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Cost Pass-Through in Differentiated Product Markets: The Case of US Processed Cheese

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Abstract

In this paper, we estimate a mixed logit model for demand in the U.S. processed cheese market. The estimates are used to determine pass-through rates of cost changes under different behavioral regimes. We find that, under collusion, the pass-through rates for all brands fall between 21% and 31% while, under Nash-Bertrand price competition, the range of pass-through rates is between 73% and 103%. The mixed logit model provides a more flexible framework for studying pass-through rates than the logit model since the curvature of the demand functions depends upon the empirical distribution of consumer types. Copyright 2008 The Authors.
COST PASS-THROUGH IN DIFFERENTIATED PRODUCT
MARKETS: THE CASE OF U.S. PROCESSED CHEESE
Donghun Kimw
RonaldW. Cotterillz
In this paper, we estimate a mixed logit model for demand in the U.S.
processed cheese market. The estimates are used to determine pass-
through rates of cost changes under different behavioral regimes. We
find that, under collusion, the pass-through rates for all brands fall
between 21% and 31% while, under Nash-Bertrand price competition,
the range of pass-through rates is between 73% and 103%. The mixed
logit model provides a more flexible framework for studying pass-
through rates than the logit model since the curvature of the demand
functions depends upon the empirical distribution of consumer types.
I. INTRODUCTION
IN THIS PAPER WE ESTIMATE COST PASS-THROUGH RATES in the market for
processed cheese under Nash-Bertrand pricing and collusive pricing. Cost
pass-through rates measure the proportion of a change in input costs that is
passed through to price. A cost change may arise from various sources,
including input price changes or changes in state or federal taxes. In
processed cheese, the main input is raw milk. A frequently asked question in
this market is: what is the impact of an increase in raw milk prices on cheese
prices, consumer surplus and profits? Our estimates of the cost-pass through
rate provide an answer to these questions.
Early studies of cost pass-through have focused on two polar cases,
perfect competition and monopoly. Under perfect competition, pass-
through is determined by the relative demand and supply elasticities. The
pass-through rate is greater when demand is more inelastic and supply more
elastic; it is 100% when input supply is infinitely elastic. By contrast, the
monopolist passes through only 50% of an input cost change when input
supply is infinitely elastic and demand is linear (Bulow et al. [1983]). Several
r2008 The Authors. Journal compilation r2008 Blackwell Publishing Ltd. and the Editorial Board of The Journal of Industrial
Economics. Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK, and 350 Main Street, Malden, MA
02148, USA.
32
THE JOURNAL OF INDUSTRIAL ECONOMICS 0022-1821
Volume LV March 2008 No. 1
We would like to thank Robert T. Masson, Oleg Melnikov, Ted O’Donoghue and George
Jakubson, anonymous referees and especially the Editor for helpful comments. The authors
remain solely responsible for any errors.
wAuthors’ affiliations: International University of Japan, Niigata 949-7277, Japan.
e-mail: dhkim@iuj.ac.jp
zDepartment of Agricultural and Resource Economics, University of Connecticut,
Connecticut 06269-4021, U.S.A.
e-mail: Ronald.cotterill@uconn.edu
studies have analyzed the effects of cost shocks under imperfect competition
(Stern [1987], Katz & Rosen [1985]; and Delipalla & Keen [1992]). Most of
the theoretical work has focused on homogeneous products with quantity
competition. The empirical work consists mainly of reduced-form analysis
using industry-level data (see, e.g., Sumner [1981]; Sullivan [1985]; Karp &
Perloff [1989]; and Besely & Rosen [1998]). Few studies have studied the
effect of cost changes on prices in differentiated product markets. The
exceptions include theoretical studies by Anderson et al. [2001] and Froeb
et al. [2005]. The former analyzes the incidence of ad valorem and excise taxes
in an oligopolistic industry with differentiated products and price-setting
firms; the latter investigates the relationship under Bertrand oligopoly
between the price effects of mergers absent synergies and the rates at which
merger synergies are passed through to consumers in the form of lower prices.
The main goal of this paper is to estimate cost pass-through rates for a
differentiated product market using a structural model. We first estimate the
