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Asia-Pacific Economic Statistics Week Seminar Component

Bangkok, 2 – 4 May 2016

Name of author: Dr. Praggya Das and Mr. Asish Thomas George Organization: Reserve Bank of India Contact address: Monetary Policy Department, Central Office Building, Shahid Bhagat Singh

Road, Fort, Mumbai, Maharashtra 400001, INDIA Contact phone: +91 22 22610422; +91 22 22610430 (Fax) Email: praggyadas@rbi.org.in and ageorge@rbi.org.in

Title of Paper

Comparison of Consumer and Wholesale Price Indices in India: An Empirical Examination of the Properties, Source of Divergence and Underlying Inflation Trends

Abstract

India has a rich history of compilation of price indices. Until 2011 the key price indices produced in India were wholesale price index (WPI) and sectoral consumer price indices that represented certain sections of working population. In absence of an all India consumer price index (CPI), WPI was the only available national level price index and was used extensively in monetary policy analysis and communication. The sectoral CPIs were used primarily for wage indexation. Starting 2011, to get an economy wide gauge of consumer price behaviour, and following the recommendations of the National Statistical Commission, the Central Statistics Office, Government of India, started publishing rural, urban and combined all India CPI. The Reserve Bank of India formally adopted the consumer price inflation as its headline measure for the purpose of monetary policy with effect from January 2014.

Historically the retail and wholesale price measures tended to move broadly in a similar fashion, barring short horizons where the divergence was wide. Of late, however, there has been considerable persistent divergence in inflation rates between the CPIs and WPI, leading to heated debates on factors driving the persistent inflation divergence and their policy implications. In this context, this paper attempts to have a detailed analysis on the CPIs and WPI in India particularly on the method of construction, distributional properties and measures of underlying inflation. Further, the paper, perhaps one of the first in India, deconstructs the observed difference in inflation into price, weight and scope effects based on the recently released disaggregate retail price data. The empirical assessment and quantification of the magnitudes of each of these effects show that multiple effects are at play in explaining the discrepancy between the indices. With a particular emphasis on the most recent period, the analysis reveals that both weight effects and scope effects played a crucial role in determining the level and duration of observed divergence between the retail and wholesale price inflation.

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I. Contents

I. Contents ................................................................................................................................ 2

II. Introduction ............................................................................................................................ 3

III.Body of Text .............................................................................................................................. 5

A. Inflation measures in India ................................................................................................. 5

A.1 A Brief History on Production and Use of Price Indices in India ..................................... 5

A.2 An Over-view of the Price Indices .................................................................................. 7

A.3 Statistical Properties of Price Indices ........................................................................... 11

B. Reconciling the Divergence between CPIs and WPI ....................................................... 16

B.1 A Methodology for Reconciliation between CPIs and WPI Inflation ............................. 16

B.2 Disaggregate Item Level Data ...................................................................................... 18

C. Results ............................................................................................................................. 19

C.1 WPI and CPI-IW ........................................................................................................... 19

C.2 WPI and CPI Data ......................................................................................................... 22

C.3 CPI-IW and CPI – A Comparative Assessment ............................................................ 23

IV. Conclusion ........................................................................................................................... 24

V. References .......................................................................................................................... 26

VI. Annex ................................................................................................................................... 27

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II. Introduction

inflation in India as measured by annual changes in wholesale and retail prices averaged

7.3 per cent and 8.1 per cent1 respectively in the last four and a half decades2 (Table 1).

The retail price here pertains to those for industrial workers as, until recently, India had

only sectoral retail inflation measures and lacked a country-wide consumer price index.

While the objective of central banks across the world to deliver price stability is based on

consumer prices, monetary policy in India historically focussed on wholesale prices in

absence of a national retail price indicator. Though inflation measured by wholesale and

retail prices moved at a distance from each other, the gap was not so large as to pose

major price stability conflict for the Reserve Bank. However, there were instances of

periodic large divergences.

In the period following global financial crisis and preceding 2014, both wholesale and

retail inflation became unhinged from their pre-crisis averages and retail inflation

hovered around double digits for four successive years. Wholesale prices lagged retail

prices that shot to double digit in 2009 following a food price shock. Since policy

focussed on wholesale prices, researchers questioned the suitability of wholesale price

index as the key indicator for monetary policy. Some even suggested that till the national

consumer price indicator is released by the Government, the consumer price index for

industrial worker should take centre stage since it is the consumption bundle of

households, includes price of services, has a large share of non-tradables and since

monetary policy has minimal role in influencing the wholesale prices that largely

reflectglobal prices of tradables (Patanaik et al., 2011). Literature during that period also

contrasted the prevailing inflation experience with the past by focussing on diffusion of

inflation across sectors, assessing the role of common and idiosyncratic factors in

explaining inflation (Darbha and Patel (2012)) and exploring the sources of inflation

persistence (Patra et al. (2014)).

1Retail prices referred here are as measured by consumer price index for industrial workers and wholesale prices are as measured by the wholesale price index.

2Average annual inflation in wholesale prices since independence of the country is 6.5 per cent

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With the release of national level consumer price index3 (CPI) since 2011 and following

the recommendations of the Expert Committee to Revise Strengthen the Monetary

Policy Framework (Chairman: Dr. Urjit R. Patel) in January 2014, the Reserve Bank

adopted CPI as the nominal anchor for monetary policy. Later the Government of India

and the Reserve Bank formalised an agreement on the monetary policy framework that

envisaged the conduct of monetary policy around a nominal anchor based on CPI.

Following the adoption of inflation targeting framework, the Reserve Bank set the

economy on a glide path for inflation, the monetary policy was tightened. This, coupled

with decline in international commodity prices and proactive supply management by the

Government unmoored inflation from the elevated levels and inflation started sliding

down. However, large fall in international commodity prices, especially crude oil, kept

wholesale price inflation in negative territory since November 2014. The history of

adopting CPI as the nominal anchor was barely a year old when the average gap

between wholesale and retail inflation that was historically less than one per cent, rose

to as high as 8 per cent in 2015.

The stark divergence in WPI and CPI again drew attention of analysts, market agents,

industry bodies, many of whom argued for sharper easing of policy rates. A renowned

economic journalist interviewing the Governor said “if we take CPI as the authentic

measure of inflation, we are worried about inflation, so we will not low interest rates; and

if we take WPI as authentic we will lower interest rates, (because) we are not worried

about inflation. It causes a huge impact on policy4”. The Chief Economic Adviser,

3Consumer price index (CPI) in the rest of the paper refers to all-India CPI Combined (Rural+Urban).

4Mr. Prannoy Roy to Governor Raghurm Rajan, November 5, 2015

Table 1: Average of Annual Inflation (per cent)

Period WP

I

CPI

-IW

CP

I

Gap

(CPI-IW

and WPI)

Gap

(CPI and

WPI)

1970s 8.6 7.6 - -1.0

1980s 8.2 9.2 - 1.1

1990s 8.1 9.6 - 1.5

2000s 5.2 5.6 - 0.3

2010s 5.7 8.9 - 3.2

Jan1970-Dec2015 7.3 8.1 - 0.8

Jan2012-Dec2015 3.8 8.1 7.7 4.4 4.0

Jan2015-Dec2015 -2.7 5.9 4.9 8.6 7.6

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Government of India said that “this diverging wedge (between CPI and WPI) is not

completely understood5” and was of the view that “in terms of the prices measured by

the national income accounts, we are closer to deflation territory and far, far away from

inflation territory6”.

