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1 ISSN Working Paper Series Nonlinear Mechanisms of he Exchange Rae Pass-Through: A Phillips curve model wih hreshold for Brazil Arnildo da Silva Correa and André Minella November, 006

2 ISSN CGC / Working Paper Series Brasília N. Nov 006 P. -30

3 Working Paper Series Edied by Research Deparmen (Depep) Edior: Benjamin Miranda Tabak Ediorial Assisen: Jane Sofia Moia Head of Research Deparmen: Carlos Hamilon Vasconcelos Araújo The Banco Cenral do Brasil Working Papers are all evaluaed in double blind referee process. Reproducion is permied only if source is saed as follows: Working Paper n.. Auhorized by Afonso San Anna Bevilaqua, Depuy Governor of Economic Policy. General Conrol of Publicaions Banco Cenral do Brasil Secre/Surel/Dimep SBS Quadra 3 Bloco B Edifício-Sede M Caixa Posal Brasília DF Brazil Phones: (556) and Fax: (556) The views expressed in his work are hose of he auhors and do no necessarily reflec hose of he Banco Cenral or is members. Alhough hese Working Papers ofen represen preliminary work, ciaion of source is required when used or reproduced. As opiniões expressas nese rabalho são exclusivamene do(s) auor(es) e não refleem, necessariamene, a visão do Banco Cenral do Brasil. Ainda que ese arigo represene rabalho preliminar, ciação da fone é requerida mesmo quando reproduzido parcialmene. Consumer Complains and Public Enquiries Cener Address: Secre/Surel/Diae Edifício-Sede º subsolo SBS Quadra 3 Zona Cenral Brasília DF Brazil Fax: (556) Inerne: hp://www.bcb.gov.br/?english

4 Nonlinear Mechanisms of he Exchange Rae Pass-Through: A Phillips curve model wih hreshold for Brazil * Arnildo da Silva Correa ** André Minella ** The Working Papers should no be repored as represening he views of he Banco Cenral do Brasil. The views expressed in he papers are hose of he auhor(s) and do no necessarily reflec hose of he Banco Cenral do Brasil. Absrac This paper invesigaes he presence of nonlinear mechanisms of pass-hrough from he exchange rae o inflaion in Brazil. In paricular, i esimaes a Phillips curve wih a hreshold for he pass-hrough. The paper examines wheher he shor-run magniude of he pass-hrough is affeced by he business cycle, direcion and magniude of exchange rae changes, and exchange rae volailiy. The resuls indicae ha he shor-run pass-hrough is higher when he economy is growing faser, when he exchange rae depreciaes above some hreshold and when exchange rae volailiy is lower. These resuls have imporan implicaions for moneary policy and are possibly relaed o pricing-o-marke behavior, menu coss of price adjusmen and uncerainy abou he degree of persisence in exchange rae movemens. Keywords: Exchange Rae Pass-Through, Threshold, Inflaion, Nonlineariy, Brazil JE Classificaion: E3, E50, E58 * We are hankful o Fabio Araújo and Tomiê Sugahara for heir paricipaion in iniial esimaions, Carlos Hamilon Araújo, Ana Beariz Galvão and Marcelo Kfoury Muinhos for suggesions, Érica Oliveira and Ibiisan Sanos for assisance wih daa, and ohers colleagues a he Research Deparmen of he Cenral Bank of Brazil for heir conribuions and commens. The views herein are hose of he auhors and do no necessarily reflec hose of he Cenral Bank of Brazil. ** Research Deparmen, Cenral Bank of Brazil. s: and 3

