Changes in the Brazilian monetary policy: Evidence of a reaction function with time-varying parameters and endogenous regressors

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1 Changes in he Brazilian moneary policy: Evidence of a reacion funcion wih ime-varying parameers and endogenous regressors Gabriela Bezerra de Medeiros PhD Suden of Applied Economics a he PPGE/UFRGS. Adress: Av. João Pessoa, 5 sala 33B - 3 andar CEP Cenro - Poro Alegre/RS - Brazil Phone gabriela.bm@homail.com Edilean Kleber da Silva Bejarano Aragón Professor of PPGE/UFPB and Pos-PhD a he PPGE/UFRGS. Adress: Av. João Pessoa, 5 sala 33B - 3 andar CEP Cenro - Poro Alegre/RS - Brazil Phone edilean@homail.com Absrac: This paper esimaes a forward-looking reacion funcion wih ime-varying parameers o examine changes in he Brazilian moneary policy under he inflaion-argeing regime. As he moneary policy rule has endogenous regressors, he convenional Kalman filer canno be applied. Thus, a Heckman-ype (1976) wo-sep procedure is used for consisen esimaion of he hyper-parameers of he model. The resuls show ha: i) here is srong empirical evidence of endogeneiy in he regressors of he policy rule; ii) he response of he Selic rae o inflaion varies considerably over ime and has shown a decreasing rend; iii) since mid-010, policy rule has violaed he Taylor principle; iv) he implici arge for he Selic rae has shown a decline over ime; v) he degree of ineres rae smoohing has shown a relaive sabiliy. Keywords: forward-looking moneary policy rule; ime-varying parameer model; Brazil. JEL Classificaion: C3, E5, C50. 1

2 1 Inroducion In he las 0 years, several papers have esimaed differen specificaions of he reacion funcion in order o sudy he decisions of he cenral banks regarding he ineres rae of he moneary policy. A quie well known specificaion is Taylor (1993) rule, given by: i i 1,5 0,5y According o ha rule, he cenral bank increases he nominal ineres rae, i, as a response o inflaion deviaions from he arge, π - π, and he oupu gap, y. Anoher specificaion which has received considerable aenion is he forwardlooking reacion funcion proposed by Clarida e al. (1998, 000): 1 i (1 ) E ( ) E ( Y ) i n n In his policy rule, he policymaker adjuss he curren ineres rae based upon he fuure values expeced for inflaion (π +n ) and oupu gap (y +n ). Several works in he Brazilian lieraure seek o esimae reacion funcions for he moneary policy. 1 Wihin ha lieraure, some papers have highlighed imporan coefficien variaions in he moneary policy rules. For example, Salgado e al. (005) noe he differen dynamics of he Selic ineres rae, during and ou of periods of exchange rae crisis. Policano and Bueno (006) show ha he responses of he Selic rae o inflaion, produc and exchange rae, were differen beween he pre and pos inflaion arge periods. Bueno (005) and Lima e al. (007) esimae a Markovswiching reacion funcion and poin ou he exisence of differen moneary policy regimes afer he Real Plan. Barcellos Neo and Porugal (007) found empirical evidence ha, during he Henrique Meirelles adminisraion, he Selic rae responded less o he deviaions of expeced inflaion from he arge inflaion and more o exchange rae variaions when compared o Arminio Fraga s adminisraion. Medeiros and Aragon (011) noe ha he Brazilian moneary auhoriy reaced more srongly o inflaion deviaions regarding he arge and o he oupu gap afer 003. In his paper, we seek o esimae a reacion funcion wih ime-varying parameers in order o analyze possible changes in moneary policy by he Cenral Bank of Brazil (BCB) during he inflaion argeing regime. Since he proposed moneary policy rule presens endogenous regressors, he convenional Kalman filer leads o invalid inferences regarding he model; herefore i mus no be applied. Due o his, we follow Kim (006) and use a wo-sep esimaion procedure, similar o ha of Heckman (1976). In his procedure, he erms of bias correcion are enered in he second sep. To correc possible regressor generaed problems, he Augmened Kalman Filer is used. We also es he null hypohesis of non-endogeneiy in he reacion funcion of he moneary auhoriy. The resuls found, indicae ha he reacion funcion parameers of he BCB are ime-varying and ha he regressors of ha funcion, are endogenous. Besides, we observed ha: i) he Selic rae responses o curren inflaion and he inflaionary expecaions, presen considerable changes and have diminished wih he passing of ime; ii) since mid-010, policy rule has violaed he Taylor principle; iii) he implici arge for he Selic rae has shown a decline over ime; iv) he degree of ineres rae 1 See, for example Silva and Porugal (001), Minella e al. (003), Holland (005), Soares and Barbosa (006), Teles and Brundo (006), and Aragón and Porugal (010).