demand system for the U.S processed cheese market using a mixed logit
model
1
We use the estimated demands in the firms’ pricing equations to back
out estimates of their marginal costs. We then change marginal costs and
solve the model to obtain the new equilibrium prices.
We use the mixed logit model to estimate demand. This model provides
greater flexibility in substitution patterns than the logit model. In the logit
model, the curvature of demand system, i.e., the second derivatives, is
determined by functional form assumptions; in the mixed logit model, it
depends to a significant extent on the empirical distribution of consumers.
This property is important for obtaining accurate estimates of cost pass-
through rates.
We estimate cost pass-through under Nash-Bertrand pricing and fully
collusive pricing in order to evaluate how pass-through depends upon
behavior. We find that cost pass-through rates for the different brands under
collusion lie between 21% and 31%. The corresponding pass-through rates
under Nash-Bertrand pricing are much higher, between 73% and 103%. We
also estimated the pass-through rates generated by the logit model to determine
the importance of a more flexible specification. We find that logit pass-through
rates are on average 12% lower than those of the mixed logit model.
We compared our pass-through estimates with those obtained from
reduced-form models. Roughly speaking, the pass-through elasticities of the
reduced-form model fall between those of Nash-Bertrand and collusive
pricing. The reduced-form model does not impose a specific price-setting
mechanism. Consequently, if the reduced form estimates are to be believed,
then markups for processed cheese are lower than the monopoly markups
1
Refer to Berry et al. (henceforth BLP) [1995] and Nevo [2001]. Nevo [2000] applied the
model for merger analysis and Petrin [2002] used the model to estimate the consumer benefits of
new products in the automobile industry.
COST PASS-THROUGH IN DIFFERENTIATED PRODUCT MARKETS 33
r2008 The Authors. Journal compilation r2008 Blackwell Publishing Ltd. and the Editorial Board of The Journal of Industrial
Economics.
but higher than Nash-Bertrand markups. Reduced form results are often
used to infer competitiveness, but notice that it would be difficult to draw
such inferences without knowing the estimates produced by the benchmark
cases of Nash-Bertrand and full collusion. This is another reason for
adopting a structural approach.
We proceed as follows. In Section II, we discuss the U.S. processed cheese
market and the data. The empirical model is presented in Section III. In
Section IV, we describe the estimation strategy. The empirical results are
presented in Section V. In Section VI, we compare the structural approach to
estimating cost-pass through rates to the reduced form approach. Section
VII concludes.
II. MARKET AND DATA
Processed cheese is used mostly in sandwiches and cheeseburgers and is
typically sold pre-sliced. According to Mueller et al. [1996], the four-firm
concentration ratio at the 5-digit SIC level was around 70% during the
sample period of 1988–1992. Franklin and Cotterill [1994] report some
additional statistics on the processed cheese market for 1992. Table I shows
the volume shares and average prices per pound of the leading processed
cheese brands. Philip Morris, whose brands include Kraft and Velveeta, is
the dominant firm with a volume share of around 50% in 1992. Borden, Inc.,
whose main brands are Borden and Lite Line, is a distant second to Philip
Morris with a combined share of around 8%. The other national
manufacturers, Land O’Lakes and H. J. Heinz Co., have very small volume
shares. The value of shipments was US$5.6 billion.
Ta b l e I
Leading Processed Cheese Brands, U.S. total,1992
Manufacturer/Brand Volume Share Average Price/lb
Philip Morris
Kraft 25.51 3.24
Velveeta 15.56 2.82
Light N Lively 0.59 4.20
Kraft Free 3.65 3.76
Kraft Lightf 3.19 2.52
Velveeta Light 1.70 3.38
Borden Inc
Borden 7.91 2.80
Lite Line 0.53 4.62
Land O’lakes
Land O’Lakes 1.28 2.42
HJ Heinz Co
Weight Watchers 0.41 3.20
Source: Franklin and Cotterill [1994].
34 DONGHUN KIM AND RONALD W. COTTERILL
r2008 The Authors. Journal compilation r2008 Blackwell Publishing Ltd. and the Editorial Board of The Journal of Industrial
Economics.
The data for this study was obtained from Information Resources,
Inc., which collects quantity and price data from supermarkets in the
most populous metropolitan areas in the U.S. The price and quantity
data are quarterly, and cover the first quarter of 1988 to the fourth quarter