The analysis of most of the agents that tried to explain the sources of divergence, lacked

analytical rigour. However, one of the recent, and perhaps the only scientific attempt, to

explain the divergence was made by Kumar and Sinha (2015). They attribute the

divergence to difference in weights of the two indices and also difference in prices of

common items. They further identified and drilled the analysis down to the items that

moved differently in the two series.

The motivation of this paper is to bring methodological rigor in explaining properties of

wholesale and retail price indices in India, identify the underlying inflation behaviour and

explain their stark divergent trends in the recent period. The paper is organised as

follows. The following section presents a brief history of the production and use of price

indices in India and their statistical properties. The next section gives the methodology

for reconciliation between CPIs and WPI and presents the results. The last section

summarises the finding.

III. Body of Text

A. Inflation measures in India

A.1 A Brief History on Production and Use of Price Indices in India

India has a rich history of compilation of price indices. The records of compilation of

wholesale price indices (WPI), the oldest among the price indices in India, are available

for as far back as early 20th century (1915). Publication of these indices started from the

period of Second World War with introduction of a ‘quick’ series using the week ended

August 19, 1939 as base and computation of the Index from January 10, 1942. With

regular publication of wholesale price index (WPI) since 1947, the index continued as a

weekly series till January 2012 and is thereafter being released as a monthly series. WPI

5 Mr. Arvind Subramanian, Chief Economic Adviser to Government of India, September 2, 2015

6 Mr. Arvind Subramanian, Chief Economic Adviser to Government of India, to Financial Times September 15, 2015

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underwent several base revisions and the present base (1993-94=100) series is

available since April 2004. The universe of wholesale price consists of all transactions at

the first point of bulk sale in the domestic market and the weighting structure is derived

from the national accounts statistics using gross value of output at an appropriate level

of disaggregation. This index provides a comprehensive measure of wholesale prices in

the economy and is widely used by the Government, industry, financial sector in their

policies and importantly in obtaining quarterly constant price national accounts

estimates. For decades WPI served as the key indicator for conduct of monetary policy

by the Reserve Bank.

The history of consumer price indices in India is also very old. The consumer price index

for industrial workers (CPI-IW) is being compiled since October 1946. Though the

coverage of CPI-IW was limited to industrial workers in three sectors under the 1960

series, with effect from 1982 the coverage was extended to seven sectors7. The

weighting diagrams for the present series (Base 2001) have been derived from the

results of Working Class Family Income and Expenditure Surveys conducted during

1999-2000. CPI-IW provides price indices for 78 different centres and is utilised for

fixation and revision of wages and for determining inflation compensation to workers in

organized sectors of the economy. While discussing retail price inflation, monetary

policies in the past occasionally discussed CPI-IW movements.

The Government also compiled another series of consumer price indices for agricultural

labourers since September 1964. The series was split into separate indices for

agricultural labourers and rural labourers from November 1995. The present base (1986-

87 = 100) uses consumer expenditure data collected in the 38th Round of National

Sample Survey8 (NSS), 1983, for deriving weighting diagrams – separately for

agricultural labourers and rural labourers. The indices utilise same retail prices of rural

markets but use different weighting pattern. Compiled separately for 20 states, these

indices have been used primarily for fixing and revising minimum labour wages.

7CPI-IW covers seven sectors viz. (i) Factories, (ii) Mines, (iii) Plantations, (iv) Railways, (v) Public Motor Transport Undertakings, (vi) Electricity Generating and Distributing Establishments, and (vii) Ports and Docks. The last four sectors were added with effect from 1982.

8 NSS is conducted by the National Sample Survey Office (NSSO).

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While the Government was publishing retail price indices for several decades, each of

these catered to a specific sector of the economy. To get an economy wide gauge of

consumer price behaviour, the National Statistical Commission in 2001 recommended

compilation of national consumer price indices for both rural and urban areas. Since

January 2011, individual rural and urban CPIs along with a combined index are being

produced by the Central Statistics Office. These indices are available at all-India level

and separately for States/Union Territories. The weighting diagrams of the latest base

(2012=100) of CPI is derived from the data of Consumer Expenditure Survey (CES),

2011-12, the 68th Round of NSS.

With the production of a national CPI, a major data gap in price measurement got

plugged. Since 2012, with the availability of all India CPI inflation numbers, the Reserve

Bank began highlighting the movements in CPI along with the discussion on price

behaviour using WPI. With effect from October 2013 the Reserve Bank started

discussing the projections and outlook for CPI along with that for WPI. Following the

recommendation of the Expert Committee to Revise Strengthen the Monetary Policy

Framework (Chairman: Dr. Urjit Patel), which submitted its report in January 2014, the

Reserve Bank adopted the CPI (combined) as the key metric of inflation for conducting

monetary policy. A glide path for disinflation based on CPI (Combined), as suggested by

the Expert Committee was adopted by the Reserve Bank to guide its medium term policy

stance. With effect from February 20, 2015, through an agreement between the

Government of India and the Reserve Bank, a flexible inflation targeting framework was

adopted for conduct of monetary policy with CPI-Combined inflation as the nominal

anchor. Since then, the monetary policy actions are guided towards bringing the CPI9

inflation within the mid-point of the inflation band of 4 +/- 2 per cent by the end of fiscal

2017-18.

A.2 An Over-view of the Price Indices

The basic description of these price indices are presented in the Table 2.There are

differences in the coverage and scope of CPI and WPI indices. With a share of around

9 In rest of the paper, CPI or CPI-C refers to the combined consumer price index produced by the Central Statistics Office, Ministry of Statistics and Programme Implementation, Government of India.

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46 per cent, food items dominate the CPI baskets, whereas food has much lower share

in WPI.