3 smoohing has shown a relaive sabiliy. Finally, he policy insrumen response o he oupu gap, presens an increasing rend/endency over he period. Besides his inroducion, his paper consiss of four secions. The second secion presens he heoreical model used in he sudy. In secion 3, we have he specificaion of he reduced form of he reacion funcion, as well as he descripions of he wo-sep esimaion procedure and he Augmened Kalman filer. The fourh secion presens he analysis of he resuls. The final conclusions of he paper are in he fifh secion. Opimal moneary policy in a forward-looking model In order o analyze opimal decisions of moneary policy, we follow Clarida e al. (1999) and we consider a hree componen model. The firs one relaes o he consrains of he conrol problem faced by he policymaker and consiss of wo equaions: an IS curve, which governs he dynamics of he oupu; and a Phillips curve, ha describes he dynamics of inflaion. The second one is he loss funcion of he cenral bank, which describes he objecives of he moneary policy. The hird componen is he opimal moneary policy rule ha shows how he cenral bank deermines he opimum pah for he nominal ineres rae..1 The srucure of economy In his subsecion, here is a brief descripion of he log-linearized version of he New- Keynesian model, wih sicky prices, analyzed by Clarida e al. (1999). According o his model, he evoluion of an economy is represened by he following wo-equaion sysem: y E y ( i E ) u (1) d 1 1 s E 1 ky u () where y is he oupu gap (his is, he difference beween he acual and he poenial oupu), π, is he inflaion rae, E y +1 and E π +1 are he expeced values of he oupu gap and inflaion rae condiional on he available informaion a, i is he nominal d s ineres rae, u and u are, a demand shock and a cos shock respecively. The φ, k and α parameers, are posiive consans. The IS curve, given by he equaion (1), is a log-linearized version of Euler s equaion for consumpion, derived from he opimum decision of households on consumpion and savings, afer he imposiion of he marke s clearing condiion. The expeced value for he oupu gap shows ha, since families prefer smoohing ou consumpion over ime, he expeced higher level of consumpion leads o an increased curren consumpion, hereby increasing he presen demand for he produc. On he oher hand, he Phillips curve, given by equaion (), grasps he characerisic of overlapping nominal price, where firms have he probabiliy α of mainaining he produc price fixed, a any period of ime (Calvo, 1983). Since he probabiliy of α is supposedly consan and independen of he ime elapsed since he las adjusmen, he average duraion in which he price remains fixed is 1/1-α. The The aggregae behavioural equaions (1) and () are explicily derived from opimizing behaviour of firms and households, in an economy wih nominal rigidiies of prices and currency (Clarida e al., 1999) 3

4 discree naure of price adjusmen, resuling from his fac, encourages each firm o se a higher price when he higher is he expecaion of fuure inflaion. d s Finally, shocks u and u comply wih he following auoregressive processes: u u u (3) d d d d ˆ u 1 u u u (4) s s s s ˆ u 1 where 0 d, s 1, u ˆ d and u ˆ s are i.i.d random variables wih zero mean and u u sandard deviaions and s, respecively. d. The cenral bank s loss funcion and he opimal moneary rule Le us suppose ha he moneary policy decisions are aken before he performance of d s he shocks u and u. Condiional on he informaion available a he end of he previous period, he moneary auhoriy seeks o choose he curren ineres rae i and a sequence of fuure ineres raes in order o minimize: 1 L (5) 0 E subjeced o he srucure of he economy, given by equaions (1) and (), where δ is he fixed discoun facor. The loss funcion a ime, L, is given by: 1 L y i i i i i i 1 in which π is he inflaion arge, is he relaive weigh on he deviaion of he oupu from he poenial level, i and Δi are relaive weighs given in order o sabilize he ineres rae around an implici arge, i, and of he ineres rae a -1, i The moneary auhoriy is supposed o sabilize inflaion around he inflaion arge, mainaining he oupu gap close o zero, and o sabilize he nominal ineres rae around he arge and ha of he nominal ineres rae a -1. To solve he opimizaion problem (5), i is assumed ha moneary policy is discreionary. 4 This implies ha he cenral bank akes he expecaions of fuure variables as given and chooses he curren ineres rae for each period. Since here is no endogenous persisence in he inflaion and oupu gap, he ineremporal opimizaion problem can be reduced o a succession of saic opimizaion problems. Thus, aking he firs order condiion, we arrive a he following expression: E E ( y ) ( i i ) ( i i ) 0 (7) 1 1 i i 1 Solving ino i, he moneary policy rule can be expressed as follows: (6) 3 The ineres rae smoohing is jusified for several reason, such as: i) presence of uncerainies regarding he value of he daa and coefficiens of he macroeconomic model; ii) grea changes in he ineres rae migh desabilize financial markes and foreign exchange; iii) consan variaion in he shor erm ineres rae, even if small, would cause grea effec on aggregae demand and inflaion. For a heoreical and empirical research on he ineres rae smoohing of moneary policy, see Clarida e al. (1998), Sack (1998), Woodford (1999, 003) and Sack and Wieland (000). 4 Palma and Porugal (011) found evidence in favour of a discreionary moneary policy in Brazil during he 000 o 010 period. 4

5 i (1 ) 0 1E 1 E 1( y ) i 1 (8) i in which 0 i ; 1 ; ;. i i i i From equaion (8) on, i can be observed ha he opimal nominal ineres rae for period responds linearly o he deviaions of he expeced inflaion from he inflaion arge and he oupu gap expeced for period. Regarding he smoohing parameer, θ, we can observe ha: i) if μ i > 0 and μ Δi > 0, hen 0 < θ < 1; ii) if μ i = 0 and μ Δi > 0, hen θ = 1; iii) if μ Δi = 0 and μ i > 0, hen θ = 0; iv) if μ i = μ Δi = 0, hen θ will be indeerminae. 3 A moneary rule wih ime-varying parameers and a wo-sep procedure Wih he aim of esimaing he reduced reacion funcion form (8), an exogenous random shock o he ineres rae, m, is included in ha expression. I is presumed ha his shock is i.i.d and can be inerpreed as he pure random componen of moneary policy. Besides, in order o capure changes in he policy conducion, i is considered ha he reacion funcion parameers are ime-varying and assume a dynamic random walk. This specificaion, proposed by Cooley and Presco (1976) has been used in several papers and, is a way of considering Lucas (1976) criicism regarding he inadequacy of economeric models wih consan parameers for policy evaluaion. 5 Finally, he expeced inflaion and oupu gap values in (8) are subsiued by heir observed values. From hese changes, we arrive a he following reacion funcion wih ime-varying parameers i ( ) y i e, e i. i. d.n(0, ) (9) 0, 1,, 1 e (1 ), i 0,1, (10) i, i,, i. i. d.n(0, ) (11) i, i, 1 i, i,, i 1 3,, 3, i. i. d.n(0,,3) (1) in which e 1, ( E 1( )), ( y E 1( y )) m. Coefficiens and 1, (β, 1, and β, ) measure he shor-run (long-run) response and hose of he Selic rae regarding inflaion and he oupu gap. As he forecased errors of inflaion and he oupu gap make up he erm e, i is possible o observe ha π and y are correlaed wih his error erm. In ha case, he esimaion of (9)-(1) hrough he convenional Kalman filer via Maximum Likelihood canno be performed because his procedure is derived under he assumpion ha he regressors and disurbances are no correlaed. In order o correc he endogeneiy problem, insrumenal variables will be used. In paricular, he relaionship beween he endogenous regressors and heir insrumens will be given by: z v, v N(0, ) (13) v1 y z v, v N(0, ) (14) v 5 Examples of oher works ha suppose he parameers of he model follow a random walk are Cogley and Sargen (001, 005), Boivin (006) and Kim and Nelson (006). 5

