AnEmpiricalModelofOptimalDynamicProduct ... · PDF fileAnEmpiricalModelofOptimalDynamicProduct ... sider the case of consumer choice under attribute ... The U.S. RTE breakfast cereal

Vol. 25, No. 1, January–February 2006, pp. 25–50issn 0732-2399 �eissn 1526-548X �06 �2501 �0025

informs ®

doi 10.1287/mksc.1050.0140©2006 INFORMS

An Empirical Model of Optimal Dynamic ProductLaunch and Exit Under Demand Uncertainty

Günter J. HitschGraduate School of Business, University of Chicago, 5807 South Woodlawn Avenue,

Chicago, Illinois 60637, [email protected]

This paper considers the decision problem of a firm that is uncertain about the demand, and hence prof-itability, of a new product. We develop a model of a decision maker who sequentially learns about the

true product profitability from observed product sales. Based on the current information, the decision makerdecides whether to scrap the product. Central to this decision problem are sequential information gathering,and the option value of scrapping the product at any point in time. The model predicts the optimal demandfor information (e.g., in the form of test marketing), and it predicts how the launch or exit policy dependson the firm’s demand uncertainty. Furthermore, it predicts what fraction of newly developed products shouldbe launched on average, and what fraction of these products will “fail,” i.e., exit. The model is solved usingnumerical dynamic programming techniques. We present an application of the model to the case of the U.S.ready-to-eat breakfast cereal industry. Simulations show that the value of reducing uncertainty can be large,and that under higher uncertainty firms should strongly increase the fraction of all new product opportunitieslaunched, even if their point estimate of profits is negative. Alternative, simpler decision rules are shown tolead to large profit losses compared to our method. Finally, we find that the high observed exit rate in the U.S.ready-to-eat cereal industry is optimal and to be expected based on our model.

Key words : new product strategy; product launch; product exit; managerial decision making under uncertainty;Bayesian learning; numerical dynamic programming; dynamic structural models

History : This paper was received July 21, 2003, and was with the author 9 months for 3 revisions; processedby Tülin Erdem.

1. IntroductionNew product introductions are common in most mar-kets. Many of these new products “fail,” i.e., exitfrom the market soon after product launch. Urbanand Hauser (1993), for example, report an averagefailure rate of 35% across different industries. Inmany markets, the failure rate is even higher; inthe U.S. ready-to-eat (RTE) breakfast cereal industry,for example, close to 70% of all new products arescrapped within two years after their introduction.1

These product failures are costly, as the developmentcosts and marketing costs during the launch periodcan no longer be recovered. A possible explanationfor these stylized facts is that firms are often uncer-tain about the demand and profitability of their newproducts, and therefore they launch products that arelater scrapped. This raises the question of how firmsshould optimally learn about the true profitability oftheir products, and how the decision to launch orscrap a product is affected by demand uncertainty.

1 This number is based on the newly launched breakfast cerealsduring 1988–1992.

What would be the value of reducing the demanduncertainty, for example, through test marketing? Fur-thermore, do high exit rates indicate that many firmsuse suboptimal product launch strategies, or maybelaunch products for reasons that are not related todemand uncertainty?This paper aims to answer these and several related

questions. To this end, we develop a model of a deci-sion maker (a firm) who decides whether to launcha new product, and, after product launch, whetherthe product should be scrapped or stay in the mar-ket. The firm is uncertain about the demand, andhence the profitability, of the new product.2 The firm’suncertainty is formalized through a prior distribu-tion on a parameter that indexes the demand func-tion. Realized sales provide new information aboutproduct demand, and allow the firm to update itsprior using Bayes’ rule. Formally, this is a sequen-tial experimentation problem (Wald 1945), where thedecision maker decides period after period whether to

2 Product launch under perfect information is just a special case ofthe model.

25

Hitsch: An Empirical Model of Optimal Dynamic Product Launch and Exit Under Demand Uncertainty26 Marketing Science 25(1), pp. 25–50, © 2006 INFORMS

acquire more information in order to test the hypoth-esis H0 = “the product is profitable.”3 The decisionto keep or scrap the product depends on the costsand benefits of being in the market, i.e., the expectedflow of profits and the marketing costs. Therefore, thefirm’s payoff function has to be based on a realisticdemand system, and some important marketing deci-sions (pricing and advertising) need to be modeledalong with the stay-or-scrap decision. Also, we takeinto account that, based on the state of knowledgeabout the newly launched product, the equilibriumprice of each product in the market may change. Themodel can be calibrated from actual data, and thenused to predict optimal launch behavior and the asso-ciated stream of profits.The model allows us to calculate the expected profit

from a product under some level of demand uncer-tainty. In the spirit of Bayesian decision theory, we cantherefore calculate the value from reduced uncertaintyin the form of increased expected profits. Togetherwith a cost function of reducing uncertainty, we canthen predict the optimal demand for information—for example, in the form of test marketing. The modelalso shows how, given a point estimate of profits, thedecision to launch or scrap a product depends on thedegree of uncertainty. For example, should fewer ormore products be launched under increased uncer-tainty? On average, given a level of uncertainty, whatis the fraction of products that “fail?” This fraction isthe optimal product exit rate, which has to be knownbefore some observed exit rate (such as the 70% exitrate in the RTE cereal industry) can be judged as “toohigh” or “too low.” Our framework is intended tobe applied normatively, as a tool for managers, in awide range of industries. In this paper, we present anapplication to the specific case of the U.S. RTE break-fast cereal industry. This industry is an interestingexample to demonstrate the managerial and economicimplications of our model, due to the historically highincidence of product entry and exit.The questions posed above are all concerned with

the relationship between the initial level of demanduncertainty, and the subsequent launch-or-scrap deci-sions and profit outcomes. Our model assumes thatfirms behave optimally, conditional on the initialprior. We do not assume, however, that the ini-tial prior itself is chosen optimally. Therefore, wedo not contradict the optimality assumption in ourmodel if we ask how subsequent behavior and out-comes change if the initial uncertainty is reduced orincreased.

3 Wald considers a decision maker who does not discount thefuture, while the decision maker in our model is impatient. SeeMoscarini and Smith (2001) for a theoretical treatment of optimalexperimentation by an impatient decision maker.

The sequential decision problem studied has tobe solved using dynamic programming techniques.While generally difficult to solve, simpler decisionrules would not correctly address the issues raisedabove—for example, how the degree of demanduncertainty is related to the launch-or-scrap decision.Using a straightforward but incorrect decision rule, adecision maker would calculate the expected presentdiscounted value of profits, given current informationabout the product’s profitability. The product wouldthen be scrapped if this value was negative or lessthan a fixed cost of keeping it in the market. Thisapproach, however, neglects that the firm can exer-cise the option of scrapping the product not only now,but also at any point in future. This option is valu-able, because it allows the firm to gather more infor-mation about the true product profitability. Exercisingthis option entails an opportunity cost; therefore, evenif the expected value of profits, given current infor-mation, is negative, the firm might optimally delayproduct exit. The option value of a project underuncertainty and irreversibility of actions has beenexamined in the real-options literature (Dixit 1989,Dixit and Pindyck 1994).4 Our paper highlights thereal-options aspect of a new product launch. In ourempirical application, we demonstrate the economicsignificance of the option, and in particular the result-ing value of additional information about the prod-uct’s profitability.The use of Bayesian decision theory in marketing

research is not new. Churchill (1995) and Lehmannet al. (1998), for example, discuss how to assign anex ante dollar value to the information to be gained ina test market. Their treatment is mainly focussed onthe methodological aspects of Bayesian decision the-ory, and not on a concrete implementation of thesemethods. Urban and Hauser (1993) provide an infor-mal discussion of market experimentation during theproduct launch phase, although only with a focus onthe marketing mix, and in particular learning aboutthe effectiveness of advertising.5 Most closely relatedto this study is Urban and Katz (1983). They use aBayesian decision tree to determine whether a prod-uct should enter a test market after pretest marketing,and whether it should be launched nationally after atest market. These two decisions are made by com-paring the realized market share at each stage to apredetermined cutoff market share. This mechanism

4 Typically, the real-options literature considers uncertainty aboutmarket conditions, while in our application the market conditionsare constant, but the decision maker is uncertain about the truestate of the world. This problem is closely related to the sequentialR&D process examined by Roberts and Weitzman (1981).5 Little (1966) and Pekelman and Tse (1980) use adaptive con-trol techniques to show how advertising experiments should beconducted.

Hitsch: An Empirical Model of Optimal Dynamic Product Launch and Exit Under Demand UncertaintyMarketing Science 25(1), pp. 25–50, © 2006 INFORMS 27

maximizes expected profits ex ante, i.e., before thepretest market results are known. However, it is notdynamically optimal, because the decision to launchthe product or not is not dependent on the learning inthe pretest market. Our model, in contrast, considerssequential learning, and the corresponding value ofnew information, as a central element of the productlaunch and testing process.6 An empirical model ofsequential learning has previously been developedand estimated by Erdem and Keane (1996), who con-sider the case of consumer choice under attributeuncertainty. Methodologically, their paper is closelyrelated to our work.Our framework builds on the existing insights from

Bayesian decision theory and extends the literatureon product testing and launch planning in severalways. First, we solve the sequential experimenta-tion problem using numerical dynamic programmingtechniques. This approach allows us to calculate theoptimal path of product exit and stay decisions withrespect to the generic objective function of the firm,i.e., the expected PDV of profits. This objective func-tion needs to be derived from a realistic demand sys-tem, such as the random coefficients logit model thatwe employ, which makes an analytic solution to thedecision problem infeasible. Second, the solution of adynamic program ensures that the decisions by thefirm are not only optimal ex ante, as in Urban andKatz (1983), but also in any future time period, con-ditional on what the firm has learned in the market.Third, the numerical solution approach allows us toincorporate intertemporal demand linkages into themodel, and then solve for the dynamically optimalmarketing mix. Our paper focuses on dynamic adver-tising, although one could extend the model to allowfor dynamic pricing.7 A managerial application to anactual product launch is feasible using a modern per-sonal computer.8

In order to simulate the model and discuss itsimplications using an actual, empirical application,we first need to estimate the model parameters. Wedevelop a two-step estimation approach. In the firststep, most demand parameters are estimated usinga generalized method of moments (GMM) approach,

6 Rao and Winter (1981) consider the related problem of selectingthe number of units—e.g., cities—that constitute a whole test mar-ket. They also use a Bayesian decision theory framework. Theirapproach, however, does not allow for sequential decision making.7 The focus on advertising is motivated by the particular applicationto RTE breakfast cereals; an examination of the data reveals thatadvertising, but not pricing, is set dynamically.8 The decision maker needs to estimate or calibrate a demand sys-tem, and specify his or her prior about the unknown demandparameter. Using an optimized computer algorithm, the solutionto the dynamic decision problem can then be found within a fewminutes.

due to Berry et al. (1995). This step reduces the com-putational burden for the second step, where weemploy a maximum likelihood (ML) estimator. TheML estimator achieves two goals. First, we can esti-mate the initial prior variance, i.e., the firms’ uncer-tainty, by matching the observed durations of theproducts in the market to the durations predictedby the model. Second, we can consistently estimatethe intertemporal effect of advertising, controllingfor a potential econometric endogeneity problem thatarises if firms advertise based on shocks to the adver-tising effectiveness that are observed by the firms,but not to the researcher. Both tasks are achieved byexploiting the structure of the model; the implemen-tation of the ML estimator therefore requires us tosolve the dynamic program (DP) at each evaluationof the likelihood function. Thus, our estimator is avariation of Rust’s (1987) nested fixed-point estima-tor. The estimation problem is much easier for a firmthat uses the model to guide its decisions, because itknows its prior and has more knowledge about theeffectiveness of its past advertising than a researcherdoes. Hence, the firm only needs to estimate prod-uct demand using the first estimation step in order toexamine the normative predictions of the model.Finally, beyond its main, normative use, the spe-

cific application of our model provides a new possi-ble explanation for the observed high product entryand exit rates in the U.S. RTE breakfast cereal indus-try. Our estimation approach allows us to estimate theinitial uncertainty that rationalizes the observed entryand exit decisions. Simulations of the model, giventhe estimated degree of uncertainty, then reveal theexpected, typical outcome in the market. We find thatthe high observed entry and exit rates can not onlybe rationalized, but are actually the typical, expectedoutcome predicted by the model. Previously, someantitrust policy makers and economists have takenthe large number of existing and entering products asevidence of product proliferation, i.e., the practice oflaunching new products to preempt entry by a newcompetitor (Schmalensee 1978).9 Our model providesan alternative explanation that should also be con-sidered when judging the performance of the cerealindustry. We would like to stress, however, that weare unable to test between the competing hypotheses,and therefore we cannot conclusively rule out that astrategic motive plays a role in the product launchprocess.The introduction concludes with a review of the

related literature. In §2, we discuss the stylized facts oftypical product launches in the U.S. RTE cereal indus-try. The model is presented in §3. Section 4 provides an

9 The brand proliferation hypothesis has later been criticized ontheoretical grounds (Judd 1985).


overview of our estimation approach and presents theestimation results. In §5, we examine the predictionsof the estimated model. Section 6 concludes.

