Monetary policy rules in a small open economy: An application to Mexico. F. Alejandro Villagómez* and Javier Orellana Polo

Transcription

1 Moneary policy rules in a small open economy: An applicaion o Mexico F. Alejandro Villagómez and Javier Orellana Polo Documeno de Trabajo Working Paper EGAP Tecnológico de Monerrey, Campus Ciudad de México EGAP, Calle del Puene 222, Col. Ejidos de Huipulco, Tlalpan, México, DF, MÉXICO fvillagomez@iesm.mx 1

2 Moneary policy rules in a small open economy: An applicaion o Mexico F. Alejandro Villagómez CIDE and EGAP-ITESM-CCM Cenro de Invesigación y Docencia Económicas A.C. (CIDE) División de Economía Carreera México-Toluca 3655 Col. Lomas de Sana Fe, Alvaro Obregón Mexico, D.F. México (5255) alejandro.villagomez@cide.edu, favillgomez@gmail.com and Javier Orellana Polo McKinsey We esimae a small-scale macro model for he Mexican economy under he New Keynesian (NK) framework and alernaive ineres rae rules for Mexico. Wih hese resuls we evaluae he performance of he Bank of Mexico agains a se of opimaliy principles derived in he NK lieraure. We show ha he Bank of Mexico holds a preference for sabilizing no only inflaion around arge, bu also acs o achieve an oupu gap close o zero. Furhermore, we show he cenral bank responds non-linearly o real exchange rae depreciaions. We also show ha, alhough he cenral bank has aemped o conain inflaion, i has no conclusively saisfied he Taylor principle, so moderae inflaion during he period may be parly a consequence of a favorable macroeconomic environmen, raher han acive policy. JEL Classificaions: E52, E58 Key Words: Taylor Rule, New Keynesian, Moneary Policy, Ineres Rae Rules, Small Open Economy 2

3 1. INTRODUCTION Price sabiliy is an explici objecive of cenral bank policy in Mexico. In he pas, moneary policy cenered on he use of he exchange rae as he economy s nominal anchor, bu when his resuled incompaible wih macroeconomic condiions, he consequence ofen enailed a balance of paymens crisis. During he las decade, Mexico s moneary policy has evolved owards he esablishmen of a precise inflaion arge, favoring (recenly) he shor-erm nominal ineres rae as policy insrumen. Explicily, he moneary auhoriy aims a achieving he convergence of inflaion o is arge level in he medium-run; however, i is plausible ha implici addiional objecives also guide policy. Hence, he comprehension of he facors o which he moneary auhoriy responds, as well as he effec of policy decisions on he economy consiue a problem of ineres. On his las poin, he effecive idenificaion of he ransmission mechanism of moneary policy is a fundamenal pillar of policy conducion. The purpose of he presen paper is o model he behavior of he Mexican economy and he response of he cenral bank o economic condiions during he pas decade. Wih his in mind, we model he economic resricions faced by policy-makers hrough a smallscale macro model in he New Keynesian (NK) radiion. This class of models incorporaes nominal rigidiies and imperfec compeiion ino he dynamic sochasic general equilibrium framework developed in he Real Business Cycle lieraure. The assumpion of nominal rigidiies generaes a srucure where moneary policy is effecively non-neural in he shor-run, while mainaining is long run-neuraliy. As such, money becomes a nonrivial elemen of he economy. We use his modeling sraegy as a reference o deermine which facors accoun in greaer par for inflaion dynamics in Mexico, as well as o deermine imporan aspecs of he ransmission mechanism. Furhermore, we model he conducion of moneary policy as endogenous wih he shor-run nominal ineres rae as insrumen hrough he use of he moneary policy rule mehodology. In our formulaion, we conras wo alernaive policy rules, and show ha moneary policy in Mexico implicily arges variables besides inflaion, herefore operaing under a flexible inflaion argeing framework (IT). Among hese variables are he oupu gap and some measure of he exchange rae. Imporanly, we show ha he cenral bank s response o exchange rae flucuaions is non linear, as previously aemped in he lieraure for Mexico. In fac, he analysis of a non-linear response o exchange rae flucuaions is imperaive in order o square he ineres rae rule wih he facs. We hen use our esimaed resuls o evaluae policy agains a se of opimaliy principles derived in he ineres rae rule and NK lieraure. We show ha he Bank of Mexico has no conclusively esablished moneary policy as an effecive nominal anchor, as i does no decisively saisfy he Taylor principle. The remainder of his paper is organized as follows. In Secion 2 we review he lieraure on moneary policy rules and is applicaion o he IT framework, in paricular we focus on ineres-rae rules. Secion 3 inroduces he macroeconomic model o be esimaed. Secion 4 presens a brief descripion of he daa used in he exercise. Secion 5 carries ou he esimaion and presens key resuls. Secion 6 evaluaes he behavior of he model under alernaive rules. Secion 7 concludes. 3

