New Keynesian Exchange Rae Pass-Through Woon Gyu Choi and David Cook February 2009 Absrac Using he heory of opimal local currency pricing, his paper consrucs a srucural equaion o esimae he rae a which foreign producer prices pass hrough he local currency prices of impored goods in he U.S. This can be viewed as measuring exchange rae pass-hrough, in line wih price sickiness in he New Keynesian Phillips curve lieraure. We esimae he srucural equaion using he generalized mehods of momens for consisen esimaes of exchange rae pass-hrough. We find ha a model wih a mix of local currency pricing and producer currency pricing fis he daa bes. The esimae of price sickiness in impor prices is comparable o exising esimaes of domesic price sickiness. JEL Classificaion Numbers: E3; F3; F4 Keywords: pass-hrough effecs; impor prices; local currency pricing; new Keynesian Phillips curve; forward-looking expecaion Auhors E-Mail Address: wchoi@imf.org; davcook@us.hk Woon Gyu Choi is a Senior Economis a he IMF Insiue of he Inernaional Moneary Fund. David Cook is an Associae Professor of Economics a he Hong Kong Universiy of Science and Technology. This Working Paper should no be repored as represening he views of he IMF. The views expressed in his Working Paper are hose of he auhors and do no necessarily represen hose of he IMF or IMF policy.
I. INTRODUCTION The degree o which flucuaions in he nominal exchange rae affec he relaive prices of real goods will in large par deermine he effec of exchange rae policy on paerns of inernaional rade. A large empirical lieraure in inernaional macroeconomics esimaes how quickly exchange rae changes ranslae ino impor prices (for example, Yang 997; and Campa and Goldberg, 2005). This speed of adusmen is referred o as exchange rae pass-hrough. In his paper, we examine he speed of adusmen in he price of expors o he U.S. in response o changes in he value of he U.S. dollar. An innovaion in our paper is an applicaion of he modern sicky price heory ha is embedded ino he New Open Economy Macroeconomics lieraure (see Obsfeld and Rogoff, 995) o creae a saisical model in which exchange rae pass-hrough can be represened as a srucural parameer immune o he Lucas criique. We hen apply some of he echniques ha have been developed o undersand he dynamics of domesic inflaion (referred o as he New Keynesian Phillips curve lieraure) o esimae our model and consisenly idenify he srucural parameer which we refer o as exchange rae pass-hrough. The idea ha he prices of impors would incorporae exchange rae changes only slowly has a long heriage. Many heoreical models were developed o explain his paricular failure of he Law of One Price. In paricular, price sickiness implies ha he Law of One Price fails o hold a any ime, and exchange rae pass-hrough is imperfec. 2 In he conex of sicky price models, Bes and Devereux (996, 2000) develop he heory of local currency pricing (LCP) o explain violaions of purchasing power pariy. In conras, when monopolisic producers se sicky prices in heir own currency, which is he case of producer currency pricing (PCP), exchange rae changes are refleced one-for-one in foreign currency prices (perfec passhrough). 2 In he earlies versions of he New Open Economy Macroeconomics lieraure, sicky prices generaed a role for moneary policy. A subsanial body of heory examines he welfare implicaions of imperfec pass-hrough. In some cases, LCP implies ha mainaining a fixed exchange rae can be an opimal moneary policy (for example, see Devereux and Engel, 2003).
To generae richer dynamics, many sicky price models have adoped a (ime-dependen) model of pricing developed by Calvo (983) and incorporaed i ino he dynamic general equilibrium modeling srucure (Yun, 996). In his ype of models, inflaion is forward-looking and can be wrien as a discouned sum of fuure marginal coss. When real marginal coss are high or expeced o be high in he fuure, firms have an incenive o raise prices inducing inflaion. The recursive form of an inflaion equaion in which inflaion is wrien as a funcion of curren marginal cos plus expeced fuure inflaion (as a proxy for fuure marginal coss) has been represened as a modern alernaive o he Phillips curve. Galí and Gerler (999) and Sbordone (2002, 2005) show ha his forward-looking represenaion of inflaion can be esimaed wih general mehods of momens (GMM) using lag variables as valid insrumens. This lieraure can be used o esimae he rae a which sicky prices change. There exiss an exac parallel o he New Keynesian Phillips curve in he LCP lieraure. Impor price inflaion will be high when he real U.S. dollar marginal cos of foreign producion is high or expeced o be high. We can decompose he real U.S. dollar marginal cos of foreign producion ino wo pars, he real marginal cos of producion in he exporing counry and he gap beween impor prices in he U.S. and he PCP price (ha is, he exchange-rae-adused price of goods in he foreign counry). Finding a consisen measure of marginal coss in he foreign counry may be difficul. However, he heory of he New Keynesian Phillips curve implies ha he measure of real marginal coss can be inferred from inflaion since real marginal coss drive inflaion. Therefore, he esimaion of a recursive, forward-looking represenaion of he LCP Euler equaion governing impor price inflaion enables us o provide a consisen esimae of he frequency wih which foreign firms change heir U.S. prices in response o changes in U.S. dollar marginal coss. We can inerpre his srucural parameer as he New Keynesian rae of exchange rae pass-hrough because one of he deerminans of hese U.S. dollar marginal coss is he exchange rae. As a byproduc of his procedure, we are able o esimae he rae a which foreign producers adus heir own home price levels wihou ever consrucing a measure of marginal cos. 2
