The Micro-Macro Disconnect of Purchasing Power Parity

Transcription

1 The Micro-Macro Disconnec of Purchasing Power Pariy Paul R. Bergin Universiy of California a Davis and NBER Reuven Glic Federal Reserve Ban of San Francisco Jyh-Lin Wu Naional Sun Ya-Sen Universiy This draf: Ocober 11, 2011 Absrac: This paper reconciles he persisence of aggregae real exchange raes wih he faser adjusmen of inernaional relaive prices in microeconomic daa. Panel esimaion of an error correcion model using a micro daa se uncovers new sylized facs regarding his puzzle. Firs, adjusmen o purchasing power pariy deviaions in aggregaed daa is no jus a slower version of adjusmen o he law of one price in microeconomic daa, as arbirage occurs in differen mares, in response o disinc macroeconomic and microeconomic shocs. Second, when half-lives are esimaed condiional on macro shocs, micro relaive prices exhibi jus as much persisence as aggregae real exchange raes. These resuls challenge heories of real exchange rae persisence based on sicy prices and on heerogeneiy across goods, and suppor an explanaion based on he presence of disinc macro and microeconomic shocs. JEL classificaion: F0, F15, F31 We han Andrew Cohn and Alec Kennedy for research assisance and Oscar Jorda for commens. The views expressed below do no represen hose of he Federal Reserve Ban of San Francisco or he Board of Governors of he Federal Reserve Sysem. P. Bergin / Deparmen of Economics / Universiy of California a Davis/ One Shields Ave. / Davis, CA USA prbergin@ucdavis.edu, fax (530) R. Glic / Economic Research Deparmen / Federal Reserve Ban of San Francisco / 101 Mare Sree, San Francisco, CA USA reuven.glic@sf.frb.org, ph (415) , fax (415) Jyh-Lin Wu /Insiue of Economics / Naional Sun Ya-Sen Universiy / 70 Lien-hai Rd. / Kaohsiung, Taiwan 804 ecdjlw@ccu.edu.w, ph (07) ex. 5616, fax (07)

2 I. Inroducion The persisence of aggregae real exchange raes as hey converge bac o a form of purchasing power pariy is a longsanding puzzle. This is especially so, since research using microeconomic daa ses has demonsraed ha convergence o he law of one price by disaggregaed inernaional relaive prices occurs a a much faser rae. Wor by Imbs e al. (2005) has documened his puzzle, as well as proposed one explanaion in which heerogeneiy in he convergence speeds among goods can produce an aggregaion bias. This paper presens addiional new sylized facs regarding he adjusmen of aggregae real exchange raes and micro prices, and we argue ha any explanaion for he greaer persisence of real exchange rae movemens should be consisen wih hese addiional facs. Our new evidence comes from esimaing panel vecor error correcion models joinly on macrolevel and micro-level price daa drawn from he Economis Inelligence Uni s Worldwide Cos of Living Survey. This approach enables us o decompose he real exchange rae adjusmen mechanism ino a nominal exchange rae componen and a local currency price componen as well as o idenify disinc macro and micro shocs. We argue ha he inconsisency beween sudies of aggregae real exchange raes and sudies of micro prices can be reconciled if one properly condiions on he disinc ypes of shocs driving he aggregaed and disaggregaed daa. The firs new sylized fac of he paper is ha adjusmen o he law of one price in he micro daa is no jus a faser version of he same adjusmen process o purchasing power pariy for aggregae daa, bu insead wors hrough a qualiaively disinc adjusmen mechanism. The heory of purchasing power pariy is ambiguous as o wheher pariy is achieved hrough arbirage in he goods mare inducing goods prices o adjus, or hrough forces in he foreign exchange mare inducing he nominal exchange rae o adjus. For aggregae daa, a number of papers applying ime-series analysis o aggregae real exchange raes have found ha mos of he adjusmen aes place hrough he nominal exchange rae. 1 Bu if one wishes o invesigae he role of arbirage in he goods mare, one should use price daa on individual goods, where he arbirage beween home and foreign varieies of a good primarily plays ou. Accordingly, a vecor error correcion model is esimaed for each good, as well as for an aggregae price index 1 See Fisher and Par (1991) who employ coinegraion analysis, Engel and Morley (2001) who use a sae-space analysis, and Cheung, Lai and Bergman (2004) who use vecor error-correcion analysis. 1

3 consruced over he goods in he sample. We find ha in disaggregaed daa, local goods prices acively adjus o resore he law of one price. However, when he micro-level daa are aggregaed ino a synheic represenaion of an aggregae real exchange rae, all adjusmen o resore PPP aes place hrough nominal exchange raes, no hrough local goods prices. The qualiaively disinc channels of adjusmen in disaggregaed and aggregaed daa can be aribued o disinc microeconomic and macroeconomic shocs driving price deviaions. These shocs can be idenified in he conex of a vecor error correcion model nesing ogeher aggregaed and disaggregaed daa and equaions in a single sysem. Variance decomposiions indicae ha he idiosyncraic goods shocs are volaile, and he responses o hem dominae he aggregae shocs in he disaggregaed daa. Bu he idiosyncraic shocs cancel ou upon aggregaion, since some shocs o price differenials are posiive while ohers are negaive. So he responses o exchange rae shocs dominae in he aggregaed daa. The second sylized fac of he paper is ha when half-lives are esimaed in his sysem condiional on macroeconomic shocs, microeconomic prices are found o be jus as persisen as aggregae real exchange raes. In conras wih he impression given by recen sudies on microeconomic price dynamics, here is acually significan persisence conained wihin micro price daa. We conclude ha properly condiioning on shocs can resolve he inconsisency beween aggregae real exchange rae sudies and micro price sudies. This resul also implies ha convenional esimaes of he speed of adjusmen ha do no allow for he disinc responses o micro and macro shocs are subjec o an omied variable bias: he single esimaed half-life is a conflaion of hose specific o micro and macro shocs, wih ha of he more volaile shoc dominaing. The finding ha proper esimaes of persisence require condiioning on he underlying shocs cauions agains an explanaion for he persisence puzzle relying primarily upon aggregaion bias arising from heerogeneiy among goods. In paricular, a significan porion of he overall heerogeneiy in adjusmen speeds among goods is found here o be associaed wih heir response o macroeconomic shocs raher han o idiosyncraic goods shocs. Because macroeconomic shocs are common o goods, aggregaion over heerogeneous response coefficiens o macroeconomic shocs does no inroduce aggregaion bias. Aggregaion bias applies only o he responses o idiosyncraic shocs. So a significan porion of he 2

4 heerogeneiy deeced in pas sudies may be of an innocuous ype when i comes o aggregaion bias. Anoher implicaion of his finding regards he usefulness of sicy price models o explain real exchange rae behavior. A convenional undersanding in his heoreical lieraure is ha PPP deviaions gradually decline as firms are able o rese prices in response o he macroeconomic shocs ha creaed he PPP deviaion. Bu our error correcion resuls show ha prices respond quie quicly o deviaions from he law of one price, and our sudy of he resuling impulse responses show ha price adjusmen accouns for a large share of correcions o hese deviaions. One model ha perhaps could coincide beer wih he evidence would be a raional inaenion sory, where firms adjus more o shocs specific o heir indusry raher han o common macroeconomic shocs. For example, Macowia and Wiederhol (2009) show in a closed-economy raional inaenion model, when idiosyncraic condiions are more variable or have larger impacs on a firm s profis and he firm has limied resources o process informaion abou shocs, i is opimal for firms o allocae more aenion o rac and respond o idiosyncraic condiions han o aggregae condiions. Carvalho and Nechio (forhcoming) presen a heoreical model where aggregaion over many goods wih heerogeneous price siciness generaes an aggregae real exchange rae ha is persisen. While his heory is a powerful explanaion consisen wih he empirical regulariy of greaer persisence in he aggregae daa, i is inconsisen wih he addiional new facs uncovered in our empirical analysis. Firs, heir heory implies ha he qualiaive mechanism of adjusmen is he same in he aggregaed and disaggregaed secoral daa, woring hrough goods prices; in conras, our empirical evidence shows ha aggregae adjusmen is qualiaively differen, woring hrough he nominal exchange rae raher han prices. Secondly, heir heory includes only aggregae shocs, so is explanaion implies ha micro secoral prices adjus quicly condiional on macro shocs. In conras, our evidence shows ha he persisence of price gaps in micro daa is jus as high as in aggregaed daa when condiional on macro shocs. We conclude ha heir explanaion for persisence canno be he whole sory, and ha our evidence calls for a differen ype of explanaion rooed in he parallel roles of micro and macro shocs. Our wor is relaed o recen research by Crucini and Shinani (2008), who also use EIU price daa o sudy law-of-one-price dynamics. Our paper differs in ha i decomposes deviaions 3

