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Quantitative Marketing and Economics
Published in:

26-10-2022

Store expensiveness and consumer saving: Insights from a new decomposition of price dispersion

Authors: Sofronis Clerides, Pascal Courty, Yupei Ma

Published in: Quantitative Marketing and Economics | Issue 1/2023

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Abstract

We build on recent work that analyzes consumers’ ability to save by exploiting price dispersion in grocery stores. We show that store expensiveness varies across consumers depending on the basket they consume, meaning that consumers can save more by shopping at a store that is cheaper for their basket rather than at a store that is cheaper overall. We incorporate this insight into a new price variance decomposition that is a refinement of existing approaches. Our results show that the ability to buy products from the store where they are cheapest is much less important than previous work had found; rather, the ability to choose the cheapest stores for one’s basket is a more important source of variation in the prices consumers pay. Our approach also provides an informal test for competing theories modeling consumers as either shopping for products or shopping for categories, and finds support for both. We conclude that the idea of consumers choosing the right store for their basket has substantial traction and is a useful addition to our arsenal of models of consumer search behavior.
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Appendix
Available only for authorised users
Footnotes
1
The literature is discussed in Section 2.
 
2
These fractions are approximate averages across several specifications.
 
3
Kaplan and Menzio ([13]), p. 24.
 
4
We use the IRI Marketing Data Set, which is similar to the Kilts-Nielsen Consumer Panel used by KM (see Section 3).
 
5
We discuss the link between the decomposition and the search literature further in Section 4.3.
 
6
These implications derive formally from Proposition 1 in Section 4.
 
7
Griffith et al. ([8]), p. 100.
 
8
See Bronnenberg et al. ([2]). The dataset has been widely used in this literature, including recently by Pires ([20]) and Ching and Osborn ([3]). It is similar in structure and content as the Nielsen dataset used by KM, though it is not as extensive.
 
9
We use the terms panelist, consumer and household interchangeably.
 
10
We say that a product is available in a given store and quarter if the store records a positive quantity for that product-quarter (see Online Appendix).
 
11
The difference with the product level computation is that at the transaction level a product that is purchased many times will be counted every time, as opposed to just once per market-quarter. There is substantial variation in product availability across markets (lower in Pittsfield than in Eau Claire), product categories (lower for milk and yogurt, higher for carbonated soft drinks) and product popularity (higher for products with larger market shares).
 
12
The average is across consumer-quarter. TSSS report very similar figures for their UK data: 71% and 94%.
 
13
Another way to measure the extend to which store unavailability prevents price comparison, it to use the notion of pairwise price comparison. A pairwise price comparison is possible for a purchased product and a store visited different from the one where the product was purchased, if the product is available in that other store. The ratio of all possible pairwise price comparisons, to the maximum number of possible pairwise price comparisons, were purchased products available in all stores visited, is 80.2%. This demonstrates that product availability does not prevent consumers from comparing prices.
 
14
\(\sum _{i} \alpha _{i} p_{i}=1\) for \({\alpha_{i}} = \frac{{\sum_{j,s}}{P_{j}}{q_{i,j,s}}}{{\sum_{i,j,s}}{P_{j}}{q_{i,j,s}}}\).
 
15
A dot ‘.’ in a variable’s subindex means that the variable is summed over that subindex, i.e. \(\omega _{i,.,s}= \sum _{j} \omega _{i,j,s}\).
 
16
Store-specific baskets in this calculation are reweighed to account for partial product availability; Appendix A explains how this is done.
 
17
We bring back the transaction component when we discuss robustness in Section 5.4.
 
18
There are 1517 store-pair-quarter observations: both stores in the pair are one of the top two stores by expenditure for at least one panelist in that quarter (the upper bound is 36 store-pairs times 48 quarters = 1728). After filtering out store pair-quarters with fewer than 50 panelists, we end up with 954 observations.
 
19
The spike at zero on Fig. 1 says that a bit more than 9% of store-pair quarters have 3.2% (bin size of .032) or fewer panelists having different rankings.
 
20
Across all market-quarters, 29% of consumers have a zero store-good component. Note that the bar at zero has been trimmed in order to display the rest of the distribution more clearly – see graph.
 
21
Interestingly, TSSS find a smaller role for multi-store sourcing at the category level: “Across all consumers (whether one- or multi-stop) the share of category spending in the category’s second store is 4 percent (panel A3, p.2317).”
 
