^{1}

^{2}

^{*}

We evaluate recent inflation-targeting using Brazilian data and also consider the framework of the macroeconomic model of adaptive learning blended with a cognitive psychology approach. We suggest that forecasters interpret the inflation target as an anchor, and adjust to it accordingly. As current inflation increases above the target level, a central bank loses credibility, and forecasters start the adjustment from the top because they expect an even higher future inflation. Then, they move back to the core target within a range of uncertainty, but the adjustment is likely to end before the core is reached, as predicted by the psychological theory of anchors. After calibrating the model, we find an asymptotic equilibrium of a 6.1 percent inflation rate, which overshoots the announced target inflation core of 4.5 percent. This example casts doubt on the very justification for inflation targeting, which is unlikely to succeed when private forecasters rely on anchoring heuristics.

In the last 20 years, many academic macroeconomists [

We collected raw inflation data based on monthly series of the Brazilian broad price index (called IPCA) from November 2001 to September 2013. We considered datapoints of monthly frequency, and used the last day of the month as representative of a month. An alternative date could be the day after the release of the so-called IPCA-15 (an index strongly correlated with the IPCA; correlation = 0.986). We choose the last day of the month because forecasters are already in possession on that date of the information of the previous month’s inflation.

The data on inflation forecasts made by professional forecasters (called “market expectation system”) are considered by the Brazilian central bank for the following 12 months (“the long run”). We took the inflation expectation data from such a central bank source and considered, as usual, the median of the time interval from November 2001 to September 2013. The median value was used in our analysis for calibrating the forecasters’ predictions 12 months forthcoming, from October 2002 to August 2014. The median is taken to prevent possible distortions in forecasts collected on a daily basis. The median is also justified because the central bank can lose credibility in the meantime, in which case private forecasters tend not to reveal their true expectations. All the data employed in this work are available at http://dx.doi.org/10.6084/m9.figshare.1310598.

Competition between the professional forecasters is promoted by the Brazilian central bank, which rewards the year’s top five forecasters. This aims to improve the quality of data collected from the market expectation system. As a result of this incentive mechanism, we considered the source of data rather than the alternative of gauging the inflation expectations embodied in the prices of assets. However, the central bank data themselves are far from perfect.

Nowadays macroeconomists usually favor a bounded rationality approach when considering how forecasters predict inflation. We considered, in particular, the model of adaptive learning [

The adaptive learning approach is a bounded rationality model in that forecasters have to choose their perceived best model of forecast in the absence of full information. Forecasters are assumed to use a statistical model to estimate a “perceived law of motion” (PLM) of the parameters involved in forecasting. This estimate is then subjectively maximized, resulting in a temporary “actual law of motion” (ALM). Reestimations of the PLM may occur after the feedback with past forecasting performance, a feature that allows calibrating the model with actual data. The process is described by a differential equation that uses the estimated parameters in the PLM. Asymptotically, the adaptive learning process may reach a rational expectation equilibrium. However, the PLM is not always an optimal learning strategy, in which case forecasters miss the rational expectation equilibrium.

