Core Inflation in Brazil
André MinellaTomiê Sugahara
Research Department - Banco Central do Brasil
VIII Annual SeminarAugust 2006
Work in Progress – Comments are Welcome
Motivation Core inflation measures are used in most countries,
but… Are core inflation measures really useful? Do they convey information about “underlying” or
future inflation? How do core measures compare to each other? Can new measures, such as those based on
common factors, be useful?
Let’s take a look at what Brazil’s experience says…
Literature Brazil
Figueiredo (2001), Bryan and Cecchetti (2001) Pichetti and Toledo (2000), Fiorencio and Moreira
(2002), Moreira and Migon (2004), Araújo and Fiorencio (2005)
Gonçalves, Schechtman and Barros (2000) Other countries
Hogan, Jonhson and Laflèche (2001), Armour (2006) D’Amato, Sanz and Paladino (2006) Cristadoro, Forni, Reichlin and Veronese (2005) Bryan and Cecchetti (1994), Bryan, Cecchetti, and
Wiggins II (1997) Roger (1997, 1998)
Presentation outline Core measures properties Core measures for Brazil
Current measures New measures
Evaluation Variability Bias Capacity to indicate future inflation
Core measures desirable properties Practical issues
Timely computable Definite figures (not revisable) Easily understood by the public
Substantial issues Reflects “underlying” inflation Forward-looking nature
Core measures in BrazilIPCA index
By exclusion Food at home and administered prices are
excluded (around 50% of the index)
Trimmed mean (non-smoothed) 20% of each tail of weighted distribution is
excluded Distribution: Monthly change of IPCA items
(47 items up to 1999:7; 52 items 1999:8-2006:6)
IPCA vs. core by exclusion vs. trimmed mean (non smoothed)
0
2
4
6
8
10
12
14
16
18
20
Jan
-97
Ap
r-9
7
Jul-
97
Oct
-97
Jan
-98
Ap
r-9
8
Jul-
98
Oct
-98
Jan
-99
Ap
r-9
9
Jul-
99
Oct
-99
Jan
-00
Ap
r-0
0
Jul-
00
Oct
-00
Jan
-01
Ap
r-0
1
Jul-
01
Oct
-01
Jan
-02
Ap
r-0
2
Jul-
02
Oct
-02
Jan
-03
Ap
r-0
3
Jul-
03
Oct
-03
Jan
-04
Ap
r-0
4
Jul-
04
Oct
-04
Jan
-05
Ap
r-0
5
Jul-
05
Oct
-05
Jan
-06
Ap
r-0
6
y-o
-y p
rice
ch
ang
e (%
)
IPCA
Trimmed mean (non smoothed)
By exclusion
Kurtosis – IPCA items
KurtosisUsing monthly price change
0
5
10
15
20
25
30
35
40
45
Jan-
95
May
-95
Sep
-95
Jan-
96
May
-96
Sep
-96
Jan-
97
May
-97
Sep
-97
Jan-
98
May
-98
Sep
-98
Jan-
99
May
-99
Sep
-99
Jan-
00
May
-00
Sep
-00
Jan-
01
May
-01
Sep
-01
Jan-
02
May
-02
Sep
-02
Jan-
03
May
-03
Sep
-03
Jan-
04
May
-04
Sep
-04
Jan-
05
May
-05
Sep
-05
Jan-
06
May
-06
Skewness – IPCA items
SkewnessUsing monthly price change
-6
-4
-2
0
2
4
6
8
Jan-
95
May
-95
Sep
-95
Jan-
96
May
-96
Sep
-96
Jan-
97
May
-97
Sep
-97
Jan-
98
May
-98
Sep
-98
Jan-
99
May
-99
Sep
-99
Jan-
00
May
-00
Sep
-00
Jan-
01
May
-01
Sep
-01
Jan-
02
May
-02
Sep
-02
Jan-
03
May
-03
Sep
-03
Jan-
04
May
-04
Sep
-04
Jan-
05
May
-05
Sep
-05
Jan-
06
May
-06
IPCA vs. (non-smoothed) trimmed mean using different cutoffs: 20%, 15% and 10%
0
2
4
6
8
10
12
14
16
18
20
Jan-
97
Apr
-97
Jul-9
7
Oct
-97
Jan-
98
Apr
-98
Jul-9
8
Oct
-98
Jan-
99
Apr
-99
Jul-9
9
Oct
-99
Jan-
00
Apr
-00
Jul-0
0
Oct
-00
Jan-
01
Apr
-01
Jul-0
1
Oct
-01
Jan-
02
Apr
-02
Jul-0
2
Oct
-02
Jan-
03
Apr