4 2. MONETARY POLICY AND THE RULES METHODOLOGY Much of he recen lieraure on moneary policy has cenered on he analysis of he IT framework. This plan of acion, which has gained in populariy since is adopion by New Zealand in 1988, and which Mexico has employed since 2002, is characerized by he adopion of a series of measures aimed a he convergence of inflaion in he medium run o a publicly announced arge. The IT framework presens some imporan and in principle desirable characerisics, as follows. Firs, he IT regime commis he moneary auhoriy o mainaining price sabiliy. Second, by no commiing o a specific acion plan o achieve convergence of inflaion o is arge value, his framework allows for cerain flexibiliy in he conducion of policy, permiing he cenral bank o use all and any ools a is disposal in order o respond o economic shocks. Finally, under he IT framework he conducion of policy is subjec o a high degree of ransparency and accounabiliy. Clear and imely communicaion of cenral bank arges and acions is a fundamenal pillar of policy, as i allows for he effecive managemen of expecaions under a credible regime. These characerisics urn he IT regime ino a desirable operaing framework. The lieraure esablishes, on he one hand, ha a policy framework under commimen reduces he inflaion bias which would be incurred by he cenral bank if i could operae under absolue discreion. A more suble, bu highly relevan, poin is made by Clarida e al. (1999) who show ha, if he price-seing process is driven by expecaions of fuure economic condiions, a cenral bank credibly commied o figh inflaion faces a more favorable oupu inflaion radeoff, as agens undersand he cenral bank will no loosen policy in he fuure if price pressures persis. Furhermore, he ransparency of he regime allows for he evaluaion of policy resuls. As argued by Svensson (2000), greaer ransparency makes he repuaion of he cenral bank more sensiive o policy acions, implying higher coss o he moneary auhoriy of deviaions from announced arges, hus increasing he incenives for he cenral bank o achieve convergence of inflaion o is argeed value. Addiionally, he lieraure based on he NK paradigm has succeeded in esablishing some principles on which sound moneary policy should res in order o conrol inflaion in he medium run. Clarida e al. (1999) survey he lieraure and poin o he main resuls derived, of which key consensus poins are worhy of noe. i. Under opimal policy, when facing a rise in expeced inflaion, nominal ineres raes should increase sufficienly o elevae real raes. ii. An opimal policy requires modifying he ineres rae in order o fully neuralize demand shocks. Given ha oupu in he long run is deermined by supply-side facors, any excess demand will lead o an excessively high price level wihou a corresponding increase in oupu in he long run. Addiionally, he increase in he price level derived from excess aggregae demand may become persisen if expecaions of high fuure inflaion are esablished. iii. When facing shocks o poenial oupu, or supply-side shocks, ineres raes should no be modified under opimal policy. In his case, for example, a negaive supply shock will lead o a one-off increase in inflaion, reflecing a change in relaive prices. If inflaion expecaions remain unaffeced, inflaion will reurn o is former level in subsequen periods. 4

5 In pracice, he IT regime may be eiher sric or flexible. In he firs case, he moneary auhoriy is only concerned wih achieving convergence of inflaion o arge, and is herefore willing o pay any price in erms of oupu or unemploymen. Under a flexible regime, on he oher hand, he cenral bank is addiionally concerned wih he evoluion of macroeconomic variables besides inflaion, and may pursue various goals simulaneously. In pracice, i is reasonable o assume ha cenral banks work owards achieving macroeconomic sabiliy in a broad sense, assigning an imporan relaive weigh o price sabiliy bu no responding exclusively o i, so he use of analyic framework which allows for he analysis of a flexible policy regime is desirable. In order o analyze he performance of moneary policy, he rules approach is aracive, and has received pleny of aenion in he lieraure. Is main srengh lies in is capaciy o sysemaically incorporae economic informaion in order o formulae a policy recommendaion. In opposiion o policy conduced under discreion, he use of credible rules may minimize he ime inconsisency problem. Addiionally, policy rules vary considerably in heir essence and complexiy. They may be classified as passive or acive, he laer of which may in urn be separaed beween simple and opimal rules, as will be furher discussed below. 1 Passive rules do no respond o changes in economic condiions. Since hey ignore some of he relevan channels hrough which markes impac he real economy, hese rules may lead o subsanial macroeconomic imbalances. Acive policy rules, on he oher hand, make use of available informaion abou he economic environmen in order o formulae policy. These addiional variables may reflec pas, presen, or expeced condiions. As such, acive rules consiue an analyical framework which allows policy o reac o a dynamic economy. Policy conduced hrough acive rules may be furher separaed ino wo broad caegories: simple and opimal rules. The firs one makes use of a subse of available economic informaion in order o generae a policy recommendaion. In he case of simple ineres rae rules, hese end o be characerized in he lieraure as linear funcions of he inflaion rae and he oupu gap. These rules are essenially ad hoc, alhough some baseline versions may be derived from sandard heory as special cases 2. However, heir simpliciy makes hem an aracive iniial sep in he evaluaion of moneary policy, as hey are able o capure some imporan aspecs of policy conducion. Conversely, opimal policy rules are he soluion o he explici opimizaion of an objecive funcion, he laer of which may be uiliy, subjec o he consrains imposed by he srucure of he economy as a whole. By using a larger informaion se and by modeling ineracions beween variables in a more sophisicaed manner, opimal rules provide a more rigorous analysis. However, heir complexiy may reach considerable levels, making he communicaion of policy objecives o he general public subsanially difficul. Furhermore, he opimal soluion is condiional on he specific funcional form of uiliy chosen for analysis, so an empirical applicaion arises issues due o funcional form uncerainy. In order o employ he policy rules mehodology o evaluae moneary policy, i is necessary o firs define he policy insrumen. During he pas years, he lieraure has focused on he analysis of he use of a shor-erm nominal ineres rae as policy insrumen, reflecing he pracice of major cenral banks. Alhough he Bank of Mexico only sared o use he nominal ineres rae as is policy insrumen in 2008, he previous insrumen, he 1 See, e.g. Woodford (2003). 2 See, e.g. Clarida e al. (1999). 5

