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An Empirical Analysis of Competi

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					    An Empirical Analysis of Competitive Pricing in a Multi-Brand, Multi-Retailer
                                         Product Market*




                              Sachin Gupta and Vrinda Kadiyali
                                          Sage Hall
                           Johnson Graduate School of Management
                                      Cornell University
                                   Ithaca, NY 14853-6201

                                        sg248@cornell.edu
                                       kadiyali@cornell.edu




                                    First version: April 2001
                                  This version: September 2001




*
  We thank participants of the Competitive Responsiveness Conference at MSI, Boston, and four
anonymous referees for their comments on the abstract submitted for this conference. We also thank Jean-
Pierre Dube for his comments.
                                          Abstract

         Most consumer goods industries are characterized by multiple competing
manufacturers selling through multiple competing retailers. In such markets, any single
entity's (manufacturer or retailer) price is determined keeping in mind reaction of other
entities (manufacturers and retailers) in this market. Competition between these entities
(manufacturers and retailers) can be one of a variety of possible types. Both the existing
theoretical and empirical literatures in marketing have been unable to address the effect
of general models of competition on pricing in channels. This study is a first empirical
attempt at this problem. Given the difficulty of building a structural model to capture
these various manufacturer-retailer interactions, we build a reduced-form model of
demand and pricing. This model is flexible enough to capture the competitive effects of
any manufacturer-retailer interaction pattern on price.
         An important facet of multiple manufacturers selling through multiple retailers is
that it sets the stage for multimarket contact, or multipoint competition. In contemplating
fierce or gentle competition, firms must weight gains and losses of these competitive
actions across multiple points of contact. We decompose these gains and losses from
pricing in multipoint competition as those that result from total pie size in these multiple
markets, and those that result from pie slices in these multiple markets. To capture the
effects of the total pie size on pricing, we specify the pricing equation as a function of
total industry sales in the market. To capture the influence of slices of pie of various
competitors, we develop a measure that captures the extent to which the distributions of
each brand’s sales across retailers deviate from what we might expect based on the
category market share of the retailer. That is, we capture the extent to which pairings
between manufacturers and retailers are tighter or looser than we would expect based on
market shares of these entities.
         Using these pricing equations, we first test if prices are higher in periods when the
total pie is large or small, i.e., in periods of high industry demand or in periods of low
industry demand. Literature in economics provides us theory and evidence that pricing
(and competition) in industries may be either positively or negatively correlated, or even
uncorrelated, with increases in demand. Second, we examine the effect of distributions
of market shares on prices in the following way. Literature on multi-market contact in
economics suggests that for any manufacturer-retailer pair, it is important to see not just
this pair's market share in this channel, but also the market shares of other manufacturers
in this and other channels. Note that the literature in multimarket contact does not
provide guidance on whether the relationship between manufacturer-retailer pairing and
prices is monotonic, or if there are thresholds that activate or deactivate this relationship.
         We test this model on data from the refrigerator, microwave and dishwasher
categories. We find that for all three categories, retail pricing is procyclical. Therefore,
in all three multipoint contact situations, an increase in pie size increases average prices.
We also find that retail pricing in the refrigerator and microwave categories is sensitive to
market share distributions or levels of pairings between manufacturers and retailers, but
dishwasher pricing is not sensitive to market share distributions. We find that these
market share distribution effects on pricing are not segmentation-based but purely
competition-based or are strategic. By examining our results across the three categories,
we find that the ability to price higher is not a monotonic function of these pairings
between manufacturers and retailers, and that there might be some threshold beyond
which an increase in pairings has no impact on prices. We therefore view this study as
providing an important exploratory empirical illustration of the workings of multimarket
competition and channels pricing. We hope these provocative empirical findings will
spur theory development in this area.

Keywords: Multi-manufacturer, multi-retailer, multimarket contact, procyclical pricing,
market share distributions, channel pricing, pricing power.




                                                                                      2
                                       1. Introduction
       Most consumer goods industries are characterized by multiple competing
manufacturers who sell branded products through a vertical channel consisting of several
competing retailers. The determination of retail prices in such markets through strategic
interaction between manufacturers and retailers is a problem of central interest in
marketing, and the focus of this paper.
       Game theory is the obvious framework to analyze such situations of strategic
interdependence. The literature on marketing using this framework comprises both
theoretical and empirical work. Some of these theoretical papers include Jeuland and
Shugan (1983), Lee and Staelin (1997), and Kim and Staelin (1999). For reasons of
tractability these models are at most able to analyze the case of 2 manufacturers
interacting with 2 retailers. Additionally, to get closed-form analytical solutions to the
optimal manufacturer and retailer pricing problems, the form of competitive behavior
between manufacturers and retailers is restricted to at most being one of three types-
Vertical Nash, manufacturer-led Stackelberg leader-follower, and retailer-led Stackelberg
leader-follower behavior.      The assumption for the inter-manufacturer behavior is
(implicitly) one of Betrand-Nash, and the same assumption is made about inter-retailer
competition. Some of these papers also demonstrate the sensitivity of the optimal pricing
rules to the demand functional form (e.g., Lee and Staelin, 1997).
       Recently, some empirical studies have estimated structural models of oligopolistic
markets with a retail channel (Besanko et al. 1998, Kadiyali et al. 2000, Sudhir 2000).
All these studies are of competition in the multiple manufacturer, single retailer setting.
Additionally, most of these papers have had to make restrictive assumptions about the
type of competition between and among manufacturers and retailers (except for Kadiyali,
et. al. 2000). The reason for these assumptions is the same as that for theoretical papers,
i.e., the difficulty of obtaining optimal pricing rules in a structural model.
       The objective of this paper is to estimate a model of channel pricing with no
restrictions on the form of the strategic interaction between manufacturers and retailers.
Specifically, we investigate differences in prices of multiple branded products for
refrigerators, dishwashers, and microwaves across several major retail channels. In such



