Merger Impacts on Equilibrium Pricing when Advertising Strategies are Dynamic

†

Michael A. Cohen

Ronald W. Cotterill

University of Connecticut

University of Connecticut

Food Marketing Policy Center

Food Marketing Policy Center

[email protected]

[email protected]

March 12, 2010

This is a preliminary draft please do not cite Abstract Unilateral analysis of a merger in a differentiated product industry, since first down with brand level scanner data in 1994, has focused on price as the sole strategic variable. Here we estimate a random coefficients logit model for RTE breakfast cereal and analyze dynamic optimal brand level advertising as well as price strategies before and after a merger. Ultimately the impact on price, which is critical for antitrust analysis, is an empirical question. Using our demand estimates we analyze the acquisition of a fringe brand Kashi GoLean Crunch! by the Post cereal company. Employing a sample of twenty five cereal brands we find that advertising is generally predatory (negative cross advertising elasticities). This suggest lower advertising levels for the merged brands post merger and thus lower demand and prices post merger ceteris paribus. However we find positive cross price elasticities for the merging brands and internalization of such more than offsets the negative effects of advertising and priced are higher post merger. † Invited paper for the conference on the Econometric Analysis of Scanner Data, sponsored by the Journal of Applied Econometrics, The Institute for Fiscal Studies, and The Center For Microdata Methods and Practice: London, 22-23 March, 2010. We would like to thank Adam N. Rabinowitz and Elena Castellari for research assistance.

1

Introduction

The evaluation of unilateral market power impacts in horizontal merger analysis in differentiated industries has relied upon estimation of brand level demand systems and focused upon the price impacts that arise from internalization of own price elasticities (Hausman, Leonard, & Zona, 1994; Nevo, 2000).1 This is in spite of the fact that economics recognizes, and empirical studies have documented, that consumer demand, prices and brand level profits are influenced by advertising. Dorfman and Steiner (1954) demonstrated in a static duopoly model a firm’s brand advertising as well as its pricing influenced its profitability. Advertising can shift and rotate demand reducing a brands’ own price elasticity of demand. This produces higher price cost margins in equilibrium and such higher margins also increase the optimal amount of advertising. Martin (2002, p. 276-280) reviews the literature that generalizes Dorfman and Steiner to a dynamic model that recognizes current period advertising contribution to a stock of advertising goodwill that depreciates over time. In this model a firm’s brand advertising influences demand in future periods as well as in the current period. Recently the theoretical literature (Doraszelski & Markovich, 2007, and cited work therein) has focused on the strategic impact of persuasive and informative advertising including government restrictions on advertising of products such as cigarettes. The empirical literature (Dub´e, Hitsch, & Manchanda, 2005, and cited work therein) has focused on dynamic price and advertising models that identify when pulsing, which is heavy ad placement in some periods and none at other times, or continuous advertising is optimal. To date no one has employed dynamic advertising and pricing models to analyze mergers in differentiated product industries. There is a broader literature that analyzes the impact of advertising as information. Shum (2004) measures how brand advertising induces consumers to switch from other brands. Rather than television and other measured media advertisements, Slade (1995) examines retail advertisement in newspapers produced within the context of a manufacturer’s trade promotion. In “retailer push” promotion programs manufacturers offer the retailer lower priced product in return for retail price reductions, aisle end display, or shelf signage, and a “price reduction” advertisement in their weekly newspaper promotion circular (Gerstner & Hess, 1991). Recently Tenn, Froeb, and Tschantz (2009) have expanded the theory of unilateral analysis 1

The first presentation in court was Exhibit C from Affidavit of Professor Ronald W. Cotterill, September 16, 1994, and Exhibit B from Supplemental Affidavit of Ronald W. Cotterill, September 26, 1994, State of New York v. Kraft General Foods et al. 93 Civ 0811 (KMW), reproduced as Cotterill and Haller (1997).

2

to include promotions as well as price but not advertising. In this paper we will specify and estimate a random coefficients logit model for ready to eat (RTE) breakfast cereal to estimate brand level price, and advertising, elasticity matrices. We will use demand estimates to simulate optimal brand pricing and advertising strategies with and without a merger. A brand’s advertising can have two impacts on merger analysis. First is the impact on demand for that and other differentiated products and hence an impact on the price after the merger. Generalizing the Bertrand oligopoly model to include demand side advertising effects destroys the unambiguous prediction wherein the internalization of positive cross price elasticities produces elevated prices for all products postmerger (Martin, 2002, p.280). Second advertising is viewed as a strategic input, i.e. an input with variable as well as fixed cost components and hence influences marginal costs. Thus one might observe “efficiency” gains that offset any estimated demand side price increases so that the prices are lower after the merger. This study examines pricing and advertising while controlling for market promotion strategies in the U.S. ready to eat (RTE) breakfast cereal industry.2 Weekly A.C. Nielsen Homescan data for 25 brands in 11 cities are aggregated to monthly market level data. Nielsen Media research data provide brand level measures of advertising penetration (Gross Rating Points), advertising frequency, and expenditures on advertising. These data permit measurement of the price per unit of advertising penetration and thus estimation of both advertising demand and cost impacts on optimal price and advertising strategies. The section continues with an introduction the the RTE cereal market. The second section of this paper introduces the model of competition. The third section details the specification and estimation procedure of the demand model. The fourth section presents and discusses the demand parameter estimates and demand elasticity estimates. The fifth section conducts a merger simulation exercise and the sixth section concludes.

1.1

The Market for RTE Cereal

Table 1 provides key descriptive statistics for the 25 brand, 11 city panel data set used in this study. The data set contains 3 Post, 1 Kashi, 5 General Mills, 12 Kellogg’s, 2 Quaker, and 2 Private Label brands. When computing market shares, the denominator is 1 serving (1 oz) of cereal per person in the market 2

A more general approach would incorporate promotion activities as strategic choice variables. Although we estimate demand as a function of manufacturer initiated price promotions, and manufacturer coupons as well as price and advertising we do specify the supply side model that generates price and advertising as part of demand estimation.

3

area per day. Potential market share of volume for a brand is thus smaller than its share of actual RTE cereal sales in the market. Post Honey Bunches of Oats has the largest market share, 5.29%. Brands with more than 4% share are GM Cheerios (4.75%), Kellogg’s Frosted Mini-Wheat (4.75%), GM Honey Nut Cheerios (4.31%), and Kellogg’s Frosted Flakes (4.26%). Kashi GoLean Crunch! brand, a leading fringe firm brand in this industry has a very respectable 1.4% market share.3 These 25 brands account for 51.8%, on average, of the potential RTE cereal market. Average price per pound across the branded cereals ranges from $3.98 for GM Multi Grain Cheerios to $1.73 for Post Raisin Bran. Private label Raisin Bran is lower at $1.64 but Post Raisin has very little brand equity. Private Label Corn Flakes is the lowest price cereal at $1.51 well below Kellogg’s Corn Flakes at $2.70. The extent of advertising, as measured by Gross Rating Points (GRPs) in Table 1 varies greatly across the 25 brands.4 The Private Label cereals and Post Raisin Bran have no advertising. The five General Mills brands have the highest advertising penetration with average GRPs ranging from 852 for Multi Grain Cheerios to 2,184 for Honey Nut Cheerios. Only Kellogg’s Frosted Flakes at 1127 has GRP above the 852 GRP minimum of the GM brands. Since GM’s share weighted average price across its brands is $2.86 and Kellogg’s corresponding share weighted average price is $2.65, the company that has the highest advertising penetration has the highest prices. This is consistent with the generalized Dorfman Steiner model. The advertising price per GRP ranges from $198 for Post Grape Nuts whose advertising is effectively zero (GRP=1.59) to a low value of $29.03 for GM Cinnamon Toast Crunch whose GRP are 1,867, the second highest advertising penetration level. Descriptive statistics for the retail promotion variables are provided in the appendix. There is no pattern across the four major firms for the percent of a brand value sold with a retail food insert newspaper ad or the percent sold on display in the store. The percent of brand volume sold with a redeemed coupon, however, is distinctly higher for the GM brands which are advertised more and are higher priced. Thus the GM price, advertising and promotion strategy implies more price discrimination than the strategies of Kellogg’s, Post, and Quaker. Kashi employs distinctly lower retail food insert newspaper ads, in store 3

The RTE cereal industry routinely recognizes adult cereals with more than 1% of actual sales and kid cereals with more than 0.5% of actual sales as brands above minimum efficient scale. Brands with lower shares risk discontinuation over time. 4 Nielsen Media Research defines GRPs as representing the combined weight of advertising from different TV sources– network, spot, syndicated and cable. They are defined by the reach and frequency of the advertising in a given time period, where ‘reach’ is the fraction of the population that has been exposed to at least one ad, and frequency is the average number of times an exposed household has seen the ad.