Year/ranking | Private forecaster | Forecast error |
---|---|---|

2009 | ||

1 | Banco CR2 S.A. | 0.09 |

2 | Petros Fundação Petrobrás de Seguridade Social | 0.0955 |

3 | Mauá Consultoria de Investimentos e Econômica Ltda. | 0.1065 |

4 | Banco do Brasil S.A. | 0.1147 |

5 | ING Bank N.V. | 0.1159 |

2010 | ||

1 | Claritas Administradora de Recursos Ltda. | 0.3364 |

2 | Opportunity Asset | 0.3371 |

3 | Safra Asset Management | 0.4479 |

4 | Banco Itaú Asset Management | 0.4480 |

5 | JGP Gestão de Recursos | 0.4491 |

2011 | ||

1 | Barclays Capital | 0.1221 |

2 | BNY Mellon ARX Investimentos | 0.1436 |

3 | BW Gestão de Investimentos Ltda | 0.1599 |

4 | Kondor Admnistração e Gestão de Recursos Financeiros Ltda. | 0.1699 |

5 | Safra Asset Management | 0.1918 |

2012 | ||

1 | BW Gestão de Investimentos Ltda. | 0.2985 |

2 | Credit Suisse Hedging-Griffo AM S.A. | 0.3123 |

3 | HSBC Asset Management | 0.3263 |

4 | Banco BNP Paribas Brasil S.A. | 0.3602 |

5 | Rabobank Internacional Brasil | 0.4056 |

2013 | ||

1 | Banco Mizuho do Brasil S.A. | 0.0826 |

2 | Brasil Plural Gestão de Recursos | 0.0827 |

3 | Mirae Asset Global Investiments Brazil | 0.0987 |

4 | MB Associados | 0.1023 |

5 | BNP Paribas Asset Management Brasil Ltda. | 0.1041 |

Source: Brazilian central bank.

The process of mapping from the PLM to the ALM is called “expectational stability” or “E-stability.” Such E-stability is similar to that of the rational expectation model. If the dynamics do not converge to the rational expectation equilibrium, it can be modeled assuming learning with a “constant-gain estimator”

where E is the expectation operator and

The PLM takes into account the constant-gain estimator and is defined as

where

E-stability provided by a differential equation formulation offers the most suitable condition for stability under adaptive learning rules using least squares [

Equation (3) is then calibrated with the values of

is met. As

The algorithm (1)-(5) can also be used as an experimental framework where heuristics can be invoked [

“Prediction is very difficult, especially if it is about the future,” goes the adage independently advanced by both physicist Niels Bohr and baseball superstar Yogi Berra. This means forecasters will find it difficult to predict inflation. That is why they will consider forecasting heuristics. From the perspective of cognitive psychology the first aspect to note is that the inflation target is an anchor for the forecasters. The anchoring heuristic occurs when people consider a particular value for an unknown quantity before estimating the quantity [

In terms of inflation targeting we considered the anchoring heuristics for forecasting as the first type, because the work of professional forecasters requires such effort. The announced target can be interpreted as the core of a region of uncertainty for the private forecasters, because they are uncertain that the central bank will meet the target. The forecasters start their mental predictions considering the anchor represented by the announced target. Then, depending on the monetary policy moves and the effects on current inflation, the forecasters adjust their estimates (and this can be thought of as a kind of learning) by mentally moving from the anchor. For example, if a central bank loses credibility as current inflation increases and menaces to depart from the core, the forecasters start the adjustment from the top because they are likely to expect an even higher future inflation. Then, they move back to the core within the range of uncertainty, but the adjustment is likely to end before the core is reached. As we will see, this example fits the interpretation we will provide for our results.

We find it useful to compute an anchoring index, A, for the inflation target

The first line in Equation (6) applies to situations when forecasters start the adjustment from the bottom because they estimate that inflation is below the target,

The anchoring index (6) is different for each forecaster. In the adaptive learning framework, there is no reason for assuming from the start that expectations are homogeneous. However, due to the feedback with the environment in the evaluation of past performance, learning allows the commuting of individual anchoring heuristics. The degree of heterogeneity in a given time period of the learning process can be gauged by a Pearson correlation, dividing the standard deviation by the mean. So the less the dispersion is between the individual forecasts on a given date, the greater the homogeneity of the forecasts. However, because the Pearson coefficient assumes the degree of heterogeneity is evaluated relative to the mean, it is useless in the presence of marked skewness. Fortunately, this restriction does not apply to our data, because we found the individual forecasts to be roughly symmetrically distributed (available upon request).

anchoring index gauges the usefulness of the announced target as a base rate and it co-varies with the credibility index (7).