                                                                                         1
markets we clearly expect both manufacturer and retailer competition to play a role in
determining prices. Also, we have no a priori reason to postulate any specific form of
strategic pricing interactions between these players. We would like the model to be
general enough to account for manufacturer and retailer power in various channels, as
well as the influence of behavior in one channel on behavior in another. Therefore, we
build a model that examines competition between manufacturers and retailers as
indicated by retail pricing of various brands within and across retail channels.
       In analyzing competition between manufacturers and retailers, we are interested
in examining whether manufacturer concentration in retail channels, or retailer
concentration in specific brands, has an effect on prices. We turn to the literature in
economics on multimarket contact (Bernheim and Whinston, 1990) to guide our model
and hypotheses. The application of this idea to the refrigerator, dishwasher and
microwave markets is by seeing various manufacturers in various retail channels; these
channels provide the multiple markets setting referred to in the argument. The key
argument of this literature is that when firms meet in multiple markets, their profits
across all these markets are very dependent on one another. For example, should a firm
cut prices in one market, its rival might retaliate by cutting prices in this market as well as
in the other markets in which these firms overlap.           Under some conditions, firms
recognize this dependence and might therefore be wary of starting price wars. Therefore,
we observe "mutual forbearance" in the marketplace (Gelfand and Spiller, 1985).
However, it is not always the case that multimarket contact will lead to mutual
forbearance (Gimeno, 1999).
       Consider the following business examples on multimarket contact.                  Pepsi
acquired the larger market-share Tropicana juices to counter Coke's MinuteMaid as an
attempt to balance its weaker position in its mainline cola business (Business Week,
1998). Similarly, Ralston Purina acquired a stake in the declining segment of moist dog
food to keep in check Quaker, the big producer in the moist dog category who was
considering expanding in to Purina's mainline dry dog food business (HBS Case, 1991).
Continental Airlines acquired some gates in Dallas, TX, a hub for American Airlines, to
counteract American Airlines' attempt to secure gates in Continental's hub of Newark,
NJ. (Wall Street Journal, 1998).



                                                                                             2
       The interaction between Time Warner and Disney (Landro, Reilly, and Turner,
1993) provides a contrast to the preceding examples of higher prices in multipoint
competition.   The common markets for these players are theme parks, movie and
television production, and television broadcasting. Time Warner also has large magazine
interests. Landro et. al. document how between 1988-93, Disney spent over $40 million
on advertising in Time-Warner magazines. About this time, Time-Warner attempted to
steal market share from Disney theme parks.          This conflagration spread as Disney
cancelled all advertising in Time-Warner magazines. This was followed by Time-Warner
canceling its corporate meeting scheduled to be held in Disney World in Florida. Disney
retorted by not broadcasting Time-Warner theme park advertisements in its Los Angeles
station. Therefore, while firms might have multipoint contact, such contact can also lead
to spreading price wars across these multiple points of contact, and hence, lower prices
overall.
       What determines whether multimarket contact will keep prices high (or
competition low and profits high) or prices low (or competition high and profits low)?1
The answer is dependent on two forces that determine the gains versus losses from
keeping prices high or low in own and rival's primary markets. These two forces are (a)
firms' temptation to cut prices in rivals' primary markets, which might lead to lower
prices (b) any firm's ability to punish a rival that cuts prices in its own primary market;
the higher the ability, the higher the prices. If firms have low temptation to cut prices and
high ability to punish, then prices in the market will be high.         If firms have high
temptation to cut prices and low ability to punish, then prices in the market will be low.
If there is a combination of high temptation to cut prices and high ability to punish, or
low temptation to cut prices and low ability to punish, it is not clear what might happen.
       Taking the argument one step further, on what are the temptation to cut prices and
ability to punish rivals based? A simple way to examine the common factors underlying
these two forces is to consider gains and losses of firms as those resulting from the total
size of pie available to all competitors, and the slices of pie available to each competitor,
under low and high price scenarios. Therefore, let us next consider how the total pie size




                                                                                             3
and pie slices affect competition when firms meet in multiple markets. As we will
discuss below, we can turn to other streams of literature in economics to examine the pie
size effect, but clear-cut theories for the pie-slice effect on prices are not as readily
available.
        To examine the effect of total pie size on prices (or competition) when firms meet
across several markets, we turn to literature in economics. This literature provides us
theory and evidence that pricing in industries may be either positively or negatively
correlated with total pie size, or increases in demand as seen in increases in total sales.
Green and Porter (1984) develop a theoretical model where firms cannot observe demand
shocks. That is, when a firm observes a drop in its competitors' prices, it is unable to
determine if this is because of aggressive competitive pricing by its competitors or
whether competitors were merely responding to sluggish demand in the industry. To
sustain cooperation, a firm will cut its own prices to punish the aggressive competitors.
In this scenario, prices will be procyclical, i.e., that as total demand in the industry falls,
prices fall. Rotemberg and Saloner (1983) develop a theoretical model with the opposite
prediction. In their model, firms observe demand shocks. Consider the situation if
current demand is lower than expected future demand. Firms realize that if they cut prices
today, competitors will cut prices in the future as a punishment for deviating from
cooperative pricing. Given future demand is high, firms are then trading off getting
larger profits today given own low pricing and hence larger market share, to a larger loss
in the future when demand is high and competitors respond by cutting prices. For
appropriate discount factors, firms will prefer to not cut prices in this situation. This
results in countercyclical pricing patterns, i.e., periods of low total pie size, or of low
demand see high prices. In marketing, the relevant paper in this literature stream is
Sudhir et al. (2001), who find evidence of such pricing for the photographic film market
in the 1981-1998 time period. In contrast to both the procyclical and countercyclical
pricing theories, Raith (1996) postulates that in differentiated products markets, there is
likely no correlation between level of competition and level of demand.                      In such



1
  Note that we will only study price levels directly in our model; the implications for competition and
profits follow from there. We cannot estimate competition levels and profit margins given our reduced
form model.