4

display, and couponing than the top four firms. Returning to advertising conduct the theoretical and empirical literature has documented that pulsing of advertising can be optimal. Dub´e et al. (2005) state: “The widespread practice of pulsing has also been a controversial topic in industry since the early 1970s. Early pulsing advocates justified this practice as an efficient means of saving money with a limited media budget (Kingman, 1970).... For instance, Krugman (1972) documented experimental evidence that three exposure were required to generate a response to advertising. Pulsing was recommended as an effective way for advertisers to generate sufficient frequency in ad exposure while managing a limited advertising budget.” Table 2 identifies brands that pulse advertising. It does so by giving the percent advertising frequency. This is the percent of 4-week periods where one or more advertisements for a particular brand appeared. Post Grape Nuts, for example, advertised in only 7.89% of the possible quad week periods. Therefore, it is pulsing its advertisements into the market in a very sporadic fashion. Kashi GoLean Crunch! brand is also pulsing its ads but ads are appearing in 47.61% of the quad week periods. General Mills in comparison does little or no pulsing. GM Lucky Charms ads, appear 86.8% of the time, for example. GM Cinnamon Toast Crunch ads, for example, appear in every quad week period in all of the 11 markets.

2

A Model of Competition

This section introduces a dynamic oligopoly model of price and advertising competition, as well as the equilibrium concept we employ. Our market, denoted as t, has J products controlled by a set of N multi-product firms. A market is defined as a designated location in a particular discrete time period t = 1, . . . , T . The firms compete in each market on price and advertising. Advertising produces goodwill, which influences product demand. First the section introduces the model of goodwill production. Next it states the demand model. Then it details firm profit a behavioral assumptions. Finally it establishes the equilibrium concept we apply. The exposition closely follows that of Dub´e et al. (2005).

2.1

Advertising

Advertising goodwill establishes the dynamic carry-over effects of advertising’s impact on demand. In other words, today’s advertising has a lasting effect that carries over to the next period and beyond. This

5

carryover effects is modeled as a distributed lag of advertising,

gjt =

∞ X

λk Γ(Aj,t−k ),

(1)

k=1

where, Γ(·) is a nonlinear goodwill production function. We assume that Γ(0) = 0 and is a non decreasing function of Ajt . Firms produce goodwill by adding to the existing stock to generate an augmented goodwill stock, augmented goodwill enters the consumer utility function directly. Augmented goodwill depreciates overtime stochastically according to,

a gj,t+1 = λgjt + νj,t+1 = λ(gjt + Γ(Ajt )) + νj,t+1 .

(2)

λ ∈ (0, 1) is a geometric decay factor and νjt is a mean zero shock included to capture the idiosyncratic aspects of advertising that are not captured by the data and not observed by firms. For example, ν may capture the impact of aspects that are particular to a television ad campaign’s effectiveness or temporal variation in television audience composition, whereas Ajt only measures the reach and frequency of an add for a particular product in a market as measured by Gross Rating points (GRPs). An expansion of equation (2) yields, gjt =

∞ X

λk Γ(Ajt−k ) + ωjt ,

(3)

k=1

here ωjt ≡

P∞

k k=0 λ νj,t−k .

Giving one the stochastic equivalent of equation (1). A Cobb-Douglas production

function is used to model goodwill production

gj,t+1 = eνj,t+1 (1 + Ajt )(1−λ) (gjt )λ .

(4)

When a discrete choice model is used as a foundation of the demand model, such as in logit and probit, one is asserting that sales response to price and advertising is s-shaped. In most market applications the market share of products in the market under consideration is small relative to the zero utility outside option purchase. This implies that most products, if not all, live on the lower tail of the sales response function, therefore market share experiences increasing returns to indirect utility. Since advertising increases indirect utility firms would have a very strong incentive to advertise if advertising goodwill enters the indirect utility

6

function in a linear fashion. The carry-over effect of advertising modeled with the constant returns CobbDouglas goodwill production function in (4) allows for the marginal return to advertising to differ across time. This fact implies that pulsing advertising policies may be adopted by firms, a fact that is consistent with many industries and observed for some brands in the ready to eat cereal industry as the data that we analyze documents.

2.2

Demand

Specifying a discrete choice demand model with random utility, consumers, denoted by i, enjoy indirect utility from consuming product j in market t according to,

a Uijt = β0j + Xjt β − αi pjt + µi ln(1 + gjt ) + ξjt + ijt .

(5)

β0j is a product specific intercept best interpreted as the intrinsic utility of consumption. β is a vector of marginal utility parameters for the vector of product characteristics Xjt . αi measures the consumer specific marginal utility of income and µi measures the consumer specific marginal utility of advertising goodwill. ξjt is an i.i.d. product specific demand shock partially observed by firms and it is unobserved by the econometrician.5 The specification is capped off with ijt , which is an i.i.d. shock that captures idiosyncracies unobserved by the econometrician and it’s assumed to come from a type I extreme value distribution. The consumer specific taste parameters [αi , µi ] are modeled as, 







 αi   α   =  + Σvi , µi µ

(6)

Where vi comes from a bivariate standard normal distribution, implying that [αi , µi ] ∼ N ([α, µ], Σ). The parameters [α, µ] characterize the mean preference over the population and Σ is assumed to be a diagonal variance matrix. Altogether these assumptions imply that the market share for product j in market t is, Z sjt = Bjt

exp(δjt + ηijt ) PJ 1 + k=1 exp(δkt + ηikt )

! φ(vi )dvi ,

(7)

5 Recall the goodwill shock, which is wrapped up in this error term and is only observed by the firm after it sets it’s advertising policy.

7

where Bjt is the consumer specific set that induces the purchase of product j in market t. The expression P can be further simplified by denoting sijt ≡ exp(δjt +µijt )/(1+ Jk=1 exp(δkt +µikt )), therefore the own- and cross- price elasticities of demand with respect to price and advertising goodwill are respectively expressed as: ∂sjt pkt ∂pkt sjt

 R   − pjt αi sijt (1 − sijt )φ(vi )dvi , if j = k; sjt = R   pjt αi sijt sikt φ(vi )dvi , otherwise, sjt

and a ∂sjt gkt a s ∂gkt jt

=

  

a gkt 1 a s 1+gkt jt

  −

a gkt a 1+gkt

R

1 sjt

µi sijt (1 − sijt )φ(vi )dvi , if j = k; R µi sijt sikt φ(vi )dvi , otherwise.

(8)

(9)

Equations (8) and (9) demonstrate the flexibility of the heterogeneous agent aggregate logit model that we apply for demand analysis in contrast to the basic logit model that suffers from strict independence of irrelevant alternatives (IIA). This version of the logit doesn’t restrict cross price elasticities to be proportional to market share follows from the fact that E[f (x)] 6= f (E[x]). Consumer switching is due to similarities and differences in consumers’ tastes for product characteristics. That is, because consumers with similar tastes make similar choices, aggregating their individual responses yields market elasticities that appreciate product characteristics as determinants of switching behavior.

2.3

Profit

The demand for product j is a function of market size M and expressed Qjt = M sjt , moreover it is determined by product characteristics, prices, advertising, and goodwill levels, as well as the vector of demand shocks: Qjt = Qj (gt , At , Pt , ξt ),

(10)

where goodwill levels, gt = (g1t , . . . , gJt ). The same goes for prices, advertising,and demand shocks. The vector of demand shocks includes the shock to goodwill unobserved by firms. Each market’s profit for firm j is πj = (pjt − cj )Qj (gt , At , Pt , ξt ) − kAjt .

8

(11)

cj is a constant marginal cost of production, and k is the advertisers price per GRP. Because prices and advertising are set before the goodwill shock is realized firms maximizes expected per period profits: Z πj = πj (gt , At , Pt ) =

(pjt − cj )Qj (gt , At , Pt , ξ)p(ξ)dξ − kAjt ,

(12)

recalling that ξ is i.i.d.. The multi-product firm maximizes profits jointly over each product in its portfolio.

