Consumer Behaviour in UK Price Indices Joe Winton, Robert O’Neill & Duncan Elliott Office For National Statistics 1.

Consumer Behaviour in UK Price Indices

Joe Winton, Robert O’Neill & Duncan ElliottOffice For National Statistics

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Overview

• UK Prices Indices

• The formula effect and current

arguments

• Estimating Economic Parameters

• Simulating Behaviour

• Clothing

• A simpler way forward?

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UK Consumer Price Indices

• Retail Prices Index (RPI)

• Consumer Prices Index (CPI)

Two different measures

• Measure different things

• Used for the same things

• Perceived as the same thing

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UK Consumer Price Indices

Why is this a Problem?

• In 2003 the Government changed inflation target to the CPI

• In 2010 the Government announced that benefits and pensions should be linked to the CPI

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UK Consumer Price Indices

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The Formula Effect….

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Differences:

• Coverage

• Weights

• The Formula Effect...

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Differences: The Formula Effect

• Changes in Price are combined using expenditure

share as weights.

• We don’t have expenditure data at the lowest level as

collecting it is costly and complicated

For Example:We know the proportion of expenditure on Fizzy Drinks compared to Fruit Juice, but we don’t know how that expenditure is split between Coke, Pepsi and (many, many) other Fizzy Drinks.

• At this level (sometimes referred to as the

“Elementary Aggregate”) prices are combined

without weights.8

Differences: The Formula Effect

• Many ways to combine prices (or price

movements)

• CPI uses mainly a geometric average of

price changes

• RPI uses mainly an arithmetic average

of price changes

• Both use the change in the arithmetic

mean of prices. Often forgotten9

UK Consumer Price Indices

• ONS estimates the contribution to the difference

between RPI and CPI of various components

each month.

• The Formula Effect is growing

• Many different reasons for choosing different

formulae

• This leads to the dreaded question...

Which one is right?10

Consumer Behaviour

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Consumer Behaviour

• One argument for choosing the Geometric mean

over the Arithmetic mean comes down to

assumptions about consumer behaviour.

• More importantly, how willing are consumers to

substitute goods in response to price change.

• We will call the measure of this willingness σ

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Theoretical Background

• UK CPI uses a geometric mean to combine price relatives for elementary aggregates (EAs) where substitution behaviour is thought to occur.

• No low level substitution assumptions in the RPI

• Annual basket update and re-basing help to account for substitution at a higher level.

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Theoretical Background

Under certain Assumptions:

• An arithmetic Mean formulae (Carli) assume no

substitution between goods (σ= 0)

• A geometric Mean formula (Jevons) assumes

substitution between goods to maintain constant

expenditure (σ= 1)

If we could estimate σ, then a Generalised mean index

formula could be calculated

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Estimating σ?

• Emergence of high frequency data.

• σ can be estimated and a judgement can

be made between GM and AM.

...Under certain assumptions.

• Do consumers behave rationally?

• Can you simplify Consumer Behaviour?

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Estimating σ – an empirical study

• Winton, O’Neill & Elliott have developed the

theory of Balk and Diewert to estimate the

Constant Elasticity of Substitution (CES) σ.

• Using consumer panel data on alcohol, σ has

been estimated for a number of categories

• Compare Jevons and Carli to “Ideal Indices”

• Does the estimate of σ help with the choice?

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Estimating σ – some of the results

Selected results from empirical study.

Sub-ClassEconometric Approach

Estimate of σ

Lager (4 Cans) 1.0Lager (12 Cans) 3.7Brandy 0.5Vodka 5.7Fortified Wine 0.6Red Wine (European) 1.0Red Wine (New World) 3.8

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Estimating σ – some of the results

• The estimate of sigma was not a reliable

indicator of whether to choose Carli or Jevons

• When combined with low level expenditure it is

very useful but that doesn’t help us here!!

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Conclusions

• σ can be estimated well and the estimates have

some meaning

• Estimates of σ have no use without expenditure

weights

• Without weights, the Economic Arguments on

index numbers are unsupported

• Substitution behaviour is not a valid argument

for choosing an EA formula

• Perfect Classroom Example....

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“Under Certain Assumptions”

Simulating Consumer Behaviour

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Simulating Consumer Behaviour

• Details in Winton, O’Neill, Elliott (2012)

• Set up the Classroom Example

• Introduce small moves away from the perfect

case to reflect a small bit of ‘reality’

• We could show any result that we wanted with

only very small changes.

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Simulating Consumer Behaviour

• Ours was a very simple simulation

• The world is far more complex.

• Even if you could capture the ‘Real World’ you

would have to constantly update the model to

account for changing tastes.

• The model can’t deal with this...

Clothing

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Clothing

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Clothing

• Differences in Clothing growing too

• Formula effect big here

• How do consumers behave when buying

clothes?

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Clothing

• “Clothing Prices Never Rise”

• How can consumers substitute in response to

price rises?

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Clothing

• Homogeneous Strata – Adding up Women’s

Dresses.

• May want to look at substitution to determine

fashion goods – negative Elasticity?

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Other Arguments?

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The Axiomatic Approach to Index Numbers

• Set of Rules or Tests to determine whether an

index is appropriate

• So many combinations of tests

• Picking a set of tests will give you the answer

you want

• No real theory behind the tests just ‘desirable

properties’

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Economic Approach

Axiomatic Approach

Lots of Theoretical Background

No Practical Application

Lots of Practical Application

No Theory

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Other Approaches to Index Numbers

The Sampling Approach to Index Numbers

• We have a target index

• We have a sampling Scheme

• What is the best estimator of our target?

The Stochastic Approach to Index Numbers

• Each price relative as an estimate of a common

price change

• The expected value of the common price change

can be derived by the appropriate averaging of a

random sample of price changes.32

Conclusions

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Conclusions

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Conclusions

Key things to do:

• Improve areas where difference is large

• Be clear and decisive about your choice and

your reasons for that choice

There will always be criticism but that is because

there is no agreement. As long as you are clear

in your arguments and what is important to you,

you can defend your position.

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Conclusions

Using Jevons at EA level is perfectly acceptable

depending on your arguments but...

“use Jevons where substitution is thought to occur”

is a lazy argument!

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Further Work

Winton, O’Neill, Elliott – Elementary

Aggregate Indices and Lower Level

Substitution Bias 2012 can be found as a

supporting paper for the April 2012 CPAC meeting

– an update will follow before the end of the year.

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Thank you for listening

Any Questions?

For more information please contact:

[email protected]

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