                                                                                                     4
industries, a cut in competitor prices does not translate as much in to loss of own market
share, and is therefore not a reason to cut own prices.
       Which of these theories of procyclical, countercyclical or noncyclical pricing
holds in the three durables categories of refrigerators, dishwashers and microwaves is an
empirical question. As discussed in the model section, we use total sales in the industry
as a pie-size measure to estimate the relationship between prices and pie size when there
is multimarket or multipoint competition. Keep in mind that issues of cyclicality are
especially salient in durable goods industries because these are bigger ticket items that
are more likely to have periods of high and low demand concurrent with economic boom
and bust cycles.
       Unlike the stream of literature discussed above for examining the effect of pie
size on prices, the literature on the effect of pie slices on price (and competition and
profit) levels is sparse. The literature on multimarket contact has focused primarily on
the extent of multimarket contact, as measured by the number of markets in which
contact occurs (e.g., Parker and Roller, 1997), to capture the opportunity for retaliation
threats that underlie mutual forbearance. However, Gimeno (1999) notes that rival firms
may have an asymmetry of strategic interests in those points of contact. Thus, if a firm
has high strategic interest in a particular market, as reflected for instance in high market
share, then this market provides stronger opportunities for credible threats. By contrast,
contact in unimportant markets might lead to increased rather than diminished rivalry.
Thus, the literature on multimarket contact does not provide clear implications on how
the distribution of market shares of rival firms across different markets affects prices.
Are profits more dependent, and hence prices higher, when firms have small shares in
each other’s primary markets or if they have larger shares in each other’s primary
markets? Additionally, another factor to keep in mind is whether market share
configurations lend themselves to relatively easy forms of collusion.
       Consider the situation of two manufacturers, M1 and M2, and two retailers, R1
and R2. Let us start with a case of relatively loose pairing. That is, while R1 sells more
of M1 than of M2, and R2 sells more of M2 than of M1, R1 and R2 have significant sales
of M2 and M1 respectively. In this case, if R1 cuts prices on M2 products in its stores,
R2 cannot retaliate as readily by cutting prices on M1 because such a price cut will hurt



                                                                                          5
itself as well. Therefore, ability to punish the rival without hurting oneself is low.
Temptation to cut price and gain market share can be high if there are economies of scale
in any one market or if there are economies of scope across the two markets. It is also
possible that temptation to cut price is low in the absence of these cost-side factors.
Therefore, it is not clear what the final pricing outcome might be. Keep in mind that in
markets with loose pairings, it is harder to sustain price leader-price follower price
patterns because of the lack of natural price leaders with large market shares, and
therefore, prices might be lower.
        Now let the loose M1-R1 and M2-R2 pairing described above become tighter.
Consider a situation where R1 largely sells M1 and R2 largely sells M2. Let R1 have
small sales of M2 and R2 have small sales of M1. How high are temptation to cut price
in rival's primary market for each M1-R1 and M2-R2 pairing and how much ability does
each pairing have to punish its rival should the rival cut price in its own primary market?
R1 might be tempted to decrease the price of M2 in its channel to gain sales from R2, but
it is also the case that R1's main profits come from M1. R1 is also aware that R2 can
punish it by cutting price on M1. Therefore, temptation to steal share may not be high,
and ability of R2 to punish R1 (and R1 to punish R2) is high.                         This keeps each
manufacturer and retailer pairing tight and prices high because M1-R1 and M2-R2 are
"mutual hostages" to each other. This also enables competitive outcomes like price
leader-price follower in markets, with R1 being the price leader for the brand of M1, R2
for the brand of M2, and R1 the price follower for the brand of M2, R2 for the brand of
M1. 2 Therefore, an increase in pairing might lead to higher prices.
        It is possible that this closer pairing of specific manufacturers and retailers is
based on simple demand differentiation or segmentation of the marketplace. That is,
each manufacturer-retailer close pairing serves a distinct demographic customer segment,
and hence, is able to charge a higher price because of lack of competition or because of
specialization, or niche-channel structures. Therefore, it is important to ensure that if we

2
  Firms often have "fighting brands" or defensive brands in rivals' primary markets; these are brands where
prices can be dropped without hurting the brand image and pricing of its primary market. In the pet food
example mentioned previously, Ralston Purina's brand in the moist dog food was a clear knock-off of
Quaker's brand, and priced much lower than Quaker's brand, and was also priced less than Purina's primary
brands in other dog and cat food. See also Kadiyali et al. (1996) for examples of P&G and Unilever using
their small brands as price followers to the rival's large price leader brands.