5 . Inroducion The presence of nonlineariies in he Phillips curve has relevan implicaions for moneary policy. The slope of he Phillips curve measuring he response of inflaion o oupu gap affecs direcly he cos of disinflaion. Schaling (004) shows ha, when he Phillips curve is convex, ha is, he sensiiviy of inflaion o economic aciviy increases wih he level of oupu, he opimal moneary policy reacion funcion is asymmeric. Nonlineariy may also be presen in he pass-hrough from exchange rae changes o prices. If he pass-hrough, for insance, is greaer when he economy is booming, we may consider ha he cenral banks reacion o a depreciaion of he domesic currency will be sronger in his conex. In fac, he invesigaion of he presence of nonlinear mechanisms in he Phillips curve has been an imporan opic in he recen lieraure. Mos sudies on nonlinear Phillips curves for developed economies have focused on he slope of he Phillips curve and he exchange rae pass-hrough. In he firs case, axon, Rose and Tambakis (999) and Bean (000) find evidence ha he Phillips curve is convex, while Sigliz (997) and Eisner (997) claim ha he Phillips curve is concave. The lieraure on exchange rae pass-hrough, in urn, repors several sources of nonlineariy, indicaing ha he degree of pass-hrough can be relaed o some macroeconomic variable, including he exchange rae. Mann (986), Goldberg (995), Gil-Pareja (000), Mahdavi (00) and Olivei (00) have found asymmeric pass-hrough relaed o he direcion of exchange rae changes, while Ohno (989) and Pollard and Coughlin (004) have indicaed he presence of asymmery associaed wih he magniude of exchange rae changes. The business cycle is also poined ou as an imporan source of nonlineariy for he pass-hrough. The ransmission of exchange rae depreciaions o domesic prices would be lower during an economic slowdown. Goldfajn and Werlang (000), esimaing a panel daa model for 7 counries, have found ha depreciaions have a higher pass-hrough o prices when he economy is booming. In he case of Brazil, Carneiro, Moneiro and Wu See, for insance, Chadha, Masson and Meredih (99), axon, Meredih and Rose (995), Dupasquier and Rickes (998), Nobay and Pell (000), Aguiar and Marins (00), Tambakis (999), and Clemens and Sensier (003). 4

6 (00) have found similar resuls esimaing a backward-looking Phillips curve wih he pass-hrough coefficien as a funcion of unemploymen rae and real exchange rae level. 3 In hese papers, he magniude of he pass-hrough coefficien is a funcion of some variables. This paper invesigaes he possibiliy of a nonlinear pass-hrough in Brazil using hreshold models. These models are par of a class of models ha consider differen saes of naure or regimes and allow differen dynamic behavior for he variables, condiional on he regime prevailing in each momen (Franses and van Dijk, 000). In he case of hreshold models, he sample is divided ino classes based on wheher he value of an observed variable surpasses or no some hreshold. This kind of model Threshold Auoregressive (TAR) Model was iniially proposed by Tong (978) and Tong and im (980) and has spread in he recen applied economic lieraure. We focus on he pass-hrough because exchange rae movemens have played a key role in he inflaion dynamics in Brazil, especially in he early years of he inflaion argeing regime wih recurren bous of exchange rae depreciaion in response o shocks, in he conex of balance of paymens vulnerabiliies. We esimae hree specificaions for he Phillips curve, which differ basically by he variable used as he hreshold for he passhrough: i) oupu gap; ii) nominal exchange rae change; and iii) exchange rae volailiy. Thus, we can deal wih differen possible sources of nonlineariy. The firs quesion is wheher economic aciviy affecs he magniude of he pass-hrough. The second one is wheher he pass-hrough is symmeric wih respec o he direcion of he exchange rae change wheher appreciaions or depreciaions have symmeric effecs on prices and o he magniude of he exchange rae change. The esimaions indicae ha he shor-run pass-hrough is higher when he economy is growing faser, when he exchange rae depreciaes above a hreshold value and when exchange rae volailiy is lower. These resuls have implicaions for moneary policy and are possibly relaed o pricing-o-marke behavior, coss of changing prices, and uncerainy regarding he degree of persisence of exchange rae changes. Filardo (998), in urn, considers ha he Phillips curve is neiher enirely convex nor concave, bu a combinaion of boh (a concave-convex curve). 3 Muinhos (00) has found mixed resuls, and Bogdansky, Tombini and Werlang (000) work wih a model for Brazil wih a nonlinear pass-hrough as well. 5