6 in which z is he vecor of he insrumens. For simpliciy s sake, i is assumed ha he relaionship among he endogenous regressors and heir insrumens, are consan. 3.1 A wo-sep Maximum Likelihood procedure The wo-sep esimaion procedure sars from he decomposiion of π e y ino wo componens: prediced componens and predicion error componens. Doing his, we have: v1 E 1 y y v v1 1v v 1, i. i. d. N, v v v where ψ -1 is he available informaion in -1 and Ω is he variance covariance marix for a vecor of predicion errors, v = [v 1 v ]'. Taking a vecor of x1 sandardized predicion errors, v = [v 1 v ]', we have he covariance srucure beween v and e : v 0 I, e N e 0 ' e e where ρ = [ρ 1 ρ ]'is a consan correlaion vecor. As in Kim (006), he Cholesky decomposiion of he covariance marix resuls in he following represenaion: v I e 0 0 I, i. i. d. N, e ' (1 ' ) e e where 0 is a x1 vecor of zeros. From (18), hen we have: 1 e 1 e 1 e (15) (16) (17) (18) e v v, N(0,(1 ) ) (19) where ω is no correlaed wih eiher v 1 or v. Equaion (19) shows ha e in equaion (9) can be broken down ino he following componens: i) v 1 and v, which are correlaed wih π and y ; and ii) he ω componen, ha is no correlaed wih π and y. Subsiuing equaion (19) in (9), resuls in: i ( ) y i v v (9') 0, 1,, 1 1 e 1 e In equaion (9'), he new error erm is no correlaed wih π, y, v 1 or v.therefore, he esimaion procedure for he Maximum Likelihood (ML) is given in wo seps: Sep 1: Esimae equaions (13) and (14) hrough ML or Ordinary Leas Squares (OLS) and obain he sandardized predicion errors, v and v. Sep : Esimae hrough ML using he Kalman filer equaion 0, 1,, 1 1 e 1 e ˆ1 i ( ) y i vˆ vˆ (9'') ogeher wih equaions (11) and (1). As highlighed by Kim and Nelson (006), he sandardized predicion errors v ˆ 1 and v ˆ are included in (9'') as bias correcion erms. This is similar o he wo-sep procedure proposed by Heckman (1976). In ha case, he bias correcion erms are ˆ 6

7 insered in order o capure possible changes in he degree of uncerainy associaed wih inflaion and oupu gap, which are aken ino accoun in he moneary policy rule The Augmened Kalman filer The reacion funcion wih ime-varying parameers (9 ) can be expressed as: i X vˆ vˆ, N(0,(1 ) ) (0) 1 e 1 e 1 e 1, i. i. d. N(0, ) (1) where X 1 y i 1, 0, 1,, and is he deviaion of he inflaion from is arge. For his model, he Kalman filer can be described using he following equaions:, 1 F 1 1 () P 1 FP 1 1 F, (3) i X v v (4), e 1 e H, 1 X P 1 X (5) 1 P X H (6), P P P X H X P Alhough he Kalman filer provides he correc inference in β,, he P -1 and P variances are incorrec measures. To correc he endogeneiy bias, he inference in β mus be condiioned o he bias correcion erms v 1 and v. In his way, equaion (7) provides he variance of β condiional on informaion up o ime, and on he bias correcion erms. In conras, he correc variance of β canno be subjeced o he bias correcion erms. In order o purge he effecs of hese correcion erms, he correc inferences of he condiional variances of β are obained by he Augmened Kalman filer, where he following equaions are insered: 1 1 e, (7) H X P X (8) P P P X H X P (9) 1, P 1 FP F. (30) For a more accurae inference abou β, he smooh values of hese parameers, β T, are esimaed in which all he informaion available in he sample is used. According o Kim (004) he smoohing filer is given by he following equaions ha are ineraced for =T-1, T-,...,1: PP ( ) (31) 1 T 1 1 T 1 P P P P ( P P ) P P 1 1 T 1 1 T An alernaive specificaion for he reacion funcion of he BCB Following Minella e al. (003), Minella and Souza-Sobrinho (009) and Aragón and Porugal (010), an alernaive specificaion of he reacion funcion will also be esimaed, which includes he deviaion of he expeced inflaion from he inflaion arge. In his case, he moneary policy rule is expressed by: (3) 7

