Variety Pass-Through: An Examination of the
Ready-to-Eat Breakfast Cereal Market
Timothy J. Richards and Stephen F. Hamilton∗
Arizona State University and California Polytechnic State University, San Luis Obispo
August 12, 2011
Abstract
There has been much public concern regarding the linkage between commodity price changes and
retail price inflation, particularly in the area of consumer food products. An important element that
controls the degree in which commodity price changes pass-through into retail prices is the breadth of the
marketing channels that connect wholesale products to multi-product retailers in downstream consumer
markets. When wholesale prices rise in a product category, retailers have an incentive to reduce the
length of their product lines, and this has the effect of softening price competition in retail markets.
Moreover, because retailers endogenously choose which products to remove from their shelves, retailers
may selectively trim product lines among relatively high-priced retail goods, censoring the data used
to calculate price pass-through terms. In this paper, we control for “variety pass-through” effects by
jointly estimating the extent to which wholesale price changes convey into the prices and product lines of
multi-product retailers. We find wholesale price changes to be shifted substantially less than one-for-one
into retail prices when not explictly controlling for product composition effects, but find evidence that
wholesale prices are shifted more than 100 percent into retail prices when accounting for the endogeneity
of product line decisions among multi-product retailers.
JEL Classification:
Keywords: differentiated products, discrete-continuous choice, distance metric, pass-through, retail competition.
∗ Richards
is the Morrison Professor of Agribusiness, Allender is a Ph.D student, and Allender is an Assistant Professor in
the Morrison School of Agribusiness and Resource Management, W. P. Carey School of Business, Arizona State University.
Hamilton is Professor in the Department of Economics, Orfalea College of Business, California Polytechnic State University,
San Luis Obispo, CA. Contact author: Richards. Address: 7171 E. Sonoran Arroyo Mall, Mesa, AZ. 85212. Ph. (480) 7271488, Fax: (480) 727-1961, email: trichards@asu.edu. Support from the Economic Research Service of the USDA is gratefully
acknowledged. Copyright 2010. Please do not cite or quote without permission.
1
Introduction
Prices for many key production inputs rose at historical rates over the period 2006-2010, raising the spectre
of retail price inflation in the popular press (Wall Street Journal, 2010). Yet, consistent with a large body of
empirical work that documents incomplete pass-through of commodity price changes to retail price changes
(Borenstein, Cameron and Gilbert 1997; Peltzman 2000; Nakamura and Zerom 2010), only a small fraction
of the rise in commodity prices appears to have translated into higher prices in consumer goods markets. In
the case of consumer food products, for example, farm commodity prices rose at a 17.4 percent annualized
rate over the period 2006-8008, while consumer food and beverage prices rose by only 4.6 percent over the
same period (BLS). This trend is consistent with the stylized fact that the movement of manufactured
products from upstream commodity markets to downstream consumer markets appears to dampen the effect
of retail price inflation in the economy. Understanding why this is so, and in particular understanding the
relationship between wholesale price changes and retail price changes in multi-product production channels
that convert commodity inputs into a wide array of finished consumer products, is essential to predicting
how retail prices will respond to contemporaneous demand and supply shocks. The relationship between
wholesale and retail prices is important for predicting the effect of exchange rate movements on traded
wholesale goods, for assessing the burden of government taxation, for understanding how manufacturer price
discounts on a particular subset of products affects consumer markets, and for establishing better forecasts
of how changes in commodity prices influence the overall rate of price inflation in industrial economies.
In many cases, the trade of wholesale products is mediated by multi-product retailers. Unlike singleproduct retailers, multi-product retailers are able to respond to changes in wholesale prices both by adjusting
retail prices and by changing the composition of retail product lines.
Following an increase in wholesale
prices, multi-product retailers can respond not only by raising consumer prices in the affected category but
also by trimming products from the retail case. To the extent that retailers respond to changes in wholesale
prices by adjusting the length of their product lines, an important issue in estimating pass-through rates from
wholesale prices to retail prices is that changes in wholesale prices alter the dimension of product lines in
which multi-product retailers compete. This paper contributes to the pass-through literature by accounting
for endogenous product line adjustments by multi-product retailers in estimating pass-through rates from
wholesale prices to retail prices.
We frame our observations around retailer decisions on product lines and prices for ready-to-eat breakfast
cereal at Los Angeles supermarkets. The breakfast cereal category is ideal for studying the joint product
1
line and price effects of wholesale price changes for three reasons: () supermarkets provide a considerably
wide array of breakfast cereal products; () supermarkets tend to make frequent changes to their breakfast
cereal product lines (and do so in our Los Angeles sample); and () farm commodity prices supporting
the production of manufactured cereal products rose at unprecedented rates in 2008 and then decreased
markedly in 2009, creating substantial variation in wholesale cereal prices over the period 2007-2010 that
encompasses our data.
Much of the previous empirical research on pass-through effects has focused on the transfer of commodity
price changes into retail prices. In models estimating exchange-rate pass-through, Goldberg and Hellerstein
(2007), Hellerstein (2008), and Nakamura and Zerom (2010) empirically document the effects of imperfect
competition, local cost conditions, and price rigidity in determining pass-through rates.
Nakamura and
Zerom (2010) use wholesale price data to separate commodity and wholesale pass-through effects in the
coffee market and find that approximately 1/3 of the change in coffee commodity prices is reflected in each
of the wholesale and retail prices, with the remaining 1/3 of the change in commodity prices absorbed by
agents in the distribution channel.
While it is important to understand the pass-through of commodity
prices through both wholesale and retail levels into consumer prices, our present purpose of decoupling input
price changes into variety pass-through and price pass-through effects is served most clearly by focusing
our attention on wholesale pass-through effects. Estimating commodity-price pass-through rates into retail
prices would otherwise require developing a vertical pricing model to encompass both wholesale and retail
pass-through terms.
Structural models of this type have been recently estimated by Hellerstein (2008),
Nakamura (2008), and Nakamura and Zerom (2010), although not in a framework that accounts for product
line adjustments by multi-product retailers.
It is well-known from models of single-product retailers that the response of retail prices to changes in costs
depends both on market structure and the curvature of demand (Bulow and Pfleiderer, 1983; Dornbusch,
1987; Bergin and Feenstra, 2001; Atkeson and Burstein, 2008). Under oligopoly, retailers can “over-shift”
changes in unit cost, or shift cost changes more than one-for-one into retail prices when consumer demand
functions are sufficiently concave (Seade, 1987).1 Recently, Hamilton (2009) considers changes in tax rates
among multi-product retailers and finds that over-shifting is more likely to occur across products carried by
multi-product retailers than in the single-product case. The reason is that multi-product retailers adjust to
a change in wholesale cost that affects a category of retail goods by reducing the length of product lines, and
1 Over-shifting of cost changes into prices occurs in the tax literature, for example, when the elasticity of the slope of demand
(“Seade’s ”) satisfies   1 (Delipalla and Keen, 1992; Hamilton, 1999; Anderson, de Palma and Kreider, 2001).
2
this softens price competition among retailers for the remaining products. We develop a multi-product retail
model along these lines that jointly accommodates price and product line length adjustments in response to
wholesale price changes and rely on this framework to estimate a structural model of wholesale pass-through.
Our method is capable of isolating the pass-through effects of wholesale price movements into retail prices
and product variety.
We compare the outcome of our model that controls for variety pass-through to a specification that does
not account for endogenous retailer decisions on product line length. We find that controlling for retailer
product line adjustments significantly increases the extent to which wholesale prices are passed along into
retail prices. Absent our control for changes in product line length on retail prices, our findings echo those
of previous studies that document incomplete pass-through of wholesale price changes into retail prices;
however, when controlling for the effect of product line adjustments on retail prices, we find retailers shift
wholesale price changes approximately one-for-one into retail prices, and indeed slightly overshift them.
The main contributions of our paper can be summarized as follows.
First, we extend the empirical
literature on pass-through to multi-product environments by accounting for the endogeneity of product
line decisions and controlling for the effect of variety pass-through on retail pricing behavior.
Second,
we empirically calculate variety pass-through effects among multi-product retailers in response to changes
in wholesale prices, an outcome of independent importance in understanding the welfare implications of
wholesale price changes in consumer markets. Third, we contribute to the body of empirical evidence on
price pass-through by documenting substantially higher pass-through effects from wholesale prices to retail
prices when controlling for product line adjustments by multi-product retailers. This finding suggests the
potential for a substantial portion of wholesale price changes to pass-through to retail prices, particularly in
product categories with relatively long product lines.
The remainder of the paper is organized as follows. In the next section, we describe our econometric
framework. In Section 3, we document our data sources, provide a preliminary analysis of the underlying
variability in the data that permits identification of our key variables, and construct a benchmark passthrough model against which our structural model of retail price and variety adjustment can be compared.
In Section 4 we present our estimation results and discuss the implications of our findings for the calculation
of pass-through effects.
We conclude in Section 5 by detailing some limitations of our research and offer
suggestions for future research.
3
2
Variety Effects on Store Competition
It is well understood that the rate of pass-through depends upon the curvature of demand, the structure
of costs, and the degree of market competition.
Our aim is to jointly consider price and variety pass-
through by endogenizing choices of supermarket retailers on product line length in response to wholesale
price changes.
We do so by modeling supermarket price and variety choices as conditional on wholesale
prices and consumer demand conditions across a range of products in a category. As in Hamilton (2009) and
Hamilton and Richards (2009), retailers determine the product lines in a multi-product oligopoly market
that incorporates spatial competition between retailers for store traffic. For analytic tractability, we consider
variety choices to be conditional on wholesale prices, and then choose retail prices based on the realization
of the variety game in a two-stage game structure.2 Wholesale price changes influence product line length
decisions (“variety pass-through”) in the first stage of the game, which then determine equilibrium retail
prices both through cost-considerations in the wholesale market and according to the extent to which variety
pass-through effects influence subsequent pricing behavior in the multi-product retail environment. We then
recover pass-through rates into retail prices by allowing for wholesale price changes to be mediated through
retailer adjustments in retail prices and product lines.
Each component of the model is estimated using
scanner data that encompass 33 months of sales among 6 major supermarket chains in the Los Angeles
market. In the remainder of this section, we describe each part of the empirical model in detail.
2.1
Consumer Demand
We consider a hierarchical demand model in which variation in retail prices and product variety ranges
affects both consumers’ store choice and selection of products once in the store. Specifically, we represent
consumer demand by a random utility model in which consumers make a discrete choice of one product
from among those represented by our sample of retail data, or else purchases a product from an alternative
retail outlet, which we define to be the outside option.
Because consumers can buy cereal from sources
other than those captured by our scanner data, we model the hierarchical nature of a consumer’s choice
process: consumers first choose whether to buy from the traditional supermarkets described by our data,
or another source, and then the specific brand.
Consequently, we adopt a Generalized Extreme Value
(GEV) model of consumer demand (McFadden, 1978). With the GEV assumption, we allow for differing
degrees of substitution among products within each group: supermarket purchases and others. Without
2 Discussions
with managers at three national supermarket chains suggest that this is a reasonable assumption as stocking
decisions are made monthly and on the basis of longer-term performance criteria than the weekly pricing decisions.
4
further modification, the GEV model still exhibits the independence of irrelevant alternatives (IIA) property
within each group, which is known to imply an unrealistic pattern of substitution.
Therefore, we allow
the product-specific preference term, the marginal utility of income, and the variety-effect to vary randomly
over individuals (Berry, Levinsohn and Pakes, 1995; Nevo, 2001; McFadden and Train, 2000). The resulting
correlation between unobserved heterogeneity and attributes of each product generates demand curvature
that, in turn, creates a general pattern of substitution among products.
The random-parameters GEV model is well-understood in the literature, so we provide only the essential
elements of our application relating to product variety. In terms of a formal utility model, the utility
consumer  obtains from consuming product  in store  during month ( ) is a function of the product’s
price in each store,  , product- and store-specific preferences,   , and the number of products sold in the
store,  ( ), where  () is concave, and a set of product attributes ( ) such that:
 =   +   +  ( ) +