6 coro, may be inerpreed as a signaling mechanism hrough which he cenral bank indicaed is preference for he marke ineres rae srucure. Therefore, following Torres (2002) and Roldán (2005), he presen analysis focuses exclusively on moneary policy rules for he deerminaion of he shor-run nominal ineres rae. The canonical example of a simple moneary policy rule is he Taylor rule, Taylor (1993). This rule describes he level of he federal funds rae and esablishes ha i should be se a an assumed level for he equilibrium long-run nominal ineres rae 3, coningen o deviaions of inflaion from arge and deviaions of oupu from is poenial level, approximaed by a smooh rend. 4 Clarida e al. (1999) show ha a rule in he spiri of he Taylor rule may be derived from an opimizaion process in which he cenral bank minimizes a quadraic loss funcion (wih deviaions of inflaion from arge and he oupu gap as is argumens), subjec o a sandard NK macroeconomic model. In his sense, a simple rule may, under cerain assumpions, consiue an adequae approximaion o opimal policy. 5 The rule obained from said process is, however, forward-looking. As such, i saes ha expeced fuure deviaions of inflaion from arge and fuure expeced oupu gaps are wha should deermine he pah of he ineres rae. (1) = i + ( E [ π π + n ]) ϕ E [ y ] Here, E [] E[ Ω ] ( ) i ϕ π + n + y + k T is he expeced value operaor condiional on he informaion se Ω, known a ime and π denoes he cenral bank s inflaion arge, which may no be consan and presens a ime subscrip. Thus, moneary policy analysis hrough he rules mehodology concenraes on examining he coefficiens ϕ π and ϕ y, which imply he preferences of he cenral bank. Alhough simple, he Taylor rule incorporaes some of he key resuls derived in he NK lieraure. Following a demand shock, boh he inflaion and he oupu gaps move in he same direcion, which induces he corresponding move in he ineres rae, hus neuralizing he demand shock. A supply shock, on he oher hand, causes opposie movemens in he inflaion and oupu gaps. For example, a emporary negaive produciviy shock or a cos-push shock will lead o a rise in inflaion, while he oupu gap will decrease. Therefore, he rise in he ineres rae suggesed by he rise in inflaion will be roughly compensaed by he decrease suggesed by he conracion of oupu. In his sense, he ineres rae will display only a mued response o he shock, consisen wih New Keynesian opimaliy principles. This rule may be wrien in erms of he real ineres rae 6, yielding (2) = r + ( ϕ π 1 )( E [ π π + n ]) ϕ E [ y ] ( ) r + n + y + k 3 This rae is relaed o Wicksell s naural ineres rae. See Wicksell (1907) for furher deails. 4 The Hodrick-Presco filer is commonly used in he lieraure o exrac he rend of he series. 5 In paricular, i is necessary o assume ha he oupu gap and real marginal coss are proporional. Addiionally, a rule ha implies a gradual adjusmen of he policy insrumen in response o real shocks is consisen wih he minimizaion of loss derived from deviaions of inflaion from arge as well as deviaions of oupu from is poenial level. These issues are furher discussed in Clarida, Galí and Gerler (1999) and Woodford (2001). 6 See Torres (2002). 6

7 Here ϕ π > 1 is required in order o guaranee ha he real ineres rae rises when inflaion is above arge, hus allowing moneary policy o conrac aggregae demand. Oherwise, ha is ϕ π < 1, moneary policy canno consiue he nominal anchor of he economy since i does no respond vigorously enough o nominal shocks, which may be persisen. Torres (2002) presens esimaions of his parameer for Mexico beween 1997 and 2001, finding ha moneary policy consiued an effecive nominal anchor. The Taylor rule has been subjec o grea scruiny, boh as a descripion of moneary policy as well as a prescripion of desirable policy. Taylor (1999) argues in favor of he normaive relevance of he rule based on he fac ha i generaes a good descripion of acual U.S. policy in a period in which i was paricularly successful in he bale agains inflaion. However, he Taylor rule, as well as he mehodology of ineres rae rules in general, has faced sharp criicism in he lieraure. Woodford (2001) presens wo of he main argumens employed agains he use of rules in he conducion of moneary policy. Firs, i has been poined ou ha he use of ineres rae rules may be insufficien o deermine he equilibrium level of prices in he economy. In response, Woodford shows ha a moneary policy rule, which for a rise in inflaion above arge of k percen implies a rise in he nominal ineres rae of more han k percen, is sufficien o deermine he equilibrium level of prices; again ϕ π > 1. In second place, i has also been suggesed ha ineres rae rules may lead o an unsable inflaionary spiral when expecaions abou fuure inflaion exrapolae recen inflaionary experience. As Woodford poins ou, his criicism has is roos in he inflaionary cumulaive process described by Wicksell (1907), in which a rise in expeced inflaion, due o any arbirary reason, lowers he real ineres rae perceived by agens, 7 which in urn simulaes aggregae demand, hus leading o ever greaer inflaionary pressures and greaer expeced inflaion, ad infinium. Neverheless, Woodford poins ou ha his criicism assumes an exogenous pah for he nominal ineres rae, ha is, a pah which does no explicily responds o realized and expeced inflaion and oupu. The endogenous process of he nominal ineres rae suggesed by he Taylor rule, if adequaely communicaed o he public, should be enough o impede an inflaionary spiral of he aforemenioned sor. As poined ou by Galí and Monacelli (2005), he feedback mechanism implied in he rule is sufficien o pin down uniquely he price level given a se of iniial condiions. Informed agens should be conscious ha, due o he rise in inflaion expecaions, he moneary auhoriy will aggressively respond o conrac aggregae demand and hence diminish he realizaion of subsequen inflaionary pressures. Even hough simple moneary policy rules incorporae some desirable elemens, hese in general make use of a limied informaion se, ignoring addiional facors which may be useful in describing he inflaionary process and is response o changes in policy. This highlighs he convenience of using augmened rules. By employing a larger informaion se, augmened rules provide a more accurae descripion of policy. 7 I is helpful o remember ha, according o he Fisher equaion, 1. 7 r 1+ i 1+ π = e

