The Welfare Effects of Price Advertising in the Supermarket Retail Industry: Structural Estimation and Simulations
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The Welfare Effects of Price Advertising in the
Supermarket Retail Industry: Structural Estimation
and Simulations
Cixiu Gao∗
Rutgers University
September 24, 2013
Abstract
This paper empirically examines the welfare implications of price advertising (promotion) in
a supermarket retail market. Theories do not provide sharp prediction about welfare effects
of price advertising. I investigate market performance by comparing equilibrium surplus and
its counterparts following small deviations in promotion intensity. Using a spatial model that
accounts for consumer shopping behavior and retailer pricing behavior, consumer demand
and the costs of promotion are estimated. The simulation results show that the equilibrium
promotion levels are socially excessive. The paper also provides efficiency implications of
counterfactuals where retailers’ local market power is removed, and where promotion cost
slightly increases.
Keywords: price advertising; supermarket retail industry; moment inequality estima-
tion; counterfactual simulation.
∗
I thank David Bell for providing the data. I thank Douglas Blair, John Landon-Lane, Hilary Sigman,
Tomas Sjöström for their comments. All errors are mine.1 Introduction
This paper empirically examines the effect of costly information on market outcome in the
supermarket retail industry. Competing supermarkets use promotions (advertised temporary
price cuts )to announce sales, attracting potential customers about price offers via a variety
of media forms, including flyers, on-line circulars, emails, mobile apps, etc. Such advertising
affects consumer demand because it makes them aware of attractive price offers at a specific
store location. Price promotion as an important instrument of competition take about 80%
of store managers’ time and energy (Bolton et al., 2010). Given the magnitude of dollars
spent on them (Levy et al., 1997), economists should be interested in examining whether
these promotions are socially efficient.
As recognized by Marshall (1919), informative advertising may play two roles: a ben-
eficial constructive role and a wasteful business-stealing role. On the one hand, the bene-
ficial constructive role means that price promotions expand sale quantity, as in models by
Stegeman (1991), Grossman and Shapiro (1984), Butters (1977), and Bagwell (2007), where
advertising announces availability of products and therefore increases demand. On the other
hand, the business-stealing externality among competing firms implies that one firm benefits
from the profit margin by advertising, while social welfare is not impacted by the simple
re-distribution of margins from one firm to another. A welfare-beneficial advertising requires
that the marginal advertising cost incurred is outweighed by the marginal surplus due to
quantity expansion. However, two facts about supermarket retail industry raise the possi-
bility that this is hard to achieve. First, in such markets, price promotions usually do not
announce product availability as shoppers are well aware of the existence of products car-
ried by stores (except for newly-introduced products). As a result, the effect of promotions
on quantity expansion is limited. Second, supermarkets carry multiple product categories
and various brands, and customers buy a bundle of products from the same store. The in-
coming customers attracted by a few promoted low prices will buy high-priced items as well.
Comparing to single-product firms, this basket shopping behavior causes a higher profit, and
therefore a stronger business-stealing effect of price advertising, in a multi-product oligopoly.
1
There is a vast theoretical literature on the efficiency of oligopoly market where single-
product firms advertise price. However, to my knowledge, theories remain silent on market
performance in a market where competing multi-product firms choose the set of products to
1
This paper focuses on the effect of informative advertising which conveys price information only. It
distinguishes with the literature that examines welfare implication of ’persuasive’ advertising Dixit and
Norman (1978); Nichols (1985); Stigler and Becker (1977), where advertisements shift consumer preference.
2advertise, like in the supermarket retail oligopoly.2 Therefore, it is an empirical issue whether
the allocation of resources in such market is efficient. I examine market performance of a
supermarket retail oligopoly by comparing social welfare in the current equilibrium and
its counterparts in simulated counterfactual situations following small deviation in . If an
extra unit of promotion improves (harms) social well-being, the private promotion intensity is
socially inadequate (excessive). This requires estimating preferences and marginal promotion
costs.
To do this, I construct a model that accounts for both consumer shopping behaviors and
retail merchandising behaviors, and structurally estimate demand preference and promotion
cost parameters. In a Baysian-Nash equilibrium, the competing retailers choose the set of
products to be promoted, and make pricing decisions for all products they carry to maxi-
mize store-level profits,3 facing the tradeoff between attracting extra store visits and paying
additional promotion costs. Promotion and pricing decisions are coordinated, in the sense
that only reduced prices are advertised. Informed by promotions, shoppers choose one of
the stores to shop. Once at the store, they decide which products to purchase given realized
prices. 4
Using scanner data of basket shoppers and store merchandising information, I estimate
the marginal promotional cost (assumed constant) with moment inequality estimation. This
methodology allows me to circumvent the dimensionality issue caused by the large number of
products a supermarket typically carries. The estimation procedure is based on the necessary
condition of profit maximization - the agent chooses strategies according to her expectations
lead to profits at least as high as feasible alternatives. By estimating demand, I am able
to predict how sales, and therefore profits, would have changed if the retailer had made
alternative decisions. The difference between actual and counterfactual profits provides the
bounds of promotion costs.
My estimation and simulation encounter three difficulties: (1)the wholesale prices, that
are necessary to predict profits, are not observed; (2)in moment inequality estimation, under
alternative promotion decisions, searching for the optimal price vector in a large-dimension
space using regular methods is extremely inefficient; and (3)in counterfactual simulations,
searching for the optimal large-dimension discrete vector of promotion decisions is practically
2
One exception is a Hotelling model of two-product duopoly sellers by Lal and Matutes (1994). But
since price advertising is free, the paper provides no welfare implications.
3
My model of store profit maximizing therefore follows models developed by Gauri et al. (2008b) and
Hosken and Reiffen (2007), as opposed to models of category profit maximizing, such as Nevo (2001), Villas-
Boas (2007), Bonnet et al. (2010), Bolton and Shankar (2003), and Bolton et al. (2010).
4
It worth noticing that the "reach" of advertising is not a choice variable of firms, but taken as given. This
is empirically plausible because, for example, it wouldn’t be possible or at least very costly for supermarkets
to adjust the amount of flyer copies on a weekly basis.
3impossible. The last two difficulties are due to the fact that both pricing and promotion
decisions are SKU-specific, and the number of products is large. I solve the first prob-
lem by estimating wholesale prices using observed prices and other merchandising decisions.
