Abstract
This study evaluates the accuracy of the private-sector forecasts of inflation and growth in industrial production collected by the Brazilian Central Bank (BCB). In addition to examining directional accuracy, we utilize as benchmarks both naïve and univariate autoregressive moving-average (ARMA) forecast and test rationality under flexible loss to allow for the possibility of asymmetric loss. Our analysis yields three important findings: First, the private forecasts are directionally accurate. Second, they are superior to the naïve forecasts and are either superior or as accurate as the ARMA forecasts. Third, the private forecasts are generally rational under either asymmetric or symmetric loss. Such findings point to the success of the BCB in anchoring private expectations. Given their importance as monetary policy inputs, we conclude that private inflation and growth forecasts are of value to the BCB for policymaking.
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Notes
In order to have a reasonable number of observations for our analysis, we have used the “rate of change in industrial production index” as a measure of growth (instead of the rate of change in real GDP which is measured on a quarterly basis).
The BCB collects the forecasts on a daily basis. The information available in the system up to 5 pm of a particular day is used to calculate the median forecast for that day. Daily consensus (median) forecasts of inflation and growth in industrial production are available at www.bcb.gov.br/
The actual data for the IPCA for month t-1 is released between the 4th and the 14th day of month t. The actual data for the industrial production index for month t-2 is released within the first 11 days of month t. The forecasts utilized in this paper are made on the 15th through 18th day of month t.
See Management Reports 2008 and Management Reports 2009 available on the Central Bank of Brazil website).
Our findings indicate some anomalies. For instance, the symmetry and rationality test results at some forecast horizons are different from those at other forecast horizons. Such anomalies (which are common in forecasting) may be explained by the fact that our study uses the consensus forecasts since the data for individual forecasters are not available. As for symmetry, Timmermann (2006) points out that forecast combination may average out idiosyncratic variation in loss functions. As such, the individual forecasts may imply asymmetric loss but the consensus forecast may imply symmetric loss. As for rationality, Dovern and Weisser’s (2008) findings, using the forecasts for G7 countries, indicate that the consensus forecasts fail to be rational even though the majority of individual forecasts are rational.
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Appendix A
Appendix A
This appendix describes how the autoregressive moving-average (ARMA) forecasts of inflation and growth are generated. To start with, we use the augmented Dicky-Fuller (ADF) test to examine the unit root behavior of the series. The results indicate that the unit root null hypothesis is rejected for both series (for inflation, the MacKinnon p-value of the calculated ADF test statistic for 1996.01–2002.12 is 0.001, and for growth, the p-value for 1996.01–2002.11 is 0.040). We utilize the inflation (growth) series for 1996.01–2002.12 (1996.01–2002.11) to estimate the autocorrelation and partial autocorrelation functions. Using these estimates and the Schwarz criterion, we then select the following ARMA models (absolute t-values are in parentheses).
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CPI inflation (P t ):
$$ \begin{array}{l}{P}_t=\underset{(7.40)}{0.590}+\underset{(9.95)}{\left(1+0.774\left.B\right)\right.}{\widehat{u}}_t\hfill \\ {}\begin{array}{cccc}\hfill \hfill & \hfill \hfill & \hfill {\mathrm{R}}^2=0.38,\hfill & \hfill p-\mathrm{value}\kern0.5em \mathrm{of}\kern0.5em Q\left[12\right]=0.575.\hfill \end{array}\hfill \end{array} $$ -
Growth in industrial production (G t ):
$$ \begin{array}{l}\left(1-\underset{(3.05)}{0323B}-\underset{(2.74)}{0295{B}^2}-\underset{(1.55)}{0.166{B}^3}\right){G}_t=\underset{(1.61)}{3.378}+{\widehat{u}}_t\hfill \\ {}\begin{array}{cccc}\hfill \hfill & \hfill \hfill & \hfill {\mathrm{R}}^2=0.49,\hfill & \hfill p-\mathrm{value}\kern0.5em \mathrm{of}\kern0.5em Q\left[12\right]=0.196.\hfill \end{array}\hfill \end{array} $$
As can be seen, the parameter estimates are generally significant. Also, the p-values of calculated Ljung-Box Q-statistics are above 0.10, indicating that the residual series are white noise and thus the ARMA models are correctly specified.
We employ the above 1996.01–2002.12 ARMA model estimates for inflation to generate the forecasts for 2003.01–2004.01. These forecasts correspond to the current-month and one- through twelve-month-ahead private forecasts made in 2003.01. Re-estimating the model for 1996.01–2003.01, we use the updated parameter estimates to generate the forecasts for 2003.02–2004.02. Again, these forecasts correspond to the current-month and one- through twelve-month-ahead private forecasts made in 2003.02. This procedure is repeated until the last set of forecasts is generated. Note that, at the time of the survey, the participants do know the actual inflation for the prior month.
For growth, we employ the above 1996.01–2002.11 ARMA model to generate the forecasts for 2002.12–2004.01 (a total of 14 forecasts). The last 13 forecasts correspond to the current-month and one- through twelve-month-ahead private forecasts made in 2003.01. Re-estimating the model for 1996.01–2002.12, we use the updated parameter estimates to generate the forecasts for 2003.01–2004.02 (a total of 14 forecasts). Again, the last 13 forecasts correspond to the current-month and one- through twelve-month-ahead private forecasts made in 2003.02. This procedure is repeated until the last set of forecasts is generated. Note that, at the time of the survey, the participants do not yet know the actual growth for the prior month.
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Baghestani, H., Marchon, C. On the accuracy of private forecasts of inflation and growth in Brazil. J Econ Finan 39, 370–381 (2015). https://doi.org/10.1007/s12197-013-9263-1
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DOI: https://doi.org/10.1007/s12197-013-9263-1