Many recen sudies examine changes in pass-hrough effecs over ime and heir conribuing facors. Taylor (2000) found a reduced pass-hrough of exchange rae changes ino consumer prices which was poenially aribuable o he lower inflaion environmen leading o less frequen price changes in general. Devereux and Yeman (2003), indeed, find ha he crosssecion of pass-hrough coefficiens is negaively relaed o he cross-secion of average inflaion. Focusing specifically on impor prices, Campa, Goldberg and Gonzalez-Minguez (2006) find a rend oward falling impor price pass-hrough in manufacured goods indusries in some Euro counries bu do no find srong evidence ha his is relaed o he adopion of he Euro currency. Frankel, Wei, and Parsley (2005), focusing on prices of specific disaggregaed goods, examine he role of moneary policy and increasing domesic disribuion coss o explain reduced passhrough. Oani, Shasuka, and Shiroa (2005) find declining raes of long-run pass-hrough ino impor prices across a range of indusries in Japan bu sable shor-run pass-hrough. Marazzi, Shees, Vigfusson, and ohers (2005) find a sharp decline in pass-hrough of exchange rae changes ino U.S. impor prices which can be aribued in par o changes in he pricing behavior of Asian exporers following he 997 98 Asian crisis. Ihrig, Marazzi and Rohenberg (2006) find falling impor price pass-hrough for he enire G7. Marazzi and Shees (2006) aribue par of he decline in pass-hrough o sraegic effecs. The approach in his paper has common and differen feaures, compared o exising sudies. Firs, exchange rae pass-hrough comprises wo pars: he pass-hrough of exchange raes ino impor prices; and ha of impor prices ino CPI. Campa and Goldberg (2006a, b) provide a number of reasons including disribuion coss why consumer prices migh be slow in response o impor prices. This paper, by conras, follows a lieraure ha examines he impac of exchange raes on impor prices. Second, as argued by Gagnon and Ihrig (2005) and Gus and Shees (2006), one reason for reduced pass-hrough can be a greaer endogenous response of moneary policy o exchange raes, which, in urn, leads o more sable prices. One advanage of he approach in his paper is ha he direc esimaion of an opimizaion-based model of price adusmens will make our esimaes robus o changes in moneary policy. Third, our model 3
focuses on aggregae srucural dynamics, whereas some sudies including Hellersein (2004) and Goldberg and Hellersein (2008) esimae exchange rae pass-hrough a he indusry level. This paper offers several findings on exchange rae pass-hrough effecs on U.S. impor prices. Firs, we find srong evidence of price sickiness in U.S. impor prices; consisen wih a srucural model in which prices change every 5 quarers on average. Second, a model in which some firms adop LCP and ohers adop PCP pricing fis he daa mos coherenly. The esimaed fracion of PCP price seers is small: 0 percen or less. Third, we find only weak evidence ha raes of price change have slowed over ime. Fourh, he degree of impor price sickiness is similar o ha of he domesic price sickiness of U.S. rading parners. Lasly, as in he New Keynesian Phillips curve, here is a subsanial forward-looking elemen o he adusmen of impor prices which is consisen wih he idea ha many firms are adusing in an opimal manner. Also, as in ha lieraure, only a smaller fracion of firms are backward-looking. II. THE MODEL We consider a model in which all firms exporing o he U.S. adus heir U.S. dollar prices infrequenly and opimally according o he local currency pricing (LCP) pass-hrough heory. A producing firm ha changes prices in he home marke chooses a price o maximize he discouned sum of expeced profis over he ime. The firm mus se producer prices in advance using he informaion se available a ime - (see Roemberg and Woodford, 997). Discouned expeced profis in he domesically oriened secor can be wrien as: ξ ξ max E PPI Q ppi ppi MC ppi ξ ξ ξ ξ ( κβ ), = where β is he discoun facor of he firm s managers, κ is he probabiliy of adusing he producer price in each period, ppi is he firm s producer price, PPI is he aggregae producer price index, Q is oupu, and MC is nominal marginal cos in erms of home currency. The opimal producer price * ppi ha maximizes he expeced profis is given by 4
ppi * ξ ξ ξ E ( κβ ) PPI Q MC = =. ξ ξ ξ ξ E ( κβ ) PPI Q = Linearizing he firs order condiions as in Galí and Gerler (999), PPI ( κ)( βκ) PPI = mc + βe + κ, () where mc = log( MC / PPI ), and PPI is he inflaion rae in foreign prices. Similarly, when imporing firms choose heir prices for impors ino he U.S., hey maximize heir profis from he U.S. marke: ξ max E IPI IM S ipi ipi MC / S ipi ξ ξ ξ ξ ξ ( νβ ), = where ipi is he firm s impor price measured in U.S. dollars, IPI is he aggregae impor price index, IM is he volume of impors, S is he spo exchange rae wih he U.S. dollar, and ν is he probabiliy of adusing he impor price in each period. The opimal impor price maximizes he expeced profis is given by ipi * E IPI IM S ( MC / S ) =. ξ ξ ξ ξ ( νβ ) = ξ ξ ξ E ( νβ ) IPI IM S = * ipi ha We can exend he Galí and Gerler (999) and Sbordone (2002) echnique o he case of impor prices and wrie IPI ( ν)( βν) IPI = E ( mc μ) + β + ν, (2) 5
