Why Does the Average Price of Tuna Fall During Lent?
ABSTRACT For many products the average price paid by consumers falls during periods of high demand. We use information from a large supermarket chain to decompose the decrease in the average price into a substitution effect, due to an increase in the share of cheaper products, and a price reduction effect. We find that for almost all the products we study the substitution effect explains a large part of the decrease. We estimate demand for these products and show the price declines are consistent with a change in demand elasticity and the relative demand for different brands. Our findings are less consistent with "loss-leader" models of retail competition.
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ABSTRACT: This paper studies a dynamic model of perfectly competitive price posting under demand uncertainty. Firms must produce output in advance. After observing aggregate sales in prior periods, firms post prices for their unsold output. In each period, the demand of a new batch of consumers is randomly activated. Existing customers who have not yet bought and then new customers arrive at the market in random order, observe the posted prices, and either purchase at the lowest available price or delay their purchase decision. We construct a sequential equilibrium in which the output produced and its allocation across consumers is efficient. Thus consumers endogenously sort themselves efficiently, with the highest valuations purchasing first. Transaction prices in each period rise continuously, as firms become more optimistic about demand, followed by a market correction. By the last period, prices are market clearing.Econometrica 01/2012; 80(3). · 3.82 Impact Factor
NBER WORKING PAPER SERIES
WHY DOES THE AVERAGE PRICE
OF TUNA FALL DURING LENT?
Working Paper 11572
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
We thank the James M. Kilts Center, GSB, University of Chicago for the data used in this study, and
Judy Chevalier, Anil Kashyap and Peter Rossi for comments on an earlier draft. The first author thanks
the NSF and the Sloan Foundation for support. The views expressed herein are those of the author(s) and
do not necessarily reflect the views of the National Bureau of Economic Research.
©2005 by Aviv Nevo and Konstantinos Hatzitaskos. All rights reserved. Short sections of text, not to
exceed two paragraphs, may be quoted without explicit permission provided that full credit, including ©
notice, is given to the source.
Why Does the Average Price of Tuna Fall During Lent?
Aviv Nevo and Konstantinos Hatzitaskos
NBER Working Paper No. 11572
For many products the average price paid by consumers falls during periods of high demand. We use
information from a large supermarket chain to decompose the decrease in the average price into a
substitution effect, due to an increase in the share of cheaper products, and a price reduction effect.
We find that for almost all the products we study the substitution effect explains a large part of the
decrease. We estimate demand for these products and show the price declines are consistent with a
change in demand elasticity and the relative demand for different brands. Our findings are less
consistent with "loss-leader" models of retail competition.
Department of Economics
2001 Sheridan Road
Evanston, IL 60208
549 Evans Hall #3880
Department of Economics
University of California
Berkeley, CA 94720-3880
A number of previous papers documented that retail prices for many products tend to fall
during periods of peak demand. Warner and Barsky (1995) show that the prices of several consumer
appliances fall in the period prior to Christmas. MacDonald (2000) documents that prices of many
food items decline in periods of seasonal demand peaks. Chevalier, Kashyap and Rossi (2003)
(CKR, hereafter) use a unique data set provided by a large retailer in the Chicago area, and find that
a price index for several products falls during periods of high demand. Examining these patterns
carefully they conclude that the decline in average prices is best explained by loss leader models of
advertising (Lal and Matutes, 1994).
It is somewhat counter-intuitive that prices do not rise during periods of high demand. As
documented by previous work, cited above, this seems to be the case in a wide range of industries.
Understanding what drives this is important for price theory and measurement. From the macro-
economic point of view, sales are a major source of nominal price variation in many retail markets.
Therefore, understanding what drives sales, and price rigidity during non-sale periods, has
implications for the macro-economy (Warner and Barsky, 1995, CKR, Bils and Klenow, 2004.)
In this paper, we build upon CKR, using their data to provide support for an alternative
explanation to the decline in the average price. Our explanation is based on a change in brand-level
demand. We focus on two changes. First, price sensitivity can be higher during periods of high
demand. If true this will lead to a lower equilibrium price. Demand might be more price elastic for
several reasons. The mix of consumers might be changing. For example, increased demand for tuna
during Lent comes mostly from a certain segment of the population that might have different price
sensitivity. Furthermore, a given consumer might be more price sensitive because the product is used
differently during a period of high demand. We provide examples below.