Relationship to the Literature. Numerical dynamicprogramming has been used in some recent market-ing studies. Among the topics examined are consumerchoice dynamics in the presence of coupons (Gönüland Srinivasan 1996), consumer choice dynamics inresponse to price promotions and stockpiling (Erdemet al. 2003, Hendel and Nevo 2005), optimal catalog-mailing policies (Gönül and Shi 1998), and durableproduct adoption decisions in the presence of qual-ity and price expectations (Melnikov 2001, Song andChintagunta 2003). Learning models with normal pri-ors have a long history in marketing; Roberts andUrban (1988), for example, examine the adoption ofdurable goods in the presence of attribute uncer-tainty.10 Closest to the formal framework in this paperis the work by Erdem and Keane (1996), who also con-sider attribute uncertainty. In contrast to Roberts andUrban, they consider consumers as forward-lookingdecision makers, which gives rise to a dynamic pro-gramming problem.11

Marketing-mix choices under demand uncertaintyhave been investigated in the literature on new prod-uct development and testing, which we referencedbefore. Montgomery and Bradlow (1999) examinepricing under uncertainty about the functional formof demand. They, however, do not account for learn-ing. The foundations of the model developed in thispaper are related to the literature on monopoly learn-ing. Aghion et al. (1991) provide a general theo-retic treatment. McLennan (1984), Trefler (1993), andRaman and Chatterjee (1995) study the pricing deci-sion of a monopolist who does not know its demandcurve, Harrington (1995) extends this work to the caseof duopoly. Two-sided learning, where both the buy-ers and the seller(s) of an experience good are uncer-tain about the product’s quality, has been studiedin a monopoly setting by Judd and Riordan (1994),and in a duopoly setting by Bergemann and Välimäki(1997). Including consumer learning in the demandside would be an interesting extension to this paper.In economics, a small but very important litera-

ture investigates the competitive effect of entry; seeBresnahan and Reiss (1991) and Berry (1992), forexample. Related to this literature, Kadiyali (1996)studies entry deterrence. This literature is only indi-rectly related to our paper. However, the uncertaintyand learning aspect considered here may become

10 See Akçura et al. (2004) for an application to consumer learningabout drug efficacies.11 See also Ackerberg (2003) for a related approach.

important for the economic entry literature oncedynamic models are considered; conversely, it wouldbe interesting to extend the work in this paper toallow for strategic interaction, for example, in productintroductions.

2. Product Launches and Product Exitin the U.S. Ready-to-Eat BreakfastCereal Industry

This section provides a brief overview of the U.S. RTEbreakfast cereal industry. We motivate the problemaddressed in this paper by some stylized facts and“reduced form” analysis, which suggests that demanduncertainty plays a role during a typical productlaunch. Also, the stylized facts indicate that adver-tising may have long-run effects, which motivates acorresponding modeling choice in the next section.12

The U.S. RTE breakfast cereal industry providesan ideal social laboratory to study how products arelaunched and scrapped. First, in this industry productintroductions have always been common. Between1985 and 1992, for example, the major national-brandcereal manufacturers introduced 78 new products.That is, on average, 10 new brands were rolled outevery year. Second, the RTE breakfast cereal industryis, relatively speaking, a “simple” industry. That is,complicating dynamic factors such as technologicalprogress, or dynamic price discrimination, as com-monly employed over the life cycle of a high-techdurable product, are absent.Kellogg and General Mills were the market lead-

ers in 1990, followed by Post (a division of Kraft),Quaker Oats, Nabisco, and Ralston Purina.13 Theindustry was populated by about 130 national brands.Each product had only a small market share, withthe exception of a few big brands such as Kellogg’sCorn Flakes (5.2% volume market share), and GeneralMill’s Cheerios (4.6% volume market share).Mature, established breakfast cereals do not exhibit

much time-series variation in their sales, price, andadvertising data. Most notably, advertising is consid-erably more volatile than sales, where the variation inadvertising (and sales) occurs around a usually stablebrand-specific mean. Newly launched breakfast cere-als, on the other hand, exhibit distinct dynamic pat-terns in their sales and advertising series. Figures 1and 2 show the national sales, price, and advertis-ing data for two new cereals, Kellogg’s Kenmei Rice

12 A detailed description of the data is provided in §4 andAppendix C is available at http://mktsci.pubs.informs.org.13 Two of these manufacturers left the market during the 1990s;Nabisco sold its cereal line to Post in 1993, and Ralston sold itsnational-brand cereals to General Mills in 1996.


Figure 1 Kellogg’s Kenmei Rice Bran

Sal

es (

mill

. lb.

)

Year1988 1989 1990 1991 1992

0

2

4

6

Pric

e ($

/lb.)

Year1988 1989 1990 1991 1992

0

1

2

3

Adv

ertis

ing

(mill

. $)

Year1988 1989 1990 1991 1992

0

2

4

6

8

Adv

ertis

ing/

sale

s ra

tio

Year1988 1989 1990 1991 1992

0

1

2

3

Figure 2 General Mill’s Apple Cinnamon Cheerios

Sal

es (

mill

. lb.

)

Year1988 1989 1990 1991 1992

0

5

10

Pric

e ($

/lb.)

Year1988 1989 1990 1991 1992

0

1

2

3

Adv

ertis

ing

(mill

. $)

Year1988 1989 1990 1991 1992

0

2

4

6

8

Adv

ertis

ing/

sale

s ra

tio

Year1988 1989 1990 1991 1992

0

1

2

3


Bran, a bran-based health cereal, and General Mill’sApple Cinnamon Cheerios. The sales of both cerealspeak shortly after product launch.14 The initial peak insales is accompanied by an initial peak in advertising.In particular, in both cases the advertising/sales ratiopeaks initially and then drops. Pricing, on the otherhand, has no apparent dynamic component. Thesepatterns are typical of all new cereal products in oursample.Only one of the brands depicted, General Mill’s

Apple Cinnamon Cheerios, was a “successful” prod-uct in the sense that it became an established brand.Kenmei Rice Bran, on the other hand, was eventu-ally scrapped. How is this outcome reflected in thedata? Most importantly, there is a large differencebetween the initial advertising/sales ratios, whichwas about 0.2 for Apple Cinnamon Cheerios andabout 2.5 in the case of Kenmei. Both products weresupported with similar average advertising spend-ing during the first two quarters after their launch(Kenmei’s advertising spending actually peaked at ahigher level than Apple Cinnamon Cheerio’s spend-ing). However, the realized product sales for AppleCinnamon Cheerios were much higher than forKenmei. After the initial peak, Kenmei’s advertis-ing spending declined strongly, whereas the declinein product sales was more gradual. The decline inApple Cinnamon Cheerio’s advertising, in contrast,was not pronounced. Table 1 shows that these datapatterns are common across all new products usedin our empirical analysis.15 Table 2 presents estimatesof a probit model and Cox proportional hazard esti-mates relating the exit decision to the initial advertis-ing/sales ratio, the total revenue from the product (asa proxy for profitability), and the time in the market.The estimates are based on all new products that wereeventually scrapped. The results indicate that the exitprobability (hazard) is positively related to the initialadvertising/sales ratio, although the effect is not mea-sured precisely.Note that firms can only set the ex ante, not the actu-

ally realized advertising/sales ratio. Therefore, a pos-sible interpretation of our findings is that firms are ini-tially uncertain about the true profitability of a prod-uct. Initial advertising spending is set to support apotentially profitable product, while sales are a signalof the true profitability. As the firm learns that sales

14 The initial low level of sales is in part due to the fact that thecereals were not launched exactly at the beginning of the calendarquarter. However, all cereals used in our analysis were rolled outsimultaneously across all regions.15 This sample includes eight products that were eventuallyscrapped and two cereals that survived. A detailed sample descrip-tion is given in §4.

Table 1 Summary Statistics

Scrapped products Surviving products

Year 1 Year 2 Year 1 Year 2

Salesa 9.13 4.81 17�86 18�10Advertisinga 3.19 0.44 4�16 4�27Adv/sales ratio 0.37 0.06 0�25 0�24Peak adv/sales ratio 0.90 0.14 0�39 0�29Priceb 2.76 2.75 2�70 2�73

Note. The sample statistics are averages in Years 1 and 2 after productlaunch.

a$ millions. b$/lb.

are in fact low, the advertising support is decreased,and eventually the product is scrapped. On the otherhand, if realized sales justify the initial ad spending,the firm learns that it has launched a profitable prod-uct that stays in the market. Of course, this argument ismore suggestive than conclusive. Our approach here isto relate the unobserved uncertainty to a variable thatmight proxy for it, and then relate this variable to theproduct exit decision. Below we will use a structuralapproach to estimate the uncertainty directly from theobserved durations until exit.We observed in the case of Kellogg’s Kenmei that

sales decline more slowly than advertising. This find-ing is consistent with intertemporal demand depen-dencies. If the decay in the impact of advertising ondemand is gradual, sales will be higher through pastadvertising, even if current advertising has been dis-continued. As the long-run effect of advertising seemsto be an important aspect of the industry studied, wewill incorporate it in the model developed in the nextsection.

Table 2 Exit Regressions

(i)a (ii)a (iii)b (iv)b

Initial adv/sales ratio 0�769 0�645 0�701 1�202�0�516� �0�806� �0�693� �0�883�

Time since launch 0�534 1�492�0�186� �0�708�

Revenue −1�275�0�656�

Average revenuec −0�235�0�174�

Constant −5�205 −8�548�1�640� �4�349�

Observations 57 57 57 57Log-likelihood −12�461 −5�486 −8�625 −6�882

Note. The estimates are based on data from all eight products that were even-tually scrapped.

aProbit model of exit.bCox proportional hazard model; duration until exit.cAverage during first two quarters after launch.


3. A Bayesian Learning Model ofDynamically Optimal ProductLaunch and Product Exit

OverviewWe focus on a decision maker (a firm, or a manager)who is uncertain about the demand, and hence theprofitability, of a new product. Some characteristicsof the product, or, more precisely, the valuations con-sumers assign to these characteristics, are unknownto the firm. The parameter � summarizes the effect ofthese valuations on demand. The firm’s uncertaintyover � is expressed in the form of a prior probabilitydistribution pt��.16 The demand uncertainty can beresolved through a product launch, as realized salesprovide the decision maker with information aboutthe profitability of the new product. Even after theproduct launch, there is a potential cost to being in themarket, because the product may in fact be unprof-itable. The timing of the model is as follows:1. At the beginning of each period, the firm decides

whether to keep or scrap the product.2. If the firm keeps the product, it sets an advertis-

ing level.3. Prices are determined through a Bertrand pricing

game by all firms in the market.4. Product demand is realized and provides the

firm with a noisy signal about the true productquality �.5. The firm updates its prior in a Bayesian fashion.

The posterior becomes next period’s prior, pt+1��.Current advertising may impact future demand

through a goodwill stock (Arrow and Nerlove 1962),i.e., a specific distributed lag of advertising. Thisintertemporal demand effect is motivated by thebreakfast cereal data used to estimate the model. Asdiscussed in §2, advertising for cereals is more volatilethan sales. Hence, current advertising can have only asmall effect on current sales. On the other hand, cere-als are advertised heavily. Hence, for such advertisingbudgets to be optimal, advertising needs to have along-term impact on sales. Furthermore, we generallyobserve that sales decline only gradually after adver-tising for a new, “unsuccessful” cereal is discontin-ued, which further suggests that current advertisingimpacts future demand. We allow for this intertem-poral demand effect to add realism to the specificapplication in this paper; it is not, however, a centralfeature of our model. While we make the advertisingdecision dynamically optimal, we are unable to allow

16 Firms may reduce some or all of their uncertainty through marketresearch and product testing before the new product launch. This isnot inconsistent with our model, because the precision of the prioris a state variable. Hence, a situation where the firm knows theproduct quality exactly is a special case of the model.

for strategic interaction in advertising, which poses asevere technical challenge.A new product launch can be thought of as a

statistical test of the hypothesis, H0 = “the productis profitable.” A frequentist approach to this prob-lem would first posit a specific power of the test,and then devise a launch mechanism such that theprobability of eventual product failure, i.e., the prob-ability of accepting the null hypothesis while infact it is false, would be below a certain threshold.In general, this approach will not be optimal withrespect to the generic objective function of a firm, theexpected present discounted value (PDV) of profits.Our approach, however, is optimal with respect to thePDV of profits by design.The value of a new product is larger than the simple

PDV of profits if there is some demand uncertainty.In a related context, this idea has been explored in thereal-options literature (Dixit and Pindyck 1994). Themain idea is that the value of the product is derivednot only from the PDV of profits, given current infor-mation, but also from the option to scrap the prod-uct at any point in time. This option allows the firmto delay product exit, an irreversible decision,17 andtherefore to gather more information about the trueproduct profitability. The firm needs to account forthis option value when making the decision to stayin the market or scrap the product. This idea can beillustrated with a simple example. Per-period profitsfrom a new product are 1 with probability q, and −1with probability 1− q. The simple expected PDV ofprofits is then given by

1 · q+ �−1� · �1− q�

1−�= 2q− 1

1−�

where 0 < � < 1 is the discount factor. According tothis objective function, the firm should scrap the newproduct if q, the probability that profits are positive, issmaller than 0�5. This approach, however, neglects theopportunity cost of exercising the option to scrap theproduct now. If the firm delays the decision to scrapthe product, it gathers more information about thetrue product profitability. In our simple example, thefirm observes profits fully after the first period. Prod-uct exit in the second period can then be made contin-gent on the information acquired in the first period,and the PDV of profits in the first period, assumingdynamically optimal decision making, is given by

2q− 1+�1 · q1−�

�

17 As a more general case, one could allow for partial irreversibil-ity through a sunk exit and start-up cost. This would only be rel-evant, however, if the firm could obtain additional informationabout product demand without having to sell the product in themarket.