IPI where μ is he logarihm of M PPI / S domesic prices (ha is, μ = ln M)., he mark-up of U.S. impors over heir (U.S. dollar) Combining equaions () and (2) o eliminae mc, we have ( ν)( βν) κ βκ = E μ βe ν + + ( κ)( βκ) ( κ)( βκ) ( ) IPI PPI PPI IPI + +. (3) Equaion (3) will form he saisical model ha we can use o measure srucural pass-hrough. This equaion reflecs an error-correcion mechanism, where μ (= ln M ) is a coinegraing vecor for U.S. impor prices, he foreign producer price level, and he exchange rae because he raio M converges in expecaion o a seady sae when firms are fully able o adus prices. The heory consrains he dynamics of equaion (3) in a number of ways. Firs, in his opimal price seing equaion, all correcions come hrough changes in foreign or impor prices, and he exchange rae only appears as par of he error-correcion erm. This is in conras wih he sandard lieraure which essenially regresses impor price inflaion (or CPI inflaion) on changes in he exchange rae. Second, he prices adus geomerically so we can include only a single lead of each kind of inflaion in he dynamic equaion. The reduced-form exchange rae pass-hrough lieraure ypically focuses on backward-looking dynamics and does no use heory o consrain he number of lags in he model. Third, he price seing firms operae under raional expecaions, so he error erm is uncorrelaed wih all variables in he informaion se available for price-seers a ime -. This produces a naural se of idenificaion condiions and allows consisen esimaion wih GMM. Fourh, he pass-hrough of real foreign marginal cos ino impor prices occurs a he same speed as exchange rae pass-hrough as implied by equaion (2). Finally, he long-erm pass-hrough is 00 percen. 6
III. THE DATA To esimae he pass-hrough effec model given by equaion (3), we need daa on domesic impor price inflaion, foreign producer price inflaion, and he relaive price of impors o foreign price levels. Deailed descripions abou daa are provided in he appendix. We also need rade weighs o aggregae foreign prices over U.S. rading parners. We calculae rade weighs for 40 rading parners of he U.S. (Appendix C). 3 Counry s share in U.S. impors of manufacured goods a quarer, w, is calculaed as impors of manufacured goods from counry divided by he sum of impors of manufacured goods from all counries in he lis of rading parners. 4 We measure he markup of impor prices over he PCP price, M, using geomeric weighs o aggregae ime series of he markup for each of he rading parners, as in Thomas and S IPI Marquez (2006). The markup for counry is defined as m, where PPI PPP S is he number of currency unis in counry needed o buy U.S. dollar in spo markes relaive o he exchange rae in 995 (Source: IFS), and 995 PPI is he producer price index of manufacured goods for counry relaive o he index in he base year 995. 5 The impor price index for he U.S. is from a daabase of OECD manufacured goods impor price indices ha spans he period 975 2002. The daa is exended forward in ime using an index of nonperoleum impor prices from BLS. 6 The variable PPP 995 is he purchasing power pariy raio from he Penn World Tables (Heson, Summers, and Aen, 2006) in he base year, 995. 3 U.S. rading parners comprises 40 counries as follows: Ausralia, Ausria, Belgium, Brazil, Canada, Chile, China, Hong Kong SAR, Colombia, Cosa Rica, Denmark, Finland, France, Germany, India, Indonesia, Ireland, Israel, Ialy, Japan, Korea, Malaysia, Mexico, Neherlands, New Zealand, Norway, Peru, Philippines, Poland, Porugal, Russia, Singapore, Souh Africa, Spain, Sweden, Swizerland, Taiwan, Thailand, Turkey, and he Unied Kingdom. 4 Campa and Goldberg (2005) find ha he mos imporan deerminan of exchange rae pass-hrough is he fracion of impors which are manufacured goods ha end o have low pass-hrough raes (relaive o energy goods). 5 The foreign price indices are from various sources and are oulined by couny in Appendix A. In many cases, he coverage of he manufacured goods producer price index is incomplee and he daa is exended back in ime using broader producer price indices, wholesale price indices, or GDP deflaors. 6 The impor price deflaor can be obained (hp://www.bls.gov/mxp/home.hm) for he period 985 presen. 7
We creae an aggregae measure of he relaive prices of goods produced in he U.S. relaive o is rading parners using geomeric rade weighs, ( ) 40 = = w k M m w k : where w k are averaged over n quarers and lagged by k quarers o eliminae endogeneiy issues. The markup does no conain any discernable secular drifs alhough i exhibis somewha persisen swings over he period 980:Q 2005:Q4, as shown in Figure. The markup is measured by he logarihm of he rade-weighed index of he relaive prices: ha is, μ = ln( M ). An augmened Dickey-Fuller es wih an inercep and four lags reecs he hypohesis of a uni roo in he series a he 5 percen level. The sandard deviaion of his series is abou 4. percen. Wide swings in his figure roughly correspond o flucuaions in he dollar. When he dollar is srong in he early 980s and near he urn of he millennium, his markup is also high. This indicaes ha impor prices are no as low as migh be expeced given he srong value of he dollar. In he mid-980s and in recen periods, he markup has been low, indicaing ha impor prices have no risen o he same degree ha he dollar has fallen. We consruc aggregae measures of foreign inflaion as weighed averages of he counry-by-counry inflaion. The impor-weighed average of foreign inflaion is given by PPI 40 = w k Δln( PPI ). Figure 2 shows he behavior of U.S. impor price inflaion = (measured in U.S. dollars) and he (weighed) inflaion of domesic producion of U.S. rading parners (measured in foreign currency). Boh were relaively high in he lae 980s and fell during he 990s. During relaively long periods of he early and lae 980s and he 990s, U.S. impor price inflaion was consisenly below foreign domesic inflaion. Similarly, we consruc aggregae measures of foreign ineres raes and exchange rae depreciaion as weighed averages of he counry-by-counry variables. The impor-weighed exchange rae appreciaion of he U.S. dollar is foreign ineres raes are i * 40 = = w k i ds 40 = w ln( k Δ S ) ; and impor-weighed = (see Appendix D for deails on foreign ineres raes). 8