X
=1
   +   +   + (1 − )  ∀ ∈   ∈ 
(1)
for the set of products  and stores , where  is the GEV scale parameter,   is an iid error term that
reflects attributes of the product that may be important to utility, but are unobserved by the econometrician
such as location on the shelf, unmeasured advertising, perceived quality or package characteristics or of the
store such as location, cleanliness or the number of services offered,  is an iid error term that reflects
unobserved consumer heterogeneity, and   is an error component that is distributed so that the entire
error   + (1 − ) remains extreme-value distributed (Cardell, 1997).
Utility associated with the
choice of the outside good is 00 = 00 . In this setting, the parameter  can be interpreted as a measure
of the degree of substitutability among groups, such that  = 1 implies perfect substitution among stores,
thereby collapsing the model to a standard logit model among products and stores. The product attributes
included in the vector x are a binary product discount variable ( ) that assumes a value of 1 if the
product is reduced in price by at least 10% from one month to the next and then returned to its previous
value in the following month, an interaction term between the discount variable and price (  ) and a
set of store and brand binary variables.3
Equation (1) explicitly incorporates consumers utility from product variety. Our specification encompasses cases in which consumer utility rises in product variety, for instance when longer product lines facilitate
better matches between consumers and brands, and can also accommodate cases in which utility decreases
in product variety, as may be the case when longer product lines increase the cost of consumer search.
3 Nutritional
attributes performed poorly in this model so were excluded from the attribute list.
5
Specifically, we consider utility to be a quadratic function of line length,  ( ) =  1  + 12 2 2 , which
allows for a trade-off between matching effects and consumer search costs of product line expansion when
the parameters  1 and  2 take different signs.
Unobserved consumer heterogeneity is an important determinant of brand choice in empirical models of
supermarket retailing (Hellerstein, 2007; Nakamura and Zerom, 2010). Therefore, we assume the marginal
utility of income (price-response) is normally distributed and a function of consumer attributes, so that
 = 0 +

X
  +        ˜  (0 1)
(2)
=1
where 0 is the mean price response across all consumers,  is the effect of consumer attribute  on price
sensitivity,  is a vector of attributes for consumer , and   is the random, consumer-specific variation
with parameter   
Product-specific preferences also depend on individual attributes, which we specify as
  =  0 +

X
   +      ˜  (0 1)
(3)
=1
where  0 is the mean preference for product  in store ,   is a vector of individual attribute effects, and
 is the random consumer-specific effect on product and store preferences.
Finally, we allow the marginal utility parameters for the variety effect to be random so that
 1 =  10 +