of 1992. The number of cities ranges from 28 in the first quarter of 1988
to 43 in the fourth quarter of 1992. Each city and quarter combination
is defined as a market so there are 680 markets represented in the data.
We focused on ten major brands. The number of brands varies from
7 to 10, depending on markets, because of the unbalanced nature of
the dataset.
The product characteristics of each brand consist of calories, fat,
cholesterol and sodium. Their values were obtained from nutrient fact
books that were published during the sample period.
Demographic information for each city in our sample was obtained from
the Current Population Survey (CPS). The information includes income,
age, number of children, and race. The selection of demographic variables is
based on previous studies of the cheese industry, which includes Gould and
Lin [1994], Hein and Wessells [1990] and Gould [1992].
Table II gives the market shares, prices and values of the product
characteristics for the ten brands. The market share for each brand is
Ta b l e I I
Market share, Prices, and Product Characteristics
Market Share Price Calories Fat (g) Cholesterol (mg) Sodium (mg)
Kraft 3.172 14.197 90 7 25 380
Velveeta 2.065 12.230 90 6 25 400
Light N Lively 0.098 17.334 70 4 15 406
Kraft Free 0.320 16.541 42 0.3 5 273
Kraft Light 0.173 15.348 70 4 20 160
Velveeta Light 0.233 12.186 60 3 15 430
Borden 0.774 12.931 80 6 20 360
Lite Line 0.0071 19.456 50 2 15 171
Land O’lakes 0.0069 11.990 110 9 26 430
Weight Watchers 0.065 15.376 50 2 7.5 400
Note: Market share (%) and price are the medians for all city-quarter markets. The unit of price is cents per
serving (28g).
Ta ble III
DemographicVariables
Median Mean Std Min Max
Log (Income) 7.923 7.935 0.912 0.396 10.876
Log (Age) 3.478 3.312 0.951 0 4.512
Child 0 0.268 0.436 0 1
Nonwhite 0 0.168 0.362 0 1
COST PASS-THROUGH IN DIFFERENTIATED PRODUCT MARKETS 35
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Economics.
calculated under the assumption that market size is equal to one serving
(28 g) per person times the number of persons in the market. The
low numbers reflect the fact that most people do not buy processed cheese.
The price is measures as cents per serving. It is net of any merchandis-
ing activity. Thus, a price reduction for a promotion is reflected in the
price. Price is deflated using the regional city CPI and converted to real price
per serving.
Table III provides summary statistics on the demographic variables.
Income is household income divided by the number of household members.
The variable Child is a binary variable that is equal to 1 if age is less than
17 years old and 0 otherwise. The binary variable Nonwhite is equal to 1 if an
individual is nonwhite and 0 otherwise.
III. MODEL
In this section we first specify the model of demand, then derive the pricing
equations under different behavioral assumptions, and finally derive the
pass-through equations.
III (i). The Demand Equations
Demand for processed cheese is estimated using a discrete choice model
similar to those of BLP [1995] and Nevo [2001].
2
Consumers choose one
unit of only one brand in each shopping trip and they choose the brand
that offers them the highest utility. The indirect utility of consumer ifrom
brand jin market mis given by Uijmðxjm;xjm;pjm ;Di;vi:yÞ, where x
jm
are
observed cheese characteristics, p
jm
is price, D
i
are observed consumer
characteristics, v
i
and x
jm
are unobserved individual characteristics and
unobserved cheese characteristics, respectively. Here yis an unknown
parameter vector to be estimated. Following Berry [1994], we specify the
indirect utility function as:
ð1Þuijm ¼xjmbiaipjm þxjm þeijm ;
where a
i
is consumer i’s marginal income utility, b
i
represents individual
specific parameters and e
ijm
is a mean zero stochastic term. Thus, the
parameters of the utility function are different for each consumer. By
contrast, in the logit model, the parameters are the same for all consumers
and consumer heterogeneity is modeled in the error term only.
The indirect utility can be divided into two parts. The first part is the mean
utility level of brand jin market m,d
jm
and the second part is the deviation
2
An alternative approach to solving the dimensionality problem in differentiated product
markets is to use a multi-level demand system for differentiated products (Hausman, Leonard
& Zona [1994]), which is an application of multi-stage budgeting.
36 DONGHUN KIM AND RONALD W. COTTERILL
r2008 The Authors. Journal compilation r2008 Blackwell Publishing Ltd. and the Editorial Board of The Journal of Industrial
Economics.