-03
Jul-0
3
Oct
-03
Jan-
04
Apr
-04
Jul-0
4
Oct
-04
Jan-
05
Apr
-05
Jul-0
5
Oct
-05
Jan-
06
Apr
-06
y-o
-y p
ric
e c
ha
ng
e (
%)
IPCA
20%
10%15%
Core measures in BrazilIPCA index
Smoothed trimmed mean For 8 items, y-o-y change instead of m-o-m
Asymmetric trimmed mean Bryan and Cecchetti (2001) Centered on the 60th percentile of the
weighted distribution 24% cutoff:
14.4% in the bottom tail 9.6% in the upper tail
IPCA vs. smoothed trimmed mean vs. asymmetric trimmed mean
0
2
4
6
8
10
12
14
16
18
20
Jan-
97
Apr
-97
Jul-9
7
Oct
-97
Jan-
98
Apr
-98
Jul-9
8
Oct
-98
Jan-
99
Apr
-99
Jul-9
9
Oct
-99
Jan-
00
Apr
-00
Jul-0
0
Oct
-00
Jan-
01
Apr
-01
Jul-0
1
Oct
-01
Jan-
02
Apr
-02
Jul-0
2
Oct
-02
Jan-
03
Apr
-03
Jul-0
3
Oct
-03
Jan-
04
Apr
-04
Jul-0
4
Oct
-04
Jan-
05
Apr
-05
Jul-0
5
Oct
-05
Jan-
06
Apr
-06
y-o
-y p
rice
ch
ang
e (%
)
IPCA
Smoothed Trimmed Mean
Asymmetric Trimmed Mean
Monthly figures
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Jan-
97
Apr
-97
Jul-9
7
Oct
-97
Jan-
98
Apr
-98
Jul-9
8
Oct
-98
Jan-
99
Apr
-99
Jul-9
9
Oct
-99
Jan-
00
Apr
-00
Jul-0
0
Oct
-00
Jan-
01
Apr
-01
Jul-0
1
Oct
-01
Jan-
02
Apr
-02
Jul-0
2
Oct
-02
Jan-
03
Apr
-03
Jul-0
3
Oct
-03
Jan-
04
Apr
-04
Jul-0
4
Oct
-04
Jan-
05
Apr
-05
Jul-0
5
Oct
-05
Jan-
06
Apr
-06
m-o
-m p
rice
ch
ang
e (%
)
IPCA
Trimmed Mean
Asymmetric Trimmed Mean
Core measures in BrazilIPCA index
Weighted median Value of the 50th percentile of the weighted
distribution
Double weighted All items are considered, but they are
reweighted according to their volatility: the greater the volatility, the lower the weight
IPCA vs. weighted median vs. double weighted
0
2
4
6
8
10
12
14
16
18
20
Jan-
97
Apr
-97
Jul-9
7
Oct
-97
Jan-
98
Apr
-98
Jul-9
8
Oct
-98
Jan-
99
Apr
-99
Jul-9
9
Oct
-99
Jan-
00
Apr
-00
Jul-0
0
Oct
-00
Jan-
01
Apr
-01
Jul-0
1
Oct
-01
Jan-
02
Apr
-02
Jul-0
2
Oct
-02
Jan-
03
Apr
-03
Jul-0
3
Oct
-03
Jan-
04
Apr
-04
Jul-0
4
Oct
-04
Jan-
05
Apr
-05
Jul-0
5
Oct
-05
Jan-
06
Apr
-06
y-o
-y p
rice
ch
ang
e (%
)
IPCA
Weigthed median
Double weighted
Core measures in BrazilCore based on common factors
Based on Cristadoro, Forni, Reichlin and Veronese (2005), index for the Euro Area
Use information of a large panel of time series
Inflation driven by common factors Core measure: projection of the medium-
and long-run component of monthly inflation on the common factors
Core measures in BrazilCore based on common factors
Inflation modeled as:
Core measure:
t
q
h
s
kkhthkttt ubx
1 0
tSt
Lttx
Lttx *
Core measures in BrazilCore based on common factors
Panel of 106 series Prices Economic activity Money, credit, and financial variables Fiscal sector External sector International economy
IPCA vs. common-factor-based core measure
0
2
4
6
8
10
12
14
16
18
20
Jan-
97
Apr
-97
Jul-9
7
Oct
-97
Jan-
98
Apr
-98
Jul-9
8
Oct
-98
Jan-
99
Apr
-99
Jul-9
9
Oct
-99
Jan-
00
Apr
-00
Jul-0
0
Oct
-00
Jan-
01
Apr
-01
Jul-0
1
Oct
-01
Jan-
02
Apr
-02
Jul-0
2
Oct
-02
Jan-
03
Apr
-03
Jul-0
3
Oct
-03
Jan-
04
Apr
-04
Jul-0
4
Oct
-04
Jan-
05
Apr
-05
Jul-0
5
Oct
-05
Jan-
06
Apr
-06
y-o
-y p
rice
ch
ang
e (%
)
IPCA
In-Sample Up to time t sample
Bias and variability
AverageStand. Dev.