X
 1  + 1    ˜  (0 1)
(4)
=1
and similarly for  0 , where  10 is the mean of the linear term in the preference for variety over all stores,
 1 is a vector of individual attribute effects on variety, and  is the random component consumer  derives
from shopping in stores with greater variety.
We aggregate over the distribution of consumers to arrive at an expression for the share of each
product variant in the entire market. Because the random-parameter logit model introduces a large number
of parameters relative to a standard logit model, we follow Nevo (2001), among others, and write the indirect
utility function in the general case in terms of two sets of variables — those that are assumed to be random
and those that are not— as follows:
 =   (        ;    ) +  (                   ) +  
6
(5)
where   is the mean level of utility that varies over products and stores, but not consumers, and  is the
idiosyncratic part that varies by consumer and product. We define the densities of  ,   and  as  (),
() and (), respectively, so that the market share of product  in store  can be obtained by integrating
over the distributions that characterize consumer heterogeneity as
 =
Z Z Z
exp( + )(1−)
X (1−)  ()()()
 (

)
(6)
∈
where  =
X
exp( + )(1−) . Expression (6) is then estimated with the simulated maximum likeli-
∈
hood (SML) algorithms of Train (2003) using the control-function method introduced by Petrin and Train
(2010) to account for the obvious endogeneity of prices in the mean utility specification. We describe this
method in more detail below.
2.2
Price and Variety Choice
We structure the game between multi-product oligopoly retailers as follows. In the first stage, retailers
make product line length (“variety”) decisions conditional on observed wholesale prices.
In the second
stage, retailers compete in prices based on wholesale prices and their product variety decisions, and in the
third and final stage, consumers select among the retailers and the products carried by retailers based on
the outcomes for prices and product variety. We analytically derive pass-through rates within this game
structure by totally differentiating the first order conditions for price and product line length with respect
to wholesale prices, and then estimate both price- and variety-pass-through using a generalized method of
moments (GMM) estimator. This approach allows us to test our core hypotheses directly without relying
on simulation methods and indirect tests.4
Retailers maximize profit by choosing prices and the length of their product lines. The profit equation
for retailer  is written as (dropping the time subscript for clarity):
 = 
X
∈
 ( −  −  ) − ( )
(7)
where  is the wholesale price paid by retailer  for product ,  is the size of the aggregate market for all
products, and ( ) reflects the cost of adding products to the retailer’s line. For tractability, we consider
the cost of maintaining a product line to be linear in the number of products stocked, ( ) = 0 + 1  ,
4 Structural models of retail pass-through are typically implemented by simultaneous estimation of demand and a retail margin
equation, and then simulating the impact of changes in cost in order to determine the rate of cost-pass-through (Goldberg and
Hellerstein, 2007; Kim and Cotterill, 2008).
7
which ensures equilibrium under circumstances where utility is concave in variety. Retailing costs, which
are assumed to be separable from wholesale purchases, are specified as linear functions of input prices. This
results in the following expression for retailing costs:
 (v ) =
XX
 0 +
∈ ∈
X
   +  
(8)
∈
where v is a vector of  retail prices,  0 are brand- and store-specific fixed-effects, and  is an iid
error term. Retailing costs are estimated after substituting equation (8) into the first-order conditions and
pass-through equations derived below.
Conditional on the product variety decisions of the retailers in stage one, retailer ’s first order condition
for the price of product  is given by
X


=   + 
( −  −  )
= 0 ∀ ∈   ∈ 


(9)
∈
Notice that equation (9) implies that each retailer internalizes all cross-sectional pricing externalities across
products within the category, but does not take into account the effect of his pricing on the sales of products
sold by other retailers. Stacking the first-order conditions across retailers and introduce an ownership matrix,
Ω, with element   = 1 if product  is sold by retailer  (and zero otherwise), we write the first-order condition
as
p = c + w − (ΩS )−1 s
(10)
where bold notation indicates a vector (or matrix), and S is the matrix of share-derivatives with element
   The specific form of these derivatives for the random-coefficient nested logit model are provided
in the technical appendix.
Retailers’ variety choices take into account the effect of a longer product line on cannibalizing sales from
other products in the line and also the effect of providing a longer product line on the prices set by rival
retailers. Rival retailers, who can no longer extend their own product lines once the product lines of rival
retailers are revealed in the pricing stage, respond to a longer product line of a rival by more aggressively
discounting prices to acquire store traffic in the subsequent pricing stage.
The first-order conditions for retailers’ variety choices are given by
8
X 
X
XX

  

=

+
( − − )
+
( − − )
−
= 0 ∀ ∈  (11)



  
∈
∈
∈ ∈
The optimal variety choice of retailer  in equation (11) depends on the relative strength of: () the own
category price-effect (first term), () the business-stealing effect of variety from rival retailers (second term),
() the effect of variety choices on market share through induced changes in the prices charged by other
retailers in the subsequent pricing stage (third term), and () the cost of stocking a longer product line
(fourth term). We solve thes equations for the optimal line length for each retailer, which gives (in matrix
notation),
N =(11 )(Ms0 P +M(p − c − w)0 S + M(p − c − w)0 S P )
(12)
where P is a vector of price-derivatives in variety, S is a vector of share-derivatives in variety and the
other variables are as defined above.
At this point, we can estimate (11) and (12) simultaneously to recover the parameters of the retailing
cost function and the cost-of-variety function using only information from the demand side and the game
structure. We can then simulate the solution for optimal price and variety choices under various assumptions
regarding changes in the wholesale price to calculate empirical pass-through rates as in Kim and Cotterill
(2008); however, in our case, a more direct alternative is available by making use of data on observed
wholesale prices.
Totally differentiating the first-order conditions in (11) and (12) with respect to the wholesale price, we
obtain analytic solutions for both the price- and variety-pass through rates. This allows a more direct test of
the primary hypothesis of our study that wholesale prices are negatively related to retailers’ variety choices,
leading to higher retail pass-through rates when controlling for the impact of variety competition on retail
price competition. Totally differentiating first-order condition (11) and collecting terms gives
Ã
X  X X
X 
 2 
+
( −  −  )
+

 

∈
Ã
X 
∈

+
XX
∈ ∈
∈ ∈
∈
X 
 2 
( −  −  )
+
 

∈
!
!