7 The aricle is organized as follows. Secion ses forh he mehodology of hreshold models wih he presence of endogenous variables. Secion 3 presens he specificaions of he Phillips curve wih hreshold and he esimaion resuls. The las secion concludes he ex.. Threshold models wih endogenous variables In hreshold models, he sample is divided ino classes based on he value of an observed variable wheher i surpasses or no some hreshold. As usual in pracice, he hreshold is no known and needs o be esimaed. The simples model is he SETAR (Self- Exciing Threshold Auoregressive Model), where he hreshold is given by a lagged erm of he dependen variable y -d, where d>0. An AR() model of wo regimes and d= can be wrien as: φ0 + φ y + ε if y τ y =, () φ 0 + φ y + ε if y τ where is he hreshold value, j φ i are he parameers i of he regime j, and ε is an i.i.d. whie noise sequence condiional on he hisory of he series, denoed by Ω y,..., y, y }, wih zero mean and variance σ. Alernaively, his model can = { p p be expressed as: y = ( φ 0 + φ y )[ I ( y τ )] + ( φ0 + φ y ) I( y τ ) + ε, () where I(.) is an indicaor funcion ha akes a value equal o eiher one or zero, depending on he regime a ime. For hese models wih exogenous regressors, here is a well-developed heory of inference and esimaion 4. In he case of models wih endogenous variables, in urn, he heory is sill working in progress. Caner and Hansen (004) develop an esimaor and an 4 See, for example, Chan (993), Hansen (996, 999, 000) and Caner (00). 6

8 inference heory for his kind of model, wih he resricion ha he hreshold variable mus be exogenous. A model wih endogenous regressors can be described as follows. e n { y, z, x} = be he informaion se, where y is unidimensional, z is an m-dimension vecor (regressors), and x is a k-dimension vecor (insrumens), wih k 6DA variable q = q x ) can be an elemen or a funcion of he vecor x. In a general way, he ( srucural equaion can be wrien as: y = θz + ζ y = θ z + ζ q τ, (3) q τ or in a more compac way, y = θ ) + z[ I( q τ )] + θzi( q τ ζ, (4) where θ j are parameer vecors, τ Τ, and T is he se of he possible hreshold values. Since he error erm ζ is correlaed wih z a leas one variable in vecor z is endogenous equaion (4) canno be esimaed by ordinary leas squares (OS) because parameers would be biased and inconsisen. The mehod proposed by Caner and Hansen (004) is based on he esimaion of a reduced form equaion for he endogenous variables as a funcion of insrumenal variables, ha is, a model wih he condiional mean of he endogenous variables as a funcion of exogenous variables. The esimaed values are plugged ino srucural equaion (4) and he hreshold value is esimaed by minimizing he sum of he squared residuals. The parameers of he srucural equaion are esimaed in a hird sep, when he sample is divided according o he esimaed hreshold. The esimaion is conduced using he wosage leas square mehod (SS) or he generalized mehod of momens (GMM). Therefore, he firs sage (condiional expecaions model of z ) is given by: 7

9 z = f ( x, β ) + u, (5) E ( u x ) = 0, (6) where β is a vecor wih parameers, u is he error erm, and f (.,.) is a funcion. In paricular, his funcion can also be condiioned on he hreshold value (which can be equal or differen from ha in he srucural equaion): 5 f ( x, β) ( β x )[ I( q τ )] + ( β x )[ I( q )]. (7) = τ as: The parameer vecor β in equaion (5) can be obained by OS, for each T, n n β ( τ ) = [ ( τ )] x x I q x z[ I( q τ )], (8) = = n n β( τ ) = [ ( τ )] x x I q x z[ I( q τ )]. (9) = = Using parameers β, we can obain he values ẑ ha will replace z in he srucural equaion. Doing i recursively for every T, he hreshold value in he srucural equaion can be chosen by he minimizaion of he sum of he squared residuals, using a grid search. For every, le Y, Z and Z G denoe he vecor y and he marices z [ I( τ )] e z [ I( τ )], respecively. Thus, he hreshold esimaor is obained from: q q τ = arg min S ( τ ), (0) τ T n where S n (τ ) is he sum of he squared residuals in he regression of Y on Ẑ and Ẑ G. The se of hreshold values in (0) should be such ha each regime has sufficien observaions 5 In his paper, we do no condiion on he hreshold value in his firs sage. 8

