As hese iems may be only inermienly unavailable during he monh, we rea iems ou of sock as available a he previously colleced price. We employ his reamen boh for calculaing frequency of price changes and ime series of inflaion raes. Alhough he BLS requires is price collecors o explain large price changes o limi measuremen errors, some price changes in he daase appear implausibly large. We exclude 6 For abou half of forced subsiuions he rae of price change impared o he CPI reflecs a BLS adjusmen aimed a capuring qualiy change. We employ hese BLS adjusmens in all price change saisics. 7

10 price changes ha exceed a facor of five. Such price jumps consiue less han one-enh of one percen of all price changes. Defining Rese Price Inflaion Secion 3 below illusraes how models wih high conrac mulipliers exhibi ineria no only in price inflaion, bu also in rese price inflaion so he behavior of rese price inflaion is a baromeer for lasing real effecs of moneary shocks. Wheher pricing is ime-dependen or sae-dependen, he desired price level for iem i in monh, P, saisfies an Euler equaion aking ino accoun effecs on curren and fuure * i, prices. Following Dosey e al. (1999), he Euler equaion is where i, denoes curren profis, u'( c ) V E (1 ) P u c P i, 1 i, 1 * i, 1 * i, '( ) i, E refers o expecaions a ime, u'( c 1) / u'( c ) is he familiar sochasic discoun facor, i, 1is he probabiliy of a price change for iem i in monh 1, and Vi, is nex period s value funcion. Noe ha he rese price can differ from 1 he opimal flexible price (he price ha maximizes curren period profis) because of fuure i price sickiness (, 1 1). Relaed, he acual price can differ from he rese price if he seller does no change is price in he curren period. Rese price inflaion for a given seller is he log firs difference of is rese price: ln( P ) ln( P ). * * * i, i, i, 1 This definiion does no require a price change a eiher or 1. Aggregae rese price inflaion is hen he weighed average of micro rese price inflaion: 8

11 * * (2.1) i,, where he weighs i, add o 1. By comparison acual inflaion is where i, i, i i, i p p and p i, i, i, 1 i, denoes he log of he acual BLS price of iem i a ime. Whereas sarred variables denoe rese values, hose wihou sars represen acual values. Le I i, be a price-change indicaor: I i, 1 if p 0 if p p i, i, 1 p i, i, 1. To consruc an empirical measure of aggregae rese price inflaion, each monh we divide iems ino hose ha change price ( Ii, 1) and hose ha do no change price ( Ii, 0 ). For prices ha change, he rese price is simply he curren price. For prices ha do no change, we index our esimae of he rese price o he rae of rese price inflaion among price changers in he curren period. Our esimae of he log rese price level for iem i in monh is p * i, pi, if pi, p i, 1 * * pi, 1 if p p i, i, 1 where ^ s denoe our esimaes. In urn, our esimae of aggregae rese price inflaion is i, ( pi, pi, 1 ) Ii, (2.2) * i. I i i, * i, 9

12 Alhough he esimae * only employs ime price changers, price changes from previous monhs are capured in he base values of * pi, 1, which are indexed o reflec prior changes. 7 In Table 1 we presen a sylized example useful for conrasing he rae of rese price inflaion ( * ) o acual inflaion ( ) and he average inflaion of price changers (call his ). The example has wo goods. Boh goods change price in period 0, esablishing base prices for calculaing rese price inflaion. Good A s price increases by 20% in period 1, wih Good B s unchanged. This yields a rae of 20% for rese price inflaion, same as he average rae of price increase condiional on changing price, while acual inflaion is 10%. Bu noe ha i also kicks up he base price for calculaing rese price inflaion by 20%, no only for Good A, bu also for Good B. Thus, when B s price increases by 20% in period 2, while A s remain unchanged, B s price jus mees is updaed rese price from period 1. As a resul, rese price inflaion for period 2 equals zero, despie he same acual inflaion rae and rae of increase for price changers, respecively 10% and 20%, as in period 1. Our esimaed rese price inflaion is equivalen o heoreical rese price inflaion under he special case of Calvo pricing. By conras, under SDP he decision o change a price reflecs selecion on he idiosyncraic componen in a seller s desired price change. For his reason, esimaed rese price inflaion * can differ markedly from heoreical rese price inflaion *. We illusrae his difference for SDP models in Secion 3 as a means of discriminaing beween he TDP and SDP models. 7 We considered an alernaive measure of rese price inflaion based on regressing each price change on monhly dummies aking he value 1 for monhs spanning each price spell. This measure parallels he Case-Shiller Home Price Index (Shiller, 1991), which allocaes price increases for homes o he monhs beween repea sales. In our daa and model economies, his regression-based measure exhibis very similar saisics o ha based on (2.2). 10

13 A key quesion for us is wha exra informaion is conained in * ha canno be gleaned from alone. Under Calvo, one can infer * from if one also knows he pricechange frequency. 8 Bu endogenous price changing, and especially selecion of changers, breaks he simple ranslaion from * o. By endogenous price changing we mean any response in he fracion of goods changing price o underlying shocks. By selecion of changers we mean ha, in conras o Calvo, he changers may be hose wih larger gaps beween acual and rese prices. Relaed, * should be direcly revealing abou sraegic complemenariies, whereas is also affeced by any response of he fracion changing. Some forces for a low conrac muliplier (selecion) or a high conrac muliplier (sraegic complemenariies) operae on * direcly, whereas heir effec on can be clouded by movemens in frequency. The persisence of may be informaive abou he conrac muliplier, bu does no say where i is coming from (frequency or rese price inflaion). Similarly, we could focus on he average price change among changers ( ) raher han consrucing he less direc measure *. In models we simulae, however, we find ha he volailiy of / does no vary wih he conrac muliplier (e.g., SDP wih or wihou complemenariies), whereas he volailiy of * We will revisi his issue in Secion 3 below. / falls sharply wih he conrac muliplier. 8 * 1 1 Under Calvo, where is he frequency of price change. 11

