Bank for International Settlements

Carlos Hamilton V Araujo

Wagner P Gaglianone

English

Research Papers in Economics

BIS Papers No 49  107
 
Survey-based inflation expectations in Brazil
1 
Carlos Hamilton V Araujo
2 and Wagner P Gaglianone
3 
1.   Introduction 
Inflation expectations play a fundamental role in the inflation formation process. However, 
since these variables are in fact latent (and thus, they cannot be directly observed) some 
proxies are usually adopted by central banks, such as: (i) expectations obtained from 
financial market data,
4 and (ii) survey-based expectations.  
In 1999, the Central Bank of Brazil implemented a daily survey as part of the transition to the 
inflation targeting system. It was created in order to monitor market expectations of roughly 
90 Brazilian banks and non-financial companies, and to improve the inputs for the monetary 
policy decision-making process.
5  
Because of the importance of the subject to monetary policy, this paper aims to identify the 
main features of Brazilian survey-based inflation expectations collected by the Central Bank 
of Brazil, as well as to map the main driving forces behind the expectation formation process. 
2.   Data 
Figure 1 depicts the Brazilian CPI headline inflation rate (IPCA), which is the inflation rate 
adopted in the inflation targeting system, together with the respective survey-based inflation 
expectations, for several forecast horizons. 
                                                  
1  The opinions in this paper are those of the authors and do not necessarily reflect the point of view of the 
Central Bank of Brazil. Any remaining errors are ours. 
2  Corresponding author. Research Department, Central Bank of Brazil (e-mail: carlos.araujo@bcb.gov.br)  
3  Research Department, Central Bank of Brazil (e-mail: wagner.gaglianone@bcb.gov.br) 
4  Inflation expectations extracted from Brazilian financial data might exhibit some problems due to the lack of 
market liquidity, and also with risk premium issues (eg how to separate expectations from risk premium, which 
depends on macroeconomic conditions). 
5  Currently, it monitors market expectations for different inflation rates, GDP growth, industrial production 
growth, the exchange rate, the Selic interest rate, fiscal variables, and external sector variables. 108  BIS Papers No 49
 
Figure 1  
CPI monthly inflation rate (IPCA)  
and respective survey-based expectations  
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IPCA (% per month)
expectation (h=1 month)
expectation (h=3 months)
expectation (h=6 months)
 
Note: The expectations represent the median values, across all consulted 
market institutions, according to the forecast horizon (h). 
Table 1 gives some descriptive statistics of the short- and medium-run expectations, in 
comparison with the respective inflation rate. Similar statistics are presented in Table 2 for 
long-run expectations. First, note that the average and median values of expectations 
approach the inflation rate as long as the forecast horizon decreases, which is a natural 
result since the available information set becomes larger. In addition, the correlation between 
the inflation rate and the expectations increases, approaching the unit value.  
Table 1  
Descriptive statistics (time series in monthly values) 
  
IPCA (% 
p.m.)  Top 5 short  Median Top 5 medium Median  Top 5 medium  Median 
      h = 1 month 
h = 1 
month  h = 3 months 
h = 3 
months  h = 6 months 
h = 6 
months 
Mean  0.559 0.509  0.483  0.449 0.439  0.434  0.438 
Median  0.460 0.450  0.450  0.400 0.400  0.400  0.400 
Maximum  3.020 1.880  1.490  1.720 1.400  1.300  1.400 
Minimum  –0.210 0.100  0.100 0.150  0.160  0.200  0.210 
Std. deviation  0.489 0.292  0.227  0.209 0.173  0.178  0.176 
Correlation with 
IPCA  1.000 0.782  0.685  0.177 0.196 –0.083  –0.077 
Note: The “Top 5” expectations represent the median values of the “Top 5” group (short or medium-run), whereas 
the so-called “median” expectations indicate the median of all consulted institutions for a given period. The 
sample period covers May 2002–December 2008 (80 observations). BIS Papers No 49  109
 
Figure 2  
CPI inflation rate – IPCA (% 12 months) 
and (median) inflation expectations  
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IPCA (% 12 months)
expectation (h = 12 months)
 
Table 2  
Descriptive statistics  
  
IPCA (% 12 
months) Median 
      (h = 12 months) 
Mean  7.092 5.567 
Median  6.060 4.920 
Maximum  17.240 13.180 
Minimum  2.960 3.370 
Std. deviation  3.922 2.010 
correlation with 
IPCA  1.000 0.172 
Note: Sample period November 2002–December 2008. 
3.   Bias investigation 
A relevant issue to be investigated regarding any inflation expectations series is the 
existence of bias. To do so, first consider the following regression:  
t
e
h t t t c c        , 2 1 , (1) 
where  t   represents  the observed inflation rate, 
e
h t t   ,  is the respective inflation 
expectations time series, formed with a forecast horizon of h periods (ie expectation of the 
inflation rate for period t, formed at period t–h), and  t   is a random residual.  110  BIS Papers No 49
 