Second, the brand preferences within a product category might change. For example, eggs
used in an Easter egg hunt can be of lower quality than eggs eaten at breakfast. Beer bought for a
July 4th barbecue party can be of lower quality, either because of a public goods problem (you are
unlikely to consume most of what you bring to the party), or because after a few beers it is hard to
2The paper also mentions brand-level analysis that was performed on a small number of brands.
distinguish different brands. Most of the analysis in CKR is performed using a variable weights price
index:2 the prices of individual items are averaged using weights proportional to quantity sold.
However, if preferences for brands shift towards cheaper products, then such an index could
potentially be misleading. Even with no changes in prices a variable weights price index might
change due to a composition effect.
In order to provide support for our explanation we re-examine the CKR data. We start by
repeating their analysis using a fixed-weights price index. A fixed weights price index will not be
affected by a change in the composition of brands, and therefore if that is all that is happening, it will
show no decline. Indeed the results suggest that, for the product categories CKR identify as loss
leaders, a fixed-weights price index displays much smaller price declines (in some cases none at all).
Next, based on the initial analysis and for reasons we motivate below, we focus our attention on
tuna, which faces a high demand peak during Lent. We find that much of the increase in the quantity
sold is due to two products. These products, which are relatively cheap, nearly triple their market
share and interestingly do not reduce their prices. Some of the competitors indeed lower their prices,
in what seems to be a response to the decline in their market shares.
We also estimate weekly item-level demand for tuna. We find, as predicted by our
explanation, that consumers are more price sensitive during Lent and that the brand preferences
seem to change during Lent. Furthermore, we find no evidence that advertising is more effective
during Lent, which is a testable implication of the loss-leader theory. While we focus on tuna, our
results seem to be more general. We repeat the analysis for the other products studied by CKR and
find similar results: we find evidence consistent with a change in price sensitivity and brand
preferences, but less consistent with a theory of loss leaders.
There are two general lessons that can be learned from our analysis. First is the importance
of seriously considering product differentiation and its implications for the results. CKR advocate
the importance of incorporating retail behavior, but do so at the cost of treating the product as
(essentially) homogenous. We, on the other hand, place more emphasis on product differentiation
and find different results. Second, our results show that one has to be careful in using prices paid by
consumers to make inferences about supply side behavior. The observed prices might be driven, at
least in part, by consumer behavior and not by pricing.
The explanation we provide here is similar to, yet distinct from, the one offered by Warner
and Barsky (1995). They suggest that scale economies in search make the demand for the product
more elastic during aggregate peak demand periods. We propose an explanation that is based on a
change in the demand for the product during idiosyncratic peak demand periods. Moreover, our
explanation is based on a change in the relative demand for different brands. These differences
imply an alternative interpretation of the data. Indeed, some of our results, which we claim as
support for our explanation, are similar to the results CKR use as evidence against the Warner and
The rest of the paper is organized as follows. In Section 2 we summarize the basic patterns
found by previous work and the models proposed to explain these patterns. In Section 3 we discuss
our explanation in some detail. In Section 4 we present the data used in the analysis and a first cut
at various price indices for different product categories. In Section 5 we focus on a single category,
tuna. We estimate a brand level demand system and use it to show that: (i) price sensitivity increases
during Lent; (ii) there seems to be a change in brand preferences for tuna brands during Lent; and
(iii) there does not seem to be an increase in the efficiency of advertising during Lent. The first two
findings support our explanation, while the third seems to cast doubt on the loss-leader story. We
also show, in Section 5.3, that the results found for tuna are also mostly present in other product
2. Previous Findings and Explanations
Temporary price reductions are common in many industries. Yet, it is only fairly recently
that the economics literature has tried to empirically document and study patterns in these sales.
Pashigian (1988) and Pashigian and Bowen (1991) study “clearance sales” in the fashion industry.
In this industry prices tend to fall over the life cycle of the product. They find that markdowns
increased over time, as variety increased, and are more common in some types of clothes, where
variety and fashion are more important. They relate these findings to the predictions of a model of
store uncertainty about the future popularity of colors, patterns and fabrics.
Warner and Barsky (1995) continue where Pashigian (1988) and Pashigian and Bowen
(1991) left off. They collect four months of daily prices for eight items in several stores. The items
they study include an action figure toy, bathroom towels, a bicycle and several small appliances.
