What difference does dynamics make? The case of digital cameras

What difference does dynamics make? The case of digital cameras☆

Weifang Lou, David Prentice ⁎, Xiangkang YinSchool of Economics and Finance, La Trobe University, 3086, Victoria, Australia

a b s t r a c ta r t i c l e i n f o

Article history:Received 12 December 2008Received in revised form 5 May 2011Accepted 7 May 2011Available online 14 May 2011

JEL Classification:D12D24L63

Keywords:Demand dynamicsDifferentiated productsDigital camerasMerger simulations

When the well-known BLPmodel is applied to products with rapid technological changes and declining pricesit tends to yield implausible results. A sequence of increasingly sophisticated dynamic demand models, mostrecently Gowrisankaran and Rysman (2009, hereafter GR), have been developed to overcome these problems.We apply both models to new data on the US digital camera market. In addition, we demonstrate that the GRmodel can be specified as a BLP model plus an additional set of terms. This suggests that a dynamic model canbe estimated as a BLP model plus a non-parametric function which is less computationally demanding. As afirst step to implementing this semi-parametric approach we estimate a BLP model augmented with age as aproxy for the non-parametric component. We find that demand for digital cameras is more elastic whendemand dynamics is accounted for in both the dynamic model and the BLP model with the age proxy. Thissuggests that the market is more competitive though the results are consistent with firms engaging inintertemporal price discrimination. Merger simulations predict the lowest price and quantity changes usingthe GR model.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

New products entering into and old products retiring frommarkets is a prevailing phenomenon. It is more noticeable in marketswhere there is rapid technological change and product prices fallsteeply and persistently. Examples of such markets include consumerelectronics like personal computers, television sets, mobile phones,digital camcorders and digital cameras. Although the static differen-tiated product demand model applied to products like cars yieldssatisfactory estimates and predictions (e.g., Berry et al., 1995,hereafter BLP), it has been observed that this model is likely todeliver counterintuitive estimates or predictions in markets withrapid product turnover and substantial price changes like con-sumer electronics (Gowrisankaran and Rysman, 2009; Melnikov,2001). To address the problem, these researchers and other

papers, such as Zhao (2007), Carranza (2010) and Conlon(2010), have introduced increasingly sophisticated and computationallydemanding dynamicmodels of demand for differentiated durable goods.1

In Gowrisankaran and Rysman (2009) (hereafter GR), for example,dynamics are included in the BLP framework by empirically modelingconsumers as solving an optimal stopping problem when choosingamong products. These papers have largely emphasized improving themethodology but the question, “How do our conclusions about durablegoods oligopolies change whenwe introduce dynamics into econometricmodels?” remains.

In this paper we analyzewhat difference does introducing dynamicsinto empirical oligopoly models make by estimating both the BLP andGR models on a new dataset of the US digital camera industry. Inaddition, we propose a third, less computationally demanding, semi-parametric approach of estimating a dynamic demand model. Wedemonstrate that the GR model can be specified as a BLP model plus anadditional set of terms and argue that under certain conditions a non-parametric function of a few variables can be used to represent theadditional terms. As a first step to implementing this approach, in ourthird empirical model, we estimate a BLP model with product age as aproxy (hereafter BLPWP) for this non-parametric function.2 Theintuition for adopting product age as a proxy is that it is negativelycorrelatedwith the demand for a product regardless whether dynamics

International Journal of Industrial Organization 30 (2012) 30–40

☆ We are grateful to seminar participants at La Trobe University and the University ofMelbourne and anonymous referees for their constructive comments. The Gauss codeused to estimate the BLP model is based on the code posted on the webpage of JamesLevinsohn and we would like to thank Steven Berry, James Levinsohn and Ariel Pakesfor making it publicly available. We also thank Gautam Gowrisankaran, AlexShcherbakov and Amil Petrin for providing their Gauss code. The Gauss code used toestimate the dynamic model is based on code provided by Gautam Gowrisankaran andMarc Rysman whom we would like to thank. We also thank Pradeep Chintagunta andJunji Xiao for providing information about data sources. The research is supported byAustralian Research Council Linkage Grant LP0455125. This paper was previously titled“The effects of product ageing on demand: The case of digital cameras”.⁎ Corresponding author. Tel.: +61 394791482; fax: +61 394791654.

E-mail address: [email protected] (D. Prentice).

1 See Aguirregabiria and Nevo (2011) for a general review.2 As we discuss in more detail below, Xiao (2008) independently used age as a

control in a non-random coefficients model of demand for digital cameras. However, itis included without any specific interpretation beyond a standard control.

0167-7187/$ – see front matter © 2011 Elsevier B.V. All rights reserved.doi:10.1016/j.ijindorg.2011.05.001

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arise from consumers expecting further technological change, futurefalling prices or just the depreciating effectiveness of advertising. Wenote that the proxy is only a partial solution and discuss how to handleresulting identification issues. Coefficients, elasticities and markupsfrom all three models are compared. Furthermore, we also compare theresults from simulating two mergers between Fujifilm and Nikon, andCanon and Sony.

We find that all three models yield plausible coefficients for thedemand and pricing equations. In general the BLP and BLPWP resultsare more similar to each other than to the GR model. The estimateddemand for digital cameras by the GR model and the BLPWP is moreelastic, which is consistent with a more competitive market. This typeof result is similar to that found by GR and Conlon (2010) andstrikingly different to the results predicted by Chen et al. (2008) intheir simulation analysis. In addition, all threemodels in the paper stillfeature declining markups over product lives, consistent with firmsengaging in intertemporal price discrimination. In the mergersimulations, the GR model predicts lower price increases followingeachmerger. These results are important as they suggest that dynamicmodels imply a more competitive oligopoly of durable goods thanstatic differentiated models. Introducing the age proxy does improveestimation in some respects in terms of expected adjustments todemand estimates.