Figure. The Trade-Weighed Index of he Relaive Prices.24.20.6.2.08.04.00 80 82 84 86 88 90 92 94 96 98 00 02 04 Noes: This figure depics he logarihm of he rade-weighed index of he relaive prices (µ ) for he period 980:Q 2005:Q4..06.05.04 Figure 2. U.S. Impor Price Inflaion and Foreign PPI Inflaion Foreign PPI Inflaion.03.02.0.00 -.0 -.02 -.03 U.S. Impor Price Inflaion 80 82 84 86 88 90 92 94 96 98 00 02 04 Noes: This figure compares inflaion in he U.S. impor price for manufacured goods wih rade weighed foreign producer price inflaion for he period 980:Q 2005:Q4. 9
IV. THE ESTIMATED RESULTS A. Defining Exchange Rae Pass-hrough The sandard exchange rae pass-hrough lieraure ypically regresses impor price inflaion or possibly CPI inflaion on changes in he exchange rae and some variables mean o conrol for he marginal cos of producion along wih lags (for example, Yang 997; Smes and Wouers, 2002; Campa and Goldberg, 2005; and Farugee, 2006). The rae of exchange rae passhrough can hen be measured as a funcion of he dynamic correlaion of exchange rae changes and domesic inflaion a differen horizons. Exising sudies sugges cross-secional differences on exchange rae pass-hrough, which depends on price seing behavior (for example, Dornbusch, 987; Kneer, 993; Devereux, Engel, and Sorgaard, 2004) or concern abou marke share (Froo and Klemperer, 989). We define exchange rae pass-hrough in a slighly differen way as deermined by he model. In he conex of an LCP model, he speed wih which exchange rae changes begin o affec impor prices depends in par on he frequency of price changes by firms. However, he degree o which firms change prices also depends on heir expecaions of he fuure dynamics of he exchange rae because hey are also forward-looking agens. From his perspecive, sandard esimaes of he exchange rae pass-hrough are subec o he Lucas criique: ha is, hey are no parameers ha policy-makers can ake as invarian o changes in exchange rae policy. We will describe exchange rae pass-hrough as being represened by a srucural parameer. We consider he degree of pass-hrough as he fracion of firms ha change heir prices in response o exchange rae pass-hrough, (-ν). A horizon, he fracion of firms ha have no adused prices will be (-ν ). B. Specificaion and Benchmark Regressions The heory implies a raional expecaions model of he form: IPI IPI PPI PPI = α0 + E αμ + α 2 + + α 3 αα 2 3 + (4) 0
where coefficiens α, α2, α 3 > 0 are funcions of he subecive discoun facor and he srucural ( ν )( βν ) parameers of price seing. Specifically, α =, α2 = β, and v ( ν )( βν ) κ α3 = ν ( κ)( βκ). Coefficienα represens he effec of exchange rae pass- hrough. The smaller isα, he slower is exchange rae pass-hrough: ha is, an increase in he producer price relaive o he impor price lead o a smaller curren increase in impor inflaion as α declines. Also, a measure of α 3< indicaes ha exchange rae pass-hrough is slower han foreign counries domesic price adusmen. We esimae he above model wih he GMM mehod. Our benchmark insrumen se includes conemporaneous impor inflaion, inflaion, PPI IPI ; conemporaneous foreign producer price IPI PPI ; along wih 4 lags of,, he markup ( μ ), he appreciaion rae of he U.S. dollar (ds ), he foreign ineres rae ( i * ), and he U.S. Federal funds rae. This insrumen lis explois he fac ha he predeermined price level is known by price seers and is hus in he informaion se a ime -. We use a one-sep Newey-Wes esimaor of he covariance marix consruced wih pre-whiened residuals. IPI The esimaed resuls of regression (4) are repored in Table. The coefficiens on μ and + ( α andα 2 ) are posiive and significan a he percen level. This allows us o consruc esimaes of he srucural parameers v and β. The esimae of he subecive discoun facor, β =.4, is wihin a sandard deviaion of is sandard esimae (say, β = 0.99 ) a a quarerly frequency. The esimae of he probabiliy of no impor price adusmen, ν = 0.754, is consisen wih price changes of impors occurring on average once per year. This is similar o esimaes of Galí and Gerler (999), as o he adusmen of domesic prices in he U.S. However, he esimae of α 3 is negaive and insignifican which makes i impossible o develop a parameer esimae of foreign price sickiness, κ. The insignificance of α 3 suggess no evidence of pass-hrough of foreign marginal cos ino U.S. impor prices. The Hansen s J-saisic es of he overidenificaion condiions of he model, which are no reeced a he 0 percen level, suggess ha our insrumens are valid.
Table. Esimaion Resuls of he Pass-Through Effec Model A. Benchmark Parameers α α 2 α 3 ν κ β J-Tes 0.069 ***.4 *** 0.033 0.754 ***.4 *** 8.5 (0.024) (0.04) (0.38) (0.09) (0.04) [0.53] Wald Tes: α4 = α2 α3 0.98 [0.657] B. No Curren Informaion: drop conemporaneous Parameers α α 2 α 3 ν κ β J-Tes 0.078 *** 0.988 *** 0.099 *** 0.785 *** 0.988 *** 8.06 (0.027) (0.20) (0.78) (0.08) (0.20) [0.385] IPI and Wald Tes: α4 = α2 α3.295 [0.255] PPI C. Full Curren Informaion: add conemporaneous μ, ds, i *, and Parameers α α 2 α 3 ν κ β J-Tes 0.050 *** 0.555 *** 0.23 *** 0.95 *** 0.763 *** 0.555 *** 20.87 (0.08) (0.082) (0.065) (0.05) (0.055) (0.082) [0.589] Wald Tes: α4 = α2 α3 0.368 [0.07] D. Only Included Insrumens: drop all lags of μ, ds, i *, and i FF Parameers α α 2 α 3 ν κ β J-Tes 0.059 *.339 *** 0.32 0.682 ***.339 *** 9.33 (0.035) (0.82) (0.367) (0.057) (0.82) [0.968] Wald Tes: α4 = α2 α3 0.004 [0.949] E. Shor Lis Insrumens: include