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1 ISSN Working Paper Series Real Balances in he Uiliy Funcion: Evidence for Brazil Leonardo Soriano de Alencar and Márcio I. Nakane February, 2003

2 ISSN CGC / Working Paper Series Brasília n. 68 Feb 2003 p. 29

3 Working Paper Series Edied by: Research Deparmen (Depep) ( Reproducion permied only if source is saed as follows: Working Paper Series n. 68 Auhorized by Ilan Goldfajn (Depuy Governor for Economic Policy). General Conrol of Subscripion: Banco Cenral do Brasil Demap/Disud/Subip SBS Quadra 3 Bloco B Edifício-Sede 2º subsolo Brasília DF Brazil Phone: (556) Fax: (556) The views expressed in his work are hose of he auhors and do no reflec hose of he Banco Cenral or is members. Alhough hese Working Papers ofen represen preliminary work, ciaion of source is required when used or reproduced. As opiniões expressas nese rabalho são exclusivamene do(s) auor(es) e não refleem a visão do Banco Cenral do Brasil. Ainda que ese arigo represene rabalho preliminar, ciação da fone é requerida mesmo quando reproduzido parcialmene. Banco Cenral do Brasil Informaion Bureau Address: Secre/Surel/Dinfo SBS Quadra 3 Bloco B Edifício-Sede, 2º subsolo Brasília DF Phones: (556) 44 (...) 240, 2402, 2403, 2404, 2405, 2406 DDG: FAX: (556) Inerne: hp:// s: cap.secre@bcb.gov.br dinfo.secre@bcb.gov.br

4 Real Balances in he Uiliy Funcion: Evidence for Brazil * Leonardo Soriano de Alencar ** Márcio I. Nakane *** Absrac The aim of his paper is o examine he relevance of a money-in-he-uiliyfuncion model for he Brazilian economy. In addiion o consumpion, he household is supposed o derive uiliy from leisure and from he holdings of real balances. The sysem, formed by he firs-order condiions of he household ineremporal problem (Euler equaions), is esimaed by generalized mehod of momens (GMM). The resuls show srong suppor for he presence of money in he uiliy funcion for Brazil. Keywords: money in he uiliy funcion, GMM esimaion. JEL Classificaion: D9, E2, E49. * This aricle is par of he firs auhor s Docorae hesis submied o he Deparmen of Economics, Universiy of São Paulo. The views expressed here are hose of he auhors and do no reflec hose of he Cenral Bank of Brasil or is members. ** Research Deparmen, Cenral Bank of Brazil. *** Research Deparmen, Cenral Bank of Brazil, and Deparmen of Economics, Universiy of São Paulo. 3

5 . Inroducion This paper presens an empirical sudy abou he relevance of a model wih money in he uiliy funcion (MIU) esimaed for Brazil. The firs order condiions for an ineremporal opimizaion problem for a represenaive agen are esimaed hrough GMM (Generalized Mehod of Momens). The framework of a represenaive agen is employed due o is analyical simpliciy. The represenaive agen derives uiliy no only from consumpion bu also from he holdings of real balances, and from leisure aciviies. The esimaed uiliy funcion parameers may be useful for researchers working in he field of moneary dynamic general equilibrium models applied o Brazil. To he bes of our knowledge, his is he firs sudy aiming a an empirical evaluaion of a model in he class of Brock (974, 975) Sidrauski (967) using Brazilian daa. I is also he firs paper o simulaneously esimae he uiliy funcion parameers incorporaing consumpion, real balances, and leisure as argumens. Reis e al. (998) make use of he same mehodology as ours o examine he exisence of precauional savings. Issler & Piqueira (2000) invesigae wheher here is an equiy premium puzzle in he counry. These wo aricles, however, only incorporae consumpion in he uiliy funcion. Anoher relaed aricle is by Cosa Val & Ferreira (2002), who esimae a model wih consumpion and leisure in he uiliy funcion o es he performance of some sandard real business cycle models calibraed for Brazil. Anoher novely of he presen paper is he use of he official series for quarerly consumpion, as calculaed by IBGE. Boh Issler & Piqueira (2000) as well as Reis e al. (998) have made use of a quarerly consumpion series calculaed by he las ones. The calculaed series is, presumably, subjec o more measuremen errors han he official esimaes. Wih regard o he inernaional lieraure, here are some papers examining he relevance of MIU models esimaed for he US economy. Holman (998) invesigaed differen uiliy funcion specificaions and found resuls favoring he Brock-Sidrauski model. Dukowsky & Dunsky (998) obained similar resuls when examined he Cosa Val & Ferreira (2002) use annual official daa for consumpion. 4

6 liquidiy of he M2 componens. There are also some less favorable resuls in he lieraure. For example, Finn e al. (990) rejeced several differen MIU specificaions whereas equivalen models wih cash-in-advance consrains could no be rejeced. The presen paper has he following srucure. The nex secion summarizes he heoreical developmens in he field. Secion 3 describes he opimizaion problem for he represenaive household and derives he respecive firs order condiions. Secion 4 briefly commens he esimaion echnique. Secion 5 describes he daa. Secion 6 presens he resuls, and Secion 7 summarizes he main findings. 2. Theoreical background Woodford (999, p.4) menions ha he presence of money in he uiliy funcion capures he imporance of he liquidiy services associaed o is holdings. Money has he role of reducing fricions in economic ransacions, which benefis he agens. Obsfeld & Rogoff (996, p.530) cie he reducion of ime spen in economic ransacions as one example of such benefis. Money reduces such fricions due o is purchasing power and i is herefore he real balances ha should be an argumen in he uiliy funcion. The money-in-he-uiliy specificaion can be inerpreed as a shorcu o models involving ransacions coss. Transacions coss can be inroduced eiher as a diversion of ime from leisure and work aciviies or else as a pecuniary cos in he household budge consrain [Saving (97), McCallum & Goodfriend (987)]. Feensra (986) formally demonsraed he funcional equivalence beween a model wih consumpion and real balances as argumens of he uiliy funcion and enering money ino liquidiy coss, which appear in he budge consrain. Liquidiy coss are supposed o have boh consumpion and real balances as argumens. Feensra also shows ha liquidiy coss appearing in budge consrains can arise in convenional Baumol-Tobin money demand models. 5