Π(gt , At , Pt ) =

X

πj (gt , At , Pt ),

(13)

j∈Gf

where Gf is the set of products in firm f ’s portfolio.

2.4

Firms

Firms play the following advertising game. At the start of period the state of the market, ðt , is observed by all firms. Upon observing the state vector firms make there pricing and advertising decisions on each product σj (gt ) = (Pjt , Ajt ). In this game firms’ decisions rely only on payoff relevant state variables. Given product demand and current goodwill levels ones has all the necessary information to simulate current a future sales from the model, meaning gt contains all the necessary payoff relevant information. Once firms observe the state vector and firms choose prices and advertising levels the demand shocks, ξt , are realized and profits are determined. The strategy profile vector σ = (σ1 , . . . , σN ) contains the price and advertising decisions of all N firms for each of their products. The expected discounted profits for firm f in state gt under strategy profile σ are " Vf (gt |σ) = E

∞ X

# β s−t Πf (gs , σf (gs ))|gt .

(14)

s=t

The firm level objective is to maximize this stream of expected profits by choosing a strategy profile σf . To maximize the stream of profits in (14) the firm needs to know how the state variables gt and consequently the strategy profiles σ(gt ) evolve. Equation (2) reveals that goodwill stock gjt evolves according to a first order Markov process whose transition density is p(·|gjt , Ajt ). Recalling that the goodwill shocks are i.i.d.

9

the state vector’s Markov transition density is

p(gt+1 |gt , At ) =

J Y

p(gj,t |gjt , Ajt ).

(15)

j=1

Because firms make pricing and advertising decision based solely on the current state vector time dependant strategies are not considered. Firm f ’s Markov strategy is σ : g → σf (g) = (Pf (g), Af (g)). Each firm makes its best move σf based on the strategy profile of competing firms σ−j = (σ1 , . . . , σN ). The Markov strategy along with equation (15) fully define equation (14).

2.5

Equilibrium

Equilibrium is described by a value function in a dynamic programming problem with strategic interactions. Each firm has a value function that satisfies the Bellman equation   Z 0 0 0 Vf (gt |σ) = supτ ∈R2+ Πf (g, τ, σ−j (g)) + β Vf (g |σ)p(g |g, τ, σ−j (g))dg

(16)

Firms choose advertising levels and prices for their products, so the supremum is taken with respect to α = (Pj , Aj ), in the first quadrant of the Cartesian plane. This Bellman equation includes the competing firms strategy profile σ−j on the right hand side, which is firm f ’s best guess at the competing strategy profile and defines the firms best response to σ−j . A Markov perfect equilibrium (MPE) of the dynamic ∗ ) such that no firm can deviate from their action σ ∗ in any game is a list of strategies, σ ∗ = (σ1∗ , . . . , σN n

subgame that starts at state g. We restrict our attention to pure strategies due to the computational difficulty of determining equilibria in a more general model that might include mixed strategies.

Define. A Markov perfect equilibrium is a Markov strategy profile σ ∗ such that ∗

Vj (g|σ ) ≥

∗ πj (g, τ, σ−j (g))

Z +β

∗ Vj (g0 |σ)p(g0 |g, τ, σ−j (g))dg0

for all unilateral deviations τ = (Aj , Pj ), states g, and firms j.

10

(17)

For a more complete and concise treatment of the MPE concept see Maskin and Tirole (2001). Ericson and Pakes (1995) and Doraszelski and Satterthwaite (2003) explore general conditions for the existence and uniqueness of an equilibrium solution. The model we consider is similar to that of Dub´e et al. (2005, p.115) who explain that: “What is relevant for their empirical study is whether an equilibrium exists for a particular set of demand parameter estimates. Existence for a specific version of the model is checked by the numerical solution algorithm.” Therefore the existence of an equilibrium is established. That being said, one cannot determine with absolute certainty whether the equilibrium is the ideal point on the Pareto front. Validity of the solution is supported by starting the numerical algorithm at different points to see if it converges to the same equilibrium.

3

Econometric Model Specification and Estimation Approach

This section introduces the specification of the exact demand model that we estimate and then explains the estimation procedure we implement.

3.1

Demand Model Specification

After integrating over the distribution of consumer tastes the demand model from equations 5 and 7 can be specified in terms of mean indirect utility to yield: ∞ X sjt ln( ) = β0j + Xjt β − αpjt + µ( λk (1 − λ)ln(1 + GRPj,t−k ) + λt−k gjt ) + ωjt + ξjt , s0t

(18)

k=0

where, ωjt ≡

P∞

k=0 λ

kν . ijt

This equation clearly contains an infinite sum, therefore we use a Koyck

transformation to difference it out. The final estimation equation is then,

ln(

sj,t−1 sjt ) − λln( ) = β0j (1 − λ) + s0t s0,t−1 L X

βl (Xljt − λXlj,t−1 ) − α(pjt − λpj,t−1 ) +

l=0 ∗ µ((1 − λ)ln(1 + GRPjt ) + (1 − λ)νjt ) + ξjt ,

11

(19)

∗ = ξ − λξ where ξjt jt j,t−1 . This equation demonstrates that new advertising levels may be used to capture

demand responsiveness to goodwill, after controlling for other product characteristics. The product characteristics, Xjt , included in our model are the merchandizing variables summarized in table A.1 of appendix A. The variables include: proportion of sales with a retail ad, proportion of sales with a retail display, and proportion of sales sold with a coupon. Prices and group rating points specified in the model were discussed in detail in section 2.

3.2

Demand Parameter Estimation Approach

Under weak regularity conditions on the density of consumer unobservables, the existence of a unique mean utility that satisfies the observed market shares has been established by Berry (1994). This fact allows one to use the condition that observed market shares must equal predicted market shares when consumer utility parameters are estimated. Empirical studies in the past rely upon the nested fixed point approach to estimate the random coefficients logit model (Berry, Levinsohn, & Pakes, 1995; Nevo, 2001). The nested fixed point estimation approach is made up of two distinct parts. First practitioners use contraction mapping to find the mean utility that makes observed share equal to predicted shares. Then they estimate the density of preference parameters in a subsequent step using a generalized method of moments (GMM) approach. The mathematical programming equilibrium condition (MPEC) approach of Dube, Fox, and Su (2009) recasts estimation of the random coefficients logit as a mathematical programming problem with equilibrium constraints. In their approach they specify the GMM objective function and minimize it with the constraint that observed market shares equal predicted market shares using state of the art optimization tools such as KN IT ROr .6 Dube et al. (2009) document several numerical concerns for the nested fixed point approach typically applied in the literature, and demonstrate that the constrained optimization approach is uniformly preferred for computational efficiency and accuracy. Since Price and advertising are endogenously determined it stands to reason that they are correlated with the aggregate demand shock since firms set price and advertising policies conditional on market specific conditions that are unobserved by the econometrician. To overcome this hurdle we apply an instrumental variable approach in the GMM framework described above. To instrument for the endogenous price we predict prices in a given market with prices in other markets to remove the market specific component 6

We adapt the estimation code of Dube et al. (2009) to estimate our model.

12

correlated with the demand shock (Hausman & Taylor, 1981; Hausman et al., 1994; Nevo, 2001). We use lagged predicted prices to control for the endogeneity of lagged price in the Koyck transformed model. To instrument for the endogeneity of advertising goodwill we use last periods advertising expenditure. Because firms set this period’s advertising based on the unobserved demand shock, next period’s goodwill will be determined in large part by this period expenditure but this periods expenditure would not be correlated with next periods demand shock. This argument establishes that advertising expenditure from last period is an ideal instrument for advertising this period as estimation results and IV tests document. To estimate the full demand model the integral in equation 8 must be simulated. We simulate this integral over 200 consumers, to accomplish this we make 200 draws from a standard normal distribution and estimate the variance matrix Σ from equation 7 using the procedure described above.

4

Demand Results

This section investigates results from the demand model estimates. First we analyze parameter estimates from several logit model specifications. Then we analyze the implied price and advertising goodwill elasticities of demand.