The second problem is solved using techniques of principal component analysis and fac-
tor analysis. The third difficulty is alleviated using a new algorithm that largely reduces
computational complexity.
The estimates imply a wide dispersion in promotion costs among stores, ranging from
$1.01 to $4.87 per promotion. Stores with high ad coverage are able to create high marginal
revenue by offering an extra promotion, which means their marginal promotion costs tend
to be high. My counterfactual simulation shows that the extra demand created is not suffi-
cient to offset the marginal promotion cost. I therefore conclude that the private promotion
intensities are socially excessive. Additionally, I consider an overall small increase in pro-
motion costs. I find that all firms promote less intensely. The reduction in promotion costs
outweighs the fall in surplus due to quantity reduction.
Motivated by Bester and Petrakis (1995) who point out that inefficiency would occur
because of higher transportation costs paid to commute to a distant retailer that offers
advertised low price, I examine market performance when a shopping trip incurs no trans-
portation cost. I find that eliminating transportation cost improves welfare by hardening
oligopoly competition and therefore expanding sales: retailers that are located geographically
isolated no longer possess local market power.
The rest of the paper is organized as follows. Section 2 presents the model of demand and
supply. Section 3 describes the dataset. Section 4 explains the estimation procedure. Section
5 contains the main results. Section 6 discusses welfare implications of counterfactuals
simulations and section 7 concludes.
2 Model
To investigate the pricing strategy and market efficiency in the supermarket retail in-
dustry, I set out a model of consumer and firm behavior. The model assumes that in a
Bayesian equilibrium shoppers choose the store that offers the greatest utility of shopping
given store characteristics and their price knowledge; stores maximize store-level profits by
making pricing and promotion decisions. They can inform shoppers about price promotions
(which items are promoted how much they are priced) to compete over sales. The use of
an estimated shopping utility function and an pricing condition will allow for counterfactual
experiments in which shoppers reallocate themselves across stores and new promotional and
pricing equilibria are computed.
42.1 Shopping Behaviors
The model assumes that prior to a shopping trip, a shopper h receives promotion infor-
mation from zero, one or more stores. Based on available price information, the shopper
constructs an expected merchandising utility of each store. Along with that, the shopper
also takes into account store valuation and transportation cost of the shopping trip, and
chooses a single store to shop. 5 Once in the store when all prices are realized, for each
product category the shopper chooses the optimal product that maximizes category utility.
The model therefore follows the discrete-choice literature and incorporates the store choice
models developed by Bell et al. (1998) and Bell and Lattin (1998) that account for both store
pricing decisions and geographical factor. I first specify the in-store shopping behavior that
shopper make product choice within each category conditional on store choice, then describe
store choice decision making.
2.1.1 Within-category Product Choice
Let Jc denote the set of product alternatives of category c. Once in the store and observe
prices and all merchandising activities, for each category a shopper h chooses a product to
maximize category utility, jc ∈ arg maxjc ∈Jc whst,jc . The product choices are independently
made across categories. The indirect utility function of product jc of category c in time t at
store s takes the form
whst,jc = χc + αc pst,jc + βc,1 mst,jc + βc,2 nst,jc + γc yjc + hst,jc , (1)
where pst,jc is the price; mst,jc is the promotion dummy; nst,jc is the dummy of in-store
display;6 yjc is a dummy vector of observed product characteristics; χc is the intrinsic utility
of category c invariant over products within the category; χc , αc , βc,1 , βc,2 , and γc are
parameters to be estimated; hst,jc is an idiosyncratic shock assumed to follow type I extreme
value distribution, i.i.d. across products, categories, stores, shoppers, and periods. Finally,
the deterministic utility of the outside option, no purchase, is normalized to zero, thus
whst,0c = hst,0c . The probability of choosing a particular product, ρst,jc , is the probability
5
The model does not take into account the "cherry-picker" behavior that a shopper choose multiple stores
in a shopping trip to assembly the bundle. Evidence shows that cherry pickers consist only a small fraction
of consumers and that their negative contribution to store profitability is small. See Smith and Thomassen
(2012), Gauri et al. (2008a), Fox and Hoch (2005), Talukdar et al. (2008).
6
In-store display, as a kind of merchandising activity, is included in estimating consumer preferences,
while is not treated as a choice variable in firm’s problem. The merchandising activities though out this
paper refer to pricing and promotions only.
5that jc ∈ arg max whst,jc , jc ∈ Jc . Following Mcfadden (1974), it is given by
exp(χc + αc pst,jc + βc,1 mst,jc + βc,2 nst,jc + γc yjc )
ρst,jc = P . (2)
1+ kc ∈Jc exp(χc + αc pst,kc + βc,1 mst,kc + βc,2 nst,kc + γc ykc )
Once the optimal product is chosen, the expected maximum utility of the category (thereafter
abbreviated to category utility) is
X
vsct = log 1 + exp(χc + αc pst,jc + βc,1 mst,jc + βc,2 nst,jc + γc yjc ) . (3)
jc ∈Jc
Let xst denote merchandising decision that consists of pricing and promotion decisions for all
products, xst = (p0st , m0st )0 , where pst and mst are vectors of price and promotion variables,
respectively. The store merchandising utility is defined as the total category utility summing
across all categories, given by
X
ust (xst ) = vsct , (4)
c∈C
where C denotes the set of product categories. The simple additive format of ust makes the
inclusion of category intrinsic utility clear: χc accounts for different "weights" of categories
in store choice decision making. A promoted price of an item from a category with higher
intrinsic utility is more powerful in attracting customer.
2.1.2 Store Choice
Prior to a shopping trip, a shopper evaluates the expected merchandising utility by
forming an expected optimal purchase bundle at s, comprised of the optimal product of
each category. The expected merchandising utility and the optimal bundle depends on the
shopper’s price knowledge. Let φs denote the probability of receiving promotion ads from
store s ∈ {1, ..., S}. Let a dummy vector ad = (ad1 , ..., ads , ..., adS )0 denote the status
of ad exposure, thus prob(ads = 1) = φs . The shopper has some prior distribution of
merchandising decision, Fs (xs ). If she didn’t receive promotion information prior to shopping
from store s (uninformed, adhst = 0), she maintains the prior price information and forms
expectation on product choices according to Fs (xs ). If she received promotion information
from s (informed, adhst = 1), then she updates price knowledge about promoted products
and perceives that the prices of the un-promoted items follow a distribution conditional
on promotion information, Fst (xst |xprom
st ), where the superscript prom denotes promoted
6items. 7 The expected merchandising utilities at s, Eust (adhst ), perceived by uninformed
and informed shoppers, respectively, are given by
Z
Euhst (adhst = 0) = us (xs )dFs (xs ) ≡ us ,
Z (5)
Euhst (adhst = 1) = ust (xst )dFst (xst |xprom
st ).