5 and adjusmen by he ype of shoc and sudies he mechanism of adjusmen via local goods prices and he nominal exchange rae wih an error correcion mechanism. Andrade and Zachariadis (2010) also decompose micro price dynamics by shoc, bu heir focus is on he disincion beween geographically global versus local shocs raher han he macro versus micro shocs we find o be imporan. Furher, hey resric heir focus o microeconomic prices, raher han drawing implicaions for aggregae real exchange raes as we do. Our findings are also complemenary o Broda and Weinsein (2008), who speculae ha nonlinear convergence raes lead o faser adjusmen among disaggregaed price deviaions because hey are dominaed by large ouliers. Our findings sugges an alernaive mechanism, based no on ouliers, bu on he disincion beween idiosyncraic indusry shocs and macroeconomic shocs. The nex secion discusses he daa se and daa characerisics, including saionariy and speeds of convergence. Secion 3 presens he main resuls in several subsecions. The firs compares error correcion dynamics esimaed separaely for disaggregaed and aggregaed daa, wih he second par providing robusness checs. The hird subsecion esimaes a combined error correcion model nesing ogeher aggregaed and disaggregaed daa, and uses his o idenify he separae roles of aggregae and idiosyncraic shocs. The las subsecion revisis he auoregressive esimaion of he pas lieraure while aing differen shocs ino consideraion, and discusses he diminished role of aggregaion bias in his conex. Secion 4 summarizes implicaions for he broader lieraure on real exchange raes. II. Daa and Preliminary Analysis II.A Daase The daa are obained from he Worldwide Cos of Living Survey conduced by he Economis Inelligence Uni (EIU), a proprieary service which records local prices for individual goods and services in ciies worldwide. 2 The EIU daa begin in 1990, and while hisorical daa are available o subscribers a an annual frequency, daa collecion acually aes place wice annually. To faciliae analysis of he ime-series dynamics of he panel, we were 2 The EIU survey is used o calculae cos-of-living indexes for mulinaional corporaions wih employees locaed around he world. The daa se is described in more deail a hp://eiu.enumerae.com/asp/wcol_helpaboueiu. 4

6 able o obain from he EIU semi-annual hisorical observaions hrough 2007 on a one-ime basis. 3 There are disinc advanages of he EIU daa ha mae i appealing for our ime-series sudy. I is he mos exensive survey of reail prices conduced by a single organizaion on a global scale ha is ongoing over a long period. Mos exising micro-price surveys are oo infrequen o be useable for addressing ime series issues, whereas he EIU daa se has a sufficien lengh o mae possible applicaion of our ime series echniques. Anoher advanage of he EIU daa se is ha goods caegories are narrowly defined, e.g. apples (1 g), men s raincoa (Burberry ype), and ligh bulbs (2, 60 wa). For many goods in he survey, prices are sampled separaely from wo differen oules, a high-price and low-price oule. For example, food and beverage prices are sampled from supermares and convenience sores. We use prices from he supermare ype oules, which are liely o be more comparable across ciies. The daa se also includes many service iems such as elephone and line, moderae hoel (single room), and man s haircu, which would mos naurally be classified as non-radable. The degree of comparabiliy across locaions is generally high, bu varies wih he general availabiliy of goods in a given ciy. Our sample focuses on he major ciy in each of 20 indusrial counries, where availabiliy migh be expeced o be more consisen. Surveyors visi only oules where iems of inernaionally comparable qualiy are available. The EIU explicily has held he aim from he beginning of is survey of mainaining ongoing consisency of is surveys across ime. I has wored o eep he same sores and he same brands and sizes in obaining he price for each iem. Given ha he survey aes place simulaneously in 140 ciies worldwide over a wo decade period, here may be subsiuions or changes in he daa sample. This may occur for example if a change in managemen leads o a corresponden being refused enrance o a sore. I may occur as cerain brands or sizes replace ohers in sores. See he daa appendix of Andrade and Zachariadis (2011) for a deailed discussion of he survey mehods employed by he EIU. Documenaion from he EIU websie noes ha here can be significan variaion in prices from one survey o he nex. Mos of he reasons cied by he EIU for his variaion correspond o economic facors of he ype we model in his paper, such as exchange rae flucuaions affecing he price of impored goods, or he fac ha some counries have periods of 3 The semi-annual observaions made available o us do no exend beyond

7 high aggregae inflaion. Oher facors reflec economic shocs specific o an indusry of he ype we ry o model, such as increased compeiion from new enrans in he mare, or local shorages of supply of a good. However, a few of he reasons provided include difficulies in mainaining consisency in an ongoing survey if goods are no consisenly available, as noed in he preceding paragraphs. The EIU noes ha daa availabiliy is more serious for emerging mares, especially in Chinese ciies. Because our sample uses only 20 indusrialized counries, i is hoped ha his sampling issue will be less severe for our case. Furher, we chec for his problem wih ess of measuremen error laer in he paper. We also confirm laer in he paper ha our resuls are robus o use of an alernaive daa sample of ha from Imbs e al (2005). We focus on bilaeral prices beween he major ciy in each of 20 indusrial counries relaive o he Unied Saes. The choice of counries reflecs hose used in pas wor on price aggregaes (such as in Mar and Sul (2008)), and he choice of ciies reflecs ha in Parsley and Wei (2002). 4 For hese locaions, he daa se has full coverage for 98 radable goods and 30 nonraded goods, as idenified by Engel and Rogers (2004) in heir sudy of price dispersion in Europe. 5 Daa Appendix Tables A1, A2 and A3 lis he ciies and goods included in he analysis. II.B. Preliminaries Define qij, as he relaive price of good beween wo locaions i and j, in period, in logs. This may be compued as qij, eij, pij,, where eij, is he nominal exchange rae (currency j per currency i), and pij, pi, pj, is he log difference in he price of good in counry i from ha in counry j, boh in unis of he local currency. As preparaion for he main analysis laer, we firs esablish ha he inernaional relaive prices are saionary. We apply he crosssecionally augmened Dicey-Fuller (CADF) es provided by Pesaran (2007) o examine he 4 Mar and Sul (2008) use he Eurosa daa from Imbs e al. (2005) for 19 goods in 10 European counries and he U.S.; we augmen he daa wih more indusrial counries o increase he power wih which o rejec uni roos in panel esimaion. We show below ha our resuls are robus o using Eurosa, raher han EIU, daa. 5 Engel and Rogers (2004) included only goods for which a price is recorded in every year for a leas 15 of he 18 European ciies in heir analysis. The daase used by Parsley and Wei (2002) conains 95 raded goods. Their se is virually idenical o ha of Engel and Rogers (2004), wih he difference ha Parsley and Wei include yogur, cigarees (local brand), cigarees (Marlboro), ennis balls, and fas food snacs, bu exclude buer, veal chops, veal fille, veal roas, women s raincoa, girl s dress, compac disc, color elevision, inernaional weely newsmagazine, paperbac novel, and elecric oaser. 6

