Endogeneity and nonlinearities in Central Bank of Brazil’s reaction functions: an inverse quantile regression approach

According to the monetary rule proposed by Taylor (1993), the central bank changes the nominal interest rate in response to deviations of the current inflation from the inflation target and to the current output gap. In turn, the policy rule formulated by Clarida et al. (2000) assumes the monetary authority adjusts the interest rate based on expected future inflation rates and on the output gap.

Kato and Nishiyama (2005) and Adam and Billi (2006) argue that, close to the zero bound, the central bank responds more strongly to a decrease in inflation rate in order to minimize the likelihood of deflation.

Chevapatrakul et al. (2009) assess monetary policy conduct in the USA and in Japan, whereas Chevapatrakul and Paez-farrell (2014) focus their analysis on Australia, Canada, and New Zealand. In turn, Wolters (2012) estimates the Federal Reserve’s reaction function.

For further details on the 2SQR method, see Amemiya (1982), Powell (1983) and Kim and Muller (2004, 2008).

This procedure was also adopted by Aragón and Portugal (2010) and Minella and Souza-Sobrinho (2013).

This requires fewer details about the specification of the distribution of \(\hbox {y}{\vert }\hbox {x}\) (Greene 2012).

This method is also known as instrumental variable quantile regression (Chernozhukov and Hansen 2006).

As pointed out by an anonymous referee, the function \(q_{\tau }(D,X{\vert }X,Z)\) in (5) is a structural quantile function. This is not the same as the conditional quantile function \(q_{\tau }(i_{t }{\vert }i_{t-1}\), \(i_{t-2}\), \(\pi _{t}- \pi ^{*}_{t}\) , \(y_{t})\) presented in (4) It is important to say that, in general, the conditional quantile function is not the same as the structural quantile function. Therefore, to test for robustness, we shall also estimate the CBB reaction function by 2SQR, which is more closely related to the conditional quantile function.

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

IPCA is calculated by the Brazilian Institute of Geography and Statistics (IBGE) and is the price index used by the National Monetary Council as benchmark for the inflation-targeting regime.

To obtain the inflation target for the next 12 months, we interpolated the annual targets using equation \(\pi _t^*=\left( {m_t /12} \right) \times \pi _{\left( 0 \right) }^*+\left[ {\left( {12-m_t } \right) /12} \right] \times \pi _{\left( 1 \right) }^*\), where \(\pi _t^*\) is the inflation target in month t for the next 12 months. The variables \(m_t \), \(\pi _{\left( 0 \right) }^*\) and \(\pi _{\left( 1 \right) }^*\) are defined in Eq. (8).

The coefficient of asymmetry was 0.45, and the coefficient of kurtosis was 2.62.

The null hypothesis of the tests is that the series is nonstationary (or unit root).

Perron and Yabu (2009) present some tests for the structural break in the trend function that do not require knowing a priori whether the noise component of the series is stationary or has a unit root. These authors also demonstrate that, in the case in which the structural break is unknown, the \(\hbox {Exp-W}_{\mathrm{FS}}\) functional of Wald’s test provides a test with almost identical limit values for a noise component I(0) or I(1). Therefore, test procedures with similar sizes can be performed for those two cases.

Exchange rate movement is the percentage variation of the Real/Dollar nominal exchange rate (mean for the period).

As underscored by Stock and Yogo (2005), the presence of weak instruments may yield biased IV estimators. Thus, following these authors, we considered instruments to be weak when the bias of the IV or GMM estimator relative to the bias of the OLS estimator was greater than any value b (for example, \(b = 5\%\)).

The critical values of this test are described in Stock and Yogo (2005).

For short-term interest rate smoothing, see Goodfriend (1991) and Rudebusch (1995).

The standard errors of the long-term responses of the Selic rate may be provided by the authors upon request.

Chevapatrakul et al. (2009) solve this problem by estimating the original Taylor rule, i.e., without the smoothing parameter. However, as the short-term interest rate smoothing is observed in CBB’s monetary policy, we opted not to follow Chevapatrakul et al. (2009), as we would have misspecification of the reaction function to be estimated.

We also estimated the reaction function using an output gap derived from a quadratic trend. The results are similar of those obtained by using a output gap derived from the HP filter. These results may be provided by the authors upon request.

We used the series (no. 11752) of the effective real exchange rate—IPCA provided by the CBB.

We also estimated reaction functions (9 and 10) including the exchange rate as one of the explanatory variables. In general, the results did not change significantly from Fig. 8. These results are available from the authors upon request.

These findings differ from those obtained by Mello and Moccero (2009) and Furlani et al. (2010), who did not find a straightforward response of the CBB to the exchange rate. These differences may occur because of the distinct periods assessed and of different concepts of exchange rate. For instance, Mello and Moccero (2009) use monthly data on the 12-month percentage change in the nominal exchange rate and analyze the 2001M07-2008M03 period, whereas Furlani et al. (2010) check whether the CBB reacts to the current quarterly variation in the nominal exchange rate in the 2000Q1-2007Q3 period. Moreover, Mello and Moccero (2009) and Furlani et al. (2010) do not take into account the possibility of change of the Selic rate response across the quantiles of the conditional distribution.