M.Bryan

Core Inflation for Emerging Economies

Global Interdependence Center Michael F. Bryan* Vice President and Senior Economist Federal Reserve Bank of Atlanta *Co-authored with Brent Meyer (Federal Reserve Bank of Cleveland) and Ellyn Terry (Federal Reserve Bank of Atlanta)

Core Inflation for an Emerging Economy 1. Food represents a huge share of the consumers’ marketbasket in an emerging economy 2. The “ex-food and energy” approach to core inflation is probably not an efficient guide for an inflation minded central bank and probably more so for a central bank in an emerging economy.

3. Some food items are actually “good” inflation indicators—some non-food goods are not.

4. Various techniques can be used to improve the signal-to-noise of a high-frequency (monthly) inflation statistic, giving the central bank the opportunity to spot worsening/improving inflation trends earlier than they might otherwise.

5. Trimmed-mean estimators offer a extremely simple technique for improving the inflation signal in the inflation data.

Important Cautions 1. I do not necessarily represent the views of the Federal Reserve Board, or the Federal Reserve Bank of Atlanta.

2. This work is still incomplete—I cannot match the official Zambian CPI exactly using the component data I have.

3. I have only a very limited knowledge of Zambian monetary policy (but hope to have greater knowledge on this subject before I return home.)

What’s the Problem that a “Core” Inflation Measure is the Answer?

Federal Reserve “Monetary” Policy Set the funds rate so to achieve two objectives: 1) maximum sustainable employment and 2) price stability.

i ff = (r* + π )+ 0.5 (y-y*) + 0.5 (π - π*) Zambian Monetary Policy Establish a level of reserves that produces the broad money growth consistent with an inflation objective.

In either case…

Policy action

Inflation result

Zambian Inflation (12-month percent change)

30

25

20

15

10

5

Inflation objective 0 2002

2003

Overall CPI

2004

2005

2006

2007

2008

2009

Zambian Inflation (12-month percent change)

30

Monthly, nsa 25

20

15

h

10

5

Inflation objective 0 2002

2003

Overall CPI

2004

2005

2006

2007

2008

2009

How Does a Central Bank Deal with the Volatility in the High-Frequency Price Data?

Computes (12-month) Trends Trends are, of course, very backward looking and can only tell the central bank when it has gone off course, not when it is going off course.

Core Inflation Statistics An attempt to preserve the timeliness of the data by reducing the noise in the data by “statistical� techniques.

Alternative “Core� Approaches Variance Weighted Price Statistics Reweight the price statistic on the (inverse) basis of its volatility.

Dynamic Factor/Kalman Filter Statistics Have the data identify a common component in the price data.

Reweight the price statistic such that the most volatile components get no weight This is the most common approach—the CPI excluding something.

CORE INFLATION STATISTICS OF SELECTED CENTRAL BANKS (* Inflation targeting countries ** Core statistic used as a target or objective) Country Core Inflation Statistic Australia** CPI less mortgage interest payments, government controlled prices, and energy items.

Belgium CPI less energy, potatoes, and fruit and vegetables.

Canada** CPI less indirect taxes, food and energy items.

Finland** CPI less housing capital costs, indirect taxes, and government subsidies.

France** CPI excluding changes in taxes, energy prices, food prices, and regulated prices.

Greece CPI excluding food and fuels.

Israel* CPI less government goods, housing, fruit and vegetables.

Japan CPI less fresh foods.

Netherlands CPI less vegetables, fruit, and energy.

New Zealand** CPI less commodity prices, government controlled prices, interest and credit charges.

Philippines A statistical trend line.

Portugal 10% trimmed mean of the CPI. Spain* CPI less mortgage interest payments.

Sweden* CPI excluding housing mortgage interest and effects of taxes and subsidies (UND1), UND1 excluding petroleum goods (UND2), and UND1 less mainly imported goods (UNDINH).

United Retail Price Index less mortgage interest payments.

Kingdom** United States CPI less food and energy items.