They find that prices tend to be marked down during weekends and before Christmas. Both are
periods of (exogenously) high demand. They interpret these patterns as support for a theory based
on increasing returns in the shopping technology. During periods of high demand consumers have
a higher incentive to be informed about prices, thus, the demand faced by a retailer is more elastic,
and therefore optimal prices are lower.
MacDonald (2000) documents a decrease in the price of food products at seasonal demand
peaks. He uses the observed quantity data in order to select periods of high demand, i.e., a peak
demand period is one in which the quantity sold is unusually high. He documents a decrease in the
national average monthly price of narrowly defined items during periods of high demand. The
analysis uses the largest selling item of the largest selling brand in each category. There are two
potential problems with this analysis. First, the demand peaks are defined using the quantity data.
In principle, the low prices might be causing the seemingly high demand. For some of the products
he examines this might seem unlikely, yet for a large number of the products this might be the case.
Second, a large number of products he examines have a peak in December, leaving the reader to
wonder if this is just a seasonal effect that is not category specific.
CKR re-examine the issue, but through the quality of the data and the careful design of the
study can address some of the potential problems in the MacDonald study. They use weekly item-
level scanner data from a single retailer in Chicago. In addition to prices and quantities, they have
a measure of wholesale price. We describe these data further below. Using this data set they examine
prices during peak and off peak demand periods. One of the major differences in the analysis is that
they define peak demand on a priori grounds, not using the observed quantity data. This allows them
3The exact number of items varies slightly between categories but is usually around 8-10.
to deal with the potential endogeneity of the definition of peak demand. Furthermore, they focus on
a smaller number of categories, carefully selected so that the peak demand periods do not fully
The first step in their empirical analysis is to document the decline in prices during the peak
demand periods. Instead of focusing on a single item in each category they generate a varying-
weights price index of the top items in each category.3 The weights are proportional to the quantities
sold of each item. They find that the log of the price index declines during peak demand periods.
Next they examine different theories that potentially explain the price declines. The first
class of theories they consider are those that suggest that demand might be more elastic than usual
during peak demand periods. Bils (1989) and Warner and Barsky (1995) are examples of such
theories. The Warner and Barsky model suggests that, with fixed costs of search and travel between
stores, consumers will search more during high demand periods. Thus, the demand facing a retailer
will be more price elastic and the optimal price is lower.
A second class of models are those that focus on dynamic interactions between firms. In the
spirit of Rotemberg and Saloner (1986), tacit collusion is sustained when the gains from defection
(i.e., charging a price below the collusive level) in the current period are lower than the expected
losses in future periods due to punishment. The incentive to cheat is highest during periods of peak
demand since the current gains from cheating are higher. Therefore, the price level that can be
sustained during high demand periods is lower. In examining the implications of this model CKR
focus on retailer competition, mainly because their results seem to suggest that retail prices decline
more than wholesale prices. Furthermore, they focus on competition across retailers for a basket of
products and not on a product-by-product level.
The third and final class of models are loss leader advertising models. CKR focus on the
formalization of Lal and Matutes (1994). In this model consumers do not know the prices of the
goods until they arrive at the store. They pay a transportation cost to get to the store and to go from
one store to another. If this cost is high enough the retailers will charge consumers their reservation
4Taken literally the model’s definition of high demand is different: it is high demand relative to the other
products. Thus, a product with seasonally high demand could still be a low demand product.
price (which is assumed identical for all consumers) once they arrive at the store, and their
transportation cost is sunk. Consumers foresee this strategy and therefore do not shop. The retailer’s
solution is to commit to a particular price by advertising it. If advertising was costless they would
advertise all products. Lal and Matutes assume that retailers pay an advertising cost per item
advertised. For items not advertised consumers assume that they will be charged their reservation.
In this model prices are not pinned down: any of the goods could be discounted enough to attract
consumers. As CKR show (in a two good case) if prices have to be non-negative then the retailer
will prefer to discount the good with the higher demand. The intuition is simple. The discount
needed for the lower demand product (given that the higher demand product will not be advertised
and priced at the reservation price) makes its price negative. CKR interpret high demand as high
demand relative to the typical demand for the product.4
CKR’s main strategy to separate these models is based on separating periods of overall high
demand (such as Christmas and Thanksgiving) and periods of product specific peak demand (such
as tuna during Lent). The first two models have a prediction for why prices are low during the
aggregate high demand periods but not during idiosyncratic peak demand periods . CKR show that
prices decline even during periods of product specific peak demand (e.g., tuna during Lent). They
provide two additional pieces of information. First, by estimating category-level demand regressions
they show that the overall demand does not seem to be more elastic, providing direct evidence
against the Warner and Barsky theory. Second, they show that products that are in peak demand are
more likely to be advertised.
