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Specification errors, nonlinearities, and structural breaks in the Central Bank of Brazil’s reaction function

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Abstract

In this paper, we investigate nonlinearities in the Central Bank of Brazil (BCB)’s reaction function that may be associated with uncertainties over potential output and effects of the output gap on inflation. We perform structural break tests to assess possible changes in the conduct of the monetary policy and estimate nonlinear reaction functions by instrumental variables (IV) and identification-robust methods. Our results indicate a stronger reaction of the Selic rate to inflation and output gaps during periods in which the BCB was chaired by Henrique Meirelles. These changes can be associated with the observed increase in the BCB’s preference for inflation stabilization in relation to interest rate stabilization. We also found empirical evidence that points to the non-identification of the parameter that measures BCB’s concern in designing a robust monetary policy to specification errors. Finally, we observed that the introduction of smoothing terms in the BCB’s reaction function impaired the identification of all coefficients.

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Notes

  1. If instruments are weak, the point estimates of IV, the hypothesis tests, and confidence intervals are not reliable, t tests show significance levels that could differ arbitrarily from their nominal values, and the two-stage least squares estimator is biased and its distribution is non-normal. For the effects of weak instruments on IV estimation, see Dufour (1997, 2003), Staiger and Stock (1997), and Stock and Yogo (2002).

  2. The AR statistic was initially proposed by Anderson and Rubin (1949).

  3. Woodford (2003a) shows that the concern for interest rate stabilization can reflect welfare costs of transactions and/or an approximation to the zero lower bound on nominal interest rates.

  4. This value for \(\lambda _i=0.2\) is similar to that calibrated by Woodford (2003a) and cannot describe the actual BCB’s preference. Therefore, we seek to estimate this parameter in Sect. 4.4.

  5. The value for \({\bar{\kappa }}\) is in accordance with estimates of the reduced-form Phillips curve presented by Machado and Portugal (2014).

  6. The construction of the inflation and output gap series is described in detail in Sect.  4.1.

  7. As highlighted by an anonymous referee, the reduced form of the monetary rule in this section is not strongly connected to the structural model. Therefore, the results of the empirical models presented in Sect. 4 should be analyzed with caution.

  8. Following Surico (2007), the interest rate smoothing terms in empirical models can result from the inclusion of the term \(\lambda _ {\Delta i_{-1}} (i_t-i_{t-1})^2+ \lambda _ {\Delta i_{-2}} (i_t-i_{t-2})^2\) in the central bank’s loss function. In this case, it is important to assume that the policymaker disregards that today’s instrument setting will affect the loss function in the next periods (Svensson 1999). Using the basic New Keynesian model, Giannoni and Woodford (2003) show that an implicit interest rule obtained from the first-order conditions in case of an optimal commitment includes the interest rates at \(t-1\) and \(t-2\).

  9. The aim of this test is to verify the null hypothesis of l breaks against the alternative hypothesis of \(l+1\) breaks. For the model with l breaks, the date estimates are obtained by using a sequential procedure. This strategy consists in testing for the presence of an additional structural break in each one of the \(l+1\) segments. The test is applied to each segment with observations \(\tilde{T}_{j-1}\) through \(\tilde{T}_j\), for \(j=1,\ldots ,l+1\). The null hypothesis of l breaks is rejected in favor of a model with \(l+1\) if the global minimum of the sum of squared residuals (under all segments where an additional break is included) is sufficiently smaller than the sum of squared residuals of the model with l breaks.

  10. Following Perron and Yamamoto (2015), we use bootstrapping with fixed regressors, as proposed by Hansen (2000), to obtain the appropriate critical values for the structural break tests in the reaction function

  11. In this part, the variables were expressed as deviation from the mean before the estimations. This simplifies the estimation of the model since \(\beta _{0}\) in Eqs. (18) and (19) need not be estimated. For Eq. (19), we also estimate \(\rho _1\) and \(\rho _1+\rho _2\).

  12. The inversion of test AR-HAC was performed based on a grid search for values \(\left( \theta _{0}, \lambda _{i,0}\right) \), given \(\Omega \). Taking the reaction function (18) as an example, we obtained \(\beta _{1}\), \(\beta _{2}\), and \(\beta _{3}\) for each \(\left( \theta _{0}, \lambda _{i,0}\right) \) and \(\Omega \) and denoted by \(\beta _{1,0}\), \(\beta _{2,0}\), and \(\beta _{3,0}\). Then, we estimated \(\left\{ i_t - \beta _{1,0}(\pi _t-\pi ^*_t) - \beta _{2,0} x_t - \beta _{3,0}(\pi _t-\pi ^*_t)^2\right\} \) on \(\left\{ Instruments\right\} \) using OLS, calculated the AR-HAC statistic, and obtained the associated p value. The coefficients whose p values are larger than the level of significance \(\alpha \) make up the confidence interval \(1-\alpha \).

  13. These estimates are known as Hodges–Lehmann point estimates (Hodges and Lehmann 1963).

  14. We used the method proposed by Newey and West (1987) with Bartlett kernel and fixed bandwidth to estimate the covariance matrix.

  15. All structural break tests were performed taking into account the sequential procedure proposed by Bai and Perron (1998) with a maximum of three breaks and using a trimming value of 15%.

  16. In this procedure, the number of bootstrap replications was equal to 1000.

  17. It is important to highlight that the identification-robust methods are subject to the instruments used in the analysis as well as the calibration of some structural parameters. In this paper, we seek to illustrate how this method can be used to clarify changes in the parameters of the reaction function rather than to make an intensive analysis of the effects of different instruments and values for calibrated parameters. Therefore, the results should be viewed with caution.

  18. Details about these values are in Sect. 2.

  19. We checked the robustness of the results against two alternative sets of calibrated parameters: \(\Omega =(0.995,1.580,0.112,0.0016)\) and \(\Omega =(0.980,1.062,0.027,0.0037)\). These values are based on Palma and Portugal (2014), Carvalho and Castro (2017), and Gomez et al. (2019). The results related to identification of all parameters in the reaction function (19) and \(\theta \) parameter in both equations were not altered. In addition, the fit in these alternatives models was lower in comparison with specifications in Table 5. The results are available from the author upon request.

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Acknowledgements

The author would like to thank the comments from the editor and two anonymous referees. The author acknowledges the Postdoctoral Fellowship (Grant No. 205133/2018-5, PDE) provided by CNPq.

Funding

This study was funded by CNPQ - Conselho Nacional de Desenvolvimento Cientfico e Tecnolgico (Grant No. 454259/2014-0, Universal 2014), of the Ministry of Science, Technology, Innovation, Communication of Brazil.

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  1. Graduate Program in Economics, Federal University of Paraiba, João Pessoa, Brazil

    Edilean Kleber da Silva Bejarano Aragón

  2. Warwick Business School, University of Warwick, Coventry, UK

    Edilean Kleber da Silva Bejarano Aragón

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Correspondence to Edilean Kleber da Silva Bejarano Aragón.

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Aragón, E.K.d.S.B. Specification errors, nonlinearities, and structural breaks in the Central Bank of Brazil’s reaction function. Empir Econ 60, 1221–1243 (2021). https://doi.org/10.1007/s00181-019-01805-2

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