7 The funcional equivalence esablishes an exac dualiy beween wo models by a redefiniion of he choice variables, such ha boh he objecive funcion and he consrains exhibi idenical forms. This is achieved by Feensra (986) by a redefiniion of consumpion ino a new variable ( gross consumpion ), aken as he sum of consumpion and liquidiy coss. However, when he labor-leisure choice is endogenous, i is no possible o obain such an isomorphism by redefining he consumpion variable. A weaker form of equivalence may be useful in his case, ha of qualiaive equivalence. Two models are said o be qualiaive equivalen when heir comparaive saic resuls are idenical in sign. Wang and Yip (992) sudy he qualiaive equivalence beween a model wih consumpion, money, and leisure in he uiliy funcion and a model wih a shoppingime echnology. The comparaive saic resuls are hose associaed o a once-and-forall change in he (consan) money growh rae. The auhors show ha boh models generae idenical comparaive saic predicions (excep for leisure 2 ) when he uiliy funcion is such ha here is Pareo complemenariy beween consumpion and leisure, beween consumpion and money, and Pareo subsiuabiliy beween leisure and money. Under such condiions, boh models predic ha an increase in he money growh rae leads o a fall in he capial sock, in labor, in money holdings, in consumpion, and in welfare. Moreover, he capial-labor raio is no affeced by he increase in he money growh rae. The liquidiy cos specificaion adoped by Feensra (986) assumes ha money is a consumpion good. Zhang (2000) generalizes he pecuniary ransacions cos o consider money alernaively as () a consumpion good, (2) a producion good, (3) an invesmen good, and (4) a consumpion as well as an invesmen good. Like Wang and Yip (992), Zhang also inroduces leisure as an argumen in he money-in-he-uiliyfuncion specificaion and also invesigaes he qualiaive equivalence of changes in he money growh rae. Zhang shows ha when he consumpion effec dominaes he real 2 An increase in he money growh rae increases leisure in he money-in-he-uiliy-funcion specificaion while he resul is ambiguous for he shopping-ime model. For he laer, here are wo opposie forces a work. Firs, here is a negaive real balance effec: he reducion in real balances arising from a higher money growh rae increases shopping ime, which decreases leisure. Second, here is a posiive consumpion effec: when he money growh rae increases, consumpion reduces, reducing shopping ime and, herefore, increasing leisure. When he laer effec is he dominan, boh models generae he same predicion for leisure as well. 6

8 balance effec (see foonoe 2), an increase in he money growh rae is accompanied by increased leisure, and by reducions in he capial sock, in labor, in real balances, in consumpion, and in welfare for all he four specificaions for ransacions coss. In addiion, when money is specified as a consumpion good, he capial-labor raio is unaffeced by he money growh rae, whereas his raio is negaively affeced by he money growh rae for he oher hree specificaions. The equivalence resuls are imporan because many heoreical implicaions of he money-in-he-uiliy-funcion models depend on he signs of he cross derivaives of he uiliy funcion, for which here are no srong priors. On he oher hand, he required resricions on he ransacions echnology are more familiar and more palaable. 3. The model In he presen paper, he represenaive agen is supposed o maximize he expeced value of his discouned uiliy flow by choosing he amoun of consumpion, he ime dedicaed o leisure i.e. he available ime no dedicaed o work, and he levels of real balances and financial asses subjec o a sequence of budge consrains: m j j E β U c j,,t h j () j= 0 P + j c ( + R ) P m + = w h + D d d + (2) P P P m where E is he condiional expecaions operaor, condiioned on he informaion se available a ime, β (0,) is he ineremporal discoun rae, c is real consumpion a ime, d is he real volume of one-period fixed income financial asses a ime, R D is he ineres rae accruing in reurn for he holdings of he financial asse payable a (+), h is he number of hours devoed o working, w is he wage rae per hour worked, and T is he oal number of hours available for working and for leisure. Following sandard noaional convenion in he lieraure, m + represens he nominal balances held by he household a he end of period, and P is he general price level a 7

9 period. We assume ha ( c m P, T h ) funcion. U + j + j+ + j + j, is a quasiconcave, ime separable The opimizaion problem faced by he represenaive agen consiss in maximizing () subjec o he budge consrain (2). The firs order condiions for his problem are he following 3 : () w U () U 3 = (3) U P U U 2 () βu ( + )( + R ) = E () R D = () ( + R ) D P + D (4) (5) Equaion (3) informs ha he household equaes he marginal uiliy of leisure o he cos of foregone consumpion. The consumpion Euler equaion (4) indicaes ha he marginal cos of reducing consumpion in one uni a period is equal o he expeced discouned value of purchasing one real uni of he financial asse a and consume he proceeds in period +. Equaion (5) reflecs he rade-offs involved in he opimal choice of real balances. 4 Holman (998) esimaed differen funcional forms for uiliy funcions wih money as one of he argumens. The resuls found by his auhor indicae ha more elaboraed specificaions do no significanly improve he empirical performance of he models for he US economy. Based on such findings, we assume ha he period uiliy funcion is well represened by a consan relaive risk aversion (CRRA) funcional form: 3 Equaions (4) and (5) are obained hrough he maximizaion wih respec o he financial asse and o he real balances. U i (), i =, 2, 3 refers o he parial derivaive of he uiliy funcion wih respec o he i h argumen evaluaed a period. 4 For issues relaed o he exisence of equilibrium in money-in-he-uiliy funcion models see Brock (974, 975). For he possibiliy of muliple sable pahs for hese models, see Calvo (979) and Obsfeld (984). For discussions on he arising of divergen speculaive pahs for such models, see Obsfeld & Rogoff (983) and Gray (984). 8