from the mean level utility, which captures the effects of the random
coefficients, m
ijm
.
ð2Þuijm ¼djmðxj;pjm ;xjm :y1Þþmijmðxj;pjm ;vi;Di;y2Þþeijm
ð3Þdjm ¼xjmbapjm þxjm
ð4Þ
mijm ¼X
L
l¼1
ZlDilpjm þsKþ1viðKþ1Þpjm
þX
L
l¼1X
K
k¼1
flkDil xjkmþX
K
k¼1
skvikxjkm
ð5Þui0m¼x0mþf0Diþs0vi0mþeiom
Hence the coefficients on the mean utility function are the same for all
individuals and the deviation from the mean utility, m
ijm
, depends on the
consumer’s observed characteristics, D
i
, and unobserved characteristics,
v
i
. The unobserved individual characteristics are random draws from the
multivariate normal distribution, N(0, I
kþ1
)), where Kþ1 draws for each
individual correspond to the price and product characteristics, of which the
dimension is K1.
Equation (5) represents the utility of an outside good, which is normalized
to u
i0m
5e
iom
. Without an outside good, a simultaneous increase in the prices
of inside goods results in no change in aggregate consumption. The share of
outside goods is defined as the total size of the market minus the shares of
inside goods. We follow Nevo [2001] and assume that the size of the market is
one serving of processed cheese per capita per day. BLP [1995] used the
number of households as market size.
Let A
jm
represent the set of values of D,v, and ethat induces the choice of
brand jin market m.
ð6ÞAjm ¼fD;v;ejuijm >uihm8h¼0;1;;;;Jg
We assume that D,v, and eare independently distributed. Here Dis drawn
from the empirical distribution, F, obtained from the Current Population
Survey; vare drawn from a multivariate normal distribution, N; and eis
drawn from an extreme value distribution. Integrating out the idiosyncratic
preference shock, the market share of brand jin market mcan be expressed
as follows:
ð7Þsjmðx;p;d;y2Þ¼ZD;v
sijm dFðDÞdNðvÞ
where sijm ¼expðdjm þmijmÞ=ð1þPJ
s¼1expðdsm þmismÞ, is the probability
of individual ipurchasing the product j.
COST PASS-THROUGH IN DIFFERENTIATED PRODUCT MARKETS 37
r2008 The Authors. Journal compilation r2008 Blackwell Publishing Ltd. and the Editorial Board of The Journal of Industrial
Economics.
III (ii). The Pricing Equations
Each firm f,f51,..., F, produces goods j51, . . . , J
f
. Marginal costs are
constant for each product but vary across markets. Thus, firm f’s profit in
market m
3
is given by
ð8ÞPm
f¼XJf
j¼1ðpjm mcjmÞMsjm ðpÞ
where mc
jm
is marginal cost of product j in market m, Mis market size, and
s
jm
(p) is the market share of jin market m.
Suppose first that firms in the processed cheese market choose their prices
simultaneously and independently. Given the prices of other brands, firm
f’s prices satisfy the first-order conditions
ð9Þ@Pm
f
@pjm ¼sjm þXJf
k¼1ðpkm mckmÞ@skm
@pjm ¼0;j¼1;......:; Jf
Note that the second term takes into account the impact of p
jm
on the
revenues of the firm’s other brands as well as on brand j. In other words, each
firm behaves like a monopolist with respect to its brands.
Suppose next that the firms collude and choose their prices to maxi-
mize their joint profits. The first-order condition for joint profit Q
F
maximization is:
ð10Þ
@Pm
F
@pjm ¼sjm þXJf
k¼1ðpkm mckmÞ@skm
@pjm
þX
F
f0¼1
f0fXJf0
s¼1ðpsm mcsmÞ@ssm
@pjm ¼0
where s51,. . .. . .. , J
f
0
j51, . . .. . .. , J
f
In this case, each firm takes into account the effect of a change in the prices
of its brands on revenues of own and other firms’ brands.
The first-order conditions, (9) and (10), can be summarized in vector
notation as (11):
ð11ÞðpmcÞDðpÞþsðpÞ¼0
3
In this paper we assume that firms solve a profit maximization problem in each market
separately rather than coordinating pricing across markets.
38 DONGHUN KIM AND RONALD W. COTTERILL
r2008 The Authors. Journal compilation r2008 Blackwell Publishing Ltd. and the Editorial Board of The Journal of Industrial
Economics.
where pis the vector of all brand prices, mc is the vector of marginal costs of
all brands, and s(p) is the vector of market shares. Here D5J
Jis a matrix
with elements;
@skðpÞ
@pj;if brands kand jare produced by the same firm in the
Nash model or by a colluder in the collusion model
0 Otherwise
8
<
:
From (11), we can solve for marginal cost for each brand for each market as
follows:
ð12Þ^
mc ¼pþDðpÞ1sðpÞ
Thus, the estimated marginal cost depends on the equilibrium price, the
parameters of the demand system, and whether the firms behave non-
cooperatively or collude.
III (iii). The Pass-Through Equations
From (11) we can also estimate the cost pass-through rate analytically.
Rewrite (11) as Q5(pmc)D(p)þs(p)50. Then, using the implicit function
theorem, the pass-through rate matrix can be derived as follows:
ð13Þ@p
@mc ¼ @Q
@p