14 Evidence on Rese Price Inflaion Table 2 conains summary saisics on our consruced measure of rese price inflaion, as well as on acual inflaion for comparison. All he monhly series are HP-filered and seasonally adjused. 9 Our measure of all goods excludes no only sheler, which is missing from he CPI-RDB, bu also energy, fresh frui and vegeables, and eggs. We exclude hese for wo reasons. Firs, hey are arguably subjec o big secoral shocks ha are absen from our models. If hese shocks are emporary, hen hey arificially lower aggregae inflaion persisence. Second, hese goods involve lile or no processing, and hence lack he sraegic complemenariies hrough slow-moving inpu prices. In addiion o he aggregae saisics, we examine acual and rese price inflaion for wo sub-aggregaes: flexible goods and sicky goods. As menioned, he BLS places individual price quoe-lines ino one of abou 300 caegories (ELIs). We calculae he average frequency of regular price changes wihin each ELI, hen classify quoe-lines as flexible or sicky based on heir ELI s frequency. We choose a hreshold frequency separaing he wo groups of 1/6, similar o he overall mean (weighed) frequency of 16.8 percen. This generaes a 70 percen share of spending on he sicky group compared o 30 percen on he flexible group. We pu more price quoes in he sicky group o miigae sampling error here, given is smaller number of price changes per observed price. The flexible goods average 3,100 price quoes per monh, compared o 8,300 for he sicky goods. The mean frequency of price changes is 33.3 percen in he flexible group, while only 9.5 percen for he sicky. 9 The HP-filer we employ is very smooh, wih a penaly parameer of one million (!). I removes a downward rend in inflaion during he firs par of he sample, and lile else. Wih no filering, resuls for rese price inflaion are nearly unchanged. As an alernaive, we subraced he 10-year inflaion forecas from he Survey of Professional Forecasers (SPF, available quarerly from 1991:Q4). For he common sample he correlaion beween HP-filered rese price inflaion and SPF-filered rese price inflaion is 0.997, wih virually idenical serial correlaions and sandard deviaions. Inflaion is likewise very similar when filered in hese wo ways. 12

15 We calculae rese price inflaion using formula (2.2) for flexible goods and sicky goods separaely. We hen calculae aggregae rese price inflaion as he weighed average of rese price inflaion for he wo groups, wih weighs 0.3 on he flexible and 0.7 on he sicky, consisen wih heir expendiure shares. We do he same in calculaing acual inflaion a he aggregae level. Consrucing rese price inflaion a he group level firs avoids overweighing frequen changers in calculaing aggregae rese price inflaion. 10 The firs row of Table 2 repors a sandard deviaion of monhly rese price inflaion of almos 1.0 percen. 11 There is no persisence in rese price inflaion as measured by is firsorder auocorrelaion. In fac his serial correlaion is noably negaive, a We provide more evidence on persisence below. The hird and fourh rows repor he comparable saisics for acual inflaion. Acual inflaion is much less volaile han rese price inflaion, wih a sandard deviaion, a 0.18%, less han one-fifh ha for rese price inflaion. This lower volailiy for acual inflaion follows mechanically from is including many zero price changes, unless variaions in he frequency of changes play a major role in inflaion movemens bu we know from Klenow and Kryvsov (2008) ha frequency changes do no play ha role. Acual inflaion (serial correlaion 0.12) is more persisen han rese price inflaion (serial correlaion 0.44). Again, his is expeced under nominal price sickiness unless he frequency of price changes is highly responsive o he inflaion rae; in fac, all models in Secion 3 predic his resul. 10 We also ried finer disaggregaion, namely calculaing rese price inflaion for each of 64 BLS Expendiure Classes (cereal, compuers, medical services, legal services, and so on), before aggregaing. The behavior of rese price inflaion volailiy, persisence is similar o ha wih our wo groups. 11 Whereas our raw sample goes from January 1988 hrough May 2008, our consruced series run from January 1989 hrough May We dropped he firs year because we require a new price o iniiae a rese price series for a given quoe-line. 13

16 Our serial correlaion for acual inflaion is lower han repored in many sudies for several reasons. Firs is our use of an HP filer (in addiion o monhly dummies o capure seasonaliy). If we do no HP-filer, he serial correlaion in acual inflaion is modesly higher (+0.06 raher han 0.12). We also exclude energy and raw food iems. Incorporaing hese caegories would noiceably raise he serial correlaion of unfilered inflaion o Finally, longer ime series exending back o he 1970s or earlier exhibi much more persisence. Persisence fell markedly by he ime our sample began in he lae 1980s. See Sock and Wason (2006) or Nason (2006), for example. Even for recen samples Sock and Wason find inflaion has a persisen componen. When we esimae an ARMA(1,1) for inflaion we ge an AR(1) coefficien of 0.89 (s.e. 0.03) and an MA(1) coefficien of 0.99 (.01). We highligh he AR(1) specificaion in our ables o be concise and o underscore ha ransiory componens dominae he variance of recen inflaion, jus as Sock and Wason find. When esimaing impulse response funcions we consider less resriced specificaions. The second and hird columns of Table 2 repea he saisics from he firs column for he flexible and sicky groups separaely. We see ha rese price inflaion is volaile in boh he flexible and sicky secors, wih sandard deviaions of 1.3 and 1.2 percen, respecively. Acual inflaion is more han wice as volaile in he flexible vs. sicky secor, reflecing he imporan smoohing effec of many unchanging prices in he sicky secor. 12 Table 2 also shows he persisence in rese and acual price inflaion across he wo secors. The flexible and sicky secors have similar persisence in rese and acual price 12 The correlaion beween rese inflaion raes in he flexible and sicky secors is only The correlaion beween acual inflaion raes in he wo secors is only The aggregae rese inflaion rae is correlaed 0.54 wih rese inflaion in he flexible secor and 0.92 wih rese inflaion in he sicky secor. The aggregae acual inflaion rae is correlaed 0.77 wih inflaion in he flexible secor and 0.73 wih inflaion in he sicky secor. 14

17 inflaion as all goods. This runs couner o he predicion of many sicky price models ha infrequen price changes ac as a force for acual inflaion ineria. 13 The price series (rese and acual) described in Table 2 reflec sale prices as well as regular prices. The resuls, however, do no hinge on his reamen. Table 3 repeas all he saisics from Table 2 bu reas sales prices as emporarily missing, carrying forward he mos recen regular price as he price for ha monh. The paerns highlighed from Table 2 are nearly unchanged in Table 3. In paricular, rese price inflaion coninues o show a srong negaive serial correlaion of 0.43 (vs in Table 2), and he serial correlaion of acual inflaion increases only modesly o 0.06 (vs in Table 2). This means ha sale prices eiher wash ou in he aggregae or mimic he movemens in regular prices. Inflaion is modesly more persisen a 0.15 (vs. 0.09) for sicky goods under his reamen. To furher invesigae he persisence properies of hese inflaion raes, we nex show impulse responses derived from univariae AR(6) regressions. (The choice of 6 monhly lags is based on he Akaike crierion.) Figure 1 gives he response of rese prices o a 1% impulse for all goods. The (level) response in rese prices is much greaer on impac han over ime. The impac effec is more han double he long-run response. This mean reversion in rese prices does no reflec emporarily sales, as he paerns are very similar for series purged of sale prices as shown in Figure 2. The shape also holds separaely for flexible and sicky goods, as depiced in Figures 3 and One concern abou Figures 1-4 is ha he shocks hemselves may be ransiory. Responses o permanen shocks may exhibi far greaer persisence. We herefore esimaed 13 These resuls are no driven by HP filering. Serial correlaions of rese price inflaion are unaffeced by he filer hey sill equal 0.41 and 0.49 for he flexible and sicky goods wihou filering. Serial correlaion is only modesly higher for acual inflaion, absen filering, a 0.07 for flexible goods and 0.08 for sicky. 15