                                                                                                         6
find results that support higher prices with tighter pairing between manufacturers and
retailers, we must be able to distinguish between pure segmentation-based results and
tacit collusion-based higher prices.
       Consider finally a further increase in the M1-R1 and M2-R2 pairing till the share
of M1 in R1 is close to 100% and of M2 in R2 is also nearly 100%. It may not be
possible here to credibly threaten to punish a rival if there isn't a toehold in the rival's
market. Will firms be tempted to cut prices in their rival's primary market because they
might gain market share, and have very little to lose given their own small share? If so,
this might lead to low pricing. Note that like the previous situation of relatively tight
pairing, it is much easier in this situation to have price leader-price follower or near
monopoly pricing, and hence average prices might be higher.
       Summarizing, existing literature does not provide us clear guidance on the
direction of the relationship between the strength of manufacturer-retailer pairing and
price levels in a multimarket, or multipoint competition setting. We have discussed
above reasons why this relationship can be positive or negative. It is also possible that
the relationship is insignificant beyond thresholds of very high or very low pairing
measures. Having data from three different categories will help refine our intuition.
Therefore, we view this study an exploratory study providing an empirical illustration of
a manner in which multi-manufacturer, multi-retailer competition might play out. We
hope this illustration can be used to develop further theories or further empirical studies
to explore in more detail the implications of this study.
       One final issue in testing the relationship between market share distributions and
prices in a multimarket setting is constructing a market share distribution measure. Our
measure of manufacturer-retailer pairing captures the extent to which the distribution of
brands' sales across retailers deviates from what we might expect based on the category
market share of the retailer. As details in section 2 reveal, this measure is comprehensive
because it captures not just any single manufacturer's or retailer's market share
distribution, but also for each of its competitors. In other words, the measure captures
strength of pairings between manufacturers and retailers; the greater the pairing, the
greater the deviation from the expected market share.




                                                                                          7
         We now turn to a discussion of details of the data and the model, followed by a
discussion of the results, and we conclude with some future directions that this stream of
research can explore.


                             2. Data, Model, and Estimation details
2.1      Data Description
         We examine three categories of kitchen appliances – refrigerators, dishwashers,
and microwave ovens. We observe quarterly purchases and retail prices of all brands of
each of the categories in various retail channels. The period of observation is 1994-99
(20 quarters) for refrigerators, and 1994-2000 (24 quarters) for dishwashers and
microwave ovens. The data are collected by a market research company via quarterly
cross-sectional surveys of random samples of households across the United States. The
average sample size per quarter is 828 households. Also available are demographics of
buyers of each brand-retailer pair in each time period.
         In our analysis we include five of the largest brands3 and five of the largest
retailers, for refrigerators and dishwashers, and six brands and six retailers for
microwaves. In Tables 1-3 we show the identities of these brands and retailers4. There
are no changes in this time period in the identity of top retailers or brands. Buyers are
grouped into four city-size groups. Since the number of purchases at this level is small,
we aggregate the data up to two city-size groups. Thus, our unit of analysis is a city-
quarter, and we have 40 time periods of observations (pooled data for 20 quarters, 2 city
types) for refrigerators, and 48 time periods of observations for dishwashers and
microwaves. The availability of cross-sectional variation helps provide good instruments
for the endogenous variables, discussed below.




3
  Our analysis focuses on brands rather than manufacturers as the unit of analysis, though in this time
period each brand is owned by a different company so there are no product line pricing issues.
4
  Kenmore, Sears’ private label appliance brand, is one of the largest selling brands in each of the three
categories. It is sold exclusively through Sears. This sets the brand apart from the remaining brands in that
this is a case of pure vertical integration or pure matching between a brand and a retailer. In the analysis
presented in this version of the paper we exclude Kenmore because including it as a manufacturer
supplying to Sears would bias the results in favor of finding tacit collusion between manufacturers and
retailers.


                                                                                                           8
                                   ______________________
                                   Tables 1, 2, and 3 about here
                                   ______________________
       In Tables 1 to 3 we provide descriptive statistics of the data for each of the three
categories. Table 1 shows that in refrigerators, General Electric is the market share
leader with an intermediate price. Interestingly, Whirlpool and Amana, the second and
third largest manufacturers, have the highest prices in the market. Among the retailers,
appliance dealers command over half the market and have the second highest price. The
two smallest players, Montgomery Ward and Best Buy, have the lowest prices.
       Table 2 shows that in the dishwasher market, the largest brands Maytag, General
Electric, and Whirlpool, have very similar market shares and together account for over
three-fourths of the market. The lowest priced brand – Frigidaire – has the lowest market
share. Kitchen Aid is a high-priced niche brand. Among retailers, Sears dominates with
42.8% share, followed by appliance dealers who have a 35.6% share. These two retailers
have the highest average prices.
       Table 3 describes the microwave oven market. Sharp is the dominant brand in this
market with an intermediate price. Whirlpool is a high-priced niche brand. Interestingly,
Walmart, which does not sell the two larger kitchen appliances, is the dominant retailer
for microwaves and maintains very low average prices. As in the other two categories,
appliance dealers have higher prices.
       To assess the quality of our market research sample data, we compare the brand
shares with market shares reported in Dealerscope magazine for the most recent available
year. The validation market shares shown in Tables 1-3 are scaled so the selected brands’
shares sum to 100%. The close similarity between the panel-based brand shares and the
validation shares is evident.
       Additionally, we collect data on a number of cost- and demand-shifter variables.
For demand shifters, we obtain monthly data on housing starts and household renovation
expenditure. We sum these monthly data to obtain quarterly data. These data are from
the U.S. Bureau of Census. For cost shifters, we obtain monthly data on cost of steel and
plastics, the major components of kitchen appliances. We average these monthly data to




                                                                                         9
obtain quarterly data. These data are Producer Price Indexes from the Bureau of Labor
Statistics.


