Local Unit Root and Inflationary Inertia in Brazil

In this paper, we study the persistence of Brazilian inflation using quantile regression techniques. To characterize the inflation dynamics we employ the Quantile Autoregression model (QAR) of Koenker and Xiao (2004, 2006), where the autoregressive coefficient may assume different values in distinct quantiles, allowing testing the asymmetry hypothesis for the inflation dynamics. Furthermore, the model allows investigating the existence of a local unit root behavior, with episodes of mean reversion sufficient to ensure stationarity. In other words, the model enables one to identify locally unsustainable dynamics, but still compatible with global stationarity; and it can be reformulated in a more conventional random coefficient notation to reveal the periods of local non-stationarity. Another advantage of this technique is the estimation method, which does not require knowledge of the innovation process distribution, making the approach robust against poorly specified models. An empirical exercise with Brazilian inflation data and its components illustrates the methodology. As expected, the behavior of inflation dynamics is not uniform across different conditional quantiles. In particular, the results can be summarized as follows: (i) the dynamics is stationary for most quantiles; (ii) the process is non-stationary in the upper tail of the conditional distribution; (iii) the periods associated with local unsustainable dynamics can be related to those of increased risk aversion and higher inflation expectations; and (iv) out-of-sample forecasting exercises show that the QAR model at the median quantile level can exhibit, in some cases, lower mean squared error (MSE) compared to the random walk and AR forecasts.