4.1

Estimation Results for Logit Demand Models

Table 3 shows results for various specifications of the simple logit demand model as well as the final full random coefficients logit specification. A quick look at this table reveals that key parameter estimates are highly significant in every model as standard error estimates testify. In all models β0 is the constant, α is the price coefficient, µ is the marginal utility of goodwill, and σν is the standard deviation of the goodwill shock. βP romo , βDisp , and βCoup are the marginal utilities of retail promotional pricing, in-store display, and coupon redemption respectively. All models are capped off with brand and DMA fixed effects.7 Columns i and ii exhibit estimates of the simple logit without instrumentation for prices an advertising. From ordinary least squares (OLS) estimates in these two columns one will observe that inclusion of retailer merchandizing variables: circular promotion (βpromo ), in store display (βdisp ), and coupon re7

A DMA is a Designated Marketing Area and defines a television market by the standards of Nielsen Media Research. They effectively correspond to major metropolitan areas and sometimes cover several states. For example, The New York DMA consists of counties in Southern New York, South West Connecticut, Northern New Jersey, and the Poconos region of Pennsylvania.

13

demption (βcoup ), remove downward bias on price sensitivity. Columns iii, iv, v, and vi exhibit parameter estimates from various simple logit specifications estimated with various instrumental variable sets using a GMM instrumental variable approach. Comparing Columns iii and iv demonstrates that instrumenting for price and advertising reduces endogeneity bias, which biases a coefficient toward zero. The difference between the model v and vi is simply that the specification in column v includes this period’s advertising expenditure as an instrument, which is potentially correlated with the demand shock. Overall regression statistics include Hansen’s J, which testifies to the degree of instrument exogeneity. An upper tail test fails to reject the null hypothesis that the instruments in each specification are correlated with the model error, which supports instrument exogeneity. First stage regression statistics testify to instrument relevance. First stage F -stats and R2 indicate that the instruments are relatively strong and valid and explain a sizeable percentage of variation in the endogenous price and advertising variables, as evidenced by first stage regression statistics. Parameter estimates for the full random coefficients demand model appear in the final column of the table. The impact of in-store display is not significantly different form zero in this specification as was the case for its simple logit counterpart from column vi. The distribution of the price sensitivity coefficient is centered at -14.984 and has a standard deviation of 6.956 which implies that 95% of the consumers have marginal price sensitivities between -28.8960 and -1.0720, consistent with the law of demand. The distribution of the advertising coefficient µ is centered at .025, the standard deviation of the coefficient’s distribution indicates that advertising goodwill has a positive effect for the majority of the population.

4.2

Elasticities

Tables 4 and 5 provide the price and goodwill advertising elasticities for selected brands. The full matrices, available upon request, are not reproduced due to page size limits. Examining the price elasticities in Table 4, each of the 15 reported own price elasticities are negative as hypothesized and are quite similar in size. The least elastic is Kellogg’s Frosted Mini-Wheats at -1.978 and the most elastic is Kellogg’s Rice Krispies at -2.323. Examining any column in Table 4 gives the percent change in volume of all other brands for a 1% change in that brands price. Since different brands have different market shares the comparison in a column reflects share imbalances between the brands as well as absolute switching behavior. For example, the elevation of the price of a brand with 1% market share that loses the same quantity of cereal to two 14

brands, one with 1% and the other with 5% share, will have a greater cross price elasticity with the lower share brand. Examining a row in 4 measures the impact on a brand’s share from a 1% increase in the price of each of the other brands. As such it is a more direct measure of switching conduct. All cross price elasticities matter in a merger impact analysis. Note in Table 4 that all reported cross price elasticities are positive. Therefore portfolio pricing of multiple brands by a firm without consideration of advertising impacts results in higher prices than independent pricing of each brand. Also, if one focuses a merger analysis only on price, the internalization of merged brands cross price effects will elevate price. Turning now to advertising elasticities, Table 5 reports the impact of changes in the level of advertising goodwill on volume sold. Reported elasticity coeeficients are for a 100% change in advertising to provide more significant digits than a 1% change. Twelve of the 15 reported own price elasticities are positive. The impact of a 100% increase in advertising has the largest impact on volume for the following 5 brands: 1. Kellogg’s Raisin Bran Crunch 1.901% 2. General Mills Cheerios Honey Nut 1.686% 3. Kellogg’s Frosted Mini-Wheats 1.593% 4. Kellogg’s Corn Pops 1.486% 5. Kashi GoLean Crunch! 1.357% Advertising cross elasticities are generally negative which indicates that brand advertising is predatory rather than cooperative (Martin, 2002, p.279). Increases in advertising generally increase a brands volume by capturing sales from other brands.8

5

Market Simulations

In this section we compute the Markov perfect equilibrium (MPE) implied by the model outlined in section 3. Next we compute MPE for a simulated merger in the taste enhanced wholesome (TEW) segment of the ready to eat cereal market and compare the counterfactual equilibria to the factual equilibria implied by the 8

Cooperative brand level advertising seems to occur in milk markets. (Tchumtchoua, 2008) documents that brand level milk advertising in Boston increases all milk sales and in fact brand advertisers would be well advised to shift ad dollars to the generic “got milk?” campaign.

15

model. The section first explains how the simulation is conducted then simulation results are presented and results are discussed including a price impact analysis of a merger between two of three firms we consider in the TEW segment.

5.1

Computing Markov Perfect Equilibrium in a Market

We use the first 12 periods of the sample to initiate advertising goodwill levels. With an average geometric decay factor of .344 the effects of advertising are effectively worn off after 12 periods, which is approximately 11 months. The goodwill levels at the end of the twelfth month establish the initial state vector for simulating the MPE from month 13 on. Results are simulated under the assumption that the discount factor β is equal to .9916 which corresponds to an annual interest rate of 11%.9 No evidence of multiple equilibria was detected when different initial starting values for MPE solution where tried. An brief primer found in appendix B of this manuscript describes the computational procedure for computing the MPE. Since demand was estimated without the limitation of supply side restrictions, price and advertising were simply covariates, we did not specify how prices and advertising were strategically generated at the estimation stage. This means that a comparison of a particular sequence of MPEs to the actual price and advertising levels is not a proper comparison. Rather one should compare the distribution of simulated MPEs to the distribution of prices and advertising levels observed in the data. To simulate a merger one computes the MPE under the assumption that the merged entity now maximizes its present discounted profits over all the products in its factual portfolio plus the new products the merged firm acquires under the counterfactual merger. We assume that marginal cost of production remains constant with and without the merger, admittedly the simulation does not capture the production efficiencies that a merge may potentially harness, however the merger simulation does in fact capture potential unit cost of advertising efficiencies. This simulation improves upon past studies that simulate mergers because it measures price effects while controlling for advertising efficiencies.

5.2

Merger Simulation of Dynamic Price and Advertising Impacts

Numerically determining the ideal point on a Pareto front for a large dynamic price and advertising game for 25 brands and 6 firms is difficult and left for future research. Instead we turn our attention to a popular 9

The discount rate β = 1/(1 + r/13), where r is the interest rate and 13 is the number of quad-week periods in a year.

16

segment of the ready to eat breakfast cereal industry. We focus upon the potential acquisition of the very successful fringe brand, Kashi GoLean Crunch!, by the Post cereal company within the confines of what the industry has labeled the “taste enhanced wholesome segment” of the adult cereal market (Cotterill & Haller, 1997).10 In a letter to Kraft General Foods proposing to evaluate the impact of couponing and trade deals on brand volume, Nielsen Marketing Research executives state: The scope of this analysis will be Taste Enhanced Wholesome (TEW) cereals. We are choosing to evaluate this part of the entire RTE cereal category for the following reasons: • The TEW segment consists of brands that possess strong interactions with each other. • Including other category segments into the evaluation may “dilute” the switching patterns observed in the data. For example, a household may always purchase a Traditional Kid cereal and a TEW cereal for different members of their household. However, the data does not reflect the intended user of each brand, and in effect may falsely indicate a witch form [sic] a Traditional Kid brand to TEW. [State of New York v. Kraft General Foods et al. 93 Civ 0811 (KMW) @ KGF048666, PX853] The reasoning supports our focus on brands in the TEW segment when analyzing a potential merger of TEW brands. The taste enhanced wholesome brands that we will use to illustrate merger impact are Kashi GoLean Crunch!, Post Raisin Bran, Post Honey Bunches of Oats, Kellogg’s Raisin Bran, Kellogg’s Raisin Bran Crunch, and Private Label Raisin Bran. Thus there are 4 firms and 7 brands. For this illustration we analyze only the Chicago market. For policy purposes one would prefer analysis with the full 25 brand model and for all 11 local markets. To demonstrate how one would asses a potential merger we asses the impact of one that occurs at the end of the twelfth period between Kashi and Post. The merger is anticompetitive if the post merger prices are higher than prices without the merger. Note that with these brands in the merged entity it is possible for some prices to go up and one or more to go down creating a welfare tradeoff if consumers choose different brands. Figures 1, 2, and 3 display the sequence of MPE price and advertising policies with and without the merger. Figure 1 shows MPEs for Post Raisin Bran. The top panel clearly indicates an increase in price for 10 The current simulation uses the simple logit demand model estimated in column (vi) of table 3. A revised version of the paper that uses the fully flexible random coefficients model should be available at the conference, and for the discussant as soon as possible.