18 he response of rese prices o a shock wih a permanen 1% impac on acual prices, idenified by imposing a long run resricion on a bivariae VAR wih rese and acual price inflaion. Rese prices overshoo heir long run response jus as much in his case. We carried ou a number of daa robusness checks. Unless noed, he serial correlaions and impulse funcions were virually unaffeced. We aggregaed he monhly ime series up o he bi-monhly, quarerly, or even annual level. We spli he monhly ime series ino wo ime periods, January 1989 hrough December 1998 and January 1999 hrough May We spli he panel o creae wo samples (boh going from January 1989 hrough May 2008) wih half as many prices in each. The variance of rese price inflaion was modesly higher in he wo subsamples, as one would expec given greaer sampling error. We dropped all price changes associaed wih produc urnover (i.e., iem subsiuions). We looked only a services, whose prices are sickies and whose spending exhibis lile volailiy (secoral shocks hus being less of a concern). In each of hese deviaions from our baseline case, our findings remain inac. Finally, we looked a bi-monhly daa for all areas (45 ciies, as opposed o he monhly daa for jus New York, Los Angeles, and Chicago areas). This imporan robusness check incorporaes much more daa (68,500 quoes per bi-monh vs. he 11,400 per monh in our baseline daase). Doing so maerially lowers volailiy by miigaing sampling error. We will reurn o hese all-area resuls when comparing models o he daa. 3. Sicky price models and rese price inflaion The leading TDP and SDP models have predicions for he behavior of rese price inflaion. We will illusrae using a Calvo TDP model and an SDP model in he spiri of 14 The impulse response funcions for rese prices look similar from an ARMA(1,1) as from he AR(6). 16

19 Golosov and Lucas (2007), respecively. They will be wo-secor models wih and wihou sraegic complemenariies, so Carvalho (2006) and Nakamura and Seinsson (2008b) are even closer anecedens. We firs skech he models, hen repor saisics from model simulaions for comparison wih he facs documened in he previous secion. The Models Infiniely-lived households have preferences over labor supply and a composie consumpion good, where composie consumpion is a CES aggregae of individual consumpion varieies. They also have access o sae-coningen bonds (in zero ne supply) for ransferring resources across ime periods, and hey choose bond holdings, consumpion, and labor supply o maximize discouned uiliy subjec o a lifeime budge consrain. Individual varieies are supplied by a coninuum of monopolisically compeiive firms. The producion funcion of a paricular firm (good) i is given by (3.1) y i A i L i i 1 x x () () () X() where Ai () denoes produciviy, Li () labor, X () i a CES aggregae of individual inermediae goods, and x he share of he composie inermediae good. Firms are grouped ino one of wo secors disinguished by how frequenly firms change price. Producion funcion (3.1) exhibis wo key feaures commonly used in macro models of price sickiness. Following Danziger (1999) and Golosov and Lucas (2007), a firm s produciviy is subjec o idiosyncraic shocks, which will be imporan for capuring he dispersion of individual price changes seen in he daa. A second key feaure is he inclusion of inermediae goods, following Basu (1995) and Dosey and King (2006). For x 0, each firm uses inermediae inpus produced by all oher firms in he economy. Inermediaes are a 17

20 way of generaing sraegic complemenariies in price-seing, as coss fully respond o a shock only when oher firms prices respond. In an excellen survey, Mackowiak and Smes (2008) sugges such macro rigidiies are promising for obaining high conrac mulipliers. Firms hire inpus and se prices o maximize expeced discouned profis subjec o a fixed cos of changing price. In he SDP models, he cos is consan over ime for each firm, bu does vary across firms depending on he firm s secor. For he TDP models, firms receive a menu cos draw of eiher 0 or in each period, wih he secor-specific probabiliy of a menu cos of zero being fixed over ime. Finally, we assume a cash-in-advance consrain on a household s nominal spending PC M. In urn, we assume he money supply evolves as follows: M 1 M (3.2) ln M ln M 1 m ln ln P 1 P where is a moneary policy shock and ln M P is seady-sae aggregae real demand. When m 0, he money supply evolves exogenously according o a geomeric random walk wih drif. We will also consider an endogenous moneary policy case, in which m 0 and money growh is inversely relaed o lagged aggregae real demand. An appendix provides a more horough mahemaical exposiion of he model, including is key parameers, and describes he soluion mehod We hank Emi Nakamura and Jon Seinsson for making he soluion rouines for hese models available on heir websie. See Nakamura and Seinsson (2008b) for a deailed descripion of he soluion procedure. 18

21 Calibraion Table 4 repors he values of economy-wide parameers in he TDP and SDP models. We consider hree specificaions: a baseline case feauring no sraegic complemenariies, a sraegic complemenariies specificaion ha generaes a conrac muliplier of 4, and a specificaion wih sraegic complemenariies and endogenous moneary policy. Mos parameers remain consan across he hree specificaions. The monhly discoun facor is 1/ We consider log uiliy in consumpion ( 1) and linear labor supply ( 0 ), while he parameer governing he disuiliy of labor supply ( ) is se so ha seady sae labor supply is 1/3. The elasiciy of demand for consumpion varieies is 4, wihin he range of values esimaed in he rade and IO lieraures, e.g., Broda and Weinsein (2006) and Hendel and Nevo (2006). 16 We se he parameers for he money growh process (,, ) o mach he mean growh rae of inflaion (0.2%), he sandard deviaion of nominal nonsheler PCE growh (0.48%), and, for he endogenous moneary policy case, he serial m m correlaion of nominal PCE growh ( 0.31) over our sample period. 17 The serial correlaion of he idiosyncraic produciviy shock is se o 0.7, based on esimaes in Klenow and Willis (2006) using he serial correlaion of new relaive prices in he CPI-RDB. Table 4 also presens parameer values deermining he degree of sraegic complemenariy in pricing. Following Ball and Romer (1990), we define srong real rigidiies (more sraegic complemenariies in his model) as low responsiveness of a firm s 16 I is also in he range used by oher sicky price papers; Midrigan (2008) uses 3, Nakamura and Seinsson (2008b) use 4, and Golosov and Lucas (2007) se We deliberaely do no calibrae he money supply process o daa on money supply as our money supply process is a sand-in for moneary policy shocks, no acual money growh. 19