For an uninformed shopper, as xs is integrated out, the expected merchandising utility is
time-invariant; while for an informed shopper, the expected merchandising utility depends
on information about promoted items because uncertainties about un-promoted items are
integrated out.
Based on available price information, a shopper chooses a store to maximize shopping
utility. Conditional on store characteristics, the indirect utility function of shopper h at store
s in time t takes the form:
Uhst (adhst ) = λs + θu Euhst (adhst ) + θd disths + ζhst , (6)
where λs is the average store valuation that accounts for factors such as services and shop-
ping environment; Euhst is the expected merchandising attractiveness at s that depends on
ad exposure adsht ; disths is the home-store distance of shopper h that allows the model to in-
clude geographic information specific to individual-store combination; ζhst is an idiosyncratic
shock assumed type I extreme value distributed, i.i.d. across individuals, stores, and time;
θu and θd are parameters associated with expected store merchandising attractiveness and
shopping distance, respectively. The deterministic utility of the outside option, no shopping,
is normalized to zero. Following the discrete choice literature, shopper h will visit store s
with probability
exp λs + θu Euhst (adhst ) + θd disths
ηhst (xst , x−st , adht , disths ) = P . (7)
1+ q∈{1,...,S} exp λq + θu Euhqt (adhqt ) + θd disthq
Let ρst be the vector of product choice probabilities, and mcst be the vector of wholesale
prices, stacked across all products. If the cdf of ad exposure is Ω(adht ) and home-store
distance follows a distribution D(disths ), the market share of s is
Z Z
Eηst (xst , x−st ) = ηhst (xst , x−st , adht , disths )dΩ(adht )dD(disths ). (8)
7
I assume there is no serial updating, and there exists a correlation of prices between promoted and
unpromoted items, which seems reasonable due to store-level profit maximization.
7Let M S be the market size. The sales revenue, that is, the revenue with wholesale costs
subtracted but excluding promotion costs and fixed cost, is the following:
Rst (xst , x−st ) = M S × Eηst (xst , x−st ) × ρst (xst )0 (pst − mcst ). (9)
2.2 Store Behavior
Retail stores simultaneously make pricing and promotion decisions for all products carried
to maximize the expected store-level profit given their expectations on rivals’ decisions. The
information set at the time of decision is denoted Hs , where Hs ∈ Hs . The strategy played
by s is a mapping xs = σs (Hs ) : Hs → Xs where Xs is the action set of s. As noted
above, the action of s can be partitioned into a pricing decision and a promotion decision,
xs = (p0s , m0s )0 . Suppose that for each item jc there is an interval from which its price will be
chosen, [ps,jc , ps,jc ], and an interval from which a promoted price will be chosen, [ps,jc , pbs,jc ]. I
impose a restriction on promoted price interval for the coordination of pricing and promotion
decisions, pbs,jc < ps,jc , in the sense that only discounted prices are promoted.
For the ease of notation I drop subscript for time t. Let E [πs (xs , x−s )|Hs ] be the expected
profit of store s, where the expectation is taken with respect to rivals’ actions. The firm’s
problem is
xs ∈ arg max E [πs (xs , x−s )|Hs ]
subject to
ms,jc = 0 or 1, (10)
ps,jc ≤ ps,jc ≤ ps,jc , if ms,jc = 0,
ps,jc ≤ ps,jc ≤ pbs,jc , if ms,jc = 1, ∀jc ∈ Jc , c ∈ C.
I assume a unit promotional cost θm,s will incur for each promoted product. The expected
profit is the expected revenue minus the total wholesale costs, promotion costs, and fixed
cost:
0
E [πs (xs , x−s )|Hs ] = E [Rs (xs , x−s )|Hs ] − θm,s · (1 ms ) − F Cs , (11)
where E [Rs (xs , x−s )|Hs ] is the expected revenue with wholesale costs subtracted, where
0
Rs (xs , x−s ) is given by (9); 1 ms represents the total number of promotions; and F Cs is
fixed cost.
There can be prediction error due to randomness in observed profits that is not known
at the time decisions are made. For example, a store s’s expectation on x−s would differ
from the outcome. The expectation error is denoted by errs = Rs − E[Rs |Hs ], and is mean
8zero conditional on the information set by construction, i.e., E[errs |Hs ] = 0. Since agent’s
strategy xs = σs (Hs ) is a function of Hs but errs 6∈ Hs , es is mean independent of xs . This
means that agents are generally right about their decisions.
The firm’s problem can be decomposed into a problem of discrete promotion decision,
and a sub-problem of pricing conditional on promotion decision. In the sub-problem, assume
the existence of an interior solution, p∗s (ms ). From (9) and (11), the first-order condition
with respect to ps is
∂ ∂
E[πs (ps , ms , x−s )|Hs ] = E[Rs (ps , ms , x−s )|Hs ]
∂ps ∂ps
=0 (12)
" #
∂Eηs 0 ∂ρs
=E · ρs (ps − mcs ) + Eηs · (ps − mcs ) + Eηs · ρs Hs .
∂ps ∂ps
ps =p∗s (ms )
Thus the original problem becomes a promotion decision making problem with an implicit
price variable satisfying (12). A necessary equilibrium condition is that the strategy played
by agent is at least as good as any alternative. That is, the optimal choice of ms satisfies
(omitting the implicit price variable)
0
h i
E [πs (ms , x−s )|Hs ] ≥ E πs (ms , x−s )|Hs , (13)
0
where ms 6= ms . From equation (9), this implies the following condition:
0 0
h i h i
E ∆Rs (ms , ms , x−s )|Hs ≡ E [Rs (ms , x−s )|Hs ] − E Rs (ms , x−s )|Hs
0 0
(14)
≥ θm,s · 1 (ms − ms ).