10 9 o generae reliable parameer esimaion. According o Franses and van Dijk (999), a safe choice is a leas 5% of he sample. Given he esimaed hreshold value τ, he sample is divided ino subsamples, and parameers of equaion (0) can be esimaed by SS as: ( ) ( ) = Y Z Z Z θ, () ( ) ( ) = Y Z Z Z G G G G G G G G G G G θ, () where Ẑ, G Ẑ, e G sand for he marices wih observaions )] ( [ τ q I z, )] ( [ τ q I z, )] ( [ τ q I x and )] ( [ τ q I x, respecively. Caner and Hansen (004) show ha hose esimaors are consisen, alhough no necessarily efficien. Their applicabiliy is condiioned on he exogeneiy of he hreshold variable. 3. Phillips curve model for Brazil Aiming o es he possibiliy of he presence of a nonlinear pass-hrough from he exchange rae o inflaion, we esimae some Phillips curve models for Brazil combined wih he mehodology of regime swiching described in he previous secion. The esimaed Phillips curve relaes inflaion o a measure of real disequilibrium (oupu gap), inflaion expecaions, pas inflaion, exchange rae changes and exernal inflaion, wih a hreshold variable: Δ + + = Δ + + = + + τ ε α π α π α α π α π τ ε α π α π α α π α π q if y e E q if y e E 4 * 4 * ) ( ) ( ) ( ) (, (3) where j i α is he parameer of a specific regressor i when he economy is in regime j, π is free IPCA inflaion (headline inflaion measured by he Broad Naional Consumer Price

11 Index, bu excluding adminisered prices), π is headline IPCA inflaion, * π is a measure of exernal inflaion (PPI in he U.S.), y is oupu gap (acual minus poenial oupu) 6, e is he naural logarihm of he average nominal exchange rae (domesic currency unis per dollar), E (.) is he expecaions operaor condiional on he informaion available a, Δ is he difference operaor ( Δe = e e andτ T, where T is he se of possible values for q. ), ε is a residual, q is he hreshold variable, The dependen variable is he free prices componen of headline inflaion because adminisered prices have a differen price dynamics, parially obeying conrac rules. Noe ha he esimaed pass-hrough refers o he ransmission from exchange rae change in he previous quarer o he curren inflaion, ha is, i capures only he shor-run effec of exchange rae movemens. To enable he join esimaion, he previous equaions become: π * ( αeπ + + ( α α) π + α( Δe + π ) + α4 y )( I[ q τ ) * ( α Eπ + + ( α α ) π + α ( Δe + π ) + α4 y )( I[ q τ ) + ε = +. (4) Based on heoreical indicaions for a nonlinear exchange rae pass-hrough, we evaluae hree hreshold variables: i) business cycle, measured by he oupu gap; ii) magniude of nominal exchange rae changes; and iii) a measure of exchange rae volailiy. We use quarerly daa from 995: hrough 005:4 and esimae using SS, wih insrumenal variables for he inflaion expecaions erm. The firs esimaed specificaion has he oupu gap as he hreshold variable. In his model, all parameers, excep for ha of he oupu gap, are subjec o regime swiching. 7 The esimaion resuls are he following (p-values in parenheses): 6 The oupu gap used in he esimaion was generaed using a producion funcion model. See, for example, he box "Mehodologies for esimaing he poenial oupu" in Banco Cenral do Brasil (003) and Muinhos and Alves (003) for a descripion of he mehodology. 7 We do no allow he coefficien on oupu gap o change because we wan o capure nonlineariies in he pass-hrough. 0