22 real price o changes in aggregae real demand. The firm s opimal price in he absence of menu coss can be expressed (ignoring consans) as (3.3) ln p( i) 1 x ln( M) 1 1 x ln( P) ln A( i). As in Woodford (2003), we define sraegic complemenariy as a posiive weigh on he aggregae price, raher han having all weigh on he aggregae money sock. Thus, when is small, prices exhibi greaer complemenariy. Our baseline model has 1 x log uiliy in consumpion ( 1), linear labor supply ( 0 ), and no inermediae goods ), so ha ( 0 x 1 x 1. This baseline case has no sraegic complemenariy (he coefficien is 0 on he aggregae price level). In our sraegic complemenariies case, we choose he inermediae inpu share o generae a conrac muliplier of 4, where he conrac muliplier is calculaed as he raio of he duraion of real effecs of a moneary policy shock o he number of periods in a ypical conrac. 18 This requires an inermediae share of.95 in he SDP model (.67 x for TDP) and yields x 1 x 0.05, or srong sraegic complemenariies (a coefficien of 0.95 on he aggregae price level). 19 As emphasized by Basu (1995), more inensive use of inermediae inpus makes he response of marginal cos o moneary shocks a funcion of no only he nominal wage bu he exen of price adjusmen a oher firms a sraegic complemenariy. Table 5 repors he values of secor-specific parameers in our models. In he SDP model, we calibrae he sandard deviaion of each secor s idiosyncraic produciviy shock 18 Specifically, we follow Chrisiano e al. (2005) by calculaing he amoun of ime i akes he expansion in aggregae real demand caused by a posiive policy shock o drop below 10% of is iniial response. We hen muliply his number by he aggregae frequency of price changes. 19 A realisic share based on BEA Inpu-Oupu Tables would be around 0.7 (Nakamura and Seinsson, 2008b). 20

23 and each secor s menu coss o generae frequencies of price change by secor of 0.33 (flexible) and 0.10 (sicky), as well as an average size of price change of 8% and 9.5% in he respecive secors. These figures correspond closely o he frequency and average size of price changes in he BLS daa by secor, excluding energy and raw food. The required shocks have sandard deviaions of 4.94% for he flexible secor and 4.75% for he sicky secor. Expended menu coss average abou 0.20% of revenue, somewha lower han he esimaes of Levy e al. (1997) and Zbaracki e al. (2004). Finally, 30% of firms are in he flexible secor and 70% are in he sicky, o mach he BLS expendiure shares on hese wo groups. For he TDP model, only he menu cos parameers differ from he SDP model. We acually embed Calvo in an SDP model wih ime-varying menu coss. Each period, he menu cos is zero for a fracion s of firms, while prohibiively large for a fracion1 s of firms. Resuls and Inerpreaion We now compare saisics from model simulaions o he daa saisics. To mach he daa sample, we simulae economies wih 3,100 firms in he flexible secor and 8,300 firms in he sicky secor for 233 periods. We run 100 such simulaions and repor he average and sandard deviaion of he saisics across he simulaions. We find ha models generaing large conrac mulipliers, eiher hrough he use of TDP or sraegic complemenariies, display unrealisically high persisence and low volailiy of rese price inflaion. Compared o he empirical daa, rese price inflaion in he models is way oo persisen and sable. 21

24 In Table 6 we presen saisics for he Calvo TDP model wihou sraegic complemenariies. This model has a conrac muliplier around wo. 20 Model rese inflaion raes are oo smooh relaive o he daa, exhibiing only one-fourh he observed variance. Rese price inflaion is also oo persisen ( 0.04 in he model vs in he daa), and he discrepancy is even greaer for acual inflaion (0.73 in he model vs in he daa). Figure 5 presens he univariae IRF for model rese prices for all goods. The model IRF is fla, meaning he average desired price fully responds on impac. Equaion (3.3) shows why: he average desired price, washing ou idiosyncraic shocks A ( i ), moves one-for-one wih a change in money supply in he absence of sraegic complemenariies. Because money growh follows a random walk, he resul is a fla impulse response funcion. Figure 5 also shows he confidence inervals from he daa for comparison; he empirical IRFs are, in conras, highly ransiory. The model and empirical bands do no overlap despie each represening +/- wo sandard deviaions. The conras is similarly sark for flexible and sicky goods separaely (no shown). Table 7 presens resuls from a Calvo TDP model wih sraegic complemenariies. The conrac muliplier here is approximaely four. The complemenariies furher depress he volailiy of rese price inflaion, so ha he model variance is now more han an order of magniude smaller han he empirical variance. The excess persisence problems seen in Table 6 (TDP wihou sraegic complemenariies) remain. Figure 6 shows ha, if anyhing, he univariae IRF for rese prices builds because of he sraegic complemenariies, in 20 Chari e al. (2000) obain a conrac muliplier near one in a Taylor model. Using heir definiion (he half-life of real effecs relaive o he half-life of a price), we obain a muliplier near one in our Calvo TDP model. We repor higher numbers in he ex using he Chrisiano e al. (2005) definiion of he duraion of real effecs relaive o he duraion of prices. The difference sems from slower-han-exponenial decay of real effecs. 22

25 conras o he falling empirical IRF. The model IRF would build more briskly if no for he sampling error from he finie sample of firms, as in he daa. Table 8 presens he SDP model wihou sraegic complemenariies. As in Golosov and Lucas (2007), he conrac muliplier in his model is well below one a 0.4. Inflaion persisence is markedly reduced relaive o he TDP models a resul anicipaed by Caballero and Engel (2007). The persisence of rese price inflaion is now wihin sriking disance of he daa ( 0.31 model vs daa). And Figure 7 shows ha he model impulse response funcion for rese prices is much closer o he empirical paern. The selecion effec sressed by Golosov and Lucas means firs-responders acually overshoo he long run response afer selecion effecs have faded. Bu he persisence of acual inflaion is sill oo high (0.38 model vs daa for acual inflaion). The gap is even larger for sicky goods (0.53 model vs daa). Finally, he volailiy of rese price inflaion is oo high in his model relaive o he daa, wih variances more han double he acual ones for all goods and sicky goods. Sill, he discrepancies are noably smaller han for he TDP models. The reduced persisence and greaer volailiy of acual inflaion for he SDP model do no reflec imporan flucuaions in he frequency of price changes under he SDP model. The sandard deviaion of he frequency of price changes is very low for he SDP model, equaling abou 0.2 and 0.4 percenage poins, respecively, for flexible and sicky goods. Direcly relaed, he average rae of price increase condiional on changing,, provides lile informaion beyond ha in acual inflaion. For insance, for sicky goods under TDP he sandard deviaion of is exacly 10 imes he sandard deviaion of acual inflaion wih or wihou complemenariies. For he SDP models his raio remains very similar, equaling 9.4. Rese price inflaion, in conras, is much more volaile for he SDP model han under TDP, 23

