Imperfect rationality and inflationary inertia: a new estimation of the Phillips Curve for Brazil

Fasolo, Angelo Marsiglia; Portugal, Marcelo Savino

doi:10.1590/S0101-41612004000400004

Abstracts

This paper presents some new estimates for the relationship between inflation and unemployment in Brazil based on a new Keynesian hypothesis about the behavior of the economy. Four main hypotheses are tested and sustained throughout the study: i) agents do not have perfect rationality; ii) the imperfection in the agents expectations generating process may be an important factor in explaining the high persistence (inertia) of Brazilian inflation; iii) inflation does have an autonomous inertial component, without linkage to shocks in individual markets; iv) a non-linear relationship between inflation and unemployment is able to provide better explanations for the inflation-unemployment relationship in the Brazilian economy in the last 12 years. While the first two hypotheses are tested using a Markov Switching based model of regime changes, the remaining two are tested in a context of a convex Phillips Curve estimated using the Kalman filter. Despite the methodological and estimation improvements provided in the paper, the impulse-response functions for the monetary policy presented the same properties shown in the literature that uses Brazilian data.

Phillips curve; expectations; inflation; NAIRU-gap; Markov switching models; Kalman filter; SUR

O artigo estima uma nova relação entre emprego e inflação para o Brasil, tendo como pano de fundo hipóteses novo-keynesianas. Quatro hipóteses são testadas e sustentadas: i) os agentes não possuem racionalidade perfeita; ii) a imperfeição na formação das expectativas pode ser determinante no componente inercial da inflação brasileira; iii) a inflação possui componente inercial autônomo; e, iv) relações não-lineares entre inflação e desemprego fornecem melhores resultados para a economia nos últimos 12 anos. Enquanto as duas primeiras hipóteses são verificadas por meio de modelo com mudanças markovianas, as últimas são testadas por uma Curva de Phillips convexa, estimadas pelo Filtro de Kalman. O uso destas estimativas não prejudica as propriedades tradicionais estimadas de funções de resposta da política monetária para o Brasil.

curva de Phillips; expectativas; inflação; hiato do desemprego; modelos markovianos; filtro de Kalman; SUR

Imperfect rationality and inflationary inertia: a new estimation of the Phillips Curve for Brazil

Angelo Marsiglia Fasolo^I; Marcelo Savino Portugal^II

^IResearch Department (DEPEP), Banco Central do Brasil

^IIProfessor of Economics at Federal University of Rio Grande do Sul (UFRGS) and associate researcher of CNPq

ABSTRACT

This paper presents some new estimates for the relationship between inflation and unemployment in Brazil based on a new Keynesian hypothesis about the behavior of the economy. Four main hypotheses are tested and sustained throughout the study: i) agents do not have perfect rationality; ii) the imperfection in the agents expectations generating process may be an important factor in explaining the high persistence (inertia) of Brazilian inflation; iii) inflation does have an autonomous inertial component, without linkage to shocks in individual markets; iv) a non-linear relationship between inflation and unemployment is able to provide better explanations for the inflation-unemployment relationship in the Brazilian economy in the last 12 years. While the first two hypotheses are tested using a Markov Switching based model of regime changes, the remaining two are tested in a context of a convex Phillips Curve estimated using the Kalman filter. Despite the methodological and estimation improvements provided in the paper, the impulse-response functions for the monetary policy presented the same properties shown in the literature that uses Brazilian data.

Keywords: Phillips curve, expectations, inflation, NAIRU-gap, Markov switching models, Kalman filter, SUR.