8 3. A SMALL OPEN ECONOMY The evaluaion of alernaive policy rules requires an analyic framework which is, as far as possible, concise and rich in he economic dynamics i is able o capure. Much of he recen lieraure on moneary policy employ models ha bring imperfec compeiion and nominal rigidiies ino he dynamic sochasic general equilibrium srucure developed in he Real Business Cycle lieraure, yielding he NK lieraure. Because of he presence of nominal rigidiies, moneary policy is non-neural. Furhermore, he srucure developed yields inuiive equilibrium condiions which are similar in srucure o he IS-LM model. 8 Because of his, he NK framework is widely used in he rules lieraure. 9 The srucure of his class of macroeconomic models, in is baseline case, is described by a sysem of equaions composed by a demand curve and a supply curve, he laer characerized as a NK Phillips Curve (NKPC). The baseline model is expanded by Svensson (2000) and Galí and Monacelli (2005) o he analysis of he small open economy, explicily formulaing addiional ransmission mechanisms relevan o he small open economy. In paricular, hey highligh he role played by he real exchange rae. In he presen paper, he model is closed wih he inclusion of an ineres rae rule o model he behavior of he cenral bank. The baseline model may be employed boh in he evaluaion of opimal rules as well as simple rules, he laer being he purpose of our paper. Each of he four relevan equaions of he model, namely aggregae demand, aggregae supply, exchange rae dynamics, and he ineres rae rule, is furher discussed below. The aggregae demand curve links financing condiions faced by agens wih heir consumpion and invesmen decisions hrough ime. This curve radiionally esablishes a negaive relaionship beween aggregae expendiure in he economy and he real ineres rae, reflecing in par he endearmen of deb as well as he decrease in he value of asses owned by agens. McCallum and Nelson (1997) show how a relaion of his sor may be derived from he ineremporal maximizaion of uiliy by a represenaive raional agen who chooses consumpion and leisure subjec o a budge consrain. The aggregae demand curve is herefore given by he consumpion Euler equaion. Hence, he forward-looking consumpion curve akes he form (3) c a r + a E [ c ] = where c is consumpion and a < 1 0. I is imporan o noe ha his form for he demand curve differs from is radiional version in he sense ha fuure consumpion is no deermined by is presen value. Raher, he expecaion of fuure consumpion deermines consumpion oday. Given ha in he baseline model consumpion represens he only source of demand in he economy, consumpion demand equals aggregae demand. Furhermore, assuming ha marginal cos is lower han he price se, producers supply any quaniy demanded, so ha aggregae demand equals oupu (Blanchard, 2008). From hese consideraions, an aggregae demand equaion is obained as (3 ) y a r + a E [ y ] = See, e.g. McCallum and Nelson (1997) for a complee discussion. 9 See, e.g. Clarida, Galí and Gerler (1999), Svensson (2000), Woodford (2001), Galí and Monacelli (2005), Roldán (2005) and Moons e al (2007). 8

9 where y is he oupu gap. Following Roldán (2005) and Moons e al. (2007), i is imporan o noe ha a specificaion like he one shown in (3 ) may be augmened o ake ino accoun addiional deerminans of aggregae expendiure. Firs, i is imporan o noe he explici role played by he real exchange rae in a small open economy. Movemens in his variable reflec movemens in relaive prices beween wo economies, which in urn have an impac on domesic demand and foreign demand for domesic goods. Because of his, i is desirable o explicily include his variable in an aggregae demand relaion for a small open economy like Mexico s. Second, i is desirable o include a erm which capures he governmen s fiscal sance, since his may be in principle an imporan componen of oal demand in he economy. Finally, i is imporan o noe ha aggregae expendiure is no necessarily enirely forward-looking. In fac, i is reasonable o assume ha consumpion decisions are made in par in an adapive manner, ha is, hey are backward-looking. This assumpion may be heoreically jusified on he grounds of a uiliy funcion which includes habi formaion wihin is argumens. Alernaively, he backward-looking componen can be jusified on he grounds of asymmeric informaion among agens, so ha, for some agens, heir bes guess abou he fuure may be an exrapolaion of he pas. These consideraions lead o a hybrid and augmened aggregae demand curve of he form D (4) [ ] y = a1 r + a2 y 1 + a3e y+ 1 + a q + a g where q is a measure of he real exchange rae (an increase denoes a depreciaion) which capures he effec of ne expors on aggregae demand, g is a measure of he governmen s fiscal sance (a posiive values denoes a fiscal defici), y is a measure of he foreign D oupu gap. The erm ε is a sochasic error erm which capures shocks o demand. I is imporan o noe ha, alhough an aggregae demand curve as presened in (4) may provide a beer fi when faced agains he daa by capuring economically relevan empirical correlaions, he inclusion of ad hoc variables presens an imporan cos, as hey urn he specificaion suscepible o he Lucas criique. 10 As he auhor poins ou, i may be dangerous o aemp o predic he effec of a change in policy based on correlaions observed in hisorical daa, as hose correlaions are subjec o he policy regime iself. In oher words, once he policy regime changes, a raional agen will face a new se of resricions, alering her behavior a he opimum. Therefore, correlaions observed in hisorical daa may no hold under he new policy. The Lucas criique suggess ha, in order o analyze a change in policy, one mus esimae he deep parameers of he model, hose ha characerize agens preferences and heir possibiliies of consumpion and producion. This pah, however, enails subsanial coss of is own, mainly in erms of explicaive power in lack of a srucural model for he economy. Due o he discussion above, esimaion resuls peraining o variables no explicily derived from a micro-founded model should be inerpreed wih care, as i is possible ha, facing a change in policy, he relaions hey describe may change oo. Noneheless, one may place greaer confidence in he resuls peraining o variables appearing in he fully specified heoreical model, such as he ineres-rae elasiciy of he oupu gap a 6 y + ε 10 See Lucas (1976) 9