26 making i a more discriminaing saisic. In paricular, for he TDP model wih sraegic complemens, he sandard deviaion of rese inflaion for sicky goods is only 4.6 imes is sandard deviaion for acual inflaion, whereas for he SDP model wihou complemenariies his raio is 8.0. Based on he CPI daa (Table 2), he observed raio is 7.6. In Table 9 we add sraegic complemenariies (inermediae share x 0.95 ) o produce a conrac muliplier of around four. Doing so makes rese inflaion much smooher, o he poin ha empirical rese price inflaion is almos four imes as volaile as rese price inflaion in he model. Model inflaion raes become more persisen as well, moving away from he daa (e.g., serial correlaion 0.24 in he model vs in he daa). Model inflaion becomes oo sable; for flexible goods he model variance is less han one-eighh is empirical counerpar. Perhaps mos problemaic, inflaion persisence is 0.73 in he model, abou 16 sandard errors from he empirical counerpars of In shor, a big conrac muliplier makes rese and acual inflaion raes way oo sable and persisen. Figure 8 plos he IRF for rese prices in he SDP model wih sraegic complemenariies. The rajecory is largely fla, in sharp conras o he plunging profiles in he SDP model wihou complemenariies (Figure 7) and in he daa (Figures 1-4). Because we can produce ime series for heoreical rese price inflaion in model economies, we can use is IRF o documen he impac of he selecion effec and sampling error on our esimaed rese price inflaion in he model. Figure 9 displays he response of he heoreical rese price in he SDP model wih complemenariies. Noe is upward sloping rajecory. Sraegic complemenariies mue he size of price changes for hose changing prices, as price seers wai for he average price o respond. Thus, heoreical rese price inflaion is small on impac bu accumulaes over ime as more firms change price. 24

27 Consruced rese price inflaion in Figure 8 differs sharply from heoreical rese price inflaion in Figure 9 in par because of a srong selecion effec (see Caballero and Engel, 2007, and Golosov and Lucas, 2007). The firms changing price in a given period are no an unbiased sample of he populaion, bu raher hose who mos benefi from a price change. The response of rese price inflaion is much greaer on impac because only firms in he ails of he disribuion change price. For example, in response o a posiive moneary shock, he average produciviy of he price changers is below he average produciviy of all firms, causing he measured rese price inflaion (which depends only on price changers) o be much higher han heoreical rese price inflaion. In he long-run, he response of hese wo measures is he same. As a resul he selecion effec also explains much of he greaer volailiy found in he SDP models relaive o he TDP models. Sampling error is anoher reason he IRF for measured rese price inflaion is flaer han ha for heoreical rese price inflaion. Our heoreical plo (Figure 9) is for he populaion (coninuum) of firms in he model economy, whereas Figure 8 is from simulaions wih a finie sample of firms o mimic he daa. Our idiosyncraic shocks (serial correlaion 0.7) are less persisen han our aggregae shocks, which follow a random walk. In finie samples he idiosyncraic shocks do no wash ou, imparing less persisence o rese price inflaion. 21 Below we presen resuls wih bi-monhly daa from all ciies, a much larger sample wih correspondingly lesser sampling error. 21 We believe our simulaions are more affeced by sampling error han is he acual daa. As menioned earlier, spli empirical samples wih half as many iems have only modesly higher variance of rese price inflaion han he whole sample. Spli simulaion samples, in conras, have much higher variance han he whole sample. Noe ha he models appear o undersae inflaion s rue volailiy. Therefore, he sampling error capured by he models, calibraed o correspond o he daa measures, will exer an exaggeraed impac on model saisics relaive o is impac on he acual daa. 25

28 A poenial explanaion for our negaive findings (oo persisen IRFs in models wih big conrac mulipliers) is ha we have negleced endogenous moneary policy, which can reduce persisence in he presence of permanen shocks. The lieraure has esimaed big conrac mulipliers over long periods (such as 1950 o 2000), bu he Fed may have reduced inflaion persisence and volailiy dramaically in he 20 years covered by our sample ( ). Auhors have documened regime changes in U.S. inflaion over he pas wo decades (e.g., Nason, 2006), as well as for many inflaion argeing counries (e.g., Benai, 2008). In his spiri, we simulae he SDP model wih complemenariies and a version of endogenous moneary policy. Specifically, we se m 0.6 (he response of money growh o lagged real money balances) in equaion (3.2) o mach he serial correlaion of nominal PCE growh ( 0.31) over our sample period. Here money growh offses movemens in he real money sock. As shown in Table 10 (summary saisics) and Figure 10 (univariae IRFs for flexible and sicky groups), his specificaion succeeds in driving down he persisence of rese price inflaion o levels observed in he daa (e.g., 0.43 in he model vs in he daa for all goods). Moreover, Figure 10 depics a model IRF for rese prices ha is spo on wih he empirical esimaes. The required endogenous moneary policy involves price level argeing raher han more convenional inflaion argeing. Gorodnichenko and Shapiro (2007) argue ha he Greenspan Fed did arge he price level. Sill, here are wo problems wih his endogenous moneary policy scenario. Firs, here is no longer a conrac muliplier above one. 22 Second and more problemaic, 22 This is wha one srucural VAR shows for he las weny years. We re-ran he srucural quarerly VAR of Alig e al. (2005) on our sample. The esimaed IRF o a moneary shock exhibis no conrac muliplier for oupu and a very ransiory inflaion response. Bu he poin esimaes are no a all precise given he shor sample. The 20 years afford only 33 degrees of freedom (dropping he firs 4 quarers o accommodae 4 lags of 11 variables), so we do no sysemaically explore srucural VARs wih many variables. 26

29 endogenous money growh saps inflaion of mos of is volailiy. Empirical rese price inflaion has six imes he variance in he endogenous money model, and empirical inflaion has hireen imes he variance in he model. The inuiion is his: if endogenous moneary policy undoes he impac of complemenariies on inflaion persisence, hen here is lile reason for rese and acual prices o respond. If prices are sicky, one will no wan o incorporae very ransiory shocks ino new prices. Thus we are lef wih he problem of reconciling a model wih srong complemenariies simulaneously wih he observed persisence and volailiy of empirical inflaion raes. This excess smoohness problem is even worse for he populaion of prices han for finie samples presened in Table 10. Sampling error dominaes he variances in finie simulaions, whereas i appears o accoun for a much smaller fracion of he empirical variances. Anoher robusness check we perform is o replace he aggregae moneary shock wih an aggregae produciviy shock. Indeed, Alig e al. (2005) argue ha shocks o aggregae produciviy are more imporan for inflaion movemens han are moneary policy shocks. Wih random walk aggregae produciviy, insead of random walk money, our resuls are virually idenical (e.g., for SDP wih complemenariies, wih or wihou endogenous money). Finally, one could argue ha we failed o enerain large, emporary secoral shocks ha do no wash ou in he aggregae. Boivin, Giannoni and Mihov (2009) provide evidence ha disaggregaed inflaion raes are much more volaile and ransiory han aggregae inflaion. Bu srong sraegic complemenariies make i hard o explain large responses o ransiory shocks, wheher hey be aggregae or secoral. And we calibraed our aggregae shocks o generae he observed variabiliy of nominal consumpion growh. Thus adding secoral shocks (or more aggregae shocks) o generae more realisic volailiy of rese price 27