JEL Classification

E310

RESUMO

O artigo estima uma nova relação entre emprego e inflação para o Brasil, tendo como pano de fundo hipóteses novo-keynesianas. Quatro hipóteses são testadas e sustentadas: i) os agentes não possuem racionalidade perfeita; ii) a imperfeição na formação das expectativas pode ser determinante no componente inercial da inflação brasileira; iii) a inflação possui componente inercial autônomo; e, iv) relações não-lineares entre inflação e desemprego fornecem melhores resultados para a economia nos últimos 12 anos. Enquanto as duas primeiras hipóteses são verificadas por meio de modelo com mudanças markovianas, as últimas são testadas por uma Curva de Phillips convexa, estimadas pelo Filtro de Kalman. O uso destas estimativas não prejudica as propriedades tradicionais estimadas de funções de resposta da política monetária para o Brasil.

Palavras-chave: curva de Phillips, expectativas, inflação, hiato do desemprego, modelos markovianos, filtro de Kalman, SUR.

Full text available only in PDF format.

Texto completo disponível apenas em PDF.

(Recebido em junho de 2003. Aceito para publicação em março de 2004).

The views expressed here are solely the responsibility of the authors and do not reflect those of the Central Bank of Brazil or its members.

ALMEIDA, C. L.; MOREIRA, T. B. S.; PINHEIRO, F. J. Q. Modelos novo-keynesianos de rigidez de preços e de inflação: evidência empírica para o Brasil. Revista Economia Aplicada, São Paulo, v. 6, n. 1, p. 49-65, jan.-mar. 2002.
BAKHSHI, H.; YATES, A. Are U.K. inflation expectations rational? Bank of England Discussion Papers, London, 1998.
BALL, L. Credible disinflation with staggered price setting. American Economic Review, v. 84, p. 282-289, March 1994.
BALL, L. Disinflation with imperfect credibility. Journal of Monetary Economics, v. 35, p. 5-23, 1995.
_______. Near rationality and inflation in two monetary regimes. NBER Working Paper, n. 7988. October 2000.
BALL, L.; MANKIW, N. G. Relative-price changes as aggregate supply shocks. Quarterly Journal of Economics, v. 110, n. 1, p. 161-193, 1995.
BARR, D. G.; CAMPBELL, J. Y. Inflation, real interest rates, and the bond market: a study of U.K. Nominal and index-linked government bond prices. NBER Working Paper, n. 5821. November 1996.
BERK, J. M. Consumers inflation expectations and monetary policy in Europe. Research Memoranda n. 2000-20, Faculteit der Economische Wetenschappen en Econometric. Holland, June 2000.
BERNANKE, B. S.; LAUBACH, T.; MISHKIN, F. S.; POSEN, A. S. Inflation targeting Lessons from the international experience. First edition. New Jersey: Princeton University Press, 1999.
BONOMO, M. A.; GARCIA, R. Tests of conditional asset pricing models in the Brazilian stock market. Textos para discussão do Centre de Recherche et Développement en Économique da Université de Montréal. Canada, 1997.
BONOMO, M. A.; CARRASCO, V.; MOREIRA, H. Aprendizado evolucionário, inércia inflacionária e recessão em desinflações monetárias Rio de Janeiro: Departamento de Economia da Pontifícia Universidade Católica do Rio de Janeiro, 2000. (Texto para discussão n. 437).
BRYAN, M. F.; CECCHETTI, S. G. Inflation and the distribution of price changes. Review of Economics and Statistics, v. 81, n. 2, p. 188-196, 1999.
CALVO, G. A. Staggered prices in a utility-maximizing framework. Journal of Monetary Economics, v. 12, n. 3, p. 983-998, Set. 1983.
CARROLL, C. D. The epidemiology of macroeconomic expectations. NBER Working Paper, n. 8695. December 2001.