This value is positive if and only if q > �1−��/�2−��.For example, if the discount factor is 0�9, whichroughly corresponds to an annual interest rate of 10%,the firm should scrap the product only if q < 0�09.The solution of the model considered below

involves the same ideas that we just illustrated usinga very simple model. The realism needed for anempirical application, however, requires considera-tion of many details, in particular on the demandfunction and also on the prior that contains the firm’sinformation. We give a full account of these detailsbelow.

Model Details

States and Decisions. The firm’s objective is tomaximize the expected PDV of the stream of profitsgenerated by a specific product, Ɛ�

∑��=t �

�−t�� st�.18The objective function is maximized with respect to asequence of decision variables �t = �EtAt�, where Etdenotes the exit �E = 1� or stay �E = 0� decision,and At is the current advertising level. These deci-sions are based on the state vector st = �ht�t�tgt�.ht denotes the age of the product, i.e., the number oftime periods passed since the product was launched.�t and �t index the current prior on the productquality parameter �. As is explained in more detailbelow, in our model this prior is a normal distribu-tion, represented by the normal probability densitypt��= p��t�

2t �. gt is the current “goodwill stock,”

a measure of the accumulated effect of advertising indemand.The expected flow of profits in period t is

��st�t� ��=∫

��st�t��f�� d�−At − k� (1)

��t denotes current profits, gross of advertising, andthe per-period cost factor k. k can be thought of asa fixed cost of production, which includes the valueof the time managers devote to the specific prod-uct, and the opportunity cost of the shelf space inthe supermarkets where the product is sold and inthe warehouses where it is stored intermittently. Theexpectation in (1) is taken with respect to the distribu-tion of �, a vector of demand shocks. The shocks arei.i.d. across time and products, but possibly depen-dent across geographic markets.The gross profit function is derived from some

underlying demand system. As will be explained indetail below, ��t incorporates a vector of equilibriumproduct prices, which are determined after the cur-rent state of the market is realized. In the frameworkconsidered here, product prices do not change thetransition process of the state vector. Hence, pricing

18 In this formulation, managers are assumed to be risk neutral.

has no dynamic effects on future profit flows, and cantherefore be separated from the dynamic decisions,advertising and product exit.

Product Demand. Product demand is modeled as arandom coefficients logit demand system (Berry et al.1995, Nevo 2001). Our approach follows Nevo (2001),who develops and estimates such a demand systemfor the case of the U.S. RTE breakfast cereal industry.Random coefficients logit models have several desir-able properties. In particular, they allow for flexiblesubstitution patterns among differentiated productsthat can be related to some underlying household het-erogeneity structure, yet they can be estimated usingmarket-level data only. Also, the potential economet-ric endogeneity of prices can be accounted for usinginstrumental variables. For a detailed discussion, werefer the reader to the aforementioned papers andNevo’s (2000) very accessible “user guide.”More generally, our framework can accommodate

any product demand system that has the same under-lying latent utility structure as our model. For exam-ple, this includes the case of a probit demand system.Even more generally, any demand system with anassociated profit function of the form ��st�t�t� ��could be employed, although such a formulation maylose the computational tractability of our model.19

We consider a market populated by a large num-ber of households who choose among several differ-entiated products. Household l’s indirect utility fromproduct i in time period t is

Ulit = �i − lPPit + x′

i�lx +#�gitAit�+ ��hit�

+�it + $lit � (2)

�i is the quality of product i, i.e., the average val-uation consumers assign to all unobserved productattributes. Everything else held constant, the marketshare of product i increases in �i, which is the sensein which the term “quality” should be understood.Pit is the product price, and xi is a �K − 1�-vectorof observed product attributes that do not vary overtime. lP is household l’s marginal utility of income,and �l

x expresses household l’s preferences for theproduct attributes in xi. Both the accumulated effectof advertising in the past and the current flow ofadvertising have an impact on demand through thefunction #, which is specified in more detail below.��hit� is a preference shock that systematically occurshit periods after product launch. This term is a sim-ple proxy for consumer learning, or variety seeking.

19 If the firm cannot infer � from observed sales up to an additiveerror, the prior and posterior will generally not be conjugate, andhence it will be difficult to represent the prior in a computationallyconvenient form.


The error term �it incorporates shocks to the effec-tiveness of advertising, and taste shocks that are cor-related across consumers. Finally, $lit is an i.i.d. Type Iextreme value distributed error term. Households canalso choose an outside alternative 0 with (normalized)utility Ul

0t = $l0t .Following Nevo (2001), we postulate the form

�l =�+�dl +��l (3)

for the household-specific taste vector �l ≡ � lP �lx�.

These preferences are related to dl, a D-vector describ-ing household l’s demographic attributes, and �l, aK-vector that captures additional unmeasured sourcesof taste heterogeneity. � is a K ×D matrix, and � isa K ×K matrix. � is the mean taste vector across allhouseholds; hence, �dl and ��l capture the deviationof household l’s preferences from this average andrelate them to demographics and other unmeasuredfactors. This random coefficients formulation allowsfor more realistic substitution patterns than the sim-ple multinomial logit model. In particular, the ownprice elasticity of a product is related to the price sen-sitivities of those consumers who have a particularpreference for that product, and the cross price elas-ticity between two products is related to “how close”the products are in attribute space.20

We can decompose the indirect utility from eachproduct choice into the mean utility component

'it = �i − PPit + x′i�x +#�gitAit�+ ��hit�+�it (4)

and the idiosyncractic components

(lit + $lit = x′it��dl +��l�+ $lit � (5)

Here, xit = �Pitxi� contains all attributes that haverandom coefficients. Using these two definitions, theindirect utility from alternative i is Ul

it = 'it + (lit + $lit .The population distribution of consumer characteris-tics in each market is described by the densities f dtand f )t . In our empirical application, f dt correspondsto the actual distribution of demographics in eachmarket, while �l is a vector of i.i.d. standard nor-mal random variables. �l and dl are independent. Themarket share of product i can be obtained by integrat-ing over household-specific logit choice probabilities:

�it =1�t

∫ exp�'it + x′it��d+��

1+∑Jj=1 exp�'jt + x′

jt��d+��

· f dt �d�f )t �� d�d�� (6)

Here, �t denotes the total market size. Equation (6)defines a function that relates the vector of mean util-ities to a vector of market shares, �t = ��1t � � � �Jt�=

20 A detailed discussion of these issues can be found in the paperscited before.

T ��t�.21 Berry (1994) shows that T can be inverted,such that the vector of mean utilities can be recov-ered from the observed market shares, �t = T −1��t�.This inversion is important both for the estimationof the demand model, and, as we will see furtherbelow, for the way the decision maker uses theobserved demand to learn about the unknown prod-uct quality �.

The Profit Function. We now derive ��t , the profitfunction implied by the demand system. The focus ison a specific product i. F firms compete in the market,and each firm manages one or more products in theset �f . Let .it ≡ 'it − PPit be the mean utility net ofthe price effect (remember that the product price Pitis a component of the attribute vector xit�. The profitflow of firm f from all the goods in its product lineis given by

/f ��tPt�=�t

∑j∈�f

�Pjt − cj ��j � (7)

Note that all determinants of demand that do not varyperiod after period are suppressed in the above profitfunction./f depends on a vector of mean utilities, �t , and

thus on the goodwill stocks, advertising levels, anddemand shocks of all products in the market. Hence,if firms use all potentially available information aboutthe market, their decisions will be based on a pro-file of state vectors for each product. Also, theywill take into account how these states evolve overtime when making their decisions. Finally, they willincorporate their competitors’ strategies as a func-tion of the realized states, now and in future, intotheir own decision making. All these factors togethergive rise to a dynamic oligopoly model that, givencurrent technology and knowledge, is infeasible tosolve with a large number of products. Hence, wemake two assumptions to reduce the complexity ofthe dynamic decision problem. First, we abstractfrom strategic interaction in advertising. Second, weassume that firms set prices only based on .j = Ɛ.jt ,the expectation of .jt , for all products j apart fromthe focal, newly launched product.22 Otherwise, each.jt becomes part of the state vector, and the dynamicprogramming problem becomes intractable.

21 More precisely, T is also a function of all product attributes�x1t � � � xJt �, the distribution of household characteristics, andthe interactions between household characteristics and productattributes described by � and �.22 Once a product has been in the market for some time, the initialconditions, given by the prior distribution p0 and the initial good-will stock, no longer impact the distribution of goodwill and adver-tising. Eventually, all the state and decision variables are distributedaccording to a stationary, ergodic distribution. In particular, in thelong run each .jt fluctuates around its mean .j = Ɛ.jt , where theexpectation is taken with respect to the ergodic distribution of .jt .


The first assumption says that competitors do notchange their advertising if a new product enters themarket. A direct assessment of how much profitsunder this assumption differ from true profits is notpossible. However, we can provide some indirect evi-dence by investigating the effect of product entry onequilibrium prices and profits. Numerical simulations,based on the parameter estimates to be presentedin §4 (Table 5), reveal that a new product launch bysome firm f leads to an average price increase of0.56% among firm f ’s products, and to an averageprice decrease of 0.60% among its rivals’ products.Furthermore, average per-product profits of firm f ,excluding the newly launched product, decrease by1.78%, while the competitors suffer an average profitloss of 1.90%. If equilibrium prices did not adjust afterthe new product entry, firm f ’s average profits wouldbe 0.21% higher, and its rivals’ profits would be 0.24%higher compared to profits under the new equilib-rium price vector. These findings suggest that profits,calculated without considering a dynamic advertis-ing equilibrium, are only slightly overstated relativeto the case where all advertising levels adjust due tostrategic behavior. We do not claim that this is a gen-eral result; rather, we believe it is specific to a marketwith a large number of competing products, wherea new product entry has only a small impact on thefirst-order conditions defining an equilibrium price oradvertising vector. In other markets, where the equi-librium impact is large, an explicit consideration ofdynamic strategic interaction may be warranted.The second assumption implies that firms do not

base their pricing decisions on all current demandshocks. Using numerical simulations, we find thatunder this assumption median prices are 1.89% higherand median profits are 3.10% higher compared to thecase where pricing is based on the realization of alldemand shocks.23

Under these two assumptions, we can now con-struct the profit function for each product i. First, sub-stitute all components j �= i in �t by .j . Each firmmaximizes (7) with respect to �Pj�j∈�f . The first-orderconditions for this problem are

∑j∈�f

�Pj − cj �1�j

1Pk+�k = 0 for all k ∈ �f � (8)

A Nash equilibrium price vector P∗t satisfies the first-

order conditions for all firms f simultaneously. Equi-librium profits for firm f are /f ��tP∗

t �. Finally, we

23 Based on means instead of medians, we find a price difference of3.98% and a profit difference of 4.72%. A visual examination of thedistribution of price and profit differences reveals some “outliers,”and we thus consider the medians as more representative of theoverall price and profit differences.

define the flow of profits from product i as the flow ofprofits directly attributable to this product, minus thecannibalization cost on the other products in firm f ’sproduct line. Eliminate product i from �f , and recom-pute the equilibrium profit vector without product iin the market. Denote the resulting equilibrium pricevector by P∗

−i t . Product i’s profits are then given by

��st�t�t��

=/f ��tP∗t �−/f ��−itP

∗−it�

=�t

[�P ∗

it−ci��it−∑

j∈�f \2i3��P ∗

−ijt−cj ��−ijt−�P ∗jt−cj ��jt�

]�

(9)

The term subtracted from product i’s direct profits isthe cannibalization effect.