8 saionariy of variables. The advanage of his es is ha i conrols for conemporaneous correlaions across residuals. Consider he following regression: q a b ( q ) c ( q ) d ( q ) ij, ij ij ij, 1 ij 1 ij ij, ij 1,..., N, 1,..., K, and 1,..., T (1) N where q qij, is he cross-secion mean of qij, across counry pairs and q q q 1. ij1 The purpose for augmening he cross-secion mean in he above equaion is o conrol for conemporaneous correlaion among ij,. The null hypohesis of he es can be expressed as H0 : b 0 for all ij agains he alernaive hypohesis H1 : b 0 for some ij. The es saisic ij provided by Pesaran (2007) is given by: where ( N, T ) is he saisic of ij (, ) N 1 ij (, ) ij1 CIPS N T N N T ij b ij in equaion (1). (CIPS sands for he cross-secionally augmened Im, Pesaran, and Shin saisic.) The op panel of Table 1 indicaes rejecion of nonsaionariy a he 5% significance level for he large majoriy of raded goods, 72 a 10%, 63 a 5%, ou of 98 raded goods in he sample. Among nonraded goods, rejecion a he 5% level is suppored for 11 a boh 5% and 10% ou of he 30 goods-- less srong han for radeds. In addiion o sudying he behavior of he individual goods prices, we can also sudy aggregae prices, consruced as a simple average K over he goods: qij, qij,. This consruced aggregae provides a useful comparison o he 1 large body of pas sudies of persisence in real exchange raes. 6 The boom panel of Table 1 shows ha nonsaionariy can be rejeced a he 1% level for he average over all raded goods. For an average over jus nonraded goods, nonsaionariy canno be rejeced. In he remainder of he paper, we will focus on he se of raded goods, for which here is sronger evidence of saionariy. 6 In principle, we could also assign weighs o he goods derived loosely from weighs in a counry s CPI. However, Crucini and Shinani (2008) find ha alernaive weighing schemes do no affec resuls for his es. 7

9 Nex, we chec he speed of convergence oward saionariy by esimaing a secondorder auoregressive model of real exchange raes wih panel daa. 7 To conrol for conemporaneous correlaion of residuals, we apply he common correlaed effecs (CCE) regressor of Pesaran (2006) o esimae he auoregressive coefficiens of real exchange raes. In oher words, we esimae he equaion: for disaggregaed daa and 2 ij, ij ij, m ij, m ij, m1 q c ( q ) for 1,..., K (2) 2 q c ( q ). (3) ij, ij ij, m ij, m ij, m1 for aggregaed daa, each augmened wih cross-secion means of righ and lef hand side variables. Two differen CCE esimaors are proposed by Pesaran (2006). One is he mean group esimaor, CCEMG, and he oher is he sandard pooled version of he CCE esimaor, CCEP. Pesaran s (2006) Mone Carlo simulaion resuls show ha, under he assumpion of slope heerogeneiy, CCEP and CCEMG have he correc size even for samples as small as N = 30 and T = 20. Pesaran concludes ha CCEP does slighly beer in small samples, so we adop he CCEP esimaor in our empirical analysis. Boh mehods deliver broadly similar resuls here. CCEP esimaes are obained by regressing equaions (2) and (3) wih augmened regressors q, q, q ) and ( q, q 1, q 2), respecively. 8 ( 1 2 Resuls in Table 2 indicae quic convergence speeds for disaggregaed goods, wih an average half-life among he goods of 1.25 years. Half-lives are compued on he basis of simulaed impulse responses 9. Adjusmen for he aggregae daa is disincly slower, wih a halflife of 2.10 years. While his half-life esimaed for aggregae prices is lower han he values ofen found in previous lieraure for more sandard aggregae daa ses, i noneheless does reproduce he finding ha he aggregae half-life is longer han ha for microeconomic daa Inclusion of addiional lags is precluded by he shor ime-span of he daa se. 8 STATA code creaed by he auhors o conduc CCEP esimaions used hroughou he paper are available upon reques. 9 The half-life is compued as he ime i aes for he impulse responses o a uni shoc o equal 0.5, as defined in Seinsson (2008). We idenify he firs period, 1, where he impulse response f() falls from a value above 0.5 o a value below 0.5 in he subsequen period, We inerpolae he fracion of a period afer 1 where he impulse response funcion reaches a value of 0.5 by adding (f( 1 ) - 0.5))/ (f( 1 ) - f( 1 +1)). 10 Previous lieraure has ended o find even larger half-lives in aggregaed daa, commonly exceeding 3 years. The somewha smaller half-life in our aggregaed daa is he direc resul of he paricular sample period, saring in 8

10 Since he second order auoregressive coefficiens are no saisically significan, we also esimae a firs-order auoregression, wih resuls in he able. The conclusion is similar, wih he half-life abou double in aggregaed daa compared o he average among disaggregaed daa, 2.13 years compared o The fac ha half-lives a he disaggregaed level are faser han for aggregaes maches he finding of Imbs e al. (2005) wih heir daa se. They hypohesize an explanaion, based on he idea ha speeds of adjusmen are heerogeneous among goods, and ha aggregaion ends o give oo much weigh o goods wih slow speeds of adjusmen and hence long half-lives. The implicaions of our daa for his hypohesis will be discussed a greaer lengh in he following secion. III. Resuls III.A. Benchmar Esimaes and he Error Correcion Puzzle This secion invesigaes he engine of convergence o he law of one price and idenifies a new sylized fac. The saionariy of micro real exchange raes implies he coinegraion of nominal exchange raes ( e ij, ) and relaive prices ( p, ) wih he coinegraing vecor being (1, 1). The adjusmen process of nominal exchange raes and relaive prices can be sudied using he following panel error-correcion model (ECM): e, ij, ije, eij, ij, 1 eij, ij, 1 eij, ij, 1 ij, ij e ( q ) ( e ) ( p ) (4a) p ( q ) ( e ) ( p ). 11 p, ij, ij, p pij, ij, 1 pij, ij, 1 pij, ij, 1 ij, This wo- equaion sysem decomposes he good-specific real exchange rae, q,, ino is wo componens, he nominal exchange rae, e ij, and he relaive price level, p ij. I regresses he firs difference of each of hese componens on he lag level of he good-specific real exchange rae, which summarizes he degree o which he law of one price is being violaed in he daa. Oher ij 1990, and he broader se of counries, 20 indusrial. When we compue sandard CPI-based real exchange raes using he sandard macroeconomic daa from he IMF s Inernaional Financial Saisics for our sample of counries and years, he half-life is esimaed a 2.05 years, very close o ha of he synheic aggregae consruced over our se of goods repored above. Exending he sample bac o 1975, resuls in a half -life esimae of So he aggregae half-life familiar from pas real exchange rae sudies is specific o he pos-breon Woods daa sample ypical in hese sudies, and he relevan half-life is somewha lower when he sample is limied o a more recen sample, as is necessary o compare o our micro daa. 11 Because his error correcion model incorporaes lags of firs differences o capure shor-run dynamics, his specificaion is analogous o he second-order auoregression esimaed previously. Inclusion of addiional lags is impossible due o he shor ime-span of he daa se. 9

11 regressors in (4a) conrol for level effecs and shor run dynamics of he variables. The coefficiens and pij, reflec how srongly he exchange rae and prices respond o e,ij deviaions from he law of one price. Because negaive movemens in hese variables wor o reduce deviaions from he law of one price, hey provide a measure of he speed of adjusmen of nominal exchange raes and relaive prices, respecively. To allow for possible cross secion dependence in he errors, we compued CCEP esimaors of he parameers by including as regressors he cross secion averages of all variables (( e, q 1, e 1, and p 1) and ( p, q 1, e 1, and p 1) for he e ij, and p ij, equaions, respecively). This pair of ECM equaions is esimaed for our panel of ciy pairs, for each of he 98 raded goods. We also esimae he following aggregae version of he wo equaion sysem, where he good-specific relaive price for good, p, is replaced by he average across all goods, p: e ( q ) ( e ) ( p ) (4b) e ij, ije, eij, ij, 1 eij, ij, 1 eij, ij, 1 ij, p ( q ) ( e ) ( p ). p ij, ij, p pij, ij, 1 pij, ij, 1 pij, ij, 1 ij, As a basis of comparison wih pas research, consider firs he consruced aggregae prices. Fisher and Par (1991) found for aggregae CPI-based real exchange raes ha he speed of adjusmen is significan for exchange rae and insignificanly differen from zero for price, concluding ha adjusmen aes place primarily hrough he exchange rae. Our mehod of esimaing he error correcion mechanism differs from heirs, pooling across counries wih panel daa for each equaion in (4), bu our conclusion for aggregae daa agrees wih heirs. As repored in panel a of Table 3, he speed of adjusmen for price, p, is jus 0.04, while ha for he exchange rae, e, is much larger a The resul is enirely differen a he disaggregaed goods level. Now we esimae he error correcion regression (4) as a panel over ciy pairs, once for each of he raded goods in he sample. Table A4 in he daa appendix shows resuls for each good separaely, and Table 3 summarizes by reporing mean values over all goods. The role of he wo variables is reversed 12 Due o our panel mehodology, boh coefficiens are saisically significan, so we canno conclude ha he price coefficien equals zero as found in pas wor. Bu he much larger coefficien (in absolue value) in he exchange rae equaion indicaes ha he exchange rae responds much more srongly han does price. Because he wo equaions in (4) are esimaed individually, we do no have he join disribuion of response coefficiens needed o conduc a formal F es. 10