1@Q
@mc

The pass-through rate depends on the first and second derivatives of the
market share function. In the mixed logit model, these derivatives depend on
the empirical distribution of observable consumer characteristics and have
to be estimated. By contrast, in the logit model, the derivatives follow
directly from functional form assumptions (Froeb et al. [2005]).
Let’s assume that there is a discrete industry-wide common shock for each
brand in each market so marginal cost changes from m
ˆcto
mc. Following the
cost shock, market prices will converge to a new equilibrium. The new
equilibrium price vector is:
ð14ÞpNew ¼
mc DðpNewÞ1sðpNew Þ
The price pass-through rate is defined as the ratio of the price change to the
change in marginal cost:
ð15ÞPass Through Rate ¼Dp
Dmc 100;
where Dpis the difference between the new equilibrium price that solves
system (14) and the old price and Dmc ¼
mc ^
mc. We perturb system (14)
with marginal cost shocks of varying sizes.
COST PASS-THROUGH IN DIFFERENTIATED PRODUCT MARKETS 39
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Economics.
As prices change with marginal cost shocks, consumer welfare will change
accordingly. The change in consumer welfare is estimated using the
compensating variation criterion. It measures the amount of income that
is needed to keep the consumer at the same utility level after a price change
occurs (e.g., McFadden [1981], Small & Rosen, [1981], Nevo [2000]). We
estimate the consumer welfare changes for each regime of competition. For
price pass-through simulations and consumer welfare calculations analysis,
we assume that neither the marginal utility of consumer income following
cost shocks nor the utility from outside goods changes.
IV. ESTIMATION
To estimate the demand function, we must control for any correlation
between prices and the error term in the mean utility function. The error
term represents product characteristics that are observed by consumers but
not by the econometrician. This correlation is likely to be positive because
higher quality could lead suppliers to set higher prices. For example,
Trajtenberg [1989] found that demand for CT scanners was estimated to be
positively sloped with price because of the omission of unobserved quality,
which was positively correlated with price.
To control for the endogeneity of price, we need to find variables that are
correlated with price but are independent of unobserved product
characteristics. Estimation requires an instrument vector with a rank at
least equal to the dimensionality of the parameter vectors. One of the
instruments typically used is a variable that represents closeness in product
space in the particular markets (BLP [1995], Bresnahan, Stern, &
Trajtenberg [1997]). Such instruments are, however, most appropriate for
dynamically changing markets in which product characteristics evolve
continuously. If a market is mature and product characteristics do not
change much, then this instrumental variable will not change across markets
and it will, as a consequence, have little identifying power. Another
approach is to exploit the panel structure of the data. Examples of this
approach are found in Hausman [1996] and Nevo [2001]. The identifying
assumption is that, controlling for brand-specific means and demographics,
city-specific demand shocks are independent across cities. Given this
assumption, a demand shock for a particular brand will be independent of
prices of the same brand in other cities. Due to the common marginal cost,
prices of a given brand in different cities within a region will be correlated
and therefore can be used as valid instrumental variables.
4
If, however, there
is a national or regional demand shock, this event will increase the
unobserved valuation of all brands in all cities and the independence
4
Refer to Bresnahan’s comment on Hausman [1996].
40 DONGHUN KIM AND RONALD W. COTTERILL
r2008 The Authors. Journal compilation r2008 Blackwell Publishing Ltd. and the Editorial Board of The Journal of Industrial
Economics.
assumption will be violated. Also, if advertising campaigns and promotions
are coordinated across cities, these activities will increase demand in the
cities that are included in the activities, so the independence assumption will
be violated for those cities.
5
We therefore use an additional set of
instrumental variables, proxies for production costs, to check the sensitivity
of the results obtained to different sets of instrumental variables. We create
the production cost proxies by multiplying input prices such as the raw milk
price, the diesel price, wages, and electricity by brand dummies to give cross-
brand variations.
Let Zbe an N-by-L matrix with row z
k
and x(y) be an N-by-1 error tem in
mean utility with row x
k
. We introduce brand dummies as well as time
dummies in the model. Hence, a brand-specific component and a time-
specific component are removed from the error term in the mean utility. The
assumption that the instrumental variables are orthogonal to the structural
error implies E½zkxkðyÞ ¼ 0. The corresponding sample moment is
mðyÞ¼1
nP
n
k¼1
zkxkðyÞ¼1
nZ0xðyÞ. Now we search for y, which minimizes the
GMM objective function. The GMM estimate is
ð17Þ^
y¼arg min
yq¼½
m0W
m;
where Wis a consistent estimate of the inverse of the asymptotic variance of
ffiffi
n
p
mðyÞ.
V. RESULTS
Table IV reports parameter estimates for the logit model with and without
instrumental variables. Using prices in other cities as the instrumental
variable, price sensitivity increases from 2.786 to 5.397. Under an alternative
specification using costdata as instrumental variables, theprice sensitivity was
4.221. The results suggest that disregarding thecorrelation between price and
unobserved demand shock can cause downward bias in price sensitivity.
Table V reports parameter estimates for the mixed logit model. Here we use
regional prices in other cities and cost variables as instrumental variables for
Model I and Model II, respectively. Overall, the two models yield similar results
even though the size of the respective parameter estimates is a bit different. The
parameters for the product characteristics are recovered from those of brand-
related fixed effects using the minimum distance method. The coefficient on
PRICE is negative and significant. The coefficient on FAT is positive and
5
A referee suggested that we include brand-level advertising spending as an independent
variable to control for aggregate demand shocks. Nevo [2001] is such an example.
Unfortunately, our advertising data was not complete and we could not include such a
variable in the model.
COST PASS-THROUGH IN DIFFERENTIATED PRODUCT MARKETS 41
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Economics.
significant, which suggests that the average consumer prefers the richer taste of
higher butterfat despite the higher health risks. Sensitivity to fat increases,
however, as income rises. This phenomenon is captured in the negative and
significant interaction term between fat and income, FAT
INCOME.
SODIUM has a negative and significant effect on the mean utility.
Table VI reports own- and cross-price elasticities based on the estimat es of
the mixed logit model. Each cell (i,j) gives the per cent change in market sha re
of brand icorresponding to a 1 per cent change in the price of brand j. Own-
price elasticities are negative but the cross-price elasticities are positive.
Table VII reports cost estimates under Nash-Bertrand and collusive
pricing respectively. For any vector of prices, marginal costs are lower and
markups are higher under collusive pricing than competitive pricing. Recall
that equation (12) implies that the estimated marginal costs are higher for
products with higher market prices and higher values forDðpÞ1sðpÞ. For
Ta b l e V
Demand Param eter Estimates: Mixed Logit
Variables Model (I) Model (II)
Constant 32.089 (0.487)