Advertising. Both past and present advertisinghave an impact on demand. At the beginning ofeach period, the firm decides how much to spendon advertising. This flow adds to goodwill gt , whichis a measure of accumulated advertising, and yieldsa quantity called added goodwill, denoted by gat .The added goodwill stock, which is “produced”from goodwill and advertising, impacts mean util-ity, and hence demand, through the function #.Between periods, goodwill depreciates stochastically.Each of these advertising components is implementedthrough some specific functional form choice. The-ory offers little guidance as to these specific choices.Instead, we experimented with different options, andfinally chose functional forms that we considereda priori plausible, made the firm’s optimization prob-lem well behaved, and yielded a good fit in the esti-mation procedure.24

We first specify #, the impact of added goodwillon demand. The multinomial logit demand (as manyother discrete-choice models) yields an S-shaped mar-ket share function. Therefore, if added goodwill isincluded linearly in mean utility, the firm will try tocapture a large share of the market until diminish-ing returns to advertising set in.25 As this outcome isunreasonable, we specify # in logarithmic form,

#�gtAt�= 5 log�1+ gat �� (10)

Under this specification the market share is wellbehaved, i.e., strictly concave in added goodwill,if 5 ≤ 1.

24 Hence, we make no claim that our functional form choices are the“correct” ones, or that different functional form choices would notyield a similar solution describing the firm’s optimal advertisingbehavior.25 At this point the firm will have captured more than 50% of themarket.


Figure 3 Added Goodwill, “Produced” from g and a

(G - g 1)/ φ (G - g 0)/φg0

g1

G

Advertising

Add

ed G

oodw

ill

Added goodwill is created by

gat =gt+6At if gt+6At≤GG+log�1+gt+6At−G� if gt+6At >G�

(11)

For small goodwill levels �gt < G�, the goodwillproduction function has constant returns, and onedollar of advertising yields 6 units of goodwill.Beyond the threshold level, G, goodwill productionhas decreasing returns. This specification includesboth the case where goodwill accumulation virtuallyalways has constant returns26 and the case wherediminishing returns already set in for the first dollarof advertising. This specific functional form allows fora strong advertising incentive at small goodwill levelsand diminishing returns to advertising at large adver-tising levels, while remaining simple and dependenton only two parameters. Figure 3 shows the goodwillproduction function for two different initial goodwillstocks g0 and g1.Added goodwill depreciates between periods, such

that the goodwill stock at the beginning of nextperiod is

gt+1 = 8t+1 · gat � (12)

The depreciation rate 8t+1 is stochastic, and assumedto be a lognormally distributed, log�8t+1�∼N��8�

28�.

Other distributional assumptions could be made; thelognormal distribution, however, is easy to param-eterize. We restrict the mean and the variance of 8such that �8 + �2

8/2< 0, which implies that Ɛ�8t+1�=exp��8+�2

8/2� < 1. Hence, goodwill decays in expec-tation from one period to the next. Conditional oncurrent goodwill and advertising, goodwill in the next

26 For a very high goodwill stock the product’s market share willbe close to 1, and the return to advertising will be smaller than thecost. The firm will therefore not advertise for such goodwill stocks.

period is also lognormally distributed, log�gt+1� ∼N�log�gat � + �8�

28�, and its transition density is

denoted by f �gt+1 �st�t�.Note that we can always express the current good-

will stock as a function of an initial goodwill stock,and the sequence of advertising levels and deprecia-tion factors:

gt = :�g1A1 � � � At−182 � � � 8t�� (13)

In this sense, goodwill can be thought of as a nonlin-ear distributed lag of past advertising.

First-Period Demand Shocks. We include the pref-erence shocks ��ht� in mean utility, which systemati-cally occur during the first Th periods (Th = 2 in ourempirical application) after product launch.27 Theseshocks can be due to demand effects such as con-sumer learning, or variety seeking. The formulationemployed allows us to control for these systematicdemand shifts after product launch in a reduced-form way.

Beliefs and Learning. The prior distribution pt��describes the firm’s belief about the unknowndemand parameter � at the beginning of period t. Theobserved market shares of all products in a cross sec-tion of M markets provide the firm with new infor-mation about �. This information is summarized ina vector t . Based on t , the firm updates its prior,pt+1�� = pt�� t�. We assume that at the time ofthe product launch, the prior is a normal distribu-tion. Under our assumptions on the demand system,the signal t has a multivariate normal distribution,and hence the posterior is also normally distributed.Therefore, the priors in each period are described bya normal probability density pt��= p��t�

2t �, and

the firm’s uncertainty can be described by the statevariables �t and �t .Our approach is based on the aforementioned

inversion of the product demand system, whichallows the firm to infer the mean utility of each prod-uct from the observed market shares:

Ti��t� = 'it = �i − PPit + x′i�x

+#�gitAit�+ ��hit�+�it� (14)

The firm observes all variables in (14), apart from theproduct quality �i and the demand error �it ; i.e.,the firm observes a noisy signal of the product qual-ity, <it = �i + �it . The vector t = �<it1 � � � <itM� col-lects these signals from all M geographic markets. Wedecompose the error �itm into a shock that is commonacross all markets, and a market-specific component,

�itm = >it + )itm >it ∼N�0�2> � and )itm ∼N�0�2

) ��

Shocks that are common across geographic marketscan arise from temporal variation of the effectiveness

27 That is, ��h�= 0 for all h> Th.


Figure 4 Solutions of the DP: The Value Function V , the Optimal Advertising Policy �A, and the Exit Rule �E

–8–6

–4

0

5

0

500

1,000

1,500

2,000

µ

Value function

g

–8

–6–4

0

5

0

5

10

15

µ

Advertising policy

g

–9 –8 –7 –6 –5 –40

1

2

3

4

5

6Exit policy

µ

g

–8–6

–4

0

0.5

1.0

0

1,000

2,000

3,000

µ

Value function

σ

–8–6

–4

0

0.5

1.0

0

5

10

15

µ

Advertising policy

σ

–9 –8 –7 –6 –5 –40

0.2

0.4

0.6

0.8

1.0

1.2Exit policy

µ

σ

Note. The exit region of the state space is shaded gray.

of the advertising copy, for example. Across productsand time, the error terms are assumed to be indepen-dent. Under these assumptions, the signal t has amultivariate normal distribution,

t ∼N��t�t�

�t =�2t +�2

> +�2) · · · �2

t +�2>

��

��2t +�2

> · · · �2t +�2

> +�2)

�

is an M-vector with all components equal to 1.Under Bayesian updating, the posterior pt�� t� has a

normal distribution with moments28

�t+1 =�t +�2t

T�−1t �t −�t� (15)

�2t+1 = �2

t �1−�2t

T�−1t �� (16)

Equation (15) implies that �t+1, conditional on thecurrent information summarized in the state anddecision vectors, has a normal distribution withmean �t and covariance matrix var��t+1�= �4

t T�−1

t .Hence, �t has a normal transition density f ��t+1 �st�t�=N��t�

4t

T�−1t �.

28 See the exposition in DeGroot (1969).


Model SolutionThe model developed above gives rise to a dynamicprogramming problem. The solution of this problemis based on the value function, i.e., the expected PDVof profits, which satisfies the Bellman equation

V �s�=max{0 sup

�A≥0Ɛ[��s��+�V �s′�

∣∣ s�]}�The numerical details of the model solution are pre-sented in Appendix A.29

We now describe the important qualitative aspectsof the optimal stay/exit and advertising decisions.Figure 4 shows the value function, advertising policy,and exit rule for a specific parameterized version ofthe dynamic programming problem. On the left-handside, the functions are displayed with respect to �and g, holding � constant. The right-hand side showsthe functions with respect to � and �, holding g con-stant. We are unable to prove that all properties of thedepicted solution hold under arbitrary assumptionson the demand system and the other model elements,such as the functional forms by which advertising andgoodwill enter demand. However, numerous simula-tions revealed that for the specific functional formschosen in this paper, the qualitative aspects of thesolution hold under a large variety of chosen param-eter vectors.

The Value Function. The value function is increas-ing in �, the conditional expectation of the productquality, and goodwill g. This result is obvious. Mostimportantly, the value of the product is increasingin � , the uncertainty about the product’s profitability.This result reflects the value of the option to scrap theproduct. This option becomes more valuable whenthe firm can acquire a large amount of new informa-tion about the true product profitability.

Optimal Product Exit. The exit policy, depictedat the bottom of Figure 4, divides the state spaceinto two halves. The exit region of the state space isshaded in gray.Remark 1. Consider a state vector s = �h��g�

at which the product exits from the market, �E�s�= 1.Then for any other state vector s0, such that h0 = h,�0 ≥ � , �0 ≤ �, and g0 ≤ g, the product will exit,�E�s0�= 1.Under certainty �� = 0�, �0 = �, and all products in

the exit region are truly unprofitable products. Hold-ing � constant, the firm is less likely to scrap a prod-uct under increasing uncertainty. This central result isa consequence of the product’s option value.Also, even under certainty, a product is less likely to

exit for large values of goodwill g. This is obvious, asgoodwill represents an additional profit component.

29 The appendix to this paper is available at http://mktsci.pubs.informs.org.

Optimal Advertising. Advertising is increasingin �. This property of the advertising policy impliesthat product sales and advertising are positively cor-related, which is also a stylized fact of the cerealdata used in this paper. The positive relationshipbetween advertising and expected sales is closelyrelated to the Dorfman and Steiner (1954) condi-tion, and its dynamic version derived in Arrow andNerlove (1962). The Dorfman-Steiner condition saysthat the optimal advertising/sales ratio for a monopo-list’s product is proportional to the ratio of the adver-tising elasticity of demand and the price elasticityof demand. The goodwill formulation in this modelimplies higher marginal revenues from advertisingfor products with higher product qualities, whichimplies that advertising is increasing in �. The pos-itive relationship between advertising and expectedsales is not a general property of all advertising mod-els; one can construct examples where it does nothold. However, such an alternative formulation of theadvertising technology would not be able to fit thedata used in this paper.The following property of optimal advertising

is relevant for the construction of the likelihoodfunction:Remark 2. Consider the optimal advertising policy

at some state vector s as a function of goodwill g.Then either (i) �A = 0 for all g ≥ 0, or (ii) advertisingis positive and strictly decreasing over the interval�0 g�, and �A = 0 for all g > g.Advertising is decreasing in goodwill because of

diminishing marginal revenues from goodwill anddiminishing returns in added goodwill “production.”For sufficiently high levels of goodwill, the marginalreturn is smaller than the constant marginal cost;hence, no more advertising occurs.30

4. EstimationIn this section we present a two-step approach to esti-mating the parameters of the product launch model.The economic implications of the estimates are thendiscussed in the next section. Before going into thetechnical details of the estimators, we will first discusswhat the estimation approach ought to accomplish,which depends on the intended use of the model.

30 Advertising is increasing in the standard deviation of the firm’sprior, although quantitatively the relationship is only weak. Thisrelationship is mostly due to the shape of a logit-based demandsystem. The advertising policy is shown over the range of expectedproduct qualities at which the logit market shares are convexin mean utility. Higher uncertainty then translates into a higherexpected value from the product; this, in turn, induces higher opti-mal advertising. Note that the firm in this model is risk neutral; riskaversion, on the other hand, could imply a negative relationshipbetween advertising and � .