10 Furhermore, i is imporan o noe ha he model presened will provide sronger resuls for shor-run analysis. Once he srucure of aggregae demand in he economy has been idenified, aggregae supply is modeled hrough a NKPC, which capures inflaion dynamics in he economy, relaing he change in prices wih demand shifs, as refleced by he oupu gap, as well as pressure on prices semming from agens expecaions. This relaion can be derived in an environmen of monopolisically-compeing firms who se ou o maximize profis, combined wih he assumpion of saggered price seing, as in Calvo (1983). The NK synhesis herefore allows he upholding of a heoreic framework of opimizing firms while a he same ime deriving a posiive relaionship beween inflaion and real economic aciviy. In opposiion o he radiional Phillips Curve, which is backward-looking in naure, he NKPC esablishes ha one of he main deerminans of inflaion is he expecaion of fuure inflaion, no is pas realizaions. Therefore, he NKPC akes he general form 11 s s (5) π = b1 E [ π + 1] + b2 y In his case, i is imporan o noe ha he inflaion model describes underlying inflaion. 12 This is due o he fac ha underlying inflaion beer characerizes price responses o aggregae demand shocks. Non-underlying inflaion, on he oher hand, ends o respond o seasonal variaions or o shocks specific o a paricular indusry, raher han o aggregae shocks. Because of his, i is convenien o separaely model boh componens of inflaion. General inflaion can hen be recovered as he weighed average of boh inflaion measures. 13 As in he case of he aggregae demand curve, for an empirical applicaion i is convenien o augmen he specificaion in order o explicily ake ino accoun addiional variables which may have a direc impac on inflaion. In he firs place, i is imporan o once more noe he role played by he exchange rae. Movemens in he exchange rae imply changes in he price of impored inpus for producion. Hence, exchange rae depreciaions have a direc impac on producion coss, affecing domesic inflaion. Foreign inflaion, on he oher hand, may be passed-hrough if here is no a one-for-one appreciaion of he nominal exchange rae. Finally, he lieraure shows, as in Ramos Francia and Torres (2006), ha inflaion dynamics are beer capured by a hybrid version of he NKPC, so he inclusion of a backward-looking componen is desirable. This resul recognizes ha here may be learning effecs, saggered conracs, or oher insiuional arrangemens in he economy which migh lead o a significan effec of pas condiions on curren ones. This leads o an augmened specificaion of he form s s s S (6) [ ] ( ) π + b y + b Δe + π + ε = b1 π 1 + b2e π Here, is he nominal exchange rae (again, an increase corresponds o a depreciaion) and π is foreign inflaion. The wo variables have a significan effec on domesic inflaion for a small open economy depending on how hey affec he cos of impored inermediae goods used in he producion process. They also impac he price of impored final goods, 4 11 A complee derivaion is available in Galí and Monacelli (2005). 12 This definiion of inflaion is based on a price index which excludes goods wih paricularly volaile prices. 13 The appropriae weighing coefficien is published by he Bank of Mexico. 10

11 S which affec CPI inflaion. The erm ε is a mean-zero sochasic erm which capures aggregae supply shocks. As in he case of he aggregae demand curve, he augmened specificaion includes ad hoc erms which complimen he heoreically-derived srucure. In paricular, his componens correspond o he pass-hough erm and he change in nominal wages. In he empirical lieraure, Roldán (2005) and Moons e al (2007) employ similar specificaions which complimen he heoreical model presened in Svensson (2000) and Galí and Monacelli (2005). Given he role played by he exchange rae in boh aggregae demand and supply in a small open economy, i is imporan o noe some of he consequences of including his variable in he model. Firs, as noed by Svensson (2000), in an open economy he exchange rae is an imporan aspec of he ransmission mechanism. For a closed economy, moneary policy has an impac on he economy via he aggregae demand channel and he expecaions channel. In he firs case, moneary policy impacs demand wih a lag due o is effec on he nominal ineres rae, which modifies credi condiions. This channel is capured in he aggregae demand curve. Demand will hen have an effec on inflaion, wih an addiional lag, via is ineracion wih aggregae supply, described in he NKPC. The expecaions channel, alernaively, allows moneary policy o affec agens expecaions, which will impac he price formaion process, such as wage negoiaions. This alers domesic inflaion by changing producion coss. Addiionally, for an open economy, he exchange rae has an effec on aggregae demand, and evenually prices, hrough is impac on he rade balance. There is also, as menioned before, a direc effec, as exchange rae movemens affec he price of impored final goods, hus impacing CPI inflaion direcly. This channel, as poined ou by Svensson (2000), has a quicker effec on prices han he aggregae demand channel. Therefore, moneary policy may be faser o ac on inflaion in an open economy han in a closed one, as i acs hrough a greaer variey of channels. Second, he exchange rae is essenially he price of an asse, so i is deermined in a forward-looking manner. Because of his, he inclusion of he exchange rae conribues o he imporance of forward-looking variables in he performance of he economy (Svensson, 2000). Finally, he exchange rae capures variaions in foreign economic condiions such as inflaion, ineres rae movemens, and counry-risk premia. All hese variables impac foreign demand for domesic goods, which will in urn affec inflaion in he home counry. For hese reasons, he class of macro models used in he moneary policy rules lieraure is enhanced by he inclusion of a specificaion ha describes he behavior of he exchange rae. For his purpose, purchasing-power-pariy (PPP) is invoked in order o express he (log) real exchange rae (7) q = e + ( p p ) where and denoe he level of domesic and foreign prices, respecively. I is assumed ha uncovered ineres rae pariy (IRP) holds, so he real exchange rae can be expressed as (8) q E [ q ] + ( r r ) = + 1 where he real ineres rae comes from an approximaion o he Fisher equaion of he form (9) r i + E [ π ] = +1 11