8 i ( ) y i e, e i. i. dn(0, ) (33) e 0, 1,, 11, 1 e (1 ), i 0,1, (34) i, i,, i. i. d. N(0, ) (35) i, i, 1 i, i,, i 1 3,, 3, i. i. d.n(0,,3) (36) e where, is he expeced inflaion, welve monhs ahead, condiioned o he 11 informaion available in. e Since, and y 11 are poenially endogenous variables, he esimaion procedure described above will be used in he following way: 6 i) he regressions z v, v N(0, ) (37) e, v1 y z v, v N(0, ) (38) v will be esimaed hrough OLS or ML and hose of sandardized predicion errors v ˆ1 and v ˆ will be obained; ii) esimae he reacion funcion by ML hrough he Kalman filer i y i vˆ vˆ (39) e 0, 1,, 11, 1 1 e 1 e e e where, 11, 11 is he deviaion of he expeced inflaion from he inflaion arge. 4 Resuls 4.1 Descripion of he daa and uni roo ess For he esimaion of he BCB s reacion funcion specificaions, monhly series were considered for he period beween January 000 and December The series were obained from he sies of he Insiue of Applied Economic Research (IPEA) and he BCB. The ineres rae variable, i, is he annualized monhly accumulaed Selic ineres rae. This variable has been used as he major moneary policy insrumen in he inflaion argeing regime. Inflaion is measured by he percenage variaion accumulaed during he las welve monhs of he Broad Consumer Price Index (IPCA). 8 The inflaion arge series refers o he accumulaed inflaion arge for he following 1 6 Regarding he deerminans of he inflaion expecaions in Brazil, see Bevilaqua e al. (007) and Carvalho and Minella (01). 7 Alhough he sample begins in January 000, he observaions used o esimae he reacion funcion (in sep wo) begin in November 001. This is due o he use of he firs 1 observaions as iniial values in he regressions, esimaed in he firs sep, and of he following 10 observaions o obain he iniial values of he regression coefficiens in sep wo. This las procedure was suggesed by Kim and Nelson (1999, 006) o diminish he effec of arbirary iniial values of he β parameers on he value of he loglikelihood funcion. 8 The IPCA is calculaed by he Brazilian Insiue of Geography and Saisics (IBGE) and is he price index used as reference for he inflaion argeing regime. 8

9 monhs. Since he Naional Moneary Council (CMN) ses inflaion arges for calendar years, he daa were inerpolaed. 9 The expeced inflaion (π e,+1) concerns he median inflaion forecas welve monhs ahead (accumulaed inflaion beween e +11) made by he marke and colleced by he BCB s Invesor Relaions and Special Sudies Deparmen (Gerin). For he period beween January 000 and Ocober 001, he BCB research does no presen direc informaion regarding he expeced inflaion for he following welve monhs bu, i provides informaion abou inflaion expecaions for he curren year and he nex. In his case, we follow Minella and Souza-Sobrinho (009) approximaing π e,+11, subracing he inflaion effecive value, unil he curren monh expecaions for he curren year and using he expecaions for he following year proporionaely o he number of remaining monhs The oupu gap (y ) is measured by he percenage difference beween he index of indusrial producion seasonally adjused (y ) and he poenial oupu (yp ), which is x = 100(y - yp )/yp. Here arises an imporan problem because he poenial produc is an unobservable variable and herefore i mus be esimaed. Given his, i has become he rend of he oupu esimaed by he Hodrick-Presco (HP) filer, as a proxy for he poenial oupu. The insrumen se includes a consan erm, 1-3 lagged values of he Selic rae and of he exchange rae (ΔE ), 1-3, 6, 9, 1 lagged values of he inflaion (or expeced inflaion) and -4, 6, 9, 1 lagged values of he oupu gap. 10 Besides hose variables, he ime dummies d 0M10 and d 08M11 for 00M10 and 008M11:009M1 were included in he regressions for he oupu gap (equaions 14 and 38), and he dummy d 0M11 for 00M11 was included in he regressions for inflaion and expeced inflaion (equaions 13 and 37). 11 Before proceeding wih he esimaions, he abovemenioned variables were esed o see if hey were saionary. To begin wih, we invesigaed he inegraion order of he variables hrough six ess, namely: ADF (Augmened Dickey-Fuller); Phillips- Perron (PP); KPSS, proposed by Kwiakowski e al. (199); ERS, by Ellio e al. (1996); and ess MZ α GLS and MZ GLS, suggesed by Perron and Ng (1996) and Ng and Perron (001). The null hypohesis of ess ADF, PP, ERS, MZ α GLS and MZ GLS is ha he series is non-saionary (uni roo es) while in he KPSS ess, he null hypohesis is ha he series is saionary. As indicaed by Ng and Perron (001), choosing he number of lags (k) was based on he Modified Akaike Informaion Crierion (MAIC) considering a maximum number of lags k max = in(1(t/100) 1/4 ) = 13. A consan erm (c) and a linear rend () were included as deerminisic componens for he cases in which hose componens were saisically significan. 9 In he consrucion of he inflaion argeing regime series, i was aken ino accoun ha he BCB pursued a se goal of 8.5% in 003 and 5.5% in 004, as well as a arge of 5.1% in 005. For deails abou he se goals and he announced goal for 005, see Open Leers of 003 and 004 sen by he BCB o he Miniser of Finance and he noes of he meeing of he Moneary Policy Commiee (Copom) of Sepember The exchange rae is he percenage variaion of he nominal exchange rae real/dollar (period average). 11 These dummies were insered o capure he srong curren inflaion increase and inflaionary expecaions a he end of 00, he economic crisis of 008 and an oulier (00:10) in he oupu gap series.. 9