CATI, R. C.; GARCIA, M. G. P.; PERRON, P. Unit roots in the presence of abrupt governmental interventions with an application to Brazilian data. Rio de Janeiro: Departamento de Economia da Pontifícia Universidade Católica do Rio de Janeiro, dez. 1995. (Texto para discussão n. 349).
CLEMENS, M. P.; KROLZIG, H-M. Modeling business cycles features using switching regime models. Discussion Paper n. 58, University of Oxford, 2001.
DAHL, C. M.; HANSEN, N. L. The Formation of Inflation Expectations under changing inflation regimes. Studies of Nonlinear Dynamics and Econometrics, The MIT Press, v. 4, n. 4, 2001.
DAVIDSON, R.; MACKINNON, J. Several tests for model specification in the presence of alternative hypotheses. Econometrica, v. 49, p. 781-793, 1981.
DAVIES, R. B. Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika, v. 64, p. 247-254, 1977.
DEBELLE, G.; LAXTON, D. Is the Phillips curve really a curve? Some evidence for Canada, the United Kingdom and the United States. IMF Staff Papers, v. 44, Jun. 1997.
ERCEG, C. J.; LEVIN, A. T. Imperfect credibility and inflation persistence. Working Papers, Board of Governors of the Federal Reserve, n. 2001-45, Oct. 2001.
ESTRELLA, A.; MISHKIN, F. S. Rethinking the role of NAIRU in monetary policy: implications of model formulation and uncertainty. NBER Working Paper, n. 6518, April 1998.
FERRI, P.; GREENBERG, E.; DAY, R. H. The Phillips curve, regime Switching, and the NAIRU. Journal of Economic Behavior & Organization, v. 46, p. 23-37, 2001.
FIGUEIREDO, F. M. R. Evaluating core inflation measures for Brazil Banco Central do Brasil, March 2001. (Discussion Paper 14)
FUHRER, J.; MOORE, G. Inflation persistence. Quarterly Journal of Economics, v. 110, p. 127-159, 1995.
GAGNON, J. E. Long memory in inflation expectations: evidence from international financial markets. Board of Governors of the Federal Reserve, International Finance Discussion Papers n. 538. February 1996.
GALÍ, J.; GERTLER, M. Inflation dynamics: a structural econometric analysis. Journal of Monetary Economics, v. 44, p. 195-222, 1999.
GARCIA, R.; PERRON, P. An analysis of the real interest rate under regime shifts. Review of Economics and Statistics, v. 78, p. 111-125, 1996.
GORDON, R. The time-varying NAIRU and its implications for economic policy. NBER Working Paper, n. 5735. August 1996.
GRANT, A. P.; THOMAS, L. B. Inflationary expectations and rationality revisited. Economic Letters, v. 62, p. 331-338, 1999.
GREENE, W. H. Econometric analysis. Fourth edition. New Jersey: Prentice Hall, 2000.
HAMILTON, J. D. Analysis of time series subject to changes in regime. Journal of Econometrics, v. 45, p. 3970, 1990.
__________. Time series analysis. Princeton University Press, 1994.
JOHANSEN, S. Likelihood-based inference in cointegrated vector autoregressive models. Oxford University Press, 1995.
KIM, S. Do monetary policy shocks matter in G-7 countries? Using common identifying assumptions about monetary policy across countries. Journal of International Economics, v. 48, p. 387-412, 1999.
KIM, C-J.; NELSON, C. R. State-space models with regime Switching Classical and Gibbs-sampling approaches with applications. Cambridge: The MIT Press, 2000.
KROLZIG, H-M. Econometric modelling of Markov-Switching vector autoregressions using MSVAR for Ox. Oxford: Nuffield College, 1998.
LIMA, E. C. R. The NAIRU, unemployment and the rate of inflation in Brazil. Rio de Janeiro: Instituto Pesquisa Econômica Aplicada IPEA, August 2000. (Discussion Paper n. 753).
LOURENCO, R. A.; GRUEN, D. Price stickiness and inflation. Reserve Bank of Australia. March 1995. (Research Discussion Paper n. 9502).