+



=
 ∀ ∈   ∈ 


where   is the retail price pass-through term and   is the “variety pass-through” term.5
5 The
full set of first- and second-order share- and price-derivatives are provided in the appendix
9
(13)
Our notion of variety pass-through merits some elaboration.
In a multi-product retail environment,
changes in wholesale prices among a category of goods, for instance breakfast cereals derived from corn,
are projected into the consumer market jointly through changes in the length of the product line and retail
prices. In response to an increase in wholesale prices, retailer margins narrow in the product category, and
retailers respond by trimming from their product lines. Because it is costly for retailers to maintain long
product lines, rising wholesale prices that pinch retail margins cause retailers to reduce the length of their
product lines. The resulting decline in product variety reduces consumer utility, and the extent to which
wholesale price changes manifest in price pass-through or variety pass-through effects depends on the relative
degree to which consumer demand in the category responds to changes in prices and changes in product
lines. To the extent that product variety increases consumer utility from purchases in the product category,
say by facilitating better matches between consumers and brands, when retailers respond to cost increases
by reducing product lines, this in turn softens price competition by de-emphasizing the role of retail prices
in the product category to generate store traffic.
Totally differentiating first-order condition (12) yields
⎛
⎜
⎜
⎝

X
XX

 
( −  −  )  + 
( −  −  ) 
−
 
∈
∈ ∈
XX

∈ ∈
⎛
⎜
⎜
⎝
= 

  + 
+
XX
∈ ∈


 ) 
 