18.445 (1.569)

Price 6.848 (0.501)

5.632 (1.337)

Fat 1.285 (0.487)

4.808 (1.569)

Sodium 3.714 (0.166)

2.489 (0.247)

Income 18.756 (7.737)
20.687 (5.879)

Nonwhite 4.611 (0.395)

5.953 (0.478)

Price
Income 12.061 (3.746)

17.063 (9.233)
Price
[Income]
2
8.141 (2.937)

9.148 (3.292)

Price
Age 2.159 (1.256)
2.751 (2.185)
Price
Child 2.537 (1.438)
2.521 (2.516)
Fat
Income 0.540 (0.043)

1. 490 (0.647)

Constant
v
1
0.929 (1.052) 1.121 (1.782)
Price
v
2
2.232 (0.462)

1.915 (0.544)

Fat
v
3
2.437 (1.716)
2.668 (0.826)

Sodium
v
5
3.245 (1.583)
3.021 (1.709)
Instruments Prices Cost
N 5,732 5,732
Note:
t-value 41,

: t-value 42. The parameters in the mean utility are recovered from the coefficients of the
brand-fixed effects using the minimum distance technique. The numbers in parentheses are standard errors.
Ta b l e I V
DemandParameter Estimates: Logit OLSand Logit with IVs
Logit OLS Logit with IVs
Price 2.786 (0.197) 5.397 (0.445) 4.221 (0.397)
Time Dummies O O O
Brand Dummies O O O
Instruments X Prices Cost
R
2
0.676
First Stage R
2
0.914 0.855
N 5734 5734 5734
Note: Dependent Variable is ln(s
jm
)–ln(s
0m
). Standard errors are in parentheses.
42 DONGHUN KIM AND RONALD W. COTTERILL
r2008 The Authors. Journal compilation r2008 Blackwell Publishing Ltd. and the Editorial Board of The Journal of Industrial
Economics.
some brands with small market shares, the elements of the latter term are
small negative numbers. Therefore, the estimated marginal costs are
determined mostly by market prices. Accordingly, some low-fat segment
brands, such as Kraft Free, Weight Watchers, and Lite Line, have high
marginal costs. This is particularly true for Lite Line, which has the highest
market price and a very low market share.
Table VIII shows the results of the estimated price pass-through rates. The
pass-through rates are defined as percentage changes in price from a one cent
per serving increase in marginal cost. Under collusion, the pass-through
rates for all brands fall in a narrow range, between 21% and 31%. Under
Nash-Bertrand competition, the level of brand pass-through rates increases
Ta b l e V I I
Marginal cost, Mar kup, and Margin
Brand
Nash-Bertrand Full Collusion
MC P-MC (P-MC)/P
100 MC P-MC (P-MC)/P
100
Kraft 7.84 6.08 42.65 4.75 9.62 67.75
Velveeta 6.69 5.53 45.03 4.13 8.44 67.97
Light N Lively 10.35 6.12 36.83 7.24 9.97 58.13
Kraft Free 10.59 5.45 34.91 7.75 8.14 51.78
Kraft Light 9.36 5.30 36.34 6.19 8.53 59.16
Velveeta Light 7.81 4.69 37.80 4.98 7.39 61.26
Borden 11.27 1.62 12.72 4.26 8.94 67.45
Lite Line 18.13 1.89 10.58 10.37 9.43 49.11
Land O’Lakes 10.56 1.37 11.70 3.62 8.37 70.74
Weight Watchers 12.88 1.95 12.58 5.65 9.43 62.51
Note: Median values for all markets. Marginal costs and markups are cents per serving.
Ta b l e V I
Ow n- and Cro ss -Elast icit ies
Borden
Light
Line
Weight
Watchers
Land
O’Lakes Kraft
Line N
lively Velveeta
Kraft
Free
Kraft
Light
Velveeta
Light
Borden 6.56 0.03 0.10 0.22 1.21 0.05 0.87 0.23 0.22 0.36
Light Line 0.12 4.62 0.02 0.03 0.15 0.04 0.27 0.08 0.04 0.06
Weight
Watchers
0.78 0.05 6.59 0.09 0.25 0.07 0.45 0.49 0.28 0.48
Land
O’Lakes
1.09 0.02 0.12 7.35 0.98 0.08 0.95 0.19 0.60 0.43
Kraft 0.75 0.01 0.04 0.24 5.07 0.04 1.23 0.16 0.21 0.27
Lite N
Lively
0.21 0.06 0.05 0.04 0.67 3.67 0.54 0.12 0.08 0.10
Velveeta 0.92 0.02 0.07 0.21 1.18 0.05 6.29 0.21 0.20 0.46
Kraft Free 0.39 0.02 0.12 0.03 0.11 0.04 0.62 4.39 0.36 0.41
Kraft Light 0.72 0.03 0.08 0.20 0.61 0.03 0.56 0.35 5.88 0.25
Velveeta
Light
0.96 0.04 0.16 0.13 0.83 0.05 0.83 0.43 0.26 7.21
Outside
Good
0.63 0.02 0.09 0.14 0..23 0.02 0.34 0.14 0.15 0.17
Note: Elasticities are median values for 210 sample markets from the fourth quarter of 1991 to the fourth quarter
of 1992. Row is iand column is j. Each cell (i,j) gives the per cent change in market share of brand icorresponding
to a 1 per cent change in the price of brand j.
COST PASS-THROUGH IN DIFFERENTIATED PRODUCT MARKETS 43
r2008 The Authors. Journal compilation r2008 Blackwell Publishing Ltd. and the Editorial Board of The Journal of Industrial
Economics.