MANKIW, N. G.; REIS, R. Sticky information versus sticky prices: a proposal to replace the new keynesian Phillips curve. Harvard Institute of Economic Research. May 2001 (Discussion Paper n. 1922).
MCCALLUM, B. Comment. NBER Macroeconomics Annual, p. 355-359, 1997.
MINELLA, A. Monetary policy and ination in Brazil (1975-2000): a VAR estimation. Banco Central do Brasil, November 2001 (Discussion Paper n. 33).
MIO, H. The Phillips curve and underlying inflation. Monetary and Economic Studies, p. 85-107, May 2001.
PASTORE, A. C. Déficit público, a sustentabilidade do crescimento das dívidas interna e externa, senhoriagem e inflação: uma análise do regime monetário brasileiro. Revista de Econometria, v. 14, n. 2, p. 177-234, Nov. 1994 Mar. 1995.
PHILLIPS, A. W. The relation between unemployment and the rate of change of money wage rates in the United Kingdom, 1861-1957. Economica, v. 25, November 1958.
PORTUGAL, M. S.; MADALOZZO, R. C. Um modelo de NAIRU para o Brasil. Revista de Economia Política, v. 20, n. 4 (80), p. 26-47, out./dez., 2000.
RAGAN, C. Deriving agents inflation forecasts from the term structure of interest rates. Bank of Canada. January 1995 (Working Paper n. 95-1).
ROBERTS, J. M. New keynesian economics and the Phillips curve. Journal of Money, Credit and Banking, v. 27, n. 4, parte I, p. 975-984, November 1995.
_______. Is inflation sticky?. Journal of Monetary Economics, v. 39, p. 173-196, 1997.
_______. Inflation expectations and the transmission of monetary policy. Board of Governors of the Federal Reserve, Finance and Economics Discussion Series Paper n. 1998-43, 1998.
_______. How well does the new-keynesian sticky-price model fix the data. Board of Governors of the Federal Reserve, Finance and Economics Discussion Series Paper n. 2001-13, 2001.
ROCHA, F. Long run limits on the Brazilian government debt. Revista Brasileira de Economia, n. 4, 1997.
SARGENT, T. J. Bounded rationality in macroeconomics. Oxford University Press, 1993.
_______. The conquest of American inflation. Princeton University Press, 1999.
SCHOR, A.; BONOMO, M. A.; PEREIRA, P. L. V. Arbitrage pricing theory (Apt) e variáveis macroeconômicas: um estudo empírico sobre o mercado acionário brasileiro. Rio de Janeiro: Departamento de Economia da Pontifícia Universidade Católica do Rio de Janeiro, dez. 1998 (Textos para Discussão n° 391).
SIMS, C. A. Interpreting the macroeconomic time series facts: the effects of monetary policy. European Economic Review, v. 36, p. 975-1000, 1992.
SÖDERLIND, P. Forward interest rates as indicators of inflation expectations. Working Paper of the Institute for International Studies of the Stockholm University. May 1995.
STAIGER, D.; STOCK, J. H.; WATSON, M. W. How precise are the estimates of the natural rate of unemployment? NBER Working Paper, n. 5477, March 1996.
_______. Prices, wages and the U.S. NAIRU in the 1990s. NBER Working Paper, n. 8320, June 2001.
TABAK, B. M.; ANDRADE, S. C. Testing the expectation hypothesis in the Brazilian term structure of interest rates. Banco Central do Brasil, November 2001 (Discussion Paper n. 30).
TAYLOR, J. B. Aggregate dynamics and staggered contracts. Journal of Political Economy, v. 88, n. 1, p. 1-24, 1980.
_______. Staggered wage and price setting in macroeconomics. In: TAYLOR, J. B.; WOODFORD, M. Handbook of macroeconomics. New York: North-Holland, 1999, cap. 15.
TEJADA, C. A. O.; PORTUGAL, M. S. Credibility and reputation: an application of the external circumstances model for the Real Plan. In: XXVIII Encontro Brasileiro de Econometria, 18. Salvador, 2001. Anais do XXVIII Encontro Brasileiro de Econometria, v. II.
WALSH, C. E. Monetary theory and policy. Massachusetts: MIT Press, 2000.

