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

• ne store because of:

1

differences across stores in the quality of any category

2

price differences across stores by category

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 xj (store size, firm, location) Consumer Survey weekly category purchases, and stores, of several thousand consumers i in Great Britain. Demographic information zi

• n the consumers is also recorded.

Price Index pijk 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 = (q1, . . . , qK ) is quantities of K categories.

Store j belongs to supermarket chain s(j). pjk is price index for category k at store j. xxic is store characteristics of combination c (e.g. distance to stores). xj is characteristics of store j (e.g. store size) zi 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:

∑

k∈K

[uick(qick) − αi ∑

j∈c

pjkqijk] + ζixxic + εic (1) where uick(.) is per-category gross utility from quantities qick = {qijk}j∈c [uick(qick) − αi ∑j∈c pjkqijk] is per-category net utility for k K is the total set of categories. αi is constant marginal utility of money ζixxic + εic is fixed utility cost of visiting store combination c. (Directly affects choice of c but not q)

ζi are consumer-varying tastes for store attributes xxic xxic include fixed per-store shopping cost and the distance from home.

εic 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 uick(qick) has a quadratic form separable in categories: uick(qick) = ∑

j∈c

βijkqijk − λk 2 [∑

j∈c

qijk]2. (2) where βijk is first order term (initial marginal utility at qijk = 0): βijk = ξs(j)k + xjβk + ziγk + σkνik

depends on store xj and consumer zi characteristics: ξsk is a time-constant unobserved utility from chain s for category k, νik draw from standard normal: consumer-category specific taste.

λk is second order term; governs the extent to which marginal utility falls in ∑j∈c qijk

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: max

qick [∑ j∈c

βijkqijk − λk 2 [∑

j∈c

qijk]2 − αd ∑

j∈c

pjkqijk] (3) s.t. qijk ≥ 0, j ∈ c, (4) When c is a single store optimal qk 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 βijk − αipjk: i prefers store j to j for cat k ⇐ ⇒ (βijk − αipjk) > (βijk − αipjk)

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: max

qijk [βijkqijk − λk

2 [qijk]2 − αipjkqijk] s.t. qijk ≥ 0, (5) Define q∗

ijk as the quantity that satisfies the first-order condition

0 = ∂ ∂qijk

• βijkq∗

ijk − λk

2 (q∗

ijk)2 − αipjkq∗ ijk

• (6)

which gives the linear conditional demand expression q∗

ijk = 1

λk (βijk − αipjk). (7) Notes: A linear demand for the category (conditional on store choice). αi/λk is the slope of this demand curve in price pjk.

Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 12 / 26

Demand and net utility from category k, conditional on c

From last slide: first order condition, conditional on store j: q∗

ijk = 1

λk (βijk − αipjk). (8) Nonnegativity constraint: consumer i visiting c will buy quantity ˜ qicjk of k in store j: ˜ qicjk = q∗

ijk · 1

• q∗

ijk ≥ 0

• if c has one store j

q∗

ijk · 1

• q∗

ijk ≥ max{0, q∗ ijk}

• if c has two stores (j, j)

As conditional demands are linear, contribution to net utility from category k is area of the consumer surplus "triangle" for quantity ˜ qicjk [βijk ˜ qicjk − λk 2 [˜ qicjk]2 − αipcjk ˜ qicjk] = λk 2 (˜ qicjk)2

Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 13 / 26

Choice Probability of Choice c

From last slide, utility from each category k is λk

2 (˜

qicj k)2. Recall that

λk 2 (˜

qicj k)2 are functions of v. The probability of choosing store pair c = (j, j) conditional on consumer

• f type vi is given by the multinomial-logit expression:

Pr[choose store pair c = (j, j)

• vi]

= exp[

• ∑k ∑j∈c

λk 2 (˜

qicj k)2 + ζixxic

• ]

∑c exp[

• ∑k ∑j∈c λk

2 (˜

qic jk)2 + ζixxic

• ]

As v is unobserved, the unconditional probability that consumer i chooses c is given by integrating over consumer unobservable νi : Pr(c|i) =

• exp[
• ∑k ∑j∈c

1 2λk(˜

qicj k)2 + ζixxic ] ∑c exp[

• ∑k ∑j∈c 1

2λk(˜

qic jk)2 + ζixxic ]dP(νi). (9) where dP(νi) is the density of the unobserved consumer characteristics νi.

Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 14 / 26

Expected category k demand at each store (unconditional)

Expected demand from consumer i of category k in shop j is given by: qijk(ξ; θ) = ∑

c ∈C (j)

• ˜

qicjk exp[

• ∑k ∑j∈c

1 2λk(˜

qicj k)2 + ζixxic ] ∑c exp[

• ∑k ∑j∈c 1

2λk(˜

qic jk)2 + ζixxic ]dP(νi) where ˜ qicjk is predicted quantity conditional on choice c C(j) is the set of choices c that include store j. C(j) includes c = (j, 0) the case of shopping only at j. In words this expression is predicted quantity ˜ qicjk conditional on choice c multiplied by the probability of visiting choice c, summing over each c that includes store j.

Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 15 / 26

Parametric specification

The price-sensitivity term αi allows higher-income households to have lower price-sensitivity: αi = (α1 + α2/[incomei]) The βijk “marginal-utility” term for category k at store j is given by: βijk = ξsk + xj βk + ziγk + σkνik (10) xj = [storesizej] zi = [householdsizei incomei](11) νik ∼ iid N(0, 1) (12) We specify the variables xxic that affect store choice as follows: xxic = [twostoresc distij + distij distij · distij cari · (distij + distij)] twostores = 1 if c comprises two stores. distij is the distance from consumer’s home to store and car = 1 if i has ≥one car.

Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 16 / 26

Parameters to be estimated

We estimate parameters for 9 chains and for 2 categories. The parameters to be estimated are [ξ; θ] = [ξ; λ0, α, β, γ, ζ, σ] with firm-cat unobserved utility: ξ = {ξsk}, s = 1 . . . 9, k = 1, 2 second order term: λ = {λk}, k = 1, 2 price sensitivity parameters: α = {α1, α2}, effect of store size on qk : β = {βk}, k = 1, 2 effect of hh chars on qk : γ = {γ1k, γ2k}, k = 1, 2 effect of store chars on c : ζ = {ζ1, ζ2, ζ3, ζ4} spread of taste shock vk: σ = {σk}, k = 1, 2 The dimension of ξ is 18 and of θ 17. The ξ are functions of the

• ther parameters (see next slide).

Two types of parameters on price: the α’s (determine choice of store) and λk’s (allow different demand slopes across categories k).

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

Identification

Identification of Firm-Category Unobserved Utility Conditional on Theta

Let Qijk be the observed quantity of category k purchased by consumer i in store j. Total observed sales of category k in chain s are as follows: Qsk =

N

∑

i=1 ∑ j∈s

Qijk (13) The model’s prediction for sales of category k in chain s is given by: qsk(ξ; θ) =

N

∑

i=1 ∑ j∈s

qijk(ξ; θ) For a given θ, the ξ are the solutions to the following S · K equations (S = 9 and K = 2): Qsk = qsk(ξ; θ), s = 1, . . . , S, k = 1, . . . , K (14) These equations have a unique solution and can be inverted to define ξ as a function of θ.

Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 18 / 26

Identification

Identification of other parameters (theta)

The θ are estimated by GMM, minimising prediction error in individual demands. That is: ˆ θ = arg min

θ

N

∑

i=1 ∑ j∈J(i) K

∑

k=1

gijk(θ) W N

∑

i=1 ∑ j∈J(i) K

∑

k=1

gijk(θ)

• with prediction error for individual store-category demands defined as

follows: gijk = Zijk

• Qijk − qijk(ξ(θ); θ)
• (15)

The weighting matrix is W = (NJK)−1

N

∑

i=1 ∑ j∈J(i) K

∑

k=1

Z

ijkZijk

−1, (16) The instruments are defined on the following slide.

Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 19 / 26

Identification: instruments

Zijk = [1, householdsizei, incomei, . . . householdsize2

i , income2 i , . . .

storesizej, disij, disij · cari, . . . storesize2

j , dis2 ij, dis2 ij · cari, . . .

[1(k = k)]k =1,...,K −1, . . . householdsizei · [1(k = k)]k =1,...,K −1, . . . incomei · [1(k = k)]k =1,...,K −1, . . . storesizej · [1(k = k)]k =1,...,K −1, . . . householdsize2

i · [1(k = k)]k =1,...,K −1, . . .

income2

i · [1(k = k)]k =1,...,K −1, . . .

storesize2

j · [1(k = k)]k =1,...,K −1, . . .

storesizej · householdsizei, storesizej · incomei, . . . priceijk, priceijk · householdsizei, priceijk · incomei]

Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 20 / 26

Identification: heuristic discussion

the data includes variation in:

category prices and demands qk over time for each consumer category prices and demands qk across consumers with different choice sets chosen stores (and store combinations c) over consumers with varying choice sets

We assume prices and other store characteristics are exogenous

This might be questioned for prices: these are set by firms We do, however, estimate unobserved utility ξks at category level for each firm; this is assumed constant over time (a fixed effect). Therefore we do not have endogeneity caused by differences in mean (over time) unobserved utility, which should account for a lot of unobserved variation. In future work we aim to control for time-varying unobserved utility using a category-specific cost shifter.

Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 21 / 26

Parameter Estimates

Where parameter enters model Variable Estimate

• St. Error

category 1 first order term storesize

• 0.546

0.064 category 2 first order term storesize

• 3.644

0.032 category 1 first order term hhsize 40.251 4.301 category 2 first order term hhsize 5.463 3.342 category 1 first order term income 25.396 3.456 category 2 first order term income 1.947 0.901 category 1 unobserved taste spread 4.946 0.456 category 2 unobserved taste spread 30.073 4.482 category 1 second order term

• 1.890

0.231 category 2 second order term

• 8.563

0.768 discrete choice of store(s) twostores 15.214 1.324 discrete choice of store(s) dist

• 9.428

0.678 discrete choice of store(s) (dist*dist) 0.01379 0.002 discrete store of store(s) car_ownership*dist 6.720 0.418 discrete store of store(s) price

• 28.852

4.341 discrete store of store(s) price/income

• 4.965

0.734 Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 22 / 26

Firm-category quality estimates

Category Firm 1 2 Aldi,Netto 9.741 1.290 Asda 9.721 3.591 Coop 9.467 1.343 Iceland 8.962 0.929 Morrison 8.688 1.453 Sainsbury 8.483 0.786 Somerfield 9.377 2.133 Tesco 9.317 1.101

Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 23 / 26

Semi-elasticities at aggregate level

SEMIELASTICITIES (effect on column firm demand of changing all prices for row firm); mean price is 1 Individual firms 1 2 4 5 7 8 9 13 14 15 16 ALDI 1

• 3.78

0.16 0.99 0.35 0.05 0.15 0.12 0.18 0.28 0.50 0.03 ASDA 2 0.15

• 3.85

1.00 0.34 0.06 0.14 0.13 0.20 0.30 0.52 0.04 COOP 4 0.12 0.13

• 2.93

0.29 0.05 0.15 0.13 0.20 0.32 0.60 0.05 ICELAND 5 0.15 0.15 1.01

• 3.98

0.06 0.15 0.17 0.27 0.35 0.65 0.07 LIDL 7 0.11 0.15 0.98 0.31

• 3.82

0.14 0.13 0.19 0.33 0.59 0.04 MORRISONS 8 0.15 0.15 1.19 0.35 0.06

• 4.29

0.15 0.22 0.37 0.61 0.05 M&S 9 0.12 0.14 1.02 0.40 0.05 0.16

• 4.20

0.31 0.33 0.67 0.08 SAINSBURY 13 0.11 0.14 1.05 0.40 0.05 0.15 0.20

• 4.20

0.37 0.74 0.09 SOMERFIELD 14 0.11 0.13 1.04 0.34 0.06 0.15 0.13 0.24

• 3.79

0.61 0.06 TESCO 15 0.11 0.13 1.09 0.35 0.06 0.14 0.15 0.26 0.34

• 3.57

0.08 WAITROSE 16 0.07 0.10 1.02 0.39 0.05 0.12 0.20 0.36 0.33 0.84

• 4.15

Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 24 / 26

Category Semi-Elasticities

SEMIELASTICITIES (effect on column firm-category of changing category k prices for row firm); mean price is 1 Individual firms ASDA LIDL M&S SAINSBURY TESCO k 1 2 1 2 1 2 1 2 1 2 ASDA 1

• 3.370
• 0.000

0.052 0.000 0.121 0.000 0.196 0.000 0.485 0.000 ASDA 2

• 0.000
• 3.625

0.000 0.043 0.001 0.088 0.002 0.118 0.005 0.329 LIDL 1 0.127 0.000

• 3.273
• 0.000

0.113 0.000 0.174 0.000 0.534 0.000 LIDL 2 0.000 0.120

• 0.001
• 4.240

0.000 0.114 0.001 0.164 0.003 0.461 M&S 1 0.000 0.086 0.048 0.000

• 3.731
• 0.000

0.291

• 0.000

0.623

• 0.000

M&S 2 0.105 0.000 0.000 0.048

• 0.001
• 4.162

0.001 0.219 0.003 0.450 SAINSBURY 1 0.000 0.109 0.046 0.000 0.182

• 0.000
• 3.755
• 0.000

0.688

• 0.000

SAINSBURY 2 0.097 0.000 0.000 0.048 0.000 0.151

• 0.001
• 4.254

0.001 0.519 TESCO 1 0.000 0.092 0.051 0.000 0.000 0.140 0.248 0.000

• 3.138
• 0.000

TESCO 2 0.094 0.000 0.000 0.047 0.100 0.000 0.001 0.180

• 0.001
• 3.770

The low cross-category effect within any firm suggests that cross-category pricing effects are small

Howard Smith Oxford University, Øyvind Thomassen University of Leuven () A demand model for grocery categories May 17, 2011 25 / 26

Conclusions and Work to Do

Done:

A utility framework suitable for estimating category demands and cross-category price effects Cross elasticities estimated using data on store choice and category demand. Suggest quite modest ‘complementarities’ between product categories within a store , arising from shopping behaviour (warning: the results are preliminary and may change)

To do:

Further specification (more categories, price instruments, non-separability between categories, two-store shopping per category...). Applications (analysis of the importance of cross-effects on Nash pricing, counterfactual where firms ignore cross-effects and price as a shopping Mall would).

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