The Impact of Search Costs on Consumer Behavior:
A Dynamic Approach
Stephan Seiler ∗
October 21, 2010
Abstract
Prices for grocery items differ across stores and time because of promotion periods. Consumers therefore
have an incentive to search for the lowest price. However, when a product is purchased infrequently, the
effort of checking the price on every shopping trip might outweigh the benefit of spending less. I propose
a structural model for storable goods, that takes inventory holdings and search into account. The model is
estimated using data on laundry detergent purchases. I find that search costs play a large role in explaining
purchase behavior, with 70 percent of consumers not being aware of the price of detergent in a given time
period. Therefore, from the retailers’ point of view it is important to raise awareness of a promotion through
advertising, displays, etc. I also find that price elasticities are overestimated when estimating a dynamic
model without search. Incorporating imperfect information in the form of search into the model, I find that
manufacturers and retailers have more market power than previously thought.
JEL Classification: D12, D83, C61, L81
Keywords: Demand Estimation, Dynamic Demand, Stockpiling, Search Costs, Imperfect Information,
Consideration Set Formation
1
Introduction
Temporary price reductions are used very frequently for grocery items and represent a large fraction of the
marketing mix budget of supermarkets and convenience stores. These promotion periods create an incentive
∗ London
School of Economics, Centre for Economic Performance and Institute for Fiscal Studies. I would like to thank my advisors
John Van Reenen and Pasquale Schiraldi for invaluable guidance and advice. I am also grateful to Michaela Draganska and Alan Sorenson
who discussed my paper for great feedback as well as participants at QME (Chicago), IIOC (Vancouver), Marketing Science (Cologne),
CEPR Applied IO (Toulouse) and seminar participants at the LSE and the IFS. I would also like to thank Rachel Griffith at the Institute for
Fiscal Studies for great help with understanding the data and detailed discussions as well as Philipp Schmidt-Dengler, Claire LeLarge and
Joachim Groeger for helpful discussions. Any remaining errors are my own. A previous version of this paper was circulated under the title
”A Dynamic Model with Consideration Set Formation”.
1
for consumers to wait with their purchase until the next reduction in price. As many consumers visit several
different stores regularly, they will search both across stores and intertemporally. Many grocery items, such as
laundry detergent for example, are bought regularly but with relatively long time intervals between purchases.
Despite having an incentive to wait for the next promotion period before buying again, it might be too much
effort to check for the price of detergent on every store visit. Finding out the price of a certain product (especially
in a very large supermarket) might actually be quite costly, as the consumer needs to spend time searching for it
in the store. Furthermore, shopping trips are very heterogeneous in many respects and on some trips only goods
from a certain category, food for example, are purchased. On other trips the overall expenditure is very small
and only a few items are purchased and the consumer spends little time in the store. On such trips it is even less
likely that consumers are aware of the price of other products.
Most discrete choice models assume that the consumer is aware of all the prices in the store on each visit. For
the reasons just outlined, this paper proposes a structural model with imperfect information, where consumers
engage in costly search. In order to do this, a pre-purchase stage is modeled in which the consumer decides
whether to search based on his expected utility from purchasing and the search cost. The novelty of this paper is
to integrate the search decision in a structural way into a dynamic demand framework where consumers hold an
inventory. This allows me to quantify the search cost as well as identify its drivers. I apply the model to laundry
detergent data, but the proposed approach can be used to analyze demand for any storable product. The search
aspect of the model will be especially relevant for products with a relatively long inter-purchase duration.
Furthermore, I will analyze across-store substitution patterns. In a dynamic model with inventory holdings,
the interaction between stores becomes relevant as a promotion in one store will lead to an increase in inventory,
and less purchases on future shopping trips. Therefore, there is a potential effect of pricing decisions at one store
on its competitors in future time periods. This is true even if consumers do not alter their store choice because
of the price change.1 In order to form a complete picture I explicitly take the identity of the stores visited into
account. Using the estimates from the model, I then compute the contemporaneous and the long-term impact of
price changes at a particular store on the store itself and other stores.
I find that the search costs are quantitatively important. About 70 percent of consumers that do go shopping
in a particular time period do not search.2 Search costs are a negative function of the overall amount of money
spent in the store and the number of products purchased in the same category. I also find that price elasticities
are overestimated in a dynamic model without search. When simulating the dynamic adjustment to a temporary
price change, I find a strong contemporaneous reaction but very little impact on future time periods. This is
in line with the lack of a post-promotion dip that is well documented in the literature.3 There is hardly any
1 Throughout
the paper I will treat the store choice decision as exogenous. Therefore there are no contemporaneous effects of one store’s
pricing on competing stores. However, consumers do visit different stores over time. A promotion in a particular time period will therefore
have an impact on purchases in competing stores in future time periods because of stockpiling.
2 This number is based on a simulation of consumer behavior using the estimated parameters of the model.
3 Many papers describe this phenomenon. Among the papers that explicitly analyze it are Hendel and Nevo (2003), Heerde, Leeflang,
and Wittnik (2000) and Neslin and Stone (1996).
2
negative effect of store-specific promotions on other stores. For permanent price reductions, the adjustment is
almost immediate with a substantial negative impact on products and stores that did not lower prices.
The findings of this paper are important for two reasons: First, the model gives insights into how important
imperfect information is. With consumers not being aware of prices on most of their shopping trips, marketing
tools other than pricing, such as advertising and preferential display, become very important. According to
the findings of this paper, retailers should raise awareness of price whenever they run a promotion. Second,
the model predicts lower price sensitivity and therefore higher market power for manufacturers and retailers.
Obtaining the correct price elasticities is an important ingredient for understanding consumer behaviour as well
as optimal pricing and the general marketing strategy on the supply side.
This paper’s general theme fits into an emerging literature which demonstrates that imperfect information
due to search frictions is an important component in the inference of consumer demand. Papers like Goeree
(2008), Moraga-Gonzalez, Sandor, and Wildenbeest (2009) and Koulayev (2009) show that including imperfect
information has an impact on the estimates of consumer preferences which is also the case here. Other papers
that estimate the magnitude of search costs include: Hortaçsu and Syverson (2004) for the mutual fund industry,
or Hong and Shum (2006) and Santos, Hortacsu, and Wildenbeest (2009) for online book purchases. Mehta,
Rajiv, and Srinivasan (2003) estimate search costs for grocery shopping but do not allow consumers to keep an
inventory. To the best of the author’s knowledge, there is no paper that estimates the magnitude of search costs
for grocery shopping whilst also taking stockpiling into account.4
The demand estimation will be based on Berry, Levinsohn, and Pakes (1995) who estimate a demand system
for the US automobile market. Their paper, along with many other applications, did not consider any dynamic
aspects in the consumers’ purchase decision. In the more recent literature many contributions try to explicitly include dynamic aspects. Other papers that use dynamic demand models to analyze consumers’ demand
for storable products include Hendel and Nevo (2006), Erdem, Imai, and Keane (2003) and Sun, Neslin, and
Srinivasan (2003).5
This paper shares some similarities with the marketing literature on consideration sets6 as this literature
also analyzes the impact of imperfect information. Conditional on purchasing a particular type of product, it
is assumed in this literature that consumers do not take all available brands into consideration when making
their purchase decision. Due to cognitive limitations, they only compare a smaller set of brands that forms their
4 There is a large theoretical literature on search in general and also on search in the context of temporary promotion periods with seminal
contributions by Stigler (1961) and Varian (1980). Other papers on sales like Salop and Stiglitz (1982), Assuncao and Meyer (1993) or
Pesendorfer (2002) explicitly incorporate stockpiling into the theoretical model, a feature that is also modeled in this paper. Empirical
studies such as Bell and Hilber (2006), Sorensen (2000) or Lach (2006) show that some the qualitative predictions from the theoretical
models can indeed be found in the data.
5 Interestingly, Hendel and Nevo (2006) and Erdem, Imai, and Keane (2003) both allude to the existence of imperfect perfection in the
way it is modeled in this paper. However, they do not model imperfect information and search explicitly. Hendel and Nevo (2006) point
out the strong effect of including a dummy for whether the product is on display in the utility function. This presumably captures that
consumers are more likely to be aware of the product when it is on display. This is exactly the way I am modeling the consumer behavior
here.
6 See for example Andrews and Srinivasan (1995), Roberts and Lattin (1991) or Bronnenberg and Vanhonacker (1996). Ackerberg
(2003), Erdem and Keane (1996) and Mehta, Rajiv, and Srinivasan (2003) look at imperfect information in a dynamic context.
3
consideration set.7 Imperfect information therefore has an impact on the choice of product, but not on purchase
incidence. This paper instead looks at imperfect information at the category decision level.8
Finally this paper is related to the literature on purchase incidence. A non-exhaustive list of papers include
Helsen and Schmittlein (1993), Jain and Vilcassim (1991), Vilcassim and Jain (1991). Seetharaman (2004) and
Seetharaman and Chintagunta (2004). In this literature, the likelihood of purchasing within a particular product
category is modeled as a function of three elements: The time elapsed since the last purchase, marketing mix
variables such as promotions,9 and household characteristics (see Fok and Paap (2009)). The impact of these
three channels is estimated in a non-structural way. However, there is a very close relationship between these
different elements and the structural parameters used in this paper.10
The paper is organized in the following way: The next section describes the data. Section three presents
some reduced-form results to further motivate the use of a particular structural model. Section four presents
the empirical model followed by a discussion of identification in section five. Section six discusses the estimation and section seven presents the estimation results followed by the simulation of short and long-term price
elasticities. Finally, some concluding remarks are made.
2
Data
I use data from the TNS worldpanel, a consumer-level panel dataset provided by the TNS (Taylor Nelson Sofres)
Marketing Research Institute. Each household in the panel is given a scanning device which it uses to scan all
products that were purchased. Receipts are then sent to TNS in order to correctly record the price paid for a
particular product. The dataset includes about 19,000 households over the period from 10/2001 to 10/2007. An
observation is the purchase of a particular product at a particular store on a particular day. Therefore, it is also
known when a particular household went to a store without buying any laundry detergent (as long as at least one
item was purchased on the trip). I concentrate on the market of detergent tablets and ignore purchases of liquid
detergent and detergent powder. Consumers rarely switch between these three different types of detergent. It is
therefore safe to look at detergent tablets in isolation.
2.1
Constructing Price Series
As the TNS Worldpanel has data at the household level, no store-level dataset of prices is readily available.
For the demand model used later, it is important to know the prices of products that were available but not
7 This awareness can originate from different sources such as previous consumption of the product or exposure to advertising for a
particular brand.
8 Imperfect information when choosing among different brands is ignored for simplicity.
9 Gupta (1991) shows that including marketing variables and past purchasing behavior improves the fit of the model.
10 Household characteristics are captured by the various types of heterogeneity. In particular, the different consumption rates explain
some of the across-household variation in interpurchase duration. The marketing variables are captured through the trip characteristics that
shift the search cost and thereby influence the purchase probability. Inventory is explicitly modeled and captures the effect of past purchases
on the current period purchase decision.
4
purchased by the household. Households in the panel are distributed over the whole of the UK, I therefore
rarely have several observations for the same store in the same week. In order to infer prices, I rely on national
pricing policies of big supermarket chains.11 However, the construction of a reliable price series is only possible
if I observe enough purchases in order to confidently infer the weekly price. Luckily, the market for detergent
tablets is very concentrated and 7 brands (Fairy, Daz, Ariel, Persil, Bold, Surf and Tesco private label) make up
about 80 percent of purchases.12 I am able to construct price series for all brands except for Surf and Persil.
Both of these brands offer many different pack-sizes and I observe only a small number of purchases for each
pack-size, which makes it impossible to construct a reliable price series. I encountered no such problems for
the other 5 brands.
The various brands are available in 4-6 different sizes and I allow consumers to buy two packs of the same
size.13 For each pack-size, I construct price series for each of the four big chains (Asda, Morrisons, Sainsburys
and Tesco), plus a residual category for all other stores. This yields a total of 125 price series (25 brand/packsize combinations at 5 supermarkets). For the four major supermarkets, the prices are identical for each store
and within each week, except for a few deviations.14 This confirms that prices from other stores of the same
chain can indeed be used to infer prices. For all other stores, a simple average of prices for a particular brand
and pack-size in a particular week is taken. Prices for this residual category will therefore be measured less
precisely. Since about 90 percent of purchases occur at the four big chains, this is not problematic.