Publication Dates

Publication in this collection
28 Sept 2009
Date of issue
Dec 2004

History

Accepted
Mar 2004
Received
June 2003

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

[1] ALMEIDA, C. L.; MOREIRA, T. B. S.; PINHEIRO, F. J. Q. Modelos novo-keynesianos de rigidez de preços e de inflação: evidência empírica para o Brasil. Revista Economia Aplicada, São Paulo, v. 6, n. 1, p. 49-65, jan.-mar. 2002.

[2] BAKHSHI, H.; YATES, A. Are U.K. inflation expectations rational? Bank of England Discussion Papers, London, 1998.

[3] BALL, L. Credible disinflation with staggered price setting. American Economic Review, v. 84, p. 282-289, March 1994.

[4] BALL, L. Disinflation with imperfect credibility. Journal of Monetary Economics, v. 35, p. 5-23, 1995.

[5] _______. Near rationality and inflation in two monetary regimes. NBER Working Paper, n. 7988. October 2000.

[6] BALL, L.; MANKIW, N. G. Relative-price changes as aggregate supply shocks. Quarterly Journal of Economics, v. 110, n. 1, p. 161-193, 1995.

[7] BARR, D. G.; CAMPBELL, J. Y. Inflation, real interest rates, and the bond market: a study of U.K. Nominal and index-linked government bond prices. NBER Working Paper, n. 5821. November 1996.

[8] BERK, J. M. Consumers inflation expectations and monetary policy in Europe. Research Memoranda n. 2000-20, Faculteit der Economische Wetenschappen en Econometric. Holland, June 2000.

[9] BERNANKE, B. S.; LAUBACH, T.; MISHKIN, F. S.; POSEN, A. S. Inflation targeting Lessons from the international experience. First edition. New Jersey: Princeton University Press, 1999.

[10] BONOMO, M. A.; GARCIA, R. Tests of conditional asset pricing models in the Brazilian stock market. Textos para discussão do Centre de Recherche et Développement en Économique da Université de Montréal. Canada, 1997.

[11] BONOMO, M. A.; CARRASCO, V.; MOREIRA, H. Aprendizado evolucionário, inércia inflacionária e recessão em desinflações monetárias Rio de Janeiro: Departamento de Economia da Pontifícia Universidade Católica do Rio de Janeiro, 2000. (Texto para discussão n. 437).

[12] BRYAN, M. F.; CECCHETTI, S. G. Inflation and the distribution of price changes. Review of Economics and Statistics, v. 81, n. 2, p. 188-196, 1999.

[13] CALVO, G. A. Staggered prices in a utility-maximizing framework. Journal of Monetary Economics, v. 12, n. 3, p. 983-998, Set. 1983.

[14] CARROLL, C. D. The epidemiology of macroeconomic expectations. NBER Working Paper, n. 8695. December 2001.

[15] CATI, R. C.; GARCIA, M. G. P.; PERRON, P. Unit roots in the presence of abrupt governmental interventions with an application to Brazilian data. Rio de Janeiro: Departamento de Economia da Pontifícia Universidade Católica do Rio de Janeiro, dez. 1995. (Texto para discussão n. 349).

[16] CLEMENS, M. P.; KROLZIG, H-M. Modeling business cycles features using switching regime models. Discussion Paper n. 58, University of Oxford, 2001.

[17] DAHL, C. M.; HANSEN, N. L. The Formation of Inflation Expectations under changing inflation regimes. Studies of Nonlinear Dynamics and Econometrics, The MIT Press, v. 4, n. 4, 2001.

[18] DAVIDSON, R.; MACKINNON, J. Several tests for model specification in the presence of alternative hypotheses. Econometrica, v. 49, p. 781-793, 1981.