10 Table 1: Uni roo ess Variable Exogenous Regressors ADF(k) PP KPSS ERS(k) MZ GLS α (k) MZ GLS (k) i c, n.s (4) -.55 n.s (4) n.s (9) -.1 n.s (9) Δi (0) n.s 1.11 (0) -3.3 (0) (0) π c n.s (13) -.7 n.s (13) (13) (13) π e,+11 c () () () -.8 () π c -.87 (0) n.s 4.84 n.s (0) (0) (0) y (0) n.s 1.77 (0) (0) -.77 (0) E (3) n.s 0.78 (3) (13) (13) Noe: Significan a 1%. Significan a 5%. Significan a 10%. n.s Non-significan. The ess in Table 1, generally show ha he roo uni hypohesis can be rejeced in he inflaion series, expeced inflaion, arge inflaion, oupu gap and exchange rae. For he Selic rae, he resuls show ha his variable is non-saionary. Since he non-rejecion of he null hypohesis of he roo uni in he Selic rae may be due o he exisence of a srucural break in he rend funcion, wo procedures were underaken. 1 Firs, he Exp-W FS saisic proposed by Perron and Yabu (009) was used, in order o es he null hypohesis of non-srucural break, in he rend funcion of he Selic rae agains he alernaive hypohesis of a break in he inercep and slope of he rend funcion a an unknown dae. 13 The value calculaed of ha saisic (8.07) implies he rejecion of he no break hypohesis a a significance level of 1%. In he face of his, wo uni roo ess wih srucural break were performed. Following Carrion-i- Silvesre e al. (009), saisics MZ α GLS and MZ GLS were used o es he uni roo null hypoheses allowing a srucural break in he unknown dae endency funcion under boh hypohesis, null and alernaive. The values obained for MZ α GLS (-9.) and MZ GLS (-3.79) allow us o rejec he uni roo hypohesis in he Selic rae a 5% significance. 4. Esimaion of he reacion funcion wih ime-varying parameers The firs sep o esimae he reacion funcion of he BCB consised in obaining he esimaes of he sandardized predicion errors, v ˆ1 and v ˆ. For his purpose, equaions (13), (14), (37) and (38), ha relae he endogenous regressors wih he insrumens, were esimaed hrough ML. As preliminary specificaion ess showed he presence of auoregressive condiional heeroskedasiciy, i was considered ha he errors of equaions (13) and (37) follow a GARCH(1,1) and GARCH(,1) process, respecively. I is also imporan o menion ha he F-saisics for he esimaed regressions in his firs sage was always above he value of 10 indicaed by Saiger and Sock (1997) as a rule-of-humb hreshold above which he weak insrumen problem is no observed. Table shows he esimaed parameers for he reacion funcion of he moneary policy (9'') wih and wihou he bias correcion erms. The esimaes for he sandard errors σ ε, i, i=0,1,, are saisically significan, suggesing ha here is a emporary variaion in he β coefficiens of he moneary policy rule. This evidence is corroboraed by he likelihood raio es (LR) calculaed o he null hypohesis of 1 See, for example, Perron (1989). 13 Perron and Yabu (009) inroduce ess for srucural breaks in he endency funcion ha do no need, a priori knowledge, if he noise componen of he series is saionary or presens a roo uni. These auhors also show ha, in he case in which he srucural break is unknown, he funcional Exp-W FS of he Wald es produces a es wih nearly idenical limi disribuions for he case of a noisy componen I(0) or I(1). Due o his, he es procedures, wih nearly he same size, can be obained for boh cases. 10

11 consan parameers (H 0 : σ ε, 0 = σ ε, 1 = σ ε, = σ ε, 3 = 0). 14 For he specificaion wih bias correcion, he value and p-value of he LR saisics were and , respecively, indicaing rejecion of he null hypohesis a a 1% significance level. Since he LR es for he parameers sabiliy is conservaive 15, he resuls found here show ha he BCB reacion o inflaion and o he oupu gap have changed along ime. Regarding he endogeneiy problem of he regressors in he reacion funcion, i can be observed ha only he esimaed coefficien for he correcion erm bias of he oupu gap, ρ, was significan. Furher sill, he value of he LR saisic (13.65) o es he null hypohesis of no endogeneiy (H 0 : ρ 1 = ρ = 0) indicaes he rejecion of ha hypohesis a a 1% significance level. These resuls show ha o ignore possible endogeneiy problems may resul in serious biases in he ime-varying coefficiens of he moneary policy rule. In order o know if he models are adequaely specified, Table also shows he Ljung-Box (LB) es for serial auocorrelaion of he sandardized predicion errors and for he squared sandardized predicion errors, and he H saisic o es he null hypohesis ha he sandardized predicion errors are homoscedasic. 16 The resuls of hese ess show ha he sandardized predicion errors are no serially correlaed and show a consan variance. Besides, he null hypohesis ha here is no condiional regressive heeroskedasiciy (ARCH effec) in hese predicion errors is no rejeced. Table : Esimaes of he reacion funcion parameers (9'') Model wih bias correcion erms Model wihou bias correcion erms Parameers Sandard Sandard Esimae Esimae errors errors σ ɛ, σ ɛ, σ ɛ, σ ɛ,3 7.43e e σ e e ρ ρ Specificaion ess LB 1 (4) (0.341) 8.00 (0.109) LB (4) (0.737) (0.947) H(41) (0.478) (0.455) ln(l) Noe: LB 1 (4) refers o he Ljung-Box saisic for serial auocorrelaion of he sandardized predicion errors up o order 4. LB (4) refers o he Ljung-Box saisic for serial auocorrelaion of he squared sandardized predicion errors up o order 4. H(41) refers o saisic H for esing he homoskedasiciy of he sandardized predicion errors. Values beween brackes refer o he p-value. The behavior of he reacion funcion coefficiens wih bias correcion erms are presened below. In Figure 1, are he β 0 T rajecories and hose of he persisence coefficien θ T, ogeher wih he confidence bands of ±1.0 sandard errors. As equaion (8) shows, he β 0 T coefficien can be inerpreed as he implici arge for he ineres rae (i ). I is possible o observe ha, during mos par of he period beween 003:1 and 14 The log-likelihood value for he model wih consan parameers and bias correcion erms was See Kim and Nelson (1999, 006). 16 Regarding he H saisic, see Commandeur and Koopman (007). 11