There are a couple of reasons to be somewhat suspicious of the loss leader theory. First,
which product goes on sale is determined by the non-negativity constraint: a retailer puts the product
on sale that allows a large enough discount. While this effect is clear in a simple model, it seems
somewhat unlikely that in a real world market, with many additional complexities, this constraint
will bind. Second, and somewhat related, many of the products CKR examine are a small part of the
overall expenditure of a household in any given shopping trip. For example, a can of tuna costs
roughly 80 cents. Even if a household buys five cans during a high demand period and the discount
is 20 cents, or 25 percent (a much larger discount than what we see in the data), then the savings are
one dollar. Surely there are other ways to offer such, or much larger, savings.
3. Our Explanation
In this section we offer an alternative explanation as to why the average price declines during
peak demand periods. This explanation is consistent with prior findings, surveyed in the previous
section. In addition, we discuss the empirical implications that allow us to separate our explanation
from the loss leader model proposed by CKR. In the next sections we test these implications.
Our explanation relies on a change in brand-level demand. We focus on two changes in
particular: a change in demand elasticity and in relative demand for different brands during peak
demand for the category. The shift in the aggregate, or average, price sensitivity can occur for
several reasons. The demand of certain households might increase more than others (consider, for
example, the demand for tuna during Lent). If price sensitivity varies by households, then the
aggregate price sensitivity will differ between Lent and non-Lent periods. Alternatively, even for
a given household price sensitivity might vary if the use of the product changes. We provide some
While overall demand for a product (e.g., tuna) might increase, we claim that the increase
might be different for different brands (e.g., StarKist). There are several reasons why this might
occur. First, there might be a shift in household-level demand for different brands. Consider the case
of canned tuna. It could be used for various dishes, including tuna salad or tuna casserole. These
different uses might require different quality. For example, tuna casserole might require a lower
quality brand. If during Lent tuna casserole is eaten more frequently than tuna salad, relative to non-
Lent periods, then the relative demand for different brands will change.
Second, if we think of brands as representing different quality, then there might be
decreasing marginal utility from quality. Consider the example of beer during July 4th. A consumer
who might normally prefer a high quality beer might prefer a lower quality (and cheaper) brand
during July 4th. This might be either because after a few beers it is harder discern their quality, or
because of a public goods problem: if you bring beer to a party, for the most part it will be consumed
Third, just as is the case for price elasticity, even if brand preferences at the household level
remain constant there could be a change in the relative weights of different households. Not all
households increase their demand proportionally. Suppose there are two types of households. Type
A prefer brand 1 and type B prefer brand 2. If households of type A have a larger increase in demand
for the product than the overall relative increase in demand will be higher for brand 1.
There are several implications of our explanation that distinguish it from alternatives. First,
our explanation implies that the effect on a category-level price index will be different if one uses
a fixed-weights index versus a variable weight index. Since we claim there is a change in brand
preferences during some periods of high demand, then the change in weights is systematic, and we
expect the fixed weights index to give a different answer. In particular, if the shift is towards cheaper
brands, then we expect the fixed weights index to exhibit smaller drops during high demand periods.
Indeed, if all that is happening is a shift between brands, then this index should not drop at all.
Second, in order to test our explanation directly we look at brand-level data. We examine
prices of different brands to see which brands reduce their prices during periods of high demand.
We also examine quantities to see if all brands experience an increase in demand during periods of
category high demand. Finally, we estimate a brand-level demand system, allowing price sensitivity
and brand preferences to change between high demand periods and other periods.
Third, loss leader models imply that the effectiveness of advertising should be higher during
high demand periods. During non-peak demand periods advertising serves to induce brand switching
and also potentially bring consumers to the store. According to the loss-leader model, the aggregate
effect of bringing consumers to the store is much larger, during peak demand periods, since overall
demand is higher. Therefore, a brand’s increase in demand due to advertising, should be much larger
during peak demand periods. Our model does not imply a differential effect of advertising. So we
5Using the retail price and the profit margin we will recover the average acquisition price. Note that while we
refer to it as the wholesale price, it is not the economic marginal cost faced by the retailer.
can test this directly in a brand-level demand system.
