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)

http://www.frbatlanta.org/index.cfm

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)

0

5

10

15

20

25

30

2002 2003 2004 2005 2006 2007 2008 2009

Inflation objective

Overall CPI


0

5

10

15

20

25

30

2002 2003 2004 2005 2006 2007 2008 2009

h

Monthly, nsa

Inflation objective

Overall CPI

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

Computes (12-month) TrendsTrends 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 StatisticAustralia** 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).

UnitedKingdom**

Retail Price Index less mortgage interest payments.

United States CPI less food and energy items.

0

10,000

20,000

30,000

40,000

50,000

60,000

0 10 20 30 40 50 60 70 80 90 100

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

Food expenditure as a share of total expenditure

Per capita GDP

Zambia

United States

Sub-Sahara Africa

Zambian Retail Price ChangesFebruary 2009 (NSA, annualized)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

‐13 ‐12 ‐11 ‐10 ‐9 ‐8 ‐7 ‐6 ‐5 ‐4 ‐3 ‐2 ‐1 0 1 2 3 4 5 6 7 8 9 10 11 12 13

Weighted Frequency

Mean = 1.4%

Standard Dev. = 6.3%

Annualized Year-To-Date Percent Change

WEIGHTED MEAN

Normal distribution

Retail Price Change Distribution Characteristics

(Arranged by average inflation, annualized)

Monthly Mean St. Dev. Skew KurtBrazil 206.2 4.0 0.6 14.6Argentina 123.2 6.3 1.2 11.0Mexico 42.8 5.1 2.6 46.2Colombia 23.2 2.4 1.0 10.1South Africa 12.0 1.7 1.6 13.1Israel 10.0 1.6 0.1 10.6UK 8.1 1.9 0.8 20.1Sweden 6.1 1.9 1.1 19.1New Zealand* 7.2 1.9 0.7 6.9US 5.2 0.7 0.3 11.6Japan 4.5 1.9 0.8 32.9Canada 3.4 1.5 0.4 22.0Germany 2.8 1.2 0.0 26.3

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

The Menu-Cost Model of Observed Price Changeswith expected inflation

frequencyfrequency

upperlimit

lowerlimit

Observed Price Change DistributionΠ

Desired Price Change DistributionΠ

Hypothetical Mixed Normal Distribution

Frequency

0

Standard normal,variance=1,kurtosis=3

High variance normal,variance=9,kurtosis=3


Frequency

0

Standard normal,variance=1,kurtosis=3

Leptokurtic, non-normal,mixed distribution,variance=5,kurtosis=4.7

High variance normal,variance=9,kurtosis=3


Frequency

0

Leptokurtic, non-normal,mixed distribution,variance=5,kurtosis=4.7

TRIMMED MEAN ESTIMATORS

∑∈−

=α

ααIi

ii xwx)