12 005:9, he esimaes for he Selic rae remained above 14% per year. In conras, during he period beween 006 and 011, he esimaed goal varied beween 6.6% and 1.44%. The reducion in β 0 seems o be consisen wih he higher sabiliy of he Brazilian economy afer 003 and wih he curren global economic crisis since 008, which favoured he BCB in pursuing lower arges boh for inflaion and Selic raes. In relaion o he smoohing coefficien of he ineres rae, he resuls reveal a relaive sabiliy of his parameer hroughou ime. Beween November 001 and December 011, his coefficien fell only from 0.94 o Figure 1: Evoluion of coefficiens β 0 T and θ T (dashed lines indicae ±1 sandard error) Figure shows he evoluion of coefficien β 1 T, which measures he long-run response of he Selic rae o he deviaions of inflaion from he arge. The resuls indicae ha ha response presened a high oscillaion during he period, varying beween -3.5 and 5.5. I can also be found ha, in approximaely 61% of he analyzed period, he ineres rae rule did no mee he Taylor principle because he value of his coefficien was less han 1 (blue line in he graph). This is in line wih he evidence obained by Bueno (005) and Lima e al. (007). When comparing he behaviour of β 1 T wih ha of he deviaion of inflaion from he arge, i can be verified ha, in general, he BCB has risen (decreased) is reply in increase (reducions) periods in his deviaion (see Fig. ). However, wo excepions may be noed. In he firs semeser of 003, he β 1 value decreased, while he inflaion remained disanced from is arge. This is observed again saring from March 011, when he inflaion gap rose and reached levels verified in 005, while he response of he Selic rae o inflaion was reduced. 1

13 Figure : Evoluion of he β 1 T coefficien (dashed lines indicae ±1 sandard error) and ha of he deviaion of inflaion from he arge. The response of he Selic rae o he oupu gap (β T ) is shown in Figure 3. To begin wih, i can be observed ha his coefficien remained high beween he fourh rimeser of 00 and he firs semeser of 003, and presened more sabiliy from 004 unil mid-008. Alhough we canno idenify a clear relaionship beween β T and he oupu gap, he esimaes sugges ha since he economic crises, he BCB has increased he Selic rae response o he real aciviy. Figure 3: Evoluion of he β T coefficien (dashed lines indicae ±1 sandard error) and he oupu gap. The esimaes of he reacion funcion parameers (39) are presened in Table 3. As in he previous model, he LR saisic (10,63) shows ha he null hypohesis of he consan parameers is rejeced a a 1% significance level. 17 Addiionally, he LR es of he model wih bias correcion, agains he model wihou correcion, leads o he 17 In his case, he specificaion wih consan parameers and bias correcion erms presened a loglikelihood equal o

14 rejecion of he null hypohesis of exogeneiy of he expeced inflaion and oupu gap in he reacion funcion of he moneary policy. Table 3: Parameer esimaes of he reacion funcion parameers (39) Model wih bias Model wihou bias correcion erms correcion erms Parameers Sandard Sandard Esimae Esimae errors errors σ ɛ, σ ɛ, σ ɛ,.13e e e-6 σ ɛ, σ e ρ ρ Specificaion Tess LB 1 (4) (0.488) 1.34 (0.377) LB (4) 3.63 (0.76) (0.91) 1/H(41) (0.11) (0.19) ln(l) Noe: LB 1 (4) refers o he Ljung-Box saisic for he serial auocorrelaion of sandardized predicion errors up o order 4. LB (4) refers o he Ljung-Box saisic for serial auocorrelaion of squared sandardized predicion errors up o order 4. 1/H(41) refers o saisic 1/H o es he homoskedasiciy of sandardized predicion errors. Values beween brackes refer o he p-value. Figures 4-6 show he rajecories of he esimaed coefficiens for he reacion funcion (39). Once again, he behaviour of β 0 T reveals a downward rend in he implici arge for he ineres rae afer 003. In addiion, Figure 4 shows he Selic rae smoohing, θ T, presened a small reducion, leaving 0.86 in 001:11 o 0.78 in 011:1. Figure 4: Evoluion of coefficiens β 0 T and θ T (dashed lines indicae sandard error) 14

15 The evoluion of he long-run response of he Selic rae o he deviaions of he expeced inflaion from he inflaion arge can be seen in Figure 5. Righ from he sar we can observe ha his response saisfies Taylor principle in mos par of he analyzed period. However, wo excepions o his behaviour can be highlighed. The firs one concerns he passiviy of he moneary policy in he monhs from March o Sepember 00, he period preceding he presidenial elecions of ha year. The second excepion is he period from 010:9-011:1, which has wo unique characerisics: i) i is a period in which he value of β 1 diminished in spie of he inflaion expecaions having increased in relaion o he inflaion arge; and ii) i is he only period in which he Selic rae response o he expeced inflaion reached negaive values. 18 When compared o esimaes β 1 T for he reacion funcion (9 ), shown in Figure, i is noeworhy ha he BCB has responded more srongly o he expeced inflaion han o he curren inflaion. This procedure is consisen wih a forward-looking policy maker and indicaes ha he BCB has been concerned, mainly, in anchoring inflaion expecaions o he inflaion arge se by he CMN. Figure 5: Evoluion of he β 1 T coefficien (dashed lines indicae ±1 sandard error) and of he expeced inflaion deviaion from he arge. 18 I is worh while poining ou ha he confidence inerval does no allow assering ha β 1 was significanly lower han zero during his period. 15