30 inflaion may require unrealisically high volailiy of real consumpion growh and/or is covariance wih inflaion. We now recap some of our key findings. Figure 11 conains bar chars of daa momens vs. momens from finie sample simulaions of he SDP model wih srong complemenariies. The op panel conains serial correlaions, and he boom panel sandard deviaions. Wihou endogenous moneary policy ( SDP Comps ), he model seriously oversaes he persisence and undersaes he volailiy of rese and acual inflaion. Endogenous moneary policy ( SDP Endo M ) largely closes he persisence gaps, bu widens he volailiy gaps. In Figure 12 we provide he same model vs. daa saisics, only for much larger bimonhly samples. Recall ha we have roughly six imes he prices per bi-monh from all ciies as we have monhly prices per monh from he op hree ciies. (So his grealy reduces he impac of sampling error for boh he daa and model saisics.) The bi-monhly serial correlaions (op panel of Figure 12) are similar o hose in he monhly samples. Wihou endogenous moneary policy he SDP model wih srong complemenariies exhibis excessive persisence, wih endogenous moneary policy i does no. 23 Bu, again, endogenous moneary policy drains mos of he volailiy ou of boh rese and acual inflaion raes (boom panel of Figure 12). We are unable o reconcile srong complemenariies wih boh he ransiory and volaile behavior we observe in rese price inflaion. Alhough no shown, a model ha comes closes o fiing all he empirical momens in Table 2 is an SDP model wih endogenous moneary policy and an inermediae goods share 23 In he case of he SDP model wihou endogenous money, he serial correlaion of rese price inflaion rises (from monhly o bi-monhly) because sampling error is so diminished. 28

31 of only 1/3. This degree of complemenariies is no sufficien o produce a conrac muliplier above 1, however, even in he absence of endogenous moneary policy. 4. Conclusion A large empirical lieraure has esimaed ha moneary policy shocks affec real variables for several years, much longer han he duraion of nominal prices. A popular explanaion for his conrac muliplier combines sicky prices and sraegic complemenariies. The complemenariies make rese prices build slowly afer permanen shocks, prolonging he real effecs beyond he duraion of nominal prices. Tha is, sraegic complemenariies impar persisence o rese price inflaion. We do no see persisence in rese price inflaion using daa underlying he U.S. CPI from Temporary shocks (or endogenous moneary policy) migh explain he low persisence of rese price inflaion, bu a he expense of failing o generae as much volailiy as seen in rese price inflaion in he U.S. from Srong sraegic complemenariies severely dampen he volailiy of rese price inflaion when shocks are ransiory. In shor, we fail o find a model specificaion wih srong complemenariies ha fis boh he low persisence and nonrivial volailiy of observed rese price inflaion. This is rue wheher we enerain moneary or produciviy shocks, and even accouning for how sampling error and emporary sales affec he persisence and volailiy of rese price inflaion. Models of complemenariies no explored here migh be able o reconcile low persisence of rese price inflaion wih a high conrac muliplier. Bu our inuiion is ha oher complemenariies (e.g., sicky wages raher han sicky inermediaes) have similar predicions for he persisence of rese price inflaion. A more promising reconciliaion may 29

32 involve sicky informaion raher han sraegic complemenariies. The conrac muliplier migh be high in response o a subse of shocks abou which firms have sicky informaion. Meanwhile, he variance and persisence of rese price inflaion may be dominaed by shocks abou which firms have more flexible informaion. Mackowiak and Wiederhol (2008) presen a DSGE model in which his is precisely he case. 24 Alernaively, he conrac muliplier may no be so high afer all. Perhaps he high inflaion persisence over longer samples reflecs he persisence of moneary shocks raher han complemenariies. The low inflaion persisence of recen decades could be because he Fed sopped adding persisence, revealing low endogenous persisence. Our conclusions overlap wih hose of several recen sudies. Cogley and Sargen (2001), Primiceri (2006), and Cogley and Sbordone (2008) all argue ha U.S. inflaion persisence over long samples sems from changes in rend inflaion (i.e., moneary regime changes). They do no rely on a high conrac muliplier per se. Klenow and Willis (2006) and Kryvsov and Midrigan (2008) find i difficul o reconcile specific ypes of sraegic complemenariies wih, respecively, large idiosyncraic price changes and counercyclical invenories/sales. Gopinah, Iskhoki and Rigobon (2007) and Gopinah and Iskhoki (2008), in conras, see sraegic complemenariies behind he incomplee pass-hrough of exchange raes o impor prices. 24 Klenow and Willis (2007) find slow responses of individual price changes o he previous price changes of oher iems. This evidence is in line wih sicky informaion (more so han sraegic complemenariies). 30

33 Appendix This appendix provides a more deailed exposiion of he price-seing models and discusses he soluion mehod we used. A represenaive household has discouned uiliy U E C L where C is composie consumpion and L is labor supply. Composie consumpion is a CES aggregae of individual consumpion varieies ci (): (A1) 1 11/ C c() i di 1. 0 The household s budge consrain is PC B (1 r ) B W L P ( i) di where P is he nominal price of a uni of composie consumpion, W is he nominal wage, B denoes holdings of sae-coningen bonds (in zero ne supply) ha pay off in period a (gross) nominal ineres rae (1 r ), and ( i) are he (real) profis of firm i. 25 The household chooses bond holdings, labor supply, and consumpion of individual varieies o saisfy he following firs-order condiions: C P 1 E 1 r 1 C P 1 (A2) 1 31

34 (A3) W P LC (A4) c() i p() i. C P Turning o producion, here are a coninuum of monopolisically compeiive firms indexed by i, which denoes he one variey each produces. Firmi has produciviy Ai ( ) and combines labor Li ( ) and a composie inermediae good X ( i ) o produce good i : (A5) 1 x x () () () X() y i A i L i i where denoes he share of he composie inermediae good. The inermediae composie x is a CES aggregae of individual inermediae goods: (A6) / x 0 Xi () (, ij) dj where x( i, j) is he quaniy of inermediae good j used by firm i. Noe ha symmery beween (A6) and he consumpion aggregaor (A1) means ha he uni price of X is equal o P, he uni price of he consumpion composie. Firms are grouped ino one of wo secors, o be indexed by s, wih he main difference beween secors being how frequenly firms change price. A firm s produciviy is subjec o idiosyncraic shocks of he following form: 2 where () i iidn0, A, s. ln A () i ln A () i () i 1 25 The uni price of composie consumpion is he dual of consumpion aggregaor (A1): P p () i di 1 32

35 Firm i in secor s maximizes is discouned (real) profis E 0 0, () i 0 where C 0, is he sochasic discoun facor and curren profis are given by C0 (A7) p() i W W () i y() i L() i X() i k() i I() i. P P P A firm s profis equal revenue less inpu coss, including he cos of changing prices (he las erm). I ( i ) is an indicaor funcion for wheher firm i changes is price in period a a cos of k () i unis of labor. For he SDP models, we se k( i) k s. Tha is, in he SDP models he menu cos is fixed over ime for each firm, bu does vary across firms depending on he firm s secor. For he TDP models, k ( i) {0, }. Specifically, we mimic he Calvo model by having firms in secor s face a menu cos of 0 wih probabiliy s and a menu cos of wih probabiliy 1. These Calvo menu cos realizaions are independen boh across firms s wihin secors and over ime. Firm choices of inermediaes saisfy a firs-order condiion comparable o consumer choices of final consumpion varieies: (A8) x(, i j) p( j). X() i P Seing producion equal o oal demand (from consumers and ohers firms) for firm i yields 33