10 9 ( ) ( ) ( ) = + + > = + + +, ln ln ln 0 and,,, φ γ α φ φ φ γ α h T P m c h T P m c h T P m c U, Ν (6) A special case of (6) ha will play a role in he empirical secion below is he Cobb- Douglas funcional form, which arises when 0 = φ. Wih he CRRA specificaion for he uiliy funcion, he firs order condiions can be rewrien as: ( ) = 0 γ c h T w (7) ( ) 0 ) ( ) ( 2 = D P P R h T h T P m P m c c E β φ γ φ α φ (8) ( ) 0 = + + D D c R R P m α (9) 4. The esimaion echnique The model presened in he previous secion will be esimaed by he Generalized Mehod of Momens (GMM) procedure. There are some excellen exbook exposiions of his echnique. See, among ohers, Davidson & Mackinnon (993), Hamilon (994), and Greene (2000). See also he surveys in Hall (993), Ogaki (993), and he volume edied by Máyás (999). Thus, his secion will only briefly ouch on some of he issues involved in GMM esimaion. The basic idea of he esimaion of he firs order condiions of an ineremporal opimizaion model hrough GMM is fairly simple and i was firs inroduced by Hansen

11 & Singleon (982). According o hese auhors, he soluion of a dynamic opimizaion problem leads o a se of sochasic Euler equaions, which has o be saisfied in equilibrium. Such equaions imply a se of populaion orhogonaliy condiions, which depends on observable variables and on unknown preference parameers. The esimaion procedure consiss in aking he sample versions of he orhogonaliy condiions as close o zero as possible according o some defined meric. The GMM esimaor is a non-linear insrumenal variable esimaor. Hansen (982) obains he sufficien condiions for his esimaor o be srongly consisen, asympoically normal, and efficien in he class of insrumenal variable esimaors defined by orhogonaliy condiions. When here are more insrumens (or sample orhogonaliy condiions) han parameers o be esimaed, he model is said o be overidenified. The overidenifying resricions can be esed hrough he J es developed by Hansen (982, p.049). Hansen & Singleon (982) menion he following wo advanages of esimaing Euler equaions hrough GMM: ) Unlike he maximum likelihood (ML) esimaor, he GMM esimaor does no require he specificaion of he join disribuion of he observed variables. ML esimaion may no be consisen when he disribuion is no correcly specified [Hansen & Singleon (982, p.278)] 5. 2) The insrumen vecor does no need o be economerically exogenous; he only requiremen is ha his vecor be predeermined in he period when he agen forms his expecaions. Thus, boh pas and presen values of he variables in he model can be used as insrumens. Moreover, he GMM esimaor is consisen even when he insrumens are no exogenous or when he disurbances are serially correlaed. However, hese feaures are relaed o he asympoic properies of he GMM echnique. As for he performance of GMM in small samples, Tauchen (986) repors favorable 5 This opic is subjec o conroversy in he lieraure on small samples. For example, Fuhrer e al. (995) found evidence favoring ML esimaion, while Cogley (200) found suppor for he GMM esimaor. According o Cogley (200, p.50), he reason for he discrepancy is relaed o he choice of he insrumens. 0

12 resuls boh for he GMM esimaor as well as for he T J overidenificaion es. The choice of he insrumens mus be made carefully hough since, as invesigaed by Nelson & Sarz (990a, b), he use of poor insrumens i.e. insrumens ha are weakly correlaed wih he regressors can lead o biased esimaes. There are many possibiliies for he choice of insrumens in he GMM esimaion since any variable in he agen s se of informaion in period can, in principle, be used. Fuhrer e al. (995, p.50) sugges a common sense soluion of using lags of he regressors as insrumens. Such variables are usually highly correlaed wih he regressors, alleviaing he poor insrumen problem. Kocherlakoa (990, p. 298) and Mao (990, p.3) recommend he use of few insrumens in small samples. According o hese auhors, he performance of he GMM esimaor and of he T J es improve significanly in his case 6. According o Mao (990, p.20), his improvemen is due o he reducion in he number of resricions being esed in one hand, and o he reducion in sampling errors in he oher. 5. Daa The sysem formed by equaions (7)-(9) was esimaed using daa for he Brazilian economy. The daa for consumpion was aken from quarerly naional accouns available a he SIDRA sysem from IBGE ( We ook he Final Consumpion for Families series. There are wo main series available, namely, a nominal one in curren moneary unis, and an index for a real one. By comparing he wo of hem, we are able o obain a series for real consumpion quoed in moneary unis, which was hen normalized o consan prices for he firs quarer of 200. Per capia consumpion is he raio of real consumpion o oal populaion. Toal populaion is available only a annual frequency. The quarerly series was obained hrough linear inerpolaion using he annual census daa for 99 and Boh Kocherlakoa (990) and Mao (990) have found ha he T J es ends o over rejec a rue model when he number of insrumens rises.