16 Figure 6: Evoluion of he β T coefficien (dashed lines indicae ±1 sandard error) and of he oupu gap (y ). Finally, Figure 6 brings he response of he Selic rae o he oupu gap (β T ).I can be observed ha his coefficien has presened he mos oscillaion beween 00 and 006. Saring in 007, ha coefficien remains relaively sable, varying beween 0.10 and Differenly o he resuls presened in figure 3, we do no observe here a clear increase of ha response saring from he economic crisis. 5 Conclusion In his paper, we have esimaed a forward-looking reacion funcion wih ime-varying parameers, o idenify possible changes in he conducion of he Brazilian moneary policy during he period. In order o solve he endogeneneiy problem of he policy rule regressors, a wo-sep procedure was used, similar o ha of Heckman (1976). This mehodology enables he consisen esimaion of he hyper-parameers and he correc inference of he variances of he model s coefficiens. Due o his, i was possible o analyze he dynamic behaviour of he BCB, in view of some macroeconomic variables such as inflaion and oupu gap. Before proceeding wih he esimaions, wo LR ess were carried ou. Firs, he validiy of he null hypohesis of consan parameers was verified. The resul showed ha he coefficiens of he BCB policy rule have changed along ime. Regarding he endogeneiy problem, he LR es rejeced he hypohesis ha inflaion and he oupu gap are exogenous variables. Therefore, ignoring he endogeneiy problems of hese variables can resul in a serious coefficien esimaion bias. The resuls obained showed imporan changes in he BCB moneary policy rule coefficiens. The implici arge for he Selic rae was reduced hroughou he period. This probably resuled from he increased sabiliy of he Brazilian economy afer 003 and was favoured by he recen global crisis. Regarding he response of ineres raes o inflaion, here was a considerable variaion in ime, albei wih a declining rend. The empirical evidence also indicaes ha: i) in general, he greaer he inflaion deviaion (observed or expeced) in relaion o he arge, he greaer he policy response o ha variable; ii) he BCB has responded more srongly o he expeced inflaion han o he observed inflaion, reflecing in his way he forward-looking behaviour of his moneary auhoriy; iii) since mid-010, he response o inflaion has been lower han 1, hus no saisfying he Taylor principle. 16

17 The response of he policy o he oupu gap differed beween he reacion funcion specificaions. When he observed inflaion was insered in he moneary rule, a relaive sabiliy of his response was noiced beween 003 and 008, and an increase since he 009 economic crisis. As o he specificaion of he reacion funcion, including he expeced inflaion, his rae remained sable afer 003. For fuure research, his work may be advanced as follows: i) perform esimaions wih ime-varying parameers for he reacion funcion specificaions ha are non-linear, due o he asymmeric preferences of he Cenral Bank (see, for example, Aragon and Porugal, 010); ii) consider ha he relaionship beween he endogenous regressors and is insrumens are ime-varying. References ARAGON, E. K. da S. B.; PORTUGAL, M. S. Nonlineariies in Cenral Bank of Brazil s reacion funcion: he case of asymmeric preferences. Esudos Econômicos, v. 40, n., 010. BARCELLOS NETO, P. C. F. de; PORTUGAL, M. S. Deerminans of moneary policy commiee decisions: Fraga vs. Meirelles. Poro Alegre: PPGE/UFRGS, 007. (Texo para Discussão, 11). BEVILAQUA, A. S.; MESQUITA, M.; MINELLA, A. Brazil: Taming Inflaion Expecaion. Brasília: Banco Cenral do Brasil, 007. (Trabalhos para Discussão, 19). BOIVIN, J. Has U.S. moneary policy changed? Evidence from drifing coefficiens and real-ime daa. Journal of Money, Credi and Banking, v. 38, n. 5, 006. BUENO, R. de L. da S. The Taylor Rule under Inquiry: Hidden saes. XXVII Enconro Brasileiro de Economeria. Anais. Naal, 005. CALVO, G. Saggered prices in a uiliy-maximizing framework. Journal of Moneary Economics, v. 1, n. 3, CARRION-I-SILVESTRE, J. L.; KIM, D.; PERRON, P. GLS-based uni roo ess wih muliple srucural breaks boh under he null and he alernaive hypoheses. Economeric Theory, v. 5, 009. CARVALHO, F. A.; MINELLA, A. Survey forecass in Brazil: a prismaic assessmen of epidemiology, performance, and deerminans. Journal of Inernaional Money and Finance, v.31, n.6, 01. CLARIDA, R. e al. Moneary policy rules in pracice: some inernaional evidence. European Economic Review, v. 4, The science of moneary policy: a new Keynesian perspecive. Cambridge: Naional Bureau of Economic Research, (Working Paper, 7147).. Moneary policy rules and macroeconomic sabiliy: evidence and some heory. Quarerly Journal of Economics, v. 115, n. 1,