12 However, empirical sudies for indusrial economies show ha IRP does no hold in pracice. 14 In paricular, due o he fac ha his is a condiion of equilibrium, no behavior, he exchange rae shows sysemaic deviaions from he level suggesed by IRP. In fac, he exchange rae may overshoo afer changes in he ineres rae srucure. This resul is presened by Eichenbaum and Evans (1995), among ohers. In order o beer characerize he behavior of he real exchange rae, herefore, i is convenien o use a more flexible specificaion, which allows a more gradual adjusmen of he variable owards is long-run equilibrium level, idenified by IRP. J q (10) q c q + c { E [ q ] + ( r r )} + ε = 1 j j= 1 j Roldán (2005) uses a specificaion of his ype for he Mexican economy. Once he dynamics of aggregae demand, he NKPC, and exchange rae dynamics have been idenified, he macro model is closed wih an ineres rae rule ha ranslaes macroeconomic condiions ino a policy sance. Our analysis of simple rules is hen cenered on he performance of his rule wihin he specified macro model. Wih his purpose in mind, and based on principles previously discussed, a rule in he spiri of he Taylor Rule is proposed as i (11) i ( 1 d )( { d + d π ) + d ( E [ π π + 1] ) + d ( E [ y ])} + d i + ε = Torres (2002) uses a rule of his kind, as his specificaion allows for a nominal ineres rae arge which varies in ime according o changes in he inflaion arge, as capured by he erm ( d 2 + d 3 π ). This fac is imporan given ha he sudy encompasses a period of disinflaion overseen by he Mexican cenral bank during he second half of he 1990s. The simple ineres rae rule is hen evaluaed agains and augmened rule which considers real exchange rae depreciaion wihin he cenral bank s reacion funcion. Even hough Torres (2002) esablishes ha he inclusion of some measure of exchange rae depreciaion does no improve he rule s fi, i is imporan o noe ha his work only considers a linear response from he moneary auhoriy o movemens in he exchange rae. The lieraure for indusrial economies shows, as in Taylor, Peel and Sarno (2001) and Chinn (2008), ha here may exis a non-linear response. I is plausible ha he cenral bank mainains an implici concern for avoiding excessive flucuaions in he real exchange rae. Thus, he cenral bank may operae under an implici scheme o mainain he variable flucuaing around a long-run objecive or a condiional mean. Consequenly, and differing from Torres (2002), we specify he augmened ineres rae rule as (12) i d 7 ( 1 d1 )( { d 2 + d3π ) + d 4 ( E [ π + 1 π + 1] ) + d5 E [ y ] 3 i ( E [ q ] )} + d i + ε = ( ) + d ( E [ q ]) See, for example, Eichenbaum and Evans (1995). 12

13 where he cubic erm in he real exchange rae capures he non-lineariy in he cenral bank s reacion funcion. 15 The macroeconomic model describing he economy is herefore given by he sysem of equaions composed by (5), (7) and (11), while (12) offers a benchmark ineres rae rule, o be compared wih he augmened case described in (13). 4. DATA This secion briefly describes he daa used for he esimaion of he macroeconomic model. The shor-run nominal ineres rae under consideraion is he 28-day CETES secondary marke rae. Even hough his is no he rae explicily argeed by he cenral bank, i is assumed ha he auhoriy holds sway over his key marke rae hrough is ineres rae arge scheme. The foreign shor-run nominal exchange rae is defined as he 4- week T-BILL secondary marke rae. 16 The oupu gap is calculaed from he log General Index of Economic Aciviy (IGAE), which is a monhly proxy for GDP. The gap is defined as he deviaion of he index from is Hodrick-Presco filered rend. Similarly, he foreign oupu gap is calculaed from he log U.S. Indusrial Producion Index (IPI). The bilaeral real exchange rae beween Mexico and he Unied Saes 17 is calculaed from he log nominal exchange rae as shown in (8). 18 The variable is expressed in erms of a deviaion wih respec o a quadraic rend. Underlying inflaion is defined as he monhly change in he seasonally-adjused underlying componen of he log Naional Consumer Price Index (CPI). Non-underlying inflaion corresponds o he monhly change in he non-underlying componen of Mexico s log CPI. This componen of inflaion is modeled as exogenous due o he fac ha underlying inflaion beer reflecs pressure on prices semming from shifs in aggregae demand. Non-underlying inflaion capures price-changes in highly volaile goods and services whose prices respond o idiosyncraic shocks, which may no necessarily reflec pressure upon oher prices in he economy. General domesic inflaion is recovered as he weighed average of boh componens. Foreign general monhly inflaion is measured as he monhly change in he log CPI for he U.S. Nominal wages are defined as he seasonally-adjused change in he log nominal hourly wage in he manufacuring indusry in Mexico, as repored by he Naional Insiue of Saisics and Geography. The governmen s fiscal sance is defined as he change in a measure of governmen srucural defici, which measures variaions in discreionary fiscal policy. This series is calculaed from he governmen s defici as in Cermeño, Roh and Villagómez (2008). 15 In his specificaion, a cubic erm is chosen o capure he non-lineariy as o disinguish beween movemens in he exchange rae which generae a posiive deviaion from rend (a seep depreciaion) and hose which generae a negaive deviaion from rend (a seep appreciaion). 16 Due o he fac ha here are no available daa for his insrumen for he firs years of he sample sudied, hese are calculaed as he implici 4-week rae in implici in 3-moh Treasury bill raes. This calculaion necessarily assumes ha he expeced monhly rae is he same hrough he hree monhs o he bond s mauriy. This assumpion is reasonable for an economy wih low levels of expeced inflaion and low inflaion volailiy, as is he case for he U.S. economy during he sample period. 17 This measure of he exchange rae is used for he Mexican economy given ha rade wih he Unied Saes heavily dominaes Mexico s Curren Accoun. 18 Wih his purpose, price-level indexes for Mexico and he Unied Saes are ransformed so as o represen an equal base year. 13