36 (A9) y () i c () i x ( j, i) dj C X 1 0 p () i P where 1 X X () idi. The aggregae resource consrains for oupu and labor are hen () 0 0 C X Y L L i k i I i di. 11/ (A10) y i di and () () () Finally, we assume a cash-in-advance consrain on a consumer s nominal spending PC M. In urn, we assume he money supply evolves as follows: M M ln M ln M P 1 1 m ln ln P 1 2 where N 0, m, and ln M P is seady-sae aggregae real demand. For seing up he firm s value funcion, i is useful o subsiue a few variables ou of he firm s profi funcion. This (along wih one assumpion described below) will allow us o express he firm s value as a funcion of only hree saes: p 1 ()/ i P, A(),and i M / P. Firs, we use firm cos-minimizaion o subsiue X ( i ) ou of profis (A7) using (A11) X WL () i X () i. 1 P X Second, we use he firm s producion funcion o subsiue L ( i) ou of profis: X X W L() i 1X X P y () i. A() i 34

37 We nex subsiue y ( i) ou of profis using he demand curve (A9) and aggregae resource consrain Y C X, and subsiue W / (real) profis are given by P ou of profis using labor supply (A3). Thus, (A12) 1 x p() i 1 LC Y p () () i P i Y k () () 1 x i I i LC. P x 1 A( i) x x We hen log-linearize he producion funcion (A5), labor supply (A3), resource consrains (A10), and equaion (A11) around he flexible-price seady sae o express Y and L ˆ as linear funcions of C ˆ, where ^ s denoe log deviaions from seady sae values. Specifically, Lˆ C X x Y Y Cˆ X 1x 1 Y where C, X and Y denoe seady sae values, and ˆ Y 1 Lˆ C. x x Finally, he cash-in-advance consrain implies C M / P. Thus, profis equaion (A12) can be expressed as a funcion of jus he hree sae variables p 1 ()/ i P, A(),and i M / P (In he Calvo case, he menu cos k ( i) is a fourh sae variable.). To wrie he firm s value funcion in erms of hese same hree sae variables, we mus make one more simplifying assumpion. The sae space of he firm s problem is acually infinie dimensional since he evoluion of he price level depends on he enire disribuion of all firms prices and produciviy levels. In he spiri of Krusell and Smih (1998), we assume ha firms perceive he evoluion of he price level as being a funcion of a 35

38 single momen of his disribuion. Specifically, P P M P 1 1 Nakamura and Seinsson (2008b) show ha his assumpion makes he model racable while sill providing highly accurae forecass of he price level. In he end, he firm s value funcion akes he recursive form. p 1() i M p() i M 1, A( i), max (), 1EV 1, A 1( i), P P p () i P 1 P 1 V i where, 1 is he sochasic discoun facor beween periods and 1. The model is hen solved using value funcion ieraion, wih he addiional requiremen ha he forecas rule be consisen wih he aggregaion of firm pricing decisions. 36

39 Table 1 Consrucing Rese Price Inflaion: A Simple Example Period 0 Period 1 Period 2 Price of Good A Inflaion for Good A 20% 0% Rese price for Good A Rese Inflaion for Good A 20% 0% Price of Good B Inflaion for Good B 0% 20% Rese price for Good B Rese Inflaion for Good B 20% 0% Inflaion ( ) 10% 10% Inflaion for changers ( ) 20% 20% Rese inflaion ( * ) 20% 0% Noe: The example assumes equal expendiure shares, equaling one half, for boh goods. I also assumes ha boh Good A and Good B exhibied a price change in period 0, esablishing he base price for calculaing rese price inflaion for period 1. The number 1.22 in he able represens exp(0.2) o wo decimal places. 37

40 Table 2 Summary Saisics for Rese and Acual Price Inflaion Saisic All Goods Flexible Goods Sicky Goods x Sandard deviaion of * 0.99% (0.05) Serial correlaion of * 0.47 (0.05) Sandard deviaion of 0.18% (0.01) Serial correlaion of 0.12 (0.06) 1.30% (0.06) 0.41 (0.05) 0.41% (0.02) 0.10 (0.06) 1.21% (0.06) 0.49 (0.06) 0.16% (0.01) 0.15 (0.08) Noes: All daa are from he CPI-RDB. Samples run from January 1989 hrough May The hreshold frequency of regular price changes is one-sixh per monh: quoe-lines in ELIs wih average frequency higher han one-sixh are in he flexible group, and hose wih lower frequency are in he sicky group. All series are monhly, are HP-filered wih smoohing parameer 1,000,000, and are seasonally adjused. Sandard errors are in parenheses. 38

41 Table 3 Summary Saisics Excluding Sale Prices Saisic All Goods Flexible Goods Sicky Goods x Sandard deviaion of * 0.95% (0.04) Serial correlaion of * 0.41 (0.05) Sandard deviaion of 0.14% (0.01) Serial correlaion of 0.05 (0.06) 1.38% (0.06) 0.42 (0.05) 0.39% (0.02) 0.05 (0.06) 1.13% (0.05) 0.40 (0.04) 0.10% (0.01) 0.09 (0.08) Noes: All daa are from he CPI-RDB. Samples run from January 1989 hrough May The hreshold frequency of regular price changes is one-sixh per monh: quoe-lines in ELIs wih average frequency higher han one-sixh are in he flexible group, and hose wih lower frequency are in he sicky group. All series are monhly, are HP-filered wih smoohing parameer 1,000,000, and are seasonally adjused. Sandard errors are in parenheses. 39

42 Table 4 Economy-Wide Model Parameers Parameer Baseline Sraegic Complemens Endogenous Moneary Policy Monhly Discoun Facor ( ) /12 Same Same Coefficien of Relaive Risk Aversion ( ) 1 Same Same Inverse of Frisch elasiciy of labor supply ( ) 0 Same Same Seady-sae Labor Supply ( L ) Same Same Elasiciy of demand ( ) 4 Same Same Inermediae Inpu Share ( x ) SDP TDP Persisence of Idio. Produciviy Shock ( ) 0.7 Same Same Mean Growh Rae of Money ( ) 0.2% Same Same S.D. of Innovaion o Money Growh ( ) 0.48% 0.48% 0.41% m Money Growh s reacion o M/P ( ) m Noes: Parameer values apply o boh he TDP and SDP models, unless oherwise noed. As shown in he ex, prices are sraegic complemens if 1 x 1. The arge seady sae labor supply is obained by varying he uiliy funcion parameer. The inermediae inpu share in he non-baseline cases is chosen o generae a conrac muliplier of 4. The parameers for he money growh process are chosen o mach he mean growh rae of inflaion, he sandard deviaion of nominal non-sheler PCE, and, for he endogenous moneary policy case, he serial correlaion of nominal PCE. 40