Table 2: Description of Various Price Indices in India

CPI CPI-IW CPI-AL CPI-RL WPI

Base year 2012 2001 1986-87 1986-87 2004-05

UniverseAll India Rural &

Urban Households

Households of

Industrial workers

Households of

Agricultural

labourers

Households of

Rural labourers

All transactions at

first point of bulk

sale

Centres/ price

quotations

1181 village

(268351 quotations)

and 1114 urban

(281001 quotations)

markets covering all

districts and 310

towns

Selected markets

in 78 selected

centres

5482 quotations

Items covered 299 393 676

Weights of major groups

Food, Beverages

and Tobacco48.24 48.39  72.94 70.47 26.07

Fuel & Light 6.84 6.42 8.35 7.9 14.91

Housing 10.07 15.29 – –

Clothing &

Footwear6.53 6.58 6.98 9.76

Miscellaneous 28.32 23.32 11.73 11.87 *

Total 100 100 100 100 100

Basis for

Weighting

Diagram

68th round

Consumer

Expenditure Survey

(2011-12)

Working Class

Family Income

and Expenditure

Survey (1999-

2000)

38th Round of

Consumer

Expenditure

Survey (1983) –

for agricultural

labourer

38th Round of

Consumer

Expenditure

Survey (1983) –

for rural labourer

Gross Value of

Output (GVO) at

current prices,

National

Accounts

Statistics (2007)

Methodology

Geometric mean for

elementary item

index and Laspeyres

Index Formula for

higher level index

Producer

Central Statistics

Office, Government

of India

 Ministry of

Commerce &

Industry,

Government of

India

* Consists of Non-Food Manufactured Products, Non-Food Primary Atricles, and Minerals

Shops and markets catering to 20

States (600 villages)

Labour Bureau, Government of India

182

Weighted arithmetic mean according to Laspeyres Index Formula

59.02

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Moreover, even within the food group, the composition of item differ in the wholesale and

retail indices (Chart 1). Moreover, a quarter of CPI consists of non-tradables like

services that are not included in WPI. On the other hand, more than 60 per cent of WPI

is either manufactured product (including farm and industrial raw materials, intermediate

goods, capital goods, etc.), or commodities such as minerals and crude petroleum.

In terms of construction of the two indices from item level to consolidated level also, there

exist differences between CPI-Combined and WPI. As discussed earlier, WPI is

constructed using a national level weighting pattern while CPI weights are based on

consumer expenditure surveys. The consumer expenditure surveys are conducted state-

wise and there is no national consumption basket that NSSO arrives at. Thus when WPI

inflation is aggregated, it is aggregated from items to item-groups to headline.

Contrastingly the construct of CPI is such that it aggregates items to item-groups not at

national but at state level and then to headline state level indices. While arriving at

national item level indices, items are aggregated across states using the share of that

item’s consumption in the states as weights. Having arrived at the item indices at all-India

level, CSO does not consolidate item-groups or aggregate headline from here. Indices

even at item-group level and headline are consolidated by aggregating these indices

across states. When national level item indices are aggregated to get item-groups, there is

difference compared to the published index, sometimes this difference is significant (Table

14.2 13.5

3.4

13.0 14.2

6.4

8.9 6.1

3.8

9.7 12.5

10.7

0

10

20

30

40

50

CPI-C CPI-IW WPI

We

igh

t in

Pri

ce In

de

x

Chart 1: Share of Food in Price Indices

Cereals Protein Vegetables & Fruits Other food

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3). This leads to the inflation from derived series to be different from published series. In

the two years ending December 2015, the inflation difference across groups/sub-groups

ranged from -90 to +50 basis points (bps). Even though at headline level, the difference is

small, this has an important implication since these differences can, while doing

nowcasting, lead to significant forecast errors.

Table 3: Difference in Indices and in Inflation Constructed by Aggregating Items to Item-groups

and Published Indices during January 2014 to December 2015

Item Description Weight Difference in Index Difference in Inflation(bps)

Max Min Average Max Min Average

Cereals and products 9.674 -0.17 -0.54 -0.40 6.8 -21.6 -6.2

Meat and fish 3.613 0.08 -0.10 0.00 3.2 -10.9 -2.6

Egg 0.431 0.00 0.00 0.00 0.0 0.0 0.0

Milk and products 6.607 0.06 -0.06 -0.01 9.2 -9.4 1.5

Oils and fats 3.557 0.09 -0.08 0.00 11.7 -8.6 0.0

Fruits 2.891 1.60 -0.80 0.33 50.0 -86.8 -23.9

Vegetables 6.039 0.34 -0.09 0.05 21.2 -22.3 -2.1

Pulses and products 2.384 0.05 -0.09 -0.01 11.2 -7.8 2.2

Sugar and confectionery 1.364 0.15 -0.10 0.03 2.0 -14.1 -7.2

Spices 2.495 0.07 -0.07 0.01 11.2 -8.7 1.4

Non-alcoholic beverages 1.259 0.09 -0.08 -0.01 8.9 -10.2 -2.2

Prepared meals, snacks, sweets etc. 5.549 0.11 -0.06 0.00 6.5 -8.3 -1.1

Food & beverages 45.863 0.12 -0.17 -0.06 4.3 -19.9 -5.1

Pan, tobacco, intoxicants 2.380 0.11 -0.08 0.00 6.4 -13.4 -0.1

Clothing 5.577 0.05 -0.04 -0.01 7.2 -2.3 1.1

Footwear 0.950 0.08 -0.07 0.01 6.2 -5.9 0.7

Clothing & footwear 6.527 0.09 -0.05 0.01 6.4 -7.5 0.0

Housing 10.070 0.06 -0.10 -0.01 3.2 -8.2 -0.7

Fuel & light 6.843 0.09 -0.08 0.01 9.1 -5.9 1.9

Household goods/services 3.803 0.11 -0.07 0.04 9.0 -13.8 1.0

Health 5.891 0.05 -0.10 -0.01 4.6 -12.6 -2.0

Transport/communication 8.590 0.08 -0.11 -0.04 14.4 -7.6 4.2

Recreation/amusement 1.682 0.10 -0.04 0.03 11.1 -7.9 1.8

Education 4.462 0.08 -0.07 0.00 8.7 -9.9 0.0

Personal care/effects 3.888 0.02 -0.14 -0.07 8.0 -9.2 1.9

Miscellaneous 28.317 0.05 -0.08 -0.02 7.4 -7.3 -0.1

All Groups 100.000 0.03 -0.08 -0.03 6.0 -2.8 1.3

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A.3 Statistical Properties of Price Indices

As a first step in analysing the movements in inflation rates across CPIs and WPI, we

undertake a comparative assessment of the moments of the CPI and WPI distribution.

The analysis of moments in this section draws on studies by Ball and Mankiw (1995),

Kearns (1998), Roger (2000), Dopke and Pierdzioch (2001), Assarsson (2003) among

others which looks into the distributional properties of price indices to analyse the impact

of volatility and relative price changes on overall inflation movements and to construct

measures of underlying inflation. Studies in the context of India based on WPI inflation,

which include Darbha and Patel (2012), Patra et al. (2014), have documented some key

stylised facts of its distribution. These include mainly the existence of sharp positive

skew, caused by large supply shocks from food and fuel prices coupled with chronic

kurtosis10. This implies that the distribution of price changes has been leptokurtic or fat

tailed wherein a large portion of the price index(WPI) experiences price changes

significantly different from the mean or headline inflation rate(Patra etal.2014).