Consider first the situation of a firm that uses themodel to calculate the optimal demand for informa-tion, or uses the model to make advertising and exitdecisions throughout the launch process. For this pur-pose, the firm needs to know the demand parame-ters, and it has to assess the fixed cost k, the discountfactor �, and its prior distribution (or uncertainty)about the product quality. In the case of the randomcoefficients logit model, most demand parameters canbe estimated using the “BLP” approach, developed byBerry et al. (1995), which is based on a GMM estima-tor. Also, if the firm observes the goodwill level ofits product, it can treat goodwill as data and directlyestimate the goodwill production function (3) and theprocess governing the evolution of goodwill (12). Fur-thermore, the impact of goodwill on demand can sim-ply be estimated by including goodwill, or rather afunction of it, as a covariate in mean utility.The estimation approach is more complicated for

a researcher who tries to evaluate actual firm behav-ior. We face two problems. First, one of our objectivesis to estimate the firms’ degree of uncertainty at thetime of product launch. This uncertainty, measured bythe prior variance, is not observed, and we thereforeneed to infer it from observed behavior. Second, theestimation of the advertising parameters is more com-plicated than in the case where goodwill is observed.Although goodwill can be expressed in terms of thesequence of advertising levels,

gt = :�g1A1 � � � At−182 � � � 8t� (17)

it is not completely observed by the researcher dueto the unobserved initial condition and depreciationshocks 8. Also, goodwill enters mean utility throughthe nonlinear functional form 5 log�1+ga�. Rememberthat the logarithm ensures that the objective functionof the firm, and hence the solution of the advertis-ing problem, is well behaved. Therefore, an estimationapproach based on a moment condition such as

Ɛ�Z · log�1+ ga�� (18)

is not feasible, because the value of this expectationat the true parameter value is not known.31 Further-more, if the firm observes the realization of the good-will stock and chooses advertising accordingly (asassumed in the model), we are faced with an econo-metric endogeneity problem, for then goodwill, anunobserved variable (to the researcher) that directlyaffects latent utility and hence demand, is correlatedwith advertising.To solve these problems, we propose a maximum-

likelihood (ML) estimator that yields consistent esti-mates of both the prior variance and the advertising

31 Note that this point would still be valid even if goodwill wasobserved up to an additive error term.

parameters. The ML estimator is based on the jointlikelihood of the sequence of exit decisions, advertis-ing levels, and market shares. The likelihood takesthe initial prior, and its effect on the subsequent evo-lution of firm decisions, explicitly into account. Thisapproach accomplishes two tasks. First, the likelihoodincorporates the probability distribution of the dura-tion until a new product is scrapped. Hence, looselyspeaking, the ML estimator matches the observedduration to the predicted duration of a product untilexit. Because the predicted duration depends on theinitial uncertainty, we can infer the prior variancefrom the data. In order to calculate the probabilitydistribution of the duration of the product in the mar-ket, we need to know the optimal exit policy, which,in turn, depends on all model parameters. Hence, wehave to solve for the optimal exit policy at each eval-uation of the likelihood function. Second, as part ofthe process to estimate the advertising parameters, weneed to derive the distribution of goodwill in eachperiod. As noted before, goodwill can be expressedin terms of the sequence of advertising levels, depre-ciation shocks, and the initial goodwill stock. Due tothe endogeneity problem, however, deriving the dis-tribution of gt is more complicated than simply apply-ing a change of variables formula. This is becauseadvertising is a function of the current realization ofgoodwill, which in turn depends on the realizationof the depreciation factor 8t . Hence, the distributionof �g182 � � � 8t�, conditional on the observed adver-tising levels, is different from its unconditional dis-tribution. Our solution to this problem is based onan inversion of the optimal advertising policy, whichlets us make an inference about the unobserved good-will level from the observed advertising decision.32

Thus, we can calculate the conditional distribution ofgoodwill in each period. Again, we need to know thefirm’s optimal policy to calculate the likelihood of thedata. Hence, we have to solve the dynamic program-ming problem at each evaluation of the likelihoodfunction. Therefore, our estimator is an example of anested fixed-point estimator, first introduced by Rust(1987).All demand parameters, including the parameters

related to the advertising technology, are identifiedfrom a sample of mature products only. The standarddeviation of the initial prior, on the other hand, canonly be identified from a sample of new products,which is obvious given the identification argumentgiven above.

32 Ching (2002) faces a similar endogeneity problem. His strategy isto approximate the policy function using a flexible functional form.This function—a polynomial in his application—is then parameter-ized and estimated jointly with the other model parameters.


Below, we discuss the estimation approach inmore detail. In the GMM step, we estimate all de-mand parameters apart from the parameters relatedto advertising. All remaining parameters are thenrecovered in the second, computationally intensive,ML step. This two-step approach eases the computa-tional burden of the estimation procedure, and we cancontrol for price endogeneity in Step 1 using an instru-mental variables approach.

Estimation FrameworkStep 1A GMM. In the first step, we estimate the

parameters governing the distribution of the prefer-ence parameters �, and the market- and time-specificfixed effects in demand. We use the BLP approach(Berry et al. 1995), which is based on a GMM estima-tor. At the heart of this method is an inversion of themarket share equation (6). As discussed before, condi-tional on the observed market shares and the param-eters in �rc = ��, we can invert this equation andretrieve the mean utility vector �tm at time t in mar-ket m. We then construct the following residual:

��itm��GMM� ≡ 'itm��tm�rc�

− �− PPitm+ bi + bt + bm�� (19)

Here, bi, bt , and bm are product-, time-, and market-specific fixed effects, and �GMM contains P , �rc, andall fixed effects. Zitm is a vector of instruments suchthat

Ɛ�Zitm · ��itm��GMM��= 0� (20)

All instruments are stacked into a matrix Z, and allresiduals stacked into a vector ��. The GMM estima-tor, based on the moment conditions in (20), is thendefined as

�GMM = argmin�

��′Z −1Z′ �� (21)

Here, the weighting matrix is a consistent estimateof Ɛ�Z′ �� ′Z�.It is important to note the difference between the

residual definition in (19) and the structural errorterm, �, that enters mean utility (4). In (19), the time-varying effect of added goodwill on demand is sub-sumed in the product-specific fixed effect. Still, themoment condition (20) will hold with an appropri-ate choice of instruments. For our application, we usean average of product prices across regional marketsas instruments in the estimation. This approach hasbeen used previously by Hausman (1996) and Nevo(2001). Our choice of instruments could violate (20)if the deviations of added goodwill from its meanare correlated with the market-specific product price.However, our data exhibit only slight time-series vari-ation in product prices. Second, our model predicts

that firms hold the added goodwill stock at a roughlyconstant level, and consequently the predicted prod-uct prices are roughly constant through time.The estimation results allow us to construct the

first-order conditions describing the equilibrium mar-ket prices. Inverting these first-order conditions, wecan recover the marginal cost of production and theprofit function of each product. Finally, we estimatethe price-adjusted mean utilities .itm by

.itm = 'itm��tm�rc�+ � PPitm− x′i ��x − bt − bm� (22)

The price-adjusted mean utilities represent the effectof the product quality parameters, advertising, andage effects on market shares, controlling for price:

.itm = �i +#�gitAit�+ ��hit�+ >it + )itm� (23)

In the second estimation step we employ the .itmsto estimate the effect of its components on marketshares.Step 2A ML. The remaining parameters are esti-

mated by maximizing the likelihood of the sample2yit3. Each data point yit = �hitAit�it Ei t+1� con-tains the age of the product, advertising, the price-adjusted mean utility vector �it , and the exit decisionat the beginning of the next period. Because �it is notdirectly observed, we replace it by the estimate �it .Below, we present an outline of the method used toconstruct the log-likelihood function. The details ofthis procedure are laid out in Appendix B, availableat http://mktsci.pubs. informs.org.The main difficulty in constructing the likelihood

concerns the distribution of advertising and the exitdecision. The densities of these variables depend onthe current state, i.e., the prior on the product qual-ity and the accumulated goodwill stock. These statevariables are unobserved. However, conditional on anassumption on the initial prior, and the past historyof the data, the current prior is uniquely determined.This is because to the econometrician, �i is a param-eter, and sales (i.e., mean utility) are observed; hence,the econometrician can infer the signals used by thefirm to update its priors from Equation (4). Now makegoodwill part of the data vector, zit = �yitgit�. Con-ditional on the initial prior, pi0, and the past “data”history, zt−1i = �zi0 � � � zi t−1�, we know the currentprior, and can then calculate the conditional densityof zit . Thus, we can calculate the joint density of theobserved data and goodwill stocks. Finally, we findthe marginal distribution of yi by integrating over thesequence of goodwill stocks and with respect to theinitial prior.The initial prior is a normal probability distribution

with mean �i0 and standard deviation �0. We assumethat �i0 is drawn from N��i�0�, i.e., firms receivean unbiased signal of the true product quality beforeproduct launch.


Table 3 Sample Statistics

Mean Median Std. dev. Min Max No. obs.

Volume share (within 1.49 1.01 1.31 0�0005 11�38 45991cereal market), %

Volume share (within 0.28 0.19 0.25 0�0001 1�99 45991potential market), %

Price, $/lb 2.69 2.72 0.48 1�1400 4�28 45991Advertising, $ mill. 3.16 2.15 2.31 0 10�32 590Advertising/sales ratio 0.13 0.12 0.17 0 2�63 590

Note. The share and price data are from the full sample used in the firstestimation step. The advertising data are from the smaller sample including32 cereals that are used in the second estimation step.

DataThe model parameters are estimated from IRI33 scan-ner data, supplemented by Leading National Adver-tisers (LNA) advertising data, demographic data fromthe Current Population Survey (CPS), and productattributes. Summary statistics are provided in Table 3.Below, we provide a brief discussion of the data; fur-ther details are given in Appendix C.The IRI data are at the quarterly level from 1988

to 1992.34 Sales and prices are observed in a crosssection of 47 geographic markets. In order to con-vert sales into market shares, we calculate the size ofthe potential market by assuming that each personcould consume at most one pound of breakfast cerealper week. The LNA advertising data are only avail-able at the national level. Advertising is measured indollars, and covers spending on 10 different mediatypes. The demographic data used for the randomcoefficients estimation are from the CPS March Sup-plement. Product attributes (sugar and fiber content)are taken from the U.S. Department of AgricultureNutrient Database for Standard Reference.The new product entries included in the sample

were chosen among all products that entered between1988 and 1990, such that each product is observedover a sufficiently long time period. Within this sub-set of products, we eliminated kids’ cereals and minorline extension. Kids’ cereals differ from other prod-uct entries in that the manufacturers often expect onlya short lifespan. Furthermore, it is doubtful whetherminor line extensions or product modifications aretruly new products. After eliminating these types ofcereals, we retained a sample of 10 new productentries. Each of these launches received extensive cov-erage in the trade press, and the associated sales,prices, and advertising spending were clearly identi-fiable from both the IRI and LNA data sources.

33 Information Resources, Inc. (IRI) is a Chicago-based market re-search company.34 Due to product entry and exit, some of the products are not ob-served during all 20 quarters.

For the first estimation step, we employ a sam-ple of 56 cereals. On average, these products accountfor about 81% of total cereal sales. This sample con-tains all cereals that have an average category shareof at least 0.5%, and all selected product entries.Only 2 of the 10 new products survived beyond1992. These two “successful” entrants, General Mills’Apple Cinnamon Cheerios and Post’s Honey Bunchesof Oats, are still sold today. In the second estima-tion step, we include all new products, and 22 outof the 25 largest established products.35 A smallersample avoids some of the heavy computationalburden of the ML estimation step. Furthermore,we discarded some products because the associatedadvertising series revealed some unusual periods ofzero advertising. If this is due to measurement error,or institutional features such as budget constraints,the estimated persistence of advertising could bebiased upwards.

Estimation ResultsStep 1A GMM. The GMM estimation approach

mostly follows Nevo (2001); hence, the presentationhere is intentionally brief. Please see Appendix D,available at http://mktsci.pubs. informs.org. for fur-ther results, in particular the first-stage regressions ofprices on the instruments, and NLLS logit demandestimates.As already mentioned, we instrument for the price

of product i in market m by taking an average ofproduct i’s price in all other regional markets. Thisyields a set of 20 (one for each quarter) instruments.To allow for heterogeneity in consumer preferences,we interact household income and age with the prod-uct price and the sugar and fiber content of eachcereal. We also allow for a random coefficient on twocategory dummies, “all-family” and “wholesome.”The main purpose of this specific choice of productattributes is to allow for some meaningful differentia-tion among the cereals. Many of the newly launchedproducts were health cereals, which are differentiatedby their fiber and sugar content. Our model specifi-cation thus allows for different substitution patternsacross the different cereal categories.36

The random coefficients logit parameter estimatesare shown in Table 4. The model also includesproduct-, market-, and time-specific fixed effects(these estimates are not displayed).37 The results are

35 These 25 largest products coincide with the sample used by Nevo(2001).36 We estimated several a priori reasonable models, and chose thefinal specification based on the GMM objective function and theindividual statistical significance of each parameter.37 Including advertising in the model leaves the parameter esti-mates virtually unchanged. This remains true if lagged values of


Table 4 Random Coefficients Logit Estimatesa

Interactions withdemographic variables

StandardMeansb deviations log(income) log�1+ age�

Price −4�903 2�200 2�594�2�579� �0�668� �2�968�

Sugar 0�420 −0�624�0�014� �0�224�

Fiber −3�808 8�783�0�100� �5�707�

All-family 17�249 11�779�0�351� �3�737�

Wholesome 3�821 4�916�0�180� �2�494�

GMM objective 21�78No. obs. 45,991% Price coefficients> 0 1�21

Median margin (%)c 43�70

aProduct-, market-, and time-specific fixed effects were included in themodel. Standard errors are in parentheses.

bEstimates from a minimum-distance procedure.cThe margins were calculated as �P − c�/c.

