Using scanner data to inform aggregation choices in Price Indexes

By Lorraine Ivancic and Kevin J. Fox

Study Motivation

     Availability of scanner data: highly detailed information on consumer purchases Price indexes estimated with scanner data volatile Reinsdorf (1999): Need some aggregation to dampen volatility Many different ways to aggregate Very little guidance in the literature about appropriate aggregation methods

Aggregation and Unit values

    Aggregation: calculate average price and total quantity across some unit – eg. time, items, stores Aggregation of prices → ‘unit value price’ Unit value is appropriate when items within the aggregation unit are homogenous Question: ‘ when is a commodity (group) – that is, a set of economic transactions sufficiently homogenous to warrant the use of unit values? ’ (Balk, 1998)

Homogeneity

 Focus of this work – test for homogeneity across supermarket chains and across stores within a chain.

In particular:  If the same item is found in a different supermarket chain should we consider the item to be homogenous across chains?

And…  If the same item is found in different stores which belong to the same supermarket chain should we consider the item to be homogenous?

Defining Homogeneity

     Economic theory: higher degree of competition and lower degree of item differentiation → equalisation of prices across sellers But, price dispersion may exist if different sellers offer different range of auxiliary services to consumers – eg. different opening hours, range of items, customer service Price of the item now reflects a ‘bundle’ of attributes, including item and service attributes Consumer not only buying item, also buying level of auxiliary service Same item is NOT homogenous across sellers if bundled with different level of service

Data

       Data collected by A.C. Nielsen Period covered: 02/02/97 – 26/04/98 (65 weeks) 111 stores, 4 supermarket chains Stores account for approx. 80% of supermarket sales in Brisbane (Capital city of Queensland) Additional information: brand name, item weight, description, EANAPN (unique identifier for each item) Item category: coffee 436,103 weekly observations

Hedonic Regression Model

 Hedonic time dummy regression model:    ln

p ti

  0 

t T

  2 

t D t



k K

  1 

k Z

Where: – P ti = price of item i in period t

tki

 – D t – Z tki = time dummy variables, 1…t = k characteristics of item i in period t Log- linear WLS used Monthly observations used 

ti

Coffee characteristics

        Product Brand (32 brands, DV) Decaffeinated (DV) Additional flavouring (DV) Bonus (DV) Espresso (DV) Freeze Dried (DV) Product weight (20 weights, spline) – Piecewise linear continuous function – 9 breakpoints allowing for changes in slope Supermarket chain (4 chains, DV)

Basic model

  Initial analysis: – Assume homogeneity across stores within a chain In line with statistical agency practice - ‘Large retail chains frequently have a common Australia-wide or state-wide pricing policy. In these cases, pricing one outlet in a chain would be considered sufficient to obtain a representative estimate of price movement for that chain’ (ABS, 2005)

Results: Aggregation across stores within a chain

Chain A Chain B Chain C Chain D Chain A Chain B Chain C Chain D **** -0.104

(-11.87) - 0.123

(-12.67) -0.034

(-2.86) 0.104

(11.87) **** -0.020

(-2.35) 0.070

(6.55) 0.123

(12.67) 0.020

(2.35) **** 0.090

(7.59) 0.034

(2.86) -0.070

(-6.55) -0.090 (-7.59) ****

Test homogeneity across stores

   Is assumption of homogeneity across stores within a chain is appropriate?

Assume no homogeneity across stores Compare results

Results: No aggregation across stores within a chain

Chain A Chain B Chain C Chain D Chain A **** Chain B Chain C Chain D -0.034

(-15.27) -0.037

(-22.92) -0.020

(-12.26) 0.034

(15.27) **** -0.003

(-1.57) 0.014

(6.65) 0.037

(22.92) 0.003

(1.57) **** 0.017

(12.26) 0.020

(12.26) -0.014

(-6.65) -0.017

(-12.26) ****

Testing for homogeneity across stores within a chain

   Aggregation of stores within a supermarket chain may not be recommended Need to determine for which chains, if any, it is appropriate to aggregate over stores Model: – Tested hypothesis of equal prices across stores within a chain – Separate regressions run for each chain – Prices in each pair of stores tested for equality

Results

 See handout: Tables 1 - 4     Chain A: Prices found to be significantly different in 1 of 325 store comparisons (0.04%) Chain B: 1 out of 36 comparisons (3%) Chain C: 101 out of 561 comparisons (18%) Chain D: 191 out of 861 comparisons (22%)

Findings

 For this data set – Same items found in different chains are not homogenous – In two chains, found very little price variation across stores within chains – Results were reversed for the two other chains – Cannot assume stores located in the same chain will necessarily have the same pricing policies – Cannot assume aggregation over stores within chain is appropriate

Index numbers

 4 different types of aggregation used – Homogeneity of items across chains – No homogeneity of items across chains – Homogeneity based on hedonic analysis – No homogeneity of item across stores  Index number results: Table 5 handout

Index number estimates

Agg. over chains No agg. Over chains Hedonic agg.

No agg. Over stores Jevons Laspe yres

1.019

1.263

Paasche Fisher Tornq vist

0.985 1.115 1.115

1.036

1.046

1.053

1.518

1.557

1.564

0.808 1.107 1.110

0.794 1.112 1.114

0.793 1.114 1.116

Findings

    Scanner data may be used to study the issue of homogeneity and associated issue of how to aggregate Non-superlative indexes: aggregation method matters Superlative indexes: aggregation method makes little difference Inform sampling methods