For a comparative analysis of the moments of the distribution, the annual average

inflation rates for CPI-IW and WPI items, weighted by their importance in the respective

indices is taken, for the period 2007 to 2015, for which item level data is available for

both WPI and CPI-IW. The choice of annual average rates was driven by consideration

of capturing a robust measure of moments, less influenced by noise in data arising out of

missing data, seasonal omission of items among others. CPI inflation KDFs starts only

from 2012 given its recent introduction. As the item level data for CPI data based on

2012 base is available only from 2014 onwards, an attempt was also made to construct

a KDF of annual average inflation for CPI items from 2012 onwards by splicing together

the common items across 2010 and 2012 base years. Charts 2, 3 and 4 plots the

weighted KDF(kernel density function) of inflation over time, based on annual average

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The fourth order moment around the mean – the kurtosis – provides a measure of peakedness or

tailedness of a distribution. The normal distribution has a kurtosis of 3. A distribution with kurtosis more

than 3 is called leptokurtic and has heavier tails and higher peak than the normal. Similarly kurtosis less

than 3 gives a platykurtic distribution that is marked by light tails relative to normal, a flat centre and

heavy shoulders.

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inflation rates, for CPI-IW, CPI and WPI. The values of the moments are given in Annex

Table 1, 2 and 3.

An examination of the KDFs of CPI-IW and WPI inflation during the pre-crisis period of

2007 and 2008 indicates an inflationary process that was getting generalised. In both

CPI-IW and WPI, weighted mean inflation rates edged up in excess of 8 percent by

2008. This was accompanied by a fall in extent of positive skew and kurtosis (though still

remaining leptokurtic) and high standard deviation indicating that by 2008 high inflation

was getting dispersed across a considerable number of key items in the CPI-IW and

WPI basket.

The first episode of divergence between CPI and WPI in the sample period considered,

occurred in 2009 when WPI inflation dropped to 2.3 per cent and CPI-IW inflation

accelerated to 10.9 per cent. The fall observed in overall WPI inflation was occurring

even as the distribution exhibited a positive skew. However, the lessening of the extent

of kurtosis coupled with high standard deviation would indicate, as noted in Kearns

(1998), that the fall in overall inflation was a result of lower inflation in the ‘core’ of the

distribution rather than due to outlying observations. CPI-IW on the other hand stood at

close to 11 per cent, with a combination of high skew, high standard deviation and low

kurtosis indicative of a generalised inflationary process with instances of asymmetric

high inflation rates in the distribution, probably further feeding the inflationary process in

vein of Ball and Mankiw (1995). The specific index properties that led to the vastly

different inflation readings between CPI-IW and WPI is examined in Section III.

The ensuing years, 2010 and 2011 saw CPI-IW inflation remaining at highly elevated

levels of 12.1 per cent and 8.8 per cent respectively. The relatively high standard

deviation in this period reinforced the positive skew leading to a high and persistent

inflationary process. WPI inflation also quickly rebounded in excess of 9 per cent in 2010

and 2011 with high dispersion and positive skew. Since 2012 WPI has been moving

downwards even as CPI-IW continued to remain elevated. In 2013 CPI-IW breached

single digits to stand at around 11 per cent. The higher order moments reveals that CPI-

IW inflationary process in 2013 was generated by high inflation reading in a subset of

items or due to fat tails in the inflation distribution. The high standard deviation, one of

the highest seen in the sample, reinforced the large positive skew. Further the high

kurtosis, the highest reading seen in the sample, along with large positive skew indicate

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a fat tailed distribution that is highly asymmetric. CPI inflation data available since 2012

also broadly followed the CPI-IW trajectory.

By 2014, WPI inflation slumped to 3.8 per cent even as CPI-IW and CPI inflation

remained at 6.2 per cent and 7.0 per cent respectively setting the stage for the second

episode of divergence between WPI and CPIs. Unlike the previous instance, the

divergence between WPI and CPIs was more acute, with WPI slipping into deflation in

the latter part of 2014while CPI inflation stood steady at around 5 per cent. It was also

more prolonged with divergence persisting for more than two years. The deflation in WPI

in 2015seems to be broad based as evidenced by sharp fall in kurtosis coupled with a

rise in standard deviation. The distribution exhibited a mild negative skew. CPI inflation

in 2015 was centered at around 5 per cent. CPI distribution was also largely symmetrical

in 2015 with skewness coefficient recording near zero values. Further, the sharp fall in

kurtosis also indicated a relatively lower concentration of outlying observations in the

distribution.

Chart 2: CPI-IW KDFs

14

Chart 3: CPI KDFs

Chart 4: WPI KDFs

15

The assessment of distribution of prices changes in the items in CPIs and WPI since

2007 showed frequent episodes on high dispersion, asymmetry and non-normality of

inflation distribution. This has important implication for using weighted mean as a

measure of overall inflationary process. In such a scenario, one also needs to assess

how the movements in underlying inflation across WPI and CPIs, after adjusting for

much of the volatility and outlying inflation reading. A way to deal with the high (positive

as well as negative) skew and chronic leptokurtosis in the inflation distribution is by way

of trimming. Trimming removes specific upper and lower tails of the distribution

corresponding to a chosen percentage of trim. For instance a 10 per cent trimmed mean

is carved out from truncating a distribution in a manner that removes items

corresponding to 5 per cent of index weight on either side. Thus both upper and lower

tails of the distribution are removed. The decision on the percentage of trim is usually

judgemental and to counter any arbitrariness, in practice users look at more than one

trim. Silver11 (2006) argued that though trimmed mean estimators can be calculated at

different levels of trim, there is a trade-off between the ability of the measure to exclude

extreme values and the loss of information. Some of the researches believe that

trimming, by addressing the tails, reduces the distribution to a normal distribution

(Aucremanne (2000) and Heath et al (2004)). Weighted median is a specific and most

effective case of trimmed mean. It is the value of middle price of an item such that half of

the index’s weight is above and half is below its value. Median, as the distribution’s

middle price change, is arrived at by making use of all information in the price set, is

easy to comprehend, and is robust against outliers or extreme values. Chart 5 4 shows

the behaviour of trimmed means for CPI, CPI-IW and WPI. The preponderance of

positive skew and excess kurtosis in CPI-IW and WPI has kept mean inflation above

median and trimmed mean for most of the time stamps. With commodity prices dragging

down the mean inflation to sub-zero zone for a year, and distribution turning negatively

skewed median inflation and trimmed mean were larger than the mean in this period.

The CPI in its short history has been through periodic swings in skewness as well as

kurtosis. Resultantly, the average headline inflation has not shown a systematic bias.

While the mean inflation has exceeded median and trimmed mean during certain

months, it has been below them during other months (Chart 5). Thus there is clear

divergence in the distribution of prices in the WPI, CPI-IW and CPI.

11

Silver Mick (2006), Core inflation measures and statistical issues in choosing them, IMF Working Paper WP/06/97, April

16

Chart 5: Trimmed Mean Measures of Inflation

B. Reconciling the Divergence between CPIs and WPI

B.1 A Methodology for Reconciliation between CPIs and WPI Inflation

The analysis in section 2, which examined the moments of WPI and CPI distribution

identified periodic episodes of divergence between the overall WPI and CPI inflation.

Section 3 attempts to do a formal reconciliation of the observed divergence in inflation.