12 from ha wih he aggregae daa: he mean speed of adjusmen for he price raio,, is large, 0.20, while ha for he exchange rae, e, is much smaller, Judging by speeds of adjusmen, he dynamic adjusmen appears o be very differen a he disaggregaed level han a he aggregaed level. While a he aggregae level i is nominal exchange rae movemens ha faciliae dynamic adjusmen o resore PPP, a he disaggregaed level i is movemens in he price in he goods mare ha does he adjusmen. I probably should no be surprising ha he nominal exchange rae canno serve he funcion of adjusmen for individual goods, given Crucini e al. (2005) has showed ha for European counry pairs here are many goods overpriced as well as underpriced. The same appears o be rue for our counry pairs. Given ha adjusmen requires movemens in opposie direcions for hese wo groups of goods, here is no way ha he exchange rae componen of hese relaive prices can mae hem move in he necessary direcions simulaneously. However, wha is surprising is ha goods prices do faciliae adjusmen a he goods level, and in fac adjusmen is faser han for aggregae prices ha have he exchange rae o move hem. p III.B. Robusness Checs In a dynamic panel model wih cross-secional dependence, convenional esimaors, such as fixed effec esimaors, generalized mehod of momen esimaors, insrumenal-variable esimaors, and CCEP esimaors are inconsisen for finie T even as N becomes infinie, bu hey are consisen when boh T and N become infinie (Philips and Sul, 2007; Sarafidis and Roberson, 2009; Grooe and Everaer, 2011). The Technical Appendix provides a deailed Mone Carlo sudy showing his conclusion applies also o a panel VECM specificaion. Two main findings are as follows. Firs, he mean biases of he esimaed responses o he error correcion erm, he parameers of mos ineres o us, are posiive, indicaing ha he CCEP esimaes end o be biased upward, implying hey oversae he rue speed of adjusmen (in absolue value). Second, an increase in N, for a given T, has only limied effec on mean bias bu i decreases he sandard deviaion and roo mean squared error of esimaes. However, an increase in T for a given N decreases he magniude of he bias as well as ha of he oher abovemenioned saisics. In addiion, we also conduc an experimen wih simulaed daa ha closely resembles our acual daa se. Daa were generaed using he coefficien esimaes ogeher wih he residuals 11

13 from he CCEP esimaion of he wo-equaion sysem (4b) for aggregaed daa, including allowing for heerogeneous error correcion adjusmen coefficiens. In each of 1000 replicaions, a sequence of innovaions for 20 counry pairs covering 34 periods was drawn from he residuals of he exchange rae and price equaions, and hese were used o generae simulaed series for price and exchange rae (as well as real exchange rae), using acual observaions as saring values. The generaed daa were hen used o esimae he model by CCEP. Resuls in Table 4 indicae ha CCEP ends o oversae he rue speed of adjusmen parameer (in absolue value), bu i is somewha smaller han in he Mone Carlo sudy described above. To show ha our resuls are robus o conrolling for poenial bias in our esimaes, we will employ he sandard double boosrap procedure of Kilian (1998) wih 1000 replicaions o obain he bias-adjused esimaes. Resuls for he VECM sysem are repored in panel (b) of able 3. While he esimaes of he speed of adjusmen are somewha lower under he bias correcion, all conclusions are he same as for he unadjused CCEP resuls: for aggregaed daa he speed of adjusmen for he nominal exchange rae is much larger han ha for he price level; for disaggregaed he speed of adjusmen in prices is faser. To chec he sensiiviy of our resul o our paricular daa se, we conduc he same error correcion esimaion using he daa se used by Imbs e al. (2005). 13 While he values of adjusmen parameers repored in Table 5 are lower across he board, he paern of relaive ranings is he same. In disaggregaed indusry level daa he speed of adjusmen for prices is more han wice ha for he nominal exchange rae; for aggregaed daa he reverse is rue, wih he speed of adjusmen for prices being half of ha for he nominal exchange rae. We here rule ou wo poenial explanaions for he puzzle. The firs hing o rule ou is measuremen error in he disaggregaed price observaions. This would seem plausible, given ha he price raio daa rely upon survey aers o subjecively choose represenaive goods wihin some caegories. If he measuremen error is correced or reversed in subsequen observaions of prices, i migh appear as if prices are adjusing o correc he price deviaion. (Of course, he exchange rae daa would no be subjec o he errors of survey collecion.) To es his explanaion, a Hausman es is conduced, esimaing a firs-order auoregression of q ij, for 13 The Imbs e al. (2005) benchmar daase we use consiss of monhly observaions exending from 1981 o 1995 for he U.S. and 10 European counries (we exclude Finland in order o mainain a balanced panel, as required for our esimaion mehodology). 12

14 each cross-secional iem (counry-goods) by wo mehods, OLS and wo sage leas squares using lagged values as insrumens, and esing he hypohesis of no measuremen error. Among he 1843 counry-good series, only 233 rejec consisency a he 5% level. This indicaes ha measuremen error is no a problem for mos of our observaions. Anoher poenial explanaion for our resul is ha he ype of aggregaion bias Imbs e al. (2005) described for auoregressions, lie our equaion (2), could have an analog for our error correcion equaion (3). Imbs e al. (2005) argued ha heerogeneiy in he speeds of convergence in he real exchange rae among disaggregaed goods can lead o an overesimae of he persisence in he aggregae real exchange rae, under condiions where hose goods wih slow speeds of adjusmen receive oo much weigh in compuing he aggregae price level. 14 To ranslae his argumen ino an explanaion for our error correcion esimaion, aggregaion would need o lead o a bias underesimaing he aggregae adjusmen speed in one variable, he prices, bu a he same ime an overesimae of he speed of adjusmen in anoher variable, he nominal exchange rae. On one hand, we can confirm ha here is heerogeneiy among he goods in erms of he size of e and p, so larger weighs on some goods could lead o esimaes of he aggregae ha are differen from he average among he goods. However, here is no heerogeneiy among goods in erms of he fac ha e p ; his is rue for all 98 of he goods in he sample. We can conceive of no weighing of goods when aggregaing ha could reverse his inequaliy in he aggregae. III.C. The Role of Disinc Shocs The finding above, ha aggregaed and disaggregae price deviaions have qualiaively disinc adjusmen mechanisms, suggess ha he wo ypes of price deviaions may have qualiaively differen origins. We conjecure ha here are idiosyncraic shocs a he good level ha are disinc from macroeconomic shocs occurring a he aggregae level. Accordingly, we apply he CCEP esimaor o a modified hree-variable vecor error correcion model, which aes he novel sep of nesing ogeher aggregae and disaggregaed price daa series: e ( q q ) ( q ) 1 2 ij, ij, e e, ij ij, 1 ij, 1 e, ij ij, 1 ( e ) ( p ) ( p ) eij,,1 ij, 1 eij,,2 ij, 1 eij,,3 ij, 1 eij,, (5) 14 This argumen has been criiqued by Chen and Engel (2005) among ohers. 13