Coef. Var. AverageStand. Dev.
Coef. Var.
IPCA 7.82 6.43 0.82 8.08 6.05 0.75
By exclusion 6.43 4.69 0.73 6.42 3.45 0.54
Trimmed mean 5.70 4.08 0.72 6.01 3.46 0.58
Smoothed trimmed mean 7.54 4.01 0.53 7.37 2.70 0.37
Asymmetric mean 7.15 4.98 0.70 7.42 4.36 0.59
Weighted median 4.86 3.56 0.73 5.27 3.03 0.57
Double weighted 6.68 4.52 0.68 7.01 3.89 0.55
Common factors 7.32 2.79 0.38
Trimmed mean 10% 6.36 4.79 0.75 6.69 4.21 0.63
Note: Monthly inflation at annual rates
1995:7-2006:4 1999:1-2006:4
Measures
Bias and variability
Measures 1996:3-2006:4 1999:1-2006:4
IPCA 2.81 3.25
By exclusion 1.20 1.11
Trimmed mean 1.37 1.24
Smoothed trimmed mean 0.51 0.48
Asymmetric mean 1.48 1.64
Weighted median 1.61 1.26
Double weighted 1.30 1.29
Common factors 0.72
Trimmed mean 10% 1.58 1.61
Note: Computed from monthly data measured at annual rates
centered moving average inflation
Root mean square error with respect a 36-month
Forecasting ctttE 12
Measures 1996:5-2005:6 2000:1-2005:6
IPCA 4.96 5.09
By exclusion 4.70 4.65
Trimmed mean 4.45 4.91
Smoothed trimmed mean 4.78 4.31
Asymmetric mean 4.50 4.75
Weighted median 4.64 5.11
Double weighted 4.46 4.75
Common factors 4.74
Trimmed mean 10% 4.45 4.81
Note: t is year-over-year price increase.
Root mean square error
Cogley’s equation 1212 tt
cttt
Measures Adjusted R2 P-value Ho: =0, =1
By exclusion 0.99 1.01 0.11 0.5944(1.28) (0.48)
Trimmed mean 4.65 2.35 0.41 0.0037(1.40) (0.45)
Smoothed trimmed mean -0.42 0.67 0.06 0.7594(0.99) (0.48)
Asymmetric mean 2.14 3.52 0.32 0.0142(1.10) (0.86)
Weighted median 5.62 2.03 0.46 0.0010(1.54) (0.34)
Double weighted 2.50 2.45 0.29 0.1021(1.33) (0.69)
Common factors
Trimmed mean 10% 5.21 3.72 0.44 0.0004(1.46) (0.69)
Notes: Standard error in parentheses. t is year-over-year price increase.
Sample: 1996:5 2005:6
Cogley’s equation 1212 tt
cttt
Measures Adjusted R2 P-value Ho: =0, =1
By exclusion 2.90 1.43 0.30 0.0613(1.38) (0.46)
Trimmed mean 4.84 2.08 0.35 0.0065(1.64) (0.57)
Smoothed trimmed mean 1.37 1.34 0.29 0.4259(1.05) (0.46)
Asymmetric mean 2.33 2.88 0.27 0.0648(1.12) (0.91)
Weighted median 5.74 1.85 0.39 0.0006(1.81) (0.46)
Double weighted 2.59 1.98 0.23 0.1523(1.34) (0.74)
Common factors 1.09 1.97 0.21 0.1742(0.84) (0.79)
Trimmed mean 10% 4.81 3.10 0.35 0.0078(1.54) (0.82)
Notes: Standard error in parentheses. t is year-over-year price increase.
Sample: 1999:1 2005:6
Conclusions (up to this point)
Core measures: are less volatile than headline inflation contain information on future inflation but some of them are biased downwards
Although results are mixed, Figueiredo’s (2001) result as to the relatively good performance of smoothed trimmed-mean core measure is held
Core based on common factors may be promising, but too early to tell - additional research is warranted
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