2.2
Descriptive Statistics: Prices
There is variation in prices across brands, pack-sizes, supermarkets and over time. Some descriptive statistics
on these various dimensions are presented in this section. In order to illustrate the degree of price variation
along each one of these dimensions, I will proceed by looking at each dimension, holding the other dimensions
fixed.
Table 1a shows the variation in prices across different brands at Tesco. The price variation is reported for
pack-sizes of 900g and 1.8kg, which are the 2 major pack-sizes.15 The mean price is very similar across brands
except for Tesco’s own brand which is cheaper. There is substantial variation in prices for a given brand and
pack-size across supermarkets and time. The larger pack-sizes show a higher standard deviation of prices as
they are promoted more often. The quantity discount on the larger pack-sizes is very similar across brands,
ranging between a 8 and 12 percent reduction in the per volume price. In the following paragraphs, I will report
11 Supermarkets do engage to some extent in price flexing, i.e. adjusting prices to local conditions, but this is only done for a small subset
of products (according to the UK Competition Commission) and does not seem to include laundry detergents.
12 All other brands have substantially lower market shares than these 7.
13 Treating 2 packs of the same size as a different product is important as ”second pack half price” promotions are frequent. The per-unit
price therefore changes when several units are purchased.
14 Specifically I define a price to be the ”correct” price if I have at least 2 observations for a week/store combination and if strictly more
than 50 percent of price observations are identical. If I cannot define a price for a given week in this way, the value is interpolated from
prices in adjacent weeks. With this method 10 percent of prices are assumed to be mismeasured and replaced by the ”correct” price.
15 The pack-sizes of the different brands are not exactly equal to 900g and 1.8kg. There are only small differences though and I will
therefore ignore these differences when looking at price variation across brands.
5
price variation across the pack-sizes and across supermarkets. In order to keep things simple, I am going to
illustrate the price variation along these dimensions by focusing on a particular brand, Fairy.
Table 1b shows descriptive statistics on the price distribution and market shares for different pack-sizes of
Fairy at Tesco. Comparing the mean prices for different pack-sizes shows that there is some discount for larger
pack-sizes. For example, the per gram price discount of a 1920g pack relative to a 936g pack, the two most
popular pack-sizes, is about 12 percent. There is also considerable variation in prices over time for the more
popular pack-sizes. The table also shows that some pack-sizes (1320g, 2340g, 2496g) are only available for a
limited duration and there is little or no variation in price for these products. They are special offers, most likely
initiated by the manufacturer, and therefore always offered at a considerable discount. For example, there is an
average discount of 25 percent for a 2340g pack relative to a 936g pack, for example.
Table 1c illustrates pricing differences across different supermarkets for one particular pack-size of Fairy:
936g. There is variation in the mean price as well as the other moments of the price distribution. The differences
in standard deviation can be roughly interpreted as differences in the frequency of price reductions, whereas the
different minimum values represent differences in the depth of promotions. Taken together, Tables 1 and 2
provide ample evidence that there is an incentive for consumers to search for the lowest price both over time
and across stores. Both tables report pricing only at one supermarket / for one pack-size, but the pattern looks
very similar for other stores / other pack-sizes. For a more complete picture of pricing and market shares of all
supermarkets / pack-size pairs of Fairy the reader is referred to Table A.1 of the appendix.16
Table 1d aggregates the market-shares at the brand, pack-size and store level. The top panel reports brand
level market shares. Ariel is the most popular brand followed by Fairy. Tesco’s own brand has the lowest market
share, but it is also the only brand that is only sold in one supermarket. The middle panel shows that 936g and
1920g are by far the most frequently purchased pack-sizes. To a large extent this is due to them being available
most of the time in most stores. When market shares are adjusted for availability, the difference in market
shares is less pronounced.17 These adjusted market shares can be interpreted as the market share of a product
conditional on being available. In terms of supermarkets, most consumers buy at Tesco followed by the other
large chains. Only about 10 percent of purchases are made in ”Other Stores”.
2.3
Selection of Relevant Households
Many households in the sample buy only very small quantities of laundry detergent or non at all. Households
with a low volume purchased per year are therefore dropped from the sample. Also households for which I
16 For simplicity, all the descriptive statistics reported here completely ignore promotions that apply only to the second unit purchased
(”second one half price”-type of promotions).
17 The adjusted market share weights the individual market shares by store weeks. Store weeks is the number of weeks the product was
available in each of the 5 supermarkets summed up over all supermarkets. With 312 weeks and 5 supermarkets this has the maximum value
of 1560. Specifically the market share is divided by store weeks and then re-scaled in order for the adjusted shares to add up to 100 percent.
6
observe no purchases for a very long period of time are dropped.18 I also drop households that are in the sample
for less than 20 weeks.19 Finally, I use only households which bought one of the 5 brands for which I construct
price series at least 75 percent of the time.20 As a result, there are 686 households that fulfill all criteria.21
Overall, I observe 113498 shopping trips and 18210 purchases for this sample of households. This corresponds
to 165 trips per household and 26.5 purchases per household. With households going shopping once or twice a
week the 165 trips correspond to 2 years of observations for a given household.
3
Some Reduced-form Results
This section presents some reduced-form results that are suggestive of the features that will be included in
the structural model. Multinomial-logit regressions with a dummy equal to one, if a particular product was
purchased on a particular shopping trip as the dependent variable, are reported in Tables 2a to 2c. Each shopping
trip is an observation whether the household purchased any detergent or not. The utility from the outside
option of not purchasing anything is normalized to zero. This corresponds to a standard static discrete choice
estimation. It is referred to as ”reduced-form” because neither the inventory formation nor the search process
are explicitly modeled. Nevertheless, some effects that we would expect to see if these two features are indeed
relevant, can be illustrated with the regressions. I include a full set of brand (i.e. brand / pack-size combinations)
dummies. The price coefficient is therefore purely identified from within pack-size variation in price. A set of
supermarket dummies is also included in all the regressions, but not reported in the table.
Column (1) of Table 2a shows the result when only price and the control variables are used as independent
variables. The price coefficient has the expected sign and is highly significant. The results in column (2) show
that the relative expenditure on a particular shopping trip also has a significant influence on the probability of
purchasing detergent. If a household spends more money overall on a particular shopping trip, it is more likely to
purchase detergent. This can be interpreted as capturing the time spent in the store.22 The coefficient on relative
expenditure in column (2) is highly significant. Column (3) includes two variables that capture whether the
consumer has purchased products from the same product category. The first variable is the number of cleaning
products other than detergent that the consumer has purchased. The second variable is the number of products
within the category ”household goods”, which includes cleaning products but is a broader category. Buying
18 Specifically, I drop households with purchases of less than 6 kilograms of detergent per year (90 percent of households buy between
10 and 35 kilograms, the mean being 20 kilograms) and households who did not buy detergent for a period of at least 16 weeks. The latter
might be due to the household going on holiday, etc. It constitutes an unusual behavior in any case that the model cannot capture.
19 TNS deems that information from ”un-committed” consumers that spend only a short period of time in the panel is less reliable.
20 Any detergent purchase of a brand other then these 5 brands is modeled as a residual category. I assume that this ”outside good” has a
pack-size of 1.28kg and a price of 3 pounds. This corresponds to the average pack-size and price of the 5 brands in the choice set. I also
allow liquid and powder detergent purchases within this residual category. Only 12 percent of purchases fall into this category.
21 I checked whether the selected households are observably different from other households and the sample and find that they are not.
22 Relative expenditure is defined as the expenditure on a particular trip divided by the average expenditure over all shopping trips for a
certain household. This adjusts the measure for across household variation in average expenditure and is therefore a better measure for time
spent in the store. The money spent on laundry detergent is excluded from these measures of expenditure in order to avoid expenditure to
be higher because of the detergent purchase itself. The expenditure measure is therefore exogenous with respect to the laundry detergent
purchase.
7
other products from the same category has a positive impact on the purchase probability, the narrower category
being more important than the broader one. In column (4) all the variables are used in the same regression. The
qualitative results for all the coefficients are the same as for the regressions described above. The results are
also robust to including a full set of household dummies, as column (5) shows.23
In the standard discrete choice model, consumers are assumed to have perfect information about the prices
of all available products at every point in time where they can make a purchase (i.e. on every shopping trip in
the case of a grocery shopping item). The fact that consumers are more likely to purchase detergent when they
spend more money on other items is at odds with this assumption. Under perfect information, there is no reason
why the characteristics of the shopping trip should determine which products are purchased (Bronnenberg and
Vanhonacker (1996)). Price and other product characteristics alone should be a sufficient statistic.24 However,
the regression results confirm that trip characteristics do matter for the purchase probability. If instead, it is
costly to search for the product, this result can be rationalized. For example: If the probability of searching is
higher when the consumer spends more money in the store, this will lead to a higher probability of purchasing.
This kind of correlation can only be explained with a model of search and not within a static or dynamic model
with perfect information.
Table 2b shows that certain dynamic patterns associated with stockpiling are present in the data. Columns
(1) and (2) show that the likelihood of a purchase increases with the time elapsed since the previous purchase
and the pack-size purchased. The consumer does not need to immediately buy again as he will consume for
a while out of his inventory. He will wait longer for the next purchase if he purchased a larger volume packsize. Column (3) shows that results are robust to including both variables in the same regression. The negative
sign on the quadratic term in column (4) shows that the likelihood of a new purchase first increases and then
decreases again as time elapses. The duration with the highest likelihood will be roughly equivalent to the
average inter-purchase duration. Taken together, the results of this table suggest that stockpiling is important.
One concern might be that consumers do buy detergent only on particular trips because they want to avoid
carrying the product home on certain shopping trips. This alternative explanation has nothing to do with search
and could still lead to a correlation of trip characteristics with the purchase probability. However, it is not
clear why the variables used in the regression would capture whether it is more or less burdensome to carry
the product. In order to assess the validity of this alternative theory I do include the distance to the store into
the regressions in Table 2c. All regressions use the same specification as column (4) of Table 2a. In addition
to the other variables, the distance to the supermarket is also included.25 In column (1), I use the full sample
and find that distance is insignificant. As some consumers use a different means of transport on different
trips, distance might not be very meaningful here. Therefore, I re-ran the same regression on several restricted
23 These enter all the options except for the outside option and therefore capture the household specific average purchase incidence
probability.
24 As I use dummy variables for each pack-size, product characteristics are controlled for in a very conservative way.
25 As there is missing data for both supermarket and consumer location, the number of observations drops in this regression.
8
samples for which distance should be more informative. In column (2), only households that do not own a
car are used. In column (3), only households that do most of their shopping trips on foot are included.26 In
both cases distance should have a similar cost across trips as there is no variation in the type of transport used.
Also, for households without a car, one would expect a stronger effect of distance relative to other households.
It is therefore encouraging that distance is insignificant in columns (2) and (3). Finally, I further restrict the
sample used in columns (2) and (3) to shopping trips that occurred on a weekend. During the week consumers
might shop close to their workplace or on their way home. The distance from the household’s address to the
supermarket is therefore more likely to capture transport costs in the case of weekend trips. As in the other
regressions, distance is insignificant also in columns (4) and (5). Although the distance to the store is an
imperfect measure for the burden of carrying the product, the results are indicative of this not being much of an
issue.27
The results from the reduced-form regression suggest that both stockpiling and search are relevant for the
purchase of laundry detergent. This provides further evidence that these aspects have to be included in a structural model that models consumer behavior in a realistic way. I will ignore transport costs in the structural
analysis and focus on imperfect information and search. The results in Table 2c confirm that this is a valid
approach.
4
The Structural Model
In order to model consumers’ behavior, I assume that they are able to store the good and receive utility from
consuming part of their inventory every period. Their decision process is modeled in two stages. In the first
stage, (the search stage, labeled as ”ss”), the consumer has to decide whether to find out the price of detergent,
i.e. to search for the product. In order to do this, he will compare the expected utility from buying at a particular
store minus the search cost, with the utility from not purchasing any laundry detergent in the current time period.