15 p ( q q ) ( q ) 1 2 ij, p, ij p, ij ij, 1 ij, 1 p, ij ij, 1 pij,1 ( eij, 1 ) pij,,2( pij, 1 ) pij,,3( pij, 1 ) pij,, p ( q q ) ( q ) 1 2 ij, p, ij p, ij ij, 1 ij, 1 p, ij ij, 1 p, ij,1 ( eij, 1 ) p, ij,2 ( pij, 1 ) p, ij,3 ( pij, 1 ) p, ij, There are wo coinegraing vecors in his sysem over he variables e, p, and p: [1 0 1] and [0 1-1]. This sysem allows for a disinc response o he aggregae price deviaion qij, 1, which is he average across all goods, and a disinc response o he purely idiosyncraic price wedge, specified as qij, 1 qij, 1, he difference beween he price wedge for one good and he average wedge across all goods. Given he definiion of q and q, he laer difference alernaely may be q q p p. wrien: ij, 1 ij, 1 ij, 1 ij, 1 Esimaes of he response parameers in he expanded VECM, repored in Table 6, suppor and exend he resuls found earlier when esimaing separae VECM sysems for aggregaes and disaggregaed daa. Again p responds o q q (p p) deviaions, and now we see explicily ha i does no respond o q deviaions. We see ha e responds o aggregae q deviaions bu no o q q (p p) deviaions. And finally, p responds only o q deviaions. These conclusions are he same for he bias-correced esimaes repored in panel b of able 6, which were compued using he mehod of Kilian (1998). The main benefi of esimaing equaion (5) is ha i provides a way o idenify idiosyncraic shocs as separae from macroeconomic shocs. We use a Cholesy ordering of he variables e, p, and p, which defines an indusry shoc as an innovaion o p for a paricular good ha has no conemporaneous effec on aggregae p (or e). We believe his is a case where a Cholesy idenificaion of shocs is paricularly well suied. An aggregae shoc is one ha maes boh p and p move conemporaneously, as i affecs goods prices on average. If desired, hese aggregae shocs may be divided ino shocs o he foreign exchange mare, idenified as all innovaions o e, or shocs o he aggregae goods mare, idenified as innovaions o p wih no conemporaneous effec on e. This esimaion is run for each of he 98 goods, and variance decomposiions and impulse responses are generaed for each. Figures 1 and 2 repor he variance decomposiions of he variables by shoc, where he numbers repored for disaggregaed daa are he averages among he 98 goods. No surprisingly, 14

16 variaion in he aggregae real exchange rae, q, is due mainly o nominal exchange rae shocs, accouning for over 80% of variaion, wih a secondary role played by aggregae price shocs, and virually no role a all played by idiosyncraic shocs. In conras, variaion in LOP deviaions in disaggregaed daa, q, are due largely o idiosyncraic indusry price shocs o p, accouning for abou 80% of variaion, wih exchange rae shocs playing a much lesser role. Impulse responses repored in Figures 3-5 help idenify he mechanisms of adjusmen. The figures repor impulse responses from simulaions of he sysem (5), where parameer values are he averages of he esimaes derived for he 98 goods. Recall from he variance decomposiions above ha mos movemens in q appear o be due o idiosyncraic shocs. The boom panel of Figure 3 shows ha he dynamics of q resemble ha for p, whereas he nominal exchange does no move. Since q = e + p, his observaion suggess ha he goods price does mos of he adjusing o resore LOP. Nex, recall from variance decomposiions ha mos of he movemens in he real exchange rae, q, were due o nominal exchange rae shocs, wih aggregae price shocs in a secondary role. The op panel of Figure 4 shows ha he response of q o exchange rae shocs loos lie ha of he e componen; his indicaes he nominal exchange rae does he adjusing. Ineresingly, for an aggregaed price shoc, he op panel of Figure 5 shows ha he response of q loos lie e; again, he nominal exchange rae does mos of he adjusing, even hough he shoc was an innovaion o p orhogonal o innovaions o e. These conclusions regarding adjusmen dynamics are formalized in Table 7 following he mehodology of Cheung e al. (2004). Defining he impulse response of variable m o shoc n as mn, (), noe ha q, n() e, n() p, n() for disaggregaed daa and qn, en, pn, q () () () for aggregaed daa. Then gen, () en, ()/ q, n() measures he proporion of adjusmen in LOP deviaions explained by nominal exchange rae adjusmen, and g () ()/ () measures he proporion explained by price adjusmen, such ha q p, n p, n q, n g () g () 1. The analogs for decomposing adjusmen for aggregaed daa are q q en, p, n q g () ()/ () and g, (), ()/, (). The values in Table 7 suppor he q en, en, qn, pn pn qn conclusions above. Adjusmen of aggregaed daa aes place mainly via adjusmen in he nominal exchange rae regardless of shoc. Adjusmen of disaggregaed daa depends upon he 15

17 shoc; for aggregae shocs (e and p), adjusmen aes place mainly via nominal exchange rae adjusmen, bu for idiosyncraic shocs adjusmen aes place via price adjusmen. Overall, we conclude ha price deviaions a he aggregaed and disaggregaed levels are very differen. Firs hey differ in erms of he shocs ha drive hem. Furher, he dynamic responses differ according o shoc: movemens in disaggregaed q are dominaed by movemens in he p componen as i adjuss in response o p shocs, while movemens in he aggregae q are dominaed by movemens in e adjusing in response o e and p shocs. This indicaes o us ha he apparen inconsisency in adjusmen dynamics observed for aggregaed and disaggregaed daa comes from he disincion beween he paricular shocs ha dominae a differen levels of aggregaion. III.D. Implicaions for he Convergence Speed Puzzle The hypohesis ha differen shocs and adjusmen mechanisms are a wor a differen levels of aggregaion also offers a promising explanaion for he persisence puzzle popularized in Imbs e al. (2005) and ohers. Why does he half-life of aggregaed real exchange raes appear o be longer han for disaggregaed daa? The error correcion models esimaed in he previous secion provide an answer. Figures 3-5 indicaes ha he half-lives of disaggregaed real exchange raes vary by he shoc o which hey are adjusing. Table 8 compues he half-life of adjusmen of he aggregae and disaggregaed real exchange raes, condiional on he shoc. 15 The half-lives for aggregaed real exchange raes, q, and disaggregaed, q, are quie similar o each oher when condiioned on aggregae e and p shocs, wih values in he neighborhood of 2 years. Bu when condiioned on idiosyncraic shocs, he half-life of disaggregaed real exchange raes falls dramaically, o a value abou half of ha for aggregae shocs. 16 The main lesson is ha when condiioned on aggregae shocs, here is no longer a conras in persisence beween aggregae and disaggregaed real exchange raes. Insead, he conras is beween aggregae and disaggregae shocs; disaggregaed daa respond slowly o he firs and quicly o he laer. This 15 Half-lives are generaed from simulaed impulse responses. Sysem (5) was simulaed 1000 imes using random draws of sysem parameers, where he mean and sandard errors of he disribuion are he average esimaes among he goods. Half-lives are compued for aggregaed and disaggregaed daa in each simulaion, and he able repors he mean of hese. Confidence inervals are no repored for he half lives because he impulse responses for he 3- equaion sysem involve a large number of parameers, each wih heir own confidence band, leading o an accumulaion of uniformly very wide confidence inervals for saisics relaed o he impulse responses. 16 No half-life is repored for he aggregae real exchange rae, since idiosyncraic shocs have essenially no effec on his variable. 16

18 indicaes ha once half-lives are condiioned on shocs, here appears o be no micro-macro disconnec puzzle. The finding in pas wor esimaing half-lives ha disaggregaed real exchange raes adjus faser can be aribued o he dominance of a differen composiion of shocs for disaggregaed daa. Panel (b) of he able repors halflives compued from he bias-correced esimaes from panel (b) of able 6, using he mehod of Kilian (1998). The bias-correced halflives are longer due o he lower esimaes of he speed of adjusmen parameers repored in panel (b) of able 6. This implies ha our model is acually closer o explaining he high degree of persisence repored in pas sudies han i may have appeared when using uncorreced esimaes. These resuls coninue o suppor our main conclusion, ha when condiional on aggregae shocs, here is no longer a conras in he persisence beween aggregaed and disaggregaed real exchange raes. This basic lesson can be ranslaed from erms of error correcions ino he more familiar erms of auoregressions esimaed in mos pas research. Consider he following aggregaion exercise. Given ha q ij, is he aggregaion of qij, 1 over goods, i is viewed as a puzzle ha esimaes of heir adjusmen speeds are so differen. Aggregaing an AR(1) version of equaion (2) over goods: 1 1 K K K qij, cij ij qij, 1 ij, 1 K 1 K K K ij, ij ij ij, 1 ij, K 1 K 1 K 1 q c q 17 (6) Wor by Imbs e al. (2005) has focused on he role of heerogeneiy of adjusmen speeds among he goods. If we allow for heerogeneiy in he auoregressive coefficien ij among goods, equaion (6) differs from an AR(1) version of he aggregae equaion (3) because 1 K ij qij, 1 ijqij, 1 K 1. If here is a correlaion beween he variaion in ij and qij, 1 among goods, so ha slowly adjusing goods have larger price deviaions, hen his will bias upward esimaes of he average speed of adjusmen. However, he vecor error correcion exercise demonsraed ha he mechanism by which a good s price deviaion is eliminaed differs in response o he componen of he price deviaion ha is common across goods and he componen ha is idiosyncraic o he paricular good. If