The methodology adopted for the reconciliation exercise follows the methodology of

Dennis and Ted (2002), McCully, Clinton P. et al. (2007) used for decomposing the CPI

and PCE divergence in the US and of Miller (2011) for explaining divergence between

CPI and RPI in the UK. It needs to be noted outright that there is no unique procedure

for reconciliation and the focus here is take quantify the divergence to a set of sources or

effects, which are highlighted in various studies on price index reconciliation that cause

overall inflation rates to vary at a point in time. These effects are broadly identified as

due to difference in formula used in construction of indices, difference in weights and

-5

0

5

10

15

Ap

r-0

5

Jan

-06

Oct

-06

Jul-

07

Ap

r-0

8

Jan

-09

Oct

-09

Jul-

10

Ap

r-1

1

Jan

-12

Oct

-12

Jul-

13

Ap

r-1

4

Jan

-15

Oct

-15

Pe

r ce

nt

(yo

y)

Headline and Median Inflation

WPI Headline WPI MedianCPI-IW Headline CPI-IW MedianCPI Headline CPI Median

-5

0

5

10

15

Ap

r-0

5

Jan

-06

Oct

-06

Jul-

07

Ap

r-0

8

Jan

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10

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Jul-

13

Ap

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4

Jan

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Oct

-15

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r ce

nt

(yo

y)

Headline and Trimmed Inflation

WPI Headline WPI 5% trimCPI-IW Headline CPI-IW 5% trimCPI Headline CPI 5% trim

17

prices for similar items, difference in items included in the price indices and other

seasonality related differences. The effects are explained below:

a. Formula Effect: Formula effects arise from difference in the choice of index used for

aggregation of the most disaggregated elementary price indices to higher level indices.

For example formulae effects becomes prominent if one price index used fixed weight

Laspeyres type index formula for compilation and the other uses say Fisher-Ideal chain-

type price index, as in the case of PCE price index in the US. By construct, other things

remaining the same, Fisher-Ideal chain-type price relative or Paasche price relative

would be lower than a Laspeyres price relative (McCully, Clinton P. et al. , 2007). The

formulae effect could also come into play if the elementary price quotes are aggregated

or price relatives are constructed based on Arithmetic Mean (AM) or Geometric Mean

(GM) (Miller, 2011). GM is better-suited to situations where there is a ‘need to reflect

substitution in the index or where there is a large dispersion in price levels or changes’

(TAC on SPCL, 2014).

b. Weight Effect: Two price indices can also show divergence if the relative weights

assigned to comparable items differ on account of different data sources. For example,

as noted in Section 1, in case of CPI the weights are based on the NSSO Consumption

Expenditure Survey, CPI-IW weights are based on Working Class Family Income and

Expenditure Survey and that for WPI is based on National Accounts Statistics.

The weight effect (WE) in case of CPI and WPI can be represented, based on McCully,

Clinton P. et al. (2007), as:

𝑊𝐸 = 𝑊𝑊𝑃𝐼𝑖 − 𝑊𝐶𝑃𝐼

𝑖 ∗ [(𝑝𝑡

𝑖

𝑝𝑡−12𝑖

) − 1]

𝑊𝑊𝑃𝐼𝑖 is the average relative weight for item i in WPI and 𝑊𝐶𝑃𝐼

𝑖 represents the weight of

similar item i in the CPI. The variable 𝑝𝑡𝑖denotes the price for item i in CPI and WPI.

c. Price Effect: As noted in Fixler, Dennis and Jaditz, Ted (2002), the price effects captures

the divergence on account of price movement for the same item after adjusting for

differences in weights. In the Indian context price effect variations, unlike the advanced

countries can be significant considering that WPI and CPI have large difference in

number of price quotations collected and also considering the large and heterogeneous

informal nature of commodity markets.

18

The price effect (PE) can be depicted as:

𝑃𝐸 = 𝑊𝑊𝑃𝐼𝑖 ∗ {[(

𝑝𝑊𝑃𝐼,𝑡𝑖

𝑝𝑊𝑃𝐼,𝑡−12𝑖

) − 1] − [(𝑝𝐶𝑃𝐼,𝑡

𝑖

𝑝𝐶𝑃𝐼,𝑡−12𝑖

) − 1]}

d. Scope Effect: The scope effect measures the contribution of inflation in items that are

only in either the CPI or WPI to the observed divergence in overall inflation. To calculate

the scope effect, first, the contribution of items in WPI but not in CPI to overall WPI

inflation is computed. In the second stage the contribution of items in CPI but not in WPI

to overall CPI inflation is computed. The difference between the WPI and CPI scope

effect is then calculated to arrive at the net scope effect. Scope effect for reconciling the

divergence between WPI and CPI assumes significance given the difference in

composition between CPI and WPI. While WPI consists of primary and intermediate

commodities as well as finished goods, CPI consists of finished goods as well as

services consumed by a typical household.

e. Other Effects: In Mc Cully et al. (2007) other effects largely capture the divergence

coming out of the differences in the revision cycles for computing the seasonal factors as

well in the methodology used for capturing seasonality of items, especially in case of

seasonal food items. In this study, other effects are taken as a residual component.

In our reconciliation exercise we start with WPI inflation and after adjusting for the

various effects try to arrive at the CPI inflation i.e inflation in CPI-IW and CPI. It can be

represented as:

𝐶𝑃𝐼 𝑦𝑜𝑦𝑡 = 𝑊𝑃𝐼 𝑦𝑜𝑦 𝑡 − 𝐹𝐸𝑡 − 𝑊𝐸𝑡 − 𝑃𝐸𝑡 − 𝑆𝐶𝑊𝑃𝐼𝑡 + 𝑆𝐶𝐶𝑃𝐼𝑡 + 𝑂𝐸𝑡

In this exercise WPI yoy inflation (WPI yoy) is first reduced for inflation arising from

difference in formulae used for WPI and CPI index construction, or formulae effect (FE),

if any. In the second stage, the WPI inflation is further reduced for effects arising out of

differences in weights or weight effects (WE) and prices or prices effects (PE), among

similar items. In the third stage the adjusted WPI inflation is further reduced for inflation

from items which are exclusive to WPI or Scope WPI effects (SCWPI). To this CPI

inflation arising from items exclusive to CPI or Scope CPI effects (SCCPI) is added to

arrive at the CPI inflation (CPI yoy). The other effects (OE) acts as the residual

balancing item.

19

B.2 Disaggregate Item Level Data

The reconciliation exercise was carried out using the item wise of data for WPI (2004-

05=100) and CPI-IW (2001=100) index baskets. For WPI the inflation rate for 676 item

level data is available from April 2005 onwards. For CPI-IW, inflation reading based on

Retail Price Index (RPI) for 393 Items in available from January 2006 onwards. The

housing index for CPI-IW was also added to the RPI. The inflation data of item level CPI

for base 2010=100 for 318 items was used for reconciliation of CPI with WPI for the

period January 2012 to December 2014. The item level inflation for CPI with base

2012=100 for 299 items was also used for attempting a reconciliation of WPI and CPI for

the period January 2015 to December 2015. Based on these item wise indices the index

items were regrouped to work out the various effects that account for the inflation

divergences. In this context it needs to be noted that the lack of publicly available price

quote data for CPIs and WPI make it difficult of to capture the formulae effect directly.