intuitive: High income and older consumers are lessprice sensitive than the average household. Also,older consumers have a relatively strong preferencefor cereals that are high in fiber content, while high-income consumers prefer cereals that are low insugar. These results are reflected in the estimatedsubstitution patterns. While the median price elas-ticity across all cereals is −3�30, health cereals, inparticular, are characterized by significantly lowerelasticities.38

The demand estimates are used to recover themarginal production cost values ci from the first-order conditions (8). The implied median gross mar-gin is 43.7%. This value is similar to the findings fromprevious research. (Cotterill 1999 reports an averagegross margin of 46.0%; Nevo’s 2001 main estimateis 42.2%.)Based on the estimates and the inferred cost val-

ues, we can calculate the gross profit functions ��, asgiven in Equation (9). Note that the profit functionsand first-order conditions are expressed in terms ofretail prices. However, our focus is on the decisionsmade by the cereal manufacturers, who have onlydirect control of the wholesale price.39 We assume

advertising are added. We take this as additional evidence that ourestimates of the price-adjusted mean utilities .itm are consistent (seethe discussion in the previous subsection).38 For example, Heartwise, a newly launched health cereal, has anestimated price elasticity of only −1�90; Special K’s estimated priceelasticity is −1�84.39 Our data also do not have enough detail to examine whether theincentives of the retailer and manufacturer to scrap or keep a prod-

Table 5 ML Parameter Estimates

(i) (ii)

Estimate Std. error Estimate Std. error

Goodwill accumulation� 0�795 0�004 0�620 0�007G 4�608 0�006 4�334 0�019

Advertising effect � 2�818 0�003 2�674 0�007Goodwill evolution

exp�� 0�567 0�007 0�613 0�0002�� 0�889 0�006 0�585 0�006

Demand shocks�� 0�588 0�007 0�547 0�007�� 0�891 0�000 0�795 0�0002

Initial demand effects� �0� 0�420 0�006 0�416 0�001� �1� 0�463 0�007 0�594 0�010

Fixed cost ($ million) k 1�393 0�385 0�750 (calibrated)Std. dev. of initial prior �0 1�311 0�005 1�041 0�0001Discount factor � 0�975 (calibrated) 0�975 (calibrated)

Mean PDV, all products 147�14Std. of PDV, all products 151�27Mean PDV, new products 31�45Std. of PDV, new products 98�72

No. obs. (shares) 25,006No. obs. (advertising) 590

Note. The estimates are based on data from 22 established and 10 new prod-ucts. In model (ii), the fixed-cost parameter k was calibrated at $0.75 million.For each model we also estimated the product-specific quality parameters �i ,which are not displayed.

that the average retail markup in the breakfast cerealindustry is 18%. This number is consistent with thetrade literature and data on retail and wholesalesprices from the Dominick’s Finer Foods database atthe University of Chicago.40 Under this assumptionon the retail markup, there is a fixed relationshipbetween the retail price P and the wholesale price Pw�P = 1�18 · Pw�, and the first-order conditions (8) canbe expressed directly in terms of the wholesale prices.

Step 2A ML. The main results from the ML estima-tion step are displayed in Table 5, column (i). Theimplications of these estimates will become clear inthe next section, where we simulate the calibratedmodel. Here we only highlight some key findings.We did not attempt to estimate the discount factor �,but instead chose a calibrated value of 0.975, which

uct coincide or not. Conversations with industry observers suggestthat manufacturers such as Kellogg and General Mills have muchchannel power, and hence we do not expect that some retailers can“force” these firms to abandon a new product sooner than privatelyoptimal for them.40 See http://gsbwww.uchicago.edu/research/mkt/Databases/DFF/DFF.html.


corresponds to an annual interest rate of 10.7%. Allparameters are estimated precisely.41

The estimated standard deviation of the initial prioris 1.311 and indicates substantial demand and profituncertainty at the time of product launch. In fact, atsmall values of �0 the likelihood of the data is 0,because the model cannot explain why some of theunprofitable products were launched. The effect ofadvertising is highly persistent; the median carry-overof current goodwill into the next period is 56.7%. Fora comparison, Appendix D presents logit estimateswith current and four lagged values of advertisingincluded. Lagged advertising has a statistically signif-icant effect, but the overall effect size is much smallerthan estimated here. This provides support for thestructural endogeneity correction provided by the MLestimator. The demand shocks are correlated acrossgeographic markets, as indicated by the standarderror of the common variance component, ��> = 0�588.Hence, even though firms receiveM signals about theproduct quality in each period, learning is impededdue to the correlation of signals across markets.The estimate of the fixed-cost parameter k is $1.393

million (per quarter). The standard error of k is muchhigher compared to the standard error of the otherparameters, which indicates that k is hard to iden-tify precisely. An identification problem arises, forexample, if k is heterogeneous across firms (or prod-ucts), or even varies across time periods. We thereforechecked the sensitivity of the results by re-estimatingthe model for different calibrated values of k chosenon a grid, k= 00�250�5 � � � million. As one example,column (ii) in Table 5 shows the parameter estimatesfor k = $0�75 million, which is the smallest fixed-cost value examined at which the likelihood of thedata was positive. Overall, we find that the parame-ter estimates do not change much, and in particularthe main predictions of the model, discussed in §5,remain mostly unchanged (see Appendix E, availableat http://mktsci.pubs.informs.org.).A product-quality parameter, �i, is estimated for

each product. These estimates are not interestingper se; instead, Table 5 presents the implied distri-bution of expected profits. Among the new products,the average expected PDV of profits is $31.45 millionand has a standard deviation of $98.72 million. Thelarge standard deviation relative to the mean reflectsthat the majority of new products in our sample hasa value of zero, while some of them are profitable.

5. Model PredictionsWe now return to the questions posed in the intro-duction. First, we show how our model can be used

41 The first step estimation error does not affect the asymptoticcovariance matrix of the step two estimator. See Appendix B for adetailed explanation.

to calculate the dollar value of improved informa-tion about product profitability. This value directlyimplies the optimal demand for information, in theform of market research. Second, we investigate howthe degree of demand uncertainty influences a ratio-nal firm’s willingness to launch new products and,at the same time, “tolerate” product failures. In par-ticular, should a firm be more, or less, willing tolaunch a new product, holding the point estimate ofexpected profits constant, if the firm is more uncer-tain about the true product profitability? We also illus-trate the value of our model relative to other, possiblysimpler, frameworks. In the introduction we stressedthe importance of the option of scrapping the prod-uct now or in the future, which is valuable becauseit allows the firm to gather more information aboutproduct demand. We demonstrate the quantitativesignificance of the value of additional informationby comparing our model to a simpler framework,where the product launch and exit decisions are basedpurely on an estimate of expected future profits. Sec-ond, we consider an alternative decision rule, wherethe decision maker launches a product only if the“failure” probability is below a certain level. A man-ager whose career prospects are linked to the numberof “successful” launches or the number of productfailures might follow such a decision rule.We explore all these issues using the empirical im-

plementation of our model for the specific case of theU.S. RTE breakfast cereal industry. A limitation of thisapproach is that the results cannot be simply general-ized to any other market. On the other hand, our spe-cific illustration of the more general concepts allowsus to discuss the magnitudes and economic impor-tance of these concepts in an industry where productlaunches are important.The results presented are obtained from counter-

factual simulations, where either the initial uncer-tainty of the decision maker, or a specific behavioralassumption about the firm’s decision rule is varied.This approach is not inconsistent with our model orthe estimation strategy, where we assumed that thedata were generated from the actions of rational firms.Both the model and the estimation results are condi-tional on some initial prior uncertainty, and we do notassume that this initial uncertainty itself is optimal.Hence, it is not contradictory to investigate how theoutcome of the launch process changes under somedifferent initial degree of uncertainty, or under somealternative, suboptimal decision rule.

Preliminaries. We first clarify some concepts dis-cussed in this section. The expected profit from aproduct with true quality �, and a decision maker’sprior p0�·��2�, is defined as

/��= Ɛ

[ �∑t=0

�t��st�t� ��

]� (24)


The dependence of expected profits on � is obvi-ous. Furthermore, the prior information on � influ-ences profits through the sequence of stay/exit andadvertising decisions taken through time. Note thedifference between this profit measure and the valuefunction of the firm,

Vt =∫/��pt��t�

2t � d�� (25)

The value function measures expected profits withrespect to the firm’s prior, while / measures expectedprofits from the point of view of an observer whoknows both the true product quality and the prior ofthe firm.A profitable product is such that /��0� > 0.

That is, if the firm is certain about the product qual-ity �, and makes its decisions accordingly, averagerealized profits are positive. For an unprofitable prod-uct, /��0� < 0. If there was no uncertainty, theproduct launch process would be trivial, and onlyprofitable products would be launched. However,under imperfect information, firms receive only anoisy signal about the true product quality. Byassumption, � ∼ N��2�, such that the initial prioris also normal, i.e., p0 = N��2�. Imperfect infor-mation leads to “wrong” decisions. For example, asufficiently negative draw of � can lead the firmto scrap a profitable product. A sufficiently positivedraw can lead the firm to launch an unprofitableproduct. Finally, advertising will be distorted relativeto its level under perfect information.Suppose a firm develops new products with qual-

ity �, where � is drawn from a distribution with den-sity f�. Under this development process, the averageloss from imperfect information can be measured by

L�� = −Ɛ�/��

= −∫∫

/��f��2�f��d�d�� (26)

The loss is minimized at � = 0. The loss functiondepends on the distribution of �, i.e., the nature ofthe firm’s product development process, in two ways.First, f� determines the scale of profits. Second, givena degree of uncertainty, the loss function will increasein the scope for “mistakes.” For example, if the firm isfaced with both profitable and unprofitable productswith equal probability, it will often launch an unprof-itable product or fail to launch a profitable product.On the other hand, if the firm always knows whetherthe product is profitable or unprofitable, even thoughthe exact level of profits is unknown, there is noscope for mistakes and hence no loss in profits due touncertainty.It is important to understand how the loss func-

tion differs from the value function of the firm. The

value function is also an expectation of future profits;however, the expectation is taken with respect to thesubjective information contained in the prior. Hence,the subjective value from the product may increase inthe standard deviation � , because a higher standarddeviation may increase the probability that the newproduct opportunity is profitable. The loss function,however, increases in the standard deviation becausethe incidence of wrong stay/exit and advertising deci-sions increases. The distinction between the loss func-tion and the value function is of utmost importancefor managerial decision making. A firm should expectthat its average profit from a new product opportu-nity decreases under a higher degree of uncertainty.However, because the value of the product increasesin the uncertainty about profits, the firm should bemore willing to launch a new product.We calculate the loss function through a simula-

tion process. First, a “product opportunity” is drawn.A product opportunity is determined by the qualityparameter �, the production cost c, and the prod-uct attributes that determine the substitution patternsincorporated in the profit function.42 Consistent withthe learning model, �0 is drawn from N��2

0 �. Wethen simulate the optimal advertising and exit deci-sions through time, and record the resulting profits.43

Finally, we calculate the resulting PDV of profits. Thesame simulation process also allows us to calculatethe percentage of all product opportunities that arelaunched, and the percentage of all launched productsthat eventually exits. The latter is called the “optimalexpected exit rate.”

The Value of Improved Information. We first in-vestigate by how much the expected profit from aproduct opportunity increases under improved infor-mation, i.e., under lower uncertainty about the prod-uct quality. From this value we can derive the optimaldemand for information, for example, in the form ofmore or better market research. Formally, if C�� rep-resents the per-product cost of obtaining a prior withprecision 1/�2, the firm should reduce its uncertaintyto the level

�∗ = argmax�≥0

2−L��−C��3� (27)

We make two different assumptions on the distribu-tion from which a new product opportunity is drawn.First, we assume that the products are drawn fromGnew, the empirical distribution of all newly launchedproducts. Second, we assume that the products are

42 Note that in the definition of the loss function above, we implic-itly assumed that products are only distinguished by their product-quality parameter. The extension to differences in production costsand substitution patterns is only a matter of changing the notation.43 For each product draw, we simulate 20 time periods.


Figure 5 Top Row: Products Are Drawn from the Empirical Distribution of All Newly Launched Products. Bottom Row: Products Are Drawn from theEmpirical Distribution of All Products in the Sample

0 0.5 1.0 1.5 2.00

2.5

5.0

7.5

10.0

12.5

(a) Relative profit loss

σ

$ m

ill.

0 0.5 1.0 1.5 2.00

0.2

0.4

0.6

0.8

1.0

(b) Percent launched

σ0 0.5 1.0 1.5 2.0

0

0.2

0.4

0.6

0.8

1.0(c) Exit rate

σ

0 0.5 1.0 1.5 2.00

2.5

5.0

7.5

10.0

12.5

(d) Relative profit loss

σ

$ m

ill.