only wo lags of all insrumens Parameers α α 2 α 3 ν κ β J-Tes 0.072 ***.72 *** 0.39 0.73 ***.72 *** 3.49 * (0.036) (0.29) (0.287) (0.034) (0.29) [0.06] Wald Tes: α4 = α2 α3 0.635 [0.425] F. Two-Sage Leas Squares Mehod Parameers α α 2 α 3 ν κ β 0.076 *.060 *** 0.049 0.765 ***.060 *** (0.042) (0.208) (0.342) (0.040) (0.208) Wald Tes: α4 = α2 α3 0.427 [0.53] Noes: This able shows he GMM esimaion resuls of a srucural model given by equaion (4) for 980:Q 2005:Q4 using differen ses of insrumens. The benchmark insrumen se includes conemporaneous impor IPI PPI IPI PPI inflaion, ; conemporaneous foreign producer price inflaion, ; along wih 4 lags of,, he markup ( μ ), he appreciaion rae of he U.S. dollar (ds ), he foreign ineres rae ( i * ), and he U.S. Federal funds rae. We are able o calculae a real esimae of κ only in he case where he esimae of α 3 > 0 (ha is, panel C). Adusmens were made o he benchmark insrumen se for panels B E as indicaed above. The J-es is Hansen s overidenificaion es for all insrumens (wih p-values in square brackes) which is only valid for opimal GMM. The Wald es is a parameer resricion es for he null hypohesis ha α4 = α2 α3 (wih p-values in square brackes). Sandard errors are repored in parenheses. In panel F, he benchmark insrumen se is used, and Newey-Wes correced sandard errors are repored in parenheses. ***, **, and * indicae significance a he %, 5%, and 0% levels, respecively. FF i 2
C. Robusness Checks: Esimaion Mehods We also repor esimaed resuls under slighly differen assumpions on he informaion se o check for robusness. Panel B shows he esimaed model afer dropping conemporaneous informaion on IPI PPI and from he lis of insrumens. The resuls are very similar o he baseline resuls. In panel C, we show he resuls when we use conemporaneous informaion abou all insrumens in our lis. This generaes some srikingly differen resuls. Firs, all of he parameers of he model are posiive and significan a he percen level. Crucially, his allows us o find an esimae of he degree of foreign price sickiness, κ, and indicaes ha foreign PPI inflaion can conrol for foreign marginal cos. Here, he esimae of he degree of price sickiness of impors is ν = 0.95 indicaing impor prices change on average every 0 quarers. The esimae degree of price sickiness in he foreign domesic price seing is very reasonably esimaed aκ = 0.786, consisen wih price changes every 4 5 quarers. However, he esimae of he subecive discoun facor is β 0.56 is very small for a quarerly discoun rae and he hypohesis ha β = 0.99 can easily be reeced a any reasonable criical value. The bias in he esimae of β makes us somewha skepical of his specificaion. Panel D repors he esimaion resul when we se he insrumen lis o include only hose variables which acually appear in he equaion (conemporaneous levels of lags of, IPI IPI PPI and and PPI, and μ ). Here, he coefficien esimaes are similar o hose in he Benchmark resuls wih he frequency of impor price changes esimaed a 3 4 quarers. The sandard errors are larger when fewer insrumens are used. We, again, canno find evidence ha foreign inflaion is conneced o impor price inflaion in his specificaion. Panel E shows esimaes when only 2 lags of each insrumen (along wih conemporaneous levels of and PPI ). Here, he esimaes again are very similar o he Benchmark esimaes. Disurbingly, he J-es of he overidenifying assumpions is reeced a he 0 percen level. Lasly, panel F shows he 2SLS esimaes using he benchmark insrumen se (wih Newey-Wes correced sandard errors) which are again similar o he GMM esimaes in Panel A. IPI 3
D. Robusness Checks: Alernae Specificaions Table 2 repors esimaion resuls wih some alernaive specificaions of he model. The chief problem wih he Benchmark specificaion is ha he dynamics of foreign inflaion seem unrelaed wih U.S. impor price inflaion. One poenial reason is ha wih coefficien α2 being esimaed as so close o one, he foreign price inflaion series appears in near firs difference form. We relax he resricions on he parameer on fuure foreign producer price inflaion in he saisical model IPI IPI PPI PPI = α0 + E αμ + α 2 + + α 3 α 4 + (5) The resuls are repored in panel A of Table 2. Relaxing he consrain haα4 = α2 α3 does no change our main resuls. Boh α3andα 4 are saisically insignifican, indicaing lile relaionship beween foreign producer price inflaion and domesic impor inflaion, eiher conemporaneously or wih a lead. The relaxaion of he consrain does no have a srong effec on he oher variables we measure. In fac, a Wald es of he hypohesis α4 = α2 α3is no reeced a he 0 percen level. To furher es he model, we esimae a modified version of he benchmark model by including a lagged erm of foreign producer price inflaion. IPI IPI PPI PPI PPI = α0 + E αμ + α2+ + α3 α2 α3 + + α5. (6) Panel B repors he resuls of he GMM esimaion of equaion (6). The esimaed coefficien on lagged foreign producer price inflaion is near 0 and is saisically insignifican. Apparenly, here is lile connecion beween foreign price inflaion and he impor price inflaion a leads or lags. We also see ha he inclusion of he lagged erm changes lile abou he oher benchmark resuls: α and α 2 are boh significanly posiive and consisen wih an average frequency of price change of abou one year and an economically reasonable subecive discoun facor. 4