However, given that both the WPI, CPI-IW and CPI (2010=100 base) used fixed weight

Laspeyres type index formula for compilation and uses arithmetic mean of the

elementary price quotes to constructing an item index, the formulae effects is in effect

negligible and errors on account of it on overall reconciliation exercise is minimal. In

case of CPI (2012=100) the item level indices were constructed using geometric mean

for averaging of price quotations unlike the WPI and other CPIs which used arithmetic

mean to average price quotes. However, the price quote level data is not available in

public domain and therefore the formulae effect cannot be captured when comparing

WPI and CPI (2012=100). Hence the reconciliation exercise attempted between CPI

(2012=100) and WPI for the period January 2015 to December 2015 is only partial.

C. Results

C.1 WPI and CPI-IW

To explain the divergence first we start with the WPI inflation and then after adjusting

WPI inflation for various effects we try to arrive at the CPI-IW inflation numbers. The

results of the reconciliation exercise between WPI and CPI-IW are given in Chart 5 and

Annex Table 2.

20

During the period January 2007 to May 2015 CPI-IW on an average was higher than

WPI by 2.8 percentage points. Chart 5 indicate episodic movements in divergence;

while in 2007 CPI-IW was higher than WPI in 2008 it reversed. Thereafter, CPI-IW

inflation was in excess of WPI inflation by around 10 percentage points by second half of

2009. In 2011 the divergence between WPI and CPI-IW inflation became zero. During

2013 the divergence again started edging up, baring for a brief period in Q2 of 2014, it

further increased to reach close to 10 percentage points by end of 2015. Given these

volatile movements in divergence, the reconciliation analysis in terms of ‘effects” points

to the following.

Weight Effects: The percentage-point contribution of the weight effect to WPI inflation is

seen to be negative for most of the time period considered (Annex Table 2 & Chart 5)

implying that for similar items, which are largely food items, weights in WPI were on an

average lower than that in CPI-IW. Weights effect can be seen to be a major factor in

explaining inflation divergence right up to 2015. In 2015, unlike 2009, weights effects

were almost nil in explaining inflation divergence implying that moderating WPI inflation

for similar items has neutralised much of the impact of divergence in weights.

Price Effects: The price effect, the mirror image of weight effect, was also largely

negative throughout the period considered, implying the differences in inflation across

-15.0

-10.0

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0.0

5.0

10.0

15.0

Jan/2

00

7

May

/20

07

Sep

/20

07

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00

8

May

/20

08

Sep

/20

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00

9

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14

Sep

/20

14

Jan/2

01

5

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/20

15

Sep

/20

15

per

cen

tag

e p

oin

ts

Chart 5: Reconciliation of CPI-IW and WPI Inflation Gap

Weight Effect Price Effect Scope WPI

Scope CPI-IW Others CPI-IW - WPI Inflation Gap

21

similar items in WPI and CPI (adjusted with WPI weights) were largely negative. This

can also be rephrased as that on an average, inflation among similar items was lower in

WPI than CPI-IW. These effects, especially for food items, reflect the higher retail prices

(as captured by CPI-IW) over the wholesale mandi12 prices (as captured by WPI). The

analysis shows that while on an average these effects are not large, there could be

some instances (such as in 2015) where margins between wholesale and retail food

pricesrise, making the price effects large.

Scope Effects: First, we try to explain the scope WPI and CPI-IW separately and then

comment on their net impact.

Scope WPI effect, which captures the contribution to WPI inflation from items that are

part of WPI and not in CPI-IW basket, was a major, albeit volatile, component explaining

divergence between WPI and CPI-IW inflation. Scope WPI consists mainly of WPI non-

food items particularly which are either basic or intermediate goods. Throughout most of

the time period considered, WPI scope effects seem to highly correlated with non-food

primary commodity price cycles. A recent example of that is 2015, where scope WPI

items on an average witnessed deflation mirroring the collapse in international

commodity prices. Some of the final finished goods in WPI could also be part of scope

WPI items on account of their non-inclusion in CPI-IW, which is based on an older base

year.

Scope CPI-IW effects, coming from items exclusive to CPI-IW, on an average, was the

predominant effect explaining inflation divergence. Scope CPI largely reflects the impact

of CPI-IW housing inflation and showed a perceptible increase in 2009 and 2010 as the

housing inflation increased due increase in HRA for Government accommodation as part

of the implementation of sixth pay commission recommendation. Other services items,

which as a category is not covered under WPI, also form part of CPI-IW scope.

Though individually scope WPI and scope CPI-IW effects were observed to be large, on

a net basis they largely cancelled out each other, with CPI-IW scope net of WPI scope

contributing only about less than a fifth to the observed higher inflation in CPI-IW over

WPI. Furthermore, CPI-IW scope inflation due to the presence of considerable non-

12

Wholesale mandis refer to wholesale markets

22

tradables and services is more sticky of the two. This shows that WPI inflation due to

scope effects, other than in episodes of high WPI scope inflation driven by international

commodity price boom, is more than counteracted not by inflation in similar items in CPI-

IW but by inflation in CPI-IW scope items. In such a situation, weight effects alone

contribute close to 70 per cent of the observed divergence between CPI-IW and WPI.

2015 was an exception to this, with weights effects close to zero and WPI scope effects

turning negative, WPI scope and CPI-IW scope effects reinforced each other to explain

about 70 per cent of the observed divergence.

C.2 WPI and CPI

CPI, especially with base 2010, which is available only for a shorter time span was used

to check the robustness of results seen with CPI-IW and also to examine the difference

in drivers of divergence with WPI inflation. As in the earlier section, the reconciliation

began with the WPI inflation and CPI inflation was arrived after adjusting WPI inflation

for the various effects. Here the reconciliation exercise is carried out for CPI (2010=100)

and CPI (2012=100) for the period January 2012 to December 2015. The results of the

analysis are presented in Chart 6 and Annex Table 3.

-9.0

-7.0

-5.0

-3.0

-1.0

1.0

3.0

5.0

7.0

9.0

Jan/2

012

Mar

/2012

May

/2012

Jul/

2012

Sep

/2012

Nov/2

012

Jan/2

013

Mar

/2013

May

/2013

Jul/

2013

Sep

/2013

Nov/2

013

Jan/2

014

Mar

/2014

May

/2014

Jul/

2014

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/2014

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Jan/2

015

Mar

/2015

May

/2015

Jul/

2015

Sep

/2015

Nov/2

015

per

cen

tag

e p

oin

ts

Chart 6: Reconciliation of CPI and WPI Inflation Gap

Weight Effect Price Effect Scope WPI

Scope CPI-C Others CPI-C - WPI (Inflation Gap )

CPI (2012=100) CPI (2010=100)

23

Weight Effect: The weights effects was negative for the time period considered, implying

that for similar items, on an average, CPI items have higher weights than WPI items.