17

every period. The top panel of Figure 2 shows MPEs for Post Honey Bunches of Oats for which price also increases. Both of these brands belonged to the firm without the merger yet with the acquisition of Kashi, Post changes advertising levels for these two brands in opposite directions. They decrease advertising on their Raisin Bran and increase advertising on the Honey Bunches of Oats label. Figure 3 shows the MPEs for Golean Crunch! under the Kashi banner and under the Post banner. The top panel of this figure indicates that under the Kashi banner prices are lower in most periods than they are under the Post banner, however it is profitable for Kashi to pulse large price increases in a few periods when it is independent. Advertising policy also clearly changes under the Post banner. The lower panel of the figure 3 documents that under Post the GoLean Crunch! brand managers engage in a more pronounced ad pulsing strategy and reduce the overall level of advertising. Thus an independent Kashi pulses price and advertising and GoLean Crunch! under Post does not pulse price and increasing pulsing of advertising. In order to assess the overall effect of the merger Table 6 summarizes the series of MPE pricing strategies. The table displays volume weighted average MPE prices for each brand for the entire simulation period. If Kashi’s GoLean Crunch! were acquired by Post the price of Post Raisin Bran goes up 5.9 cents (3.25%). Post Honey Bunches of Oats price goes up 1.2 cents (.49%); and, Kashi GoLean Crunch! price goes up 5.8 cents (2.2%). The prices of other brands in the segment also go up but at a lower rate. Therefore after including the dynamic effects of advertising on demand and cost, the merger still has a positive impact on prices of brands in the TEW segment.This analysis incorporates changes in the unit cost of advertising, however it does not measure changes in the marginal cost of production for other inputs.

6

Conclusions and Suggestions for Further Research

This analysis documents methods, for a differentiated product industry, whereby one can analyze the price impacts of a merger in a dynamic model of strategic choice where firms maximize profits over time by setting advertising as well as price levels. The generalized Dorfman Steiner model provides no robust qualitative predictions as to price impact when advertising conduct is considered. Price analysis in the generalized model is essentially an empirical question. For a potential merger in the taste enhanced segment of the RTE cereal industry we find positive cross price elasticities of demand, which support price elevation due

18

to merger when price is the only strategic choice variable. Simulating merger impacts in the general model we find significantly different time paths for advertising as well as price. Most significant the merger still elevates prices in the generalized Dorfman Steiner model. Further research however is needed to strengthen the empirical foundations of dynamic analysis of merger price impacts that incorporate non price strategic variables. One should consider optimization over more brands then we were able to include in our study. In the future we would expand our merger simulation to include all 25 brands and 11 markets in our study. One could also introduce other non price instruments to the analysis such as manufacturer initiated trade promotions and manufacturer coupons. Finally one might attempt to model retail as well as manufacturer conduct in a vertical pricing game.

References Berry, S., Levinsohn, J., & Pakes, A. (1995). Automobile Prices in Market Equilibrium. Econometrica, 63, 841–889. Berry, S. T. (1994). Estimating Descrete Choice Models of Product Differentiation. RAND Journal of Economics, 25 (2), 242–262. Cotterill, R., & Haller, L. (1997). An Econometric Analysis of the Demand for RTE Cereal: Product Market Definition and Unilateral Market Power Effects. Food marketing policy center research report series, working paper 35, Food Marketing Policy Center, University of Connecticut. Doraszelski, U., & Markovich, S. (2007). Advertising Dynamics and Competitive Advantage. RAND Journal of Economics, 38 (3), 557. Doraszelski, U., & Satterthwaite, M. (2003). Foundations of Markov-perfect industry dynamics: Existence, purification. Tech. rep., and multiplicity, Working paper, Hoover Institution, Stanford. Dorfman, R., & Steiner, P. (1954). Optimal Advertising and Optimal Quality. The American Economic Review, 44 (5), 826–836. Dub´e, J.-P., Hitsch, G. J., & Manchanda, P. (2005). An Empirical Model of Advertising Dynamics. Quantitative Marketing and Economics, 3, 107–144. 19

Dube, J., Fox, J., & Su, C. (2009). Improving the Numerical Performance of BLP Static and Dynamic Discrete Choice Random Coefficients Demand Estimation. Working paper 14991, National Bureau of Economic Research, Cambridge MA. Ericson, R., & Pakes, A. (1995). Markov-Perfect Industry Dynamics: A Framework for Empirical Work. The Review of Economic Studies, 62 (1), 53–82. Gerstner, E., & Hess, J. (1991). A Theory of Channel Price Promotions. The American Economic Review, 81 (4), 872–886. Hausman, J., Leonard, G., & Zona, J. (1994). Competitive Analysis with Differenciated Products. Annales d’Economie et de Statistique, 159–180. Hausman, J., & Taylor, W. (1981). Panel Data and Unobservable Individual Effects. Econometrica, 49 (6), 1377–1398. Kingman, M. (1970). Adem See Pulsing as a Way to Beat Soring TV Time Costs. Advertising Age, 48 (27), 27–29. Krugman, H. (1972). Why Three Exposures may be Enough. Journal of Advertising Research, 12 (6), 11–14. Martin, S. (2002). Advanced Industrial Economics (Second edition). Blackwell Publishers. Maskin, E., & Tirole, J. (2001). Markov Perfect Equilibrium I. Observable Actions. Journal of Economic Theory, 100 (2), 191–219. Nevo, A. (2001). Measuring Market Power in the Ready-to-Eat Cereal Industry. Econometrica, 69 (2), 307–342. Nevo, A. (2000). Mergers with Differentiated Products: The Case of the Ready-To-Eat Cereal Industry. RAND Journal of Economics, 31 (3), 395–421. Shum, M. (2004). Does Advertising Overcome Brand Loyalty? Evidence from the Breakfast-Cereals Market. Journal of Economics & Management Strategy, 13 (2), 241–272.

20

Slade, M. (1995). Product Rivalry with Multiple Strategic Weapons: An Analysis of Price and Advertising Competition. Journal of Economics & Management Strategy, 4 (3), 445. Tchumtchoua, S. (2008). Advertising and Dynamic Demand for Differentiated Products. Ph.D. Dissertation, University of Connecticut. Tenn, S., Froeb, L., & Tschantz, S. (2009). Mergers when Firms Compete Choose Both Price and Promotion. Public law and legal theory, working paper 07-09, Law School, Vanderbilt University.

Table 1: Descriptive Statistics of Share, Price Per Pound, Advertising Penetration (Gross Rating Points) and Advertising Price Per GRP Brand

Pct Share Mean1 Std. Dev.

Post Grape-Nuts Post Raisin Bran Post Honey Bunches of Oats Kashi GoLean Crunch! General Mills Cheerios General Mills Cinnamon Toast Crunch General Mills Cheerios Honey Nut General Mills Lucky Charms General Mills Cheerios Multi Grain Kelloggs Apple Jacks Kelloggs Corn Flakes Kelloggs Corn Pops Kelloggs Froot Loops Kelloggs Frosted Flakes Kelloggs Frosted Mini-Wheats Kelloggs Raisin Bran Kelloggs Raisin Bran Crunch Kelloggs Rice Krispies Kelloggs Smart Start Kelloggs Special K Kelloggs Special K Red Berries Quaker Cap ’N Crunch Quaker Life Private Label Raisin Bran Private Label Corn Flakes

1.13% 1.53% 5.29% 1.40% 4.75% 2.53% 4.31% 1.83% 0.61% 1.50% 1.05% 1.24% 1.75% 4.26% 4.70% 2.70% 1.11% 1.69% 1.00% 1.10% 1.66% 0.92% 1.65% 1.37% 0.82%

1.10% 1.16% 2.60% 0.94% 1.81% 1.25% 1.50% 0.97% 0.47% 0.81% 0.68% 0.63% 0.90% 1.65% 2.51% 1.27% 0.74% 0.84% 0.68% 0.64% 1.08% 0.61% 1.33% 0.86% 0.63%

Price/lb Mean1 Std. Dev. 1.92 1.73 2.34 2.86 2.91 2.63 2.70 3.02 3.98 2.80 2.70 2.77 2.84 2.28 2.31 2.01 2.51 3.31 3.02 3.81 3.64 2.38 2.34 1.64 1.51

0.38 0.37 0.27 0.40 0.33 0.37 0.32 0.55 0.90 0.59 0.46 0.62 0.55 0.34 0.27 0.26 0.37 0.50 0.46 0.57 0.37 0.47 0.42 0.22 0.33

28-day GRPs Mean1 Std. Dev.