0 0.5 1.0 1.5 2.00

0.2

0.4

0.6

0.8

1.0(e) Percent launched

σ0 0.5 1.0 1.5 2.0

0

0.2

0.4

0.6

0.8

1.0(f) Exit rate

σ

drawn from Gall, the empirical distribution of allproducts, new and established, in our sample. Thefirst distribution contains a larger fraction of unprof-itable products than the second (Table 5).Figures 5(a) and (d) show L��0� − L�0�, the profit

loss under a specific �0 (the standard deviation of theprior at the time of product launch) relative to thebaseline profit under perfect information.44 The profitloss can be large; at the estimated standard deviation�0 = 1�31, it is $11.8 million under Gnew and $8.4 mil-lion under Gall. As a percentage of the expected profitunder perfect information, the loss is 37.5% underGnew and 5.7% under Gall. The reason for this differ-ence is straightforward. Under the empirical distribu-tion of all newly launched products the incidence ofunprofitable products is higher than under the empir-ical distribution of all products in the market. Hence,the average profitability of a new product is lower($31.45 million versus $147.14 million), and the scopefor making the wrong entry or exit decision is higher.Hence, relative to average profits under certainty, thevalue of information is higher under Gnew.

Optimal Entry and Exit Rates. We next turn to thequestion of how firms should change the fraction of

44 All profit numbers shown are in 2004 dollars.

new product opportunities launched under increasingdemand uncertainty. Furthermore, we calculate theoptimal exit rate. Figure 5 displays the percentage ofnew product opportunities launched and the productexit rate under Gnew and Gall.45 Under full informa-tion, 30% of all product opportunities are launchedunder Gnew, and 78% of product opportunities arelaunched under Gall.46 The difference in the launchrates reflects the underlying occurrence of profitableproducts under the two distributions. The percent-age of products launched increases strongly in thedegree of uncertainty. If products are drawn fromGnew, 96.5% of all product opportunities should opti-mally enter the market at the estimated uncertainty,�0 = 1�31. Even under much smaller levels of uncer-tainty, more than 80% of all product opportunitiesshould be launched. Consequently, firms incur largeproduct exit rates; for example, under Gnew closeto 80% of all newly launched products exit if the ini-tial uncertainty �0 is larger than 0.25. Hence, optimal,forward-looking behavior can imply that under even

45 The exit rate is defined relative to all products that were actu-ally launched, i.e., not including product opportunities that neverentered the market.46 In other words, 30% and 78% of all new products drawn fromthese two distributions are profitable.


Figure 6 Expected Profit Loss, Entry, and Exit Under Different Product Qualities

00.25

0.500.75

1.0

–7–6–5–4–30

4

8

12

16

20

σ


λ

$ m

ill.

0 0.250.50

0.751.0

–7–6

–5–4

–30

0.2

0.4

0.6

0.8

1.0

σ


λ 0

0.25

0.50

0.75

1.0

–7–6

–5–4

–3

0

0.2

0.4

0.6

0.8

1.0

λ

(c) Exit rate

σ

small degrees of uncertainty, a large fraction of allpossible new products should be tested in the mar-ket. Furthermore, in our example a high incidence ofproduct exits is fully consistent with optimal decisionmaking.

Profit Loss, Entry, and Exit Given a ProductQuality �. Clearly, the expected profit loss, and theproduct entry and exit rates, are dependent on the dis-tribution of product qualities and hence profits. Fig-ure 6 clarifies these dependencies. The expected loss,entry rate, and exit rate are depicted conditional onthe true product quality �, and a degree of uncer-tainty �0.47 As � increases, products become moreprofitable. In this specific example, there is a prof-itability threshold �≈−4�25 such that products withquality � > � are profitable, and products with qual-ity �≤ � are unprofitable. Under perfect information,firms select only the profitable products. For exam-ple, if � = −5�5, the new product opportunity is notlaunched in the market. Under imperfect informa-tion, however, product entry rises strongly in �0, hold-ing � constant. For example, if � = −5�5 and �0 = 1,the product entry rate is 90.8%. This is despite thefact that more than 89% of the �0 draws are belowthe entry threshold � (remember that �0 ∼ N��0�).That is, with probability 0.89 the firm’s best guessof the product quality parameter � is such that theproduct is unprofitable, but nonetheless the productis launched. In this example, optimal market experi-mentation leads firms to minimize Type I errors underthe null hypothesis H0 = “the product is profitable.”Profitable products are mostly correctly classified, andfirms would rather launch an unprofitable productthan miss a profitable one. As a consequence of this

47 The numbers shown are for Kellogg’s Heartwise, a new healthcereal that was eventually scrapped.

rational selection process, we observe a large inci-dence of Type II errors, i.e., product exits.Figure 6(a) shows that the profit-loss peaks at val-

ues of � that are slightly below the profitabilitythreshold. The value of information will therefore behighest if product opportunities are drawn from a dis-tribution of qualities centered around the profitabilitythreshold.

Effect of a Fixed Cost of Entry. The previous ex-periments were performed under the implicitassumption that the product had already been devel-oped, and, accordingly, that the firm did not haveto incur an entry cost. We now investigate how theresults change if the cost of entry is positive. Thiscounterfactual experiment corresponds to the situa-tion where the firm is uncertain about the true prod-uct profitability, but has to incur some sunk costbefore it can start collecting information in the mar-ket. These costs can include product developmentcosts, costs to develop a distribution channel, etc. Thedecision process of the firm has to be modified underthis scenario. If the expected value of the new productis larger than the sunk cost of entry, the product entersthe market. Otherwise, the fixed cost is not incurred,and the product is never launched.Figure 7 shows the loss function and the entry and

exit rates for a fixed cost $10 million (top row) and$20 million (bottom row). Such development costs areplausible in the case of the cereal industry. Productopportunities are drawn from Gnew. As expected, thevalue of information is higher for a larger fixed cost ofentry, holding the degree of demand uncertainty con-stant. For example, at �0 = 1�31, the expected profitloss is about $28 million if the entry cost is $10 mil-lion, and about $39 million for an entry cost $20 mil-lion. The firm’s willingness to launch new productsis more “conservative” relative to the case of no fixedentry cost, although the change is less dramatic than


Figure 7 Product Types Are Drawn from Empirical Distribution of All Newly Launched Products

0 0.5 1.0 1.5 2.0

0 0.5 1.0 1.5 2.0

0

10

20

30

40


σ

$ m

ill.

0 0.5 1.0 1.5 2.0

0 0.5 1.0 1.5 2.0

0 0.5 1.0 1.5 2.0

0 0.5 1.0 1.5 2.0

0

0.2

0.4

0.6

0.8

1.0

0

0.2

0.4

0.6

0.8

1.0

0

0.2

0.4

0.6

0.8

1.0

0

0.2

0.4

0.6

0.8

1.0


σ

(c) Exit rate

σ

0

10

20

30

40

(d) Relative profit loss

σ

$ m

ill.

(e) Percent launched

σ

(f) Exit rate

σNote. The fixed cost of entry is $10 mill. (top row) and $20 mill. (bottom row).

one might expect. Comparing Figures 5 and 7, we seethat the percent of products launched is still stronglyincreasing in the uncertainty � . At �0 = 1�31, the per-centage of launched products is about 82% for botha fixed cost of $10 million and $20 million, and theconcomitant exit rates are approximately 76%.

Interpreting the Stylized Facts in the U.S. CerealIndustry. The previous findings have strong impli-cations for our interpretation of the observed styl-ized facts—high entry and exit rates—in the U.S. RTEbreakfast cereal industry. Indeed, we find that at theestimated degree of uncertainty, the observed entryand exit rates are as expected from our model of fullyoptimal decision making. It is important to note thatwe do more than just rationalize the data: We showthat the stylized facts correspond to typical, expectedbehavior. A simple way to rationalize the launch ofan unprofitable product is as follows. Assume that thefirm’s initial prior on � is such that �0 > � is abovethe profitability threshold. Then, we would say theproduct was launched because the firm overestimatedthe true profitability. We could invoke this argumentfor all unprofitable products launched. Of course,this would be implausible under rational behavior,

although possible in principle (and thus have a pos-itive likelihood). However, the high rate of productlaunches (Table 5b) implies that even if the firm hasa prior such that �0 is somewhat below �, it willstill launch the product under the estimated degree ofuncertainty. Therefore, the observed entry rates andconcomitant product failures are to be expected if thecereal manufacturers are as rational as the firms in ourmodel. Of course, this argument is conditional on theestimated degree of uncertainty; given that we do notobserve the cost of reducing uncertainty below thislevel, we are unable to make any statements about theoptimality of the initial uncertainty choice.

Suboptimal Behavior: Disregarding the Value ofAdditional Information. We previously stressed theimportance of the sequential experimentation aspectof the product launch problem. Optimal dynamicdecision making is forward looking, and takes intoaccount that more information about the true prod-uct quality can be obtained if the product is launchedor stays in the market. We contrast the fully optimalbehavior to a simpler form of decision making thatis focused on a forecast of profits given current infor-mation only. This alternative decision process doesnot take into account the option value of scrapping


Figure 8 Suboptimal Decision Making: The Value of Additonal Information by Delaying Exit Is Not Taken into Account

0 0.5 1.0 1.5 2.00

5

10

15

20

25

(a) Profit loss relative to fully optimal behavior

σ0 0.5 1.0 1.5 2.0

σ0 0.5 1.0 1.5 2.0

σ

$ m

ill.

0

0.2

0.4

0.6

0.8

1.0

0

0.2

0.4

0.6

0.8

1.0

(b) Percent launched (c) Exit rate

Note. Products are drawn from the empirical distribution of all products in the sample.

the product at any point in the future, which allowsthe firm to gather additional information by delay-ing exit. In order to demonstrate the economic impor-tance of this additional information, we recomputethe decision problem and assume that the decisionmaker does not anticipate the future change of hisprior when the realized sales provide new informa-tion about the product’s profitability. That is, insteadof anticipating that the belief on the product qualitytomorrow, �t+1, can change in response to the infor-mation provided by product sales, the decision makeracts as if �t+1 = �t . On the other hand, we retain theassumption that advertising is set in a fully optimal,forward-looking fashion.Figure 8(a) displays the difference in profits

between fully optimal behavior and the suboptimaldecision rule described before. The value of additionalinformation and the option value of delay can belarge. For example, at �0 = 1�31, their combined valueis about $20.7 million. What is the major source ofthe profit loss under suboptimal behavior? Compar-ing Figures 5(b) and 8(b), we see that relative to fullyoptimal behavior, the percent of product opportuni-ties launched hardly increases in the amount of uncer-tainty. Hence, many profitable product opportunitiesare foregone. As the firm does not recognize the fullvalue of the product, it now tolerates a larger frac-tion of Type I errors, i.e., rejects too many profitableproducts.

Suboptimal Behavior: Avoiding “Product Fail-ures.” In our final counterfactual experiment, wecompare optimal product launch behavior to an alter-native strategy, where a manager launches a productonly if the “failure” probability is below a thresh-old, or, equivalently, tries to keep the average prod-uct exit rate below that threshold. If a large exit rateis taken as indicative of “bad” decision making, thisalternative decision rule might be optimal from the

manager’s point of view. In particular, a managerwhose career prospects are influenced by the num-ber of product launches that resulted in a failure willoptimally avoid a high exit probability. However, wealready know that large exit rates can be consistentwith fully optimal behavior, where optimality is mea-sured with respect to the expected PDV of profits asthe objective function. Limiting product exit is analo-gous to a “frequentist” approach to testing if the prod-uct is profitable, with an upper bound on the Type IIerror probability imposed.Figure 9 shows the profit loss, entry, and exit rates

under the alternative product launch procedure. Inorder to avoid exceeding an exit threshold of 20%,the firm decreases the rate at which new productsare launched relative to fully optimal behavior. Theresulting profit loss can be huge. For example, at�0 = 1�31, the loss is $27.5 million; at � = 2, it is$45.9 million. We conclude that if a firm’s or a man-ager’s product development and introduction processis judged by the “failure rate” of new products, theresulting change in managerial decision making canstrongly decrease profits.

6. ConclusionsThis paper deals with the classic marketing problemof optimal new product launch. We specifically focuson product launch under demand uncertainty and itsconsequences for the optimal launch and product exitdecision, and the price a firm should pay to reduceits demand uncertainty by a given amount. Formally,a product launch under demand uncertainty is akinto a sequential experimentation problem in statisti-cal decision theory, where the firm uses the mar-ket as a laboratory to acquire information about thetrue demand for its product from observed sales.


Figure 9 Suboptimal Decision Making: Products Are Not Launched If the Expected Exit Rate Exceeds 20%

0 0.5 1.0 1.5 2.00

10

20

30

40

50

(a) Profit loss relative to fully optimal behavior

σ0 0.5 1.0 1.5 2.0

σ0 0.5 1.0 1.5 2.0

σ

$ m

ill.