The unit promotion cost, θm,s , can be estimated by computing the difference between the
current expected revenue and counterfactual expected revenues generated by alternative
h 0
i
promotion decisions. To recover counterfactual expected revenue E Rs (ms , ·)|Hs , a price
vector associated with the alternative promotion decision will be re-optimized according to
the first-order condition.
3 Data
To carry out the empirical investigation, I use a dataset of individual scanner panel data
across 24 product categories originally obtained from IRI. The data was drawn from the
metro area of a large U.S. city, and covers a 104-week period from June 1991 to June 1993.
9The market has 548 households and five retail stores. The dataset contains two components,
household level data and store level data. The household level data includes records of a
total of 81,105 unique shopping trips over the period. For each household in a given week,
it provides information of whether the household shops, which store is visited if shop, which
items are purchased, and how much is paid. The store-level component contains a history
of merchandising activities, including prices, promotions, and in-store displays. The dataset
also contains proxy measures for the distance to each store for each of the 548 households,
using the households’ and stores’ five-digit zip codes.
Two of the five stores in this market explicitly advertise as operating an "every-day-low-
price"(EDLP) format. The third store uses a "high-price low-price" (HiLo) strategy with
frequent price adjustments. The remaining two stores are high tier(HT) retailers from the
same chain. The five stores are denoted EDLP1, EDLP2, HiLo, HT1, and HT2, respectively.
Figure 1 shows the geographical location of stores that was first published in Bell et al. (1998).
In this model, since each SKU(stock keeping unit) is treated as a separate product and the
total number of products is very large (6364), the firm’s profit maximizing problem becomes
extremely complex. For this reason, a special effort was made to select categories and
products. First, I select categories that are frequently bought given information on quantity
sold while keeping some variety. 18 categories out of 24 were processed for the purpose of
this study: Bacon, Butter, Breakfast Cereal, Toothpaste, Ground Coffee, Crackers, Laundry
Detergent, Eggs, Hot Dogs, Ice Cream, Peanuts, Frozen Pizza, Potato Chip, Soap, Tissue
Paper, Paper Towl, and Yogurt. Second, for each selected category, I eliminate private label
items, items that are not carried by all five stores, and items with market share less than 0.5
percent. This restriction reduces the number of items within each category from a range of
47 to 729 to a smaller range of 16 to 79, and the total number of product from 6364 to 794.
From the records of shopping trips, I found that households may visit multiple stores in a
given week. To be compatible with the logit store choice model, I keep the observation with
the greatest transaction amount in that week and removes others, based on the assumption
that the smaller transactions are made to meet unplanned or urgent consumption needs.
4 Estimation
The goal of estimation is to find the promotion cost parameter, θm,s , s ∈ {1, ..., S}. This
requires parameter estimates of product preference, store preference, and the wholesale prices
that will be used to recover counterfactual profits. My Estimation of the behavioral model
will implement three major methodologies. First, the demand system will be estimated using
10simple logit regression and simulation method.8 Second, the wholesale costs are estimated
using GMM with observed merchandising decisions based on the firm’s first-order condition.
Third, the promotional cost parameter will be estimated using moment inequality method.
4.1 Demand
In stage one, I estimate parameters related to product choice within each category(Θ1 =
{χc , αc , β1,c , β2,c , γc , all c ∈ C}) conditional on observed purchase behavior using logit re-
gressions, category by category. The observable product characteristics included in yjc are
dummies of package size and brand. The parameter of category-intrinsic utility, χc , is iden-
tified from purchase incidence, i.e., a product from the category is purchased. The outside
choice in here refers to the behavior that a shopper arrives at a store but makes no purchase
from that category.
In stage two, parameters related to store choices (Θ2 = (θd , θu , λ)) and ad exposure (φ)are
jointly estimated by maximizing the likelihood of the observed store choices given stage one
estimates, Θ̂1 . The approximated cdf of prior knowledge, F̂s (ps , ms ), is approximated by
the empirical distribution; the approximated updated price knowledge, F̂st (xst |xprom st ), is
a marginal density function where the prices of promoted items are simply equal to the
promoted prices, and the prices of un-promoted items are discretely approximated using
the price correlation matrix. The distribution of ad exposure status Ω(ad) remains to be
empirically specified. Let AD denote the set of all possible exposure statuses. There are 2S
mutually different statuses in the set. Assuming shoppers are independently exposed to ads
sent by different stores, the probability of being in status ad = (ad1 , ..., adS )0 is
Y
prob(ad) = ads · φs + (1 − ads )(1 − φs ). (15)
s
The log-likelihood function of store choice is
!
XX X X
l(φ, Θ1 , Θ2 ) = prob(ad) · log ηhst (xt , ad, disths ; Θ1 , Θ2 ) · I(storehst = 1) ,
t h ad∈AD s
(16)
where I(·) is an indicator function. Given the parameter estimates of within-category choice
preference, Θ̂1 , the identified φ and Θ2 are the parameters that jointly maximize the store-
8
Bell and Lattin (1998); Bell et al. (1998) and I use the same data set to estimate store choice. The
primary difference is that the two models do not account for price advertising thus consumers know no more
than a prior distribution of prices.
11choice likelihood:
(φ, Θ2 ) ∈ arg max l(φ, Θ̂1 , Θ2 ). (17)
The store choice likelihood needs to be constructed by integrating over Fs , as store choice
probability depends on price knowledge (see equations (5) and (7)). Practically, I com-
pute this likelihood function using simulation by randomly drawing prices from F̂s (xs ) and
F̂st (xst |xprom
st ), approximated using the method discussed above.
Besides jointly estimating φ and Θ2 = (λ, θu , θd ), I estimate Θ2 under the following two
alternative assumptions to see how store choice estimates may be biased when restrictions are
imposed to shoppers’ price knowledge: (1) shoppers have perfect knowledge about promotion
and price information (φs = 1, all s); (2) shoppers have no better knowledge than the prior
distribution (φs = 0, all s). Under (1), the regressors are a constant, disths , and ust that
is constructed with observed merchandising decisions and Θ̂1 . Under (2), since there is
no time variation in store utility, the regressors include a constant, disths , and expected
merchandising utility Eus constructed by simulation.