XX
2
 

( −  −  ) 
+

( −  −  ) 
+




∈
∈
∈
XX
2


( −  −  ) 2 


 
+

 
¶
2
( −  −  ) 
2 +

(14)
XX
∈
µ
( −  −
2



∈ ∈
 ∀ ∈ 
⎞
⎟ 
⎟
⎠ 
where the restriction  2  2 = 0 is imposed to ensure a tractable solution.6 Each element of (13)
and (14) is derived from parameters estimated from the demand model, except for the price- and variety
pass-through terms, which we estimate as unobserved parameters.
Assuming the pass-through rates are
constant over all observations, we express these two equations in estimable form by writing the demand-side
information as variables, and adding an econometric error term gives an expression for the price-pass-through
model:
6 Each
of the derivatives presented here is derived in the appendix.
10
⎞
⎟ 
⎟
⎠  +
 =    +   +  
(15)
and for the variety-pass-through model:
 =    +    +  
(16)
where  is the vector of share-derivatives in price on the right-side of (13),   is the matrix of sharederivatives in the first line of (13),  is the matrix of share-derivatives in the second line of (13),  is
the vector of share-derivatives in variety on the right-side of (14),   is the matrix of share-derivatives
in the second line of (14),   is the matrix of share-derivatives in the first line of (14), and  and 
are iid error terms.
We estimate the entire empirical model in two stages: first estimating the demand model in (6), and then
using the implied share derivatives in price and variety to estimate equations (15) and (16) after substituting
in the cost equation (8). As explained in detail below, we estimate the entire system of pricing and variety
equations using generalized method of moments (GMM) to account for the endogeneity of prices and market
share terms in the model.
3
Data and Estimation Methods
3.1
Data
Our empirical application considers the ready-to-eat breakfast cereal market. Breakfast cereal is one of the
most scrutinized product categories in the empirical industrial organization and marketing literatures (see,
e.g., Schmalensee, 1986; Cotterill, 1986; Nevo, 2001; Nevo and Wolfram, 2002). It is ideal for the purposes
at hand because: () breakfast cereals are widely purchased by consumers across all income strata, () the
supply-side of the market is dominated by two major manufacturers (Kellogg and General Mills), which
intensifies price and non-price competition at the wholesale level, () supermarket retailers offer similar
breakfast cereal assortments, and () cereal is derived from agricultural commodity inputs that exhibit
marked price fluctuation over the period encompassed by our data.
Our data describes 33 months (June 2007 - March 2010) of supermarket chain-level retail sales of readyto-eat breakfast cereal in the Los Angeles retail market. We acquire our data from IRI InfoScan for the top
six supermarkets in Los Angeles: Albertsons, Food 4 Less, Ralphs, Safeway, Stater Brothers, Vons and Vons
Pavilions and include all branded UPCs, both private labels and national brands, in the breakfast cereal
11
category.7
We focus our analysis on the 19 top brands (by volume share) and subsume all other brands
in the outside option.
Our set of top brands is selected based on market share ranking among the six
stores in our sample, subject to the constraint that each brand is sold in all stores. We define the outside
option broadly in a manner consistent with Berry, Levinsohn and Pakes (1995). Namely, we define the total
market as the population of Los Angeles and use per capita consumption data (USDA, ERS) to impute a
total-market consumption level.8 The outside option is then calculated as the total market less the cereal
sales captured in our data. In this way, the outside option captures not only the brands excluded from our
sample, but cereal purchased through retailers that do not participate in the IRI InfoScan data syndication
system, for instance Wal*Mart, Sam’s Club and Costco, as well as through foodservice, convenience and
institutional outlets.
It is important to note that an important limitation of syndicated scanner data is the absence of data
from mass merchandisers. An advantage of framing our empirical study in the Los Angeles retail market
is that Wal*Mart maintains a small presence in Los Angeles relative to other major U.S. markets, which
minimizes the effect of the “Wal*Mart gap” noted in other studies.9 Accordingly, IRI’s market coverage is
relatively high ( 70%) in the Los Angeles market.
Table 1 documents the extent of the variation in prices and product line length among our sample stores.
Notice that the stores in our sample differ considerably in their overall price level, line length and promotion
frequency. Take for example the contrast between Albertsons and Food 4 Less. Albertsons selects breakfast
cereal prices at roughly the sample average across supermarkets ($0.226/oz), but stocks 27.6% more brands
than the sample mean and promotes 9.4% more frequently; Food 4 Less sets prices 7.4% below the sample
average, but stocks 27% fewer brands than the average store and promotes infrequently. In terms of the
relationship between prices and product line length, the correlation among our sample stores is 47.3%,
suggesting that stores that choose to provide a larger range of product variety also tend to charge higher
prices. High-price stores also promote more frequently, as the correlation between price and promotion
frequency is 79.6%.
Table 2 depicts the composition of sales between supermarkets in terms of prices and market share.
Notice that the variation in price and market share is specific to each brand across stores. For Cheerios,
7 We
include Vons and Vons Pavilions as separate chains because Pavilions stores are managed independent of Vons, and
maintain a fundamentally different variety/pricing strategy. According to a company spokesman, Pavilions sells a greater variety
of organic foods, wine, produce and specialty items.
8 Implicitly, we assume individuals in Los Angeles consume breakfast cereal at approximately the same rate as consumers in
the U.S. as a whole.
9 Wal*Mart is represented in Nielsen’s HomeScan product; however, HomeScan is a household-level data set that is not
well-suited to our purpose here.
12
for example, the coefficient of variation in price across stores is 3.8%, while the coefficient of variation in
market share is over 30%; for Life cereal, the coefficient of variation in price across stores is 11.4% while the
coefficient of variation in market share is 26.7% .
[tables 1 and 2 here]
We acquire wholesale cereal prices from the Price-Trak data service provided by Promodata, Inc. These
data represent prices paid to grocery wholesalers by supermarket retailers and encompass nearly all the
cereal brands sold by major manufacturers (including all brands in our sample). Price-Trak data reports
prices charged by manufacturers prior to the application of allowances, markups of price over unit cost by
wholesalers to retailers, the effective date of new case prices, “deal allowances” (off-invoice items offered to
retailers by the wholesaler), the type of promotion suggested by the wholesaler to the retailer, and the
allowance date.
Of these variables, we define the wholesale price to be the price charged to the retailer
net of allowances. A limitation of this data source is that it represents prices charged by wholesalers to
only non self-distributing retailers. Because retailers in our sample generally self-distribute, we implicitly
assume in making use of these data that wholesale prices are highly correlated across self-distributing and
non self-distributing retailers, for instance due to pricing restrictions under the Robinson-Patman Act.10 To
the extent that the prices our retailers pay differ from the wholesale prices in the dataset, our wholesale
price may be measured with error. Nevertheless, we believe the use of these data represent a significant
advancement over alternative approaches that rely on imputed wholesale prices.
All retailer input-price data are from the Bureau of Labor Statistics (BLS, 2010a). These data include
average weekly earnings by workers in the grocery retailing industry, an index of healthcare costs paid
by retailers, and an index of utility prices.
We rely on primary BLS data on wages from the Current
Employment Statistics (CES) survey (BLS, 2010b), which provides detailed industry data on employment,
hours, and earnings of workers, and acquire utility prices from the market-specific indices provided in the
BLS Consumer Price Index program (BLS, 2010a). Finally, we use the Bureau of Census (2010) mean and
standard deviation for each socio-economic and demographic variable (age, household size and income) for the
Los Angeles market to create random draws from the distribution of each variable in the random-coefficient
nested logit model (Berry, Levinsohn and Pakes, 1995). We also rely on Census data for population figures
for the Los Angeles metropolitan area, which we match with per-capita cereal consumption values from the
Economic Research Service of the USDA (ERS).
An alternative to estimating a fully structural model of retail pass-through is to estimate a reduced-form,
1 0 Nakamura
and Zerom (2010) also use wholesale prices from Price-Trak to describe purchase costs for coffee retailers.
13
ordinary least squares regression of retail prices on wholesale prices, retailing input costs and market- and
brand-fixed effects. Nakamura and Zerom (2010) use such a model to provide preliminary insight into whether
there is any fundamental relationship between wholesale and retail prices in their coffee data. We adopt this
approach to estimate a simple model of retail pricing in which retail and wholesale prices are assumed to
be linearly related with the coefficient on wholesale prices representing the empirical pass-through rate. We
also estimate a second reduced-form model in which retail variety depends on wholesale prices and a set of
brand and store fixed effects. The results from both of these models are shown in Table 3. In our breakfast
cereal data, we find that the reduced form pass-through rate, before accounting for demand curvature or
variety feedback effects is 0.637 (t-ratio = 7.616), which implies that changes in wholesale prices pass through
incompletely into retail prices, adjusting by less than $0.02/oz in response to a $0.03/oz change in wholesale
prices.
Wholesale price changes also alter variety provision.
A $0.01/oz change in wholesale prices (on
average 5% of the retail price) causes retailers to reduce the length of their product lines by slightly more
than 3 stock-keeping-units (SKUs) (t-ratio = -7.594). These estimates are only preliminary, however; they
account for neither the structure of demand nor the endogeneity of retail product variety.
[table 3 here]
3.2
Estimation Methods and Identification
We estimate our structural model of demand and pass-through in two stages. We first estimate the demand
model using the control function method of Petrin and Train (2010), and then employ the Generalized
Method of Moments estimator (Davidson and MacKinnon, 2004) for the second-stage pricing model. Retail
prices are likely to be endogenous in aggregate, market-level scanner data, and we test for this possibility
using a Hausman (1978) specification test. We select this approach based on the possibility that unobserved
factors embodied in the error term of the estimated demand equation, for instance shelf-facing, the size of
the display area, and magnitude of in-store promotions, may be highly correlated with the observed retail
prices. If the estimator does not to take this into account, the resulting parameter estimates are biased
and inconsistent.
Addressing endogeneity using the simulated generalized method of moments (SGMM)
approach has become a workhorse in the empirical industrial organization and marketing literatures; however,
Berry, Linton and Pakes (2004) show that the contraction algorithm underlying this method, which matches
predicted and observed market shares to impute a vector of mean utilities, is highly sensitive to sampling
error, a feature that suggests the use of multiple markets and multiple stores in each market. Consequently,
we adopt the “control function” approach developed by Petrin and Train (2010).
14
The “control function” method has its econometric basis in the sample-selection models of Heckman
(1978) and Hausman (1978). With this approach, we control for the bias likely to arise from the endogeneity
in prices using a two-stage estimation method. In the first stage, we estimate an instrumental variables (IV)
regression in which we regress the endogenous prices on a set of variables likely to serve as valid instruments.
We then use the residuals from this regression as explanatory variables in the mixed-logit demand equation,
which is then estimated using simulated maximum likelihood (SML, Train, 2003). By introducing the IV
residuals into the demand model, we account for unobservable factors that may be correlated with errors in
the demand equation. To account for the error in the second-stage demand model associated with using the
residuals as explanatory variables, we bootstrap the standard errors in the mixed logit model and use the
bootstrap distribution to derive inference from the model (Cameron and Trivedi, 2005).
Our identification strategy is conventional in the literature. The goal is to acquire instruments that are
correlated with the endogenous prices in the model, but which are uncorrelated with unobserved variables in
the demand equation. Unobservable factors that are likely to influence prices for breakfast cereal products
include market-specific advertising, chain-level merchandising efforts, or variations in local tastes that are
not accounted for in the demographic variables encompassed by the demand model. We employ a variety
of instruments to control for these factors.
First, because product-specific variation in costs will tend to
be correlated with prices for the same product but uncorrelated with unobservable factors in the demand
equation, we interact retail and production input prices with the set of binary brand-indicators. Second,
we include a set of lagged share values in order to pick up any state dependence in demand that may arise
from habit formation, learning or inertia.
From the perspective of current-period demand, lagged share
values are pre-determined, and we accordingly employ lagged share values as our instruments. Third, we
include brand-specific binary variables to account for idiosyncratic supply factors or quality levels that may
be important in determining retail prices. First-stage instrumental variables regressions results show that
this set of instruments explains over 60% of the variation in our endogenous price variables (F-statistic is
39.79) and hence are not “weak” in the sense of Staiger and Stock (1997).
On the supply-side of the model, retail markups on products and the depth of product assortments are
also likely to be endogenous. For this reason, we estimate the price- and variety-pass-through equations
using GMM. In the same sense that variables that independently vary in supply can be used to identify
the demand-side parameters, instruments on the supply-side must similarly reflect variation in demand that
is independent of unobservable variables in the pricing equation.
We accordingly capture brand-specific
variation in demand by including demographic variables such as income, age, and average household size
15
and interacting these variables with brand-specific dummies.
as proxies for current-period margins.
Second, we include lagged margin values