19 his disincion in adjusmen mechanism affecs he speed of adjusmen, his suggess ha he specificaion of he auoregression should be expanded as follows o allow for his disincion: or equivalenly 1 2 ij, qij, qij, ij, 1 ij, 1 qij, ij, 1 qij,, q c q q q (7a) ij, q, ij q, ij ij, 1 q, ij q, ij ij, 1 q, ij, q c q q. (7b) 2 Here capures he adjusmen in relaive price of good o aggregae macroeconomic price q, ij 1 deviaions, and ij capures he response o price deviaions ha are specific o he good. For compleeness, an analogous expansion of an AR(1) version of he aggregae equaion (3) can be defined (for each ). 1 2 ij, q, ij q, ij ij, 1 ij, 1 q, ij ij, 1 q, ij, q c q q q. (8) Now aggregae up equaion (7a): 1 1 K K K 1 2 qij, cq, ij q, ij qij, 1 qij, 1 q, ijqij, 1 q, ij, 1 K 1 q K K K K c q q q Term A Term B ij, q, ij q, ij ij, 1 ij, 1 ij, 1 q, ij q, ij, K 1 K 1 K 1 K 1 (9) One observaion is ha, while heerogeneiy in can lead o a heerogeneiy bias in Term A 1 q, ij in he same way as seen in equaion (6), in conras, heerogeneiy in has no impac on 2 q, ij aggregaion of Term B, as he common componen qij, 1 passes hrough he summaion operaor. So par of he heerogeneiy among goods in erms of adjusmen speed documened by Imbs e al. (2005) may be of an innocuous ype, depending on how much applies o adjusmen o aggregae qij, deviaions, and how much o good specific deviaions o q ij,. Table 9 shows he resuls of esimaing equaions (7a) and (8). The firs resul is ha he apparen inconsisency of he equaions (2) and (3) has disappeared, when esimaed in he augmened form of equaions (7a) and (8). If we focus on he response o aggregae deviaions qij, 1, he average response coefficiens in he wo equaions are nearly he same. In he disaggregaed equaion he average coefficien is 1 K 2 q, ij K 1 =0.79, and in he aggregae 18

20 equaion he average coefficien is 1 K 2 qij, K 1 =0.80. So if one focuses jus on responses o aggregae deviaions, he aggregaion puzzle disappears. Furher, Table 9 indicaes he degree of heerogeneiy in he coefficiens in erms of he sandard deviaion of he esimaes across goods. By his measure, he heerogeneiy for he coefficien on he aggregaed real exchange rae (q) appears o be of similar magniude o ha for he idiosyncraic deviaion (q -q). Recall ha i is only heerogeneiy in he laer coefficien ha fails o cancel ou upon aggregaion and hereby could lead o aggregaion bias of he ype described by Imbs e al. Equaion (7a) also suggess ha he esimaions by Imbs e al. (2005) of an equaion lie (2) are subjec o a poenially large omied variable bias. Wrie equaion (7b) as q c q q 1 3 ij, qij, qij, ij, 1 qij, ij, 1 qij,, where q, ij q, ij q, ij (10) Esimaing equaion (2) ignores he second erm. Generalizing he sandard omied variable bias formula o he case of our panel daa, he bias would be: 1 N N 1 1 ( ij, 1 w ij, 1 ) ( ij, 1 w 1) ij1 ij1 E Q M Q Q M Q N N 1 3 Qij, 1 MwQij, 1 Qij, 1 MwQij, 1 ij1 ij1 ( ) ( ) (11) where Q ( q, q,..., q ) ; M = I- W( WW ) W; W=( W, W,... W) ; 1 ij,-1 ij,1 ij,2 ij, T 1 w 2 3 T W (1, q, q ); Q =( q, q,..., q ) ; Q ( q, q,..., q ) T ij,-1 ij,1 ij,2 ij, T1 and is he coefficien of he cross-secional mean in he augmened equaion of (10) (see he appendix for he derivaion). Our findings also bring evidence o bear on he conjecure by Broda and Weinsien (2008) ha lower persisence in disaggregaed relaive prices may be due o nonlinear adjusmen. Previous wor has demonsraed significan nonlineariies in aggregae real exchange rae adjusmen, where convergence is faser for real exchange rae deviaions ha are large. 17 This may reflec he presence of coss of engaging in arbirage, discouraging arbirage responses o 17 See Parsley and Wei (1996), Taylor e al. (2001), and Wu e al. (2009). 19

21 price deviaions oo small o generae sufficien profis o cover hese coss. Broda and Weinsein (2008) sugges ha if here is heerogeneiy among goods in erms of he volailiy of heir price deviaions, OLS esimaes of convergence speed will place a heavy weigh on he observaions where he absolue value of deviaions is large, hereby ending o find fas convergence. Bu as daa are aggregaed, hey conjecure, large posiive and negaive price deviaions are liely o cancel, so he weigh given o small price deviaions will increase, hereby ending o find slower convergence. Our empirical wor suppors he idea, in a general sense, ha faser convergence in disaggregaed daa is associaed wih greaer volailiy. When we compue he sandard deviaions of real exchange rae deviaions a he goods level for each of he 98 goods in our daa se, heir average sandard deviaion is 4.8 imes ha of he aggregae real exchange rae (10.67% and 2.22% respecively). However, we do no find much heerogeneiy among goods in his regard. For every one of our 98 goods, he sandard deviaion of price deviaions exceeds ha of he aggregae real exchange rae; he heerogeneiy among goods is small compared o he gap beween heir average and he aggregae daa. The same conclusion holds for convergence speeds: even hough here is some variaion in he convergence speeds among he goods in our sample when esimaing equaion (2), he price gap for every one of he 98 goods in our sample has a faser convergence speed han does he aggregae real exchange rae. Insead of poining o a disincion among goods, where cerain goods wih smaller volailiy and slower convergence do no cancel ou upon aggregaion, our resuls insead poin o disinc componens of each good s price deviaion, due o aggregae and idiosyncraic shocs, respecively, where he laer can reasonably be expeced o have larger volailiy and faser convergence, as well as o cancel ou upon aggregaion. This would seem o be a helpful way of reframing he role of nonlineariy conjecured in Broda and Weinsein (2008); he disincion beween aggregae and idiosyncraic shocs maes his conjecure operaional. Finally, our findings have revealing implicaions for he use of sicy price models o describe real exchange rae behavior. Cheung e al. (2004) argued agains sicy price models, emphasizing ha he adjusmen dynamics of he aggregae real exchange rae are dicaed by he adjusmen dynamics of he nominal exchange rae, no hose of gradually adjusing sicy prices. On he one hand our resul conrass wih his finding, showing ha he adjusmen in disaggregaed real exchange raes is dicaed by he dynamics of prices in he goods mare. 20