4.2 Supply
4.2.1 Wholesale Costs
To recover the counterfactual profits under alternative promotion decisions, the wholesale
cost vector(mcs ) must be known. However, I do not observe wholesale prices or other data
that can be used to approximate this variable. I estimate mcs using the first-order condition
in the firm’s problem conditional on the observed merchandising decisions. Suppose the
wholesale cost vector takes the form:
mcst = mcs + τst , (18)
where mcs is the vector of mean wholesale cost vector to be estimated, and τst is a vector
of unobservable (to the econometrician) disturbances. The first-order condition in equation
(12) implies
" " ##−1
∂Eηst ∂ρst
mcs = pst + E · ρst + Eηst · (Eηst · ρst ) Hst − τst . (19)
∂pst ∂pst
Since τst is observed by store at the time of decision, it is potentially correlated with prices.
I use IVs to correct for the problem. The moment condition for estimating mcs is that at
12the true parameter Θ0 , the vector of wholesale price disturbances, τs , satisfies
E[τs (Θ0 )zq ] = 0. (20)
where z is a vector of instrumental variables. The estimation proceeds with GMM. The
variable included in z is the price of a different item at a different store q (so z is the
permutation of the price vector). The identification assumption is that the wholesale price
disturbance of item jc at s is uncorrelated with the price of a different item kd at a different
store q. Prices of the same product at different stores may be correlated because they could
all be affected by the wholesale cost disturbance. The price of another item at the same store
may not work because retail prices of all items are potentially correlated due to store-level
profit maximization.9
4.2.2 Market Share
Using the discrete distribution of ad exposure status, the market share in (8) becomes
Z X
Eηst (xst , x−st , φ) = prob(ad)ηsht (xst , x−st , ad, distsh )dD(distsh ). (21)
ad∈AD
4.2.3 Promotion Decisions
The goal in this section is to estimate the unit cost of promotion, θm , using equilibrium
expected revenue and revenue generated by alternative promotion decision m0st . I use mo-
ment inequalities as the estimation method that preserves the discrete nature of the variable.
My estimation methods draws intensively from Pakes (2010) and Pakes et al. (2006). Iden-
tification of the parameters is based on the condition that a store’s expected profits from its
observed choice are greater than its expected profits from alternative choices. Since in the
counterfactual the manager makes different decisions, the counterfactual profits contains dif-
ferent promotional costs. A necessary condition for profit maximization is that each store’s
expected profit from choosing actual ps and ms is at least as good as its expected profit
from alternative choices. The difference between the actual and the counterfactual profits
provides the boundaries of promotional costs. The large size of the product space allows me
to construct a sufficient number of alternative promotion decisions to estimate promotion
cost. Therefore, I am able to estimate this cost specific to each store given the observed
store decisions.
9
A violation of this assumption would be the situation where other marginal costs are included in mc,
such as delivery cost that may affect all items’ pricing at all stores.
13I use the following marginal cost function:
θm,st = θm,s + θ̃m,st , (22)
where θm,s is the mean promotion cost of s to be estimated, and θ̃m,s captures cost variations
known to the store but not to the econometrician. This cost variation is contained in the
information set of the agent thus will be conditioned on in decision making. The promotion
costs may vary due to variations in labor cost of the marketing team, advertising contracting
between store and media, etc. The inequality condition in (14) implies that
0 0 0
h i
E ∆Rst (mst , mst , x−st )|Hst ≥ (θm,st + θ̃m,st ) · (1 (mst − mst )). (23)
I consider small deviations from the observed promotions as alternatives, that is, to alter
0
the promotion decision of only one item, so that 10 (ms − ms ) = ±1. This implies two
classes of counterfactuals: to drop a promotion of a promoted item, and to add a promotion
to an unpromoted item, keeping promotion decisions of all other items unchanged. Note
that in the counterfactual, the deviated item will be repriced subject to the discount price
constraint. I discuss the two classes of counterfactuals as follows.
0
1. Drop the promotion of item jc if it is currently promoted, i.e, ms = ms − es,jc , ms,jc =
1, where es,jc is a vector of zeros of the same length as m except the jcth element equals one.
Dropping off the promotion saves the promotional cost but results in a smaller expected
revenue as it reduces the store’s attractiveness. The equilibrium condition requires that the
cost saved must not exceed the decrease in expected revenue:
0
h i
E ∆Rs (ms , ms , m−s )|Hs ≥ θm,s + θ̃m,s . (24)
00
2. Add a promotion to a non-promoted item, so ms = ms +es,jc , ms,jc = 0. In equilibrium
the additional cost will not cover the increment in expected revenue resulting from the extra
promotion:
00
h i
E ∆Rs (ms , ms , m−s )|Hs ≥ −(θm,s + θ̃m,s ) (25)
Suppose there are instruments z s = (zs,1 , ..., zs,i , ...) ∈ Hs with E[θ̃m,s |zs ] = 0. If h(·) is
a nonnegative function, from equations (24) and (25),
0 00
h i h i
E ∆Rs (ms , ms , m−s )h(zs,i ) ≥ θm,s h(zs,i ) ≥ E −∆Rs (ms , ms , m−s )h(zs,i ) . (26)
14Suppose in observation t, the number of products on promotion is Jst,1 and the number of
products not promoted is Jst,2 . Each element in z s contributes two moments that define an
upper and lower bound for θm,s . For each instrument zs,i used in forming moment inequalities,
the sample analogue of the interval is
θ̂m,s,i ∈ [LBs,i , U Bs,i ] ,
where
1 PT 1 P 0
T t=1 Jst,1 m0s ∆Rst (mst , mst , m−st )h(zst,i )
LBs,i = 1 PT 1 P 0
(27)
T t=1 Jst,1 mst h(zst,i )
1 PT 1 P 00
T t=1 Jst,2 m00s
∆Rst (mst , mst , m−st )h(zst,i )
U Bs,i = − 1 P T 1 P 00 .