100(21

1

CONSUMER PRICE INDEX

1.0

1.5

2.0

2.5

3.0

3.5

4.0

1992 1994 1996 1998 2000 2002

12-month percent change

CPI, all items

Median CPI

Various trimmed-mean measures

EFFICIENCY OF VARIOUS CPI TRIMMED-MEAN ESTIMATORS

1.00

1.25

1.50

1.75

2.00

0 5 10 15 20 25 30 35 40 45 50

Mean absolute error

Trim

CPI percent change over centered 35 months

STANDARD DEVIATION OF CPI COMPONENTS: ZAMBIAN CPI, s.a., 2002-2009

0 10 20 30 40 50Gr e e n hose pi pe

R a w c a ssa v a t ube r sP i ne a ppl e s

M e di c a l sc he meEl e c t r i c a l c ook e r

M i l l e tS i ngl e B l a nk e t

P umpk i n l e a v e sBoy s U nde r pa nt s

Gi nge r A l eM e ns Le a t he r S hoe s

C he st X - r a yToy ot a c or ol l a

Te r r y Na ppyWoode n door

R e gi st r a t i on f e eEl e c t r i c i t y Ta r i f f

Boy s S c hool S hoe sN e wspa pe r

C i ne ma Cha r ge sDi e se l

Whi t e Rol l e rB i c y c l e Tube

B a k i ng powde rEl e c t r i c I r on dr y

Ta k e a wa y c hi c k e n & c hi psB oy s S c hool S we a t e r

Ta bl e sa l tRa z or B l a de

B unI nst a nt c of f e e i mpor t e d

D e t e r ge nt P a st eBr i sk e t

Toi l e t S oa pChi t e nge ma t e r i a l l oc a l

Food itemNon-food item

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

House rent (medium cost) 1.9 15.3 4.5%

White breakfast 0.7 3.5 3.7%

Toyota hilux 0.8 6.8 3.2%

Toyota corolla 1.4 7.1 3.2%

Nissan sunny 1.6 8.4 3.2%

Nissan pick_up 1.1 6.5 3.2%

Mixed Cut 1.1 2.1 3.2%

Dressed chicken 0.9 4.2 3.0%

Bread 1.1 1.4 2.9%

White sugar 1.0 4.1 2.2%

House rent (low cost) 1.5 7.3 1.6%

Tomatoes 1.5 12.3 1.6%

Cooking oil Imported 1.1 2.5 1.4%

Cooking oil Local 1.2 2.6 1.4%

Mini Bus Fare Town/Chilenje 1.3 5.3 1.4%

Coach Fare Lusaka/Kitwe 0.9 5.5 1.4%

Petrol 0.8 4.9 1.3%

Diesel 0.7 4.7 1.3%

Bun 1.7 2.9 1.2%

Mosi 1.2 2.3 1.1%

Rhino Lager 1.2 2.7 1.1%

Castle Lager 1.1 2.5 1.1%

Beef Sausages 1.0 3.3 1.1%

Dried beans 1.4 5.0 1.0%

Rape 1.4 10.5 1.0%

Water & Sewerage charges 0.3 7.6 1.0%

Water & Sewerage charges 0.6 8.2 1.0%

Laundry 0.9 3.0 0.9%

Dry Clean 0.9 3.7 0.9%

Dried Kapenta 1.6 6.3 0.8%

Dried Kapenta 1.3 4.1 0.8%

Refrigerator 0.4 5.7 0.8%

Television B&W 1.2 5.0 0.7%

Television Colour 0.0 3.3 0.7%

Detergent Powder 0.7 3.0 0.7%

Shake shake 0.7 4.0 0.6%

3 piece lounge suit low price 1.5 6.2 0.6%

3 piece lounge suit high price 2.0 17.3 0.6%

Charcoal 1.3 3.6 0.6%

Radio cassette Recorder 0.3 9.4 0.6%

Mean Varian. WeightMean Varian. WeightCommodity Commodity

*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)

‐25‐20‐15‐10‐505

1015202530354045505560657075

2003 2004 2005 2006 2007 2008 2009

High-Income CPI 4% Trim 10% Trimn Median CPI

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

‐25‐20‐15‐10‐505

1015202530354045505560657075

2003 2004 2005 2006 2007 2008 2009

High-Income CPI 5% Trim 21% Trim Median CPI

EFFICIENCY OF VARIOUS ZAMBIAN CPI TRIMMED-MEAN ESTIMATORS

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

0 5 10 15 20 25 30 35 40 45 50

Root Mean Squared Error, seasonally adjusted data

Trim

CPI percent change over next 24 months

42% trim Median CPI

Grey area within 10%

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)