22 Noneheless, our finding suppors he overall conclusion of Cheung e al; i does no bolser he case for convenional ypes of sicy price models. Our resul indicaes ha prices acually adjus quie quicly a he disaggregaed level, indicaing small menu coss or frequen Calvo signals o rese price. IV. Conclusions Pas papers have been surprised ha inernaional price deviaions a he goods level adjus faser han do aggregae real exchange raes. The firs conribuion of he paper is o offer a deeper undersanding of his macro-micro disconnec. This paper shows ha adjusmen in real exchange raes o purchasing power pariy is no jus a slower version of he adjusmen in microlevel prices bac o he law of one price: while he nominal exchange rae does he adjusing a he aggregae level, i is he price ha does he adjusing a he disaggregaed level. The reason is ha here are disinc shocs driving price deviaions a hese wo levels of aggregaion. The disaggregaed level is dominaed by idiosyncraic shocs specific o he good, which cancel ou upon aggregaion and have minimal impac upon aggregae dynamics. The second conribuion of he paper is o offer a resoluion o he micro-macro disconnec. Once half-lives are esimaed condiional on macroeconomic shocs, microeconomic prices are found o be jus as persisen as aggregae real exchange raes. In conras wih he impression given by recen sudies on microeconomic price dynamics, here is acually significan persisence conained wihin micro price daa. The hird conribuion is o cauion agains an explanaion for he persisence puzzle relying primarily upon heerogeneiy among goods and aggregaion bias. In paricular, a significan porion of he overall heerogeneiy in adjusmen speeds among goods is found here o be associaed wih heir response o he macroeconomic shocs raher han o idiosyncraic goods shocs. Because he macroeconomic shocs are common o goods, heerogeneiy in hese coefficiens will cancel ou upon aggregaion. So a significan porion of he heerogeneiy deeced in pas sudies may be of an innocuous ype when i comes o aggregaion bias Finally, he analysis has imporan implicaions for he widespread use of sicy price models o explain real exchange rae behavior. We see evidence ha here is rapid adjusmen in prices o arbirage opporuniies a he microeconomic level, indicaing a fair degree of price flexibiliy. However, hese price movemens selecively respond mainly o idiosyncraic shocs 21

23 a he goods level, and appear o cancel ou upon aggregaion wih minimal implicaions for aggregae variables lie he aggregae real exchange rae. This finding does no coincide well wih sandard sicy price models of real exchange rae behavior, where siciness resuls from he inabiliy o rese prices rapidly and does no disinguish beween shocs. A model ha poenially could coincide beer wih he evidence would be a raional inaenion or sicy informaion sory, where firms adjus o shocs specific o heir indusry raher han common macroeconomic shocs. If a firm has limied resources o process informaion abou shocs, and if indusry specific shocs are more variable or have larger impacs on a firm s profis, i can be opimal for firms o allocae more aenion o rac and respond o idiosyncraic condiions han o aggregae condiions. Our empirical resul suggess he usefulness of fuure heoreical wor in his direcion. 22

24 References Andrade, Philippe and Marios Zachariadis, Trends in Inernaional Prices, mimeo. Broda, Chrisian and David E. Weinsein, Undersanding Inernaional Price Differences Using Barcode Daa, Universiy of Chicago mimeo. Carvalho, Carlos and Fernanda Nechio, "Aggregaion and he PPP Puzzle in a Sicy-Price Model," American Economic Review, forhcoming. Chen, Shiu-Sheng and Charles Engel, Does Aggregaion Bias Explain he PPP Puzzle? Pacific Economic Review 10, Cheung, Yin-Won, Kon S. Lai and Michael Bergman, Dissecing he PPP Puxxle: The Unconvenional Roles of Nominal Exchange Rae and Price Adjusmens, Journal of Inernaional Economics 64, Crucini, Mario J. and Moosugu Shinani, Persisence in Law-of-One-Price Deviaions: Evidence from Micro-daa, forhcoming in he Journal of Moneary Economics. Crucini, Mario J., Chris I. Telmer and Marios Zachariadis, Undersanding European Real Exchange Raes, American Economic Review 95, De Grooe, Tom and Gerdie Everaer, Common Correlaed Effecs Esimaion of Dynamic Panels wih Cross-Secional Dependence, Ghen Universiy Woring Paper 2011/723. Engel, Charles and Morley, J. C., The Adjusmen of Prices and he Adjusmen of he Exchange Rae, NBER Woring Paper no Engel, Charles and John H. Rogers, European Produc Mare Inegraion afer he Euro, Economic Policy 39, Fisher, Eric. and Joon Y. Par, Tesing Purchasing Power Pariy Under he Null Hypohesis of Co-inegraion, The Economic Journal 101, Imbs, Jean, H. Mumaz, Moren Ravn and Helene Rey, PPP Sries Bac: Aggregaion and he Real Exchange Rae, Quarerly Journal of Economics 70, Kilian, Luz, Small-Sample Confidence Inervals For Impulse Response Funcions, Review of Economics and Saisics 80, Macowia, B. and Wiederhol, M., Opimal Sicy Prices under Raional Inaenion, American Economic Review 99(3),

25 Mar, Nelson C. and Donggyu and Sul, PPP Sries Ou: The Effec of Common Facor Shocs on he Real Exchange Rae. Nore Dame woring paper. Parsley, David and Shang-jin Wei, Convergence o he Law of One Price Wihou Trade Barriers or Currency Flucuaions, Quarerly Journal of Economics 111, Parsley, David and Shang-jin Wei, Currency Arrangemens and Goods Mare Inegraion: A Price Based Approach, Woring paper. Pesaran, M. Hashem, 2006, Esimaion and Inference in Large Heerogeneous Panels wih a Mulifacor Error Srucure, Economerica 7, Pesaran, M. Hashem, A Simple Panel Uni Roo Tes in he Presence of Cross-Secion Dependence, Journal of Applied Economerics 22, Phillips, Peer C. B. and Sul, Donggyu, "Bias in Dynamic Panel Esimaion wih Fixed Effecs, Incidenal Trends and Cross Secion Dependence," Journal of Economerics, 137(1), Sarafidis, Vasilis and Donald Roberson, On he impac of Cross secion Dependence in Shor Dynamic Panel Esimaion, Economeric Journal, 12(1), Seinsson, Jon, The Dynamic Behavior of he Real Exchange Rae in Sicy Price Models, American Economic Review 98, Taylor, M. P., Peel, D. A. and Sarno, L., Non-linear Mean Reversion in Real Exchange Raes: Toward a Soluion o he Purchasing Power Pariy Puzzles, Inernaional Economic Review 42, Wu, Jyh-Lin, Chen, Pei-Fen and Lee, Ching-Nun, Purchasing Power Pariy, Produciviy Differenials and Non-Lineariy, The Mancheser School 77,

26 Table 1: Saionariy of relaive prices (mean) (mean) (mean) significance Sample b -sa # obs. 1% 5% 10% Disaggregaed daa: Traded: (ou of 98) Nonraded (ou of 30) Aggregaed daa: Traded: Yes Yes Yes Non-raded No No No Noe: For disaggregaed daa, he able repors esimaes of b in he equaion: qij, aij bij ( qij, 1) cij ( q 1 ) dij ( q ) ij, ij 1,..., N, 1,..., K, and 1,..., T N where q qij, is he cross-secion mean of qij, across counry pairs and q q q 1.The ij1 null hypohesis of he es is H0 : bij 0 for all ij agains he alernaive hypohesis H1 : bij 0 for some ij. The b coefficiens and -sas are calculaed as means over he individual goods resuls, and significance resuls repor he number of goods ha rejec nonsaionariy a he specified significance level. For aggregaed daa, he able repors esimaes of he equaion: qij, aij bij ( qij, 1) cij ( q 1 ) dij ( q ) ij, ij 1,..., N and 1,..., T N where q qij, is he cross-secion mean of qij, across counry pairs and q q q 1. ij1 25

27 Table 2. Half-lives in auoregressions of real exchange raes AR(2): Sample (Mean) 1 (Mean) -sa (Mean) 2 (Mean) -sa (Mean) #obs. (Mean) Half-life Disaggregaed daa Aggregaed daa AR(1): Disaggregaed daa Aggregaed daa Noe: For disaggregaed daa, he able repors esimaes of in he equaion 2 ij, ij ij, m ij, m ij, m1 q c ( q ) for 1,..., K. The coefficiens and -sas are calculaed as mean values of 1, 2 and heir associaed -saisics across all goods. Esimaes for aggregaed daa are based on he equaion 2 q c ( q ) ij, ij ij, m ij, m ij, m1 he parameer esimaes. Half-life in years are calculaed from simulaed impulse responses derived from 26