The rest of the paper is organized as follows. The next sectionreviews the dynamic demand model of GR, compares it with the BLPmodel, and then proposes a semi-parametric approach to ease thecomputation burden of estimating the GR model. It further discussesestimation and identification. The data is described in Section 3 whileestimation results and merger simulations are compiled in Section 4.The final section concludes the paper.

2. Model and estimation

In Gowrisankaran and Rysman (2009, GR), consumers may delaypurchasing one of the available products because they believetechnology will improve rapidly and they prefer to wait to purchaseone of the improved products that they expect to come along. Thissection specifies the conditions under which the GR model can besimplified to the static demandmodel of BLP. These conditions suggestthat it may be possible to extend the BLP model by introducing a non-parametric function to control for de facto competition from futurepurchases and still estimate the other parameters of the model. As afirst step in this direction, we argue that product age could be used as aproxy to represent this non-parametric function. We conclude bydescribing the three sets of equations we estimate and also discussidentification and estimation issues.

2.1. Dynamic demand model of Gowrisankaran and Rysman

The main way the dynamic GR model differs from the static BLPmodel is that the demand for a product depends not only on its priceand characteristics but also on the expected utility from purchasingnew products offered in the future. Formally, suppose there are Jtdistinct products marketed in period t. Each product, indexed by j=1,2, …, Jt, is infinitely durable. Suppose further that there are Itconsumers/households in market t and they have an infinite horizon,discounting the future utility with a common factor of ρ. Like GR weavoid complications associated with secondary markets by assumingthat if a consumer already owns a product, it is effectively discardedupon purchase of a new product. In each period, the consumer decideswhether to purchase one of the Jt products or make no purchase. Ineach period household i that purchases product j receives flow utility:

δ fijt ≡ ∑

K

k=1β kix jk + ξ jt ; ð1Þ

where x jk is the quality measure of observable characteristic k (k=1,2, …, K, including brand dummies) and ξ jt is a product-specificcharacteristic observable to consumers but unobservable or immea-surable to researchers. The coefficients β ki in Eq. (1) measure themarginal utility of characteristic k and are subscripted with i to allowfor randomness in consumption utility.3 The outside choice (i.e., nopurchase) is denoted by j=0with flow utility δ i0t

f . If consumer i is notholding any product before period t, δ i0t

f is normalized to zero. Forthose already owning a product, δ f

i0t = δ fi jt, where j and t are the

product and time of the most recent purchase. Thus, the net flowutility from purchase is:

uijt = δ fijt−αi ln pjt

� �+ ε ijt ; ð2Þ

where pjt is the price of product j in period t and coefficient αi

measures the marginal disutility of price. The idiosyncratic shock toutility, ε ijt, is assumed to have a type-I extreme value distribution.Except for being defined in terms of flow utility rather than lifetimeutility, the utility function in Eq. (2) is very similar to that used in BLP.

For durable goods, each consumer's choice is influenced by theircurrent state, described by state variables, and expectations about thefuture. In addition to the type of product initially held by the consumerthere are two sets of state variables. The first set, denoted by εi.t≡(ε i0t,…, ε iJtt), is the vector of idiosyncratic shocks for the Jt+1 goods(including the outside choice) the consumer decides over in period t.The second set of state variables is all attributes of current products andfactors influencing future product attributes as denoted by Ωt. Ωt isassumed to evolve according to a Markov process. Hence the vector ofstate variables for consumer i at time t is (εi.t,δ i0t

f ,Ωt). Denote Vi(εi.t,δ i0t

f ,Ωt) as the value function and EVi(δ i0tf ,Ωt)=∫Vi(εi.t,δ i0t

f ,Ωt)dPεas

the expectation of the value function after integrating out εi.t. Hence, theBellman equation for consumer i is:

Vi εi:t ; δfi0t ;Ωt

� �= max

j=0;1;…; Jtuijt + ρE EVi δ f

ijt ;Ωt + 1

� �jΩt

h in o: ð3Þ

It is useful at this point to denote δijt as the expected net utilityfrom purchasing brand j conditional on consumer i's information attime t and δi0t as the conditional expected utility from not making apurchase at time t as follows:

δijt = δ fijt−αi ln pjt

� �+ ρE EVi δ f

ijt ;Ωt + 1

� �jΩt

h ið4Þ

δi0t = δ fi0t + ρE EVi δ f

i0t ;Ωit + 1

� �jΩit

h i: ð5Þ

GR demonstrate that given the sufficient assumptions specified intheir paper the state space can be reduced to two variables: theinclusive value and the flow utility from not purchasing, where thelogit inclusive value for consumer i at time t is defined as:

δit = ln ∑j=1;…; Jt

exp δijt� � !

: ð6Þ

Hence, the value function in Eqs. (3), (4) and (5) can beconditioned on δ i0t

f and δit rather than δ i0tf and Ωt. It is worth noting

that the probabilities associated with future values of the inclusivevalue are not derived assuming rational expectations but rather theinclusive value is assumed to evolve as a Markov process.

3 However, in practice the randomness of βki is often restricted to reducecomputational burden and/or insure convergence. For instance, Melnikov (2001)and GR take βki as non-random constants across consumers.

31W. Lou et al. / Int. J. Ind. Organ. 30 (2012) 30–40

The probability of consumer i purchasing good j, rather than takingthe standard multinomial logit form, is simplified by GR to:

sijt δfi0t ; δijt ; δit� �

=exp δijt

� �exp EVi δfi0t ; δit

� �−γ

� � ð7Þ

where γ is Euler's constant.We then aggregate across consumers and construct a demand side

moment condition, with ξjt as the error. Estimation is computationallyintensive as it requires solving dynamic programming problems foreach simulated consumer as well as similar steps to those required toestimate a BLP type demand model.