This step related to the optimal search decision, which is embedded in a dynamic structural model, has not been
modeled in the previous literature. I am assuming that the consumer will include either all brands in his choice
set or none. Therefore, there is no variation in the number of products in the choice set, but only a binary
decision whether to consider detergent as a product category or not.28 If the consumer decides to search, he
then has the option of buying one of the available products or nothing at all. This second stage, (the purchase
stage, labeled as ”ps”), looks like the purchase decision in a standard dynamic demand model. The timing is
illustrated in Figure 1.
26 A survey on all consumers in the dataset was conducted. Among other things they were asked for the number of cars they owned and
which mode of transport they most frequently used for shopping. The restrictions used here are based on these survey questions.
27 Unfortunately, I cannot observe whether the household uses a car on a specific shopping trip. With this information a more direct test
of whether transport costs matter would be possible. One would expect a purchase to be more likely on a shopping trip by car as transport
costs are lower.
28 In most of the marketing literature on consideration sets, the number of products included in the set is the main focus. Here the
consideration decision is modeled purely as a category level decision similar to Ching, Erdem, and Keane (2009).
9
The search process for a storable, low cost consumer good like detergent works quite differently from many
other markets. For durable and high value products, say a car or TV purchase, the consumer would go and
visit several stores only for the purpose of finding out about prices and products at these different stores. For a
low-cost, repeat-purchase product like detergent, no consumer would visit several stores only to search for the
best price. Rather, the consumers goes shopping for various other reasons and each shopping trip represents
an opportunity to also search for the price of detergent, i.e. to go down to the detergent aisle in the particular
supermarket. This is exactly the way search is modeled in this paper. Specifically, the timing is as follows: At
the beginning of each time period the consumer enters a store and has to decide whether to search, i.e. walk
to the detergent aisle. If he decides not to search, he will not have the opportunity to buy any detergent. If he
searches, prices are revealed, and the consumer then makes his purchase decision. Note that more information
is available in the purchase stage. The search and purchase decisions therefore have to be modeled as two
consecutive decisions.
It is further assumed that the intention to purchase detergent never causes the household to go shopping.
Instead, shopping trips are undertaken for reasons exogenous to the decision of buying detergent. This can be
justified as detergent makes up only a small fraction of total expenditure on the average shopping trip.29 This
also accords with findings that there are small effects, if any, on store-traffic from promotions on individual
items (see Urbany, Dickson, and Sawyer (2000), Walters (1991) or Walters and Rinne (1986)). The search
process is therefore modeled as a decision to search or not within each store for an exogenously given sequence
of shopping trips.30 The choice of visiting a particular store is not something I attempt to model here. In order
to model consumer choice recursively, I assume that the consumer is uncertain about the identity of the store he
will visit the next time period. He will therefore form an expectation of the identity of the store he will visit the
next time period.31
I do not explicitly model optimal consumption behavior. Rather, I assume that households are consuming detergent according to some function c(it ) which is only determined by inventory holdings, i.e. optimal
management of inventory given the household preferences. This disregards any effect of purchase behavior on
consumption, i.e. households are not allowed to react to promotions by increasing their consumption. This
absence of a category expansion effect seems to be a valid assumption for a product like detergent. It is presumably consumed at a fairly constant rate with little scope and incentive for adjusting consumption (see for
example Bell, Iyer, and Padmanabhan (2002)).
Furthermore, the cost of search will be allowed to vary across shopping trips. Mitra (1995) provides some
experimental evidence that choice sets are not stable over time, but vary across purchase occasions.32 I am
29 On
average detergent purchases make up about 2 percent of total expenditure in my sample.
is similar to the way Hartmann and Nair (2010) model consumers visiting different stores over time.
31 The optimization problem will be set up as a infinite horizon model. Using a deterministic, finite stream of store visits is therefore not
feasible.
32 This fact has been captured in many papers by variables such as whether the product was on promotion or on display as well as the
positioning within the shelf or aisle (see for example Bronnenberg and Vanhonacker (1996) or Allenby and Ginter (1995)). These variables
30 This
10
therefore using data on how costly it is to consider the category as a whole, using the same trip characteristic
variables that were also used in the reduced-form regressions. I assume that the search decision is taken at a
point in time where the identity of the store as well as the search cost and therefore trip characteristics are known.
In terms of timing, this decision could either happen in the store or at home when a consumer is writing down
his shopping list and decides whether to include detergent in the list. The only constraint that I am imposing is
that store identity and trip characteristics are already in the consumer’s information set.
4.1
Flow Utility
The consumer receives the following one-period utility for each of his possible choices at time t after having
searched. This is referred to as the ”purchase stage” (ps). The utility is therefore indexed ups,t (The utility in
the ”search stage” (ss) is represented by uss,t ). Note that for simplicity of exposition, the consumer subscript i
is omitted from the following equations. If the consumer does not purchase any product he gets utility
ups,t (j = 0) = v(c(it )) − T (it ) + ε0,t
Where v(·) is utility from consumption c(·). The consumer’s inventory is denoted by it . T (·) represents the
storage cost of inventory holdings.
If he decides to purchase product j he instead receives
ups,t (j ∈ J) = −αpj,t + ξ j + v(c(it )) − T (it ) + εj,t
This is equivalent to the expression above, but for the inclusion of a negative utility term from having to pay
price pj,t and an unobserved (to the econometrician) product quality term ξ j . A product in this case is defined as
a brand / pack-size combination. All the variables in the flow utilities are known to the consumer after searching.
Prior to the search he does not have full information about these variables. Most importantly, the realization of
prices pj,t (j ∈ J) is unknown prior to search. The exact information structure will be explained in more detail
later. eps,t = (ε0,t , ε1,t , ..., εJ,t ) are consumer specific taste shocks and are unobserved to the econometrician.
Note that the inventory is also unobserved by the econometrician. However, I do infer the rate of consumption
from the average volume purchased per time period and treat the inventory as observable.33
The one-period utility prior to search is defined in a similar way. If the consumer does not search he will
not be able to make a purchase. He therefore receives utility
uss,t (d = ns) = v(c(it )) − T (it ) + εns,t
will pick up how likely it is for a consumer to consider a particular brand. In this model I am analyzing whether the whole category is
considered.
33 Given the initial inventory and the rate of consumption the evolution of a consumer’s inventory can be constructed. How the unobserved
initial inventory is dealt with is explained later. As mentioned above the optimal consumption decision is not explicitly modeled.
11
This is the same utility he receives if he searches but does not buy anything, except for a different error term
εns,t . If he searches he receives
uss,t (d = s) = E{maxj [ups,t (j)]} − st + εs,t
where d ∈ {s, ns} denotes whether the consumer searches or doesn’t search. A particular feature of the
model is that prior to searching the current period flow utility is unknown. Therefore the consumer has to form
an expectation over the flow utility in the purchase stage knowing that he will take the optimal purchase decision
conditional on the information that will be available to him then.34
st denotes the search cost which is unobserved (by the econometrician). εns,t and εs,t are unobserved (by
the econometrician) iid extreme value error terms. Let ess,t = (εns,t , εs,t ) be the vector of idiosyncratic shocks
for time period t in the search stage. Note that different sets of error terms enter the model before and after
search. It is assumed that search is a category level decision (see discussion above). The consumer decides
whether he wants to incur the cost of searching for detergent by making the effort of walking to the detergent
aisle. ess,t is therefore a vector of category level taste shocks, whereas eps,t is a vector of shocks that influences
the consumer’s choice across products.
4.2
The Dynamic Optimization Problem
Formally, a consumer chooses an infinite sequence of decision rules µ in order to maximize the expected, present
discounted sum of future utility
∞
X
β t gt (µt ) | xt ,et }
max{µt }∞
E{
t=0
t=0
where µt = {(dt ), (jt | dt = s)}. dt denotes the consumer’s search decision with dt = s if he decides to
search and dt = ns if he does not search. jt ∈ J ∪ {0} denotes the purchase decision conditional on having
searched (dt = s). et = (eps,t ,ess,t ) is the vector of error terms in both decision stages. xt is a vector of state
variables. Finally
gt (µt ) =


 ups,t (j) + εj,t − st + εs,t

 uss,t (d = ns) + εns,t
if dt = s and jt ∈ J ∪ {0}
if dt = ns
where ups,t (uss,t ) represent utility ups,t (ups,t ) excluding the error term.
34 Note that the use of the max-operator in the above equation constitutes an abuse of notation. The consumer will make a choice in
the purchase stage that maximizes the present discounted value and not the flow utility. The maximization is therefore with respect to the
choice-specific value function vps,t rather than ups,t .
12
The specific feature of this model is that the consumer has (potentially) two consecutive decisions to make
in one time period. He first has to decide whether to search or not (dt ∈ {s, ns}). If he does not search, he
does not have to make another decision in the current time period. If he decides to search, he then has to decide
which product to purchase (or not to purchase anything): jt ∈ J ∪ {0}. I will therefore define two different
value functions depending on whether the consumer has searched or not: Vss (the value function in the search
stage) and Vps (the value function in the purchase stage). They depend on one another and must be solved
simultaneously.
4.2.1
Choice-Specific Value Functions
The choice-specific value function in the purchase stage can be written as follows. The value function is specific
to a choice of product j
vps,j (xps,t ,eps,t )
= ups,t (j) + εj,t + βE{maxd [vss,d (xss,t+1 ,ess,t | xps,t ,eps,t , jt )]}
= v ps,j (xps,t ,eps,t ) + εj,t
where ups,t represents utility excluding the error term and vps,j and vss,d are the choice specific value
functions for the purchase and search stage respectively. v ps,j denotes the choice-specific value function in the
purchase stage excluding the error term. Furthermore, j ∈ J ∪ {0}, i.e. the option of no purchase is included.
Note that the state variables xps,t and xss,t are also specific to the search / purchase stage value function, as
different factors will be driving the search and purchase decisions. The value function in the search stage next
period is a function of the state variables xss,t+1 and error terms ess,t . The consumer forms expectations about
these variables based on current states xps,t , error terms eps,t and action jt in the purchase stage.
When entering the store, the consumer has to decide whether to search or not. If he doesn’t search he
receives utility
vss,d=ns (xss,t ,ess,t )
= uss,t (d = ns) + εns,t + βE{maxd [vss,d (xss,t+1 ,ess,t+1 | xss,t ,ess,t , dt = ns)]}
= v ss,d=ns (xss,t ,ess,t ) + εns,t
If he does search he receives
13
vss,d=s (xss,t ,ess,t )
=
E{maxj [vps,j (xps,t ,eps,t | xss,t ,ess,t , dt = s)]} − st + εs,t
=
v ss,d=s (xss,t ,ess,t ) + εs,t
The value functions can be easily expressed in terms of their choice-specific counterparts
Vss (it , xss,t ,ess,t )
Vps (it , xps,t ,eps,t )
4.2.2
n
o
= max v ss,d=s (xss,t ,ess,t ) + εs,t , v ss,d=ns (xss,t ,ess,t ) + εns,t
n
o
= maxj∈J∪{0} v ps (xps,t ,eps,t ) + εj,t
Ex-Ante Value Functions
As in Rust (1987), let EVps (EVss ) denote the expectation of the value function, integrated over the realization
of eps,t (ess,t ), which follows from Rust’s conditional independence assumption.35
Z
EVps (xps,t )
=
e
ps,t
Vps (xps,t ,eps,t )dPeps
Z
EVss (xss,t )
=
e
ss,t
Vss (xss,t ,ess,t )dPess
Assuming that the error terms (eps,t (ess,t ) are iid extreme value distributed, the integration yields the following expressions:
EVps (xps,t )
=
log

X

EVss (xss,t )
=
exp(ups,t (j) + βE{EVss (xss,t+1
j


| xps,t , jt )})

exp uss,t (d = ns) + βE{EVss (xss,t+1 | xss,t , d = ns)}
+ exp E{EVps (xps,t | xss,t , d = s)} − st
log
The term EVps (xps,t ) can be interpreted as the inclusive value of searching on the shopping trip in time
period t, excluding the search cost. In the search stage, the consumer will compare the expected utility of this
inclusive value with the utility of not purchasing. This is very similar to the optimal stopping point problem
in replacement models for durable goods (for example Melnikov (2001), Gowrisankaran and Rysman (2007)
or Schiraldi (2009)). The difference is that the consumer has to form an expectation about the current period
35 Note, that in order to apply this simplification we need to assume that the consumer in the search stage does not know the realization
of the purchase stage error terms.