13 Money is measured as M 7. The source for he M series is he Brazilian Cenral Bank. The nominal values a he end of each quarer were firs aken and hen deflaed by he General Price Index IGP-DI calculaed by FGV. The price-adjused series was hen divided by oal populaion o obain he per capia M series. Two alernaive ineres raes were used as proxies for he rae of reurn on he financial asse, namely: he overnigh selic rae, obained from he Cenral Bank; and he reurn on fixed-rae cerificaes of deposis, calculaed by ANDIMA, and obained from IPEADATA ( Boh series were originally available on a monhly basis and hey were boh convered ino quarerly frequencies by capializing he corresponding monhly observaions. There is no available informaion for he number of hours worked nor for wages paid per worker for he counry as a whole. We proxied hem by aking he series called number of hours paid in producion per worker oal indusry and real payroll per worker oal indusry, boh available a he Pesquisa Indusrial Mensal Dados Gerais survey. However, he daa collecion for his survey was sopped in March 200 and was replaced by Pesquisa Indusrial Mensal do Emprego e Salário, which sared in January 200. Boh daa ses are from IBGE, and he quarerly arihmeic means were inerpolaed o generae series from he firs quarer of 99 o he firs quarer of These series, however, are only available as index numbers. In order o obain a measure of he acual number of hours worked we followed Burnside e al. (993, p.252) and Eichenbaum e al. (988, p. 58) and fixed he ime endowmen of each represenaive agen as he oal number of non-slep hours. The ime endowmen for each agen was se o 428 hours per quarer he same assumpion as in Eichenbaum e al. (988) and he original series was hen normalized in such a way ha, along he sample period, he represenaive agen had a fory-hour working week, close o he sauory one. Wih regard o he real wage per hour worked, we equaed he average index for he real payroll per worker series for 2000 o one-fourh of he sum of he accouns remuneraion of employees and remuneraion of self-employed found a he 7 One limiaion of he M series is ha i is no possible o spli he shares held by he households from hose held by he firms and by he governmen. 2

14 Brazilian Naional Accouns for The index series was hen used o find he remaining observaions. 6. Empirical Resuls Figure shows he evoluion of he ransformed variables ha will be used in he empirical esimaion of he model. The daa spans he firs quarer of 99 he firs available observaion for quarerly consumpion series unil he firs quarer of 2002, and he series were convered ino per capia erms as explained in he previous secion. Figure : Transformed Variables Used for Esimaion Growh of real balances Growh of real consumpion Growh of leisure (M/price)*[CD/(+CD)]/consumpion (M/price)*[over/(+over)]/consumpion CD real reurn Overnigh selic real reurn wage*leisure/real consumpion Noe: Series shown are quarerly daa on per capia erms. Wage means real wage per hour worked. As can be seen in Figure, here is a srucural break in he ( m + P )[ RD ( + RD )] c series saring in he hird quarer of 994, he launching of he Real Plan. The GMM 3

15 esimaor is srongly consisen, asympoically normal, and efficien as long as boh he insrumen se and he ransformed variables are saionary. On his accoun, esimaions of he model will be only performed for he sub-sample saring in he hird quarer of 994. Due o he same reason, boh he ( m + P )[ RD ( + RD )] c series as well as he real ineres raes were adjused for possible deerminisic rends in he sub-sample saring in he hird quarer of 994. The procedure was o, firs, ake he residuals of a regression of each series on an inercep and a rend. The rend-adjused variable is hen he sum of he residual wih he sample mean for he respecive variable. 8 GMM esimaion requires ha here are a leas as many momen resricions as parameers o be esimaed. The model is called over-idenified when here are more momen resricions han parameers. In such a case, a weighing marix deermines he relaive imporance of each momen resricion. Hansen (982) showed ha i is possible o choose his marix opimally in he sense ha i yields an esimaor wih he smalles asympoic covariance marix among he class of esimaors ha uses weighing marices. A necessary condiion o obain efficien esimaes is o equae he weighing marix o he inverse of he sample momens covariance marix. The esimaor used here will be robus o heeroskedasiciy and serial correlaion of unknown form (HAC). The lieraure presens differen weighing marix esimaors 9. We follow Ogaki (993, p.477) who saes ha Mone Carlo evidence recommends he use of prewhiened sample momens and quadraic specral kernel ogeher wih Andrews (99) auomaic bandwidh parameer 0. In order o avoid biased esimaion and poor performance of he GMM esimaor, he chosen insrumen se for each firs order condiion include a consan and he 8 Robusness ess checking he influence of his derending mehod in he resuls are repored below. 9 See Ogaki (993, Secion 6), and Cushing & McGarvey (999). 0 On he oher hand, he Mone Carlo resuls presened by Cushing & McGarvey (999, p.82) do no lead o a clear conclusion abou which HAC esimaor has he bes small sample performance. This performance would depend on he disribuion of he error process. Their resuls also show ha he use of HAC esimaors lead o quasi -saisics ha rejec a rue null more ofen han heir nominal size, impairing inference. 4