Income and Food Expenditure (sample of 114 nations, 1996 data) 60,000

Per capita GDP

50,000

Sub-Sahara Africa 40,000

United States 30,000

20,000

Zambia

10,000

0 0

10

20

30

40

50

60

70

80

90

Food expenditure as a share of total expenditure

100

Zambian Retail Price Changes February 2009 (NSA, annualized) 0.18

Weighted Frequency

WEIGHTED MEAN

Mean = 1.4% 0.16

Standard Dev. = 6.3% 0.14

0.12

0.1

0.08

Normal distribution

0.06

0.04

0.02

0 ‐13 ‐12 ‐11 ‐10 ‐9

‐8

‐7

‐6

‐5

‐4

‐3

‐2

‐1

0

1

2

3

4

5

6

7

Annualized Year-To-Date Percent Change

8

9

10

11 12 13

Retail Price Change Distribution Characteristics (Arranged by average inflation, annualized)

Monthly Brazil Argentina Mexico Colombia South Africa Israel UK Sweden New Zealand* US Japan Canada Germany

Mean

St. Dev.

Skew

Kurt

206.2 123.2 42.8 23.2 12.0 10.0 8.1 6.1 7.2 5.2 4.5 3.4 2.8

4.0 6.3 5.1 2.4 1.7 1.6 1.9 1.9 1.9 0.7 1.9 1.5 1.2

0.6 1.2 2.6 1.0 1.6 0.1 0.8 1.1 0.7 0.3 0.8 0.4 0.0

14.6 11.0 46.2 10.1 13.1 10.6 20.1 19.1 6.9 11.6 32.9 22.0 26.3

Data for New Zealand are not available on a monthly basis, so we report values * computed from quarterly data.

The Menu-Cost Model of Observed Price Changes with expected inflation frequency

frequency

lower limit

upper limit

Î Desired Price Change Distribution

Î Observed Price Change Distribution

Hypothetical Mixed Normal Distribution Frequency

Standard normal, variance=1, kurtosis=3

High variance normal, variance=9, kurtosis=3

0

Hypothetical Mixed Normal Distribution Frequency Leptokurtic, non-normal, mixed distribution, variance=5, kurtosis=4.7

Standard normal, variance=1, kurtosis=3

High variance normal, variance=9, kurtosis=3

0

Hypothetical Mixed Normal Distribution Frequency Leptokurtic, non-normal, mixed distribution, variance=5, kurtosis=4.7

0

TRIMMED MEAN ESTIMATORS

xα =

1 1 − 2(

α

100

∑wx

)

i∈ I α

i

i

CONSUMER PRICE INDEX 4.0

12-month percent change Median CPI

3.5 3.0 2.5 2.0 1.5

Various trimmedmean measures CPI, all items

1.0 1992

1994

1996

1998

2000

2002

EFFICIENCY OF VARIOUS CPI TRIMMED-MEAN ESTIMATORS 2.00

Mean absolute error

1.75 CPI percent change over centered 35 months

1.50

1.25

1.00 0

5

10

15

20

25

Trim

30

35

40

45

50

STANDARD DEVIATION OF CPI COMPONENTS: ZAMBIAN CPI, s.a., 2002-2009 C hi t e nge ma t e r i a l l oc a l Toi l e t S oa p B r i sk e t D e t e r g e n t P a st e I n st a n t c o f f e e i m p o r t e d B un R a z or B l a de T a b l e sa l t B o y s S c h o o l S we a t e r T a k e a wa y c h i c k e n & c h i p s El e c t r i c I r o n d r y B a k i n g p o wd e r

Food item Non-food item

B i c y c l e Tube Wh i t e R o l l e r D i e se l C i ne ma C ha r ge s N e wsp a p e r B oy s S c hool S hoe s El e c t r i c i t y T a r i f f R e g i st r a t i o n f e e Wo o d e n d o o r Te r r y N a ppy Toy ot a c or ol l a C h e st X - r a y M e ns Le a t he r S hoe s Gi n g e r A l e B oy s U nde r pa nt s P umpk i n l e a v e s S i ngl e B l a nk e t Millet El e c t r i c a l c o o k e r M e d i c a l sc h e m e P i ne a ppl e s R a w c a ssa v a t u b e r s Gr e e n h o se p i p e

0

10

20

30

40

50

CHARACTERISTICS OF THE 40 LARGEST ITEMS IN THE ZAMBIAN CPI* (Representing 63% of total expenditure for high-income urban consumers) Commodity

Mean

Varian.