[19] DAVIES, R. B. Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika, v. 64, p. 247-254, 1977.

[20] DEBELLE, G.; LAXTON, D. Is the Phillips curve really a curve? Some evidence for Canada, the United Kingdom and the United States. IMF Staff Papers, v. 44, Jun. 1997.

[21] ERCEG, C. J.; LEVIN, A. T. Imperfect credibility and inflation persistence. Working Papers, Board of Governors of the Federal Reserve, n. 2001-45, Oct. 2001.

[22] ESTRELLA, A.; MISHKIN, F. S. Rethinking the role of NAIRU in monetary policy: implications of model formulation and uncertainty. NBER Working Paper, n. 6518, April 1998.

[23] FERRI, P.; GREENBERG, E.; DAY, R. H. The Phillips curve, regime Switching, and the NAIRU. Journal of Economic Behavior & Organization, v. 46, p. 23-37, 2001.

[24] FIGUEIREDO, F. M. R. Evaluating core inflation measures for Brazil Banco Central do Brasil, March 2001. (Discussion Paper 14)

[25] FUHRER, J.; MOORE, G. Inflation persistence. Quarterly Journal of Economics, v. 110, p. 127-159, 1995.

[26] GAGNON, J. E. Long memory in inflation expectations: evidence from international financial markets. Board of Governors of the Federal Reserve, International Finance Discussion Papers n. 538. February 1996.

[27] GALÍ, J.; GERTLER, M. Inflation dynamics: a structural econometric analysis. Journal of Monetary Economics, v. 44, p. 195-222, 1999.

[28] GARCIA, R.; PERRON, P. An analysis of the real interest rate under regime shifts. Review of Economics and Statistics, v. 78, p. 111-125, 1996.

[29] GORDON, R. The time-varying NAIRU and its implications for economic policy. NBER Working Paper, n. 5735. August 1996.

[30] GRANT, A. P.; THOMAS, L. B. Inflationary expectations and rationality revisited. Economic Letters, v. 62, p. 331-338, 1999.

[31] GREENE, W. H. Econometric analysis. Fourth edition. New Jersey: Prentice Hall, 2000.

[32] HAMILTON, J. D. Analysis of time series subject to changes in regime. Journal of Econometrics, v. 45, p. 3970, 1990.

[33] __________. Time series analysis. Princeton University Press, 1994.

[34] JOHANSEN, S. Likelihood-based inference in cointegrated vector autoregressive models. Oxford University Press, 1995.

[35] KIM, S. Do monetary policy shocks matter in G-7 countries? Using common identifying assumptions about monetary policy across countries. Journal of International Economics, v. 48, p. 387-412, 1999.

[36] KIM, C-J.; NELSON, C. R. State-space models with regime Switching Classical and Gibbs-sampling approaches with applications. Cambridge: The MIT Press, 2000.

[37] KROLZIG, H-M. Econometric modelling of Markov-Switching vector autoregressions using MSVAR for Ox. Oxford: Nuffield College, 1998.

[38] LIMA, E. C. R. The NAIRU, unemployment and the rate of inflation in Brazil. Rio de Janeiro: Instituto Pesquisa Econômica Aplicada IPEA, August 2000. (Discussion Paper n. 753).

[39] LOURENCO, R. A.; GRUEN, D. Price stickiness and inflation. Reserve Bank of Australia. March 1995. (Research Discussion Paper n. 9502).

[40] MANKIW, N. G.; REIS, R. Sticky information versus sticky prices: a proposal to replace the new keynesian Phillips curve. Harvard Institute of Economic Research. May 2001 (Discussion Paper n. 1922).

[41] MCCALLUM, B. Comment. NBER Macroeconomics Annual, p. 355-359, 1997.

[42] MINELLA, A. Monetary policy and ination in Brazil (1975-2000): a VAR estimation. Banco Central do Brasil, November 2001 (Discussion Paper n. 33).