18 COGLEY, T.; SARGENT, T. Evolving Pos World War II U.S. inflaion dynamics. In: NBER Macroeconomics Annual 16 (org. Ben Bernanke and Kenneh Rogoff). Chicago: The Universiy of Chicago Press, Drifs and volailiies: moneary policies and oucomes in he pos WWII U.S. Review of Economic Dynamics, v. 4, n., 005. COMMANDEUR, J. J. F.; KOOPMAN, S. J. An inroducion o sae space ime series analysis. Oxford: Oxford Universiy Press, 007. COOLEY, T.; PRECOSTT, E. Esimaion in he presence of sochasic parameer variaion. Economerica, v. 44, n. 1, ELLIOTT, G.; ROTHENBERG, T. J.; STOCK, J. H. Efficien ess for an auoregressive uni roo. Economerica, v. 64, n. 4, HECKMAN, J.J. The common srucure of saisical models of runcaion, sample selecion, and limied dependen variables and simple esimaor for such models. Annals of Economic and Social Measuremen, v HOLLAND, M. Moneary and exchange rae policy in Brazil afer inflaion argeing. XXXIII Enconro Nacional de Economia. Anais. Naal, 005. KIM, C. J. Time-Varying-Parameer Models wih Endogenous Regressors: A Two- Sep MLE Approach and an Augmened Kalman Filer (Disponível em: SSRN: hp://ssrn.com/absrac= ) KIM, C. J. Time-varying-parameer models wih endogenous regressors. Economics Leers, v. 91, 006. KIM, C. J.; NELSON, C. R. Sae-space models wih regime swiching classical and gibbs-sampling approaches wih applicaions. Cambridge: The MIT Press, Esimaion of a forward-looking moneary policy rule: a ime-varying parameer model using ex pos daa. Journal of Moneary Economics, v. 53, 006. KWIATKOWSKI, D.; PHILLIPS, P. C. B.; SCHMIDT, P; SHIN, Y. Tesing he null hypohesis of saionary agains he alernaive of a uni roo. Journal of Economerics, v. 54, 199. LIMA, E. C. R.; MAKA, A.; MENDONÇA, M. Moneary policy regimes in Brazil. Insiuo de Pesquisa Econômica Aplicada (IPEA). Rio de Janeiro, 007. (Texo para Discussão, 185a). LUCAS, R. E. Jr. Economeric policy evaluaion: a criique. Carnegie Rocheser Conference Series on Public Policy, v. 1, n. 1,

19 MEDEIROS, G. B.; ARAGÓN, E. K. S. B. Tesando assimerias nas preferências do Banco Cenral em uma pequena economia abera: um esudo para o Brasil. XXXIX Enconro Nacional de Economia. Anais. Foz do Iguaçu, 011. MINELLA, A. e al. Inflaion argeing in Brazil: consrucing credibiliy under exchange rae volailiy. Brasília: Banco Cenral do Brasil, 003. (Trabalhos para Discussão, 77). MINELLA, A.; SOUZA-SOBRINHO, N. F. Brazil hrough he Lens of a Semi- Srucural Model. Brasília: Banco Cenral do Brasil, 009. (Trabalhos para Discussão, 181). NG, S.; PERRON, P. Lag lengh selecion and he consrucion of uni roo ess wih good size and power. Economerica, v. 69, n. 6, 001. PALMA, A. A.; PORTUGAL, M. S. Preferences of he Cenral Bank of Brazil under he Inflaion Targeing Regime: Commimen vs. Discreion. Revisa Brasileira de Economia (Impresso), v. 65, n.4, 011. PERRON, P. The grea crash, he oil price shock and he uni roo hypohesis. Economerica, v. 57, n. 6, PERRON, P; NG, S. Useful modificaions o some uni roo ess wih dependen errors and heir local asympoic properies. The Review of Economic Sudies, v. 63, n. 3, PERRON, P; YABU, T. Tesing for shifs in he rend wih an inegraed or saionary noise componen. Journal of Business and Economic Saisics, v. 7, 009. POLICANO, R.; BUENO, R. A sensibilidade da políica moneária no Brasil: XXXIV Enconro Nacional de Economia. Anais. Salvador, 006. SACK, B. Does he Fed ac gradually? A VAR analysis. Washingon, DC: Board of Governors of he Federal Reserve Sysem, (Finance and Economics Discussion Series, 17). SACK, B.; WIELAND, V. Ineres-rae smoohing and opimal moneary policy: a review of recen empirical evidence. Journal of Economics and Business, v. 5, n. 1-, 000. SAIGER, D.; STOCK, J. H. Insrumenal variables regression wih weak insrumens. Economerica, v. 65, n. 3, SALGADO, M. J. S. e al. Moneary policy during Brazil s Real Plan: esimaing he cenral bank s reacion funcion. Revisa Brasileira de Economia, v. 59, n. 1, 005. SILVA, M. E. A. da; PORTUGAL, M. S. Inflaion argeing in Brazil: an empirical evaluaion. Poro Alegre: PPGE/UFRGS, 001 (Texo para Discussão, 10). 19

20 SOARES, J. J. S.; BARBOSA, F. de H. Regra de Taylor no Brasil: XXXIV Enconro Nacional de Economia. Anais. Salvador, 006. TAYLOR, J. B. Discreion versus policy rules in pracice. Carnegie-Rocheser Conference Series on Public Policy, v. 39, TELES, V. K.; BRUNDO, M. Medidas de políica moneária e a função de reação do Banco Cenral do Brasil. XXXIV Enconro Nacional de Economia. Anais. Salvador, 006. WOODFORD, M. Opimal moneary policy ineria. Cambridge: Naional Bureau of Economic Research, (Working Paper, 761).. Opimal ineres-rae smoohing. The Review of Economics Sudies, v. 70, n. 4,