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Monetary policy in Brazil: evidence of a reaction function with time-varying parameters and endogenous regressors

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Abstract

This paper estimates a forward-looking reaction function with time-varying parameters to examine changes in the Brazilian monetary policy under the inflation-targeting regime. As the monetary policy rule has endogenous regressors, the conventional Kalman filter cannot be applied. Thus, the two-step procedure proposed by Kim and Nelson (J Monet Econ 53:1949–1966, 2006) is used for consistent estimation of the hyper-parameters of the model. The results indicate that the reaction function parameters of the Central Bank of Brazil are time-varying and that the regressors of that function are endogenous. Besides, we observed that: (i) the monetary policy interest rate (Selic rate) responses to current inflation and the inflationary expectations present considerable changes and have diminished with the passing of time; (ii) since mid-2010, policy rule has violated the Taylor principle; (iii) the implicit target for the Selic interest rate has shown a decline over time; and (iv) the degree of interest rate smoothing has shown a relative stability. Finally, the policy instrument response to the output gap presents an increasing trend over the 2010–2011 period.

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Notes

  1. The aggregate behavioral equations (1) and (2) are explicitly derived from optimizing behavior of firms and households, in an economy with nominal rigidities of prices and currency (Clarida et al. 1999).

  2. The interest rate smoothing is justified for several reason, such as: (i) presence of uncertainties regarding the value of the data and coefficients of the macroeconomic model; (ii) great changes in the interest rate might destabilize financial markets and foreign exchange; (iii) constant variation in the short term interest rate, even if small, would cause great effect on aggregate demand and inflation. For a theoretical and empirical research on the interest rate smoothing of monetary policy, see Clarida et al. (1998), Sack (2000), Woodford (1999, 2003) and Sack and Wieland (2000).

  3. Palma and Portugal (2011) found evidence in favor of a discretionary monetary policy in Brazil during the 2000–2010 period.

  4. Examples of other works that suppose the parameters of the model follow a random walk are Cogley and Sargent (2001, 2005), Boivin (2006) and Kim and Nelson (2006).

  5. As suggested by an anonymous referee, we estimated (13) and (14) assuming that \(\delta _{1}\) and \(\delta _{2}\) follow a random walk. However, the results of the likelihood ratio (LR) tests showed that the null hypothesis of constants parameters into (13) and (14) cannot be rejected at a significance level of 10 %. These results are available from the authors upon request.

  6. Regarding the determinants of the inflation expectations in Brazil, see Bevilaqua et al. (2008) and Carvalho and Minella (2012).

  7. Although the sample begins in January 2000, the observations used to estimate the reaction function (in step two) begin in November 2001. This is due to the use of the first 12 observations as initial values in the regressions, estimated in the first step, and of the following ten observations to obtain the initial values of the regression coefficients in step two. This last procedure was suggested by Kim and Nelson (1999, 2006) to diminish the effect of arbitrary initial values of the \(\beta \) parameters on the value of the log-likelihood function.

  8. The IPCA is calculated by the Brazilian Institute of Geography and Statistics (IBGE) and is the price index used as reference for the inflation-targeting regime.

  9. In the construction of the inflation-targeting regime series, it was taken into account that the CBB pursued a set goal of 8.5 % in 2003 and 5.5 % in 2004, as well as a target of 5.1 % in 2005. For details about the set goals and the announced goal for 2005, see Open Letters of 2003 and 2004 sent by the CBB to the Minister of Finance and the notes of the meeting of the Monetary Policy Committee (Copom) of September 2004.

  10. We used a smoothing parameter of \({\uplambda } = 14,400\) in the HP filter. In addition, we followed Ravn and Uhlig (2002) and estimated the regressions using \({\uplambda } = 129600\). The results were similar to those described in this article. These results are available from the authors upon request.

  11. The exchange rate is the percentage variation of the nominal exchange rate real/dollar (period average).

  12. These dummies were inserted to capture the strong current inflation increase and inflationary expectations at the end of 2002, the economic crisis of 2008 and an outlier (2002:10) in the output gap series.

  13. Initially, we estimated (13)–(14) and (37)–(38) without the time dummies, but the residuals usually showed problems of serial autocorrelation and non-normality. As this violates the assumptions about the errors, we chose to include the dummies in the regressions. Furthermore, the results for the \(\upbeta _t\!\)’s showed no significant changes when using the forecast errors arising from the regressions (13)–(14) and (37)–(38) without the time dummies.

  14. See, for example, Perron (1989).

  15. Perron and Yabu (2009) introduce tests for structural breaks in the tendency function that do not need, a priori knowledge, if the noise component of the series is stationary or presents a root unit. These authors also show that, in the case in which the structural break is unknown, the functional Exp-W\(_\mathrm{FS}\) of the Wald test produces a test with nearly identical limit distributions for the case of a noisy component I(0) or I(1). Due to this, the test procedures, with nearly the same size, can be obtained for both cases.

  16. The log-likelihood value for the model with constant parameters and bias correction terms was \(-\)93.88.

  17. See Kim and Nelson (1999, 2006).

  18. Regarding the H statistic, see Commandeur and Koopman (2007).

  19. In this case, the specification with constant parameters and bias correction terms presented a log-likelihood equal to \(-68\).

  20. It is worth while pointing out that the confidence interval does not allow asserting that \(\beta _{1}\) was significantly lower than zero during this period.

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Acknowledgments

The authors would like to thank the editor, two anonymous referees, Marcelo S. Portugal and the participants of the \(40^{\circ }\) Brazilian Economics Meeting for their helpful comments and suggestions. Edilean Aragón acknowledges the support of the Graduate Program in Economics at the Federal University of Rio Grande do Sul during your visit in 2012. Edilean Aragón acknowledges financial support (postdoctoral fellowship) from the Coordination for the Improvement of Higher Level Personnel (CAPES). Gabriela Medeiros acknowledges the financial supports provided by the National the Brazilian Council of Science and Technology (CNPq).

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Authors and Affiliations

  1. Post Graduate Program in Economics (PPGE), Universidade Federal da Paraíba (UFPB), Jardim Cidade Universitária, João Pessoa, PB , CEP 58.051-900, Brazil

    Edilean Kleber da Silva Bejarano Aragón

  2. Post Graduate Program in Economics (PPGE), Universidade Federal do Rio Grande do Sul (UFRGS), Av. João Pessoa, 52 sala 33B - 3° andar, Centro, Porto Alegre, RS , CEP 90040-000, Brazil

    Gabriela Bezerra de Medeiros

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  1. Edilean Kleber da Silva Bejarano Aragón
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Correspondence to Edilean Kleber da Silva Bejarano Aragón.

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da Silva Bejarano Aragón, E.K., de Medeiros, G.B. Monetary policy in Brazil: evidence of a reaction function with time-varying parameters and endogenous regressors. Empir Econ 48, 557–575 (2015). https://doi.org/10.1007/s00181-013-0791-5

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