2.2. Comparison of the BLP and GR models

To enable a comparison between the static BLP model and thedynamic GRmodel, rather than using the simplified expression for theindividual's probability of purchasing good j as in Eq. (7) we return toEq. (3), make the same assumptions required to reduce the size of thestate space, and re-express the problem in the standard multinomiallogit form:

sijt δi0t ; δijt ; δit� �

=exp δijt

� �

exp δi0tð Þ + ∑Jt

k=1exp δiktð Þ

=exp δijt−δi0t

� �

1 + ∑Jt

k=1exp δikt−δi0tð Þ ð8Þ

where all δ.t are defined as in GR. The last term in Eq. (8) is in the sameform as in the BLP model except that the utility from not purchasingthe product is included explicitly, rather than normalized to zero. Thedifference in utilities, δijt−δi0t, can be re-expressed as follows:

δijt−δi0t = ∑K

k=1βkixjk−αi ln pjt

� �+ ξjt + ζijt ð9Þ

where ζijt≡ρE[EV(δijtf ,δit+1)|δit]−δi0tf −ρE[EV(δi0tf ,δit+1)|δit]. There-fore the only substantial difference between Eq. (8) and theequivalent probability of purchase in BLP is the term, ζijt, whichcaptures the expected benefit from the discounted flow utility of goodj stemming from the purchase at time t over an earlier purchase or notholding any product at all. The term ζijt is unobservable. But if thegoods are not durable and the usual normalization of δi0tf equal to zerois applied, then ζijt equals to zero and Eq. (8) becomes the standardBLP model.

For durable goods, if it is possible to represent ζijt by a non-parametric function, consistent estimates of the other parameters ofthe model can be obtained without estimating the dynamic demandmodel. This has two advantages. First, it saves on computation time—

particularly if repeated estimation is required to generate observa-tions to construct intervals on predicted outcomes. Second, it mayenable a richer specification of individual heterogeneity by allowingmore random coefficients on the explanatory variables. In practicewhen dynamic models have been estimated the extent of heteroge-neity in consumers has often been limited to save on computationtime.

However, it is not immediately obvious that this is possible becauseζijt, as expressed, is a function of variables, such as δit, which are jointlyderived in estimation of the GR model. Though these variables areultimately functions of the set of product characteristics, it is notfeasible to construct a non-parametric function using the large set ofcharacteristics themselves. Even a function of the characteristics, such

as a linear combination of characteristic variables, is problematic assuch functions are already being used as instruments.

2.3. A semi-parametric approach (BLPWP)

An alternative feasible, though imperfect, approach to constructinga non-parametric control function is to use a proxy variable that iscorrelated with ζijt but not used in estimation. If as emphasized by GR,dynamic behavior by consumers is motivated by changing productcharacteristics, under certain conditions the age of the product is apossible proxy. Denote δijtf (t ′) as the flow utility from product jintroduced at time t′ and δiktf (t ′−1) as product k introduced at time t′−1. If δijtf (t ′)Nδiktf (t ′−1) for each product k introduced at time t′−1,then, as δit evolves according to a Markov process, ζijt decreases withthe age of the product, given the current product held by theconsumer. Intuitively, this requires sufficiently rapid technologicalprogress and not too much consumer heterogeneity so that allconsumers have relatively strong preference for a new product overits older counterpart. This assumption is probably not appropriate foran industry like the car industry, but for the point-and-shoot segmentof digital camera market it is quite plausible in our sample periodwhen the technology of digital cameras improved substantially in arelatively short time period.

To implement this proxy we propose that ζijt is composed of acomponent that is common to all consumers, ζjt, and an individualspecific component. Hence we include a constant coefficient (i.e., meancoefficient over all consumers) on the age variable and an individualspecific random coefficient on age. Using age as a proxy for ζijt isimperfect for two reasons. First, as flow utilities depend on character-istics aswell as the age of theproduct, age does not inherently control fordifferences in ζijt due to different characteristics. In effect we do notcontrol for a certain component of ζijt. Second,we do not observe the ageof the product that is held by each simulated consumerwhen estimatingthe BLP model. Allowing for a random coefficient on age only partiallydeals with the latter problem because the product held by the consumervaries over time and non-randomly. A complete treatment for thisproblemwould require the individual specific error to change over timeas well but it is not immediately obvious how to implement this. Theformer problem could be addressed in part by interacting age withcharacteristics though it cannever completely remove themeasurementerror from the specification. As afirst stepwe treat age as correlatedwithξjt and instrument for it.

So far we have emphasized consumers reacting to expected changesin the flow utility from products over time due to technological change.An alternative motivation for dynamic behavior by consumers empha-sized by Zhao (2007) in her empirical analysis is that consumers expectprices of individual products to fall over time either due to fallingmarginal costs or strategic reasons such as intertemporal pricediscrimination or intensifying competition. As a consequence, con-sumers who have a high willingness-to-pay for their favored goodsenter themarket soon after the new products have been launched. Highprice-elastic consumers with a low willingness-to-pay tend to delaytheir purchases and wait until their preferred alternatives are pricedbelow their reservation prices. There is an extensive theoreticalliterature which analyzes firm incentives to intertemporally pricediscriminate (see Koh (2006) as a recent example and literature citedtherein). There is also an even more extensive literature, reviewed inWaldman (2003), around the Coase conjecture which has beendeveloped to specify conditions under which intertemporal pricediscrimination (or indeed any market power) cannot occur. Ausubeland Deneckere (1987) though do cast doubt on its applicability tooligopolies. If the Coase conjecture holds and product prices do fall overtime it must be due either to falling costs or, as cited in Zhao (2007),intensifying competition. Competition may intensify presumably asinnovations are followed by imitations by their competitors.