Price Effect: The price effect, though small in magnitude was also largely negative

throughout the period considered implying that, on an average after adjusting with WPI

weights, for similar items, inflation in CPI was higher than that in WPI, for the reasons

explained in the previous section.

Both weight and price effects contributed to around 30 per cent of the observed higher

inflation in CPI compared to WPI.

Scope Effect: During the period January 2012 to December 2015, scope CPI more than

offset scope WPI, so that on a net basis, scope effects alone accounted for 45 per cent

of the observed divergence between CPI and WPI. High CPI scope effects was not just

through housing inflation, but also the inclusion of a significant number of other services

in CPI whose inflation are highly sticky. In 2015, negative scope WPI effects reinforced

scope CPI effects resulting in the contribution of scope effects in explaining inflation

divergence to jump to 65 per cent.

C.3 CPI-IW and CPI – A Comparative Assessment

A comparative assessment at the reconciliation exercise of WPI with CPI-IW and CPI,

for the overlapping period of 2012 to 2014, showed striking differences in composition of

effects contributing to inflation divergence as well as similarities. In term of similarity,

scope CPI effects were seen to be large and quite similar in magnitude in CPI-IW and

CPI owing to the role of services, especially housing rentals, in driving the overall

inflation in this category. The lower weight for housing in CPI was to an extent offset by

inclusion of large number and higher weights for other services in CPI vis-a-vis CPI-IW.

The magnitude of price effects in CPI-IW and CPI were also largely similar. It term of

dissimilarities, first, is the role of weight effect which are substantial in case of CPI-IW

and of lesser magnitude in case of CPI. Weight effects are largely driven by the weights

assigned to food items, which are largely similar across the price indices. In general food

items in CPI-IW have the highest weights, followed by CPI and then WPI and it is this

lower weight on food items in CPI than in CPI-IW that has resulted in compression of

weight effects. Second, WPI scope effects are seen to be substantially higher when CPI-

24

IW inflation reconciliation is considered than in case of CPI. Some part of it can be

attributed to recent base for CPI and its inclusion of much of finished goods that are

represented in WPI. In that sense, fuel expenses which are largely excluded or miniscule

in CPI-IW are well captured in CPI. As a result while net scope effects (CPI scope net of

WPI scope) in CPI reconciliation contributed to around 45 per cent of the divergence, net

scope effects in CPI-IW reconciliation accounted for only a third of observed divergence.

IV. Conclusion

Episodes of divergence in inflation between WPI and CPI over the past decade have

been a major source of debate on macro-monetary policy, especially since the latter part

of 2014 when WPI experienced deflation and CPI inflation remained elevated, but on a

path of disinflation. This has led to contrasting call on monetary policy stance and state

of economy, with calls for monetary easing or tightening depending on which inflation

one chose to follow. This paper tried to analytically document the episodes of divergence

through an analysis of moments and a statistical reconciliation of difference in inflation

between CPIs and WPI.

The analysis conducted for the period 2007 to 2015 showed distinct episodes of

divergence between CPI and WPI inflation. Decomposing the episodic bursts of

divergence to various ‘effects’, the analysis shows that though some index characteristic

or effects would create a seemingly permanent wedge between CPI and WPI inflation,

large divergences are brought about by the volatile movements in particular group of

items- specifically scope WPI items. Composition of food items and to some extent fuel

items are seen to be largely similar across CPIs and WPI. However, higher weight in

CPIs for food items and the reporting of higher price in the retail market compared to

wholesale market, especially in the case of food, creates a permanent source of higher

inflation in CPI over WPI. This wedge is accentuated by a sticky and relatively high

inflation in CPI non-tradable services related items. Services as a component is absent

in WPI, instead non-food WPI is largely made up of basic and intermediate commodities

and industrial products. These are largely internationally traded goods, domestic prices

of which are closely linked to global commodity price cycles, which are by nature volatile.

High inflation in global commodity prices, especially in the run up to the 2008 crisis, and

continuous rise again after a short-lived post-crisis collapse, led to sharp persistent

increase in WPI scope items(i.e. items exclusive to WPI) which in turn masked the high

25

inflation in CPI scope items that are driven largely by non-tradable services. Whenever,

global commodity price collapsed the ‘structural’ factors that would cause higher CPI

inflation over WPI inflation – brought about by higher weight to food in consumption

basket, higher prices of retail over wholesale and most importantly higher sticky inflation

in non-tradables vis-a-vis tradables - becomes more apparent. The effects of large

volatility inherent in WPI scope items were seen from the latter part of 2014 when in

response to falling global commodity prices, scope WPI items registered persistent

deflation. Going forward, scope WPI inflation is expected to remain low given the

prospect of a protracted downturn in global commodity prices. However, the scope CPI

(i.e. items exclusive to CPI) inflation could increase or at best remain at current levels as

more and more services are brought into the ambit of CPI and also considering the

impact of the implementation of the 7th pay commission recommendation on housing

inflation. Even if the divergence between CPI and WPI at an aggregate level, at a point

in time, turns out to be zero, the analysis points out that this is more of an unstable

“knife-edge” equilibrium rather than an enduring process brought about by congruence

of underlying factors. These observations have large implications on the choice of

appropriate index for monetary policy formulation. First, it reinforces the appropriateness

of the adoption of CPI (the all India CPI) inflation as the nominal anchor for monetary

policy formulation in India recently13. The analysis brings out the inherent price stickiness

in CPI scope items and its importance in explaining inflation divergence. Hence, along

the lines of Aoki (2001), for monetary policy purposes, scope CPI carries more

information on the most persistent price components or underlying inflationary

pressures. Furthermore, given the growing evidence of the persistence in food and fuel

prices and its importance for understanding underlying inflation (Cashin and Anand,

2016), CPI offers a better way for capturing its transmission to non-food non-fuel

categories, given the finding that food and fuel effects captured across CPIs and WPI

are largely similar.

13

Based on the Report of the Expert Committee to Revise and Strengthen the Monetary Policy Framework (Chairman: Dr. Urjit R. Patel), which submitted its report on January 21, 2014, the Reserve Bank adopted the CPI (combined) as the key metric of inflation for conducting monetary policy. A glide path for disinflation based on CPI (combined), as suggested by the Expert Committee was adopted by the Reserve Bank to guide its medium term policy stance. The glide path is also included in the formal agreement on monetary policy framework between the Reserve Bank and the Ministry of Finance, Government of India, signed on February 20, 2015which mandates the Reserve Bank to bring inflation below 6 per cent by January 2016; and ultimately specifies target rate of 4 per cent for CPI inflation with a band of +/- 2 per cent.

26

Acknowledgement: The authors acknowledge the officials at the Central Statistics Office, Ministry of

Statistics and Programme Implementation for their valuable inputs on the work. The views expressed

are those of the authors and not of the organization to which they belong.

V. References

[1] Assarsson, B., (2003), “Inflation and Higher Moments of Relative Price Changes”, BIS

Papers, 19.