22
As a technical point, the consumer may not purchase goods in the same proportion in the store-basket and store-good indexes.
 
23
Normalized prices take only two values in the following example: (a) all stores pay the same cost for each product, possibly varying from product to product, and then each store chooses a markup for each product that may be low or high; and (b) stores sell the same quantity share of low and high products. Since there is no temporal variation, we can omit without loss of generality the i sub-index on the transaction price \(P_{j,s}\), and we also have \(\mu _{i,j,s}=\mu _{j,s}\). Statement (a) says that stores charge price \(P_{j,s}=c_{j} \alpha _{e}\) for expensive products and \(P_{j,s}=c_{j} \alpha _{c}\) for cheap ones, where \(c_{j}\) is the cost of product j and \(\alpha _{e}>\alpha _{c}\) are the markups. Denote by \(E_{j}\) the set of stores where product j is expensive. Applying KM2 (see Eq. 1), we have \(P_{j} = c_{j}(\alpha _{e} {x_{e}^{j}} + \alpha _{c} (1-{x_{e}^{j}}))\), where \({x_{e}^{j}}=\frac{\sum _{i,s\in E_{j}}q_{i,j,s}}{\sum _{i,s}q_{i,j,s}}\) is the quantity share of product j sold at an expensive price. According to statement (b) \({x_{e}^{j}}\) is constant across j, \({x_{e}^{j}}=x_{e}\). Applying KM1, we obtain that the normalized prices are \(\mu _{j,s}=\frac{\alpha _{e}}{x_{e} \alpha _{e}+(1-x_{e})\alpha _{c}}\equiv e\) for expensive products and \(\mu _{j,s}=\frac{\alpha _{c}}{x_{e} \alpha _{e}+(1-x_{e})\alpha _{c}} \equiv c\) for cheap ones.
 
24
To show that \(\mu _{s}=1\), applying Eq. 4, we have \(\mu _{s}= e \frac{\sum _{i,j \; s.t.\; s\in E_{j}} P_{j,s}q_{i,j}}{\sum _{i,j,s} P_{j,s}q_{i,j,s}}+c \frac{\sum _{i,j \; s.t.\; s\notin E_{j}} P_{j,s}q_{i,j,s}}{\sum _{i,j} P_{j,s}q_{i,j,s}}\) which does not depend on s because the expenditure share of expensive products, \(\frac{\sum _{i,j,s\in E_{j}} P_{j,s}q_{i,j,s}}{\sum _{i,j} P_{j,s}q_{i,j,s}}\), is constant across stores. Moreover, plugging the above formula for \(\mu _{s}\) in the weighted average \(\sum _{s} \frac{\sum _{i,j} P_{j,s}q_{i,j,s}}{\sum _{i,j,s} P_{j,s}q_{i,j,s}} \mu _{s}\), we obtain that \(\sum _{s} \frac{\sum _{i,j} P_{j,s}q_{i,j,s}}{\sum _{i,j,s} P_{j,s}q_{i,j,s}} \mu _{s}=1\) and conclude that \(\mu _{s}=1\).
 
25
The store-specific basket price index is \(p_{i,s}=\sum _{j} \mu _{j,s} \omega _{i,j,.}\) and by assumption \(\omega _{i,j,.}=\frac{1}{n}\) for n products and \(\omega _{i,j,.}=0\) for the remaining ones. We also have \(\mu _{j,s}=c\) for a single purchased product j and \(\mu _{j,s}=e\) for the remaining \(n-1\) products in the consumer’s basket. The store-specific basket is \(p_{i,s}=\frac{1}{n}c+\frac{n-1}{n}e\) for each store and this is also the value of \(p^{sb}_{i}\).
 
26
We also merge the PL products sold in stores that belong to same chain (this applies to two pairs of stores in Pittsfield). All remaining PLs (PLs from different chains) are treated as different products.
 
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Metadata
Title
Store expensiveness and consumer saving: Insights from a new decomposition of price dispersion
Authors
Sofronis Clerides
Pascal Courty
Yupei Ma
Publication date
26-10-2022
Publisher
Springer US
Published in
Quantitative Marketing and Economics / Issue 1/2023
Print ISSN: 1570-7156
Electronic ISSN: 1573-711X
DOI
https://doi.org/10.1007/s11129-022-09258-1