2.2     Model
        We develop reduced form pricing equations for the average retail category price.
The average retail category price is the share-weighted average of brand prices. As
discussed in the introduction, it is not possible to obtain a structural model of behavior for
this multi-brand, multi-retailer setting that allows for non-restrictive forms of
competition.    Additionally, our data are for retail prices of various brands in various
retail outlets, and we do not have data for manufacturer prices charged to retailers.
Therefore, this data limitation also restricts the type of structural model we can use had
we decided to go that route (for example, we would have to assume either Nash or leader-
follower behavior between retailers and manufacturers to recover manufacturer prices).
In sum, for both theoretical and data reasons, we prefer to use a reduced form model.
        We consider the appropriate measure of price to test the pairing effect to be the
average retail price for all brands (i.e., the category average price) within a retail channel.
Other possible measures that we considered include the retail price for only a single (e.g.,
primary) brand, or average brand prices across various retail outlets. We considered these
options to be less appropriate for several reasons. First, note that neither the multimarket
competition management theory nor the segmentation theory provides implications for
pricing of any one brand within any one market or channel when more than one brand is
sold in any channel. We would like to examine how pairings affect profitability, and it is
safe to assume that higher category prices make for higher profitability for retailers.
Average prices of any brand across retail channels do not result from any player's profit
maximization, nor do they reflect pairings between manufacturers and retailers, in
contrast to average retail prices within a retail chain that reflect both the idea of pairings
between manufacturers and retailers and retailer's profit maximization.
        We show below the specification of the demand and pricing equations:




                                                                                            10
Pricing equation:
               M 1        3
    Pjct     j Di   q Dqt  Tt TOTSALct   DEVct   k Z kt   jct                          (2)
               j 1       q 1                                               k

where
     Pjct is the average (across brands) price of retailer j in city c, quarter t.

     Di is a retailer-specific fixed effect that is 1 if i=j, 0 otherwise

     Dqt is a quarterly dummy

     Tt is a time trend variable that measures years from 1 to 5

     TOTSALct is total category sales across all retailers in city c, quarter t (measures total
         pie size across multiple points of contact for manufacturers and retailers)
     DEVct is a measure of asymmetry in brand-retailer pairing, defined below (measures
         the extent of pairings between manufacturers and retailers across multiple points
         of contact)
     Z kt is the k-th cost-shifter variable
         The variable DEV is constructed to measure strength of brand-retailer pairing as
follows5. Let Sij denote share of brand i in retailer j, such that            Si   j
                                                                                         ij    1 . Let Si . and

S. j denote total shares of brand i and retailer j respectively. Then, if the distributions of

shares across brands and across retailers are independent, we can compute the expected
share of brand i in retailer j as follows
                                              ESij  Si. * S. j

A normalized measure of deviation from expected share for brand i, retailer j, is then
                                                      ( ESij  Sij ) 2
                                         DEVij 
                                                           ESij

and the measure of deviation for the market as a whole is the sum across all pairs:
                                       DEV   DEVij                                             (3)
                                                  j    i




5
 Readers familiar with the chi-square statistic for contingency tables will note that the motivation for the
definition of DEV comes from that measure.


                                                                                                             11
The following simplified example serves to illustrate the definition and role of DEV.
Consider a market with two brands and two retailers, with distribution of shares as
follows
                                       Brand 1    Brand 2
                          Retailer 1                        0.20
                          Retailer 2                        0.80
                                       0.30       0.70      1.00


Under independence of distributions of shares across brands and retailers we expect to
see
                                       Brand 1   Brand 2
                          Retailer 1 0.06        0.14       0.20
                          Retailer 2 0.24        0.56       0.80
                                       0.30      0.70       1.00


Imagine that instead we see the following distribution:
                                       Brand 1   Brand 2
                          Retailer 1 0.12        0.08        0.20
                          Retailer 2 0.18        0.62        0.80
                                       0.30      0.70        1.00
We note that brand 1, the small brand, has a disproportionate share of the small retailer's
business, while brand 2 has a disproportionate share of the large retailer's business. For
this example, the measure of deviation is 0.1071. If the distribution of shares was more
skewed in the same direction, e.g.,
                                       Brand 1   Brand 2
                         Retailer 1 0.18         0.02       0.20
                         Retailer 2 0.12         0.68       0.80
                                       0.30      0.70       1.00


the deviation measure would be larger, namely, 0.4286. Therefore, a higher value of
DEV captures tighter pairing between manufacturer and retailer.


                                                                                        12
        As seen in equation (2), we allow for a non-linear effect of DEV on pricing.
Specifically, taking the square root of DEV accommodates diminishing returns, which we
would expect. That is, it is not clear that prices can increase or decrease linearly or in a
convex way when DEV increases or decreases.
Demand specification:
        We model retail category sales as a linear function of own category retail price, an
index of competing retailers’ prices, retailer fixed effects, quarterly dummies and a time
trend, demographic profiles of retail buyers, and demand shifter variables. Own and
competitive price effects are modeled as retailer-specific by interacting prices with the
retailer fixed effects. The retailer-level demand specification is:
              M 1         3
  q jct     j Di   q Dqt  Tt   own, j Pjct   cross,i Pjct   kWkt  Z jct   jct   (1)
              j 1        q 1                                            k

where
    q jct is sales of retailer j in city c, quarter t.

    D j is a retailer specific fixed effect that is 1 if j=i, 0 otherwise

    Dqt is a quarterly dummy

    Tt is a time trend variable that measures years from 1 to 5

    Pjct is the average (across brands) price of retailer j in city c, quarter t.

    own, j and  cross, j are the own- and cross-price effects of retailer j respectively

    Pjct is the sales-weighted average price of all retailers other than j

    Wkt is the k-th demand-shifter variable

    Z jct is a demographic characteristics of consumers of retailer j

        Conceptually we could model aggregate demand as the outcome of consumer
choice among all brand-retailer pairs (25 pairs in refrigerator and dishwasher markets,
and 36 in the microwave market). However, we have insufficient data to estimate such a
model without placing unreasonable restrictions. Therefore, we pool data across the
retailers to obtain 200 data points (20 quarters, 2 city types, 5 retailers) for refrigerators
and dishwashers each, and 288 observations (24 quarters, 2 city types, 6 retailers) for
microwave ovens, which provide adequate degrees of freedom to estimate the demand


                                                                                                       13
system above. Note that this also makes the demand system consistent with the pricing
model.
         An alternative approach to modeling (both demand and) retailer prices is to model
pricing for brand-retailer pairs. This would have provided many data points. We chose
not to pursue this approach because as discussed in the introduction, we do not have
theory-based expectations of how prices are affected by share distributions across brand-
retailer pairs.