[2] Ball, L. and N. G. Mankiw, (1995), “Relative-Price Changes as Aggregate Supply

Shocks”, Quarterly Journal of Economics, Vol. 110:1, 161–93, February.

[3] Cashin, P. and R. Anand. Ed. (2016) “Taming Indian Inflation”, International Monetary

Fund, February.

[4] Darbha, G. and U. R., Patel, (2012), “ Dynamics of Inflation ‘Herding’: Decoding

India's Inflationary Process”, Global Economy and Development (Brookings), Working

Paper 48.

[5] Dopke, J. and C. Pierdzioch, (2001), “Inflation and the Skewness of the Distribution of

Relative Price Changes: Empirical Evidence for Germany”, Kiel Working Paper No.

1059, July.

[6] Fixler, D., and T. Jaditz, (2002), “An Examination of the Difference Between the CPI

and the PCE Deflator”, Bureau of Labor Statistics Working Paper no. 361, June.

[7] Government of India, 2015, Agreement on Monetary Policy Framework between the

Government of India and the Reserve Bank of India, February. Available at

http://finmin.nic.in/ reports/MPFAgreement28022015.pdf

[8] Government of India, (2015), “Consumer Price Index Numbers for Industrial Workers,

Annual Report 2014”, Labour Bureau, Ministry of Labour and Employment.

[9] Kumar Ashish and D.K. Sinha (2015), “Divergence between CPI and WPI”. Paper

presented at the Conference of Indian Association of National Income and Wealth,

November.

[10] McCully, C. P., Brian C. Moyer, and K. J. Stewart, (2007), “A Reconciliation Between

the Consumer Price Index and the Personal Consumption Expenditures Price Index”,

Survey of Current Business, Volume 87(11), Bureau of Economic Analysis, November.

[11] Miller, R., (2011), “The Long-Run Difference Between RPI and CPI Inflation”, Office for

Budget Responsibility, Working Paper No. 2, November.

[12] Patra, M. D., Khundrakpam, J. and A. T. George, (2014), “Post-Global Crisis Inflation

Dynamics in India: What has Changed?”, in Shekhar Shah, Barry Bosworth and Arvind

Panagariya eds. India Policy Forum 2013-14, Volume 10, Sage Publications, July.

27

[13] Patanaik I., A. Shah and G. Veronese, (2011), “How Should Inflation be Measured”,

Economic and Political Weekly, Volume XLVI, No. 16, April

[14] Reserve Bank of India, 2014, Report of the Expert Committee to Revise and

Strengthen the Monetary Policy Framework, January.

[15] Kearns, J., (1998), “The Distribution and Measurement of Inflation”, Research

Discussion Paper 9810, Economic Analysis Department, Reserve Bank of Australia,

September

[16] Roger, S., (2000), “Relative Prices, Inflation and Core Inflation”, IMF Working Paper,

WPI/00/58, March.

[17] Silver Mick (2006), “Core inflation measures and statistical issues in choosing them”,

IMF Working Paper WP/06/97, April

[18] Aucremanne, L. (2000), “The use of robust estimators as measures of core inflation”,

National Bank of Belgium Working Paper - Research Series, No.2, March

[19] Heath A, ID Roberts and TJ Bulman (2004), ‘Inflation in Australia: measurement and

modelling’, in C Kent and S Guttmann (eds), The future of inflation targeting,

Proceedings of a Conference, Reserve Bank of Australia, Sydney, pp 167–207.

28

VI. Annex

Table 1: Moments of WPI, CPI-IW and CPI Inflation (yoy)

Mean WPI CPI-IW CPI

2006 6.1 2007 4.8 6.4

2008 8.7 8.3 2009 2.3 10.9 2010 9.5 12.1 2011 9.4 8.8 2012 7.5 9.3 9.0

2013 6.2 10.9 10.2

2014 3.8 6.2 7.0

2015 -2.7 5.9 4.9

Standard Deviation WPI CPI-IW CPI

2006 9.5 2007 8.9 8.7

2008 10.4 8.0 2009 12.2 13.1 2010 12.2 10.7 2011 10.5 9.3 2012 10.4 9.4 7.0

2013 11.8 14.1 11.0

2014 8.1 8.5 6.2

2015 10.4 9.7 7.1

Skewness WPI CPI-IW CPI

2006 2.5 2007 2.9 3.0

2008 1.7 0.1 2009 1.8 2.2 2010 2.5 1.3 2011 1.0 1.8 2012 3.8 -0.6 0.4

2013 6.3 6.4 8.0

2014 2.9 1.1 1.6

2015 -0.4 1.8 -0.2

29

Table 1: Moments of WPI, CPI-IW and CPI Inflation (yoy)-Continued

Kurtosis WPI CPI-IW CPI

2006 18.8 2007 28.9 27.6

2008 8.1 9.4 2009 9.4 10.6 2010 18.0 15.3 2011 5.7 19.1 2012 71.1 11.3 15.4

2013 79.5 63.7 81.7

2014 27.9 19.4 24.8

2015 7.5 16.9 15.1

Table 2: Reconciliation of CPI-IW Inflation with WPI Inflation (Annual Average)

Year

20

07

20

08

20

09

20

10

20

11

20

12

20

13

20

14

20

15

Av

era

ge

WPI Inflation (yoy) (per cent) 4.9 8.7 2.4 9.6 9.5 7.5 6.3 3.8 -2.7 5.6

Less: Weight Effect (percentage points) -2.9 -1.9 -3.4 -2.6 -1.2 -1.8 -4.1 -2.0 0.0 -2.2

Less: Price Effect (percentage points) 0.0 -1.7 -1.3 0.2 -0.9 -1.4 -0.9 -0.5 -1.5 -0.9

Less: WPI Scope Effect (percentage points) 3.1 6.3 -0.5 5.3 6.2 4.4 3.4 2.1 -3.4 3.0

Plus: CPI-IW Scope Effect (percentage points) 2.1 2.5 3.7 6.2 4.2 3.8 3.9 2.4 2.5 3.5

Plus: Other Effects (percentage points) -0.4 -0.2 -0.5 -0.8 -0.7 -0.8 -0.9 -0.4 1.2 -0.4

Equals: CPI-IW (yoy) (per cent) 6.4 8.3 10.8 12.1 8.9 9.3 10.9 6.4 5.9 8.8

Table 3: Reconciliation of CPI Inflation with WPI Inflation (Annual Average)

Year 2012 2013 2014 2015 Average

WPI Inflation (yoy) (per cent) 7.5 6.3 3.8 -2.7 3.8

Less: Weight Effect (percentage points) -0.2 -1.5 -1.0 0.0 -0.7

Less: Price Effect (percentage points) -1.0 -0.1 -0.5 -0.9 -0.6

Less: WPI Scope Effect (percentage points) 3.6 2.2 1.6 -2.3 1.3

Plus: CPI Scope Effect (percentage points) 3.6 3.7 2.9 2.6 3.2

Plus: Other Effects (percentage points) 0.9 0.7 0.5 1.8 1.0

Equals: CPI (yoy) (per cent) 9.7 10.1 7.2 4.9 8.0