T t=1 Jst,2 mst h(zst,i )
The identified set of θ̂m,s is
θ̂m,s ∈ max{LBs,i }, min{U Bs,i } . (28)
i i
If there exists no such θm that satisfies all moment restrictions, a point estimate will be
found that minimizes the sum of the amount by which each inequality is violated. Suppose
that from the moment condition in (26), we have Ns inequalities, momentn (∆Rs , θm,s ) ≥
0, n = 1, ..., Ns . The point estimate is
Ns
X
θm,s ∈ arg min k min{momentn (∆Rs , θm,s ), 0} k . (29)
θ∈Θ
n=1
Confidence intervals of (1 − α) level are constructed as the way in Pakes et al. (2006). The
interval is the set of parameters that satisfy the sample moment restrictions with probability
(1 − α).
The variables in z used to construct instruments need to be uncorrelated with the cost
disturbance θm,st and be included in agent’s information set. I use a constant term, the
exogenous number of products on shelf, and the number of in-store displays as instruments.
The assumption made here is that the cost disturbance is uncorrelated with the intensity
of another kind of marketing activity, measured by the number of displays (although it is
correlated with the display vector, as seen in the firm’s problem). These instrument variables
are all observed by the promotion manager thus they are included in her information set.
154.2.4 Computational Issues
Practically, I set the bounds in the firm’s problem using empirically observed measures.
For un-promoted products, the bounds ps,jc and ps,jc are respectively set to be the observed
minimum price, and the most frequently observed price (the "regular" price). The upper
bound of a promoted price, p̂s,jc , is set to be 90 percent of regular price.
Reducing Dimensionality
To recover counterfactual expected revenues and predict market outcome under alternative
behaviors, I need to solve for the optimal promotion and pricing decisions. Unfortunately,
realizing that the number of items supermarket carries is of thousands, the dimensionality
issue as well as the discrete nature of promotion decision make it practically impossible to
jointly solve for p and m using standard algorithms: 10 first, searching for the optimal p in
the subproblem of firm is itself time-exhausting and inefficient; second, searching for m is of
complexity #J 2 if the number of product items is #J. I use principal component technique
and factor analysis to deal with the first issue, and an "ordered" promotion decision rule for
the second problem. See Appendix 1 for details.
4.3 Roadmap - A Summarize
To better summarize my empirical implementation, I provide a roadmap to what needs
to be accomplished in this section, step by step:
1. For each product category, estimate the parameters associated with within-category
product choice given observed purchases, Θ1 = {χc , αc , β1,c , β2,c , γc , all c ∈ C}. This is
stage one demand estimation;
2. Using step-one estimates Θ̂1 , jointly estimate parameters associated with store choice
Θ2 = {θd , θu , λ} and ads exposure φ. This is stage two demand estimation;
3. Using Θ̂1 , Θ̂2 and φ̂, estimate wholesale cost vector mcs ;
4. Construct actual expected revenue E[R(m, ·)|·] and counterfactual revenue
E[R(m0 , ·)|·];
10
Heuristic algorithms such as genetic algorithm are available in solving the mixed-integer optimization
problem, but they tend to be time-consuming when the number of integer variables to solve is large.
165. Estimate promotion cost θm,s by finding the difference between E[R(m, ·)|·] and
E[R(m0 , ·)|·].
5 Results
5.1 Within-category Choice
In order to predict sales and profits generated by alternative pricing decisions, I need to
estimate demand. Table 1 displays the results of stage-1 demand estimation by regressing
product choice probabilities on observable marketing activities and product characteristics.
The regression in column i includes prices, display and feature dummies only. Column ii
also includes brand and size dummies. Once the two observable characteristics are included
as regressors, the price coefficients increase in absolute value (except Butter and Eggs).
All price coefficients are of negative sign, and feature and display dummies affect utility
positively. The estimate variances are shown in parenthesis. The estimates of all categories
are significant at 1% level.
I use intercept χc to measure the intrinsic category utility. They also serve as "weights",
in forming store attractiveness - frequently bought categories weigh more in store choice
consideration. They cannot be identified from observed purchases only, as it’s common for
all products of the same category. They are identified using both observed purchases and
outside-choice observations - shoppers who enter the store but didn’t purchase the category.
The estimates of χc varies largely across categories. A small value of χc implies the purchase
incidence of the category is low.
To see the effect of price promotion in sales, I compute the semi-elasticity of promotion,
the percentage change in within-category market share to simultaneous promotion and a
price cut. 11 The semi-elasticities are computed at the regular price of each product, and
the price cut takes the value of 10 percent of its "regular" price. Table 2 provides the
maximum, the mean, and the standard deviation of this semi-elasticity of each category
among the five stores. The results show that promoted price cuts are considerably effective
in driving sales: they would cause 1 to 8 percent increase in quantity of the price promoted
item on average, and one fourth to third increase in categories of detergents, hotdogs, tissue
papers, and yogurt. This is partly due to the small number of items considered in those
11
Let ∆pjc be the price cut. The semi-elasticity of simultaneous promotion and price cut is computed as
follows:
∆ρjc pjc ∆ρjc 1
elas = + = α(1 − ρjc ) × 0.15 + βc,1 (1 − ρjc ). (30)
∆pjc ρjc ∆mjc ρjc
17categories: since the semi-elasticity is greater when market share is smaller, the category
with a relatively smaller number of items will have greater semi-elasticities.
5.2 Store Choice
Parameters of ad exposure probabilities and coefficients associated with store preferences
(φ, λ, θd , θu ) are jointly estimated by maximizing the likelihood of observed store choices
using simulation and numerical search. The simulation here is to compute the store choice
likelihood as discussed in section 4.1, and numerical search is conducted to find the param-
eter value that maximizes the simulated log-likelihood. The process requires the expected
marketing attractiveness constructed using the estimates obtained from stage-1 estimation,
(αc , β1,c , β2,c , χc ). The results are displayed in the first column of Table 3. The estimated
ad exposure probability φ has a reasonable range, from 0.03 to 0.19. estimate a set of
ad-reading probability parameters using a similar method, though their estimates seems to
be unrealistically high: the ad exposure probability ranges from XX to XX. As for the sub-
stitution pattern between merchandising attractiveness and travel distance, my estimates
imply that a shopper would be indifferent between enjoying an additional promotion with
a 15 percent price cut and travelling another 0.008 to 0.023 miles. 12 (how to get the
t-statistics?)