2.3      Estimation Issues
         In the demand equation prices are endogenous. Similarly, in the pricing equations
both market share and DEV are endogenous regressors. We deal with the endogeneity by
choosing appropriate instrumental variables for these endogenous variables. There are
two types of instruments we can use. First, we can instrument for price in the demand
model by using appropriate cost-side exogenous variables, and for market share and DEV
in the price model by appropriate demand-side exogenous variables.
         Second, recall that we have data from 2 different city-types. Following Nevo
(2001), we can instrument for price in the demand model in any one city-type with price
in the other city-type (and similar arguments work for market share and DEV in the
pricing equation). The argument works as follows: let us assume that city-specific error
terms in the demand model are uncorrelated across cities. Therefore, prices across cities
are correlated because of common cost conditions (and hence make great demand-side
instruments) but are uncorrelated to market-specific valuation (or utility or demand) of
product. The assumption of city-specific error terms being uncorrelated is violated if
there is a national demand shock that might make unobserved city-specific valuations
correlated; or if local advertising and promotions are coordinated across city borders and
these affect demand. Nevo's application of this instrumental variable technique is to
cereal pricing across different markets, a situation not different from ours in a strategic
sense. Therefore, we believe it is appropriate for us to use instruments from other city
type. Summarizing, we use two types of instruments in our analysis- exogenous demand
or cost shifters from the same city-market, and the value of the endogenous variable from
the other city-market.



                                                                                        14
       A couple of other issues come up in the estimation of the model. The first
question is which demographic variables to use in the demand model estimation. We
find that by looking at simple correlations, most demographics are not likely to provide
tremendous explanatory power in either the demand or pricing equation. Therefore, in
the demand and pricing equation, we only choose those demographics that are likely to
provide explanatory power. The second and related issue is that we attempt to use the
most parsimonious demand and pricing equation to conserve degrees of freedom. As will
be seen in the results section, despite this parsimonious formulation, the lowest number
of parameters in any equation across the two demand and two pricing equations is 13, the
highest is 17. Given that we have only 200 (288 for microwaves) data points, we
currently estimate demand and pricing equations separately rather than as a system of two
equations simultaneously.


                                         3. Results
       As discussed in the data and model section above, we estimate demand and
pricing equations at retailer level. While our interest is primarily in the pricing equations,
the demand equations are estimated in addition essentially to assess face validity of the
data. We expect a well-behaved demand system to have a negative own price coefficient
and positive cross-price coefficient. In Table 4 we show a summary of the sign and
significance of the relevant price coefficients.
                                    ______________________
                                        Table 4 about here
                                     _____________________
       The results in Table 4 indicate that of the six coefficients of interest, five are
correctly signed, and four of these are significant. These results broadly indicate face
validity of the demand systems.
Pricing equations
       Of greater interest than the demand models are the models for pricing, or the
supply side. The estimates are in tables 5-7.
                                    ______________________
                                      Tables 5-7 about here
                                    ______________________


                                                                                           15
        A couple of minor points of interest in the pricing equations. First, the cost
shifters (prices of steel and plastic) have varied explanatory power. Second, different
quarter dummies are significant across the three categories, and manufacturer and retailer
dummies point to the variance across these. The two key variables in these models are
Total Sales and Square Root of Dev.6
        We see that the coefficient of total sales is positive and significant for all three
categories.    This provides strong support for procyclical pricing at the retailer level.
Contrast it to the countercyclical pricing result for photographic film in Sudhir et al.
(2001). To repeat the argument from the introduction, the Rotemberg-Saloner (1983)
theory says that if there is low demand in the current time period with an expectation of
higher demand in the future time period, firms do not want to cut prices now. This is
because this price cut leads rivals to retaliate in the future higher demand periods and ruin
the higher profits then. Durable goods have more cyclical and more predictably cyclical
demand than photographic film.           This fact fits better with the assumption of the
Rotemberg-Saloner model of countercyclical pricing than of the assumptions of
procyclical pricing of the Green-Porter model. Therefore, one possible explanation for
the difference in results is that firms in durable goods have higher discount factors for the
period under study. Another explanation is that the film market with countercyclical
pricing is largely a duopoly whereas each of the appliance markets with procyclical
pricing has at least five retailers and five manufacturers, so the coordination problem in
pricing is much harder. This might cause unraveling of price coordination in low demand
periods. The procyclical pricing result in all three appliance categories also indicates that
retail outlets are not differentiated so much that there is no correlation between level of
competition and level of demand, as postulated by Raith (1996).
        The results for the pairing measure, DEV, vary across the retail categories. For
refrigerators, DEV is positive and significant; for microwaves it is negative and
significant, and the parameter is not significant for dishwashers. The average values of
DEV for these categories are 0.26, 0.63 and 0.89 respectively.                 This confirms our
intuition that the relationship between DEV and price levels is not monotonic. That is,


6
  We ran the pricing model with non-linear affects of total sales and linear effects for DEV, and the
qualitative results were identical.


