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Inflation Report \ Banco Central Do Brasil \ December 2018 Figure 2 – Autocorrelation Quarterly Basis 1.0

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Inflation Report \ Banco Central Do Brasil \ December 2018 Figure 2 – Autocorrelation Quarterly Basis 1.0 Informational content of the IPCA cross-sectional distribution The analysis of the disaggregated inflation allows a better understanding of the transitory or permanent factors affecting the inflationary process. In general, this type of analysis focuses on items, subitems or special aggregations, for example, inflation cores by exclusion. This box assesses whether the information is available on disaggregated data from the viewpoint of the inflation cross-section distribution at the level of the IPCA1,2 subitems. In particular, it analyzes the persistence of selected percentiles of the distribution and their correlation with the headline inflation (IPCA) and the output gap. In addition to the median – the distribution percentile more often utilized in the literature or by other central banks3 – this box also evaluates percentiles 10, 25, 75 and 90. Figure 1 shows the seasonally adjusted quarterly series of these percentiles and the headline inflation from 2006 to 2017.4 The lower volatility of the median compared with inflation and higher volatility of extreme percentiles (particularly percentiles 10 and 90) may be observed. In addition, it is worth noting that the median tends to underestimate the headline inflation, reflecting the positive asymmetry of the distribution.5 Figure 1 – Headline inflation and percentiles Quarterly seasonally-adjusted (%) 10 8 6 4 2 0 -2 -4 -6 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Percentiles 10 to 90 Percentiles 25 to 75 IPCA Median Figure 2 shows the autocorrelogram of quarterly variations of each percentile when compared with the headline inflation. It may be observed that, among the analyzed percentiles, the median is the most persistent, followed by the 25th percentile. Both are more persistent than the headline inflation itself which, in the first three time horizons, has persistence levels more similar to the 10th and 75th percentiles. It is also noteworthy the low persistence of the 90th percentile, reflecting the fact that very high price variations tend not to be followed by other variations, either in the same or another subitem. 1/ For the period before January 2012, it was recalculated according to the current weighting structure. The distribution and its moments, including percentiles, were calculated every month by using actual data (except for the compatibility with POFs) without seasonal adjustment. As for the persistence exercises and the crossed correlation (with the headline IPCA inflation and the output gap), the quarterly variations were calculated on the basis of monthly variations before being seasonally adjusted. 2/ This level of disaggregation was chosen because it allows a more precise characterization of the cross-section distribution of price variations. 3/ With regard to the academic literature, see Bryan and Cecchetti (1994). As for the utilization by Central Banks, it could be cited the examples of Canada, Australia, New Zealand and, in the United States, the FED of the state of Cleveland. 4/ The period analyzed excludes the year 2018 in order to mitigate the edge issue related to seasonal and trend filters applied to the analysis. 5/ In general, monthly cross-sectional IPCA distributions show a positive asymmetry (extreme positive variations are more usual than negative variations in the same magnitude) and excess of kurtosis (heavy or long tails). 38 \ Inflation Report \ Banco Central do Brasil \ December 2018 Figure 2 – Autocorrelation Quarterly basis 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 1 2 3 4 5 6 7 8 Median P10 P25 P75 P90 IPCA The exercise proceeds by analyzing how each percentile is correlated with the headline inflation (Figure 3). In general, the distinct percentiles show high contemporaneous correlation with the IPCA (around 0.80), except the 10th percentile, for which the contemporary correlation is lower, 0.68. As for the correlation between each percentile and the expected IPCA, it may be observed that the median and the 25th percentile have a stronger correlation than the other percentiles up to two quarters ahead. The 75th and 90th percentiles are always less correlated than the others, especially from the 2018Q2 onwards. It should be also emphasized that the correlation of the 10th percentile with inflation, for horizons longer than three quarters ahead, is as much or even more significant than the correlation of the 25th and 50th percentiles. Figure 3 – Correlation with IPCA Percentile (t) x IPCA (t+h). Quarterly basis 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 P50 P10 P25 P75 P90 Figure 3 also shows an inverted anticipation relationship, from the IPCA to the percentiles (shown with horizons with a negative signal). The percentiles that are more correctly anticipated by the headline inflation are the 25th and the 50th. The 75th and the 90th percentiles have a similar correlation with them for horizons from three to five quarters. Among the other percentiles, the 10th percentile is the least anticipated by the headline inflation, especially when considering the three to four quarters horizons. Furthermore, this box analyzes how the headline inflation and the percentiles are correlated with a measure of the output gap (Figure 4).6 Starting with the headline inflation, the maximum output gap correlation (0.45) occurs with inflation four or five quarters ahead – in line with the understanding that the monetary policy, when impacting the aggregate demand, has a lagged effect on inflation. As for the likely anticipation of GDP by the IPCA, the correlation is negative, with the maximum (absolute value) occurring with a leg of four or five quarters – in line with systematic responses from the monetary authority to inflation deviations with some lagged impact on the economic activity. The correlogram for the 50th percentile is similar to that of the IPCA, but with a maximum correlation of 0.52, four quarters ahead. The 10th percentile has a more contemporaneous correlation pattern with the 6/ For the sake of simplicity, the results for the output gap obtained by applying the Hodrick‑Prescott (HP) filter for the GDP volume index are shown. They are qualitatively robust when compared with other measures of economic slack. December 2018 \ Banco Central do Brasil \ Inflation Report \ 39 Figure 4 – Correlation with output gap Output gap (t) x Percentile or IPCA (t+h). Quarterly basis 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 P50 P10 P25 P75 P90 IPCA output gap (maximum correlation of 0.42 for the current quarter and one quarter ahead), but with a limited anticipation potential, and the 90th percentile anticipates the output gap as well as the headline inflation, for horizons from one to three quarters, but it is scarcely anticipated by this activity indicator. Therefore, the most extreme positive variations observed in the IPCA cross-section distribution are not likely explained by the economic activity, probably reflecting idiosyncratic and sporadic components, the reason why they also reveal low persistence. Conversely, for the extreme negative variations, reasonable degrees of persistence and correlation with the activity and the headline inflation are observed. Among the analyzed percentiles, the median is the measure with the best performance in the three comparison scenarios. The results of the exercises carried out in this box, together with those presented in the box “Predictive Ability and Bias of Underlying Inflation Measures”, in this Inflation Report, corroborates the perception that information is effectively available in the IPCA disaggregated analysis from the viewpoint of its cross-sectional distribution. 40 \ Inflation Report \ Banco Central do Brasil \ December 2018.
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