12 π π * = 0.75E π π ( Δe + π ) + 0.4y if y.89% (0.00) (0.3) (0.78) (0.00) * = 0.58Eπ π ( Δe + π ) + 0.4y if y.89% (0.0) (0.) (0.03) (0.00) Sample period: 995: 005:4 Sandard errors esimaed using Newey-Wes consisen esimaors P-values in parenheses Impulse dummy variable for 999:: 0.0, p-value: 0.00 Insrumenal variables: cons., dummy variable, π, π, Δ * * e, Δe, π, π, y R-squared: 0.50 Adjused R-squared: 0.43 Breusch-Godfrey Serial Correlaion M es, p-values: lag: 0.54, 4 lags: 0.33 Whie Heeroskedasiciy Tes, p-value: 0.7 Jarque-Bera Normaliy Tes, p-value: 0.57 Wald es α =, p-value: 0.04 α According o he esimaion resuls, here is a nonlineariy in he pass-hrough erm relaed o he business cycle: he exchange rae pass-hrough is no saisically differen from zero in he regime when he economy is below he hreshold, whereas i is around 9% when economic aciviy is higher. According o he Wald es, we rejec he null ha he wo pass-hrough coefficiens are equal. The exchange rae pass-hrough is significanly greaer when oupu is above some hreshold 8, esimaed a.89% below he poenial oupu. This means ha, during an economic slowdown, an exchange rae variaion will have a smaller impac on domesic prices. This is usually poined as one of he facors ha limied he pass-hrough in Brazil during he 999 exchange rae crisis. One limiaion of his resul is is implicaion ha exchange rae appreciaions have a higher pass-hrough when he economy is booming han when he oupu gap is below he hreshold. The oher parameer esimaes are in line wih hose found in he lieraure using models wihou a hreshold variable. Excep for he backward-looking erm, all coefficiens are saisically significan a 5%. In addiion, he esimaed value for he hreshold splis he sample ino wo approximaely equal pars (9 observaions when y <. 89 %, and 5 when y. 89 %). This means ha, alhough he sample size is no large, none of he 8 This resul is in line wih hose in Goldfajn and Werlang (000), and Carneiro, Moneiro and Wu (00).

13 regimes was esimaed wih an exremely low number of observaions. 9 Acually, we have ried several specificaions, using differen insrumens for he expecaions erm, and he resuls were robus. The second esimaed model considers nominal exchange rae changes as he hreshold variable. Similarly o he previous model, all parameers are allowed o vary wih he regime change, excep for he oupu gap parameer, kep consan in boh regimes. The esimaion resuls are he following 0 : π * = 0.58E π π + 0.0( Δe + π ) + 0.7y if Δe (0.00) (0.00) (0.3) (0.0).0% π * = 0.44E π π + 0.( Δe + π ) + 0.7y if Δe.0%. (0.0) (0.07) (0.03) (0.0) Sample period: 995: 005:4 Sandard errors esimaed using Newey-Wes consisen esimaors P-values in parenheses Impulse dummy variable for 999:: 0.03, p-value: 0.08 Insrumen variables: cons., dummy var., π, π, π 3, Δ e, Δe, π, π, y R-squared: 0.50 Adjused R-squared: 0.43 Breusch-Godfrey Serial Correlaion M es, p-values: lag:.00, 4 lags: 0.38 Whie Heeroskedasiciy Tes, p-value: 0.69 Jarque-Bera Normaliy Tes, p-value: 0.3 Wald es α =, p-value: 0.06 α * * Those resuls indicae ha he shor-run effec of exchange rae changes on inflaion is asymmeric. In he case of large exchange rae depreciaions, he esimaed pass-hrough for he following quarer is around %, whereas appreciaions or small depreciaions do no have a saisically significan effec. The Wald es rejecs he null hypohesis ha boh coefficiens are equal. Therefore, he pass-hrough is greaer when quarer-on-quarer depreciaions are equal o or larger han.%. Alhough he resuls on he effec of an 9 Including he period previous o he launch of he Real Plan is no recommendable because he inflaion dynamics in a high inflaion regime is subsanially differen, disoring he esimaion. 0 In ha specificaion, we have used for he backward-looking inflaion and oupu gap erms he average of A A superscrip A means acual values. Tha specificaion generaes beer fiing. A A heir values a - and -, ha is, π = ( π + π )/ and y = ( y + y )/, where he

