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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

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

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

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

f06¼fXJf0

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

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(p–mc)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

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

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

ﬃﬃﬃ

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

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

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

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

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

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

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.

REFERENCES

Anderson, Simon P.; de Palma, Andre and Kreider, Brent, 2001, ‘Tax Incidence in

Differentiated Product Oligopoly,’ Journal of Public Economics, 81, pp. 173–192.

Besley, J. Timothy and Rosen, Havey S., 1998, ‘Sales Taxes and Price: An Empirical

Analysis,’ NBER Working Paper 6667, July.

Berry, S., 1994, ‘Estimating Discrete-Choice Models of Product Differentiation,’ Rand

Journal of Economics, 25, pp. 242–262.

Berry, S.; Levinsohn, J. and Pakes, A., 1995, ‘Automobile Prices in Market Equilibrium,’

Econometrica, 63, pp. 841–889.

Bresnahan, F. Timothy, Stern, Scott and Trajtenberg, Manuel, 1997, ‘Market

Segmentation and the Sources of Rents from Innovation: Personal Computers in the

Late 1980s,’ Rand Journal of Economics, 28, pp. s17–s44.

Bulow, Jeremy I and Pﬂeiderer, Paul, 1983, ‘A Note on the Effects of Cost Changes on

Prices,’ Journal of Political Economy, 91, pp. 181–185.

Delipalla, Soﬁa and Keen, Michael, 1992, ‘The Comparison Between Ad Valorem and

Speciﬁc Taxation Under Imperfect Competition,’ Journal of Public Economics, 49, pp.

351–367.

Franklin, Andew W. and Cotterill, Ronald W., 1994, Pricing and Market Strategies in the

National Branded Cheese Industry, (Food Marketing Policy Center, University of

Connecticut).

Froeb, Luke; Tschantz, Steven and Werden, Gregory J., 2005, ‘Pass-Through Rates and

the Price Effects of Mergers,’ International Journal of Industrial Organization, 23, pp.

703–715.

Gould, B. W., 1992, ‘At-Home Consumption of Cheese: A Purchase-Infrequency Model,’

American Journal of Agricultural Economics, 74, pp. 453–459.

Gould, B. W. and Lin, Huei-Chin, 1994, ‘The Demand for Cheese in the United States:

The Role of Household Consumption,’ Agribusiness, 10–1, pp. 43–59.

Gron, Anne and Swenson, Deborah L., 2000, ‘Cost Pass-Through in the U.S. Automobile

Market,’ Review of Economics and Statistics, 82 (2), pp. 316–324.

Hausman, J., 1996, ‘Valuation of New Goods under Perfect and Imperfect Competition,’

in Bresnahan, T. and Gordon, R. eds., The Economics of New Goods: Studies in Income

and Wealth, 58, National Bureau of Economic Research, Chicago.

Hausman, J.; Leonard, G. and Zona, J. D., 1994, ‘Competitive Analysis with

Differentiated Products,’ Annales D’Economie et de Statistique, 34, pp. 159–80.

COST PASS-THROUGH IN DIFFERENTIATED PRODUCT MARKETS 47

Economics.

Hein, Dale M. and Wessells, Cathy R., 1990, ‘Demand Systems Estimation with

Microdata: A Censored Regression Approach,’ Journal of Business & Economic

Statistics, 8 (3), pp. 365–371.

Karp, Larry and Perloff, Jeffrey, 1989, ‘Estimating Market Structure and Tax Incidence:

Japanese Television Market,’ Journal of Industrial Economics, 38 (3), pp. 225–239.

Katz, Michael and Rosen, Harvey, 1985, ‘Tax Analysis in an Oligopoly Model,’ Public

Finance Quarterly, 13, pp. 3–19.

McFadden, D., 1981, ‘Econometric Models of Probabilistic Choice,’ in Manski, C. and

McFadden, D. eds., Structural Analysis of Discrete Data, pp. 198–272 (MIT Press,

Cambridge).

Mueller, Willard; Marion, Bruce W.; Sial, Maubool H. and Geithman, F. E., 1996,

Cheese Pricing: A Study of the National Cheese Exchange, (Department of Agricultural

Economics, University of Wisconsin-Madison).

Nevo, Aviv, 2001, ‘Measuring Market Power in the Ready-to-Eat Cereal Industry,’

Econometrica, 69, pp. 307–342.

Nevo, Aviv, 2000, ‘Mergers with Differentiated Products: The Case of the Ready-to-Eat

Cereal Industry,’ Rand Journal of Economics, 31 (3), pp. 395–421.

Petrin, A., 2002, ‘Quantifying the Beneﬁts of New Products: The Case of the Minivan,’

Journal of Political Economy, 110, pp. 705–729.

Small, K. A. and Rosen, H. S., 1981, ‘Applied Welfare Economics with Discrete Choice

Models,’ Econometrica, 49, pp. 105–130.

Stern, Nicholas H., 1987, ‘The Effects of Taxation, Price Control and Government

Contracts in Oligopoly,’ Journal of Public Economics, 32, pp. 133–158.

Sullivan, Daniel, 1985, ‘Testing Hypotheses About Firm Behavior in the Cigarette

Industry,’ Journal of Political Economy, 93, pp. 586–598.

Sumner, Daniel A., 1981, ‘Measuring of Monopoly Behavior: An Application to the

Cigarette Industry,’ Journal of Political Economy, 89, pp. 1010–1019.

Trajtenberg, M., 1989, ‘The Welfare Analysis of Product Innovation, with an Application

to Computed Tomography Scanners,’ Journal of Political Economy, 94, pp. 444–479.

48 DONGHUN KIM AND RONALD W. COTTERILL

Economics.