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

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r-0

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r-0

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r-0

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Ap

r-0

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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

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-98

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99

May

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-99

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00

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01

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-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

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-99

Jan-

00

May

-00

Sep

-00

Jan-

01

May

-01

Sep

-01

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May

-02

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-02

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-03

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May

-04

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-04

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05

May

-05

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-05

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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-

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Apr

-02

Jul-0

2

Oct

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Jan-

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Apr

-03

Jul-0

3

Oct

-03

Jan-

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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

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14

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Jan-

97

Apr

-97

Jul-9

7

Oct

-97

Jan-

98

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-98

Jul-9

8

Oct

-98

Jan-

99

Apr

-99

Jul-9

9

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-99

Jan-

00

Apr

-00

Jul-0

0

Oct

-00

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Jul-0

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Oct

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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-

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Apr

-02

Jul-0

2

Oct

-02

Jan-

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Apr

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Jul-0

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Oct

-03

Jan-

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-04

Jul-0

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Oct

-04

Jan-

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Apr

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Jul-0

5

Oct

-05

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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