[43] MIO, H. The Phillips curve and underlying inflation. Monetary and Economic Studies, p. 85-107, May 2001.

[44] PASTORE, A. C. Déficit público, a sustentabilidade do crescimento das dívidas interna e externa, senhoriagem e inflação: uma análise do regime monetário brasileiro. Revista de Econometria, v. 14, n. 2, p. 177-234, Nov. 1994 Mar. 1995.

[45] PHILLIPS, A. W. The relation between unemployment and the rate of change of money wage rates in the United Kingdom, 1861-1957. Economica, v. 25, November 1958.

[46] PORTUGAL, M. S.; MADALOZZO, R. C. Um modelo de NAIRU para o Brasil. Revista de Economia Política, v. 20, n. 4 (80), p. 26-47, out./dez., 2000.

[47] RAGAN, C. Deriving agents inflation forecasts from the term structure of interest rates. Bank of Canada. January 1995 (Working Paper n. 95-1).

[48] ROBERTS, J. M. New keynesian economics and the Phillips curve. Journal of Money, Credit and Banking, v. 27, n. 4, parte I, p. 975-984, November 1995.

[49] _______. Is inflation sticky?. Journal of Monetary Economics, v. 39, p. 173-196, 1997.

[50] _______. Inflation expectations and the transmission of monetary policy. Board of Governors of the Federal Reserve, Finance and Economics Discussion Series Paper n. 1998-43, 1998.

[51] _______. How well does the new-keynesian sticky-price model fix the data. Board of Governors of the Federal Reserve, Finance and Economics Discussion Series Paper n. 2001-13, 2001.

[52] ROCHA, F. Long run limits on the Brazilian government debt. Revista Brasileira de Economia, n. 4, 1997.

[53] SARGENT, T. J. Bounded rationality in macroeconomics. Oxford University Press, 1993.

[54] _______. The conquest of American inflation. Princeton University Press, 1999.

[55] SCHOR, A.; BONOMO, M. A.; PEREIRA, P. L. V. Arbitrage pricing theory (Apt) e variáveis macroeconômicas: um estudo empírico sobre o mercado acionário brasileiro. Rio de Janeiro: Departamento de Economia da Pontifícia Universidade Católica do Rio de Janeiro, dez. 1998 (Textos para Discussão n° 391).

[56] SIMS, C. A. Interpreting the macroeconomic time series facts: the effects of monetary policy. European Economic Review, v. 36, p. 975-1000, 1992.

[57] SÖDERLIND, P. Forward interest rates as indicators of inflation expectations. Working Paper of the Institute for International Studies of the Stockholm University. May 1995.

[58] STAIGER, D.; STOCK, J. H.; WATSON, M. W. How precise are the estimates of the natural rate of unemployment? NBER Working Paper, n. 5477, March 1996.

[59] _______. Prices, wages and the U.S. NAIRU in the 1990s. NBER Working Paper, n. 8320, June 2001.

[60] TABAK, B. M.; ANDRADE, S. C. Testing the expectation hypothesis in the Brazilian term structure of interest rates. Banco Central do Brasil, November 2001 (Discussion Paper n. 30).

[61] TAYLOR, J. B. Aggregate dynamics and staggered contracts. Journal of Political Economy, v. 88, n. 1, p. 1-24, 1980.

[62] _______. Staggered wage and price setting in macroeconomics. In: TAYLOR, J. B.; WOODFORD, M. Handbook of macroeconomics. New York: North-Holland, 1999, cap. 15.

[63] TEJADA, C. A. O.; PORTUGAL, M. S. Credibility and reputation: an application of the external circumstances model for the Real Plan. In: XXVIII Encontro Brasileiro de Econometria, 18. Salvador, 2001. Anais do XXVIII Encontro Brasileiro de Econometria, v. II.

[64] WALSH, C. E. Monetary theory and policy. Massachusetts: MIT Press, 2000.