4. Data and Preliminary Analysis
The data set used for the analysis is the same as the one used by CKR, and comes from the
Dominick’s Finer Foods (DFF) database at the University of Chicago Graduate School of Business.
DFF is the second largest supermarket chain in the Chicago metropolitan area, with a market share
of approximately 25 percent. The data are weekly store level data by universal product code (UPC)
and include units sales, retail price, profit margin (over the average acquisition price)5 and a deal
code. The deal code indicates what type of promotional activity, if any, took place. CKR report some
mistakes in the classification of the various activities. Thus, we will only use a binary variable which
equals one if any activity took place. The data cover approximately 400 weeks starting September
1989, in 29 different product categories. The data, including a detailed description of the variables
and the collection process, can be found at http://gsbwww.uchicago.edu/kilts/research/db/dominicks.
The key variables are defined, following CKR, as follows. Holiday dummy variables, which
capture high demand periods around holidays, equal 1 for the two weeks prior to the holiday, zero
otherwise. The Lent dummy variable equals 1 for the four weeks preceding the two week Easter
shopping period. The post Thanksgiving dummy variable equals 1 for the week following
Thanksgiving. The Christmas dummy variable equals one for the two weeks prior to Christmas as
well as the week after, in order to capture the New Years’s shopping period.
We supplement the DFF data with weather information from the Chicago Mercantile
Exchange daily data, creating weekly temperature corresponding to the DFF weeks. Using the mean
temperature (TEMP) we generated two variables: HOT = max(0, temp-49), COLD = max(0, 49-
temp). Forty nine degrees Fahrenheit is approximately the mean, and median, temperature in
We focus on the categories that CKR identified and we follow their definitions of a-priori
high demand periods. One of the advantages of following the CKR classification is that it is pre-
determined from our point of view. The categories we study are tuna, beer, oatmeal, cheese and
snack crackers. CKR study two additional seasonal categories: eating soup and cooking soup. We
decided to not examine these categories, since we felt uncomfortable in our ability to classify
products into each category. We also do not study the non-seasonal categories identified by CKR
(analgesics, cookies, crackers and dish detergent), since they seem to have little relevance for our
explanation. Summary statistics for the main variables for each of the product categories we used
are displayed in Table 1.
The expected periods of peak demand for each category, identified by CKR, are as follows.
For beer, hot weather, Memorial Day, July 4th, Labor Day and Christmas. The logic is that the
summer holidays are peak picnic time and Christmas includes a run up to New Year’s Eve. We also
added Superbowl Sunday. For tuna, the expected peak demand is Lent, a period in which many
Christians abstain from eating meat and eat fish instead. The cheese category has an expected peak
during Thanksgiving and Christmas, when cheese would either be used for cooking or served at
parties. A similar logic applies to peak demand for snack crackers at Thanksgiving and Christmas.
Finally, consumption of oatmeal is expected to go up during cold weather.
For each category we include the top 30 UPC’s. These products account for a significant
share, as can be seen in the last row of Table 1.
4.2 Preliminary Analysis
Before we examine the behavior of prices we present in Table 2 the change in total quantity
sold aggregated across stores and products within a week. The dependent variable is the quantity
sold, measured in thousands of pounds. Similar results can be found if we use either revenue or
quantity measured in units.
Next we examine the behavior of category level price indices. The indices are computed in
the following way. The price data are collected by store, UPC and week. Let be the price per
ounce of product (i.e., UPC) j at store s in week t. The price index in time t is
where are weights. We report results using two price indices. The first is a variable weight price
index, in which is the quantity share of product j sold in store s in week t of the total quantity sold
in t. The second is a fixed weight in which is the quantity share of product j sold in store s in the
sample period of the total quantity sold in the sample period, normalized so the shares in each week
sum to one. The variable weight index is analogous to the one used by CKR (we discuss the
difference below). We also report results where we replace the retail price with the retail markup
(retail price minus the wholesale price). We also computed, but do not report, these indices using
revenue shares instead of quantity shares, and using the logarithm of price instead of price.
Table 3 reports results from OLS regressions where the dependent variable is the weekly price
index in each category. In columns titled Fixed and Variable, the price index is a fixed- and variable-
weight price index, respectively. As we described in the previous section we focus on the categories
identified by CKR as having potential for loss leader periods. Bold type indicates a period of
expected high demand peaks, following CKR’s classification.