14
inclusive value, whereas in the replacement models the current value is known, but the consumers’ expectations
about the future evolution of the inclusive value influence the purchase decision.
The structure of the model is slightly different from other dynamic optimization problems as there are
potentially two consecutive decisions within one time period. The consumer endogenously decides whether he
will make two decisions in the current time period by deciding whether to search or not. If he decides to search,
new information will be obtained and he has to make a decision which product to buy. Because of the arrival
of new information, the purchase decision will be based on different state variables than the search decision. In
the search stage the consumer is therefore forming expectations about the current period state variables in the
purchase stage. If the consumer decides not to search, he will not have to make a second decision in the same
time period and the next decision will be the search decision in time period (t + 1). In terms of state transitions
I therefore have to specify Pr(xps,t | xss,t , dt ), Pr(xss,t+1 | xss,t , dt ) and Pr(xss,t+1 | xps,t , jt ). These are the
three possible sequences of state / time-period combinations (this can be seen in Figure 1).
4.2.3
Simplifications and Assumptions
In order to make the problem tractable, the dimensionality of the state space has to be reduced. In order to do
this, certain assumptions about the relevant state variables and the formation of expectations regarding future
realizations of the state variables are made.
In the search stage, it is assumed that the relevant state variables xss,t are the consumer’s inventory it , the
identity of the store he is visiting kt and the search cost st . The consumer does not know the prices pt of the
different pack-sizes at this point, but forms expectations based on the identity of the store kt . I assume that the
consumer knows the distribution of prices at each store.36
Once the consumer has searched, he obtains information about the actual prices pt . Besides prices, his
inventory is also part of the state variables in the purchase stage xps,t . The current search cost st has already
been incurred and is not relevant anymore for the purchase decision. Neither is the identity of store as the
consumer now knows the actual realizations of prices at the store. st and kt are therefore not part of the
purchase stage state space xps,t
Independent of whether the consumer has searched or not, he forms expectations about future search costs
and the identity of the store visited next time period. The expectations regarding future prices enter only indirectly through the expectations of the store identity next time period kt+1 as prices are not known in the search
stage in (t + 1). The consumer also forms expectations about future values of the search cost based on the
distribution of search costs. As for price expectations, the expectations about search costs and store identity in
36 Note that I do not model a Markov-process for prices and price expectations are not influenced by past prices at all. This is necessary
as I cannot distinguish whether the consumer decided not to search or if he searched and did not purchase. Therefore I do not know when
the consumers’ information set was ”updated” with new prices and when not. This makes the simplification of basing price expectations
purely on the identity of the store visited necessary.
15
(t + 1) do not depend on past realizations of any variable.37 I also assume that the transition process for the
inventory is known to the consumer. It is given by the consumption that enters the per-period utility and the
pack-size of the detergent that was purchased in the previous period (if any was purchased):
it = it−1 − c(it−1 ) + ∆it−1
The pack-size purchased in t − 1 is denoted by ∆it−1 . The other variables were defined previously. The
only component that is unobserved by the econometrician is the rate of consumption c(it−1 ), which will be
estimated from the data. There is no noise in the transition process, therefore the consumer perfectly predicts
the inventory next period. For simplicity, the expectations about the inventory are not going to be explicitly
written down in the value functions.
The value function can now be written only in terms of the relevant information at each stage.
exp uss,t (d = ns)+βEkt+1 ,st+1 {EVss (it+1 , kt+1 , st+1 )} +exp Ept {EVps (it , pt ) | kt }−st
EVss (it , kt , st ) = log
EVps (it , pt ) = log

X

j


exp(up,t (j) + βEkt+1 ,st+1 {EVss (it+1 , kt+1 , st+1 )})

Note that in the search stage the expectations regarding the current prices is conditional on the store identity
kt , whereas the expectations regarding kt+1 and st+1 are unconditional ones (as was explained above). The
state variables kt and st are not decision-relevant anymore in the purchase stage as the search cost is sunk and
the actual price realizations at store kt are known.
4.3
Choice Probabilities and Likelihood Function
The probability Ps,t that a consumer searches in time period t (the consumer index i is omitted) can now be
determined from the following equation:
Z
Ps,t
=
P r v ss,d=s (it , kt , st ) + εs,t ≥ v ss,d=ns (it , kt , st ) + εns,t
e
ss,t
The probability of not searching Pns,t is determined similarly. The same logic can be applied to the probability of purchasing product e
j conditional on having searched Pej|s,t .
37 This is mainly done in order to reduce the computational burden. In principle, a Markov-process could be estimated for the search cost
and also the store-visit probability.
16
Z
Pej|s,t
=
e
ps,t
P r v ps,j=ej (it , pt ) + εej,t ≥ v ps,j (it , pt ) + εj,t , ∀j ∈ J ∪ {0}
Given the iid extreme value distribution of the error terms the probabilities can be expressed in the following
way:
Ps,t
=
=
Pns,t
=
exp(v ss,d=s (it , kt , st ))
exp(v ss,d=ns (it , kt , st )) + exp(v ss,d=s (it , kt , st ))
exp(Ept [EVps (it , pt ) | kt ] − st )
exp(uss,t (d = ns) + βEkt+1 ,st+1 [EVss (it+1 , kt+1 , st+1 )]) + exp(Ept [EVps (it , pt ) | kt ] − st )
1 − Ps,t
Pej|s,t
=
exp(v ps,j=ej (it , pt ))
P
j∈J∪{0}
=
exp(v ps,j (it , pt ))
exp(ups,t (e
j) + βEkt+1 ,st+1 [EVss (it+1 , kt+1 , st+1 )])
exp(u
ps,t (j) + βEkt+1 ,st+1 [EVss (it+1 , kt+1 , st+1 )])
j∈J∪{0}
P
J denotes the set of all available pack-sizes. The consumer also has the option e
j = 0 of not purchasing
anything.
As the search decision is not observable, it is only reflected in the purchase probabilities. In terms of
observables we have the following probabilities:
Pej,t = Pej|s,t ∗ Ps,t
Pno−purchase,t = Pns + (P0|s,t ∗ Ps,t )
With e
j ∈ J (i.e. the option of not purchasing is not included). The theoretical probabilities derived above
can now be used in order to form the likelihood function.
L=
YY
t
y
Pj,tj,t
j
Or in logarithmic form:
LL =
XX
(ln Pj,t )yj,t
t
j
17
yj,t with j ∈ {no − purchase, purchase − e
j ∈ J} is a variable that takes the value one for the decision
actually taken in a particular period and zero otherwise. Therefore, this maximization tries to make the probabilities of the observed choices as close as possible to one. Within the estimation routine, I solve the value
functions using a fixed point algorithm.
Some details of the model and how it is applied to the data are discussed in greater detail in section 6.
This includes a more extensive treatment of how expectations are modeled, as well as details on consumer
heterogeneity. How the unobserved initial inventory is dealt with will also be explained.
5
Identification
In order to apply the model to the data, a specific form for the utility from consumption and the storage cost has
to be chosen. I assume storage costs to be linear in inventory:38 T (it ) = cstorage ∗ it and define consumption
to be determined by c(it ) = τ ∗ log(it + 1), where τ is a parameter to be estimated.39 The utility from
consumption v(c(it )) is not identifiable in my model. This is due to the fact that households in my sample are
always consuming detergent. I do not model an outside option of not using any detergent which would allow
me to estimate v(c(it )).40 Formally, I define v(c(it )) = ν ∗ c(it ) and set ν = 1. I also restrict the vector of
product qualities ξ j . A product j is a brand / pack-size combination in the model, but product quality does not
vary across different pack-sizes. Therefore, I estimate a set of brand specific, but not pack-size specific, fixed
effects and multiply the fixed effect with the pack-size purchased. This is done because the choice of pack-size
will be informative about the dynamic parameters of the model such as the storage costs. Estimating a full brand
/ pack-size specific set of fixed effects would eliminate useful variation and make it difficult to identify these
parameters.
Finally, the search cost st has to be parameterized. I choose the following functional form:
st = se ∗
exp(x0t β)
1 + exp(x0t β)
Where xt is a vector of trip characteristics, which were already used in the reduced-from regressions. Specifically, I use the relative expenditure in the store as a proxy for the time spent in the store and the number of
products bought in the same category. The latter captures whether the consumer is in the relevant part of the
store. I define two variables for a wider and more narrow definition of product category.41 se and β are parameters to be estimated. The functional form makes sure that for no values of x is the search cost negative, as this
38 I tried to include higher order terms, but they were not significantly different from zero. I therefore use only the linear term in the main
regression.
39 The log-form reflects an optimal consumption path in a dynamic model. I assume that preferences are such that consumers will
optimally scale back their consumption when their inventory is low, due to concerns about running out. The proposed logarithmic functional
form reflects this relationship without explicitly modeling consumption choice.
40 This is similar to the situation of a static demand model without an outside option. In that kind of model it is impossible to estimate a
constant term in the utility function. For the same reasons v(c(it )) cannot be identified.
41 For more details on these variables, see the reduced-form regressions in section 3.
18
would not make any economic sense. This non-negativity is given as long as se ≥ 0. For se = 0, there is no
search cost. A simple t-test on this coefficient will therefore allow me to test for the relevance of search costs.
The functional form also makes the incorporation of expectations regarding future search computationally easy,
as the search cost varies on the compact set se ∗ [0, 1].42
The parameters to be estimated are the price coefficient α, product quality ξ j , the parameterized functions
c(it ) and T (it ) and the search cost st as a function of trip characteristics. The discount factor cannot be identified and is set equal to 0.998.43 Each parameter will be discussed separately in the following paragraphs. Note
that although the search process is not observed, it is standard in the literature to infer the decision in the search
stage from observed purchases. Some early contributions have used direct survey data on the consideration
decision (Roberts and Lattin (1991)). However, Nierop, Paap, Bronnenberg, Franses, and Wedel (2005) show
that a direct approach using only purchase data yields similar estimation results as one which uses additional
survey data on the considered options. This is reassuring as a direct approach is also employed here.
5.1
Rate of Consumption
The rate of consumption is defined by c(it ) = τ ∗ log(it + 1) in the model. As I observe consumers over a
long period of time in the sample, I can infer the average rate of consumption by dividing the total amount
of detergent purchased by the overall time in the sample. This will allow me to identify the parameter τ that
represents the speed of consumption.
5.2
Trip Characteristics
The identification of the trip characteristics that enter the search stage comes from a kind of ”exclusion restriction”. As argued before there is no theoretical reason why the trip characteristics would enter into the
optimization of a perfectly informed consumer (Bronnenberg and Vanhonacker (1996)). Therefore, they cannot
be part of the product characteristics which influence the choice after the consumer has searched (the second
stage in this model), and only enter in the search stage. If the consumer knows the actual prices of all products
at every store he visits, whatever else he is doing on the shopping trip should not have an impact on his choice
of a particular product. However, if search is costly, the consumer will be less likely to know about prices on
trips where his search costs are higher. This will lower his purchase probability on these trips. This would also
lead to a higher likelihood of buying detergent on particular shopping trips, something that cannot be explained
without a search stage. The impact of trip characteristics, which leads to variation in the search cost, can therefore be identified. They have an impact on the purchase probability only through the search process but do not
affect utility from the purchase directly.
42 This
43 This
makes it easy to define an appropriate grid. I will elaborate more on this in the following section.
corresponds roughly to a 10 percent annual interest rate.
19
5.3
Search Cost
The overall importance and magnitude of the search cost, represented by se in the parametric specification, is
closely linked to the relevance of the trip characteristics. While the vector of coefficients β identifies which one
of the trip characteristics has the largest impact on search costs, it is se that determines how much all of the trip
characteristics matter relative to other components of the utility function. If trip characteristics explain a large
part of the variation in purchase behavior, the magnitude of the search costs has to be relatively high.
5.4
Price Elasticity
There is a very rich price variation that can be exploited for the purpose of identification, as prices vary across
brands, pack-sizes and over time. The price coefficient α will influence brand and pack-size choice as well as
the timing of purchases. As will be explained in the following paragraphs, pack-size choice and purchase timing
provide identifying variation for storage and search costs and the price coefficient. However, brand choice has
explanatory power only for the price coefficient: The choice of a particular brand conditional on the pack-size
and time of purchases does not provide any information regarding storage costs as the increase in inventory is
unaffected by the brand chosen. Similarly, the model assumes that the consumer knows about the prices of all
products after searching. Which brand he purchases, therefore does not help to make any inference about search
costs. Brand choice conditional on pack-size choice and timing therefore helps to identify the price coefficient
separately from storage and search costs.