Weight

Commodity

Mean

Varian.

Weight

House rent (medium cost)

1.9

15.3

4.5%

Rhino Lager

1.2

2.7

1.1%

White breakfast

0.7

3.5

3.7%

Castle Lager

1.1

2.5

1.1%

Toyota hilux

0.8

6.8

3.2%

Beef Sausages

1.0

3.3

1.1%

Toyota corolla

1.4

7.1

3.2%

Dried beans

1.4

5.0

1.0%

Nissan sunny

1.6

8.4

3.2%

Rape

1.4

10.5

1.0%

Nissan pick_up

1.1

6.5

3.2%

Water & Sewerage charges

0.3

7.6

1.0%

Mixed Cut

1.1

2.1

3.2%

Water & Sewerage charges

0.6

8.2

1.0%

Dressed chicken

0.9

4.2

3.0%

Laundry

0.9

3.0

0.9%

Bread

1.1

1.4

2.9%

Dry Clean

0.9

3.7

0.9%

White sugar

1.0

4.1

2.2%

Dried Kapenta

1.6

6.3

0.8%

House rent (low cost)

1.5

7.3

1.6%

Dried Kapenta

1.3

4.1

0.8%

Tomatoes

1.5

12.3

1.6%

Refrigerator

0.4

5.7

0.8%

Cooking oil Imported

1.1

2.5

1.4%

Television B&W

1.2

5.0

0.7%

Cooking oil Local

1.2

2.6

1.4%

Television Colour

0.0

3.3

0.7%

Mini Bus Fare Town/Chilenje

1.3

5.3

1.4%

Detergent Powder

0.7

3.0

0.7%

Coach Fare Lusaka/Kitwe

0.9

5.5

1.4%

Shake shake

0.7

4.0

0.6%

Petrol

0.8

4.9

1.3%

3 piece lounge suit low price

1.5

6.2

0.6%

Diesel

0.7

4.7

1.3%

3 piece lounge suit high price

2.0

17.3

0.6%

Bun

1.7

2.9

1.2%

Charcoal

1.3

3.6

0.6%

Mosi

1.2

2.3

1.1%

Radio cassette Recorder

0.3

9.4

0.6%

*characteristics computed on seasonally adjusted data over the 2002-2009 subperiod.

Zambian Inflation (Measured by various n.s.a. CPI trims, annualized monthly percent change)

75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 ‐5 ‐10 ‐15 ‐20 ‐25 2003

2004

High-Income CPI

2005

2006

4% Trim

2007

10% Trimn

2008

Median CPI

2009

Zambian Inflation (Measured by various s.a. CPI trims, annualized monthly percent change)

75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 ‐5 ‐10 ‐15 ‐20 ‐25 2003

2004

High-Income CPI

2005

2006

5% Trim

2007

21% Trim

2008

Median CPI

2009

EFFICIENCY OF VARIOUS ZAMBIAN CPI TRIMMED-MEAN ESTIMATORS 70.00

Root Mean Squared Error, seasonally adjusted data CPI percent change over next 24 months

60.00 50.00 40.00

Grey area within 10%

30.00 20.00 10.00

42% trim

Median CPI

0.00 0

5

10

15

20

25

Trim

30

35

40

45

50

Source: Monitoring Inflation in a Low-Inflation Environment (Bryan and Higgins, 2007)

Remaining Issues (That perhaps the Zambian Central Bank can advise me on?)

1. The Zambian CPI distribution appears to be positively “skewed”.

These (and other) estimators will need to be asymmetrically trimmed (or rebalanced) so that the core inflation indicator is an unbiased estimate of the object the central bank is trying to control.