16 ransformed variables appearing in ha firs order condiion. Only one wo-period lag of he insrumens is used.. The daa se consiss of quarerly observaions; so i is expeced ha seasonaliy may be presen in some series. To deal wih his issue, seasonal dummies will be included boh in he esimaed equaions and in he insrumen se, when hey are significanly differen from zero a he 5 percen level 2. Table presens he benchmark resuls for he CRRA specificaion. The T J-es indicaes non-rejecion of he money-in-he-uiliy-funcion model a he usual significance levels. In addiion, he esimaed parameer for real balances, α, is posiive and significanly greaer han zero a he percen level. This resul provides some suppor for he view ha real money balances provide liquidiy services ha conribue direcly o uiliy in Brazil, which means ha he use of models in he class of Brock- Sidrauski seems o be valid. Moreover, he resuls do no seem o be influenced by he use of alernaive measures for he ineres rae. TABLE Parameers Esimaes from a CRRA Uiliy Funcion Ineres Rae β φ α γ T J CD (0.0032) (0.30) (0.000) (0.0272) (0.5266) Over selic (0.0033) (0.263) (0.004) (0.0276) (0.5283) Noe: Esimaed sandard deviaions appear in parenheses under he parameers esimaes. P-values are in parenheses below he T J Saisics. The weighing marix follows Andrews (99) mehodology wih quadraic specral kernel and prewhiening. The insrumen se for each Euler equaion includes a consan and he ransformed variables enering in he respecive Euler equaion, wih only one lag of wo periods. The sample period is 994(3)-2002(). The esimae for he ineremporal discoun rae, β, is close o one and significanly greaer han zero a he percen level. The poin esimaes are greaer han he ones found by Reis e al. (998, p.265) [beween 0.8 and 0.89] and in line wih he esimaed median (0.97) obained by Issler & Piqueira (2000, Table c) boh sudies The wo-period lag is jusified by Ogaki (993, p.477) on he grounds ha nominal variables in moneary models are no aligned over ime in he same way as hey are in he corresponding real model. In addiion, agens informaion ses are also considered differenly in moneary and real models. 2 Ogaki (993, p.475) saes ha deerminisic seasonal dummies can be viewed as arificial saionary sochasic processes, and can herefore be included in sysems esimaed by GMM. The robusness of he resuls o seasonally adjused daa is checked below. 5

17 using quarerly daa wih seasonal dummies. The esimaed discoun rae is smaller han ha found in sudies wih U.S. daa Holman (998), for example, esimaes a discoun rae close o 0.96 using annual daa, which is equivalen o a quarerly discoun rae of 0.989, which denoes a greaer impaience of he Brazilian consumers. One possible reason for such behavior, as suggesed by Reis e al. (998, p.264), is he low per capia income in Brazil. The poin esimaes for he relaive risk aversion coefficien φ are negaive bu hey are no significanly differen from zero. Thus, a reducion o Cobb-Douglas preferences canno be rejeced. 3 The esimaed values for φ are smaller han he ones repored by Reis e al. (998, p.265) [beween 3.6 and 6.43], and by Issler & Piqueira (2000) [median value of.7 for quarerly daa wih seasonal dummies]. The comparison, however, is no appropriae due o he inclusion of differen argumens in he uiliy funcion for each sudy. The esimaed coefficien relaed o leisure, γ, is also posiive and significanly greaer han zero. For comparison, he esimaes are close o he.430 value obained by Araújo & Ferreira (999, p. 46) 4. However, comparisons across differen sudies can be misleading because γ depends on he choice of oal ime endowmen and on he assumpion abou he average hours worked per week. Esimaes for γ can herefore change wih differen ses of assumpions abou hese values. Moreover, he value of γ can also change wih differen adjusmens for income axaion. Two ses of robusness checks were performed. Table 2 presens he resuls wih differen reamens for seasonaliy and for derending. Table 3 presens esimaion resuls when alernaive weighing marices are used. 3 We presen below he esimaes for he Cobb-Douglas uiliy funcion. 4 Araújo & Ferreira (999) obained he value for his parameer calibraing a real business cycle model using 995 Brazilian daa. 6

18 TABLE 2 Parameers Esimaes from a CRRA Uiliy Funcion [ Differen approaches o seasonaliy and rend Ineres Rae: CD ] Approach β φ α γ T J SAd (0.0080) (.6368) (0.000) (0.035) (0.6746) SAdTr (0.063) (2.8049) (0.004) (0.032) (0.770) Tr (0.004) (0.280) (0.0008) (0.0360) (0.75) Noe: Esimaed sandard deviaions appear in parenheses under he parameers esimaes. P-values are in parenheses below he T J Saisics. SAd means ha seasonally adjused daa were used. SAdTr means ha seasonally adjused daa and non-derended daa were used. Tr means ha non-derended daa were used and ha seasonaliy was reaed using seasonal dummies. TABLE 3 Parameers Esimaes from a CRRA Uiliy Funcion [ Differen weighing marices Ineres rae: CD ] Covariance β φ α γ T J Marix ABP (0.0032) (0.20) (0.000) (0.027) (0.5252) AQ (0.0036) (0.77) (0.0006) (0.054) (0.330) AB (0.0032) (0.097) (0.0005) (0.045) (0.2467) NWFBP (0.0024) (0.292) (0.0005) (0.020) (0.46) NWFB (0.0028) (0.35) (0.0005) (0.057) (0.2966) NWBP (0.002) (0.243) (0.0006) (0.0272) (0.608) NWB (0.0036) (0.384) (0.0006) (0.066) (0.4452) Noe: Esimaed sandard deviaions appear in parenheses under he parameers esimaes. P-values are in parenheses below he T J Saisics. ABP is he mehod due o Andrews (99) wih Barle kernel and prewhiening. AQ is he mehod due o Andrews (99) wih quadraic specral kernel and wih no prewhiening. AB is he mehod due o Andrews (99) wih Barle kernel and wih no prewhiening. NWFBP is he mehod due o Newey & Wes (987) wih fixed bandwidh, Barle kernel and prewhiening. NWFB is he mehod due o Newey & Wes (987) wih fixed bandwidh, Barle kernel and wih no prewihening. NWB is he mehod due o Newey & Wes (994) wih Barle kernel and prewihening. NWB is he mehod due o Newey & Wes (994) wih Barle kernel and no prewihening. The insrumen se as well as he sample period is he same as in Table. Wih regard o seasonaliy, one can eiher include seasonal dummies in each equaion o be esimaed or else seasonally adjus he daa. Seasonal adjusmen was made hrough he muliplicaive X- mehod. Table 2 shows ha, apar from he relaive risk aversion coefficien φ, he resuls are no sensiive o differen seasonal adjusmens or o he 7