http://www.frbatlanta.org/index.cfm

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

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

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

Probability Break is Identified

Trimmed mean CPI

Median CPI

Core CPI

CPI

Months until break identified

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


0

5

10

15

20

25

30

2002 2003 2004 2005 2006 2007 2008 2009

Initially announced inflation objective

Monthly, nsa

Overall CPI

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

0

5

10

15

20

25

30

2002 2003 2004 2005 2006 2007 2008 2009

Overall CPI Rural High Income Urban Low Income Urban

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

‐20‐15‐10‐505

1015202530354045505560657075

2002 2003 2004 2005 2006 2007 2008 2009

Overall CPI Rural High Income Urban Low Income Urban

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

Commodity Mean St. Dev. Weight Cum. Wt.Green hosepipe 12.44823384 71.61848918 0.000552 0.000552Salted peanuts 5.241725361 43.79150285 0.00002 0.000572Watermelon 7.423151079 42.51392153 0.000184 0.000756PTA Contribution 5.723105927 37.54348891 0.003257 0.004013Peas 5.804479272 36.18308369 0.000247 0.00426Pawpaw 5.78843851 33.77371163 0.000109 0.004369Lettuce 6.817777767 32.72386727 0.000186 0.004555Pineapple chunks 3.792698665 32.11631734 0.000036 0.004591Spinach 4.673422205 31.19553659 0.000234 0.004825Pipe tobacco 2.997283256 29.32643098 5.00E-06 0.00483Sweet potatoes 5.38065539 28.27511114 0.00255 0.00738Raw cassava tubers 4.953983048 27.7418862 0.000073 0.007453Plasters 1.570540052 25.05923256 0.000111 0.007564

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

STANDARD DEVIATION OF CPI COMPONENTS:ZAMBIAN CPI, n.s.a., 2002-2009

0 10 20 30 40 50Gr e e n hose pi peS we e t pot a t oe s

S pr i ng oni onI nst a nt c of f e e

S a mpGe nt s ' Two P i e c e S ui t

S we e t pa t a t o l e a v e sBoy s shor t s

La di e s Le a t he r shoe sR i c e I mpor t e d

Gi nge r A l eS pa r k pl ugs

Dr i e d K a pe nt aCol our Fi l m

P l a st i c buc k e tEl e c t r i c P l ug

P owde r e d mi l kWhi t e R ol l e r

M i ni Bus Fa r eTr a i n Fa r e Ka pi r i / Da r

Te l e v i si on B & WM a r ma l a de

A spi r i nDr y C l e a n

Vodk aWhe a t P l a i n Fl our

Ta k e a wa y c hi c k e n & c hi psTy r e r a di a l

C oc oaD e t t ol

Cook i ng oi l Loc a lT - bone

Ye a stC onsul a t e

C hi k


EFFICIENCY OF VARIOUS ZAMBIAN CPI TRIMMED-MEAN ESTIMATORS

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

0 5 10 15 20 25 30 35 40 45 50

Root Mean Squared Error, n.s.a. data

Trim

CPI percent change over next 24 months

46% trim18% trim Median CPI

Grey area within 10%

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

Mean Variance SkewnessUnadjusted Component Data 2.74 34.2 0.45

Seasonally Adjusted Data 2.66 20.9 0.85

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

Seasonally Variance reduction fromUnadjusted adjusted seasonal adjustment

CPI 16.95 10.40 6.55Core CPI 6.06 1.11 4.9516% Trim 1.82 0.69 1.13Median 0.79 0.66 0.13

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

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50 60 70


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

MAE

Trim percentages Time series average

Retail Price Change Distribution Characteristics

(Arranged by average inflation, annualized)

Monthly Mean St. Dev. Skew KurtBrazil 206.2 4.0 0.6 14.6Argentina 123.2 6.3 1.2 11.0Mexico 42.8 5.1 2.6 46.2Colombia 23.2 2.4 1.0 10.1South Africa 12.0 1.7 1.6 13.1Israel 10.0 1.6 0.1 10.6UK 8.1 1.9 0.8 20.1Sweden 6.1 1.9 1.1 19.1New Zealand* 7.2 1.9 0.7 6.9US 5.2 0.7 0.3 11.6Japan 4.5 1.9 0.8 32.9Canada 3.4 1.5 0.4 22.0Germany 2.8 1.2 0.0 26.3

Data for New Zealand are not available on a monthly basis, so we report valuescomputed 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 “Core” 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 generalmovement 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)


"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)


"I venture to maintain that such ideas…are root-and-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)

Documents

M.Bryan