ADV Price/GRP Mean1 Std. Dev.

1.59 0.00 700.54 181.09 1345.35 1867.15 2184.28 1773.73 852.65 828.06 368.05 638.80 759.87 1127.97 686.77 368.07 837.83 780.79 368.34 525.74 504.32 145.22 119.79 0.00 0.00

198.07 n/a 83.74 89.84 156.00 29.03 99.82 29.48 83.51 34.20 50.31 30.55 30.66 33.24 79.98 50.34 102.67 68.39 53.44 74.74 79.23 45.46 79.07 n/a n/a

6.68 0.00 295.31 240.91 986.63 1195.51 1374.80 1262.33 994.80 776.77 527.14 584.11 630.67 665.67 618.55 527.13 604.10 556.58 527.07 579.88 590.46 249.53 219.91 0.00 0.00

142.12 n/a 59.37 74.31 152.06 24.31 112.82 24.18 88.08 46.86 63.00 28.73 32.75 28.02 78.78 63.03 75.26 59.99 55.94 63.97 75.51 59.13 89.66 n/a n/a

Total Pct. Share of 25 Brands 51.85% Note: GRP is the Gross Rating Points from television advertising, defined as the sum of the number of telecasts (minutes, messages) among households (persons) in a frequency group times the percent of households (persons) accounted for in the respective frequency group. n/a indicates no advertising took place for the respective brand 1 The mean value is the average across the entire panel which has 38 quad week periods for 11 cities. Source: Author’s Calculations

21

Figure 1: Price and Advertising (GRP) of Post Raisin Bran with and without the Merger: Chicago DMA

22

Figure 2: Price and Advertising (GRP) of Post Honey Bunches of Oats with and without the Merger: Chicago DMA

23

Figure 3: Price and Advertising (GRP) of Kashi GoLean Crunch! with and without the Merger: Chicago DMA

24

Table 2: Percent Advertising Frequencies Brand

Mean1

Std. Dev.

Min

Max

Post Grape-Nuts 7.89% 0.00% 7.89% 7.89% Post Raisin Bran 0.00% 0.00% 0.00% 0.00% Post Honey Bunches of Oats 100.00% 0.00% 100.00% 100.00% Kashi GoLean Crunch! 47.61% 0.79% 47.37% 50.00% General Mills Cheerios 96.17% 1.81% 94.74% 100.00% General Mills Cinnamon Toast Crunch 100.00% 0.00% 100.00% 100.00% General Mills Cheerios Honey Nut 98.09% 2.07% 94.74% 100.00% General Mills Lucky Charms 86.84% 0.00% 86.84% 86.84% General Mills Cheerios Multi Grain 73.68% 0.00% 73.68% 73.68% Kellogg’s Apple Jacks 78.95% 0.00% 78.95% 78.95% Kellogg’s Corn Flakes 55.26% 0.00% 55.26% 55.26% Kellogg’s Corn Pops 73.68% 0.00% 73.68% 73.68% Kellogg’s Froot Loops 89.71% 0.79% 89.47% 92.11% Kellogg’s Frosted Flakes 97.37% 0.00% 97.37% 97.37% Kellogg’s Frosted Mini-Wheats 76.08% 2.75% 73.68% 78.95% Kellogg’s Raisin Bran 55.26% 0.00% 55.26% 55.26% Kellogg’s Raisin Bran Crunch 94.74% 0.00% 94.74% 94.74% Kellogg’s Rice Krispies 86.84% 0.00% 86.84% 86.84% Kellogg’s Smart Start 60.53% 0.00% 60.53% 60.53% Kellogg’s Special K 82.78% 1.37% 81.58% 84.21% Kellogg’s Special K Red Berries 76.32% 0.00% 76.32% 76.32% Quaker Cap ’N Crunch 42.11% 0.00% 42.11% 42.11% Quaker Life 39.47% 0.00% 39.47% 39.47% Private Label Raisin Bran 0.00% 0.00% 0.00% 0.00% Private Label Corn Flakes 0.00% 0.00% 0.00% 0.00% Note: This table displays percent advertising frequencies across all 11 markets. Percent advertising frequency is the percent of 4-week periods that at least one advertisement appeared. 1 The mean value is the average across the entire panel which has 38 quad week periods for 11 cities. Source: Author’s Calculations

25

Table 3: Logit and Random Coefficients Demand Model Estimation Results Parameter β0 α

Logit OLS (i) (ii) -2.047 (0.066) -5.452 (0.296)

0.010 (0.003) 0.324 (0.012) 0.003 (0.007)

-2.058 (0.069) -4.925 (0.308) 0.033 (0.080) 0.363 (0.121) 0.189 (0.063) 0.010 (0.003) 0.325 (0.012) 0.003 (0.007)

0.547

0.548

βP romo βDisp βCoup µ λ σν R2

Test of Overidentifying Restrictions Number of Restrictions Hansen’s J p-value First-stage Regression Statistics Price R2 Price F -test Goodwill R2 Goodwill F -test Instruments

Logit IV

Random Coefficients mean s.d.

(iii)

(iv)

(v)

(vi)

-1.579 (0.125) -13.685 (1.505)

-2.051 (0.066) -5.436 (0.295)

-1.576 (0.142) -14.425 (1.970) 0.174 (0.098) -0.138 (0.143) 0.446 (0.149) 0.029 (0.012) 0.341 (0.016) 0.003 (0.007)

-2.392 (0.148) -14.984 (2.244) 0.182 (0.110) -0.130 (0.151) 0.501 (0.165) 0.025 (0.007) 0.344 (0.038) 0.129 (0.172)

0.012 (0.003) 0.344 (0.016) 0.004 (0.007)

0.027 (0.006) 0.323 (0.012) 0.004 (0.007)

-1.573 (0.141) -14.439 (1.969) 0.175 (0.098) -0.138 (0.143) 0.446 (0.149) 0.026 (0.006) 0.341 (0.016) 0.002 (0.007)

18 14.815 0.6746

1 0.046 0.8309

19 15.476 0.6919

18 15.453 0.6307

15 10.039 0.8173

0.564 173.175

0.739 23.613 0.571 22.430

0.739 24.558 0.527 19.819

0.739 24.558 0.527 19.819

Prices, Lag Prices,

Prices, Lag Prices,

Advertising Expenditure, Lag Advertising Expenditure,

Prices, Lag Prices, Advertising Expenditure, Lag Advertising Expenditure,

Lag Advertising Expenditure,

Lag Advertising Expenditure,

0.699 25.701

Prices, Lag Prices

Source: Author’s Calculations Notes: Dependant variable is ln(Sjt) − ln(Sot). Based on 10,175 observations. All regressions include brand and DMA fixed effects. Asymptotically robust s.e. are reported in parentheses.