Table 2. Esimaing he Pass-hrough Effec Model: Alernaive Specificaions A. Equaion (5): unresriced coefficien on PPI + Parameers α α 2 α 3 α 4 J-Tes 0.069 ***.087 *** 0.032 0.064 8.65 (0.024) (0.08) (0.4) (0.83) [0.42] B. Equaion (6): wih a lagged PPI inflaion, PPI Parameers α α 2 α 3 α 5 J-Tes 0.072 ***.086 *** 0.056 0.024 7.72 (0.023) (0.05) (0.45) (0.057) [0.474] C. Equaion (7): wih a backward-looking erm, IPI Parameers α α 2 α 3 α 6 J-Tes 0.072 ***.05 *** 0.076 0.075 8.39 (0.022) (0.) (0.25) (0.060) [0.430] κ ( κ)( βκ) = 2 D. Equaion (8): imposing [ ] Parameers α α 2 J-Tes 0.05.29 *** 8.2 (0.00) (0.06) [0.573] κ ( κ)( βκ) = 2 ; α α8 Parameers α α 2 α 8 J-Tes 0.069 ***.4 *** 0.003 8.5 (0.024) (0.04) (0.0) [0.53] E. Equaion (9): imposing [ ] Noes: This able shows he GMM esimaion resuls of a srucural model given by equaion (4) for 980:Q IPI 2005:Q4. In all panels, he insrumen se includes conemporaneous impor inflaion, ; conemporaneous foreign PPI IPI PPI producer price inflaion, ; along wih 4 lags of,, he markup ( μ ), he appreciaion rae of he U.S. dollar (ds ), he foreign ineres rae ( i * ), and he U.S. Federal funds rae. The J-sa is Hansen s overidenificaion es for all insrumens (wih p-values in square brackes). Sandard errors are repored in parenheses. ***, **, and * indicae significance a he %, 5%, and 0% levels, respecively. As a more general check, we also esimae a hybrid pass-hrough effec model wih forward- and backward-looking expecaions given by IPI IPI PPI PPI IPI = α0 + E αμ + α2+ + α3 α2 α3 + + α6 (7) This equaion is analogous o a hybrid New Keynesian Phillips curve à la Galí, Gerler, and Lopez-Salido (2005), which ness he pure forward-looking model as a special case. As shown in panel C, we find no evidence ha he lagged variable eners significanly. The inclusion changes neiher he basic resul ha α and α 2 are boh posiive and saisically significan nor he esimae of he frequency of impor price changes. 5
To assess wheher our resuls are biased by he lack of significance of he foreign producer price inflaion erm, we re-esimae he model afer calibraing he erm κ =2, which would be consisen wih κ =0.75 and β =. The regression will hen ( κ)( βκ) be of he form: IPI IPI 0 2 2 PPI 2 2 PPI = α + E α μ + α + + α α α + (8) We repor he resuls in panel D. The esimae of ν is close o he benchmark level wih a fairly narrow sandard error. However, he coefficien α is very small and only marginally significan. This model, by imposing he consrain ha foreign producer price inflaion passes hrough ino impor price inflaion proporionaely o he markup of impor prices over he PCP price, resuls in a very low level of exchange rae pass-hrough. Furher, we can reec he hypohesis ha β =0.99 a he 5 percen level. Panel E repors he resuls from a specificaion ha relaxes he assumpion ha foreign producer price inflaion passes hrough ino impor price inflaion a he same rae as exchange raes. We esimae he specificaion IPI IPI 0 2 8 2 PPI 2 8 2 PPI = α + E α μ + α + + α α α + (9) No surprisingly, afer dropping he proporional assumpion we reurn o our benchmark resuls in erms of α and α 2 bu find a negaive esimae ofα 8. The hypohesis ha α = α 8 was easily reeced a he 5 percen level, suggesing ha he impac on domesic impor inflaion of foreign price inflaion appears o be quie differen from ha of he nominal exchange rae. We view he negaive esimae of he coefficien on foreign inflaion in LCP models (Tables and 2) as a resul of ignoring he role of PCP firms. In he following subsecions, he coefficien esimaes on foreign inflaion become posiive (and ofen significan) in he mix of LCP and PCP models, which enables us o repor significan esimaes of srucural parameers. 6
E. Pass-hrough Effec Model wih A Mix of LCP and PCP The above models assume ha all firms exporing o he U.S. adus heir U.S. dollar prices infrequenly and opimally according o he local currency pricing (LCP) pass-hrough heory. We relax his assumpion by modeling a world in which some fracion of firms (ha is, PCP firms) price heir goods in heir home currency based on changes in aggregae prices. In producer currency pricing (PCP), firms have sicky prices in heir own currency while heir invoice prices in U.S. dollar adus auomaically as exchange raes change. We assume ha a fracion, λ, of firms se prices in heir home currency and pass on he prices ino impor goods wih a one-period lag. = ds IPI, PCP PPI We assume ha hese firms are randomly disribued and heir home prices adus he same as oher firms. For he LCP firms, we model he inflaion in he sandard way IPI, LCP IPI, LCP PPI PPI = α0 + E αμ + α 2 + + α 3 α2 α 3 + (0) IPI IPI, PCP IPI, LCP Toal impor price inflaion can be wrien as = λ + ( λ). { 0 E 2 + 3 2 3 + } = λ + ( λ) α + α μ + α + α α α IPI IPI, PCP IPI, LCP PPI PPI λ = λ + λ α + αμ + α + α α α ( λ) IPI IPI, PCP IPI, PCP + PPI PPI ( ) 0 E 2 3 2 3 + IPI, PCP, = λ + α2e IPI + λ IPI PCP ( ) { PPI PPI + + λ α0 + E αμ + α 3 α2 α 3 + } () IPI, PCP PPI where = ds. We esimae equaion () wih GMM using he benchmark se of insrumens and repor he resuls in Table 3 (panel A). 7
The fracion of firms ha operae as PCP firms is esimaed as very small as indicaed by he λ esimae, which is abou 6 percen and significan a he percen level. 