                                                                                                  16
while DEV of 0.26 helps retailers charge a higher prices for refrigerators, DEV of 0.63
has a negative effect on pricing because of lower ability to punish and a greater
willingness to cut prices resulting from low market shares in rivals' primary markets. For
dishwashers, with an average DEV of 0.89, manufacturer-retailer pairs might be too
distinct to even need to cooperate to charge high prices, indicating a threshold beyond
which the relationship between manufacturer-retailer pairing and pricing is deactivated.
Examining the Segmentation Explanation
        As noted previously, one reason why we observe higher than expected shares of
manufacturer-retailer pairs or tighter pairing may be that certain manufacturers and
certain retailers target the same demographic consumer segment. Thus, for example, a
manufacturer whose brands are targeted to upper income, older consumers, may match up
with a retailer who targets consumers with a similar demographic profile. We would then
observe that this manufacturer-retailer pair has sales higher than what we might expect
based on the total sales of the manufacturer and retailer respectively.
        To examine this hypothesis, we divide our sample of consumers into demographic
segments and test whether the observed distribution of sales across brand-retailer pairs
within each of the segments continues to display large deviations from expected sales.
Large deviations within demographic segments would challenge the segmentation
hypothesis.
        For each of the three product categories, we conduct twelve tests as follows. Six
demographic variables are available to segment consumers. On each of the demographic
variables, the overall sample of buyers is split into two sub-samples, using an arbitrary
cut-off. For example, the sample is divided based on the age of the buyer into those who
are 50 or older, and those younger than 50. Within each of the twelve sub-samples thus
obtained, we conduct a chi-square test of the null hypothesis that the distribution of sales
across brands is independent of the distribution of sales across retailers. For these tests
we use cumulative sales for the last two available years.
        The null hypothesis of independence is resoundingly rejected (p < 0.001) in all
twelve sub-samples in all three categories. Thus it is unlikely that the segmentation
hypothesis explains the observed pattern of distribution of sales across manufacturer-
retailer pairs.



                                                                                         17
       Combining the results of the demand and pricing equations above, we can reach
the following conclusions. Demand equations provide face validity to the data and
model. There is evidence for collusive pricing at retail level. As the total pie increases at
the retail level, prices rise, i.e., there is procyclical pricing. The results on DEV across
the three categories provides preliminary support for the idea that there is an optimum
level of pairing that balances the need to cooperate, and the willingness to do so results in
higher prices. In refrigerators, this level is clearly present; in microwaves this level is
exceeded to the detriment of prices, and in dishwashers the pairing is so high that
manufacturers and retailers carve out markets in a manner to make collusion irrelevant.


                             Conclusions and Future research
       This is the first study to our knowledge that examines competitive pricing issues
in a multi-manufacturer, multi-retailer setting. The primary purpose of this paper was to
understand the competitive determinants of pricing in a multi-manufacturer, multi-retailer
setting. As discussed in the introduction, the theoretical and empirical literature streams
in this area do not provide general guidance on the direction of these effects. We
recognize that a structural model of generalized competition in this multi-manufacturer,
multi-retailer setting is very difficult to construct and estimate. Therefore, we built a
reduced-form model of demand and competitive pricing at the brand and retailer level.
This model was general enough to allow for a variety of possible competitive interaction
patterns between manufacturers and retailers. We tested the model using data on the
refrigerator, dishwasher and microwave markets.
       The fact of multiple manufacturers selling through multiple retailers sets the stage
for multimarket contact, or multipoint competition. We decompose the gains and losses
from multimarket contact as those related to the total pie size available to these
competitors across the multiple markets in which they meet, and those related to pie
slices of various competitors across these multiple markets. We find evidence that the
size of the pie, as captured by total sales in the industry, is an important determinant of
retail pricing, or that retail pricing is procyclical. To capture the influence of slices of pie
of various competitors, we develop a measure that captures the extent to which the
distributions of each brand’s sales across retailers deviate from what we might expect



                                                                                             18
based on the category market share of the retailer. That is, we capture the extent to which
pairings between manufacturers and retailers are tighter or looser than we would expect
based on market shares of these entities. We find evidence that the relationship between
this pairing measure and pricing is non-monotonic across the categories. We are able to
show that the relationship between pairing and pricing is not a result of segmentation, and
therefore is strategic or competitive in nature.
        There are at least two possible directions in which this paper can be extended.
First, note that that the definition of the pairing measure, DEV, is currently agnostic to
whether DEV is high because a large manufacturer-large retailer sales are larger than
expected, or whether a small manufacturer-small retailer sales are larger than expected
(and other combinations of manufacturer and retailer sizes). Studies of profitability
indicate that high levels of concentration positively affect profitability of large firms, but
not of smaller firms (see Schmalensee, 1989). A change in the definition of DEV might
help us test this prediction.
        Second, if data on more categories can be obtained, especially in categories with
overlapping retailers and manufacturers, a cross-category multimarket competition model
can be developed and tested. That is, multimarket contact can be not only through
various manufacturer-retailer pairing for any one product, but such pairing across
products as well. Standard scanner data in marketing can be used to test these hypotheses
as well. It would be especially interesting to observe how the relationship between DEV
and pricing is a function of number and size of competitors, discount factors of these
competitors, differences in cost structures of these competitors etc.
        Finally, a more ambitious direction for future research relates to theory
development. The theories of multimarket contact do not provide clear guidance on the
effect of this contact on profitability or pricing. We therefore view this study as providing
an important exploratory empirical illustration of the workings of multimarket
competition and channels pricing. In particular, our finding of a non-monotonic
relationship between pricing and the pairing measure, DEV, across the three categories
studied is provocative. As discussed in the introduction, the two forces of temptation to
cut prices (gains from price cuts) and the ability to punish a price-cutting rival (losses
from price cuts) determine the sign and magnitude of this relationship. For a different



                                                                                           19
number of competitors, size of competitors, heterogeneity of demand and cost conditions
facing competitors in industries other than appliances, it is entirely possible that
relationship will be non-monotonic in a different way, or that thresholds for the lack of
relationships might also be different. We hope the results from these three categories in
this paper will spur the development of more theories on multi-manufacturer, multi-
channel competition.