19 inclusion of non-derended daa. The poin esimaes for φ change subsanially bu neiher of hem are saisically significan. The comparison of he resuls presened in Table 3, which uses alernaive weighing marices, o he resuls of Table shows ha lile differences emerge wih he excepion, again, of he esimaes for φ. The range of variaion for he esimaed β is in he inerval o 0.977, which is much narrower han he range repored by Reis e al. (998, p. 265) and by Issler and Piqueira (2000). The poin esimaes for γ showed variaions ranging from.3278 o The variaion found for he esimaes of α ranged from o The larges inerval of values was obained for φ, for which he esimaes ranged from 0.05 o Moreover, hree of he repored esimaes for his coefficien are significanly differen from zero. In view of he discrepan resuls obained for he coefficien of relaive risk aversion, wo oher ses of esimaion were performed. In he firs of hem, he resricion leading o Cobb-Douglas preferences (φ = 0) was imposed and in he oher one, he resricion leading o logarihmic preferences (φ = ) was imposed. Tables 4 o 6 repor he esimaes for he Cobb-Douglas uiliy funcion as well as he resuls of he same robusness checks. None of he esimaions are rejeced by T J es. The overall conclusion is ha he esimaed values for he oher parameers change very lile across he differen specificaions. The range of variaion found for β, α, and γ are, respecively [0.9690, ], [0.046, 0.065], and [.306,.4045]. TABLE 4 Parameers Esimaes from a Cobb-Douglas Uiliy Funcion Ineres Rae β α γ T J CD (0.0032) (0.0009) (0.0262) (0.6766) Over selic (0.0033) (0.004) (0.0269) (0.6733) Noe: Same as for Table. 8

20 TABLE 5 Parameers Esimaes from a Cobb-Douglas Uiliy Funcion [ Differen approaches o seasonaliy and rend Ineres Rae: CD ] Approach β α γ T J SAd (0.0035) (0.000) (0.036) (0.784) SAdTr (0.0053) (0.004) (0.02) (0.7576) Tr (0.0040) (0.0007) (0.0337) (0.7663) Noe: Same as for Table 2. TABLE 6 Parameers Esimaes from a Cobb Douglas Uiliy Funcion [ Differen weighing marices Ineres rae: CD ] Approach β α γ T J ABP (0.0032) (0.0009) (0.026) (0.6790) AQ (0.002) (0.0004) (0.006) (0.3779) AB (0.003) (0.0005) (0.024) (0.3505) NWFBP (0.0025) (0.0004) (0.078) (0.5023) NWFB (0.0025) (0.0004) (0.04) (0.433) NWBP (0.0023) (0.0005) (0.0230) (0.6522) NWB (0.0024) (0.0004) (0.022) (0.4866) Noe: Same as for Table 3. Tables 7 o 9 repor he esimaions for he logarihmic uiliy funcion. The T J overidenifying resricion es does no rejec any of he esimaed equaions. One can see ha, for his funcional form, he esimaed values lie in a wider inerval. The range of variaion for β, α, and γ are, respecively, given by [0.9008, ], [0.043, 0.088], and [.3069,.4358]. 5 5 Esimaed values for β are found o be much lower only when seasonal dummies are included. 9

21 TABLE 7 Parameers Esimaes from a Logarihmic Uiliy Funcion Ineres Rae β α γ T J CD (0.000) (0.0008) (0.0335) (0.847) Over selic (0.00) (0.002) (0.0345) (0.827) Noe: Same as for Table. TABLE 8 Parameers Esimaes from a Logarihmic Uiliy Funcion [ Differen approaches o seasonaliy and rend Ineres Rae: CD ] Approach β α γ T J Sad (0.0050) (0.000) (0.09) (0.5379) SAdTr (0.0064) (0.007) (0.02) (0.5669) Tr (0.072) (0.0009) (0.0344) (0.6024) Noe: Same as for Table 2. TABLE 9 Parameers Esimaes from a Logarihmic Uiliy Funcion [ Differen weighing marices Ineres rae: CD ] Approach β α γ T J ABP (0.0099) (0.0009) (0.0330) (0.9076) AB (0.0067) (0.0005) (0.06) (0.344) NWFBP (0.0074) (0.0005) (0.029) (0.738) NWFB (0.0069) (0.0005) (0.055) (0.349) NWBP (0.0074) (0.0005) (0.029) (0.738) NWB (0.0065) (0.0004) (0.066) (0.3365) Noe: Same as for Table 3. Summing up, he esimaes for he relaive risk coefficien show a grea range of variaion across differen specificaions. In mos of he esimaions, his coefficien is no significan implying ha he reducion o Cobb-Douglas preferences is no rejeced. The esimaes for he ineremporal discoun rae are reasonable and, apar from he logarihmic preferences, here are no subsanial differences across he differen specificaions. Mos imporanly, he money-in-he-uiliy funcion model was no 20

22 rejeced in any of he differen esimaes. In all of he esimaes, he parameer linked wih real balances was found o be always posiive, significan, and robus o differen specificaions. Such resuls are favorable evidence o he view ha real balances provide services ha are valued by he agens. 7. Conclusions In his paper we esimaed and esed a represenaive agen model relaing consumpion, ineres raes, real balances, hours worked, and wage. The model was esimaed by Generalized Mehod of Momens (GMM) echniques. Robusness checks were performed for differen definiions of ineres raes, differen reamens o seasonal and derending adjusmens, differen weighing marices, and differen uiliy funcions. In none of he cases, he model was rejeced for he usual significance levels. Moreover, he esimaed coefficien for real balances was found o be robus o such variaions. The main conribuion of he paper was o find favorable evidence for he Brazilian economy o he view ha real balances play a posiive role for he welfare of agens. Therefore, here is an empirical jusificaion for he developmen of money-in-he-uiliy funcion models applied o Brazil. Anoher conribuion of his paper is he esimaion of some behavioral parameers, which may be useful for hose researchers working wih models calibraed for Brazil. 2