When inflation accelerates, the central bank’s credibility plummets, and then the anchoring index drops. This means actual inflation becomes more relevant for forecasts than the target inflation. Here we arguably are in the second line of the A-index (6). The adjustment starts from the top and we expect it to stop well above the anchor given by the inflation target.

As the private forecasters learn that actual inflation becomes a better predictor, expectations turn more homo- geneous, and this reduces “inflation surprise” (actual minus expected inflation). Because the same actual in- flation ends up generating less inflation surprise, this again strongly suggests an underlying process of learning at work. Take the final years in

Considering the constant-gain estimator given by Equation (1) into the PLM Equation (2), we can estimate

parameters

Note that

Considering the inflation target of 4.5 ± 2 percent announced for the final period by the Brazilian central bank (

Of course, our adaptive learning equilibrium does not collapse to the rational expectation equilibrium.

Testing for bias (test A) is the simplest way to evaluate forecast accuracy. The test assess whether inflation expectations are centered on the “right” value. The accuracy is gauged by the constant

Test B evaluates whether there is information in the predictions that could be used to predict the inflation surprise. Accepting the null hypothesis of rationality means no other information conveys prediction power over inflation. The p-value of 0.015 shown in

Parameters of Equation (2) | |
---|---|

13.0333^{*} | −1.1359^{*} |

Note: ^{*}significant at 1 percent.

Test A Testing for bias | |
---|---|

1.09 (0.239348)^{*} | |

Test B Is the information in the forecast fully exploited? | |

−0.38 (0.1564)^{**} | |

3.15 (0.8692)^{*} | |

Adjusted R² | 0.034 |

p-value | 0.015 |

Test C Are forecasting errors persistent? | |

0.961 (0.023)^{*} | |

0.02 (0.07) | |

Adjusted R² | 0.925 |

Test D Are the macroeconomic data fully exploited? | |

−0.973 (1.13) | |

−0.251 (0.193) | |

0.064 (0.132) | |

−0.348 (0.113)^{*} | |

0.888 (0.175)^{*} | |

Adjusted R² | 0.21 |

p-value | 0 |

Note: Standard deviation in parentheses; ^{*}significant at 1 percent; ^{**}significant at 5 percent.

Test C assesses whether today’s forecast error can be used to predict tomorrow’s error (serial autocorrelation). If expectations are rational, serial autocorrelation cannot exist.

Test D examines whether public macroeconomic information was taken into account by forecasters in their predictions. The test runs a regression considering the expectations of current IPCA inflation rate formed with a 12-month lag

When central banks adopt inflation targeting they create an illusion of the understanding of and control of inflation forecasts. They tend to understate the uncertainty of forecasting the future. The basic reason: They rely on models that assume the random shocks hitting the economies are independent and identically distributed. Jumps that lead to non-i.i.d. forecasts are dismissed by design, which means central banks assume economic shocks are of mild type I randomness [

Our finding of an asymptotic adaptive learning equilibrium that overshoots the anchor is thus dependent on both the adaptive learning model we consider as a framework [

While predicting, forecasters may use simple heuristics (simple rules, usually imperfect, aiming to find answers to questions of difficult judgment). We consider this cognitive psychology perspective to the conventional macroeconomic literature of bounded rationality with adaptive learning and suggest the presence of an anchoring heuristic at work for predicting the inflation target. The treatment considered Brazilian data.

Calibrating the data to the dynamic convergence of an adaptive learning asymptotical state, we found the professional forecasters to increasingly homogenize their forecasts, but the convergence value of the inflation expectation overshot the official announced target.

We found that the forecasters didn’t believe the core target of 4.5 percent, and instead used a forecast of 6.1 percent inflation, which was near the upper band of 6.5 percent because the tolerance range was

Evelin Da Silva,Sergio Da Silva, (2015) Anchoring Heuristic Messes with Inflation Targeting. Open Access Library Journal,02,1-10. doi: 10.4236/oalib.1101450