26

6.956 (4.213) 0.017 (0.010) 0.087 (0.067) -

27

3

4

5

6

7

9

14

16

17

18

19

20

*1 P.L. Raisin Bran -2.084 0.078 0.071 0.053 0.071 0.066 0.086 0.076 0.063 0.089 0.072 0.066 0.074 2 P.L. Corn Flakes 0.100 0.090 0.075 0.079 0.081 0.068 0.095 0.074 0.058 0.071 0.076 0.081 0.102 3 Post Grape-Nuts 0.085 -2.057 0.080 0.068 0.071 0.062 0.083 0.070 0.055 0.085 0.081 0.087 0.087 *4 Post Raisin Bran 0.087 0.089 -2.261 0.072 0.078 0.076 0.075 0.081 0.050 0.071 0.084 0.082 0.106 *5 Post Honey Bnch. of Oats 0.063 0.087 0.075 -2.025 0.080 0.060 0.073 0.061 0.049 0.065 0.074 0.091 0.111 *6 Kashi GoLean Crunch! 0.086 0.082 0.071 0.072 -2.243 0.073 0.086 0.080 0.053 0.068 0.067 0.071 0.105 7 G.M. Cheerios 0.083 0.066 0.073 0.069 0.091 -2.093 0.070 0.087 0.053 0.054 0.069 0.063 0.098 8 G.M. Cinn. Toast Crunch 0.107 0.070 0.063 0.068 0.080 0.071 0.086 0.080 0.064 0.074 0.066 0.067 0.094 9 G.M. Cheerios Honey Nut 0.096 0.091 0.075 0.068 0.081 0.070 -2.290 0.079 0.066 0.069 0.067 0.080 0.094 10 G.M. Lucky Charms 0.104 0.094 0.079 0.074 0.079 0.066 0.086 0.075 0.059 0.081 0.083 0.087 0.103 11 G.M. Cheerios Multi Grain 0.078 0.106 0.078 0.076 0.071 0.049 0.085 0.063 0.057 0.078 0.078 0.094 0.094 12 Kel. Apple Jacks 0.067 0.068 0.076 0.090 0.086 0.067 0.075 0.070 0.062 0.057 0.075 0.083 0.106 13 Kel. Corn Flakes 0.092 0.075 0.079 0.067 0.086 0.071 0.086 0.080 0.062 0.064 0.078 0.073 0.113 14 Kel. Corn Pops 0.084 0.076 0.078 0.062 0.088 0.086 0.073 -2.189 0.053 0.065 0.069 0.067 0.102 15 Kel. Froot Loops 0.104 0.066 0.061 0.056 0.076 0.067 0.083 0.074 0.069 0.070 0.070 0.056 0.086 16 Kel. Frosted Flakes 0.105 0.083 0.077 0.065 0.076 0.063 0.101 0.079 -2.182 0.076 0.081 0.077 0.094 *17 Kel. Frosted Mini-Wheats 0.108 0.102 0.072 0.061 0.060 0.059 0.075 0.072 0.057 -1.978 0.081 0.073 0.087 *18 Kel. Raisin Bran 0.099 0.091 0.084 0.074 0.076 0.068 0.073 0.071 0.059 0.075 -2.219 0.079 0.103 *19 Kel. Raisin Bran Crunch 0.076 0.106 0.080 0.086 0.071 0.057 0.081 0.061 0.055 0.066 0.074 -2.139 0.100 20 Kel. Rice Krispies 0.084 0.083 0.082 0.080 0.088 0.073 0.082 0.081 0.051 0.072 0.076 0.075 -2.329 21 Kel. Smart Start 0.108 0.093 0.075 0.054 0.061 0.063 0.079 0.076 0.058 0.090 0.074 0.070 0.077 22 Kel. Special K 0.071 0.066 0.076 0.082 0.084 0.085 0.069 0.075 0.049 0.056 0.072 0.074 0.108 23 Kel. Spec. K Red Berries 0.094 0.065 0.069 0.066 0.086 0.074 0.090 0.076 0.054 0.058 0.054 0.066 0.095 24 Quaker Cap ’N Crunch 0.076 0.088 0.093 0.078 0.085 0.067 0.080 0.080 0.056 0.072 0.078 0.086 0.113 25 Quaker Life 0.087 0.083 0.069 0.064 0.085 0.073 0.090 0.087 0.053 0.072 0.067 0.067 0.093 Note: Cell entries i, j, where i indexes row and j indexes column are the percent change in market share of brand i given a one percent change in price of brand j. Each cell is the average of the elasticities from the 11 markets and 10,450 observations. The full matrix is available upon request. * Brands used in the merger simulation

1

Table 4: Selected Average Price Elasticity of Demand

0.062 0.067 0.057 0.074 0.072 0.071 0.085 0.068 0.064 0.073 0.057 0.091 0.079 0.078 0.068 0.070 0.055 0.074 0.066 0.076 0.066 -2.104 0.065 0.075 0.065

22

0.053 0.065 0.067 0.071 0.070 0.063 0.059 0.058 0.064 0.065 0.069 0.072 0.062 0.061 0.054 0.067 0.060 0.065 0.068 0.069 0.063 0.065 0.054 -2.164 0.056

24

28

3

4

5

6

7

9

14

16

17

18

19

20

22

24

*1 P.L. Raisin Bran 0.000 0.000 0.000 0.012 -0.019 -0.047 -0.058 -0.051 -0.012 -0.029 -0.040 -0.042 0.032 0.007 0.005 2 P.L. Corn Flakes 0.000 0.000 0.000 -0.052 -0.064 -0.052 -0.073 -0.081 -0.081 -0.049 -0.050 -0.084 -0.014 -0.026 -0.026 3 Post Grape-Nuts 0.000 0.000 0.000 0.006 -0.023 0.004 -0.037 -0.010 -0.025 -0.008 -0.006 -0.037 0.020 0.023 0.032 *4 Post Raisin Bran 0.000 0.000 0.000 -0.044 -0.065 -0.097 -0.058 -0.092 -0.081 -0.044 -0.061 -0.105 -0.051 -0.026 -0.037 *5 Post Honey Bnch. of Oats 0.000 0.000 0.000 -0.032 -0.045 0.004 -0.014 -0.033 -0.007 -0.017 -0.020 -0.035 0.039 0.026 0.038 *6 Kashi GoLean Crunch! 0.000 0.000 0.000 -0.086 1.357 -0.069 -0.082 -0.110 -0.093 -0.052 -0.046 -0.090 -0.043 -0.033 -0.048 7 G.M. Cheerios 0.000 0.000 0.000 -0.010 -0.057 0.804 -0.035 -0.074 -0.016 -0.020 -0.014 -0.050 0.007 -0.006 0.012 8 G.M. Cinn. Toast Crunch 0.000 0.000 0.000 -0.028 -0.053 -0.063 -0.056 -0.112 -0.045 -0.042 -0.043 -0.058 0.015 -0.018 -0.009 9 G.M. Cheerios Honey Nut 0.000 0.000 0.000 -0.048 -0.066 -0.076 1.686 -0.090 -0.093 -0.059 -0.046 -0.066 -0.033 -0.029 -0.042 10 G.M. Lucky Charms 0.000 0.000 0.000 0.016 -0.020 -0.017 -0.054 -0.028 -0.028 -0.022 -0.017 -0.036 0.012 0.013 0.006 11 G.M. Cheerios Multi Grain 0.000 0.000 0.000 -0.034 -0.057 -0.053 -0.072 -0.082 -0.081 -0.045 -0.060 -0.079 -0.043 -0.030 -0.035 12 Kel. Apple Jacks 0.000 0.000 0.000 -0.071 -0.093 -0.096 -0.088 -0.099 -0.099 -0.069 -0.069 -0.120 -0.094 -0.050 -0.049 13 Kel. Corn Flakes 0.000 0.000 0.000 0.074 -0.035 0.039 -0.008 -0.039 0.015 -0.016 0.005 -0.022 0.056 0.035 0.045 14 Kel. Corn Pops 0.000 0.000 0.000 -0.054 -0.086 -0.072 -0.075 1.486 -0.102 -0.054 -0.048 -0.084 -0.056 -0.051 -0.029 15 Kel. Froot Loops 0.000 0.000 0.000 -0.025 -0.076 -0.057 -0.051 -0.081 -0.055 -0.039 -0.031 -0.070 -0.011 -0.017 -0.003 16 Kel. Frosted Flakes 0.000 0.000 0.000 -0.005 -0.049 -0.034 -0.059 -0.060 1.333 -0.027 -0.027 -0.067 0.015 -0.025 -0.009 *17 Kel. Frosted Mini-Wheats 0.000 0.000 0.000 -0.047 -0.063 -0.061 -0.101 -0.092 -0.097 1.593 -0.046 -0.094 -0.029 -0.036 -0.030 *18 Kel. Raisin Bran 0.000 0.000 0.000 0.010 -0.012 0.005 -0.032 -0.019 -0.004 -0.015 0.120 -0.024 0.021 0.016 0.008 *19 Kel. Raisin Bran Crunch 0.000 0.000 0.000 -0.044 -0.058 -0.068 -0.055 -0.073 -0.089 -0.048 -0.066 1.901 -0.034 -0.038 -0.031 20 Kel. Rice Krispies 0.000 0.000 0.000 0.063 -0.011 0.039 0.005 -0.019 0.009 0.000 0.008 -0.008 -0.906 0.032 0.076 21 Kel. Smart Start 0.000 0.000 0.000 -0.095 -0.087 -0.086 -0.085 -0.117 -0.081 -0.049 -0.076 -0.109 -0.091 -0.040 -0.067 22 Kel. Special K 0.000 0.000 0.000 0.034 -0.048 0.010 -0.009 -0.058 -0.016 -0.014 0.002 -0.031 0.025 0.004 0.022 23 Kel. Spec. K Red Berries 0.000 0.000 0.000 -0.051 -0.083 -0.089 -0.056 -0.094 -0.075 -0.040 -0.032 -0.056 -0.005 -0.029 -0.007 24 Quaker Cap ’N Crunch 0.000 0.000 0.000 0.042 -0.023 0.021 -0.018 -0.021 -0.001 -0.016 -0.019 -0.029 0.087 0.027 -0.302 25 Quaker Life 0.000 0.000 0.000 -0.032 -0.067 -0.070 -0.057 -0.097 -0.076 -0.052 -0.047 -0.071 -0.021 -0.026 -0.023 Note: Cell entries i, j, where i indexes row and j indexes column are the percent change in market share of brand i given a 100 percent change in average goodwill of brand j. Each cell is the average of the elasticities from the 11 markets and 10,450 observations. The full matrix is available upon request. * Brands used in the merger simulation