32 W. Lou et al. / Int. J. Ind. Organ. 30 (2012) 30–40

Regardless of the reason, if consumers expect prices to fall, thenlater purchasers will tend to have lower valuations of the product. Themost general model allowing for this would have coefficients on theprice and characteristics varying with the age of the product. None ofthe existing models fully deal with the issue in this way. Alternatively,the individual specific component could vary systematically with age.This implies both the mean and individual specific components of ζijtchange with age. Introducing age into the mean utility along withindividual specific components is a first attempt to control for thesechanges in the types of consumers purchasing the product over time ifprices are expected to fall.

In addition, if a brand (product) is launched with a considerableamount of advertising, the value of which diminishes over time, thenthe age variable may also capture this influence. Though notnecessarily a direct determinant of utility, under this interpretation,we follow earlier papers, such as Ackerberg (2003), in including suchdeterminants in the demand equation. Promotion activities are likelyto be designed to complement intertemporal price discrimination oreven be adjusted for the fact that technological progress will renderany specific brand obsolete fairly quickly.

Finally, it is worthwhile to notice that to a certain extent, the agevariable can be considered as a characteristic of a product in itself.Consumers may view two products with identical characteristics asdifferentiated goods if one was launched after the other. They maydiscount the value of a product purely because it has been in themarketfor too long. Since themean utility of a product declines as time goes by,two consumers buying the exact same product at different time pointsreveal their difference in willingness-to-pay. Thus, the age variable candepict the evolution of consumerwillingness-to-paywhich gives rise todynamics in demand and pricing.

2.4. Supply side of the model

In this section we describe the pricing model that is jointlyestimated with each of the demand models. If the production ofproduct j incurs a marginal cost mcjt then for a multi-product firm, f,the profit at period t can be expressed as:

Πft = ∑j∈Jft

pjt−mcjt� �

Ttsj pt ; xt ; ξð Þ; ð10Þ

where Tt is the aggregate market size at time t, sj(pt,xt,ξ) is the marketshare of product j and Jft is the product set of firm f. We define a Jt× Jtmatrix, Δ(pt,xt,ξ), where each element in the matrix is given by:

Δjl pt ; xt ; ξð Þ =−∂sl pt ; xt ; ξð Þ

∂pjt; l; j∈Jft

0; otherwise

:

8><>:

Furthermore, we define the hedonic marginal cost function, whichrelates the marginal cost of a product to a set of broadly availablequality measures, χj, a time trend, t, to control for technologicalprogress, and unobservable cost characteristics, ϖjt:

ln mcjt� �

= γf χj + λf t + ϖjt ; j∈Jft ; ð11Þ

where γf is a vector of coefficients measuring the marginal effect of aparticular observable characteristic on the logarithm of the product'smarginal cost. The observable part of characteristics χj can includepart or all of those included in the demand equations, xj. Hence the Jtfirst-order conditions from the profit maximization problem can berearranged as a pricing equation moment condition:

ϖ = ln pt−Δ pt ; xt ; ξð Þ−1s pt ; xt ; ξð Þ� �

−γχ−λt: ð12Þ

The pricing equation moment condition given in Eq. (12) is usedjointly with the demand side moment condition to generate theobjective functions for GMM estimation. Note that we do not imposeany restriction in any of the models that the firms are engaged inintertemporal price discrimination.

With random coefficients we use simulated generalized method ofmoments as has been commonly used before for these models. Somerecent papers such as Dubé et al. (2008) and Knittel and Metaxoglou(2008) have raised questions about the computational practices whenperforming simulation estimation in the BLP framework. Thus, we usea convergence criterion 1.0E-8, stricter than BLP.

2.5. Specifications for estimation, identification and instruments

We estimate three sets of demand and pricing equations asspecified by the relevant moment conditions: BLP, BLPWP, and GR.The pricing equations are identical for all three models. The demandside of the BLP equation is based on Eqs. (1) and (2) with thequalification that lifetime rather than flow utility in each period isbeing modeled. Alternatively, the BLP model is equivalent to the GRmodel with ζijt=0 and the coefficients on characteristics reflectinglifetime utility. The demand side of the BLPWPmodel includes age as aproxy for ζijt. And the GR model is as specified in Section 2.1. In allthree demand models the continuous characteristics are logged. TheBLP and BLPWP models include a time trend. The GR model does notneed a time trend. To make the BLP and BLPWPmodels comparable tothe GR model, price and the constant term have random coefficientsbut the marginal utility of each characteristic is a non-randomconstant. 4 When product age is included as a proxy, it has a randomcoefficient.

Identification issues arise because as well as age being endogenousand an imperfect proxy, the disturbances ξjt and ϖjt are correlatedwith price pjt since the price is chosen by the firm knowing the valueof the unobservable characteristics. In addition, it is often argued inthe hedonics literature that the weight of a product may proxy forunobserved features which, when included, increase the weight of aproduct. Hence, we treat the weight variable as potentially correlatedwith the unobservable characteristics of the products. To deal withthese endogeneity issues, we use the BLP-type instruments. Theinstruments for the price of product j produced by firm f are theexogenous characteristics of model j, the sums of the exogenouscharacteristics of all other products produced by firm f and the sums ofthose that are produced by all other firms excluding f. In other words,for each product j∈ Jft, zjkt, ∑

l≠j;l∈Jftzlkt and ∑

l∉Jftzlkt are used as instrument

variables. In addition we include, as instruments, two measures of thenumbers of products in the market — the number of products offeredby a firm and the number of products offered by their competitors. Onthe demand side, the change in the number of available options canaffect the probability of a consumer purchasing a particular good(Ackerberg and Rysman (2005) make a related argument). On thesupply side, the numbers of products provided by a single firm and thatproduced by all other firms affect pricing strategies since firms have toset appropriate prices simultaneously for all their products. Allinstruments are constructed using the observations within theassociated market (period) that each observation is drawn from.