14 Daa are used in monhly frequencies, and correspond o he period following he Tequila crisis and is subsequen period of volailiy. Thus, he sample encompasses 1998:01 o 2008:07. This period provides a sample suiable for he sudy of inflaion dynamics under ha IT regime, as well as a period for he analysis of exchange rae dynamics under a floa. 5. ESTIMATION OF THE MACRO MODEL AND INTEREST RATE RULES Esimaion resuls are presened in wo secions. Firsly, he aggregae demand curve, he aggregae supply curve, and he exchange rae relaion are repored. In he second secion, resuls for he alernaive ineres rae rules are shown. Due o he forward-looking naure of he esimaion, however, a brief explanaion of he mehod employed is perinen a his ime. Given ha he equaions describing he dynamics of he economy include forwardlooking variables, i is necessary o employ a mehod which allows he incorporaion of his characerisic. I is imporan o noe ha, in principle, i should be possible o obain daa on he expecaions of agens abou hese variables (his is paricularly rue in he case of inflaion expecaions, on which periodic surveys are conduced). However, as poined ou by Torres (2002), he use of hese measures may bring abou problems in is own righ, paricularly if he expecaions of agens are sysemaically differen from hose held by he cenral bank, he laer being he relevan se in he formulaion of policy. In he case of inflaion expecaions repored by professional forecasers, for example, i is essenial o noe ha forecasers face asymmeric coss for under-forecasing and over-forecasing inflaion, which may lead o a sysemaic forecas bias. Addiionally, i is necessary o recognize ha here are no available explici measures for agen s expecaions of variables such as he oupu gap or he real exchange rae. Because of hese consideraions, and following he lieraure, he relaions are esimaed using he Generalized Mehod of Momens (GMM). This esimaion mehod uses ex-pos values of non-predeermined variables as insrumens for heir ex-ane values. As such, he error erm in he regression becomes a linear combinaion of an exogenous shock and he forecas errors of forwardlooking variables. Consequenly, i is possible o obain unbiased esimaors of he regression coefficiens if he forecas errors have zero mean. To his end, GMM uses a se of insrumenal variables, known a ime and meaningful for he formaion of expecaions abou non-predeermined variables, in order o obain a se of orhogonal resricions which are hen used o find a se of regression coefficiens which guaranee mean-zero forecas errors. Wih hese consideraions in mind, he equaions describing he dynamics of he economy are hen esimaed. Table 1 presens resuls for he esimaion of he aggregae demand equaion. 14

15 TABLE 1: Aggregae demand curve y y ( ) ( ) ( ) ( ) E [ ] y +1 ( ) ( ) ( ) ( ) r ( ) r ( ) ( ) ( ) q ( ) q ( ) ( ) ( ) g ( ) y ( ) y ( ) Adjused R Sandard Error of Regression J Insrumens used in he regression: Δy(-1 a -6, -9, -12); r(-1 a -6); Δy(-1 a -6) Sandard errors robus o arbirary forms of auocorrelaion and heeroskedasiciy are repored.,, H : β 0 is rejeced a he 10%, 5% and 1% significance level respecively. 0 = We can poin ou some ineresing resuls. Firs, under all specificaions boh he one-period lag and one-period lead of he oupu gap are saisically significan and presen he expeced sign. This oucome is consisen wih he lieraure which esimaes hybrid aggregae demand equaions, boh for developed and developing economies. Addiionally, he magniude of he esimaed coefficiens is worhy of noe, as hey sugges ha ha boh he lead and he lag of he oupu gap have similar weighs in he deerminaion of he oupu gap. Second, under all specificaions he coefficien corresponding o he elasiciy of he oupu gap o he real ineres rae is negaive, as prediced by heory. However, only under specificaion 4 is i saisically significan a he 95% confidence level and is magniude lies wihin he range esimaed for oher small open economies. 19 The real exchange rae, on he oher hand, repors he expeced posiive sign, as real exchange rae depreciaions, refleced by a rise in q, should simulae foreign demand for domesicallyproduced goods. The posiive and saisically significan sign suggess ha he Marshall- Lerner condiion is saisfied, so ha demand for expor goods is sufficienly elasic and 19 See, for example, Moons e al. (2007). 15

16 depreciaion has a posiive ne effec on he rade balance. Once he variable represening he governmen s fiscal sance is included, i does no prove o be saisically significan, alhough i presens he expeced posiive sign. Finally, foreign demand seems o play an imporan role in he deerminaion of Mexico s oupu, as seen by he correlaions beween Mexico s oupu gap and is U.S. counerpar, Mexico s chief inernaional rade parner. Specificaion 4 generaes adequae fi, and, mos imporanly, provides saisically significan coefficiens wih he sign suggesed by heory. Thus, his specificaion is laer employed in he model. Resuls for he aggregae supply curve are presened in Table 2. TABLE 2: Aggregae supply curve s π π s 1 s [ ] E + 1 ( ) ( ) ( ) π ( ) ( ) ( ) y ( ) y ( ) ( ) Δe π Δe π Δ 1 w w ( ) ( ) ( ) ( ) Δ ( ) ( ) Adjused R Sandard Error of Regression J Insrumens used in he regression: π s (-1 a -6); Δy(-1 a -6); Δe(-1 a -6); Δw(-1 a -6) Sandard errors robus o arbirary forms of auocorrelaion and heeroskedasiciy are repored.,, H : β 0 is rejeced a he 10%, 5% and 1% significance level respecively. 0 = In he case of he aggregae supply curve, he oucome suggess ha underlying inflaion in Mexico is sill backward-looking o a large degree. Under all specificaions considered, he coefficien corresponding o he lagged variable is beween hree o four imes larger han he one corresponding o is expecaion. This robus resul poins o srong inerial behavior for underlying inflaion. However, here are oher variables which significanly correlae wih inflaion. Concreely, he oupu gap coefficien is robus 16

17 hroughou all specificaions, and shows he expeced posiive sign. An increase in he oupu gap reflecs excess aggregae demand, which pus upward pressure on prices in he economy. On he oher hand, i is ineresing o noe ha, even hough here is a saisically significan and posiive pass-hrough effec of foreign inflaion on underlying CPI inflaion in Mexico, i is remarkably small. This resul is in line wih sudies which sugges ha his facor has los relaive imporance as a driver of inflaion in Mexico. Changes in nominal wages, conversely, do no appear o explain inflaion during his period. Under no specificaion is a saisically significan coefficien recorded. Specificaion 3 shows good fi wih he daa and provides coefficiens wih he signs suggesed by heory, herefore i seleced as he bes specificaion. Subsequenly, Table 3 shows resuls for he esimaion of exchange rae dynamics. TABLE 3: Real exchange rae q q ( ) ( ) ( ) ( ) q ( ) ( ) ( ) q ( ) ( ) q E ( ) ( ) ( ) ( ) ( ) [ q ] + ( r r ) Adjused R Sandard Error of Regression J Insrumens used in he regression: q(-1 a -6, -9, -12); Δy(-1 a -6, -9, -12); {E[ q]+r-r}(-1 a -6) Sandard errors robus o arbirary forms of auocorrelaion and heeroskedasiciy are repored.,, H : β 0 is rejeced a he 10%, 5% and 1% significance level respecively. 0 = In his case, i is ineresing o noe ha he coefficien for he ineres rae pariy condiion is posiive and saisically significan under all specificaions. Addiionally, he esimaed coefficien is robus. The daa suggess ha he exchange rae channel (assuming ha here is a movemen in he real exchange rae) is relevan in a small open economy like Mexico s. Furhermore, lagged values of he real exchange rae also conain useful informaion abou is curren value. The resuls obained sugges ha, in agreemen wih he empirical lieraure, he real exchange rae shows persisence, alhough i conains an imporan forward-looking elemen. Thus, he ineres rae pariy condiion should be inerpreed as a long-run equilibrium condiion, bu here may be emporary deviaions from his equilibrium level in he shor and medium run. 17