5.5
Storage Costs (and Search Cost)
Despite the fact that variation in trip characteristics can identify search costs, the dynamics of consumers’
purchase behavior offer an independent source of identification for the magnitude of the search costs together
with storage costs.44 In the following discussion, I will assume that the price coefficient is identified (see
previous paragraph).
In particular, two types of variation in prices and purchase behavior will help me to identify both search
and storage costs. First of all, consumers differ in their willingness to change the timing of their purchases
in reaction to variation of prices over time. They might, for example, purchase detergent earlier than they
intended because they encounter a promotion. This behavior of ”purchase acceleration” has the disadvantage
of increasing inventory above the usual level. On the other hand, the consumer benefits from the lower prices.
If he waited with his purchase he would avoid the higher inventory, but he knows that the price will most
likely be back up at the regular level when he makes the purchase. Figure 2 illustrates the dynamics of this
decision. If consumers do not react to promotions by accelerating their purchase, this could be explained by
44 It
would therefore be possible to estimate search costs even in the absence of information on trip characteristics.
20
high storage costs. In this case, the disutility from the larger inventory outweighs the benefit of the lower price.
Alternatively, this behavior is consistent with a high search cost. This implies that the consumer was not aware
of the promotion and therefore did not react to it. Only with this type of variation it is not be possible to
separately identify search and storage costs.
Secondly, consumers differ in the pack-size that they purchase. Big pack-sizes lead to a larger increase in
inventory and therefore higher disutility from storage costs. At the same time the per volume price is lower for
larger pack-sizes. If consumers buy bigger packs, this might be due to them having low storage costs. In this
case, the benefit of a lower per volume price is larger than the disutility from the increase in inventory. Another
explanation for this type of behavior is high search costs: Buying a large pack-size increases the time-span until
the next purchase. As a purchase always entails that search costs have to be incurred, buying a large pack-size
leads to savings on future search costs. Again, search and storage costs offer equally valid explanations for this
particular type of consumer behavior.
Taken together, pack-size choice and the degree to which consumers react to promotions allow me to disentangle storage costs and search costs. For example: low storage costs imply large pack-sizes and consumers
accelerating their purchase, whereas high search costs imply the purchase of large pack-sizes and no purchase
acceleration.
Finally, despite the fact that both low search costs and high price sensitivity lead to purchase acceleration
in promotion periods, the impact of the two somewhat differs. The presence of storage costs will lead to
the reservation price rising slowly over time as inventory decreases. However, limited information leads to a
discrete jump: in one time period the consumer does not know about prices, in the next he searches for price
information. If we observe an upwards jump in the price (the end of a promotion period) and a purchase after the
jump, this is only consistent with the existence of imperfect information. The distinction between the gradual
effect of the storage technology on purchase behavior and the discrete change implied by limited information
is more difficult to make with imperfectly observed inventory. It has to be noted that the identification relies
only on correct information regarding the change of inventory over time. An incorrectly inferred level would
not be problematic. Since the change in inventory is estimated from average consumption data, this is relatively
reliable.
6
6.1
Estimation
Expectations
I have to compute consumers’ expectations about current price pt prior to search (i.e. his expectation about
prices in the purchase stage when making the search decision in the search stage). Furthermore, households
form expectations regarding the identity of the store visited next period (kt+1 ) and next period search costs
21
(st+1 ).
For the expectations regarding the purchase stage utility in the current time period EVps (it , pt ), i.e. the expected utility from searching for laundry detergent, it is assumed that the consumer knows the price distribution
for each of the products at each store.45 The expected utility is calculated based on these store-specific price
distributions, which are inferred from all the weekly prices over the whole sample period.46 In order to compute
the expectation regarding the identity of the store that is visited next period, the sample frequencies of the visits
to different supermarkets are taken, i.e. the number of trips to a particular supermarket is divided by the total
number of shopping trips over the whole sample period. A similar approach is taken for the search cost. Based
on the estimates of se and the vector β, I calculate the search cost for all the shopping trips and compute the
continuous distribution of the search costs over all trips. A grid for different possible values of the search cost is
constructed.47 Then probabilities are assigned to each grid point based on the derived search cost distribution.
Note that a particularly simple form of non-time-varying expectations are used here. The expectation regarding kt+1 and st+1 do not depend on any current variables. Only the expectation about current period prices
pt , is based on the current period store identity kt . A first or higher order Markov-process on the evolution
of prices is frequently used in the literature, but unfortunately this is not possible here as it is unknown when
new price information is obtained (see earlier discussion).48 It would be possible to use a Markov-process for
the store-visit probabilities and the search costs. As this would increase the state space49 and therefore the
computational burden, it is not done at this point.
6.2
Heterogeneity
In order to reduce the computational burden of the maximization routine, I will not be able to calculate individual
specific value functions for each household in my sample. In order to capture some heterogeneity, I do consider
different types of households. Specifically, I allow for different price coefficients α for above and below median
income households, different τ , i.e. different per-period consumption, and different storage costs cstorage for
households of different size. As consumption is taken as exogenous here and in order to keep the computation
simple, I use average consumption over the whole sample period in order to form groups of high and low
consumption households50 . For these two groups different values of τ are estimated. A different storage cost
45 As discussed earlier, I define five different categories of stores: the ”big four” supermarket chains and a residual category for trips to
other supermarkets or convenience stores that sell detergent.
46 In practice most price distributions are bi-modal with one mass-point at the regular price and another one at the promotional price.
Despite this, I do allow for a continuous distribution of price.
47 This is made particularly easy by the functional form chosen, as the search cost has to be an element of the interval s
e∗ [0, 1]. In practice
I use a grid of value between zero and one and compute the distribution of exp(x0t β)/[1 + exp(x0t β)]. This term is then multiplied by se.
48 It is also questionable whether price information from the same or a different store should be treated symmetrically, as it is usually
done in the literature. Presumably a promotion in a particular store in time period t will imply different things for the price in the same
store in t + 1 then in a different store in t + 1.
49 The value of the search cost and the identity of the store visited in the current time period would have to be included in the state space.
50 Average consumption is calculated simply by dividing the aggregate amount of detergent purchased by the duration of the household
being in the sample. Households are assigned to one of the two groups depending on whether they have above or below median average
consumption.
22
parameter (cstorage ) is estimated for households above and below a size of four people. Finally I allow for a
different search cost se for above and below median income households. Note that for above and below median
income types I estimate different price coefficients α and different values of se.
Together this yields a total of 23 = 8 types of households. For each one of these groups a different value
function has to be calculated. In terms of coefficients, I obtain two values for α based on income, two values
for τ based on average consumption and two cost parameters for differently sized households. Note that the
expectation regarding prices in the current period prior to searching are based on the sample frequencies of
prices for each store and therefore do not vary across households. The expectations regarding st+1 are different
for above and below median income households as they have different search cost distributions. Finally, I allow
a different probability distribution (i.e. expectations) for the store-visit next period kt+1 for each of the 8 types.
As no additional coefficients are estimated and type-specific value functions have to be calculated anyway, this
comes at no cost. The store choice probabilities for each of the types is based on their respective means.
6.3
Initial Inventory
I also try to deal with the problem of an unknown initial inventory. As a logarithmic form is used for the
unobserved consumption, some convergence will happen over time51 and the impact of the initial inventory will
fade. I start with the first observed purchase for each household and assume that no inventory was held before
that time period. I then calculate the evolution of the inventory implied by the estimated consumption parameter
τ and the observed purchases. Only after the first ten weeks is the observed behavior used in order to form
the likelihood function. This helps to mitigate the initial inventory problem. As a sensitivity check, I also tried
excluding the first 20 weeks instead of only 10 from the estimation. This had little impact on the results.
7
Results
Table 3 presents the results for the main regression using all the dimensions of heterogeneity presented above,
and covariates that move the search cost.
I will first turn to the estimated coefficients other than the search cost terms. The coefficients all have the expected sign and are significant at conventional levels. Heterogeneity enters in the expected way. I find that richer
households are less price sensitive as they receive less disutility from paying a higher price. Households with
more than 4 members have lower storage costs. The utility from consumption is higher for high consumption
households.52
51 Households with a higher inventory will consume more than those with a low inventory. Over time the path of inventory will be less
influenced by the initial inventory.
52 This result is unsurprising as I used the average consumption rates to group the households into high and low consumption types.
It helps to capture heterogeneity in the consumption patterns more appropriately, which leads to more precise estimates on the other
parameters. As consumption is assumed to be exogenous, this a priori grouping of high and low consumption household is consistent with
the model.
23
As for the variables influencing the search costs, again, the coefficients have the expected sign and are
precisely estimated. In terms of heterogeneity, I find that richer households have higher search costs. Search
costs are lower when the relative expenditure is high, which makes intuitive sense as less time is spent in the
store. If other products in the same product category are purchased, this also lowers the search costs. This
reflects that the consumer spends time in the correct aisle, which lowers the search cost. Also in terms of
magnitude the results seem reasonable as the number of products in the narrower product category lowers the
search cost by a larger amount.
In terms of magnitude, the search cost varies on the interval [0, 4.7576] for low income households and
[0, 5.1430] for high income households. A shopping trip where each of the trip characteristics takes on its
respective average value in the sample has a search cost of 3.3046 associated with it. In order to get a feeling
for the importance of search costs, it is most informative to look at the proportion of trips on which consumers
engage in search. When simulating the households’ behavior, the estimated search cost translates into 70 percent
of consumers not searching in a given time period. The reader is referred to the next section for more details on
the simulation.
I also run the estimation without the search stage in order to compare the results (see Table 3). A comparison
of the results shows that the fit is much better in the model with search. For both the AIC and BIC, I find an
improvement of about 45 percent. Of particular interest is also the change in the price coefficient. It is larger
in the model without search relative to the case with search cost. This can be explained by the fact that a high
price sensitivity (relative to the magnitude of storage costs) is needed in order to explain why consumers buy
large pack-sizes in non-promotion periods. In a world without imperfect information about prices and search,
the only reason for buying large packs is a lower per volume price. This quantity discount is actually relatively
small (about 12 percent for a 1.8kg pack relative to a 900g pack).53 In a model with search costs, another reason
for buying large packs is embedded in the model. As was discussed in the identification section, purchasing
larger packs will lead to lower future search costs. This mechanism is absent in the perfect information model.
Therefore, when search costs are controlled for, the price sensitivity needed to explain the remaining variation
in brand choice and temporal purchase patterns drops.
From a theoretical point of view, it is not a priori clear, that the price coefficient should decrease in the
estimation with search costs. Apart from the mechanism described above, there is another force that will tend
to drive the coefficient in the other direction. In order to explain an absence of purchase acceleration, a model
without search will give a low estimate of price sensitivity. In a model with search, the burden of explaining why
consumers are not reacting to promotions is partly loaded onto the search cost. I.e. consumers might not react
to a promotion because they were not aware of it. The same amount of purchase acceleration will therefore be
associated with a higher price coefficient when including search in the estimation. This argument is very similar
53 Furthermore, the smallest available pack lasts for a much longer time than until the next shopping trip. Therefore, the fear of running
out of detergent unexpectedly cannot explain the purchase of larger packs.
24
to the one discussed in Draganska and Klapper (2009).54 In the estimation in this paper, it seems that the first
effect outweighs the second one and the price coefficient therefore drops. This is closely related to the earlier
discussion on identification.
In order to check how sensitive the results are to the functional form assumptions, I vary the specification in
several ways. I try to include a quadratic storage cost term for small and large size households. Both coefficients
are positive but not significantly different from zero. With regards to the search costs, I experiment with different
functional forms and again find no effect on the qualitative results of the model.55
8
Price elasticities
Because of the search stage and the dynamic nature of the model, price elasticities cannot be computed analytically from the price coefficient. Instead I will simulate the change in market shares for different kinds of
price changes by taking draws from the distribution of error terms and aggregating the choices of all simulated
consumers into market shares. In order to look at the impact of both temporary and permanent price changes, I
compute the market shares for several time periods.