3. Data

Data on digital camera prices and sales volumes were purchasedfrom NPD Market Research, a US market research company — thesame source as used by Song and Chintagunta (2003), Zhao (2007)and Xiao (2008). This data set includes monthly prices and salesquantities at the camera model level, covering the period from

4 We discuss some results with more random coefficients below.

33W. Lou et al. / Int. J. Ind. Organ. 30 (2012) 30–40

January 2003 to May 2006. The reported prices and sales arenationwide, accounting for more than 80% of the US digital cameramarket. We supplement the characteristics supplied by NPD withmore detailed data on characteristics through extensive web search-ing. The final dataset includes the top six brands of point-and-shoot(P&S) digital cameras (Canon, Fujifilm, Kodak, Nikon, Olympus andSony).5 This comes to a total of 4253 model/month observations,representing 351 distinct camera models.

Table 1 summarizes the sales of the top six brands during thesample period. In general, the combined sales volume of P&S digitalcameras from the top six brands exceeds 32 million units, taking up83.8% of the entire US P&S camera market. Three leading brandsrepresent nearly 60% of the market, indicating a highly concentratedmarket.

The sales of digital cameras grew significantly during the sampleperiod, as demonstrated clearly by Fig. 1. For instance, the total saleswere below 0.3 million units in January 2003 but it doubled to about0.59 million units in the same period three years later. Along with thegeneral upward trend in sales, there is a significant seasonal effect. Forthe three Christmas seasons included in the data set, P&S camera salesin each December were approximately three (five) times of that in theNovember (October) of the same year, illustrating that the Christmassales are extremely important for the digital camera industry.6 Digitalcameras' prices declined considerably over the sample period. Themean price in the beginning of 2003 was around US$360 per unit, andended up at around $250 in May 2006.

There are six product characteristics in the analysis: imageresolution, optical zoom range of lens, the size of LCD screen, thesize and weight of camera, and digital zoom. While the first five arecontinuous variables, the last is a dummy variable with 1 indicating acamera has a digital zoom and 0 indicating otherwise. The volumeweighted average characteristics and age for selected months arereported in Table 2.

Table 2 demonstrates an overall upward trend in the character-istics of resolution, LCD and optical zoom. The average resolution, LCDsize and the optical zoom range increased by approximately 99%, 25%and 29%, respectively, in the sample period. However, camera size andweight fell continuously until the end of sample period. The twomeasures started at 24.56 in.3 in size and 9.86 oz. in weight and thendropped dramatically to less than or nearly a half of their initialvalues, reaching 11.33 in.3 and 5.49 oz. respectively.

For each camera model, its age is measured as the time elapsed (inmonths) since the model was launched. For all models that had beenintroduced into themarket before the beginning of the sample period,their actual introduction dates are collected from the internet.7 Fig. 2illustrates average price and sales of digital cameras, whereobservations of the top six brands over the 41-month sample periodare grouped by their ages. It reveals that the mean price exhibits asharp downward trend as cameras get older until they reach their ageof 20 months. However, beyond that age, the mean price fluctuatessignificantly. Examining our sample data, it shows that cameras whichsurvived longer than two years were usually high-end products. Theywere priced well above five hundred dollars at the time when theywere introduced to the market. Even after nearly two years of falling

prices, their prices were still higher than those of new low-endentrants.

Before proceeding, it is worth noting that the digital cameramarket is a natural market with which to explore questions related todynamic differentiated product demand, in the same way as the earlystudies of static models used data on cars.8 Xiao (2008) applies a staticlogit-type model to the digital camera market, including age as one ofa set of exogenous characteristics, while focusing on other character-istics to analyze the welfare implications of features that improveusability. Other papers on digital cameras, such as Song andChintagunta (2003), Carranza (2010) and Zhao (2007) build on thedynamic programming approach developed by Melnikov (2001). Theinterest of Song and Chintagunta (2003) is in how consumers adoptnew products and their data covers the infant period of the digitalcamera industry (April 1996 to May 1999) with three brands (Sony,Casio and Kodak). Carranza (2010) estimates the joint distribution ofutility function and participation function by a reduced-form solutionto account for the dynamic optimization problem. Zhao (2007)intends to explain the reasons for the fast price decline in the USdigital camera market from 2001 to 2004 and finds that cost savingsby technological progress contributes two thirds of the price fall andshrinking price — cost markup explains what remains. However,Zhao's (2007) model focuses on overall market trends rather thanprice dynamics of individual products.

4. Results

In this section we present and compare the results from estimatingthe BLP, BLPWP and GR models. As well as discussing estimates of thecoefficients, elasticities and market power, we also simulate twomergers and compare the predictions of the three models of themerger outcomes.

4.1. Estimates of the three models

Table 3 reports the estimated coefficients for the three demandmodels. The first two columns report the estimates for the BLP modelwith and without the age proxy. The third column reports estimatesfrom the GR model.

First we compare the coefficients on price and the characteristics.Examining the first two columns we see that unlike some of the otheranalyses of durable goods, the results for the BLP model and BLPWPmodel are basically plausible. However the coefficients on price inboth static models are substantially lower than that from the dynamicmodel. Both Gowrisankaran and Rysman (2009) and Conlon (2010)find a similar pattern of results across the static and dynamic models.This is in contrast to Chen et al. (2008) who compare estimates with

Table 1Sales and market share of the top six brands in the US P&S market.