18 Nex, we presen he esimaion resuls for he specified ineres rae rules. Firs, Table 4 shows he esimaed coefficiens for he simple ineres rae rule as defined in (12). TABLE 4: Simple ineres rae rule d 1 d 2 d 3 d 4 d 5 Coefficien Sandard Error ( ) ( ) ( ) ( ) ( ) Adjused R 2 Sandard Error J of Regression Insrumens used in he regression: 1; π π (-1 a -6, -9, -12); y(-1 a -6, -9, -12); i(-1 a -6, -9, -12) Sandard errors robus o arbirary forms of auocorrelaion and heeroskedasiciy are repored.,, H : β 0 is rejeced a he 10%, 5% and 1% significance level respecively. 0 = These resuls indicae ha here is effecively an imporan inerial componen in he deerminaion of he ineres rae, as refleced in he high relaive value of d 1. This obeys o he fac ha he mos frequen policy decision is o mainain he ineres rae arge unchanged. On he oher hand, i is imporan o noe ha he coefficien d 4, corresponding o he weigh assigned by he cenral bank o deviaions of inflaion from arge, is posiive and saisically significan. However, even hough he esimaed coefficien is greaer han uniy, i is no saisically so. 20 This suggess ha during he period under sudy moneary policy has no been sufficienly aggressive o mainain prices anchored. In ligh of his, and as suggesed by Melick and Galai (2006), i is no convenien o ignore he possibiliy ha he relaively low levels of inflaion seen during he pas few years in Mexico may be caused in par by a favorable macroeconomic environmen, beyond moneary policy. This resul is furher discussed laer in his paper. Addiionally, i is ineresing o noe ha he coefficien peraining o he oupu gap, d 5, is likewise posiive and saisically significan. Furhermore, he esimaed coefficien is close in value o ha peraining o deviaions of inflaion from arge. This suggess ha, effecively, he cenral bank assigns a posiive weigh o he behavior of real economic aciviy when formulaing policy. This iniial resuls seems o corroborae he hypohesis ha he Mexican cenral bank operaes under a flexible inflaion argeing framework, where boh nominal and real variables are arge variables for he insiuion. Taking he simple rule as a benchmark, an augmened ineres rae rule is also esimaed, as described by (13). Esimaion resuls are presened in Table A Wald es rejecs he null hypohesis d 1 a he 95% confidence level. 4 > 18

19 TABLE 5: Augmened ineres rae rule D 1 d 2 d 3 d 4 d 5 d 6 d ( ) ( ) ( ) ( ) ( ) ( ) ( ) Adjused R Sandard Error of Regression J Insrumens used in he regression: 1; π π (-1 a -6, -9, -12); y(-1 a -6, -9, -12); i(-1 a -6, -9, -12); e(-1 a -6, -9, -12) Sandard errors robus o arbirary forms of auocorrelaion and heeroskedasiciy are repored.,, H : β 0 is rejeced a he 10%, 5% and 1% significance level respecively. 0 = The exercise for he augmened ineres rae rule sugges ha he esimaed effec is robus for he coefficiens corresponding o he cenral bank s response o deviaions of inflaion from arge, as well as deviaions of oupu from is poenial level. The esimaed degree of ineres rae ineria in he rule is also robus. Again, worhy of noe is he fac ha d 4 is greaer han uniy, bu no saisically so. 21 Therefore, he esimaion of he augmened rule confirms he key resul obained from he esimaion of he simple rule. Concreely, boh esimaions quesion he aggressiveness wih which moneary policy in Mexico has been conduced hroughou he period under sudy, as i canno be conclusively deermined ha i consiued he key facor behind moderae inflaion raes in he las years. The lieraure for Mexico presens opposing resuls wih which o compare his oucome. While Torres (2002) finds a coefficien for deviaions of inflaion from arge saisically greaer han uniy, Galindo and Guerrero (2003) do no obained his resul. A second ineresing resul corresponds o he esimaed response of he cenral bank o movemens in he real exchange rae. Upon firs examinaion, he coefficien peraining o exchange rae depreciaion, d 4, is negaive, albei small. Given ha he real exchange rae is measured as a deviaion from rend, he negaive coefficien seems o sugges ha he cenral bank lowers he nominal ineres rae when he currency weakens. This resul, aken alone, is couner-inuiive, and conradics convenional heory. In par, and as poined ou by he empirical lieraure, 22 his resul may be due o he fac ha he exchange rae is an exremely difficul variable o forecas a shor ime horizons. Consequenly, his negaive correlaion may be a produc of he high volailiy presen in he variable. More imporanly however, he resul may be raionalized by he presence of a non-linear response from he moneary auhoriy o movemens in he exchange rae. Thus, i is imporan o noe ha he coefficien for he cubic erm on he exchange rae gap, d 7, is saisically significan and shows he correc sign. Moreover, he esimaed effec is relaively large. This resul srongly suggess ha he auhoriy aggressively responds o large deviaions of he exchange rae wih respec o a arge, which in pracice may be a long-run equilibrium level. 21 Again, a Wald es rejecs he null hypohesis d > 4 1 a he 95% confidence level. 22 See, for example, Chinn (2008). 19