1

Table 5: Selected Average Goodwill Elasticity of Demand

Table 6: Merger Impact Analysis Without Merger Brands of the Merging Firms Post Raisin Bran Post Honey Bnch. of Oats Kashi GoLean Crunch! Brands in the Other Firms Kel. Frosted Mini-Wheats Kel. Raisin Bran Kel. Raisin Bran Crunch Source: Author’s Calculations

A

Weighted Average Price With Merger Increase Due to Merger

Pct Increase

1.828 2.441 2.417

1.887 2.453 2.476

0.059 0.012 0.058

3.25% 0.49% 2.42%

2.483 1.711 2.856

2.516 1.726 2.871

0.033 0.016 0.015

1.33% 0.91% 0.54%

Appendix

This appendix describes the procedure implemented for computing MPE. We apply an iterative constrained optimization approach to solve for the MPE of our multi firm game. Each firm’s objective function is given by the bellman equation show in equation 16. We maximize this objective subject to: the first order conditions determining optimal markup, positive levels of advertising, and V1 (g0 ) = T (E[V0 (g0 )]). The final constraint is the typical contract mapping, T (·), for the stochastic bellman equation, see Judd(1998).

Begin with an initial guess of the full strategy profile σ0 = [P0 , A0 ] for each firm at iteration n = 0.

n−1 First: Compute the strategy profiles σfn for each of the firms given the initial guess σ−j .

Second: Compare the full strategy profile σ n to σ n−1

Third: Check ||σ n − σ n−1 || <  to see if convergence criteria have been met. If so, stop. Otherwise go back to the first step.

The integral from equation 16 is simulated using Monte Carlo integration.

29

B

Appendix Table B.1: Descriptive Statistics of Merchandising Variables Brand

Pct Oz Sold with Retail Ad Mean1 Std. Dev.

Pct Oz Sold with Display Mean1 Std. Dev.

Post Grape-Nuts 3.95% 12.15% 0.37% 3.01% Post Raisin Bran 7.58% 14.17% 3.70% 9.70% Post Honey Bunches of Oats 6.19% 7.42% 3.89% 6.51% Kashi GoLean Crunch! 1.40% 4.95% 0.99% 3.63% General Mills Cheerios 5.49% 5.81% 4.35% 5.48% General Mills Cinnamon Toast Crunch 7.24% 10.10% 4.68% 8.01% General Mills Cheerios Honey Nut 5.39% 6.09% 3.77% 5.31% General Mills Lucky Charms 7.16% 10.86% 4.47% 8.63% General Mills Cheerios Multi Grain 7.83% 16.43% 2.30% 8.47% Kelloggs Apple Jacks 8.30% 12.21% 5.48% 10.57% Kelloggs Corn Flakes 6.08% 11.04% 1.90% 5.96% Kelloggs Corn Pops 8.28% 14.19% 5.26% 10.53% Kelloggs Froot Loops 7.24% 10.76% 5.18% 8.67% Kelloggs Frosted Flakes 6.62% 7.66% 4.77% 6.53% Kelloggs Frosted Mini-Wheats 6.11% 7.69% 3.07% 4.83% Kelloggs Raisin Bran 8.19% 11.25% 4.58% 7.88% Kelloggs Raisin Bran Crunch 4.85% 11.61% 1.60% 6.62% Kelloggs Rice Krispies 8.27% 11.24% 4.31% 7.80% Kelloggs Smart Start 4.01% 8.37% 1.09% 4.62% Kelloggs Special K 6.57% 12.26% 2.11% 5.70% Kelloggs Special K Red Berries 4.62% 8.64% 2.65% 7.71% Quaker Cap ’N Crunch 5.77% 12.45% 4.65% 11.07% Quaker Life 4.74% 11.02% 3.15% 8.29% Private Label Raisin Bran 1.51% 6.25% 0.61% 2.97% Private Label Corn Flakes 2.85% 11.11% 1.06% 7.13% 1 The mean value is the average across the entire panel which has 38 quad week periods for 11 cities. Source: Author’s Calculations

30

Pct Oz Sold with Coupon Mean1 Std. Dev. 10.56% 12.48% 15.03% 4.95% 21.97% 20.06% 19.83% 23.14% 23.96% 10.26% 5.06% 11.32% 9.16% 8.55% 11.67% 7.72% 7.64% 9.48% 12.57% 10.75% 10.17% 7.31% 12.27% 3.43% 1.84%

20.07% 17.34% 12.48% 10.42% 13.17% 15.98% 12.51% 18.79% 25.22% 15.94% 10.11% 17.29% 11.94% 11.11% 12.32% 9.85% 14.55% 13.45% 18.44% 15.26% 13.83% 15.19% 17.71% 10.06% 7.35%

Table B.2: Markov Equilibrium Price Per Pound and GRP of Cereal in the Chicago DMA Before and After Post Acquires Kashi GoLean Crunch! (a) Markov Equilibrium Price Per Pound

Brand

Mean

Private Labels Post Raisin Bran Post Honey Bunches of Oats Kashi Golean Crunch! Kellogg’s Frosted Mini-Wheats Kellogg’s Raisin Bran Kellogg’s Raisin Bran Crunch

1.710 1.828 2.441 2.836 2.488 1.711 2.856

Before the merger Std. Dev. Min

Max

Mean

1.700 1.805 2.418 2.086 2.179 1.687 2.832

1.717 1.852 2.465 6.150 2.545 1.755 2.900

1.814 1.857 2.470 2.445 2.500 1.710 2.855

Before Merge Std. Dev. Min

Max

Mean

0.004 0.012 0.012 1.065 0.065 0.015 0.015

After the Merger Std. Dev. Min 0.016 0.014 0.014 0.014 0.015 0.015 0.015

Max

1.772 1.825 2.438 2.414 2.476 1.686 2.831

1.840 1.881 2.494 2.470 2.547 1.757 2.902

After Merge Std. Dev. Min

Max

(b) GRP of Cereal Brands

Brand

Mean

Post Raisin Bran 2184.673 1934.189 0.001 5478.640 Post Honey Bunches of Oats 2880.636 1927.957 50.664 5524.130 Kashi Golean Crunch! 1427.991 586.321 271.562 2853.150 Kellogg’s Frosted Mini-Wheats 3287.426 2146.275 37.383 7462.068 Kellogg’s Raisin Bran 2452.503 2006.953 0.000 7423.798 Kellogg’s Raisin Bran Crunch 2367.845 2380.945 0.000 8644.535 Source: Author’s calculations from simulation of Markov perfect equilibrium

31

1369.042 3926.016 1142.560 3576.473 2479.432 2058.378

1804.921 2523.554 1320.751 2686.549 2274.368 1897.867

1.838 2.600 3.161 6.144 10.813 18.262

6932.998 7373.761 3893.198 8365.523 8576.103 6772.963