Brand Observations Units Market share withinsix brands

Overall marketshare

Canon 924 8,508,226 25.91% 21.71%Sony 946 7,677,646 23.38% 19.59%Kodak 695 6,711,926 20.44% 17.13%Olympus 761 4,064,932 12.38% 10.37%Nikon 470 3,615,261 11.01% 9.23%Fujifilm 457 2,256,409 6.87% 5.76%Total 4253 32,834,400 100.00% 83.79%

Source: NPD Market Research Company. The reported sales for each brand is the sumover a 41-month period from January 2003 toMay 2006. The sales volume of the overallmarket is calculated upon observations of all P&S cameras by 46 brands listed in theoriginal dataset, which takes up above 80% of overall sales in the US market during thisperiod.

5 More details on data collection and statistics are provided in Lou et al. (2008)including a justification for choosing the top six brands for the analysis.

6 We treat seasonality differently to GR. Rather than seasonally adjusting the datawe include monthly dummies. While we agree that products purchased at Christmasare unlikely to have different functionality than those purchased at other times of theyear, it is likely that a different type of consumer is purchasing the product. Socontrolling for Christmas can be interpreted as controlling for consumer hetero-geneity. The results of Warner and Barsky (1995) provide some support for this.

7 There is a potential censoring problem with the age variable. However mostmodels live for no more than two years, and the number of longer lived models in thefinal period is relatively small and they make up a very small share of the market. Webelieve that the functional form of age is fairly well identified even at higher ages.

8 Though GR use camcorders, they used digital cameras in an early version of thepaper.

34 W. Lou et al. / Int. J. Ind. Organ. 30 (2012) 30–40

simulated data and find the opposite outcome. The industries (or thetechnique) seem to be behaving differently to that simulated andestimated in Chen et al. (2008).

As expected, the marginal values for product attributes such ascamera resolution, the size of LCD screen, and optical zoom range are allpositive but the weight of a camera is negative across the three models.Given the general trend in consumer electronics towards smallerdevices, it was expected that size would have a negative sign but theBLP model returns a significantly positive sign and the BLPWP and GRmodels yield estimates that are insignificantly different from zero. Itseems that theweightvariable is pickingup this effect. For the coefficienton digital zoom range, only the estimate for the BLPWP model has acorrect sign and is statistically significant while the estimates from theother two models have wrong signs although the estimate for the BLPmodel is insignificant. The age variable is unique to the BLPWP modeland its estimated coefficient has the expected sign and is statisticallysignificant. For those characteristics that tend to trend downwards (sizeand weight), introducing the age proxy tends to make their coefficientssubstantially closer to those of the GR model. For those characteristicsthat tend to trend upwards, the age proxy results in their coefficientsbeing further away from those of the GR model. This suggests that theageproxy,which tends to trenddownwards, controls for someaspects ofthe changing technological characteristics available to consumers. Theordering of the brand dummies from BLPWP is also much closer, thanthat from BLP, to that estimated for the GR model, with only one

difference, though in terms of size the result is mixed. The significantlynegative coefficient of Nikon brand dummy in the BLP model seemscounter-intuitive as Nikon is widely considered as a premium brandalthoughNikon is probablymore famous inprofessional cameramarketsthan in point-and-shoot camera markets.

Table 4 presents the results from estimating the pricing equationsfor the three models. The signs, significance and size are largely similaracross the threemodels, with only resolution in the BLP model and LCDin the BLPWPmodel being statistically insignificant. The positive valueson most characteristics imply that the higher the value for thesefeatures, themore costly it is forfirms toproduce a camera. The negativesign on the digital zoom may be picking up a more general qualitydifference between cameras with and without this feature. During oursample period most low-end and cheap cameras feature digital zoomrange but have no optical zoom options. The marginal cost of digitalcamera is negatively related to cameras' size, which suggests thatsmaller cameras can only be produced at a higher marginal cost. Theparameters associated with log weight are positive and significantlydifferent from zero. Thus, it is generallymore costly for firms to producecameras with more robust material and extra components, confirmingthat the weight signals some favored unobservable components orquality of a camera. Again, it is the coefficients on size and weight, aswell as optimal zoom, which are closer between the GR and BLPWPmodels than with the BLPmodel. More strikingly, while the ordering ofthe coefficients on thebranddummiesvaries across all threemodels, thecoefficients from the BLPWPmodel are substantially closer to that of theGR than the BLP model. This suggests that the BLPWP model is, to agreater extent, picking up the generally lower mark-ups in the digitalcamera market suggested by the results of the GR model. Finally, notethat all threemodels feature decliningmarginal costs over time and thatthe size of the decline is greater for the GR model. 9

While adding age improves the performance of the BLP model, wealso perform the non-nested Lavergne–Vuong specification testcomparing the BLPWP and GR models (Lavergne and Vuong, 1996).

9 We also attempted to estimate the BLP, BLPWP and GR models with a differentspecification for the utility function, emphasizing consumer heterogeneity in themarginal utility of product characteristics. We were unable to obtain estimates for theGR model but the BLP and BLPWP specifications differed to a greater extent than here,with BLPWP featuring less price-responsiveness consistent with Chen et al. (2008).These results are reported in Appendix A.

0

500

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ntity

'000

$220

$240

$260

$280

$300

$320

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Pric

e

Jan03 Jul03 Jan04 Jul04 Jan05 Jul05 Jan06 Jul06

Price (dollar) Quantity in thousand

Fig. 1. P&S sales volume and price of top six brands. Based on 4253 observations,covering all P&S cameras of top six brands (Canon, Fujifilm, Kodak, Nikon, Olympus andSony). The sales figures plotted are the monthly sum. The prices are sales weightedaverage prices in US dollars.

Table 2Product characteristics of P&S cameras.