2. The “efficient” trim estimate can be judged in several different ways.

You may wish to identify the trimmed-mean on the basis of its correlation to broad money (M3).

3. Inflation is always and everywhere a monetary pheonomenon. … but what are the driving sources of inflation when a nation’s GDP is heavily influenced by a world inflation hedge (i.e. copper)?

Core Inflation for Emerging Economies

Global Interdependence Center Michael F. Bryan* Vice President and Senior Economist Federal Reserve Bank of Atlanta *Co-authored with Brent Meyer (Federal Reserve Bank of Cleveland) and Ellyn Terry (Federal Reserve Bank of Atlanta)

Figure 2c: Identifying Breaks in the Inflation Trend (monthly data, break = 0.5 percentage point)

1.0

Probability Break is Identified Trimmed mean CPI

0.9 0.8 0.7

Median CPI

0.6 0.5

Core CPI

0.4 0.3 0.2 CPI

0.1 0.0 0

5

10

15

20

25

30

35

40

45

Months until break identified

50

55

60

65

70

Source: Monitoring Inflation in a Low-Inflation Environment (Bryan and Higgins, 2007)

Zambian Inflation (12-month percent change)

30

Monthly, nsa 25

20

15

10

5

Initially announced inflation objective 0 2002

2003

Overall CPI

2004

2005

2006

2007

2008

2009

Zambian Inflation (by major demographic subgroup, 12-month percent change)

30

25

20

15

10

5

0 2002

2003

Overall CPI

2004

2005

Rural

2006

2007

High Income Urban

2008

2009

Low Income Urban

Zambian Inflation (by major demographic subgroup, annualized monthly percent change)

75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 ‐5 ‐10 ‐15 ‐20 2002

2003

Overall CPI

2004

2005

Rural

2006

2007

High Income Urban

2008

2009

Low Income Urban

The Most Volatile Commodities in the Zambian CPI (Arranged by average inflation, annualized) Commodity Green hosepipe

Mean St. Dev. 12.44823384 71.61848918

Weight 0.000552

Salted peanuts Watermelon PTA Contribution

5.241725361 43.79150285 7.423151079 42.51392153 5.723105927 37.54348891

0.00002 0.000184 0.003257

Peas Pawpaw Lettuce Pineapple chunks Spinach Pipe tobacco

5.804479272 5.78843851 6.817777767 3.792698665 4.673422205 2.997283256

36.18308369 33.77371163 32.72386727 32.11631734 31.19553659 29.32643098

0.000247 0.000109 0.000186 0.000036 0.000234 5.00E-06

Sweet potatoes Raw cassava tubers Plasters

5.38065539 28.27511114 4.953983048 27.7418862 1.570540052 25.05923256

0.00255 0.000073 0.000111

* Calculations based on data from 2002-2009 (February)

Cum. Wt. 0.000552 0.000572 0.000756 0.004013 0.00426 0.004369 0.004555 0.004591 0.004825 0.00483 0.00738 0.007453 0.007564

STANDARD DEVIATION OF CPI COMPONENTS: ZAMBIAN CPI, n.s.a., 2002-2009 C hi k C o n su l a t e Ye a st T - bone C ook i ng oi l Loc a l D e t t ol C oc oa Ty r e r a di a l T a k e a wa y c h i c k e n & c h i p s Wh e a t P l a i n F l o u r

Food item Non-food item

Vo d k a Dr y Clean A sp i r i n M a r ma l a de T e l e v i si o n B & W Tr a i n Fa r e Ka pi r i / Da r M i ni Bus Fa r e Wh i t e R o l l e r P o wd e r e d m i l k El e c t r i c P l u g P l a st i c b u c k e t Col our Fi l m D r i e d K a pe nt a S pa r k pl ugs Gi n g e r A l e R i c e I mpor t e d L a d i e s L e a t h e r sh o e s B o y s sh o r t s S we e t p a t a t o l e a v e s Ge n t s ' T wo P i e c e S u i t S a mp I n st a n t c o f f e e S pr i ng oni on S we e t p o t a t o e s Gr e e n h o se p i p e