Apart from their type, consumers also differ by the inventory they hold and the stores they visit in a particular time period. Both of these things are going to have an impact on their choices. I therefore have to take
the distribution of inventories and the probability of visiting a particular store into account when simulating
the consumers’ reaction. The discrete probability distribution of store-visits can easily be computed, and was
actually already used when the expectations regarding the store visit in the next period were formed. The distribution is computed from the sample frequencies of store visits and is therefore independent of any parameters
of the estimation. For each simulated consumer and time period, I randomly draw which store was actually
visited from the type-specific distribution of store visits. I also have to simulate values for the various extreme
value error terms embedded in the model. These have to be drawn in each time period for the search stage
and purchase stage. In order to calculate the inventory distribution, I start with assigning a particular gridpoint
value of the inventory vector to each consumer. I give equal weight to each gridpoint and therefore end up with
a uniform distribution of the inventory gridpoints in my sample of simulated consumers. I then simulate the
consumers’ behavior over 40 time periods assuming that the price for each product is equal to the respective
sample average in all time periods. I update the inventory each period according to the rate of depreciation
derived in the estimation and the simulated purchases. The inventory changes very little from period to period
at the end of the 40 simulated time periods.56 I then use this ”steady state” inventory distribution as the initial
54 Their
paper uses aggregate data and looks and substitution between different brands. They find that including imperfect information
increases the price coefficient. The general logic of their argument is the same as the one presented here.
55 Specifically I use s
e ∗ exp(x0t β) and exp(α + x0t β). Note that I do need to specify a functional form that prevents the search cost from
becoming negative for any possible value of xt .
56 It takes a low consumption type consumer less than 20 time periods in order to run down his inventory completely, even if he started
with the maximum possible inventory (the largest gridpoint value). Therefore it makes sense that the impact of the initial inventory (here
25
inventory for the simulation of price changes.
I can now simulate the choices consumers take in each of the time periods. This yields market shares for
each of the different pack-sizes as well as the proportion of consumers that search but do not buy, and those that
do not even search. Note that I am also able to compute store-specific market-shares, which can shed some light
on the impact of store-specific promotions on competing stores.
I use a total of 10,000 simulated consumers for each one of the 8 types. Total market shares are calculated
by weighing the market share of each type-group of consumers with the frequencies of the respective type in
the sample. I first run the simulation with prices equal to the averages of the respective price distributions for
10 time periods and find that only 15 percent of all consumers buy detergent in a given week, 70 percent do not
search and 15 percent search but do not buy. The relative importance of search is therefore quite high. This
is in line with findings that the search stage explains a large part of the variation in purchase incidents such as
Hauser (1978). Also, Dickson and Sawyer (1990) and Hoyer (1984) find that many consumers do not pay much
attention to the price of a product they buy and spend very little time making their selection in the store.57 This
anecdotal evidence lends further support to the large relative importance of the search stage.
I then compute the reaction to both temporary and permanent price reductions. In order to illustrate the
general pattern of price elasticities, I look at the price change for a 936g pack of Fairy at Tesco.58 The price
elasticities and dynamic pattern look similar for other store / pack-size combinations. The dynamic adjustment
path for a 50 percent price decrease is shown in Figure 3.59 I calculate short term price elasticity for temporary
and permanent changes and the long term price elasticities for permanent changes.60 In the framework of
the model, consumers might switch from a different product at the same store or switch from purchasing at a
different store. A price change might also induce them to start searching. In order to get a complete picture I
compute the own price elasticity, the cross price elasticity with other products and / or stores, the cross elasticity
with respect to the outside option and with respect to search. Separate own price elasticities for the purchase of
one or two units of the product are calculated.61 The elasticities are reported in Table 4.
I find a large contemporaneous reaction to the price reduction. The effect is particularly large for purchases
of 2 packs of the same size, which accords with the incentives for stockpiling. The temporary increase in
market share is caused by both substitution away from other Tesco pack sizes, and to a lesser extent from the
outside option. By construction, consumers cannot substitute away from other stores contemporaneously.62 A
the uniform distribution) should have faded completely after this time span.
57 They observe shoppers whilst they do their shopping in the supermarket and also interview them after they made their purchases.
58 936g is the most popular pack-size. Tesco has the largest market-share of all supermarkets.
59 Note that the graph shows only 5 time periods as market shares settle to a new equilibrium very quickly.
60 By construction, a temporary price change has no long term effect. Therefore, long term elasticities cannot be calculated for this case.
61 As I do allow consumers to purchase 1 or 2 units of each pack-size, these are treated as different goods in the estimation. As price
changes will apply to one or several units of a certain pack size, I do aggregate all units of the same pack size in order to compute the market
share. In order to do this I treat the outside option as one unit. The total market size is not fixed in this case, as even with a fixed number of
consumers the total number of units (of inside and outside goods) can vary.
62 As store choice is fixed, an unanticipated change in prices has no influence on store traffic in the time period of the price change. It can
only have an impact on market shares in time periods after the initial price change because of changes in inventory holdings.
26
permanent price change leads to a similar contemporaneous reaction with markets shares staying at the new
level afterwards. Note that with a lower expected price, the incentive to search has become stronger. Contrary
to the temporary reduction, we now see a contemporaneous substitution away from other stores. This happens
as consumers that visit stores other than Tesco now have a higher incentive to wait for a trip to Tesco. This
reduces the share of other stores to the benefit of Tesco.
I observe almost no post-promotion dip, despite a very large contemporaneous reaction. This is driven by
the small proportion of consumers that are actually aware of the price change, 70 percent do not search for
detergent. Thus, there is a strong reaction from those that are aware of the change and bring their purchase
forward, but on aggregate this does not cause a significant decrease in sales in later periods. This is consistent
with lack of a post-promotion dip in aggregate data (see Hendel and Nevo (2003), Heerde, Leeflang, and Wittnik
(2000) and Neslin and Stone (1996)).
I also look at price changes for all pack-sizes of Fairy at one particular store (Tesco) and for one product (a
936g pack of Fairy) across all stores and find largely similar patterns of adjustment. The price elasticities and
the adjustment for these cases is reported in the appendix (Table A2 and Figure A1).63
9
Conclusion
A structural model that incorporates search and stockpiling is presented in this paper. The same framework
can be used for the analysis of any storable grocery item. Modeling search will be particularly relevant for
products where the inter-purchase duration is relatively long. When applying the model to purchase data for
laundry detergent, I find that search costs are statistically and economically significant. They have a large
impact on purchase behavior, as around 70 percent of shopping trips without a purchase can be attributed to the
consumer not searching for the product. I also find that the probability of considering a purchase is a function
of trip characteristics. Overall expenditure in the store and the number of other products purchased in the same
category significantly lower the search cost, with the number of other cleaning products having the biggest
impact.
With consumers not being aware of prices on most of their shopping trips, marketing tools other than pricing,
such as advertising and preferential display, become very important. According to the findings of this paper,
retailers should raise awareness of price whenever they run a promotion.
Furthermore, I am able to analyze substitution patterns between products and stores in more detail than
previous research. The simulation of price elasticities accords with the well-known absence of a post-promotion
dip. Temporary price reductions have little impact on competing stores, but a large impact on the product / store
for which the price was lowered. Permanent reductions also lead to substantially higher sales, with market
63 I
use the same set of random draws for each of the different cases.
27
shares adjusting almost immediately. Supermarkets suffer significantly from permanent price reductions in
competing stores.
Finally, the model predicts lower price sensitivity and therefore higher market power for manufacturers and
retailers. Obtaining the correct price elasticities is an important ingredient for understanding consumer behavior
as well as optimal pricing and the general marketing strategy on the supply side.
In future research it would be interesting to incorporate category level search and brand level search in one
unifying framework. This would allow the researcher to look at substitution across brands as well as pack-sizes
and stores.
28
References
ACKERBERG , D. A. (2003): “Advertising, Learning, and Consumer Choice in Experience Good Markets: An
Empirical Examination,” Management Science, 44(3), 1007–1040.
A LLENBY, G. M.,
J. L. G INTER (1995): “The Effects of In-Store Displays and Feature Advertising on
AND
Consideration Sets,” International Journal of Research in Marketing, 12, 67–80.
A NDREWS , R. L.,
AND
T. C. S RINIVASAN (1995): “Studying Consideration Effects in Empirical Choice
Models Using Scanner Panel Data,” Journal of Marketing Research, 32(1), 30–41.
A SSUNCAO , J. L.,
R. J. M EYER (1993): “The Rational Effect of Price Promotions on Sales and Con-
AND
sumption,” Management Science, 39(5), 517–535.
B ELL , D. R.,
AND
C. A. L. H ILBER (2006): “An empirical test of the theory of sales: do household storage
constraints affect consumer and store behavior?,” Quantitative marketing and economics, 4(2), 87–117.
B ELL , D. R., G. I YER ,
AND
V. PADMANABHAN (2002): “Price Competition Under Stockpiling and Flexible
Consumption,” Journal of Marketing Research, 39(3), 292–303.
B ERRY, S., J. L EVINSOHN , AND A. PAKES (1995): “Automobile Prices in Market Equilibrium,” Econometrica,
63(4), 841–890.
B RONNENBERG , B. J.,
AND
W. R. VANHONACKER (1996): “Limited Choice Sets, Local Price Response and
Implied Measures of Price Competition,” Journal of Marketing Research, 33(2), 163–173.
C HING , A., T. E RDEM ,
AND
M. K EANE (2009): “The Price Consideration Model of Brand Choice,” Journal
of Applied Econometrics, 24, 393–420.
D ICKSON , P. R.,
AND
A. G. S AWYER (1990): “The Price Knowledge and Search of Supermarket Shoppers,”
The Journal of Marketing, 54(3), 42–53.
D RAGANSKA , M.,
AND
D. K LAPPER (2009): “Choice Set Heterogeneity and the Role of Advertising: An
Analysis with Micro and Macro Data,” unpublished manuscript.
E RDEM , T., S. I MAI ,
AND
M. P. K EANE (2003): “Brand and Quantity Choice Dynamics Under Price Uncer-
tainty,” Quantitative Marketing and Economics, 1, 5–64.
E RDEM , T.,
AND
M. P. K EANE (1996): “Decision-Making under Uncertainty: Capturing Dynamic Brand
Choice Processes in Turbulent Consumer Goods Markets,” Marketing Science, 15(1), 1–20.
F OK , D.,
AND
R. PAAP (2009): “Modeling Category-Level Purchase Timing with Brand-Level Marketing
Variables,” Journal of Applied Econometrics, 24, 469–489.
29
G OEREE , M. S. (2008): “Limited Information and Advertising in the US Personal Computer Industry,” Econometrica, 76(5), 1017–1074.
G OWRISANKARAN , G., AND M. RYSMAN (2007): “Dynamics of Consumer Demand for New Durable Goods,”
unpublished manuscript.
G UPTA , S. (1991): “Stochastic Models of Interpurchase Time with Time-dependent Covariates,” Journal of
Marketing Research, 28, 1–15.
H ARTMANN , W. R.,
AND
H. S. NAIR (2010): “Retail Competition and the Dynamics for Tied Goods,” Mar-
keting Science, 29(2), 366–386.
H AUSER , J. R. (1978): “Testing the Accuracy, Usefulness, and Significance of Probabilistic Choice Models:
An Information-Theoretic Approach,” Operations Researc, 26(3), 406–421.
H EERDE , H. J. V., P. S. H. L EEFLANG ,
AND
D. R. W ITTNIK (2000): “The Estimation of Pre- and Postpro-
motion Dips with Store-Level Scanner Data,” Journal of Marketing Research, 37(3), 383–395.
H ELSEN , K.,
AND
D. C. S CHMITTLEIN (1993): “Analyzing Duration Times in Marketing: Evidence for the
Effectiveness of Hazard Rate Models,” Marketing Science, 12(4), 395–414.
H ENDEL , I.,
AND
A. N EVO (2003): “The Post-Promotion Dip Puzzle: What do the Data Have to Say?,”
Quantitative Marketing and Economics, 1(4), 409–424.
(2006): “Measuring the Implications of Sales and Consumer Inventory Behavior,” Econometrica, 74(6),
1637–1673.
H ONG , H.,
AND
M. S HUM (2006): “Using price distributions to estimate search costs,” RAND Journal of
Economics, 37(2), 257–275.
