Besides this introduction this article

Besides this discover this info here introduction, this article has four sections. Section 2 discusses concepts that are important in the study of disagreement and presents the notation that we use throughout the paper. Section 3 presents some basic results related to the term structures of disagreement regarding inflation expectations as measured by the IPCA, the SELIC rate, the growth rate of industrial production and the exchange rate (BRL/USD). Section 4 studies the relationship between disagreement in expectations and its potential macroeconomic determinants, paying special attention to the measure of monetary authorities’ credibility proposed by de Mendonça and Souza (2007, 2009). At last, Section 5 summarizes the main results of the paper and suggests some directions for future research.
Definitions, concepts and notation The analysis of disagreement requires discussing a few concepts and presenting some notation: t represents the instant in which the forecast is made,i identifies the agent responsible for the forecast (i∈I, here I is the group of agents surveyed; the number of agents in I is I), X is the variable to be forecasted and EX represents the forecast calculated by the ith agent at time t about the value that variable X will take in the end of year a+j. If j=0, then EX represents the forecast about the value of X in the end of the current year; if j=1, then EX denotes the forecast about the value of X in the end of the next year and so on. The mean value of the distribution of expectations at t about the value that X will take in the end of year a+j is given by . The standard deviation of the same distribution at time t is given by . denotes the minimum value of the distribution, while represents its maximum value. The range of the distribution is defined below: The range RX is the measure of disagreement that we use throughout the paper, as other measures require the knowledge of the entire distribution of expectations. As told in the introduction, we work with forecasts for the IPCA inflation rate (π), the SELIC interest rate (s), the exchange rate (BRL/USD) (e) and the growth rate of industrial production (g), therefore X=π, s, e, g. Forecasts like EX are known as fixed event forecasts because the time horizon until the end of year a+j decreases as t advances through a, the year in which expectations are computed. This issue is better understood by an example. Suppose that an agent, in March 2000, computes his expectation about the value of the inflation rate in the end of 2000. In Nonsense mutation case we can say that the time horizon of the forecast is 10 months because the first 2 months of 2000 have already passed and inflation figures for both months are known. By the same line of reasoning, when this agent computes his inflation expectation in September 2000 about the value of the inflation rate at the closing of 2000, the time horizon of his forecast decreases to only 4 months. This pattern of decreasing forecasting horizons as t advances through the year brings about a seasonal behavior in disagreement measures based on fixed event forecasts, since expectations dispersion tend to decrease as the forecasting horizon shrinks (see Appendix 2). It is to avoid the seasonal behavior inherent to disagreement measures based on fixed event forecasts that most articles in the literature recur to fixed horizon forecasts, in which the forecasting horizon does not vary with the passage of time. As proposed in Dovern et al. (2012), the conversion of fixed event forecasts into fixed horizon forecasts is accomplished by applying the formula below: In Eq. (2), m represents the month in which the forecast is made (or the month containing t) and EX denotes the average of agents’ expectations about the value that variable X will take in the end of the next 12(j+1) months. The same formula is used to interpolate minimum and maximum forecasts, which are put into (1) to compute the values of the disagreement measure RX. In the end of the process we obtain something that resembles a term structure of disagreement in expectations, which is comprised by the “vertices” RX12, RX24, RX36, etc. Given the fact that the CBB discloses forecasts for the current year, the next year and the following 3 years, formula (2) can be used with j=0, 1, 2, 3, 4; therefore, we can always interpolate forecasts for the fixed time horizons of 12, 24, 36 and 48 months.