According to Grant and Thomas (1999), the existence of bias, or a “weak form of rationality”,
6 
can be verified through the following null hypothesis Ho:     1 ; 0 ; 2 1  c c
7 Tables 3 and 4 show 
the results of this “bias existence test” applied to the survey-based inflation expectations in 
Brazil.  
Table 3  
Bias existence test Ho:     1 ; 0 ; 2 1  c c  
Sample period  Top5short Median  Top5medium Median Top5medium Median  Median 
May 2002–
December 2008  h = 1month  h = 1month  h = 3months h = 3months h = 6months h = 6months  h = 12months
1 ˆ c   –0.107  –0.153  0.373 0.316 0.658 0.652 5.224 
Std.  dev.  0.066  0.128  0.209 0.242 0.224 0.223 1.882 
2 ˆ c   1.309 1.474  0.413  0.553  –0.229 –0.213  0.335 
Std.  dev.  0.169  0.345  0.519 0.608 0.348 0.342 0.234 
p-value  0.192  0.360  0.088 0.148 0.001 0.001 0.020 
Note: The hypothesis test is based on Newey and West’s (1987) HAC covariance matrix of residuals. For the median 
(h = 12 months) regression, the CPI inflation rate (% 12 months) is used as dependent variable, with a sample period 
November 2002–December 2008. 
Table 4 
Bias existence test Ho:     1 ; 0 ; 2 1  c c  
Sample period  Top5short Median  Top5medium Median Top5medium Median  Median 
January 2004–
December 2008  h = 1month  h = 1month  h = 3months h = 3months h = 6months h = 6months  h = 12months
1 ˆ c   0.035  0.041  0.161 0.102 0.157 0.180 3.266 
Std.  dev.  0.086  0.088  0.117 0.150 0.173 0.195 0.914 
2 ˆ c   0.943  0.952  0.704 0.857 0.704 0.651 0.397 
Std.  dev.  0.156  0.167  0.249 0.349 0.392 0.476 0.146 
p-value  0.915  0.770  0.361 0.484 0.548 0.470 0.000 
Note: The hypothesis test is based on Newey and West’s (1987) HAC covariance matrix of residuals. For the median 
(h = 12 months) regression, in which the CPI inflation rate (% 12 months) is again used as dependent variable, the bias 
test for a sample period January 2005–December 2008 generates a p-value = 0.563, in sharp contrast to the p-value = 0, 
obtained from the sample January 2004–December 2008. 
Note from Table 3 that the null hypothesis is rejected at a 5% confidence level only for longer 
horizons (six and 12 months), whereas for one and three months the results suggest the 
non-existence of a forecast bias. In addition, results with recent samples (see Table 4) 
indicate that the survey-based expectations might be unbiased in all considered horizons. 
                                                  
6   According to the authors, the “strong” form of rationality requires the forecast errors to be uncorrelated to any 
relevant available economic information. 
7   Obstfeld and Rogoff (1996, p 79) argue that rational expectation is a mathematical expectation conditional on 
the available information set. In other words, the rational expectations hypothesis does not require the 
forecasts to be strictly correct in all periods but, instead, requires the forecast errors to be unbiased and 
uncorrelated with any information in which the forecast is conditioned. See also Clements (2005, p 5) for 
further details. BIS Papers No 49  111
 