H ORTAÇSU , A.,
AND
C. S YVERSON (2004): “Search Costs, Product Differentiation, and Welfare Effects of
Entry: A Case Study of SP 500 Index Funds,” The Quarterly journal of economics, 119(4), 403–456.
H OYER , W. D. (1984): “An Examination of Consumer Decision Making for a Common Repeat Purchase
Product,” The Journal of Consumer Research, 11(3), 822–829.
JAIN , D. C.,
AND
N. J. V ILCASSIM (1991): “Investigating Household Purchase Timing Decision: A Condi-
tional Hazard Function Approach,” Marketing Science, 10, 1–23.
KOULAYEV, S. (2009): “Estimating Demand in Search Markets: The Case of Online Hotel Bookings,” FRB
working paper.
30
L ACH , S. (2006): “Existence And Persistence Of Price Dispersion: An Empirical Analysis,” The Review of
Economics and Statistics, 84(3), 433–444.
M EHTA , N., S. R AJIV,
AND
K. S RINIVASAN (2003): “Price Uncertainty and Consumer Search: A Structural
Model of Consideration Set Formation,” Marketing Science, 22(1), 58–84.
M ELNIKOV, O. (2001): “Demand for Differentiated Durable Products: The Case of the U.S. Computer Printer
Market,” unpublished manuscript.
M ITRA , A. (1995): “Advertising and the Stability of Consideration Sets over Multiple Purchase Occasions,”
International Journal of Research in Marketing, 12, 81–94.
M ORAGA -G ONZALEZ , J. L., Z. S ANDOR ,
AND
M. R. W ILDENBEEST (2009): “Consumer Search and Prices
in the Automobile Market,” unpublished manuscript.
N ESLIN , S. A.,
AND
L. G. S. S TONE (1996): “Consumer inventory sensitivity and the postpromotion dip,”
Marketing Letters, 7(1), 77–94.
N IEROP, E. V., R. PAAP, B. B RONNENBERG , P. H. F RANSES ,
AND
M. W EDEL (2005): “Retrieving Unob-
served Consideration Sets from Household Panel Data,” Econometric Institute Report.
P ESENDORFER , M. (2002): “Retail Sales. A Study of Pricing Behavior in Supermarkets,” Journal of Business,
75(1), 33–66.
ROBERTS , J. H.,
AND
J. M. L ATTIN (1991): “Development and Testing of a Model of Consideration Set
Composition,” Journal of Marketing Research, 28(4), 429–440.
RUST, J. (1987): “Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher,”
Econometrica, 55(5), 999–1033.
S ALOP, S.,
AND
J. E. S TIGLITZ (1982): “The Theory of Sales: A Simple Model of Equilibrium Price Disper-
sion with Identical Agents,” American Economic Review, 72(5), 1121–1130.
S ANTOS , B. I. D. L., A. H ORTACSU ,
AND
M. W ILDENBEEST (2009): “The Price Consideration Model of
Brand Choice,” NET Institute Working Paper, (09-23).
S CHIRALDI , P. (2009):
“Automobile Replacement:
A Dynamic Structural Approach,” Unpublished
Manuscript, London School of Economics.
S EETHARAMAN , P. B. (2004): “The Additive Risk Model for Purchase Timing,” Marketing Science, 23(2),
234–242.
31
S EETHARAMAN , P. B.,
AND
P. K. C HINTAGUNTA (2004): “The Proportional Hazard Model for Purchase
Timing: A Comparison of Alternative Specifications,” Journal of Business and Economic Statistics, 21,
368–382.
S ORENSEN , A. (2000): “Equilibrium Price Dispersion in Retail Markets for Prescription Drugs,” Journal of
Political Economy, 108(4), 833–850.
S TIGLER , G. J. (1961): “The Economics of Information,” Journal of Political Economy, 69(3), 213–225.
S UN , B., S. A. N ESLIN , AND K. S RINIVASAN (2003): “Measuring the Impact of Promotions on Brand Switching When Consumers Are Forward Looking,” Journal of Marketing Research, 11, 389–405.
U RBANY, J. E., P. R. D ICKSON ,
AND
A. G. S AWYER (2000): “Insights Into Cross- and Within-Store Price
Search: Retailer Estimates Vs. Consumer Self-Reports,” Journal of Retailing, 76(2), 243–258.
VARIAN , H. R. (1980): “A Model of Sales,” American Economic Review, 70(4), 651–659.
V ILCASSIM , N. J., AND D. C. JAIN (1991): “Modeling Purchase-timing and Brand-switching Behavior Incorporating Explanatory Variables and Unobserved Heterogeneity,” Journal of Marketing Research, 28, 29–41.
WALTERS , R. G. (1991): “Assessing the Impact of Retail Price Promotions on Product Substitution, Complementary Purchase, and Interstore Sales Displacement,” Journal of Marketing, 55(2), 17–28.
WALTERS , R. G.,
AND
H. J. R INNE (1986): “An Empirical Investigation into the Impact of Price Promotions
on Retail Store Performance,” Journal of Retail, 62(3), 237–266.
32
900 g
Ariel
Bold
Daz
Fairy
Tesco
Mean
Std . Dev.
Min
Max
Weeks
Available
Market
Share
2.59
2.50
2.38
2.62
1.86
0.203
0.194
0.114
0.203
0.248
2.09
2.25
1.88
2.42
1.00
2.94
3.00
2.60
3.02
3.00
267
235
267
267
312
25.43
23.20
16.89
23.96
10.51
Mean
Std . Dev.
Min
Max
Weeks
Available
Market
Share
4.56
4.57
4.31
4.72
3.43
0.484
0.435
0.381
0.500
0.511
2.48
3.29
2.99
3.00
2.23
5.15
5.15
4.79
5.15
3.98
312
310
270
296
263
35.72
11.13
12.38
20.55
20.22
1.8 kg
Ariel
Bold
Daz
Fairy
Tesco
Table 1a: Descriptive Statistics: Prices and Market Shares (across Brands). The table shows the price
distribution for different brands across supermarkets and over time. The two most common pack-sizes 900g
and 1.8kg are reported. The table also reports how many weeks each pack-size was available for (out of 312
weeks in total) as well as the market share over the sample period.
Fairy at
Tesco
640 g
936 g
1320 g
1920 g
2340 g
2496 g
Mean
Std. Dev.
Min
Max
Weeks
Available
Market
Share
n.a.
2.62
3.48
4.72
4.88
5.15
0.203
0.000
0.500
0.000
0.008
2.42
3.48
3.00
4.88
5.15
3.02
3.48
5.15
4.88
5.19
267
45
296
14
24
43.75
4.52
45.51
4.52
1.70
Table 1b: Descriptive Statistics: Prices and Market Shares (Fairy at Tesco). The table shows the price
distribution for different pack-sizes of Fairy at Tesco. It also reports how many weeks each pack-size was
available for (out of 312 weeks in total) as well as the market share over the sample period. A 640g pack was
never sold at Tesco (but at other supermarkets) and is therefore denoted by n.a.
33
Fairy,
936 g
ASDA
Morrisons
Other Stores
Sainsbury’s
Tesco
Mean
Std. Dev.
Min
Max
Weeks
Available
Market
Share
2.59
2.64
2.77
2.75
2.62
0.189
0.213
0.261
0.198
0.203
2.42
1.99
1.99
2.49
2.42
2.88
2.99
3.47
2.99
3.02
265
269
268
312
267
25.97
21.18
9.48
10.00
33.37
Table 1c: Descriptive Statistics: Prices and Market Shares (Fairy, 936g Pack). The table shows the price
distribution for a 936g pack of Fairy at different supermarkets. It also reports how many weeks the product was
available for at each supermarket (out of 312 weeks in total) as well as the market share over the sample period.
The market share is based on all pack-sizes at all 5 supermarkets.
Store
Weeks
Market
Share
Adjusted
Market
Share
Brand
Ariel
Bold
Daz
Fairy
Tesco
30.79
17.17
16.73
21.35
13.96
Pack-Size
640 g
936 g
1320 g
1920 g
2340 g
2496 g
293
1381
243
1331
38
80
1.45
50.23
6.18
38.77
2.24
1.13
2.92
21.52
15.05
17.23
34.88
8.39
Store
ASDA
Morrisons
Other
Sainsbury’s
Tesco
19.26
15.91
10.44
16.08
38.32
Table 1d: Descriptive Statistics: Aggregate Market Shares. The table shows the aggregate market shares
for each brand, pack-size and the market share for each supermarket. The market-shares are based on a simple
count of purchases, i.e. different pack-sizes are all weighted equally. Store weeks denotes the sum of the
number of weeks the product was available at each store. With 312 weeks and 5 supermarkets the maximum
possible number of store week is 1560. The adjusted market shares use the store weeks as weights and shows
how popular the product was conditional on being available. Specifically the market share is divided by store
weeks and then re-scaled in order for the adjusted shares to add up to 100 percent. This adjustment is only
done for the pack-size dimension as there is little variation in availability across the other dimensions (except
for Tesco’s own brand of detergent, which is not available in any other supermarket).
34
Dependent Variable
Sample
Household Dummies
Price
(1)
(2)
(3)
(4)
(5)
Purchase
Dummy
Purchase
Dummy
Purchase
Dummy
Purchase
Dummy
Purchase
Dummy
Full
Sample
Full
Sample
Full
Sample
Full
Sample
Full
Sample
No
No
No
No
Yes
-0.419***
(0.0468)
-0.442***
(0.0465)
-0.218***
(0.0616)
-0.222***
(0.0667)
-0.252***
(0.0708)
0.177***
(0.0430)
0.395***
(0.0589)
Relative
Expenditure
0.889***
(0.0294)
Other Products in
the same Category (1)
0.221***
(0.0125)
0.212***
(0.0131)
0.234***
(0.0149)
Other Products in
the same Category (2)
0.0470***
(0.00197)
0.0453***
(0.00261)
0.0325***
(0.00385)
686
686
686
Number of
Households
686
686
Table 2a: Multinomial Logit (Reduced-Form) Estimation: Trip Characteristics. The table shows results
from multinomial logit regressions. *** denotes significance at the 1 percent level, ** at the 5 percent level and
* at the 10 percent level. An observation is a shopping trip of a particular household, time periods without a
shopping trip are dropped. The dependent variable is a dummy equal to one for one of the available options in
each time period. The household can choose to purchase one of the available products (see text for details) or not
purchase anything. The utility of the outside option is normalized to zero. All reported covariates are discussed
extensively in the text. A set of supermarket dummies is included, but not reported in the table. When household
dummies are included in column (5), they enter all the options except the outside option and effectively capture
the household specific average purchase probability. In these regressions none of the variables have a structural
explanation in the sense of representing parameters in an agent’s utility function.
35
(1)
(2)
(3)
(4)
Dependent Variable
Purchase
Dummy
Purchase
Dummy
Purchase
Dummy
Purchase
Dummy
Price
-0.418***
(0.0499)
-0.410***
(0.0499)
-0.424***
(0.0502)
-0.426***
(0.0502)
Time since last
Purchase
0.0350***
(0.0026)
0.0404***
(0.00266)
0.114***
(0.0115)
Time since last
Purchase squared
-0.00255***
(0.00045)
Volume previously
purchased
Number of
Households
-0.384***
(0.0372)
-0.453***
(0.0378)
-0.481***
(0.0382)
686
686
686
686
Table 2b: Multinomial Logit (Reduced-Form) Estimation: Stockpiling. The table shows results from multinomial logit regressions. *** denotes significance at the 1 percent level, ** at the 5 percent level and * at the
10 percent level. An observation is a shopping trip of a particular household, time periods without a shopping
trip are dropped. The dependent variable is a dummy equal to one for one of the available options in each time
period. The household can choose to purchase one of the available products (see text for details) or not purchase
anything. The utility of the outside option is normalized to zero. All reported covariates are discussed extensively in the text. A set of supermarket dummies is included, but not reported in the table. In all regressions,
lagged purchase characteristics are included. The first observation for each household is therefore the shopping
trip after their first purchase. Before this the lagged variable cannot be defined. ”Time since last purchase” is
a count of the weeks elapsed since the last purchase. The results are to be interpreted as reduced-form as they
show the importance of dynamic aspects by including proxy variables into a static framework. The variables do
not have a structural explanation in these regressions.