14 appreciaion in he previous quarer on curren inflaion were no saisically significan, we should no infer ha appreciaions are no ransmied o prices. This ransmission can ake place wih more lags han in he case of depreciaion. As before, he esimaed parameers are robus wih respec o he insrumens used and are saisically significan a 5% (excep he coefficien on lagged inflaion when Δ e.0% ). Moreover, he number of observaions in each regime was reasonably balanced (5 observaions in he large depreciaion regime, and 9 in he oher) and he esimaed values for he coefficiens are close o hose repored in he lieraure. Noe ha in boh esimaions he forward-looking inflaion coefficien is greaer han he backwardlooking componen. Since he esimaed hreshold is no zero, is slighly posiive value (close o %) suggess he presence of menu coss or some adjusmen coss of prices, where small exchange rae changes are no promply ransmied o prices. If price changes are cosly, a small change in he currency value can be accommodaed wihin he markup margin. In his case, firms end o pospone heir decisions, adjusing heir markup in he shor-run. However, if exchange rae changes surpass some limi, even if he change is emporary, he coss of no adjusing prices are higher, leading firms o change prices more rapidly. Consequenly, he presence of menu coss increases he possibiliy ha firms will adjus price mainly if exchange rae changes surpass some hreshold, resuling in an asymmeric pass-hrough relaed o small and large exchange rae changes. Furhermore, pricing-o-marke heory delivers an explanaion for a parial passhrough and for an asymmery relaed o appreciaions and depreciaions in he exchange rae. Consider he domesic secor formed by subsidiaries of foreign firms ha produce abroad and sell heir producs inernally. In he case of an exchange rae depreciaion, hose firms have hree opions: i) o reduce heir markup o keep sable he price in local currency (absence of pass-hrough); ii) o keep heir markup, increasing he price charged in local currency o reflec compleely he exchange rae change (complee pass-hrough), which may imply a marke share reducion; or iii) a combinaion of he previous wo possibiliies (parial pass-hrough). When subsidiary firms are rying o build up or keep heir marke shares, a local currency depreciaion resuls in a lower pass-hrough han ha when here is an 3

15 appreciaion. Neverheless, if he depreciaion of he domesic currency is high, here is less room for markup adjusmens, and a leas parially he depreciaion is ransmied o domesic prices o avoid losses. In he case of appreciaion, firms profis increase if hey keep consan domesic prices, which could resul in a longer period o adjus prices downwards. The exension of hese effecs on he price level in he economy depends on he price-elasiciy of demand for hese firms goods and on he degree of openness of he economy. In addiion, if he firms ha produce abroad face a resricion on heir producion capaciy, an exchange rae appreciaion can resul in a lower pass-hrough han in he case of a depreciaion. The resricion capaciy limis he fall in domesic price ha he appreciaion could generae. The previous esimaed models do no make any disincion beween he pre-999 period, when he exchange rae was managed following in pracice a crawling peg sysem and he following period of a floaing rae. In fac, when we include a sep dummy ino he exchange rae erm, he resuls deeriorae subsanially in erms of signs and saisical significance of he parameers. This resul may be relaed o he increase in he number of parameers o be esimaed when we include a dummy variable, reducing he degree of freedom of he esimaion. Because of hose limiaions, we have esimaed a hird model, using exchange rae volailiy as he hreshold variable. This esimaion would end o resolve, a leas parially, he problem of he separaion of he exchange rae regimes (before and afer January 999) because he hreshold esimaion ends o classify he observaions of he managed sysem period ino he low volailiy regime. In principle, he low volailiy esimaed regime could also conain observaions from when he exchange rae was relaively sable during he floa period. In addiion, ha esimaion aims o capure he inflaionary effecs in wo differen siuaions: i) when agens perceive exchange rae changes as ransiory; and ii) when hey perceive hem as permanen. When agens consider exchange rae variaions as more permanen, more promply hey will be ransmied o prices. Our assumpion is ha he probabiliy ha agens consider changes as permanen is higher in periods of low exchange 4