7 The inclusion of he IPI, PCP IPI, PCP and + erms has lile effec on he esimaes of α and α 2, which are sill consisen wih an economically reasonable subecive discoun facor and impor price changes wih a frequency beween 4 and 5 quarers. The coefficien on foreign price inflaion, α 3, is posiive bu no significan. We are able o esimae a parameer of probabiliy of foreign producer price sickiness of κ 0.4 alhough is sandard errors are so large ha i is no saisically differen from 0 or. F. Pass-hrough Declining? Much of he recen lieraure has focused on wheher exchange rae pass-hrough has slowed down. To check his hypohesis, we spli he sample in wo pars, one running hrough 99 and he oher from 992 o 2005. Given he relaive success of he model wih parial producer currency pricing, we esimae equaion () for each of he wo sub-samples by GMM wih conemporaneous measures of IPI and owing o he shorness of he sample period. PPI and only wo lags of each of he insrumens In boh sub-samples, we find considerably more evidence for he pass-hrough of foreign price inflaion ino U.S. impor inflaion as shown by posiive esimaes of α 3. Panel B in Table 3 shows he parameers from he regression for 980 99. The esimaes of α and α 2 are boh posiive and of a size consisen wih he benchmark regressions. The esimaed frequency of impor price changes is on average once per 5 quarers. The average frequency of foreign producer price changes is esimaed a around once per 4 quarers. Ineresingly, in his period, he fracion of PCP firms is near zero ( λ =0.029), and we canno saisically reec he hypohesis ha λ =0 a he 0 percen level. 7 Gopinah, Iskhoki, and Rigobon (2007) examine disaggregaed micro daa and find ha foreign firms ha se heir impor prices in dollars experience very slow pass-hrough while firms ha se heir prices in oher currency experience very quick pass-hrough. 8
In he 992 2005 period (panel C), we esimae a frequency of impor price change ha is slower by abou a quarer han ha during he earlier sample period: price changes occurring on average abou once per 6 quarers. I should be noed ha he esimae of he frequency of price changes, ν, in he firs period is wihin he single sandard error confidence range of he laer period esimae. Furher, we find a much larger fracion of PCP firms, as suggesed by he λ esimae of 3.5 percen. A larger fracion of producer currency pricing firms migh offse he impac of slower price changing. In boh sub-samples, he esimae of he subecive discoun facor is wihin a sandard error of an economically reasonable number. I should be noed ha he model resrics he daa along a number of dimensions, and in he laer sample period he overidenifying resricions are marginally reeced a he 0 percen level. An ineresing finding is ha he esimae of he speed of foreign price changes is much more precisely esimaed in each of he sub-samples han in he whole sample. One possible explanaion is ha srucural changes in foreign moneary policy allow for more reliable relaionships beween he insrumens and fuure inflaion in he sub-samples han in he whole sample. We find ha in each sub-sample, he speed of foreign price changes is significan a he percen level and similar in size o ypical esimaes of price change frequency using he New Keynesian Philips curve lieraure (see Galí, Gerler, and Lopez-Salido, 2005). We find some evidence for diminishing pass-hrough. Firs, he direc effec of exchange rae pass hrough (measured by α ) declined from 8 percen o small and insignifican size of 2 percen. Second, he effec of foreign price inflaion on impor price inflaion (measured by α 3) decreased slighly, reflecing ha he frequency of price changes by U.S. imporers declined more han ha of foreign producers did. Third, he increased fracion of PCP firms (measured by λ ) from a small and insignifican level o he 3.5 percen, however, offse he declining passhrough owing o he firs wo facors. 9
Table 3. Esimaing he Pass-hrough Effec Model: A Mix of LCP and PCP A. Full Sample 980:Q 2005:Q4 Coefficien Esimaes α α 2 α 3 J-es 0.067 ***.032 *** 0.036 6.40 (0.023) (0.9) (0.27) [0.565] Srucural Parameers ν κ β λ 0.784 *** 0.420.032 *** 0.066 *** (0.023) (0.432) (0.9) (0.08) B. Sub-Sample 980:Q 99:Q4 Coefficien Esimaes α α 2 α 3 J-es 0.080 * 0.945 *** 0.609 9.65 (0.049) (0.277) (0.45) [0.40] Srucural Parameers ν κ β λ 0.796 *** 0.749 *** 0.945 *** 0.029 (0.052) (0.060) (0.277) (0.050) C. Sub-Sample 992:Q 2005:Q4 Coefficien Esimaes α α 2 α 3 J-es 0.024.069 *** 0.534 *** 0.67 (0.08) (0.04) (0.34) [0.099] Srucural Parameers ν κ β λ 0.839 *** 0.802 ***.069 *** 0.35 *** (0.047) (0.053) (0.04) (0.08) Noes: This able repors he GMM esimaion resuls of a pass-hrough model wih a mix of local currency pricing (LCP) and producer currency pricing (PCP), srucural equaion () for differen sample periods. For he full sample, he benchmark insrumen se is used. For he sub-sample regressions (panels B and C), we use conemporaneous measures of IPI and PPI and only wo lags (raher han four lags) of each of he variables included in he benchmark insrumen lis. The J-es is Hansen s overidenificaion es for all insrumens (wih p-values in square brackes). Sandard errors are repored in parenheses. ***, **, and * indicae significance a he %, 5%, and 0% levels, respecively. G. Regional Models and Counry-Specific Expors The BLS collecs impor price indices a finer levels of aggregaion based on he locaion of he originaing counry. From 99, BLS has repored impor price indices for manufacured goods from indusrial counries and from developing counries. We sub-divide our lis of 40 counries ino wo groups and consruc aggregaes of foreign producer prices, foreign ineres 20