36
Dependent Variable
Sample
(1)
(2)
(3)
(4)
(5)
Purchase
Dummy
Purchase
Dummy
Purchase
Dummy
Purchase
Dummy
Purchase
Dummy
Full
Sample
Households
without a car
Household that
mostly shop on
Foot
Households
without a Car
Household that
mostly shop on
Foot
Only Weekend
Trips
Only Weekend
Trips
Distance
-1.131
(0.69)
-2.301
(4.973)
-3.41
(5.019)
1.048
(4.025)
-1.073
(4.49)
Number of
Household-Trips
113498
17100
10425
4950
2850
Table 2c: Multinomial Logit (Reduced-Form) Estimation: Transport Costs. The table shows results from
multinomial logit regressions. *** denotes significance at the 1 percent level, ** at the 5 percent level and *
at the 10 percent level. An observation is a shopping trip of a particular household, time periods without a
shopping trip are dropped. The dependent variable is a dummy equal to one for one of the available options in
each time period. The household can choose to purchase one of the available products (see text for details) or not
purchase anything. The utility of the outside option is normalized to zero. All regressions replicate column (4) of
table (2a) in terms of covariates, but also include the distance to the supermarket. They regressions differ in the
selection of observations. Column (1) reports the coefficient on distance for the full sample. Columns (2) and (3)
only use households that do not own a car or do not use it for shopping. Distance should be a more meaningful
measure of transport costs as the trips do not vary in terms of the means of transport. Columns (4) and (5)
additionally condition on weekend trips as the distance from the household’s home might be a more appropriate
measure for these trips. During the week a store visit might happen on the way to work. Distance is insignificant
in all regressions. The number of observations (household-week combinations) decreases substantially when
restricting the sample.
37
Price
Coefficient
(α)
Rate of
Consumption
(τ )
Below Median Income
Above Median Income
Low Average Consumption
High Average Consumption
Storage
Cost
(cstorage )
Household Size Less than Four
Search
Cost
(e
s)
Below Median Income
Trip
Characteristics
Household Size Four or Larger
Above Median Income
Relative Expenditure
# of Products Purchased in the Same
(Narrow) Product Category
# of Products Purchased in the Same
(Wider) Product Category
Observations
Households
Purchases
Shopping Trips
Log-likelihood
AIC
BIC
With
Search Stage
Without
Search Stage
0.4489***
(0.0027)
0.4410***
(0.0025)
0.5293***
(0.0018)
0.5715***
(0.0023)
0.3780***
(0.0087)
0.5848***
(0.0089)
0.1842***
(0.0034)
0.4031***
(0.0039)
0.2514***
(0.0042)
0.2405***
(0.0039)
0.2955***
(0.0011)
0.2664***
(0.0013)
9.5152***
(0.0383)
10.2860***
(0.0394)
-0.0976***
(0.0025)
-0.2138***
(0.0020)
-0.0037***
(0.0003)
686
18210
113498
686
18210
113498
-80991
162014
162168
-117120
234262
234368
Table 3: Estimation Results from the Dynamic Model. The table shows results from estimating the full dynamic model with and without a search stage. *** denotes significance at the 1 percent level, ** at the 5 percent
level and * at the 10 percent level. The full sample of households and time periods is used in the estimation.
The parametrization of the model is discussed in the text as well as the different types of heterogeneity. For α,
τ , cstorage and se different parameter values are estimated for different subsamples of the population. se denotes
the overall scale of the search cost, whereas the three trip characteristics shift the search cost.
38
936g Pack of Fairy
in Tesco
Temporary Price Change
(Immediate)
Permanent Price Change
(Immediate)
Permanent Price Change
(Long Term)
Own
(total units)
1 Pack
2 Packs
Other
Products
(Same
Store)
Other
Stores
(Same
Product)
Outside
Option
Search
3.307
1.406
10.836
-0.671
0.000
-0.183
0.000
3.642
1.649
11.664
-0.080
-0.619
-0.063
-0.021
3.224
1.732
9.819
-0.072
-0.563
-0.065
-0.021
Table 4: Price Elasticities: 936g Pack of Fairy in Tesco The table reports detailed information on price
elasticities for a 936g pack of Fairy at Tesco, the most popular brand / pack-size / supermarket combination in
the sample. This particular combination is used to illustrate the general pattern. Price elasticities are reported
for temporary changes and permanent changes in the time period of the change (short term elasticity) as well
as after 5 time periods for the case of a permanent change (long term elasticity). Reactions of one and two unit
purchases of the product on promotion are reported. The effect on the outside option is also reported as well as
the impact on other brands and pack-sizes (at the same store) and on the same brand / pack-size combination
(i.e. Fairy 936g) in other stores. Changes in the search behavior are reported in the final column.
39
no search (d=ns)
j=0
Search Stage (t)
Search Stage (t+1)
no purchase
j=1
search (d=s)
j=2
Purchase Stage (t)
purchase
...
j=J
Figure 1: Timing in the Structural Model. The graph illustrates the decisions a consumer has to take in a
given time period. First he has decide whether to search (d=s) or not to search (d=ns). If he decides to search
he then has to take a decision which product (j ∈ J ∪ {0}) to purchase. If he does not search, he does not have
to take another decision in the current time period. The consumer will start the next time period again in the
search stage.
40
Inventory
Time
Purchase Now
Inventory
Promotion!
Time
Wait
Inventory
Promotion!
Time
Figure 2: Inventory Dynamics: Purchase Acceleration All three graphs represent the dynamic behavior of
consumer inventory over time. The dashed grey arrows represent a slow decrease in inventory due to consumption. The solid grey arrows represent a discrete jump in the inventory holding when a new purchase is made.
The top graph illustrates the general pattern of purchases and consumption in the absence of promotions. The
middle and the bottom graph illustrate the consumer’s option when encountering a promotion whilst still having
a relatively large inventory. He can either choose to purchase immediately (middle graph) or to wait until his
inventory has decreased further (bottom graph). A purchase acceleration will lead to a higher than usual inventory but the product can be purchased at a lower price. If the consumer waits instead, the promotion will most
likely be over when he purchases, but he will be avoid an increase in inventory.
41
Figure 3: Dynamic Adjustment to Price Changes. The graphs show reaction to temporary (left graph) and
permanent (right graph) price changes. The dynamic adjustment is shown for a 936g pack of Fairy at Tesco.
The two graphs show reactions to a 50 percent price reduction. The units on the x-axis are time periods, with
the change in price occurring in period 2. In case of a temporary change prices are back to the original level in
time period 3. On the y-axis the reaction in terms of purchases is measured in percentages.
42
Appendix
Mean
Std. Dev.
Min
Max
Weeks
Available
Market
Share
0.189
0.272
0.223
2.42
2.39
3.18
2.88
3.48
4.98
265
49
170
13.05
2.10
4.11
0.213
0.259
0.474
0.004
0.092
1.99
2.89
3.49
4.88
4.99
2.99
3.89
5.39
4.89
5.19
269
34
252
24
15
10.64
0.43
4.17
0.51
0.17
0.216
0.261
0.397
0.609
0.22
1.99
2.39
2.91
2.69
3.47
4.09
8.46
293
268
64
311
1.45
4.76
0.82
3.32
0.224
4.99
5.82
27
0.09
0.198
0.425
0.485
2.49
2.39
3.18
2.99
3.59
5.39
312
51
302
5.02
1.11
9.73
0.085
5.19
5.39
14
0.23
0.203
0.000
0.500
0.000
0.008
2.42
3.48
3.00
4.88
5.15
3.02
3.48
5.15
4.88
5.19
267
45
296
14
24
16.76
1.73
17.44
1.73
0.65
ASDA
640 g
936 g
1320 g
1920 g
2340 g
2496 g
n.a.
2.59
3.4
4.76
n.a.
n.a.
640 g
936 g
1320 g
1920 g
2340 g
2496 g
n.a.
2.64
3.48
4.73
4.88
5.14
640 g
936 g
1320 g
1920 g
2340 g
2496 g
2.10
2.77
3.45
4.78
n.a.
5.25
640 g
936 g
1320 g
1920 g
2340 g
2496 g
n.a.
2.75
3.39
4.96
n.a.
5.35
640 g
936 g
1320 g
1920 g
2340 g
2496 g
n.a.
2.62
3.48
4.72
4.88
5.15
Morrisons
Other Stores
Sainsbury’s
Tesco
Table A1: Descriptive Statistics: Prices and Market Shares. The table shows the price distribution for
different pack-sizes of Fairy at the 5 different supermarkets. It also reports how many weeks each pack-size was
available for, out of 312 weeks in total, as well as the market share over the sample period. Pack-sizes that were
never sold at a particular supermarket are denoted by n.a.
43
936g Pack of Fairy
(All Stores)
Temporary Price Change
(Immediate)
Permanent Price Change
(Immediate)
Permanent Price Change
(Long Term)
Fairy (All Sizes)
in Tesco
Temporary price change
(immediate)
Permanent price change
(immediate)
Permanent price change
(long term)
936g Pack of Fairy
in Tesco
Temporary price change
(immediate)
Permanent price change
(immediate)
Permanent price change
(long term)
Own
(total units)
1 Pack
2 Packs
Other
Products
(Same
Store)
Outside
Option
Search
3.204
1.543
10.622
-0.711
-0.433
0.000
2.994
1.645
39.038
-0.775
-0.384
-0.054
2.774
1.561
36.938
-0.764
-0.362
-0.052
Own
(total units)
2 Packs
Other
Stores
(Same
Product)
Outside
Option
Search
1 Pack
2.826
0.570
3.796
0.000
-0.379
0.000
3.865
0.548
4.514
-0.458
-0.443
-0.085
3.146
0.536
3.878
-0.606
-0.309
-0.080
Own
(total units)
2 Packs
Other
Products
(Same
Store)
Other
Stores
(Same
Product)
Outside
Option
Search
1 Pack
3.307
1.406
10.836
-0.671
0.000
-0.183
0.000
3.642
1.649
11.664
-0.080
-0.619
-0.063
-0.021
3.224
1.732
9.819
-0.072
-0.563
-0.065
-0.021
Table A2: Price Elasticities. The table reports price elasticities for three types of changes: for one particular
pack-size of Fairy across all stores, for all sizes of Fairy at one store and for one size of Fairy at one particular
store. 936g and Tesco are the pack-size and supermarket used to illustrate the pattern. Price elasticities are
reported for temporary changes and permanent changes in the time period of the change (short term elasticity)
as well as after 5 time periods for the case of a permanent change (long term elasticity). Reactions of one and
two unit purchases of the product on promotion are reported. The effect on the outside option is also reported in
all cases. The reaction of other pack-sizes (at the same store) and of the pack-sizes on promotion in other stores
are reported (where appropriate). Changes in the search behavior are reported in the final column.
44
Price change for one product in all stores: temporary and permanent
200
200
150
150
100
100
50
50
0
-50
0
1
2
3
4
5
-100
-50
1
2
3
4
5
-100
936g Pack
Other Pack Sizes
936g Pack
Outside Option
Other Pack Sizes
Outside Option
Price change for all products in one stores (Tesco): temporary and permanent
200
200
150
150
100
100
50
50
0
0
-50
1
2
3
Tesco
4
5
-50
1
2
3
Tesco
Other Stores
4
5
Other Stores
Outside Option
Outside Option
Price change for one product in one stores (Tesco): temporary and permanent
200
200
150
150
100
100
50
50
0
-50
0
1
2
3
4
5
-50
1
2
3
4
936g Pack (Tesco)
936g Pack (Tesco)
Other Pack Sizes / Stores
Other Pack Sizes / Stores
Outside Option
Outside Option
5
Figure A1: Dynamic Adjustment to Price Changes. The graphs show reactions to temporary (left column)
and permanent (right column) price changes. The three rows of graphs show the dynamic adjustment for one
particular size across all stores, for all sizes of Fairy at one store, and for one pack-size of Fairy at one particular
store. 936g and Tesco are the pack-size and supermarket used to illustrate the pattern. All graphs show reactions
to a 50 percent price reduction for the respective type of promotion. The units on the x-axis are time periods,
with the change in price occurring in period 2. In case of a temporary change, prices are back to the original
level in time period 3. On the y-axis the reaction in terms of purchases is measured in percentages.
45