                                                                                      20
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                                                                                          21
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                                                                                      22
                Table 1: Descriptive statistics of the refrigerator market

Manufacturers             Market Share         Validation Market       Average Price per
                            (units)                 Share*                   Unit

Amana                          21.5%                 19.2%                      $ 862
Frigidaire                     15.4%                 16.8%                      $ 732
General Electric               29.6%                 32.0%                      $ 825
Maytag                         10.7%                  9.1%                      $ 831
Whirlpool                      22.8%                 22.9%                      $ 840
* From Dealerscope 1999

Retailers                          Market Share (units)          Average Price per Unit

Appliance/Television Dealers              53.6%                              $ 858
Best Buy                                   8.7%                              $ 664
Circuit City                              11.6%                              $ 762
Montgomery Ward                            7.5%                              $ 697
Sears                                     18.6%                              $ 880




                                                                                          23
                Table 2: Descriptive statistics of the dish-washer market

Manufacturers             Market Share        Validation Market       Average Price per
                            (units)                Share*                   Unit

Maytag                        28.5%                 24.5%                      $450
General Electric              25.8%                 27.6%                      $375
Whirlpool                     24.1%                 28.1%                      $399
Kitchen Aid                   13.0%                  9.8%                      $567
Frigidaire                     8.6%                 10.1%                      $350
* From Dealerscope 1999

Retailers                          Market Share (units)        Average Price per Unit

Sears                                     42.8%                             $419
Applicance/TV stores                      35.6%                             $451
New Home Builders                          8.1%                             $302
Circuit City                               8.2%                             $380
Best Buy                                   5.2%                             $374




                                                                                        24
                Table 3: Descriptive statistics of the microwave market

Manufacturers             Market Share       Validation Market      Average Price per
                            (units)               Share*                  Unit

Sharp                        40.1%                 42.9%                     $165
General Electric             20.2%                 20.3%                     $229
Panasonic                    16.6%                 18.2%                     $155
Samsung                       8.2%                  8.4%                     $109
Emerson                       7.8%                  5.0%                     $107
Whirlpool                     7.1%                  5.2%                     $247
* From Dealerscope 1997

Retailers                         Market Share (units)        Average Price per Unit

Walmart                                  26.9%                            $119
Sears                                    26.8%                            $203
Applicance/TV Stores                     17.8%                            $261
Best Buy                                 10.1%                            $152
Kmart                                     9.3%                            $116
Circuit City                              9.1%                            $191




                                                                                       25
         Table 4: Summary of Demand-side Estimates: Sign and (significance)*

                                    Retailer Demand
           Category                    Own Brand price                Competitive Brand Price
Fridge                               Negative (p < 0.06)               Positive (p < 0.01)
Dishwasher                           Positive                          Positive (n.s.)
Microwave                            Negative (p < 0.02)               Positive (p < 0.01)

* p-value is for a one-tailed test of the hypothesis that own price coefficient is negative
and cross-price coefficient is positive.




                                                                                         26
                       Table 5: Refrigerator pricing equation
                        Dependent variable: Retailer price

R-Square = 0.4091                        Adj R-square = 0.3710

Explanatory variable                       Parameter estimate    Std error   t-value

Intercept                                               366.13    788.91       0.46
Year                                                    -17.98     17.09      -1.05
First quarter dummy                                      48.04     31.07       1.55
Second quarter dummy                                     34.48     29.14       1.18
Third quarter dummy                                      69.22     28.79       2.40
Retailer 1 dummy                                        -21.28     31.22      -0.68
Retailer 2 dummy                                       -215.03     31.22      -6.89
Retailer 3 dummy                                       -117.35     31.22      -3.76
Retailer 4 dummy                                       -184.43     31.43      -5.87
Total sales                                               1.77      0.35       5.10
Square root of DEV                                      862.63    473.88       1.82
Price of plastics                                         0.72      1.45       0.50
Price of steel                                           -2.08      6.89      -0.30




                                                                                  27
                  Table 6: Dishwasher retailer-level pricing equation
                          Dependent variable: Retailer price

R-Square = 0.6961                         Adj R-square = 0.6795

Explanatory variable                         Parameter estimate     Std error    t-value

Intercept                                                184.84         251.34     0.74
Year                                                       0.34           0.42     0.81
First quarter dummy                                       -7.68          13.24    -0.58
Second quarter dummy                                      21.10          12.69     1.66
Third quarter dummy                                       16.77          12.54     1.34
Retailer 1 dummy                                         219.90          13.85    15.88
Retailer 2 dummy                                         264.57          13.85    19.11
Retailer 4 dummy                                         152.39          13.92    10.95
Retailer 5 dummy                                          82.99          13.85     5.99
Total sales                                                0.45           0.15     3.06
Square root of DEV                                       135.52         146.28     0.93
Price of plastics                                         -0.39           0.61    -0.64
Price of steel                                            -1.18           2.02    -0.59




                                                                                      28
                    Table 7: Microwave retailer-level pricing equation
                           Dependent variable: Retailer price

R-Square = 0.7318                           Adj R-square = 0.7191

Explanatory variable                          Parameter estimate     Std error    t-value

Intercept                                                  307.81        117.10     2.63
Year                                                        -0.08          0.18    -0.42
First quarter dummy                                          9.23          7.66     1.21
Second quarter dummy                                        19.84          7.70     2.58
Third quarter dummy                                         11.73          7.49     1.57
Retailer 1 dummy                                           -56.57          6.42    -8.82
Retailer 2 dummy                                            24.53          6.42     3.82
Retailer 3 dummy                                            69.64          6.42    10.85
Retailer 4 dummy                                           -35.42          6.42    -5.52
Retailer 5 dummy                                           -73.43          6.42   -11.44
Total sales                                                  0.17          0.09     1.77
Square root of DEV                                        -213.62         99.30    -2.15
Price of plastics                                           -0.48          0.27    -1.81
Price of steel                                               0.63          0.81     0.78




                                                                                       29

				
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