The credibility index is computed according to de Mendon

The credibility index is computed according to de Mendonça and Souza (2007, 2009). The index equals 1 if the median of the distribution of inflation expectations for the next 12 months coincides with the target pursued by monetary authorities for the same methane monooxygenase . The value of the credibility index decreases as the distance between and increases; it becomes zero when or when . The upper and lower bounds and derive from the limits of the band assigned by the National Monetary Council for the inflation rate to be observed at the closing of the current and the next year. Formalizing this measure in mathematical terms: The inflation target specified for the next 12 months is computed by means of a formula similar to (2), that is: In (8), m represents the month in which the target for the next 12 months is calculated (or the month containing time t), denotes the inflation target pursued by monetary authorities for the current year (or the year containing time t) and is the target specified for the year that follows. Formula (8) was also used to interpolate the upper and lower limits of the bands that are fixed around the targets set by the National Monetary Council. Regressions (3)–(6) are estimated by ordinary least squares (OLS), two-stage least squares (2SLS) and the generalized methods of moments (GMM). In all three cases we use the Newey-West estimator to provide an estimate of the covariance matrix of the parameters even in the presence of heteroscedasticity and serial correlation in the error terms. In the cases of 2SLS and GMM, the variable cred is replaced by two instruments, and . The variable is the time series formed by the credibility measures calculated by applying formulas (7) and (8) to the last working day of each month. The usage of instruments in this case is mandatory because cred is based on the first moment of the distribution of inflation expectations, which is probably contemporaneously affected by the same shocks hitting disagreement measures, that essentially reflect second order moments of the same distribution (in other words, shocks affecting the entire distribution of expectations also impact instantaneously its moments of first and second order). The variables gap, X and vol X do not necessarily require instruments because a shock in the general level of disagreement in expectations (which essentially reflects the opinions of experts regarding the future values of X) do not affect them at the same time. This identification hypothesis stems, for example, in the model proposed by Carroll (2003), which holds that the projections made by experts spread slowly in the population in a way that resembles a disease. According to this model, a shock that hits the distribution of experts’ expectations does not affect contemporaneously (i.e. at the same month that the shock occurs) the expectations of other agents, therefore this shock does not affect instantaneously their pricing and production decisions, as well as other economic choices. In the next subsections we investigate the driving factors of disagreement in expectations regarding the future values of the IPCA inflation rate (Section 4.1), the SELIC interest rate (Section 4.2), the exchange rate (Section 4.3) and the growth rate of industrial production (Section 4.4). As mentioned before, we are especially interested in studying the relationship between the general level of disagreement in expectations regarding the future values of each variable and two potentially relevant explanatory variables, the output gap and our measure of monetary authorities’ credibility.
Conclusion The results of Sections 4.1–4.4 suggest that the levels of the four term structures of disagreement in expectations have a negative relationship with the output gap. This effect is statistically significant in most of the cases, being very strong (i.e. not depending on the specific regression being estimated or the estimation method) in the case of disagreement in expectations regarding the exchange rate. This evidence highlights the importance of providing a solid ground for economic growth, since agents see less uncertainty and disagree less about future of the economy during periods of prosperity.