0

10

20

30

40

50

EFFICIENCY OF VARIOUS ZAMBIAN CPI TRIMMED-MEAN ESTIMATORS 70.00

Root Mean Squared Error, n.s.a. data CPI percent change over next 24 months

60.00 50.00

Grey area within 10%

40.00 30.00 20.00 18% trim

10.00

Median CPI

46% trim

0.00 0

5

10

15

20

25

Trim

30

35

40

45

50

Table 1: Cross-sectional Distribution Characteristics of Monthly CPI Data Seasonally and nonseasonally adjusted components (annualized percent, 1998-2007)

Unadjusted Component Data Seasonally Adjusted Data

Mean 2.74 2.66

Variance Skewness 34.2 0.45 20.9 0.85

Table 2: Monthly Time-Series Variance of Alternative Inflation Measures Seasonally and nonseasonally adjusted component data (percent, 1998-2007)

Unadjusted CPI 16.95 Core CPI 6.06 16% Trim 1.82 Median 0.79

Seasonally adjusted 10.40 1.11 0.69 0.66

Variance reduction from seasonal adjustment 6.55 4.95 1.13 0.13

MEAN and ST. DEVIATION OF ZAMBIAN CPI COMPONENTS: Seasonally adjusted, 2002-2009

8 7

Food item Non-food item

6 5 4 3 2 1 0 0

10

20

30

40

50

60

70

TRIMMED-MEAN FORECAST ACCURACY (NAÏVE FORECAST OF CPI, NEXT 12 MONTHS) MAE

Trim

per

cen tage

s

rag e v a s rie e s e Tim

e

Retail Price Change Distribution Characteristics (Arranged by average inflation, annualized)

Monthly Brazil Argentina Mexico Colombia South Africa Israel UK Sweden New Zealand* US Japan Canada Germany

Mean

St. Dev.

Skew

Kurt

206.2 123.2 42.8 23.2 12.0 10.0 8.1 6.1 7.2 5.2 4.5 3.4 2.8

4.0 6.3 5.1 2.4 1.7 1.6 1.9 1.9 1.9 0.7 1.9 1.5 1.2

0.6 1.2 2.6 1.0 1.6 0.1 0.8 1.1 0.7 0.3 0.8 0.4 0.0

14.6 11.0 46.2 10.1 13.1 10.6 20.1 19.1 6.9 11.6 32.9 22.0 26.3

Data for New Zealand are not available on a monthly basis, so we report values * computed from quarterly data.

2. (Core) Inflation Estimation “The core rate is the trend increase of the cost of the factors of production [that o]riginates in the long-term expectations of inflation.�

Eckstein (1981)

Is “Coreâ€? Inflation a Sensible Concept? ‌"It is evident...that prices must constantly change relatively to each other, whatever happens to their general level. It would be idle to expect a uniform movement in prices as to expect a uniform movement for all bees in a swarm. On the other hand, it would be as idle to deny the existence of a general movement of prices ... all move alike, as to deny a general movement of a swarm of bees because the individual bees have different movements."

Irving Fisher (1922)

Is “Core� Inflation a Sensible Concept?

"We mean by the rise or fall 'in the value of money' the hypothetical movement which would have been brought about if the 'changes on the side of money', i.e. the changes which tend to affect all prices equally, had been the only changes operating and there had been no forces present 'on the side of the things' tending to change their prices relatively to one another."

Irving Fisher (1922)

Is “Core” Inflation a Sensible Concept?

"I venture to maintain that such ideas…are rootand-branch erroneous. …There is no bull's eye.

There is no moving but unique centre, to be called the general price level or the objective mean variation of general prices, round which are scattered the moving price levels of individual things. There are all the various, quite definite, conceptions of price-levels of composite commodities appropriate for various purposes ...

There is nothing else. Jevons was pursuing a mirage."

J. M. Keynes (1930)