Besides jointly estimating φ and other store choice parameters, I estimate (λ, θu , θd ) with
restrictions φ = 0 and φ = 1, respectively. The results are displayed in the last two columns
of Table 3. When restrictions on φ are imposed, I still obtain negative distance coefficients,
and the marketing attractiveness enters store attractiveness positively. As expected, the
parameter associated with sensitivity to us , θu , is underestimated(overestimated) when re-
striction of φ = 1(φ = 0) is imposed. However, how estimate of distance sensitivity is biased
is more complicated. If a distant store offers frequent promotions which result in a large
variation in us , restriction of φ = 0 would underestimate θd , as the store visits actually
attracted by promotion information is explained by a smaller travel sensitivity. If frequent
promotions are offered by relatively nearby stores, θd would be overestimated when imposing
φ = 0. The biased estimates under restriction of φ = 0 would imply a greater sensitivity to
travel distance. The results in Table 6 indicates it is likely that the first scenario fits the
subjects invested: realizing the disadvantage of its location, the distant store decides to offer
a great number of promotions to avoid being squeezed out of the market.
12
Bell et al. (1998); Ho et al. (1998) use the same data set to estimate the fixed cost but provide no
substitution patterns between them. The magnitudes of my estimated θd and θu are somewhat different
from Bell et al. (1998). The reason may be that I include much more items and categories in constructing
us and vsc . Thus my θu is smaller.
18To measure how effective a price promotion is in driving store visits, and, in stealing
rivals’ business, I simulate the semi-price-promotion elasticity, self and cross, in store-choice
market shares, when one of the five stores offers an additional promotion with price cut. I
first compute the current market share implied by the estimates contained in the first row
of Table 4, then simulate the semi-elasticities using the estimated store choice parameters.
The results, averaging across all product items, are reported in bottom part of Table 4. It
shows that price promotion is the most effective in driving store visits at EDLP2, and the
least at HT1.
The parameter of ad exposure φ plays a crucial role in stores competition: a store is
able to attract a large amount of additional customers, either switched from rivals stores or
non-shopping, if a good portion of them is able to respond to promotion information. As the
results show, the magnitude of store choice semi-elasticities are closely related to the value
of ad exposure probability. The self store choice probability is the most elastic at EDLP2 for
which ad exposure is the greatest, and least at HT1 for which ad coverage is the smallest.
According to standard logit analysis where the probability of being informed is assumed
one, the elasticity of the choice alternative with the lowest choice probability (ηs ) is the
highest. However, the semi elasticity in here depends not only on its market share but also
the proportion of informed consumers (φs ), as store choice probabilities of the uninformed
consumers won’t change.
5.3 Promotion Costs
The promotional costs are estimated by comparing the actual profits generated by the
actual merchandising decisions, and the alternative profits led by small deviations in m.
For the store-side observations that spans over 104 weeks, the number of feature promotions
varies quite a bit across stores and weeks (from 15 to 136), as does the total number of items
on shelf(1399 to 2356). The number of deviations is computed based on these two numbers
at each store in each week.
Table 5 displays the estimates of promotion cost at each store. The top block provides
the results when only a constant term is used as an instrument. The bottom block expands
h(z) to include the constant term, the number of items on shelf, and the number of displays.
As instruments are included, I obtain point estimates of θm . The magnitude of promotional
costs varies largely across stores because the estimation depends largely on the self semi-
promotion elasticity of store-choice: if store s obtains a greater profit increment by offering
one more promotion than store q does, then s is expected to be able to afford a higher
unit promotion cost. The promotion cost is estimated from the lowest $1.01 at EDLP1 to
19the highest $4.87 at EDLP2. Since φs of EDLP2 and HiLo are the highest among the five
store(Table 5), we expect them to be able to obtain a large amount of extra store visits and
profits by offering the final promotion. Not surprisingly, the estimate of θm of these two
stores are the highest.
6 Counterfactuals
6.1 Welfare
I examine market efficiency by simulating counterfactual outcomes and computing sur-
pluses following small deviations to private promotion levels. If providing an additional
promotion improves social welfare, the private advertising level is socially inadequate, other-
wise excessive. Social welfare for the retail market is measured as the total producer surplus
and consumer surplus:13
X X
W (x) = P Ss (x) + CSh (x)
s h (31)
= P S(x) + CS(x)
The producer surplus is measured as the expected payoff excluding fixed cost, and consumer
surplus is the expected net gain of a shopping trip, induced by strategy portfolio x =
(x1 , ..., xs , ..., xS ). See Appendix 2 for algebra.
To get an idea how the market performs, I simulate the market outcome of the current
equilibrium, displayed in the top half of Table 6 (in order to be comparable with counter-
factual outcomes, the current equilibrium outcome is not from data but computed using
parameter estimates and the algorithm discussed in section 8.1). Besides surpluses, the mar-
ket outcome includes the total number of promotions, store visit market share, the average
price index, and profit, of each store. The average price index is computed as the average
ratio between optimal price and its regular price, weighted by market share.
Next, I simulate P S, CS, Ws0 , and the change in expected revenue ∆E[R()], when each
of the five stores offers one extra or less promotion holding actions of other stores constant.
The prices under the deviated promotion decision are re-optimized. Simulation results are
reported in Table 7, in which top and bottom halves are for one extra and one less promotion,
respectively. Given the result that ∆W < 0 when one extra promotion is offered and
∆W > 0 when one promotion is withdrew, for all five stores, It implies that the private
promotion levels are inefficient and are socially excessive: an additional promotion won’t
13
The producer surplus considered here accounts for the retail market, not the upstream manufactures.
20expand quantity sufficiently to offset the promotion cost, while withdrawing one will save
the society more than the loss from declined sales.
In the neighborhood of optimum, the extra gain in revenue of the store with the ex-
tra promotion almost covers the additional promotion cost, thus social welfare would be
improved if consumer surplus from expanded sales overweights the decline in rival stores’
revenue. However, this would be hard to achieve, for two reasons: first, additional demand
created would be limited as only a portion (φs ) of the non-shoppers would be informed by
the additional promotion; second, consumer surplus of those, who either switched from rival
stores or used to be non-shopping, would be eroded by transportation cost. Furthermore, the
effect of the additional promotion on profit generating is more effective at stores with larger
market share and larger φ. These stores also suffer from bigger losses in profits when a rival
store offers the additional promotion(similar effect applies when withdrawing on promotion).