0

0.2

0.4

0.6

0.8

1.0

0

0.2

0.4

0.6

0.8

1.0

(b) Percent launched (c) Exit rate

Note. Products are drawn from the empirical distribution of all products in the sample.

We develop a model that incorporates this sequen-tial experimentation aspect and predicts the opti-mal path of stay-or-exit decisions, advertising, and(equilibrium) prices. The optimality of these decisionsis judged with respect to the firm’s generic objec-tive function, the expected PDV of profits, which isderived from an underlying random coefficients logitdemand system. The model is solved using numeri-cal dynamic programming techniques. The model canbe solved on a modern personal computer, and thesolution can be used as a decision tool to aid manage-rial decision making during an actual product launch.The model parameters are estimated using a tech-nique that accounts for an econometric endogeneityproblem in advertising, and furthermore allows usto recover the firms’ initial degree of demand uncer-tainty. A firm that uses the model as a decision toolfaces a simpler estimation task and only needs to esti-mate the demand parameters—for example, using theBLP method.Our model is illustrated for the case of the U.S. RTE

breakfast cereal industry. We find that in this specificexample, the value of reducing demand uncertaintycan be substantial. An important strategic lesson isgained by examining how the launch and exit deci-sions depend on the current degree of demand uncer-tainty. We discussed the crucial distinction betweenthe loss function and the value function. Under higherdemand uncertainty, the average profit loss due to“mistaken” launch-or-exit decisions increases, but thevalue function of the product also increases. Hence, adecision maker who confuses the value function withthe loss function will launch fewer (scrap more) prod-ucts under higher uncertainty. The opposite behavior,however, is optimal.A stylized fact of the cereal industry is that a large

fraction of all newly launched products “fail,” i.e.,exit soon after product launch. The optimality of an

observed failure rate can be judged using our model.For the example of the RTE cereal industry, we pre-dict that firms should strongly increase the fraction ofnew product opportunities launched for even smalldegrees of uncertainty. Hence, the optimal test ofthe null hypothesis, H0 = “the product is profitable,”largely avoids Type I errors, i.e., scrapping or notlaunching a truly profitable product. Consequently,firms should optimally tolerate high product exit rates(Type II errors). In fact, we find that the observedproduct failure rate in the cereal industry is approx-imately optimal, given the estimated demand uncer-tainty of the firms in our sample.If there is a positive fixed cost of entry, the percent

of products launched decreases relative to the entryrate under no fixed cost. However, the entry rate stillincreases strongly in the degree of uncertainty.We repeatedly stressed that the value from a new

product is more than the expected PDV of profitsunder the current prior. A firm also needs to value theadditional information about the product’s profitabil-ity that it can acquire by delaying exit. This informa-tion is valuable to the firm because it has the optionof scrapping the product at any time in the future,conditional on its posterior. Our simulations showthat the value of additional information is economi-cally important, and can lead to a large profit loss ifneglected.Finally, our results imply that the stakeholders in

some firms should not only be concerned about highproduct exit rates, but also about low exit rates.A manager who, due to career concerns, tries to limitthe probability of a product failure may reduce therate at which new product opportunities are launchedto a suboptimal level. This can have a strong negativeimpact on profits. Hence, a low product “failure” rateper se should not be taken as indicative of optimalmanagerial decision making.


Beyond the normative use of our model, it alsoprovides a new, alternative explanation for the highobserved product entry and exit rates in the U.S.RTE cereal industry. As we already mentioned, theobserved launch and exit rates are optimal, condi-tional on the estimated degree of demand uncertainty.Of course, because we do not observe the cost ofreducing the uncertainty, we do not know whetherthe initial prior uncertainty was chosen optimally. Wewould like to stress that although we provide an alter-native explanation for the stylized facts in the cerealindustry, we are unable to test between our explana-tion and the leading alternative explanation based onproduct proliferation as entry deterrence. A direct testbetween the alternative explanations is left for futureresearch.A main limitation of our model is that we do not

explicitly take into account strategic behavior withrespect to decision variables that have consequencesover time. For example, we do not solve for adynamic advertising equilibrium, and we do notallow for the possibility that a new product launchmay result in competitive product entry or exit. Wehave argued that in the specific application of ourmodel to the case of the U.S. RTE breakfast cerealindustry, the omission of dynamic advertising compe-tition is unlikely to affect the main conclusions. Thejustification of this claim was based on the particu-lar market structure of this industry, in particular thepresence of a large number of competing products. Inother markets, however, the explicit consideration ofdynamic strategic interaction will be important. Incor-porating such strategic aspects into a model of prod-uct launch or product entry is left as an importantarea for future research.

AcknowledgmentsEarlier work on this project started with the author’sPh.D. dissertation at Yale University. The author is greatlyindebted to his dissertation advisors, John Rust, SteveBerry, and Chris Timmins, for their guidance and sup-port. The author thanks Prof. Ronald Cotterill, the direc-tor of the Food Marketing Policy Center at the Univer-sity of Connecticut, for providing him with data and manyinsights on the U.S. ready-to-eat breakfast cereal industry.He is greatful to Peter Rossi for his many helpful andinsightful comments at various stages of this project. Theauthor has also greatly benefitted from the comments ofthe area editor and two anonymous reviewers, and discus-sions with Pat Bayer, Pradeep Chintagunta, Eugene Choo,Tim Conley, J. P. Dubé, Ricky Lam, Puneet Manchanda,Oleg Melnikov, Harikesh Nair, and Peter Reiss. Seminarparticipants at Berkeley, Columbia, Cornell, MIT, Stanford,the University of Connecticut, the University of Chicago,University of Pennylvania, and Yale provided helpful com-ments. This research was supported by the Kilts Center ofMarketing and a True North Communications Inc. Schol-arship at the Graduate School of Business, University ofChicago.

ReferencesAckerberg, D. A. 2003. Advertising, learning, and consumer choice

in experience good markets: A structural empirical examina-tion. Internat. Econom. Rev. 44(3) 1007–1040.

Aghion, P., P. Bolton, C. Harris, B. Jullien. 1991. Optimal learningby experimentation. Rev. Econom. Stud. 58 621–654.

Akçura, M. T., F. F. Gönül, E. Petrova. 2004. Consumer learning andbrand valuation: An application on over-the-counter drugs.Marketing Sci. 23(1) 156–169.

Arrow, K. J., M. Nerlove. 1962. Optimal advertising policy underdynamic conditions. Economica, New Series 29 129–142.

Bergemann, D., J. Välimäki. 1997. Market diffusion with two-sidedlearning. RAND J. Econom. 28(4) 773–795.

Berry, S. T. 1992. Estimation of a model of entry in the airline indus-try. Econometrica 60(4) 889–917.

Berry, S. T. 1994. Estimating discrete-choice models of product dif-ferentiation. RAND J. Econom. 25(2) 242–262.

Berry, S. T., J. Levinsohn, A. Pakes. 1995. Automobile prices in mar-ket equilibrium. Econometrica 63(4) 841–890.

Bresnahan, T. F., P. C. Reiss. 1991. Entry and competition in con-centrated markets. J. Political Econom. 99(5) 977–1009.

Ching, A. T. 2002. Consumer learning and heterogeneity: Dynam-ics of demand for prescription drugs after patent expiration.University of Toronto, Ontario, Canada.

Churchill Jr., G. A., 1995. Marketing Research, 6th ed. The DrydenPress, Chicago, IL.

Cotterill, R. W. 1999. High cereal prices and the prospects forrelief by expansion of private label and antitrust enforcement.Agribusiness 15(2) 229–245.

DeGroot, M. H. 1969. Optimal Statistical Decisions. McGraw-Hill,New York.

Dixit, A. 1989. Entry and exit decisions under uncertainty. J. PoliticalEconom. 97(3) 620–638.

Dixit, A. K., R. S. Pindyck. 1994. Investment Under Uncertainty.Princeton University Press, Princeton, NJ.

Dorfman, R., P. O. Steiner. 1954. Optimal advertising and optimalquality. Amer. Econom. Rev. 44 826–836.

Erdem, T., M. P. Keane. 1996. Decision-making under uncertainty:Capturing brand choice processes in turbulent consumer goodsmarkets. Marketing Sci. 15(1) 1–20.

Erdem, T., S. Imai, M. Keane. 2003. Brand and quantity choicedynamics under price uncertainty. Quant. Marketing Econom. 15–64.

Gönül, F., M. Z. Shi. 1998. Optimal mailing of catalogs: A newmethodology using estimable structural dynamic program-ming models. Management Sci. 44(9) 1249–1262.

Gönül, F., K. Srinivasan. 1996. Estimating the impact of consumerexpectations of coupons on purchase behavior: A dynamicstructural model. Marketing Sci. 15(3) 262–279.

Harrington, J. E. 1995. Experimentation and learning in adifferentiated-products duopoly. J. Econom. Theory 66 275–288.

Hausman, J. A. 1996. Valuation of new goods under perfect andimperfect competition. T. F. Bresnahan, R. J. Gordon, eds. TheEconomics of New Goods. University of Chicago Press, Chicago,IL, 209–237.

Hendel, I., A. Nevo. 2005. Measuring the implications of sales andconsumer stockpiling behavior. NBER Working Paper 11307.

Judd, K. L. 1985. Credible spatial preemption. RAND J. Econom.16(2) 153–166.

Judd, K. L., M. H. Riordan. 1994. Price and quality in a new productmonopoly. Rev. Econom. Stud. 61(4) 773–789.

Kadiyali, V. 1996. Entry, its deterrence, and its accommodation:A study of the U.S. photographic film industry. RAND J.Econom. 27(3) 452–478.


Lehmann, D. R., S. Gupta, J. H. Steckel. 1998. Marketing Research.Addison-Wesley, Reading, MA.

Little, J. D. C. 1966. A model of adaptive control of promotionalspending. Oper. Res. 14(6) 1075–1097.

McLennan, A. 1984. Price dispersion and incomplete learning inthe long run. J. Econom. Dynam. Control 7 331–347.

Melnikov, O. 2001. Demand for differentiated durable products:The case of the U.S. computer printer market. Manuscript, YaleUniversity, New Haven, CT.

Montgomery, A. L., E. T. Bradlow. 1999. Why analyst overconfi-dence about the functional form of demand models can leadto overpricing. Marketing Sci. 18(4) 569–583.

Moscarini, G., L. Smith. 2001. The optimal level of experimentation.Econometrica 69(6) 1629–1644.

Nevo, A. 2000. A practitioner’s guide to estimation of random-coefficients logit models of demand. J. Econom. ManagementStrategy 9(4) 513–548.

Nevo, A. 2001. Measuring market power in the ready-to-eat cerealindustry. Econometrica 69(2) 307–342.

Pekelman, D., E. Tse. 1980. Experimentation and budgeting inadvertising: An adaptive control approach. Oper. Res. 28(2)321–347.

Raman, K., R. Chatterjee. 1995. Optimal monopolist pricing underdemand uncertainty in dynamic markets.Management Sci. 41(1)144–162.

Rao, V. R., F. W. Winter. 1981. A Bayesian approach to test marketselection. Management Sci. 27(12) 1351–1369.

Roberts, J. H., G. L. Urban. 1988. Modeling multiattribute utility,risk, and belief dynamics for new consumer durable brandchoice. Management Sci. 34(2) 167–185.

Roberts, K., M. L. Weitzman. 1981. Funding criteria for research,development, and exploration projects. Econometrica 49(5)1261–1288.

Rust, J. 1987. Optimal replacement of GMC bus engines: An empir-ical model of Harold Zurcher. Econometrica 55(5) 999–1033.

Schmalensee, R. 1978. Entry deterrence in the ready-to-eat breakfastcereal industry. Bell J. Econom. 9 305–327.

Song, I., P. K. Chintagunta. 2003. A micromodel of new productadoption with heterogeneous and forward-looking consumers:Application to the digital camera category. Quant. MarketingEconom. 1(3) 371–407.

Trefler, D. 1993. The ignorant monopolist: Optimal learningwith endogenous information. Internat. Econom. Rev. 34(3)565–581.

Urban, G. L., J. R. Hauser. 1993. Design and Marketing of NewProducts, 2nd ed. Prentice Hall, Englewood Cliffs, NJ.

Urban, G. L., G. M. Katz. 1983. Pre-test-market models: Validationand managerial implications. J. Marketing Res. 20(3) 221–234.

Wald, A. 1945. Sequential method of sampling for deciding betweentwo courses of action. J. Amer. Statist. Association 40 277–306.

Documents

AnEmpiricalModelofOptimalDynamicProduct ... · PDF fileAnEmpiricalModelofOptimalDynamicProduct ... sider the case of consumer choice under attribute ... The U.S. RTE breakfast cereal