16 rae volailiy and smaller in periods of greaer volailiy. Thus, we would expec a lower pass-hrough in periods of higher exchange rae insabiliy. We have used he sandard deviaion of daily changes in he exchange rae wihin each quarer as he measure of volailiy. The esimaion resuls were he following : π * 0.5Eπ π ( Δe + π ) + 0.3y if σ e, = (0.74) (0.83) (0.) (0.00) 0.07% π * 0.30Eπ π ( Δe + π ) + 0.3y if σ e, = (0.07) (0.00) (0.05) (0.00) 0.07%. Sample period: 995: 005:4 Sandard errors esimaed using Newey-Wes consisen esimaors P-values in parenheses Impulse dummy variable for 999:: 0.03, p-value: 0.00 Insrumenal variables: cons., dummy variable, π, π, Δ * * e, Δe, π, π, y R-squared: 0.5 Adjused R-squared: 0.45 Breusch-Godfrey Serial Correlaion M es, p-values: lag: 0.69, 4 lags: 0. Whie Heeroskedasiciy Tes, p-value: 0.3 Jarque-Bera Normaliy Tes, p-value: 0. Wald es α =, p-value: 0.5 α In erms of magniude, he poin esimaes indicae a greaer pass-hrough in low volailiy periods han in high volailiy momens (80% and 7%, respecively). However, he esimaed pass-hrough is no saisically significan in he low volailiy regime, alhough i is significan in he oher regime and he parameer values are close o hose repored in he lieraure for he periods of managed and floaing exchange raes. 3 The resuling sample division assigned mos of he observaions of he managed sysem o he Albuquerque and Porugal (006), for example, explore he relaionship beween exchange rae volailiy and inflaion in Brazil, using a bivariae GARCH model. In ha specificaion, we have used for he backward-looking inflaion erm he average of heir values a - π A A A, and for he oupu gap erm, he average a - and - 3, - and -3, ha is, = ( π + π + π )/ 3 A generaed beer fiing. A, ha is, y = ( y + y )/, where he superscrip A means acual values. Tha specificaion has 5

17 low volailiy regime. The observaions corresponding o values below he hreshold comprise he 995:4 998: period. Neverheless, according o he Wald es, we canno rejec he null ha boh coefficiens are equal, and he resuls of his Phillips curve specificaion are less robus han hose of he wo previous models. Therefore, hese resuls should be considered wih more cauion. Figure illusraes he resuls concerning he firs model esimaed. I presens he quarerly free price inflaion, he exchange rae change (lagged one period), and a line ha indicaes he hreshold value (-.89%) of oupu gap. This line separaes he periods when oupu gap is above and below he hreshold. We poin ou some periods, described in Table, in which he esimaed model can explain, a leas parially, he relaion beween exchange rae changes and free price inflaion. The able records he corresponding values, besides including headline inflaion (measured by IPCA). Figure Free price inflaion, exchange rae changes and he oupu gap Free price inflaion (%) d + d d + d + a + I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III Free price inflaion Period ou pu gap above he hr eshol d Period ou pu gap bel ow he hreshold Exchange rae change (-) Exchange rae change (%) 3 Muinhos and Alves (003), por insance, have found a coefficien reducion from 5% o 6% afer he change in he exchange rae regime, and Albuquerque and Porugal (005), using a Kalman filer model, have esimaed parameers values around 4% and 4%, respecively. 6

18 Period Table Inflaion and exchange rae changes in seleced periods Characerisic Headline inflaion Headline inflaion Free price inflaion in - in in - in in - 999: II d :III d :II d :III d :III d :IV d :IV a :I a :II a Noe: d + means depreciaion wih booming d means depreciaion wih recession a + means appreciaion wih booming a means appreciaion wih recession The exchange rae change is calculaed based on he quarerly exchange rae average Free price inflaion Exchange rae change In he second quarer of 999 (immediaely afer he floa), for insance, in spie of he 39% exchange rae depreciaion in he previous quarer, free price inflaion was only 0.49% and he headline inflaion sood a.05%, boh below he previous quarer values. In ha period, he oupu gap was below he esimaed hreshold (economic slowdown), which implies, according o he model, a low pass-hrough o inflaion. The depreciaions in he hird quarer of 000 and during 00, in urn, were followed by higher increases in he inflaion rae. In ha period, he oupu gap was higher han he esimaed hreshold. In mid-00, when he economy was growing faser, a srong depreciaion was accompanied by a grea inflaion rise. In he las quarer, for insance, when he depreciaion in he previous quarer reached %, free price inflaion wen from.56% o 6.34%, and headline inflaion rose from.58% o 6.56%. On he oher hand, alhough inflaion fell along 005, i did no follow so promply he exchange rae appreciaion sared in he las quarer of 004. One possible explanaion lies on he asymmery of he shor-run pass-hrough wih respec o appreciaion and depreciaion, pu in evidence by he model wih he hreshold given by exchange rae changes. Furhermore, iniial movemens of appreciaion were possibly no perceived immediaely as having longer duraion, posponing he effec on prices. In fac, he model esimaes he shor-run pass-hrough, ha is, he effec on curren inflaion of he change in 7