As in the case of the demand model, the pricing instruments also
include a set of product-specific binary variables to capture brand-specific preferences that are otherwise not
accounted for in the continuous instruments. We evaluate the appropriateness of our instruments on the
basis of two tests: a test of the goodness-of-fit of the instruments in explaining variation in the endogenous
variables and a test of the overidentifying restrictions implied by the GMM estimator.
For the latter
purpose, we conduct a J-test (Davidson and MacKinnon, 2004) with degrees of freedom equal to the number
of overidentifying restrictions. For the price- and variety-pass-through system, the J-test statistic is 265.368
(critical value is 69.832), which suggests the set of instruments is not ideal; however, a first-stage regression
of the instruments on endogenous retail prices provides an 2 value of 0.598 (F = 69.03) and on retail
assortments gives an 2 value of 0.541 (F = 209.55), suggesting that our instruments are not weak.
4
Results and Discussion
In this section, we present and interpret the results obtained by estimating the structural model of priceand variety-pass-through rates. We first present the demand-side estimates and then the pass-through
model.
Compared to the reduced-form model presented above, this model controls for the curvature of
demand in both prices and varieties, the feedback effects from choosing varieties endogenously and both
retailing costs and the costs of additional assortment. When presenting the pass-through model results, we
compare estimates from a model in which we do not control for the endogeneity of prices or variety (nonlinear seemingly unrelated regressions) to those obtained from the GMM model. In this way, we compare
the pass-through rate estimates between a more conventional model and one in which both variables are
endogenous.
Our demand model differs from a simple logit model in three ways: () we allow for hierarchical choice
among stores using a GEV specification, () we allow for unobserved consumer heterogeneity by treating
the constant term, the marginal utility of income and variety terms as random functions of age and income,
and () we estimate the demand model using the control function method of Petrin and Train (2010) as
described above. To evaluate the performance of our model in relation to the simpler logit framework, we
conduct specification tests to assess the appropriateness of each of these modeling elements. Specifically,
we test the GEV specification by conducting a t-test on the GEV scale parameter (), we test the random
coefficients specification both by implementing t-tests of each element of the random-parameter function and
16
by conducting a likelihood ratio (LR) test of the model relative to the fixed-coefficient alternative, and we
test the control function method both by evaluating of the parameters associated with the control function
and by a LR test. Table 4 presents the results of these specification tests. Evidence from the GEV scale
parameter (t = 216.743) suggests that the GEV model outperforms the simple logit specification. The entries
in Table 4 also suggests the random coefficients model as our preferred specification, as the t-ratios for each
element of the random coefficient model (including the means and standard deviations of the parameters as
well as the components of the random parameter functions) is significantly different from zero and the LR
test statistic comparing the random coefficient model with the fixed coefficient alternative yields a chi-square
value of 1,077.322 (with 16 degrees of freedom), which easily rejects the fixed-coefficient model. Use of the
control function approach is appropriate, as both  and  are significantly different from zero. Moreover, the
LR test statistic comparing the random coefficient nested logit model estimated with the control function
method to one that is not results in a LR statistic value of 20.124 (with 2 degrees of freedom), which again
rejects the simpler alternative in favor of the more complete model. As a result of these tests, we adopt the
random coefficients nested logit model and use the estimated coefficients to calculate elasticity values and
to use as inputs in the second-stage pass-through model.
[table 4 here]
A number of findings are of interest in our demand estimates. First, we find that a temporary price reduction leads to an outward shift and negative (counterclockwise) rotation of demand. This finding suggests
that consumer demand becomes more elastic during periods associated with retailer price-promotions, which
may indicate a degree of anticipation among consumers for promoted items that a “better deal” may come
along. Second, we find that the mean utility from shopping at Albertsons and Vons Pavilions is significantly
lower than at Vons (our excluded category), while Food 4 Less is the most preferred chain. Third, among
cereal brands we find that Special K has the highest mean utility of the 19 top-selling brands in our sample
and, based on the data in Table 2, it is also among the most expensive cereals.11 Other cereals with high
marginal preference parameters, most notably Frosted Flakes and Frosted Mini-Wheats, have higher average
market share, but sell for lower prices. Not surprisingly, the correlation between mean utility, market share
and sugar content is very high in our sample. Finally, with respect to product variety we find that the
quadratic specification of product line length in utility is supported by the data, and implies an optimal
line length of 428 products in the cereal category. Given that the store with the longest product line in our
1 1 Special K comes in a number of variants: Red Berries, Almonds, Blueberries and Chocolate.
variants as they are all managed under the Special K brand.
17
We aggregated over these
data is Albertsons with 420, on average across stores, this outcome suggests that stores in our sample are
effectively space-constrained in the cereal aisle. Using the parameters from the random coefficient function,
optimal assortment depth falls with both age and income, a finding that is consistent with more habitual
purchasing patterns among older and higher income shoppers.
Table 5 presents the matrix of own- and cross-price elasticities derived from the estimates in Table 4
for a single store in our sample.
The elasticity matrices for all the other stores reveal slightly different
patterns of substitution, which justifies our use of the GEV specification.12 Allowing for a flexible pattern
of substitution both among brands and among stores is important for our primary objective of examining
equilibrium rates of price and variety pass-through.
[table 5 here]
Table 6 shows the results obtained by estimating the pass-through system.
The entries in Table 6
compare the estimated outcomes from our preferred instrumental variables estimator (GMM) with one that
does not control for retailer variety adjustments in response to changes in wholesale prices (NLSUR). Based
on the chi-square statistics comparing their explanatory abilities to a null alternative, both the NLSUR and
GMM estimators provide acceptable fits to the data; however, a Hausman (1978) test yields a test statistic
value of 78.453, rejecting the non-IV estimator out of hand.13
Nevertheless, it is helpful to compare the
pass-through estimates of the two models to better understand the role of retailer product line adjustments in
jointly determining pass-through rates of wholesale price changes into retail prices and product variety. We
interpret the coefficient on the wholesale price as the “direct pass-through rate”, as it reflects only the direct
effect of wholesale price variation on the retail price and we interpret the coefficient on , which takes into
account the optimizing behavior of the retailers, as the “total pass-through rate”. The total pass-through
rate accounts for the effect of joint retailer competition in variety and prices on the retailers’ ability to pass
wholesale price increases into consumer prices.14 In terms of the specific parameter estimates, we find that
assortment costs rise in the number of SKUs, as expected, which ensures an equilibrium assortment level
with concave utility. Notice that the variety pass-through rate () is negative and significant in both models,
suggesting that retailers indeed reduce the length of their product lines in response to an increase in wholesale
prices. The intuition is straightforward: in response to rising wholesale prices, ceteris paribus, retailers are
faced with lower margins to recover the fixed costs of maintaining their product lines and accordingly reduce
1 2 Elasticity
1 3 Our
matrices from all stores in the sample are available from the authors.
Hausman (1978) test statistic is chi-square distributed with 11 degrees of freedom, which implies a critical value of
19.675.
1 4 For expedience, we do not break out estimates for each equation in Table 6. Most parameters are shared across the two
equations due to the cross-equation restrictions implied by the structural derivation.
18
line length.
The implication of retail product line adjustment for price pass-through is apparent from a comparsion of
the estimates. When failing to account for the endogeneity of retailer product line decisions, we find evidence
of incomplete price pass-through (0.730), an outcome broadly consistent with previous research (Hellerstein,
2008; Nakamura and Zerom, 2010); however, accounting for the endogeneity of retailer product line decisions
reveals moderate degree of over-shifting (significant at the 10% level) of wholesale prices into retail prices.
Our estimates suggest that product line adjustments by retailers are capable of preserving retailer margins,
as retail prices at the sample mean adjust nearly in lock-step with changes in wholesale cereal prices.
Our empirical application focuses on sales of breakfast cereals among supermarket retailers, but the
implications of this finding are much broader.
Retailers are generally defined by the fact that they sell
various types of products, many of which are related in demand. For this reason, virtually any category of
product sold by multi-product retailers can be subject to the same type of product line adjustments we find
here. In an environment of rapidly-rising wholesale prices, the implications for more general price inflation
are clear. While the results of previous research on price pass-through among retailers with fixed product
lines implies that retailers serve to absorb a portion of wholesale price increases, our findings suggest that
this may not be the case in a multi-product framework with endogenous product line adjustments. Rather
than dampening the effects of rising wholesale prices with imperfect pass-through into retail prices, retailers
may instead respond by trimming their product lines, leading to higher pass-through rates, and potential
over-shifting of cost changes into consumer prices.
5
Conclusions and Implications
In this study, we investigate the extent to which wholesale price changes are passed into retail markets jointly
through price and product composition effects among multi-product retailers. While the literature contains
many examples of research that documents incomplete pass-through of cost changes into retail prices in a
fixed category of products, our method controls for the endogenous product line length decisions of multiproduct retailers and results in estimated pass-through effects slightly in excess of 100% of wholesale price
changes. Correcting for product line adjustments by retailers is essential for understanding the degree to
which changes in input costs are passed along to consumers, and we find evidence that retailers respond to
increased procurement costs for wholesale goods by trimming the length of product lines in the category. This
reduction in product line length softens price competition among rival retailers, allowing retailer margins
19
to be preserved in the category. Our findings in this sense echo those of Hamilton (2009), who shows that
excise taxes are more likely to be over-shifted into consumer prices when levied on multi-product retailers
than on single-product retailers due to product line adjustments.
Our observations are based on evidence from a structural model of the grocery retailing market for
ready-to-eat breakfast cereals, a product category that has experienced rapid wholesale price increases (and
subsequent reductions) in recent years.
We employ a random-coefficient nested logit model of demand
at the brand-level for six retailers in the Los Angeles market and derive structural equations for retailprice and retail-variety pass-through from a general framework of oligopoly competition in retail prices and
product variety. By relying on observed wholesale prices, we are able to estimate direct and indirect passthrough rates that account for the simultaneous price and product line decisions of competitive supermarkets.
We find that wholesale price increases are associated with reductions in the length of retail product lines
both using estimation techniques that account for the endogeneity of price and variety choices and using
a seemingly unrelated regression framework that does not explicitly control for variety decisions in retailer
pricing behavior. When the endogeneity of product lines is not controlled for in the estimation process, we
find wholesale-price pass-through rates significantly less than 100%; however, when instrumenting for the
endogeneity of prices and product lines in a GMM framework, we find evidence of nearly 1-to-1 shifting of
wholesale price changes into retail prices.
Our findings have significant implications for assessing the degree to which cost changes are passed
along to consumers. Apparel retailers, toy stores, liquor vendors and even banks experience wholesale-price
variation similar to the supermarkets described in this paper. When wholesale prices rise, retailers are faced
with a choice of passing the cost increase on to consumers at the expense of sales levels, absorbing some of
the price increase, or preserving margins in the product category by making product line adjustments. In
this research, we show that when the choice among retailer is to reduce product variety, the resulting cost
increase passed through to consumers is magnified by strategic considerations.
The phenomenon we identify here of product line adjustment in response to cost changes is likely to be
observed in any multi-product retail environment. Future research is needed to test this prediction in other
product categories. In addition to the examples cited above, computer retailers, auto vendors, and healthcare
insurance companies all offer multiple products that may be subject to the same market forces described
here. Future research is needed to consider a broader set of markets and products. Further, it is well known
that empirical models of price pass-through are particularly sensitive to assumptions regarding functional
form. We maintain a random coefficients nested logit model as a reasonable and flexible alternative, but
20
future innovations in technique may be capable of addressing the inherent multiple-discrete nature of cereal
purchases more explicitly.
21
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6
Appendix: Share Derivatives for Structural Model
25
Up.”
In this appendix, we derive the expressions for the first- and second-order share derivatives in price and
variety used in the price- and variety-pass-through equations.15
1. Derivative of market share in price:

