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

2. Overview UK Prices Indices The formula effect and current arguments Estimating Economic Parameters Simulating Behaviour Clothing A simpler way forward? 2

3. 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 3

4. 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 This is a big deal! 4

5. UK Consumer Price Indices 5

6. The Formula Effect…. 6

7. Differences: Coverage Weights The Formula Effect... 7

8. 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

9. 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 forgotten 9

10. 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

11. Consumer Behaviour 11

12. 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 12

13. 13 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.

14. 14 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

15. 15 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?

16. 16 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?

17. 17 Estimating σ – some of the results Selected results from empirical study. Sub-Class Econometric Approach Estimate of σ Lager (4 Cans)1.0 Lager (12 Cans)3.7 Brandy0.5 Vodka5.7 Fortified Wine0.6 Red Wine (European)1.0 Red Wine (New World)3.8

18. 18 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!!

19. 19 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

20. Perfect Classroom Example.... 20 “Under Certain Assumptions”

21. Simulating Consumer Behaviour 21

22. 22 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.

23. 23 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...

24. Clothing 24

25. Clothing 25

26. Clothing Differences in Clothing growing too Formula effect big here How do consumers behave when buying clothes? 26

27. Clothing “Clothing Prices Never Rise” How can consumers substitute in response to price rises? 27

28. Clothing Homogeneous Strata – Adding up Women’s Dresses. May want to look at substitution to determine fashion goods – negative Elasticity? 28

29. Other Arguments? 29

30. 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’ 30

31. Economic Approach Axiomatic Approach Lots of Theoretical Background No Practical Application Lots of Practical Application No Theory 31

32. 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

33. Conclusions 33

34. Conclusions Making a choice is very difficult. In a perfect world the formula effect will be minimal In reality some things are difficult to measure – this is OK. There is NO right answer There are very strong opinions beliefs! Taking different approaches leads to different conclusions – all have their flaws 34

35. 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. 35

36. 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! 36

37. 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. 37

38. Thank you for listening Any Questions? For more information please contact: joseph.winton@ons.gov.uk 38