Therefore, the previous results support a “weak form of rationality” for the Brazilian survey-
based inflation expectations, partially reflecting the degree of sophistication of the models 
and frameworks used by the Brazilian market agents when forming their inflation 
expectations.
8  
Another feature of expectations usually discussed in the literature is whether forecast errors 
 t e  are positively correlated to changes in the inflation rate. According to Henzel (2008), this 
feature would be compatible with the empirical evidence that agents often over-predict 
inflation during periods of a falling inflation rate, and vice versa. In order to verify this feature 
in the Brazilian data, consider the following regression: 
t t
e
h t t t t e              2 1 ,  (2) 
Table 5  
Forecast error   t e  
Sample period  Top5short Median  Top5medium Median Top5medium Median  Median 
Jan 2004–Dec 
2008  h = 1month  h = 1month h = 3months h = 3months h = 6months  h = 6months h = 12months
1 ˆ    0.013 0.023  0.048  0.048  0.042  0.045  0.143 
Std. dev.  0.027  0.027  0.036  0.037  0.038  0.039  0.337 
2 ˆ    0.463 0.523  0.494  0.468  0.454  0.486  2.118 
Std. dev.  0.067  0.066  0.091  0.084  0.086  0.088  0.633 
Note: The estimations are based on Newey and West’s (1987) HAC covariance matrix. For the median (h = 12 months) 
regression, the CPI inflation rate (% 12 months) is used as regressor. In this case, the sample period January 2005–
December 2008 produces  2 ˆ   = 1.512. 
Notice from Table 5 that  2 ˆ   is statistically significant, positive, and (except for last column) 
also less than unit, reflecting a relatively low response of expectations to changes in the 
inflation rate, corroborating Henzel (2008). This empirical evidence might be linked to results 
from Tables 1 and 2, which indicate a lower sample standard deviation compared to the 
inflation rate series itself. Besides that, results from Table 5 are in line with some papers in 
the literature, such as Ball and Croushore (1995) and Mankiw et al (2003), in which agents 
seems to react slowly to new information during the formation of inflation expectations.  
4.   Some driving forces behind the expectation formation process 
In this section, some driving factors behind the expectation formation process are presented, 
in order to reveal some additional features of the Brazilian inflation expectations. In Tables 6 
and 7, some specifications of inflation expectations are shown, based on the following 
regressors: autoregressive term, inflation target (next 12 months), inflation rate (IPCA) and 
Selic short-term interest rate (both in percentage over 12 months), nominal exchange rate 
(Reais/USD), industrial production, Embi + Br and industrial capacity utilisation (UCI).
9  
                                                  
8   The formation of expectations of some US surveys is analysed by Mankiw et al (2003), in which the authors 
investigate the hypotheses of adaptive, rational or “sticky-information” expectations. 
9   All variables in log terms, excepting IPCA, Selic, target and expectation, which are used in log (1 + rate/100). 
None of the regressions has intercept, since inflation target is constant in the adopted sample period. 112  BIS Papers No 49
 
Table 6  
Dependent variable: inflation expectations  
e
t t , 12    
Regressors  I II  III  IV 
Expectation (t + 11,t–1)  0.723 0.720 0.684 0.709 
  (0.000) (0.000) (0.000) (0.000) 
Inflation target (t + 12,t)  0.207 0.210  –0.005 –4.100
  (0.000) (0.001) (0.977) (0.229) 
IPCA (t)  0.155 0.161 0.133 0.142 
  (0.000) (0.000) (0.004) (0.002) 
Selic (t)  –0.071 –0.074 –0.068 –0.051
  (0.000) (0.000) (0.000) (0.045) 
FX rate (t)  0.007 0.007 0.004  0.008 
  (0.043) (0.032) (0.173) (0.033) 
Δ(ind. production (t))    0.014    
   (0.130)    
Embi + Br (t)     0.002  
     (0.211)   
Uci (t)      0.043 
      (0.208) 
R2  0.936 0.939 0.939 0.938 
Adjusted  R2  0.931 0.933 0.933 0.932 
LM residuals autocorrelation       
Test (p-value,4 lags)  0.117 0.094 0.172 0.116 
It can be seen from Table 6 that the autoregressive coefficient (around 0.70) indicates quite a 
significant persistence of inflation expectations. In addition, expectations are positively 
related to the inflation target, as well as to the current inflation and FX rates. On the other 
hand, results also suggest a negative coefficient for the Selic short-term interest rate, which 
reveals a significant reaction of long-term inflation expectations due to changes in monetary 
policy, also reflecting the credibility of monetary authority, according to market agents.
10  
Table 7 presents the behaviour of inflation expectations, in quarterly rates, with a three-
month forecast horizon. First, a lower persistence is obtained in comparison to the previous 
results, probably due to the higher frequency of the inflation expectation rate. In addition, the 
coefficient for inflation is again positive, but the responses for the target and Selic seem to be 
not significant. Nonetheless, results of Table 7 also suggest that past FX rate volatility has a 
positive impact on short-/medium-term inflation expectations. 
 