It implies that the big players in the market are more sensitive to rivals’ behavior, and are
more powerful in influencing other players’ payoffs and social welfare.
To see the result, let W ∗ denote the equilibrium welfare induced by the equilibrium
0 0
portfolio x∗ , and let Ws (x ) denote the welfare induced by a deviated portfolio, in which
s uses an alternative action. Suppose store s is now offering one promotion of item jc in
0
addition to its optimal level, ms = m∗s + ejc . The newly promoted product is now priced at
the sale price, and prices are re-optimized at the deviated promotion decision. This deviation
will result in promotional cost θm , and changes in consumer surplus and all firms’ producer
surplus:
0
∆Ws =W (xs ) − W (x∗ )
X
=∆P Ss + ∆P Sq + ∆CSs
q∈−s
X
=∆E[Rs (x)] − θm,s + ∆E[Rq (x)] + ∆CSs (32)
q∈−s
=(∆E[Rs ]stay + E[Rs ]switch + Rsnew ) − θm,s +
X
∆E[Rq ]
q∈−s
+ (∆CSsstay + ∆CSsswitch + CS new ).
∆Rs is the change in own revenue with three sources: the staying consumers (∆E[Rs ]stay ),
the consumers switched from rival stores (E[Rs ]switch ), and new shopper who didn’t shop
(Rsnew ). The purchase incidence of category c of the staying consumers would be raised by
the extra promotion, while their behaviors at other categories wouldn’t change. The other
two classes of consumers will not only purchase the newly promoted category but also other
categories. This indicates the strong incentive of promotion that could steal the entire basket
21of profit margins from rival stores. The magnitude of ∆Rs depends on preference parameters
P
and φs . Finally, the change in rivals’ profits, q∈−s ∆Rq , is due to the fact that a portion of
consumers who used to shop at −s now has switched to s, indicating the business-stealing
effect. The change in consumer surplus is decomposed into the part of the staying consumers
(∆CSsstay ), the switched consumers (∆CSsswitch ), and the new shoppers (CS new ).
In general, social welfare will be improved by adding promotion as long as the social gain
due to expanded quantity offsets the advertising cost. This logic applies here, except that
the gain in consumer surplus would be eroded by transportation cost. Since it is bared by
consumers, a shopper is now in favour of a more distant store s as long as the transportation
cost can be overweighted by the extra promotion. Therefore, the surplus transferred from
s to the switching consumers is eroded by transportation cost. This applies to consumers
who now visit a further store s, and those who used not to shop (of course, there are also
consumers who could save the transportation cost by switching to s). In the neighborhood
of optimum, it is expected that ∆E[Rs ]stay + E[Rs ]switch + Rsnew ) ≈ θm,s . So social welfare
would be improved if consumer surplus from expanded sales overweights the decline in rival
stores’ revenue, ∆CSsstay + ∆CSsswitch + CS new + q∈−s ∆E[Rq ] > 0. However, this would
P
be hard to achieve, for two reasons: first, only a portion (φs ) of the non-shoppers would be
informed by the additional promotion; second, consumer surplus of the switched and new
consumers would be eroded by transportation cost.
6.2 Counterfactual Simulations
I simulate two counterfactual outcomes: 1. eliminate transportation cost, and 2. a small
increase in promotion cost. The outcome is simulated by finding the new equilibrium under
the counterfactual settings, since in a Bayesian equilibrium agents’ belief must be consistent
with their optimal actions. Starting from the current equilibrium, I iterate market evolution
until it converges. The criteria of convergence is that the expectation of merchandising
attractiveness, us , is sufficiently close to the value in the last iteration.
6.2.1 Eliminating Transportation Costs
Due to the transportation cost that each shopping trip incurs, spatial model of store
competition predicts that each firm possesses some local market power. I eliminate this
market power by setting θd = 0, in order to examine market outcome, expecting more
rigorous competition among the firms and less inefficient allocation. It would provide some
insights for markets where the fixed cost of each purchase is negligible, for instance, online
grocery ordering that has recently been emerging.
22The simulation result in the bottom half of Table 7 shows that when local market power
is eliminated (θd = 0), competition among the firms become harder. Price indexes have been
driven down by 5 to 12 percent, and promotion intensity has increased by 9 to 24 percent.
Interestingly, the elimination of transportation cost brings HT1 and HT2 extra store visits
more than revenue decline due to harder competition, and therefore increases their profits.
On the other hand, the rest three stores no longer possess local market power, and suffer from
profit decline. Moreover, the elimination of transportation cost raises the probabilities of
visiting all five stores by removing the fixed cost of shopping. The higher shopping instances,
together with lower prices and more intense promotion activities, result in a greater quantity
sold and a higher consumer surplus. The overall effect on welfare is that the increase in
consumer surplus overweights the decline in producer surplus. Welfare is improved for two
reasons: a greater quantity result from harder competition, and the elimination of wasteful
transportation costs.
6.2.2 Change in Promotion Cost
Since in the current equilibrium the private promotion intensity is socially excessive,
I increase the promotion cost and simulate market outcome, expecting to see this higher
promotion cost could drive promotion levels closer to social optimality. Because of the
discrete nature of promotion decision, I allow for a 5 percent deviation in promotion cost,
instead of the usual 1 percent, to induce some changes in store decisions and, in turn,
market outcome. Table 8 reports the percentage changes in market outcome. The increase
in promotion cost reduces promotion intensity by 6 to 10 percent, and increases the price
level by 0.6 to 1.4 percent. For this reason, it negatively impacts shopping probabilities and
purchase incidences, and harms consumer surplus. Because of the 5 percent increase in θm ,
the total promotion expense is smaller(the percentage change in the number of promotions
is greater than 5 in all five stores). It causes industry profit to increase, as the promotion
shrinking saves the firms more costs than the revenue decline due to quantity decrease. The
impact on welfare is positive, for the reason that promotion costs saved overweights demand
decrease. It implies that as the private promotion levels are socially excessive, welfare can
be improved if the government imposes a specific tax. As the simulation shows, this tax will
effectively reduce the intensity of promotions but won’t sizably impact consumer surplus.
Conclusion
Pure price advertising may simply reallocate demand between firms without any aggre-
gate output effect. In the context of supermarket retailing, the advertising is ’informative’
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