Time Resolution(MP)

Opticalzoom

LCD(inch)

Size(inch3)

Weight(oz)

Age(months)

All observations4.20 3.03 1.80 14.77 6.80 8.31

Monthly observations200301 2.81 2.72 1.69 24.56 9.65 9.90200307 3.30 2.87 1.60 18.61 8.19 8.01200401 3.66 2.93 1.59 18.51 8.33 10.65200407 3.86 3.03 1.70 15.21 7.17 7.53200501 4.33 3.12 1.78 14.59 6.86 9.34200507 4.66 3.34 1.92 13.07 6.29 7.40200601 5.10 3.29 2.04 12.33 6.18 9.05200605 5.59 3.41 2.19 11.33 5.49 6.55

All statistics reported in the table are the means of the characteristics of productsweighted by their sales within each month.

$180

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e

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ntity

0 10 20 30 40

Average sales for each age group Price

Fig. 2. Average sales and prices at different ages. The age reported for each model isdetermined upon the actual first on-market date, not subject to the first-time observedsales in the dataset. The information regarding actual introduction date is obtainedfrom the internet; including firms' own websites and other public ones, e.g. www.dpreview.com. Only the top six brands of P&S cameras (4253 observations) arereported. The reported sales are the total sales volume at each age averaged by thenumber of models within each age group. The prices are the average prices of modelswithin each age group.

35W. Lou et al. / Int. J. Ind. Organ. 30 (2012) 30–40

With a test statistic of 19.82, we reject at 1% the null hypothesis thatthe twomodels have the same residual variance. The residual variancefrom the GRmodel is much lower suggesting that the GRmodel does amuch better job of explaining the data.

Summing up, all three models yield results that seem plausible.Compared to the static BLP model, some of the changes made in theBLPWPmodel, particularly on size andweight as well asmarginal costs,are in the right direction towards the dynamic GR model, suggestingthat it is partially effective in controlling for dynamic influences onconsumer choices.

4.2. Mark-ups and elasticities

In this sectionwe compare the elasticities andmarkups for the 143brands offered for sale in the last month of our sample, May 2006, asreported in Table 5.10 For the GR model we estimated the elasticity ofdemand in response to a permanent change in the price of therelevant good so to make it most directly comparable with theelasticities implied by the two static models. As implied by thecoefficients the estimates for the BLP and BLPWP models are moresimilar to each other than to those from the dynamic GR model.

The BLP model returns fairly low own-price elasticities of demandwhich imply markups between 81% and 94%. Unless product develop-ment and advertising costs are extremely high this suggests that there isvery substantial market power in this market which is not immediatelyplausible. The BLPWP model returns somewhat better results withmuch lowermarkups starting from61%. Bothmodels, however, as is thecase for other applications of theBLPmodel, return fairly lowcross-priceelasticities of demand. The very low results heremay also be due in partto the limited randomness of demand permitted by the model.11 Both

own and cross price elasticities of demand are higher for the BLPWPmodel and there is a greater range of markups which seems moreplausible.

In comparison, the GR model returns own-price elasticities ofdemand of around 3.4% and markups of around 32%. Though stillsubstantial, these results are much more similar to estimates ofmarket power in other papers. The cross-price elasticities of demandalso tend to be higher than their counterparts from the BLP andBLPWP models. The only perturbing feature of the results for theGR model is how small the dispersion of the own-price elasticitiesand therefore the implied difference of markups across brands.While the prices of the 143 digital cameras in our sample lie be-tween $89 and $501, one might still expect greater variation in mark-ups between very cheap cameras and more expensive ones. Inthis regard, the larger dispersion implied by the BLPWP seems morereasonable.

As highlighted in Section 2 one focus of theoretical work ondurable goods, as well as the empirical work of Zhao (2007) has beenwhether firms can engage in intertemporal price discrimination orwhether the Coase conjecture applies. In Fig. 3, we report the relativemarkups over the life of the top-selling products of six top brands. Byrelative, we mean the markup relative to the markup in the firstmonth, e.g. a relative markup of −50% in month 10 means themarkup in month 10 is 50% of the markup in month 1. There are twoimportant results from this figure. First, for all six products, therelative markups, estimated from all three models, decline substan-tially and fairly uniformly over their lives, consistent with eitherintertemporal price discrimination or intensifying competition.Second, the relative markups all decline in a very similar way acrossthe threemodels. To a certain extent this was anticipated by the resultthat the time trend in the pricing equationwas fairly similar across thethree models. In none of the cases was the decline in costs so large asto explain all of the decline in prices.

4.3. Merger simulation

As the final stage of our comparison between the three approachesto modeling demand we simulate two mergers. The first merger is

10 All markups are calculated as the ratio of the difference between price andmarginal cost compared with price.11 With an alternative utility function, as reported in footnote 9, the BLPWP modelyielded lower elasticities and greater markups than the BLP model. Both modelsfeatured greater elasticities and lower markups than the results in this section. Therewas also considerable dispersion in markups. This may have been due to includingmore random coefficients as well as a different utility function. Because we could notestimate a matching GR model we cannot determine if the differences between thetwo sets of models are smaller. This is discussed in more detail in the appendix.

Table 3Demand equations for three models.