raes and exchange raes ha correspond o each counry group. 8 Table 4 repors he esimaed resuls of a mix of LCP and PCP model for boh counry groups. Noe ha he source for he impor prices in his able (he BLS) is differen from ha for he previous impor prices (a splice of OECD and BLS daa). Again, owing o he shorness of he sample period, all regressions are esimaed wih conemporaneous IPI and PPI and 2 lags of each of he insrumens. In panel A, we repor he resuls for he indusrial counries. All parameer esimaes are significan a he percen level includingα 3, he coefficien on foreign producer price inflaion. The esimae of he subecive discoun facor is low compared o sandard esimaes, and he hypohesis ha β =0.99 can be reeced a he 5 percen level. The coefficien on he markup of impor prices over he PCP price ( α ) is low alhough precisely esimaed. Accordingly, he price sickiness is exreme, wih he probabiliy of boh impor prices and foreign prices remaining fixed in any given quarer above 0.9, while a subsanial fracion of firms ac according o PCP wih λ 6 percen. The overidenifying resricions are reeced a he 0 percen level. Among he developing counries, price sickiness is even more exreme. In his sample, he coefficien on he markup erm ( α ) is negaive indicaing no convergence of impor prices o he PCP price. As a resul, we canno esimae a parameer of price sickiness. We also find a very small (6.9 percen), bu saisically significan, fracion of manufacuring impors are se according o PCP in developing counries. Finally, we esimae he parial PCP model for manufacuring impors from Canada and Japan. The BLS produces impor price series for goods from hese counries, again beginning in 99. Since his exercise involves daa from a single counry, we do no need o aggregae prices, exchange raes, or ineres raes over counries. The resuls are repored in panels C and D of Table 4. We find very similar resuls for boh counries: (i) very low and saisically insignifican coefficiens on he markup of impor prices over marginal cos are accompanied by 8 The indusrial counry group comprises Ausralia, Ausria, Belgium, Canada, Hong Kong SAR, Denmark, Finland, France, Germany, Ireland, Ialy, Japan, Korea, Neherlands, New Zealand, Norway, Porugal, Singapore, Souh Africa, Spain, Sweden, Swizerland, Taiwan, and he Unied Kingdom. The developing counry group is confined o Brazil, Chile, China, Colombia, Cosa Rica, India, Indonesia, Israel, Malaysia, Mexico, Peru, Philippines, Poland, Russia, Thailand, and Turkey, considering heir shares in U.S. impors. 2
Table 4. Regional Pass-hrough Effec Models: A Mix of LCP and PCP A. Indusrial Counries Coefficien Esimaes α α 2 α 3 J-es 0.023 *** 0.642 *** 0.507 ***.55 * (0.007) (0.30) (0.098) [0.073] Srucural Parameers ν κ β λ 0.947 *** 0.90 *** 0.642 *** 0.64 *** (0.00) (0.02) (0.30) (0.04) B. Developing Counries Coefficien Esimaes α α 2 α 3 J-es 0.003. *** 0.569 *** 7.84 (0.0) (0.094) (0.086) [0.25] Srucural Parameers ν κ β λ. *** 0.069 *** (0.094) (0.07) C. Canada Coefficien Esimaes α α 2 α 3 J-es 0.003.28 *** 0.400 *** 0.35 (0.07) (0.7) (0.066) [0.] Srucural Parameers ν κ β λ 0.872 *** 0.855 ***.28 *** 0.075 *** (0.060) (0.0) (0.7) (0.026) D. Japan Coefficien Esimaes α α 2 α 3 J-es 0.02 0.969 *** 0.29 9.00 (0.02) (0.46) (0.240) [0.74] Srucural Parameers ν κ β λ 0.92 *** 0.84 *** 0.969 *** 0.073 *** (0.033) (0.083) (0.46) (0.008) Noes: This able repors he GMM esimaion resuls of a pass-hrough model wih a mix of local currency pricing (LCP) and producer currency pricing (PCP), equaion (), for he indusrial and he developing counry groups in panels A and B, respecively. Panels C and D show he GMM esimaion resuls of he model for manufacuring impors from Canada and Japan, respecively. In all regressions, we use conemporaneous measures of IPI and PPI and only wo lags of each of he variables included in he benchmark insrumen lis. The J-es is Hansen s overidenificaion es for all insrumens (wih p-values in square brackes). Sandard errors are repored in parenheses. ***, **, and * indicae significance a he %, 5%, and 0% levels, respecively. 22
fairly sluggish impor prices (wih v being close o 0.9): he average price change frequency is abou 0 quarers; (ii) posiive esimaes of he impac of foreign producer prices on impor inflaion ( α 3) render foreign price adusmen subsanially sluggish (wih κ around 0.85); (iii) a small bu saisically significan fracion of firms (around 7 percen) follow producer currency pricing; and (iv) he esimaed subecive discoun facor is no significanly differen from he sandard esimae ( β =0.99). V. CONCLUDING REMARKS In his paper, we esimae a srucural parameer ha is crucial for deermining he effeciveness of exchange rae policy: he frequency wih which sicky-price firms are able o change prices in response o changes in exchange raes or marginal coss. Our esimae of passhrough effec of abou 7 percen per quarer suggess ha a depreciaion of he U.S. dollar would no increase he U.S. impor price in dollars subsanively. We also find ha he sickiness of impor prices is slighly increased over ime bu he increase is neiher sizable nor significan. As noed by Taylor (2000), here exiss a poenial complemenariy beween moneary sabiliy and policy effeciveness. Since price seing and pass-hrough effecs could be endogenous (Devereux and Yeman, 2003; Devereux, Engel, and Sorgaard, 2004), higher exchange rae volailiy could induce an increase in impor price pass-hrough by reducing domesic price ineria. 9 Tha is, higher exchange rae volailiy reduces moneary sabiliy bu increases impor price pass-hrough effecs. Pass-hrough effecs in he U.S. would be more suscepible o a change in exchange rae volailiy because our findings provide evidence on forward-looking expecaions in he deerminaion of pass-hrough effecs. We acknowledge ha our pass-hrough effec models based on he opimizaion framework wih he New Keynesian Phillips curve rea he impor price seing parameer (v) as a ime-invarian, deep parameer, bu 9 If local currency pricing remains o hold for some reasons (for example, concern abou marke share), however, large and frequen exchange rae changes may resul in increased exchange rae volailiy wihou curving impor demand pressures since local currency pricing eliminaes he pass-hrough from changes in exchange raes o consumer prices (Devereux and Engel, 2002). 23
his parameer iself could be chosen endogenously for opimizaion when he degree of moneary sabiliy could vary. 24
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