=

µ
 
1−
¶
(1 − | − (1 − ) )   = 
(17)
¶
(18)
and:

=−

µ
 
1−
(−| − (1 − ) )   6= 
where | is the conditional share of product  in the total sales of store , and  is the marginal share (of
the total market) of product  in store .
2. Derivative of market share in variety:

= ( 1 +  2  ) (1 − | )   = 

(19)

= ( 1 +  2  ) |    6= 

(20)
and:
where | is the conditional share of product  in store 
3. Second derivative of share in variety:
 2 
( 1 +  2  )2
2
2
=
(
+


)

(1
−

)
−
 | (1 − | )


|
1
2
2
1−
(21)
 2 
( 1 +  2  )2
2
=
(
+


)


(1
−

)
−
 2| 


|
|
1
2
2
1−
(22)
if  = , and:
if  6= .
4. Second derivative of share in price and variety:
1 5 Villas-Boas
and Zhao (2005) provide a similar derivation for a Box-Cox nested logit model without variety effects.
26
 2 
 
µ
¶

( 1 +  2  ) (1 − | )(1 − | − (1 − ) ) +
1−
¶
µ
¶µ
( +  2  )
 
−( 1 +  2  ) (1 − | ) + 1
| (1 − | ) 
1−

=
(23)
if  = , and:
 2 
 
=
µ
¶

( 1 +  2  ) | (−| − (1 − ) ) +
1−
¶
µ
¶µ
( +  2  )
 
−( 1 +  2  ) | + 1
| | 
1−

(24)
if  6= .
5. Second derivative of share in price:
 2 
=
2
µ

1−
¶

(1 − | − (1 − ) ) +

µ

1−
¶
 (−
|

− (1 − )
)


(25)


(1 − | ) if  = , and |  = − 1−
| | for  6= , and:
where |  = | 1−
 2 
=
 
µ

1−
¶

(1 − | − (1 − ) ) +

µ

1−
¶
 (−


)
| | − (1 − )
1−

(26)
 ((1 − )
|

+
 (1 − | ))

1 −  |
(27)


)
| | + (1 − )
1−

(28)
and:
 2 
=−
2
µ

1−
¶

(| + (1 − ) ) −

µ

1−
¶
and:
 2 
=−
 
µ

1−
¶

(| − (1 − ) ) −

µ

1−
¶
 (−
if  6= ,  6=  and  6= .
6. Derivative of price in variety. Using the implicit function theorem and the first-order condition for
optimal pricing, we find:


 
 2 
+
+  ( −  −  )
= 0

 
 