43 Table 5 Secor-Specific Model Parameers Parameer Baseline Sraegic Complemens Endogenous Moneary Policy Menu Coss (SDP Only) Flexible 0.168% Same Same Sicky 0.218% Same Same S.D. of Idiosyncraic Produciviy Shocks Flexible ( Af, ) 4.93% 4.94% 4.94% Sicky ( As, ) 4.70% 4.75% 4.75% Probabiliy of Zero Menu Cos (TDP Only) Flexible ( ) Same - f Sicky ( ) Same - s Secor Weighs Flexible Same Same Sicky Same Same skw s SS Noes: Expended menu coss are evaluaed a he seady sae wage and scaled by seady sae revenue,. PY SS SS Alhough he expended menu coss are similar across secors, he labor cos ( k s ) of changing prices is acually more han four imes greaer in he sicky secor because he frequency of price change ( s) is 3/10 as large in he sicky secor. The labor cos of changing prices also varies grealy across he model specificaions. One can show expended menu coss are proporional o sks(1 x), so specificaions wih higher inermediae inpu shares have larger labor coss of changing prices. 41

44 Table 6 Summary Saisics on Rese and Acual Price Inflaion TDP Model (no sraegic complemenariies) Saisic All Goods Flexible Goods Sicky Goods x Sandard deviaion of * 0.49% (0.03) Serial correlaion of * 0.04 (0.07) Sandard deviaion of 0.12% (0.01) Serial correlaion of 0.73 (0.05) 0.51% (0.03) 0.07 (0.07) 0.21% (0.02) 0.60 (0.05) 0.49% (0.03) 0.04 (0.07) 0.10% (0.01) 0.84 (0.04) Noes: Saisics are averages across 100 model simulaions, each of 233 periods. Sandard deviaions across simulaions are in parenheses. Each simulaion consiss of 3,100 firms in he flexible secor and 8,300 firms in he sicky secor. 42

45 Table 7 Summary Saisics on Rese and Acual Price Inflaion TDP Model (sraegic complemenariies) Saisic All Goods Flexible Goods Sicky Goods x Sandard deviaion of * 0.29% (0.02) Serial correlaion of * 0.02 (0.07) Sandard deviaion of 0.08% (0.01) Serial correlaion of 0.80 (0.05) 0.28% (0.01) 0.12 (0.07) 0.12% (0.01) 0.62 (0.06) 0.32% (0.02) 0.04 (0.07) 0.07% (0.01) 0.87 (0.04) Noes: Saisics are averages across 100 model simulaions, each of 233 periods. Sandard deviaions across simulaions are in parenheses. Each simulaion consiss of 3,100 firms in he flexible secor and 8,300 firms in he sicky secor. 43

46 Table 8 Summary Saisics on Rese and Acual Price Inflaion SDP Model (no sraegic complemenariies) Saisic All Goods Flexible Goods Sicky Goods x Sandard deviaion of * 1.79% (0.08) Serial correlaion of * 0.31 (0.06) Sandard deviaion of 0.28% (0.02) Serial correlaion of 0.38 (0.07) 1.34% (0.07) 0.38 (0.06) 0.40% (0.02) 0.16 (0.07) 2.01% (0.10) 0.29 (0.06) 0.25% (0.02) 0.53 (0.06) Noes: Saisics are averages across 100 model simulaions, each of 233 periods. Sandard deviaions across simulaions are in parenheses. Each simulaion consiss of 3,100 firms in he flexible secor and 8,300 firms in he sicky secor. 44

47 Table 9 Summary Saisics on Rese and Acual Price Inflaion SDP Model (sraegic complemenariies) Saisic All Goods Flexible Goods Sicky Goods x Sandard deviaion of * 0.52% (0.02) Serial correlaion of * 0.24 (0.06) Sandard deviaion of 0.11% (0.01) Serial correlaion of 0.73 (0.05) 0.40% (0.02) 0.34 (0.05) 0.14% (0.01) 0.43 (0.08) 0.67% (0.03) 0.27 (0.06) 0.11% (0.01) 0.76 (0.05) Noes: Saisics are averages across 100 model simulaions, each of 233 periods. Sandard deviaions across simulaions are in parenheses. Each simulaion consiss of 3,100 firms in he flexible secor and 8,300 firms in he sicky secor. 45

48 Table 10 Summary Saisics on Rese and Acual Price Inflaion SDP Model (endogenous moneary policy) Saisic All Goods Flexible Goods Sicky Goods x Sandard deviaion of * 0.41% (0.02) Serial correlaion of * 0.43 (0.05) Sandard deviaion of 0.05% (0.002) Serial correlaion of 0.12 (0.06) 0.37% (0.02) 0.46 (0.05) 0.10% (0.004) 0.04 (0.06) 0.53% (0.03) 0.45 (0.04) 0.04% (0.002) 0.17 (0.07) Noes: Saisics are averages across 100 model simulaions, each of 233 periods. Sandard deviaions across simulaions are in parenheses. Each simulaion consiss of 3,100 firms in he flexible secor and 8,300 firms in he sicky secor. 46

49 Figure 1 Empirical Impulse Response of Rese Prices, All Goods Figure 2 Empirical Impulse Response of Rese Prices, All Goods, Excluding Sale Prices Noes for Figures 1 and 2: Dashed lines denoe 95% confidence inerval. Esimaes reflec accumulaed responses o a univariae VAR for rese price inflaion wih 6 monhly lags. 47

50 Figure 3 Empirical Impulse Response of Rese Prices, Flexible Goods Figure 4 Empirical Impulse Response of Rese Prices, Sicky Goods Noes for Figures 3 and 4: Dashed lines denoe 95% confidence inerval. Esimaes reflec accumulaed responses o a univariae VAR for rese price inflaion wih 6 monhly lags. 48

51 Figure 5 Impulse Response of Rese Prices, All Goods (TDP Model, No Sraegic Complemenariies) Figure 6 Impulse Response of Rese Prices, All Goods (TDP Model, Sraegic Complemenariies) Noes for Figures 5 and 6: Dashed lines denoe 95% confidence inerval. Esimaes reflec accumulaed responses o a univariae VAR for rese price inflaion wih 6 monhly lags. Shaded area denoes he 95% confidence inerval for esimaes based on CPI-RDB daa. 49

52 Figure 7 Impulse Response of Rese Prices, All Goods (SDP Model, no Sraegic Complemenariies) Figure 8 Impulse Response of Rese Prices, All Goods (SDP Model wih Sraegic Complemenariies) Noes for Figures 7 and 8: Dashed lines denoe 95% confidence inerval. Esimaes reflec accumulaed responses o a univariae VAR for rese price inflaion wih 6 monhly lags. Shaded area denoes he 95% confidence inerval for esimaes based on CPI-RDB daa. 50