 
                                                  
10   Note that we have obtained a different response for the interest rate, in comparison with Minella et al (2003) or 
Cerisola and Gelos (2005), probably due to the sample period considered in this paper, which covers only the 
last five years of inflationary dynamics. BIS Papers No 49  113
 
Table 7  
Dependent variable: inflation expectations  
e
t t , 3    
Regressors  I II  III  IV 
Expectation (t + 2,t–1)   0.535 0.534 0.499 0.547 
  (0.000) (0.000) (0.000) (0.000) 
Inflation target (t + 12,t)   0.033 0.033  –0.059 –3.141 
  (0.361) (0.366) (0.554) (0.397) 
IPCA (t)  0.071 0.071 0.058 0.053 
  (0.015) (0.016) (0.093) (0.133) 
Selic (t)   0.001 0.001  –0.002 0.019 
  (0.939) (0.939) (0.853) (0.446) 
FX rate volatility (t–2)  0.166 0.165 0.132 0.223 
  (0.001) (0.028) (0.003) (0.016) 
Δ(ind. production (t))   0.000    
   (0.987)    
Embi + Br (t)     0.001   
     (0.317)  
Uci (t)      0.031 
      (0.392) 
R2  0.654 0.654 0.660 0.660 
Adjusted  R2  0.629 0.622 0.629 0.629 
LM residuals autocorrelation       
Test (p-value,4 lags)  0.901 0.904 0.514 0.806 
Note: All regressions are based on Newey and West’s (1987) 
HAC covariance matrix. Sample period is January 2004–
December 2008 (60 observations). P-values are shown in 
parentheses, and the 5% level significant coefficients are 
presented in bold. In Table 6, inflation expectations (median 
across all agents) are in percentage over 12 months, with a 
forecast horizon of h  =  12 months. In Table 7, inflation 
expectations (median of Top5 medium-term) are in quarterly 
percentage, with a forecast horizon of h=3 months. FX rate 
volatility refers to a 3-month moving average of the volatility of the 
monthly nominal exchange rate. 
5.   Conclusions 
Nowadays, inflation expectations are frequently monitored by the vast majority of central 
banks, due to its importance on inflation forecasting setups. Departures from rational 
expectations represent a serious matter of concern to policymakers, since forecasting 
devices are usually based on a rational expectations hypothesis.  
In this paper, we aim to provide a simple investigation of Brazilian survey-based inflation 
expectations, with respect to statistical properties and bias existence, as well as to identify 
some driving forces behind the expectation formation process. Empirical exercises indicate 
that expectations might be unbiased, and that different factors might help explaining short- 
and long-term inflation expectations in Brazil.  114  BIS Papers No 49
 
6. References 
Ball, L and D Croushore (1995): “Expectations and the effects of monetary policy”, NBER 
Working Paper no 5344. 
Cerisola, M and RG Gelos (2005): “What drives inflation expectations in Brazil? An empirical 
analysis”, IMF Working Paper WP/05/109. 
Clements, MP (2005): Evaluating econometric forecasts of economic and financial variables, 
Palgrave Macmillan, first edition. 
Grant, AP and LB Thomas (1999): “Inflationary expectations and rationality revisited”, 
Economics Letters 62, 331–8. 
Henzel, S (2008): “Learning trend inflation – can signal extraction explain survey forecasts?” 
Institute for Economic Research at the University of Munich, Ifo Working Paper no 55. 
Mankiw, NG, Reis, R and J Wolfers (2003) “Disagreement about inflation expectations”, 
NBER Working Paper no 9796. 
Marques, AB, Fachada, P and DC Cavalcanti (2003): “Sistema banco central de 
expectativas de mercado”, Notas Técnicas do Banco Central, no 36. 
Minella, A, Freitas, PS, Goldfajn, I and MK Muinhos (2003): “Inflation targeting in Brazil: 
constructing credibility under exchange rate volatility”, Journal of International Money and 
Finance 22 (7), 1015–40. 
Newey, WK and KD West (1987): “A simple, positive semi-definite, heteroskedasticity and 
autocorrelation consistent covariance matrix”, Econometrica 55, 703–708. 
Obstfeld, M and K Rogoff (1996): Foundations of international macroeconomics, MIT Press. 

A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix”,

Disagreement about inflation expectations”,

Evaluating econometric forecasts of economic and financial variables, Palgrave Macmillan, first edition.

Expectations and the effects of monetary policy”,

Foundations of international macroeconomics,

Inflation targeting in Brazil: constructing credibility under exchange rate volatility”,

Inflationary expectations and rationality revisited”,

Learning trend inflation – can signal extraction explain survey forecasts?”

Sistema banco central de expectativas de mercado”, Notas Técnicas do Banco Central, no 36.

What drives inflation expectations in Brazil? An empirical analysis”, IMF Working Paper WP/05/109.

Monetary policy and the measurement of inflation: prices, wages and expectations

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Monetary policy and the measurement of inflation: prices, wages and expectations

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