(29)
which we then solve for   for all products,  and retailers, , by substituting in the appropriate
matrices above.
27
Table 1: Price, Variety and Discount Variation by Retailer
Store
Measure Units
Mean
Std. Dev Min
Max
Albertsons
Price
$/oz
0.226
0.085 0.070 0.518
Variety
#
420.424
34.475 0.367 0.464
Discount
%
0.276
0.447 0.000 1.000
Food 4 Less
Price
$/oz
0.210
0.057 0.080 0.350
Variety
#
243.879
17.700 0.221 0.279
Discount
%
0.209
0.407 0.000 1.000
Ralphs
Price
$/oz
0.234
0.066 0.080 0.434
Variety
#
372.273
27.098 0.333 0.420
Discount
%
0.279
0.449 0.000 1.000
Stater Brothers
Price
$/oz
0.238
0.074 0.083 0.522
Variety
#
309.364
13.704 0.287 0.330
Discount
%
0.258
0.438 0.000 1.000
Vons Pavilion
Price
$/oz
0.228
0.055 0.130 0.412
Variety
#
306.061
17.845 0.285 0.356
Discount
%
0.249
0.433 0.000 1.000
Vons
Price
$/oz
0.222
0.056 0.121 0.384
Variety
#
325.242
18.595 0.304 0.374
Discount
%
0.242
0.429 0.000 1.000
N
627
627
627
627
627
627
627
627
627
627
627
627
627
627
627
627
627
627
Note: All data are for breakfast cereal sold by retailers in Los Angeles market, June 2007 March 2010.
28
Table 2: Table 2. Price and Share Varia
Brand
Cheerios
Cinnamon Toast Crunch
Lucky Charms
Corn Flakes
Frosted Flakes
Raisin Bran
Special K
Frosted Mini Wheats
Rice Krispies
Cap’n Crunch
29 All-Bran
Honeycomb
Honey Bunches of Oats
Kashi
Kix
Life
Albertsons
Price Share
0.262 0.039
0.182 0.098
0.249 0.025
0.156 0.082
0.121 0.183
0.153 0.127
0.264 0.085
0.171 0.116
0.209 0.054
0.172 0.073
0.236 0.009
0.196 0.020
0.256 0.012
0.257 0.009
0.267 0.019
0.199 0.033
Food 4 Less
Price Share
0.248 0.017
0.183 0.116
0.235 0.044
0.195 0.094
0.126 0.323
0.159 0.052
0.250 0.061
0.182 0.067
0.226 0.025
0.127 0.150
0.243 0.002
0.171 0.036
0.276 0.003
0.225 0.002
0.266 0.024
0.153 0.029
Pric
0.26
0.21
0.29
0.18
0.15
0.17
0.28
0.16
0.23
0.18
0.25
0.22
0.26
0.24
0.30
0.21
Table 3: Reduced-Form Pass-Through Model.
Retail Price
Retail Variety
Pass-Through
Pass-Through
Variable
Estimate t-ratio.
Estimate
t-ratio.
Wages
-0.073
-0.882
Health Care
-0.500*
-3.303
Utilities
0.308*
2.175
Wholesale Price
0.637*
7.616
-0.313*
-7.594
Cheerios
0.040*
8.845
0.002
1.020
Cinnamon Toast Crunch -0.009*
-1.978
-0.003
-1.412
Lucky Charms
0.036*
7.159
0.008*
3.047
Corn Flakes
-0.005
-1.063
-0.006*
-2.371
Frosted Flakes
-0.042*
-8.614
-0.007*
-2.822
Raisin Bran
-0.026*
-4.925
-0.010*
-3.805
Special K
0.053*
11.573
0.002
1.024
Frosted Mini Wheats
-0.022*
-4.519
-0.006*
-2.601
Rice Krispies
0.015*
3.292
0.002
0.782
Cap’n Crunch
-0.026*
-5.592
-0.004
-1.512
All-Bran
0.039*
7.562
-0.009*
-3.612
Honeycomb
0.001
0.168
-0.003
-1.292
Honey Bunches of Oats
0.055*
12.070
0.001
0.427
Kashi
0.045*
9.639
-0.005
-1.942
Kix
0.066*
14.615
0.000
0.072
Life
0.002
0.449
-0.008*
-3.185
Nature’s Path
0.147*
32.235
0.002
1.078
Oatmeal Squares
0.042*
9.111
-0.003
-1.208
Albertsons
0.330*
7.570
0.456*
93.969
Food 4 Less
0.315*
7.208
0.278*
58.104
Ralphs
0.338*
7.745
0.407*
84.208
Stater Bros.
0.344*
7.884
0.343*
71.076
Vons Pavilion
0.333*
7.620
0.340*
69.926
Vons
0.327*
7.492
0.360*
73.976
R2
0.563
0.863
* Indicates significance at the 95% level. Model is estimated using ordinary least squares.
30
Table 4: Random Coefficient Nested Logit Demand Model:
- March 2010.
Non-Random
Parameters
Variable
Estimate t-ratio.
Discount
0.219*
9.256
Discount*Price
-0.853*
-7.226
Albertsons
-0.579*
-26.534
Food 4 Less
0.691*
28.889
Ralphs
0.285*
20.099
Stater Bros.
0.326*
27.908
Vons Pavilion
-1.377*
-112.989
Cheerios
0.131*
3.776
Cinnamon Toast Crunch
0.223*
5.989
Lucky Charms
0.100*
2.408
Corn Flakes
0.154*
3.208
Frosted Flakes
0.234*
5.119
Raisin Bran
0.195*
4.989
Special K
0.390*
8.660
Frosted Mini Wheats
0.235*
4.955
Rice Krispies
0.136*
3.056
Cap’n Crunch
0.128*
2.942
All-Bran
-0.128*
-3.987
Honeycomb
-0.124*
-2.658
Honey Bunches of Oats
-0.072
-1.696
Kashi
-0.119*
-3.211
Kix
0.048
1.260
Life
0.020
0.393
Nature’s Path
0.203*
4.440
Oatmeal Squares
-0.056
-1.053 Quarter 1
0.154*
29.775
Quarter 2
-0.010*
-2.343
Quarter 3
-0.028*
-5.302
1
0.608*
2.593
1
0.000*
-2.793

0.768*
216.473
LLF
1,181.03
Chi-Square
2,362.06
RTE Breakfast Cereals, Los Angeles, June 2007
Random
Parameters
Variable
Estimate
t-ratio.
Means of Random Parameters
Price
-2.800*
-11.110
Variety
25.918*
17.022
Variety2
-30.259*
-13.964
Constant
-11.671*
-42.433
Std. Deviations of Random Parameters
Price
0.964*
39.047
Variety
0.412*
32.245
Variety2
0.592*
19.586
Constant
0.050*
16.527
Rand. Para. Functions: Age and Income
Price(Age)
0.004*
2.264
Price(Income)
0.043*
6.048
Variety(Age)
-0.090*
-3.221
Variety(Income)
-0.760*
-8.426
Variety2(Age)
0.144*
3.524
Variety2(Income)
1.095*
8.468
Constant(Age)
0.013*
2.890
Constant(Income)
0.120*
7.794
Estimate of Std. Deviation
Std. Dev.
0.170*
148.213
* Indicates significance at the 95% level. Model is estimated using simulaed maximum likelihood.
31
Table 5: Price Elasticities of Demand: RTE Breakfast
Brand
Cheerios
Cinnamon Toast Crunch
Lucky Charms
Corn Flakes
32 Frosted Flakes
Raisin Bran
Special K
Frosted Mini Wheats
Rice Krispies
Brand
-2.984
0.127
0.075
0.099
0.143
0.127
0.153
0.131
0.086
0.098
Cheerios
0.127
-2.165
0.121
0.145
0.189
0.173
0.199
0.177
0.132
0.144
Cinn.
Toast
Crunch
0.075
0.121
-3.076
0.093
0.137
0.121
0.147
0.125
0.080
0.092
Lucky
Charms
0.099
0.145
0.093
-2.196
0.161
0.145
0.171
0.149
0.104
0.116
Top Ten Brands: Elasticity of Row Brand with respect to Price Change in Col
Table 6: Price and Variety Pass-Through Model: NLSUR and GMM.
NLSUR
GMM
Estimate
t-ratio
Estimate
t-ratio
Constant
0.737*
60.316
0.849*
3.834
Wages
-0.458*
-30.243
-0.574*
-2.458
Health Care
-0.952*
-30.146
-1.946*
-4.671
Utilities
-0.029
-0.541
1.855
1.759
Wholesale Price
1.968*
308.294
2.184*
25.639

0.730*
664.310
1.010*
164.498

-8.125*
-160.216
-9.655*
-53.922
2
-0.016*
-51.638
-0.022*
-11.299
LLF
3567.663
265.368
Chi-square
* Indicates significance at the 5% level.  is the indirect price-pass-through rate,
and  is the variety-pass-through rate.
33