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26 Banco Cenral do Brasil Trabalhos para Discussão Os Trabalhos para Discussão podem ser acessados na inerne, no formao PDF, no endereço: hp:// Working Paper Series Working Papers in PDF forma can be downloaded from: hp:// Implemening Inflaion Targeing in Brazil Joel Bogdanski, Alexandre Anonio Tombini e Sérgio Ribeiro da Cosa Werlang 2 Políica Moneária e Supervisão do Sisema Financeiro Nacional no Banco Cenral do Brasil Eduardo Lundberg Moneary Policy and Banking Supervision Funcions on he Cenral Bank Eduardo Lundberg 3 Privae Secor Paricipaion: A Theoreical Jusificaion of he Brazilian Posiion Sérgio Ribeiro da Cosa Werlang 4 An Informaion Theory Approach o he Aggregaion of Log-Linear Models Pedro H. Albuquerque 5 The Pass-hrough from Depreciaion o Inflaion: A Panel Sudy Ilan Goldfajn e Sérgio Ribeiro da Cosa Werlang 6 Opimal Ineres Rae Rules in Inflaion Targeing Frameworks José Alvaro Rodrigues Neo, Fabio Araújo e Mara Balar J. Moreira 7 Leading Indicaors of Inflaion for Brazil Marcelle Chauve 8 The Correlaion Marix of he Brazilian Cenral Bank s Sandard Model for Ineres Rae Marke Risk José Alvaro Rodrigues Neo 9 Esimaing Exchange Marke Pressure and Inervenion Aciviy Emanuel-Werner Kohlscheen 0 Análise do Financiameno Exerno a Uma Pequena Economia Carlos Hamilon Vasconcelos Araújo e Renao Galvão Flôres Júnior A Noe on he Efficien Esimaion of Inflaion in Brazil Michael F. Bryan e Sephen G. Cecchei 2 A Tes of Compeiion in Brazilian Banking Márcio I. Nakane Jul/2000 Jul/2000 Jul/2000 Jul/2000 Jul/2000 Jul/2000 Jul/2000 Se/2000 Se/2000 Nov/2000 Mar/200 Mar/200 Mar/200 25

27 3 Modelos de Previsão de Insolvência Bancária no Brasil Marcio Magalhães Jano 4 Evaluaing Core Inflaion Measures for Brazil Francisco Marcos Rodrigues Figueiredo 5 Is I Worh Tracking Dollar/Real Implied Volailiy? Sandro Canesso de Andrade e Benjamin Miranda Tabak 6 Avaliação das Projeções do Modelo Esruural do Banco Cenral do Brasil Para a Taxa de Variação do IPCA Sergio Afonso Lago Alves Evaluaion of he Cenral Bank of Brazil Srucural Model s Inflaion Forecass in an Inflaion Targeing Framework Sergio Afonso Lago Alves 7 Esimando o Produo Poencial Brasileiro: Uma Abordagem de Função de Produção Tio Nícias Teixeira da Silva Filho Esimaing Brazilian Poenial Oupu: A Producion Funcion Approach Tio Nícias Teixeira da Silva Filho 8 A Simple Model for Inflaion Targeing in Brazil Paulo Springer de Freias e Marcelo Kfoury Muinhos 9 Uncovered Ineres Pariy wih Fundamenals: A Brazilian Exchange Rae Forecas Model Marcelo Kfoury Muinhos, Paulo Springer de Freias e Fabio Araújo 20 Credi Channel wihou he LM Curve Vicorio Y. T. Chu e Márcio I. Nakane 2 Os Impacos Econômicos da CPMF: Teoria e Evidência Pedro H. Albuquerque 22 Decenralized Porfolio Managemen Paulo Couinho e Benjamin Miranda Tabak 23 Os Efeios da CPMF sobre a Inermediação Financeira Sérgio Mikio Koyama e Márcio I. Nakane 24 Inflaion Targeing in Brazil: Shocks, Backward-Looking Prices, and IMF Condiionaliy Joel Bogdanski, Paulo Springer de Freias, Ilan Goldfajn e Alexandre Anonio Tombini 25 Inflaion Targeing in Brazil: Reviewing Two Years of Moneary Policy 999/00 Pedro Fachada 26 Inflaion Targeing in an Open Financially Inegraed Emerging Economy: he case of Brazil Marcelo Kfoury Muinhos Mar/200 Mar/200 Mar/200 Mar/200 Jul/200 Abr/200 Ago/2002 Abr/200 Maio/200 Maio/200 Jun/200 Jun/200 Jul/200 Ago/200 Ago/200 Ago/200 26

