A demand model for grocery categories Howard Smith Oxford - PowerPoint PPT Presentation

A demand model for grocery categories Howard Smith Oxford University Øyvind Thomassen University of Leuven May 17, 2011 Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 1 / 26

Inter-product pricing effects: state of the literature Theory literature has extensively analyzed cross—category price incentives (Lal and Matutes (1994), Bliss (1988), Klemperer (1992), Armstrong and Vickers (2008)): products that are independent in demand (when abstracting from store choice decision) become pricing complements when store choice is considered consequently, supermarket prices are lower in equilibrium than if the firms set prices without internalizing these inter-category price effects. So far, very little empirical estimation of inter-category pricing incentives for retailers Existing measurement of market power for goods sold in supermarkets has tended to ignore the multi-category pricing incentives of the retailers that stock them: e.g. Nevo (2001) Villas-Boas (2005). Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 2 / 26

A Model of Demand for Grocery Categories: Overview We use data on shopping patterns to estimate a model of consumer demand at category-store level. Consumers (fully informed): demand a number K of product categories k may source these from a number of stores j ∈ J , incurring a shopping cost for each additional store visited. have heterogeneous shopping costs Consumers buying several categories may prefer to visit more than one store because of: differences across stores in the quality of any category 1 price differences across stores by category 2 Paper is preliminary: currently consider two categories ( K = 2 ) . Aim to expand to more (say 10) e.g. “fruit and vegetables”, “dairy”, “meat and poultry”, “frozen goods”, etc.. Estimate (negative?) cross-elasticities between products at same store. Ultimately compute Nash prices (of product categories) allowing for cross-effects. Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 3 / 26

The Data: Store Characteristics and Consumer Survey Period Oct 2002-Sept 2005. (Use a weekly period. Suppress time subscripts in our notation.). Store data all stores j ∈ J and their characteristics x j (store size, firm, location) Consumer Survey weekly category purchases, and stores, of several thousand consumers i in Great Britain. Demographic information z i on the consumers is also recorded. Price Index p ijk for each firm,category, and week, for 6 demographic types of consumer, using the product-level prices observed in the consumer data. Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 4 / 26

Store Characteristics of Main Firms Fascia Stores Store Size Market Share Market Share Spending Range price # Avg. (Sq. Ft) Trips (%) Expenditure(%) Per Customer (£) #Lines ASDA 263 45411 12.49 18.10 25.28 39794 1.01 Morrisons 294 30661 6.32 8.65 23.93 36014 1.03 Sainsbury’s 502 29431 11.65 15.44 23.16 42574 1.18 Tesco 975 23579 21.28 28.58 23.44 44956 1.12 Discounter 484 7842 6.56 4.52 12.03 18183 0.82 Iceland 621 4863 3.90 2.20 9.83 11560 1.17 Co-op 1599 4247 7.72 3.49 7.90 24512 1.26 Somerfield 793 8608 5.35 3.33 10.88 31680 1.22 Other 886 9813 19.26 11.69 10.59 30453 1.12 Marks & Spencer 284 8655 3.35 1.96 10.20 9749 1.92 Waitrose 165 19203 2.14 2.03 16.56 23493 1.48 Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 5 / 26

Concentration of Shopping in Top Two Stores Share (%) Cumul. (%) Households in Each Shopping Type One Store per Week 61 61 Two Stores per Week 26 87 One Trip per Week 53 53 Two Trips per Week 26 79 Share of All Spending Largest Weekly Store 86 86 Second Largest Weekly Store 11 97 Largest Weekly Trip 79 79 Second Largest Weekly Trip 15 93 Two-Trip Shoppers only: Proportion that go to Same Firm 35 Proportion that go to Same Store 32 Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 6 / 26

Categories Broad Category Category Share of Spending 1 Alcohol 2% 1 Bakery 6% 1 Dairy 12% 1 Dry 32% 2 Fruit/Veg 10% 2 Frozen 15% 2 Household 13% 2 Meat 11% “Broad category” represents the aggregation to two categories used in this version of the paper “Category” represents the level of aggregation we intend to use in next version. Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 7 / 26

The Model: Notation Each week shopper i takes action ( c , q ) : c = ( j , j � ) is combination of up to two stores j , j � ; ( j = 0 indicates no store). q = ( q 1 , . . . , q K ) is quantities of K categories. Store j belongs to supermarket chain s ( j ) . p jk is price index for category k at store j . xx ic is store characteristics of combination c (e.g. distance to stores). x j is characteristics of store j (e.g. store size) z i is demographic characteristics of individual i Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 8 / 26

Utility from choice of store combination Consumer i ’s utility from pair c = ( j , j � ) and category bundle q : ∑ [ u ick ( q ick ) − α i ∑ p j � k q ij � k ] + ζ i xx ic + ε ic (1) j � ∈ c k ∈ K where u ick ( . ) is per-category gross utility from quantities q ick = { q ij � k } j � ∈ c [ u ick ( q ick ) − α i ∑ j � ∈ c p j � k q ij � k ] is per-category net utility for k K is the total set of categories . α i is constant marginal utility of money ζ i xx ic + ε ic is fixed utility cost of visiting store combination c . (Directly affects choice of c but not q ) ζ i are consumer-varying tastes for store attributes xx ic xx ic include fixed per-store shopping cost and the distance from home. ε ic is distributed Type-1 Extreme Value; Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 9 / 26

Per-category utility Per-category gross utility u ick ( q ick ) has a quadratic form separable in categories: β ij � k q ij � k − λ k u ick ( q ick ) = ∑ 2 [ ∑ q ij � k ] 2 . (2) j � ∈ c j � ∈ c where β ij � k is first order term (initial marginal utility at q ij � k = 0): β ij � k = ξ s ( j � ) k + x j � β k + z i γ k + σ k ν ik depends on store x j � and consumer z i characteristics: ξ sk is a time-constant unobserved utility from chain s for category k , ν ik draw from standard normal: consumer-category specific taste. λ k is second order term; governs the extent to which marginal utility falls in ∑ j � ∈ c q ij � k Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 10 / 26

Optimal Category Demands I Given store pair c consumer maximizes net utility for each k : β ij � k q ij � k − λ k q ij � k ] 2 − α d ∑ q ick [ ∑ 2 [ ∑ max p j � k q ij � k ] (3) j � ∈ c j � ∈ c j � ∈ c j � ∈ c , s . t . q ij � k ≥ 0 , (4) When c is a single store optimal q k in that store follows by first order condition . When c is a pair of stores it is optimal for i to source each category k from only one of the two stores in c this is because we have not allowed store -specific diminishing marginal utility, so indifference curves at store level are linear and corner solutions obtain a simplifying assumption (can be dropped in later work) The optimal store j ∈ c for category k is the one with greater β ijk − α i p jk : i prefers store j to j � for cat k ⇐ ⇒ ( β ijk − α i p jk ) > ( β ij � k − α i p j � k ) Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 11 / 26

Optimal Category Demands II Conditional on store j for category k , consumer maximizes net utility: q ijk [ β ijk q ijk − λ k 2 [ q ijk ] 2 − α i p jk q ijk ] s . t . q ij � k ≥ 0 , max (5) Define q ∗ ijk as the quantity that satisfies the first-order condition � � ∂ ijk − λ k ijk ) 2 − α i p jk q ∗ β ij � k q ∗ 2 ( q ∗ 0 = (6) ijk ∂ q ijk which gives the linear conditional demand expression ijk = 1 q ∗ ( β ijk − α i p jk ) . (7) λ k Notes: A linear demand for the category (conditional on store choice). α i / λ k is the slope of this demand curve in price p jk . Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 12 / 26