Examining the results in the Variable columns we generally find results similar to CKR. The
price index tends to go down during expected high demand periods. Our results tend to be less
significant than theirs, and we tend to find more unexpected price reductions (for example in the
cheese and snack crackers categories). The differences between our results and CKR’s finding could
be explained by differences in the construction of the data. The set of UPC’s we use do not match
exactly: we have a larger number of UPC’s. We created the index using price, instead of logarithm
of price, and quantity shares, instead of revenue shares. Finally, we report ordinary least square
results, with robust standard errors, instead of generalized least squares. Of all of these, the difference
that seems to matter the most is the functional form. Repeating our analysis using the logarithm of
price we re-produce almost exactly the CKR numbers.
The results in the Fixed columns tend to present a somewhat different picture. Several of the
expected effects are no longer statistically significant. Furthermore, some of the effects are much
smaller in magnitude. For example, the coefficient on Lent in the tuna category using the fixed-
weights index is roughly a third of the same coefficient using a variable-weights index. This suggests
that much of the reduction in the average price of tuna during Lent is coming from a substitution
effect, as we suggested.
The prices of tuna during Christmas and Thanksgiving provide us with another opportunity
to see how the two price indices differ. The results in the variable column suggest that the price of
tuna during Christmas and Thanksgiving is higher. One could think of this as evidence for the loss-
leader story: since the demand for tuna is low during these periods they are not used as loss-leaders
and are therefore less likely to be on sale. However, when we look at the results in the Fixed column
a different picture emerges. It is not that tuna is more expensive, but that there seems to be
substitution towards more expensive brands, a result that is both intuitive and consistent with our
If all that was happening during peak demand periods was a substitution effect, then the fixed-
weights index would not change. The fact that it is decreasing suggests that at least some products
are reducing their price. That, in most cases, the reduction in the fixed weights index is substantially
smaller than the reduction in the variable weight index, suggests that a large part of the story is due
to a change in composition. The remaining drop is due to a reduction in prices that could be due to
several stories that we try to separate below.
CKR motivate the use of a variable weights index by claiming that the products are close
substitutes and therefore from the consumer’s perspective this is the relevant measure. They claim
that a fixed weights index will not capture the effective price level. Whether or not these brands are
indeed close substitutes is an empirical matter. However, even taking their claim as given, this is not
the relevant argument. We are not asking if consumers are better or worse off. We are using the price
index to summarize an average price in order to learn about the supply side.
In Table 4 we present results from the same regressions as those reported above, using
markups as the dependent variables. In order to construct the markup we subtracted the average
acquisition cost from the retail price. If a price reduction was completely driven by a change in the
retail price, then the coefficients in Table 4 should be identical to those in Table 3. On the other hand,
if the price reductions are only because the wholesale price drops and the reductions are passed-
through completely to consumers, then the coefficients in Table 4 should be insignificant.
The results for the tuna and oatmeal categories suggest that much of the price reductions in
these categories during Lent and cold weeks, respectively, are driven to a large extent by changes in
the wholesale prices. On the other hand, the results in the beer, cheese and snack crackers categories
suggest that the reduction in these categories are driven by reduction at the retail level. As we
discussed in Section 2, the way CKR propose to separate between their model and some of the
alternatives, is by comparing overall high demand periods (like Christmas and Thanksgiving) to
category specific peak demand periods (like Lent for tuna and cold for oatmeal). These results
suggest that retailer behavior is driving the price reduction in categories that have expected peaks
during periods of overall high demand, while retail behavior is not significant in those cases where
the demand is category specific. This provides another piece of evidence that the loss-leader model
might not be as relevant as CKR propose.
5. Detailed Analysis of Tuna
In this section we take a closer look at the canned tuna category. Later, in Section 5.3, we
check if the results we find for tuna are also present in the other product categories. We focus on tuna
for several reasons. First, this category seems to have the most robust results in support of the CKR
loss leader model. It is the only category in Table 3 in which our results very closely reproduce the
patterns found in CKR, and for which the patterns are present not only for the variable price index
but also the fixed price index. Second, as CKR note, and as we discussed in Section 2, a key to
separating the loss leader model from alternatives is to focus on products that have their own seasonal
peak demand. The tuna category is probably the cleanest example of such an effect among the
categories we focus on. Beer also has well defined idiosyncratic peak demand periods that are not