28 27 Complemenaridade e Fungibilidade dos Fluxos de Capiais Inernacionais Carlos Hamilon Vasconcelos Araújo e Renao Galvão Flôres Júnior 28 Regras Moneárias e Dinâmica Macroeconômica no Brasil: Uma Abordagem de Expecaivas Racionais Marco Anonio Bonomo e Ricardo D. Brio 29 Using a Money Demand Model o Evaluae Moneary Policies in Brazil Pedro H. Albuquerque e Solange Gouvêa 30 Tesing he Expecaions Hypohesis in he Brazilian Term Srucure of Ineres Raes Benjamin Miranda Tabak e Sandro Canesso de Andrade 3 Algumas Considerações Sobre a Sazonalidade no IPCA Francisco Marcos R. Figueiredo e Robera Blass Saub 32 Crises Cambiais e Aaques Especulaivos no Brasil Mauro Cosa Miranda 33 Moneary Policy and Inflaion in Brazil ( ): a VAR Esimaion André Minella 34 Consrained Discreion and Collecive Acion Problems: Reflecions on he Resoluion of Inernaional Financial Crises Arminio Fraga e Daniel Luiz Gleizer 35 Uma Definição Operacional de Esabilidade de Preços Tio Nícias Teixeira da Silva Filho 36 Can Emerging Markes Floa? Should They Inflaion Targe? Barry Eichengreen 37 Moneary Policy in Brazil: Remarks on he Inflaion Targeing Regime, Public Deb Managemen and Open Marke Operaions Luiz Fernando Figueiredo, Pedro Fachada e Sérgio Goldensein 38 Volailidade Implícia e Anecipação de Evenos de Sress: um Tese para o Mercado Brasileiro Frederico Pechir Gomes 39 Opções sobre Dólar Comercial e Expecaivas a Respeio do Comporameno da Taxa de Câmbio Paulo Casor de Casro 40 Speculaive Aacks on Debs, Dollarizaion and Opimum Currency Areas Aloisio Araujo e Márcia Leon 4 Mudanças de Regime no Câmbio Brasileiro Carlos Hamilon V. Araújo e Geúlio B. da Silveira Filho 42 Modelo Esruural com Seor Exerno: Endogenização do Prêmio de Risco e do Câmbio Marcelo Kfoury Muinhos, Sérgio Afonso Lago Alves e Gil Riella Se/200 Nov/200 Nov/200 Nov/200 Nov/200 Nov/200 Nov/200 Nov/200 Dez/200 Fev/2002 Mar/2002 Mar/2002 Mar/2002 Abr/2002 Jun/2002 Jun/

29 43 The Effecs of he Brazilian ADRs Program on Domesic Marke Efficiency Benjamin Miranda Tabak e Eduardo José Araújo Lima 44 Esruura Compeiiva, Produividade Indusrial e Liberação Comercial no Brasil Pedro Cavalcani Ferreira e Osmani Teixeira de Carvalho Guillén 45 Opimal Moneary Policy, Gains from Commimen, and Inflaion Persisence André Minella 46 The Deerminans of Bank Ineres Spread in Brazil Tarsila Segalla Afanasieff, Priscilla Maria Villa Lhacer e Márcio I. Nakane 47 Indicadores Derivados de Agregados Moneários Fernando de Aquino Fonseca Neo e José Albuquerque Júnior 48 Should Governmen Smooh Exchange Rae Risk? Ilan Goldfajn e Marcos Anonio Silveira 49 Desenvolvimeno do Sisema Financeiro e Crescimeno Econômico no Brasil: Evidências de Causalidade Orlando Carneiro de Maos 50 Macroeconomic Coordinaion and Inflaion Targeing in a Two- Counry Model Eui Jung Chang, Marcelo Kfoury Muinhos e Joanílio Rodolpho Teixeira 5 Credi Channel wih Sovereign Credi Risk: an Empirical Tes Vicorio Yi Tson Chu 52 Generalized Hyperbolic Disribuions and Brazilian Daa José Fajardo e Aquiles Farias 53 Inflaion Targeing in Brazil: Lessons and Challenges André Minella, Paulo Springer de Freias, Ilan Goldfajn e Marcelo Kfoury Muinhos 54 Sock Reurns and Volailiy Benjamin Miranda Tabak e Solange Maria Guerra 55 Componenes de Curo e Longo Prazo das Taxas de Juros no Brasil Carlos Hamilon Vasconcelos Araújo e Osmani Teixeira de Carvalho de Guillén 56 Causaliy and Coinegraion in Sock Markes: The Case of Lain America Benjamin Miranda Tabak e Eduardo José Araújo Lima 57 As Leis de Falência: uma Abordagem Econômica Aloisio Araujo 58 The Random Walk Hypohesis and he Behavior of Foreign Capial Porfolio Flows The Brazilian Sock Marke Case Benjamin Miranda Tabak 59 Os Preços Adminisrados e a Inflação no Brasil Francisco Marcos R. Figueiredo e Thaís Poro Ferreira Jun/2002 Jun/2002 Ago/2002 Ago/2002 Se/2002 Se/2002 Se/2002 Se/2002 Se/2002 Se/2002 Nov/2002 Nov/2002 Nov/2002 Dez/2002 Dez/2002 Dez/2002 Dez/

30 60 Delegaed Porfolio Managemen Paulo Couinho e Benjamin Miranda Tabak 6 O Uso de Dados de Ala Freqüência na Esimação da Volailidade e do Valor em Risco para o Ibovespa João Maurício de Souza Moreira e Eduardo Facó Lemgruber 62 Taxa de Juros e Concenração Bancária no Brasil Eduardo Kiyoshi Tonooka e Sérgio Mikio Koyama Dez/2002 Dez/2002 Fev/ Opimal Moneary Rules: The Case of Brazil Charles Lima de Almeida, Marco Aurélio Peres, Geraldo da Silva e Souza e Benjamin Miranda Tabak 64 Medium-Size Macroeconomic Model for he Brazilian Economy Marcelo Kfoury Muinhos e Sergio Afonso Lago Alves 65 On he Informaion Conen of Oil Fuure Prices Benjamin Miranda Tabak 66 A Taxa de Juros de Equilíbrio: Uma abordagem múlipla Pedro Calhman de Miranda e Marcelo Kfoury Muinhos 67 Avaliação de Méodos de Cálculo de Exigência de Capial para Risco de Mercado de Careiras de Ações no Brasil Gusavo S. Araújo, João Maurício S. Moreira e Ricardo S. Maia Clemene Fev/2003 Fev/2003 Fev/2003 Fev/2003 Fev/

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