19 he exchange rae in he previous quarer. The appreciaion conribued for he reducion in inflaion, bu probably wih lags greaer han one quarer. 4. Conclusions This paper explores he possibiliy of he presence of a nonlinear pass-hrough from he exchange rae o inflaion in Brazil. We have esimaed models for he Phillips curve combined wih he mehodology of hreshold models. In hese models, he parameer values depend on which regime he economy is, which are deermined endogenously by means of an observed variable. The choice of variables used was based on he possible sources of nonlineariy of he pass-hrough repored in he lieraure. In paricular, we have examined hree sources: i) business cycle; ii) exchange rae changes; and iii) exchange rae volailiy. The esimaions indicae he presence of nonlinear mechanisms in he shor-run pass-hrough in Brazil. The shor-run pass-hrough is higher when he economy is booming, when he exchange rae depreciaes above some hreshold, and when exchange rae volailiy is lower. These resuls have imporan implicaions for moneary policy and are possibly relaed o a pricing-o-marke behavior, menu coss o change prices, and uncerainy abou he degree of persisence of exchange rae changes. 8

20 References Aguiar, A. and M. F. Marins (00), Trend, cycle and nonlinear rade-off in he Euro-area ", CEMPRE. Albuquerque, C. R. and M. S. Porugal (005), Pass-hrough from exchange rae o prices in Brazil: An analysis using ime-varying parameers for he period, Revisa de Economía, Monevideo, (): Albuquerque, C. R. and M. S. Porugal (006), Tesing nonlineariies beween Brazilian exchange rae and inflaion volailiies, Banco Cenral do Brasil Working Paper Series no. 06, May Banco Cenral do Brasil (003), Inflaion Repor, p. 6-8, Dec. Bean, C. (000), The convex Phillips curve and macroeconomic policymaking under uncerainy, mimeo, ondon School of Economics. Blonigen, B. A. and S. E. Hayes (00), Anidumping invesigaions and he pass-hrough of anidumping duies and exchange raes, American Economic Review, 9(4): 044-6, Sep. Bogdansky, J., A. Tombini, and S. Werlang (000), Implemening inflaion argeing in Brazil, Banco Cenral do Brasil Working Paper Series no., July. Caner, M. (00), A noe on leas absolue deviaion esimaion of a hreshold model, Economeric Theory, 8(3): 800-4, June. Caner, M. and B. Hansen (004), Insrumenal variable esimaion of a hreshold model, Economeric Theory, 0(5): 83-43, Oc. Carneiro, D., A. M. Moneiro, and T. Wu (00), Mecanismos não-lineares de repasse cambial para o IPCA, Deparameno de Economia PUC-Rio, Texo para Discussão no. 46, Aug. Chadha, B., P. Masson, and G. Meredih (99), Models of inflaion and he coss of disinflaion, IMF Saff Papers, 39(): , June. Chan, K. S. (993), Consisency and limiing disribuion of he leas squares esimaor of a hreshold auoregressive model, The Annals of Saisics, (): , Mar. Clemens, M., and M. Sensier (003), Asymmeric oupu gap effecs in Phillips curve and murk-up pricing models: evidence for he U.S. and he U.K, Scoish Journal of Poliical Economy, 50(4): , Sep. 9

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