28 Table 3: Vecor error correcion esimaes (mean) (mean) -sa Heerogeneiy (Sd.Dev.) #obs. a) CCEP Esimaes: Disaggregaed Daa (for 98 raded goods): Exchange rae equaion Price raio equaion Aggregaed Daa: Exchange rae equaion Price raio equaion b) Bias-Correced CCEP Esimaes: Disaggregaed Daa (for 98 raded goods): Exchange rae equaion Price raio equaion Aggregaed Daa: Exchange rae equaion Price raio equaion Noe: The able repors esimaes wih disaggregaed daa for he equaion sysem: e, e ( q ) ( e ) ( p ) ij, ije, eij, ij, 1 eij, ij, 1 eij, ij, 1 ij, p, ij, ij, p pij, ( ij, 1 ) pij, ( ij, 1 ) pij, ( ij, 1 ) ij, p q e p. and wih aggregae daa for he sysem: e eij, ije, eij, ( qij, 1 ) eij, ( eij, 1 ) eij, ( pij, 1 ) ij, p pij, ij, ppij, ( qij, 1 ) pij, ( eij, 1 ) pij, ( pij, 1 ) ij,. For he disaggregaed daa, he coefficiens for he exchange rae and price equaions are calculaed as means of,, across goods, respecively. The repored sandard deviaion of esimaes across goods is provided e p as a measure of heerogeneiy among goods. The bias correcion is carried ou via he Kilian (1998) boosrap mehod wih 1000 ieraions. The -saisics are compued from sandard errors derived using he doubleboosrap mehod of Kilian (1998). 27

29 Table 4: Mone Carlo experimen for CCEP esimaor Pesaran Coefficien Average Mone Carlo Coefficien 5% 95% Exchange rae equaion Price raio equaion Noe: Daa were generaed using he sysem: e e ˆ ˆ ˆ ij, e, ij ( qij, 1 ) e, ij ( eij, 1 ) e, ij ( pij, 1 ) ij, p p ˆ ( q ) ˆ ( e ) ˆ ( p ). ij, p, ij ij, 1 p, ij ij, 1 p, ij ij, 1 ij, where he Pesaren coefficien values for e and p are aen from CCEP esimaion of he woequaion sysem (4b) wih aggregaed daa, repored in Table 3, panel a.. In each of 1000 replicaions, a sequence of innovaions for 20 counry pairs covering 34 periods were drawn from he (demeaned) residuals of he esimaed exchange rae and price equaions, and hese were used o generae series for price and exchange rae (as well as for he real exchange rae), using acual observaions as saring values. The generaed daa were hen used o re-esimae he model by CCEP. The Mone Carlo coefficiens denoe he average coefficiens across he 1000 replicaions, as well as he 5% and 95% cuoffs of he disribuion of esimaes. 28

30 Table 5: Vecor error correcion esimaes using daa se from Imbs e al. (2005) (mean) (mean) -sa Disaggregaed Daa: Exchange rae equaion Price raio equaion Aggregaed Daa: Exchange rae equaion Price raio equaion Noes: The able repors esimaes wih disaggregaed daa for he equaion sysem: e, e ( q ) ( e ) ( p ) ij, ije, eij, ij, 1 eij, ij, 1 eij, ij, 1 ij, p ( q ) ( e ) ( p ). p, ij, ij, p pij, ij, 1 pij, ij, 1 pij, ij, 1 ij, and wih aggregae daa: e e ( q ) ( e ) ( p ) ij, ije, eij, ij, 1 eij, ij, 1 eij, ij, 1 ij, p ( q ) ( e ) ( p ). 18 p ij, ij, p pij, ij, 1 pij, ij, 1 pij, ij, 1 ij, For disaggregaed daa, he coefficiens for he exchange rae and price equaions are calculaed as means of,, across goods, respecively e p 18 Because his error correcion model incorporaes lags of firs differences o capure shor-run dynamics, his specificaion is analogous o he second-order auoregression esimaed previously. Inclusion of addiional lags is impossible due o he shor ime-span of he daa se. 29

31 Table 6: 3-Equaion vecor error correcion esimaes a) CCEP esimaes: Mean Response o q -q Mean -sa Heerogeneiy: SdDev 1 Mean Response o q Mean -sa Heerogeneiy: SdDev Mean #obs. Exchange rae equaion Aggregaed Price equaion Disaggregaed Price equaion b) Bias-correced CCEP esimaes: Exchange rae equaion Aggregaed Price equaion Disaggregaed Price equaion Noes: The able repors esimaes wih disaggregaed daa for he equaion sysem: 1 2 e ( q q ) ( q ) ( e ) ( p ) ( p ) ij, ij, e e, ij ij, 1 ij, 1 e, ij ij, 1 e, ij,1 ij, 1 e, ij,2 ij, 1 e, ij,3 ij, 1 e, ij, 1 2 ij, p, ij p, ij ( ij, 1 ij, 1 ) p, ij ( ij, 1 ) pij,1 ( ij, 1 ) p, ij,2 ( ij, 1 ) p, ij,3 ( ij, 1 ) p, ij, p q q q e p p 1 2 ij, p, ij p, ij ( ij, 1 ij, 1 ) p, ij ( ij, 1 ) p, ij,1 ( ij, 1 ) p, ij,2 ( ij, 1 ) p, ij,3 ( ij, 1 ) p, ij, p q q q e p p The coefficiens for exchange rae, aggregae price, and disaggregaed price responses are calculaed as he means of,,,, e e p p p p across goods, respecively. The repored sandard deviaion of parameer esimaes provides a measure of heerogeneiy across goods. The bias correcion is carried ou via he Kilian (1998) boosrap mehod wih 1000 replicaions. The - saisics are compued from sandard errors derived using he double-boosrap mehod of Kilian (1998). 30

32 Table 7: Relaive conribuions of nominal exchange rae and price adjusmens o PPP and LOP Reversion Wih an exchange wih an aggregae wih a disaggregae rae shoc price shoc price shoc Disaggregaed q : years q g ee, q q p, e g ep, q q p, p q g ep g p, p Aggregaed q: years q q q q g ee, g pe, g ep, g pp, q q ep, g pp, q Noe: The columns g i, j indicaes he proporion of adjusmen in he relaive price q explained by adjusmen in q variable i, condiional on shoc j. The columns g i, j indicae he same proporion for adjusmen in he aggregaed real exchange rae q. 31

33 Table 8. Esimaes of half-lives condiional on he shoc e shoc p shoc p shoc CCEP Esimaion: Disaggregaed q Aggregaed q CCEP Bias-Correced Esimaion: Disaggregaed q Aggregaed q Noe: Half-lives in years, esimaed from impulse responses of he equaion sysem: 1 2 e ( q q ) ( q ) ( e ) ( p ) ( p ) ij, ij, e e, ij ij, 1 ij, 1 e, ij ij, 1 e, ij,1 ij, 1 e, ij,2 ij, 1 e, ij,3 ij, 1 e, ij, 1 2 ij, p, ij p, ij ( ij, 1 ij, 1 ) p, ij ( ij, 1 ) pij,1 ( ij, 1 ) p, ij,2 ( ij, 1 ) p, ij,3 ( ij, 1 ) p, ij, p q q q e p p 1 2 ij, p, ij p, ij ( ij, 1 ij, 1 ) p, ij ( ij, 1 ) p, ij,1 ( ij, 1 ) p, ij,2 ( ij, 1 ) p, ij,3 ( ij, 1 ) p, ij, p q q q e p p The bias correcion is carried ou via he Kilian (1998) boosrap mehod using 1000 replicaions. 32

34 Table 9. Esimaes of speeds of adjusmen in expanded auoregression Mean Response o q -q Mean -sa Heerogeneiy: SdDev 1 Mean Response o q Mean -sa Heerogeneiy: SdDev 1 #obs. Disaggregaed daa Aggregaed daa Noe: Esimaes for disaggregaed daa from he equaion:,, 1,, 1, 1 2 qij cqij qij qij qij qij, qij, 1 qij,, and for aggregaed daa from: 1 qij 2, cq, ij q, ij qij, 1 qij, 1 q, ijqij, 1 q, ij,. Sandard deviaion of parameer esimaes are repored across goods. 33

35 Fig. 1 Variance decomposiion of q p conribuion e conribuion p conribuion Fig. 2 Variance decomposiion of q e conribuion p conribuion p conribuion 34