as does the variation across brands, with rates ranging between 73% and
103%. To examine the robustness of results, we simulated the cost pass-
through for cost shocks that vary in size from 0.1 cent per serving to 1.2 cents
per serving. The results were similar to those reported in Table VIII.
Not surprisingly, the simulation results indicate that average pass-
through rates are lower than the rates predicted by a linear demand with a
homogenous product. With constant marginal cost, cost pass-through is
100% in the competitive case and 50% in the monopoly case (Bulow et al.
[1983]). Note that, in a differentiated product market, the mixed logit
specification allows for price pass-through rates above and below 100%.
Differences in the shape of a brand’s market share function across markets
means that the same brand can have different cost pass-through rates in
different markets.
The curvature of the demand function in the mixed logit model, i.e., the
second derivative of the demand function, is determined by the product
characteristics and the distribution of consumer characteristics. To check on
the importance of this flexibility, we compared the results of the mixed logit
model with those of the logit model. Under Nash-Bertrand pricing, we find
that the average pass-through rate in the logit model for a one-cent per
serving change in costs is 71%. This is 12 per cent lower than the average
pass-through rate for mixed logit models.
Table IX shows the change in consumer welfare as measured by the
compensating variation. CV1 and CV2 represent the compensating
variations under Nash-Bertrand and collusive pricing, respectively. In the
former case, the CV is 0.63 cents per person for a 1 cent marginal cost
decrease and in the latter case, it is 0.23 cents. The ratio of CV2 to CV1 is
37%. Thus, the increase in consumer welfare following a one cent decrease in
cost is substantially lower in the collusive regime than in the Nash-Bertrand
equilibrium.
Ta b l e V I I I
Pa s s - T h r o u g h R at e ( % )
Nash Bertrand Collusion
Kraft 93.61 30.42
Velveeta 91.56 28.74
Light N Lively 88.72 26.45
Kraft Free 90.12 26.98
Kraft Light 99.93 30.34
Velveeta Light 93.29 30.83
Borden 102.89 30.12
Lite Line 73.33 23.70
Land O’Lakes 88.36 21.25
Weight Watchers 76.86 25.45
Overall 82.67 27.04
MC shock 1.0 1.0
Note: Median values for all markets. Marginal cost shocks are cents per serving.
44 DONGHUN KIM AND RONALD W. COTTERILL
r2008 The Authors. Journal compilation r2008 Blackwell Publishing Ltd. and the Editorial Board of The Journal of Industrial
Economics.
VI. STRUCTURAL VERSUS REDUCED-FORM ESTIMATES
Reduced-form models have been used extensively in the cost pass-through
literature partly because the analysis is easily implemented. To compare the
results of the structural model with those of a reduced-form model, we use
the following reduced-form model:
ð16ÞlnðpriceitÞ¼g0iþg1lnðinput CosttÞþoit
Here ln(price
it
) is a log of processed cheese prices for brand iand time t,
ln(input Cost
it
) is a log of input price at time t, and o
it
represents an error
term. Following Gron and Swenson [2000], we estimate a log-linear
regression to obtain a unit-free measure of the pass-through rate. In our
model, g
0i
is a brand fixed effect and g
1
represents the pass-through elasticity.
The brand fixed effects capture time-invariant markups.
We use raw milk prices, wages, and diesel prices as proxies for input costs.
The milk price is the raw milk price from USDA federal milk order statistics.
Wage and diesel prices are obtained from Bureau of Labor Statistics indices.
Table X reports summary statistics on the input prices.
Table XI reports the estimates of the reduced form model. The estimated
pass-through elasticities for milk and diesel prices and wage are 0.034, 0.237,
and 0.375, respectively. In order to compare these estimates to the pass-
through rates obtained from the structural model, we converted them into
pass-through elasticities (see Table XII). The pass-through elasticity is 0.07
for collusive pricing and 0.5 for Nash-Bertrand pricing. These are the
averages for different size cost shocks. The reduced-form results fall between
those of full collusion and Nash price competition. If the reduced-form
results capture the market structure of the processed cheese market
correctly, it suggests that the market is less competitive than Nash-Bertrand
Ta b l e X
Input Pr ices
Mean Std Dev Min Max
Milk(US $/100 pounds) 11.69 1.03 10.07 14.50
Wage (PPI) 106.78 5.73 95.70 114.50
Diesel (PPI) 63.16 9.55 44.00 91.93
Ta b l e I X
CompensatingVariation
Nash-Bertrand (A) 0.63
Collusion (B) 0.23
B/A(%) 37%
MC Shock(Cents) 1.0
Note: Cents/per serving/per person, median values for all markets.
COST PASS-THROUGH IN DIFFERENTIATED PRODUCT MARKETS 45
r2008 The Authors. Journal compilation r2008 Blackwell Publishing Ltd. and the Editorial Board of The Journal of Industrial
Economics.
price competition but more competitive than collusive pricing. If, however,
we do not know the results of benchmark cases of pass-through elasticities, i.
e., those of Nash-Bertrand pricing and collusion, it may be difficult to infer
behavior from the results of a reduced-form analysis. Meanwhile, if we
assume along with many previous studies (e.g., BLP [1995]) that firms
behave as posited by Nash-Bertrand model, the reduced form results yield
biased estimates of cost pass-through.
VII. CONCLUSION
In this paper we estimate a demand system and pricing relationship for a
differentiated product market and implement pass-through simulations and
related welfare analysis. There is a gap in the literature, as analysts have paid
little attention to cost pass-through in differentiated product markets. This
study attempts to fill this gap. In the mixed logit model that we use for
demand specification, the curvature of demand depends on the empirical
distribution of consumer characteristics. This property provides flexible cost
pass-through rates that are not driven solely by the functional form
assumption. This paper is the first attempt to examine this issue.
Empirical results indicate that the pass-through rates for the U.S.
processed cheese market are greater under Nash-Bertrand pricing than
under collusive pricing. This implies that changes in consumer welfare
following cost shocks are greater under Nash-Bertrand competition. We
also compare the results of the structural model with those of the reduced-
form models. We find that the pass-through elasticities of the reduced-form
models fall between those of Nash-Bertrand competition and collusion. The
results suggest that, without knowing the benchmark pass-through
Ta b l e X I
Results of Reduced-Form Models
Independent variables Dependent Variable: ln(price)
ln(Milkprice) 0.034 (0.019)
ln(Diesel) 0.237 (0.010)
ln(Wage) 0.375 (0.029)
R
2
0.672 0.702 0.702
Note: Each regression includes brand-fixed effects. The numbers in parentheses are standard errors.
Ta b l e X I I
Pass-ThroughElasticities: Structural model
Nash-Bertrand Competition Collusion
0.47 0.066
46 DONGHUN KIM AND RONALD W. COTTERILL
r2008 The Authors. Journal compilation r2008 Blackwell Publishing Ltd. and the Editorial Board of The Journal of Industrial
Economics.
elasticities, it may be difficult to infer the degree of market competitiveness
from a reduced-form analysis. They also suggest that the reduced form
results are biased.
We have focused here on the Nash-Bertrand equilibrium and collusion.
Similar studies pertaining to other equilibrium concepts, such as semi-
collusion and a firm’s deviation to or from collusion using a cost shock as a
focal point, would be possible. A related avenue would be to analyze a
dynamic model that could account for changes in firm strategies over time.
Still another direction for future research would be to analyze the pass-
through rate from manufacturer to retailers and from retailers to consumers.
In this paper we implicitly assume that manufacturers and retailers are
vertically integrated.
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48 DONGHUN KIM AND RONALD W. COTTERILL
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