Variable BLP model BLPWP model GR model§

Parameter estimate Standard error Parameter estimate Standard error Parameter estimate Standard error

Mean price −2.610⁎⁎⁎,⁎⁎,⁎ 0.124 −2.878⁎⁎⁎ 0.276 −4.402⁎⁎⁎ 0.315Random price 0.802⁎⁎⁎ 0.062 1.006⁎⁎⁎ 0.135 0.037⁎⁎⁎ 0.010Resolution 2.480⁎⁎⁎ 0.089 0.962⁎⁎⁎ 0.113 4.378⁎⁎⁎ 0.159LCD 1.443⁎⁎⁎ 0.162 0.906⁎⁎⁎ 0.161 2.184⁎⁎⁎ 0.094Opt. zoom 1.528⁎⁎⁎ 0.075 0.997⁎⁎⁎ 0.075 3.763⁎⁎⁎ 0.193Size 1.376⁎⁎⁎ 0.120 0.073 0.122 −0.027 0.175Weight −3.869⁎⁎⁎ 0.208 −0.589⁎⁎⁎ 0.228 −1.378⁎⁎⁎ 0.359Dig. zoom −0.323 0.247 0.907⁎⁎⁎ 0.200 −1.296⁎⁎⁎ 0.281Age −0.956⁎⁎⁎ 0.058Random age 0.416⁎⁎⁎ 0.148Nikon −0.581⁎⁎⁎ 0.083 −0.092 0.080 0.093 0.103Sony 0.869⁎⁎⁎ 0.067 0.577⁎⁎⁎ 0.064 0.821⁎⁎⁎ 0.080Canon 0.491⁎⁎⁎ 0.057 0.239⁎⁎⁎ 0.057 0.723⁎⁎⁎ 0.064Olympus −0.624⁎⁎⁎ 0.060 −0.364⁎⁎⁎ 0.058 −0.519⁎⁎⁎ 0.074Kodak −0.200⁎⁎⁎ 0.069 −0.212⁎⁎⁎ 0.067 −0.568⁎⁎⁎ 0.083Fujifilm −0.852⁎⁎⁎ 0.076 −0.655⁎⁎⁎ 0.077 −1.530⁎⁎⁎ 0.085Trend −0.113 0.089 −0.065 0.161Constant 2.272⁎⁎⁎ 0.417 −6.226⁎⁎⁎ 0.981 1.090 1.683Random constant 0.472 0.501 4.834⁎⁎⁎ 0.896 9.932⁎⁎⁎ 0.456

§ Note, all coefficients, except for those on price and its standard deviation, are scaled up by 100 times for comparability with the static models. See Gowrisankaran and Rysman(2009) for more details.

⁎⁎⁎ Denotes the 1% significance level.⁎⁎ Denotes the 5% significance level.⁎ Denotes the 10% significance level.

36 W. Lou et al. / Int. J. Ind. Organ. 30 (2012) 30–40

between two of the smaller sellers of the top six in the point-and-shoot camera market, Fujifilm and Nikon. Hence a merger betweenthem is less likely to be immediately rejected by an anti-trustauthority. However, in combination they make up a significant shareof low to mid priced cameras so a merger has potential consequencesfor market power in these segments of themarket. The secondmergeris between the two largest firms, Sony and Canon, and is much lesslikely to be approved by an anti-trust authority without substantialdivestitures. However, it is useful for demonstrating the influences onoutcomes.

The sample used for the analysis is the last month of our data, May2006. To assist with understanding we divide the cameras by pricesand show the share of sales of the top six for each firm within eachgroup in Table 6. The market has several features. First there are alarge number of small brands. The largest market share for a model isfor one sold by Canon (5.85%). However, the top four models acrossthe brands make up just under 20% of the market and the top 16makeup just under 50% of sales leaving 127 much smaller models makingup the rest of themarket. Second, the top six firms compete for sales ofcameras between $100 and $300 which make up most of the sales.Canon tends to have the largest market share of cameras priced $300ormore. Sony has also a substantial share in this segment and the nextsegment below this. Kodak has the largest share in cheap cameras(below $100).

We performed the analysis in two steps. First, we used the modelsreported in Section 4.1 to predict quantities and prices before themerger. In all cases, the predicted values were very close to the actual

values. The post-merger prices and quantities were obtained byreassigning the ownership of the brands of the two mergedcompanies to a single company in the matrix Δ(pt,xt,ξ) and re-simulating the model to yield predicted prices and quantities. For theFujifilm–Nikon merger we calculated 95% confidence bounds on thepredicted prices in three steps. First we generated 50 sets ofcoefficients for the BLP and BLPWP models, and 55 sets for the GRmodel, each drawn from a normal distribution with the estimatedmean and standard deviation from the model. Second, for each set ofcoefficients, we re-simulated prices and quantities before and afterthemerger. Third, we estimatedmeans and standard deviations of thepredicted prices from the 50 (or 55) sets of prices and calculated their95% confidence intervals.

To address the precision with which we estimate the post-mergerprices, we limit our analysis to the Fujifilm andNikonmerger to avoidunnecessary duplication. In Table 7 we report the mean, standarddeviation and confidence intervals for the most and least expensivemodel from Fujifilm and Nikon for each of the three models. First, wenote that there are no large differences between the predicted pricesacross the three specifications. This is mainly because, as will beshownmore extensively in Table 8, the merger does not lead to largeprice changes in any of the specifications. The largest price increasesare recorded for the BLPWP model and the smallest price increasesare recorded for the GRmodel. Second, we note that the estimates forthe GRmodel have the tightest confidence intervals and the estimatefor the BLPWP model has the broadest confidence intervals.However, the confidence intervals are nested within each other, sothe broadest interval contains the confidence intervals for the othertwo specifications.

In Table 8 we report the average percentage changes in price andquantity following the Fujifilm–Nikon and Canon–Sony mergers. Wedo not report the changes for other brands as these are typicallyrelatively very small. First, note that all proportional price changes aresmall when compared with the SSNIP (small but significant non-transitory increase in price) criterion of 5% as suggested in the 2010Department of Justice Merger Guidelines for defining productmarkets. Across the models, the BLPWP model returns the largestaverage price and quantity changes through the Fujifilm–Nikonmerger, followed by the BLP model, and the GR model returns thesmallest average changes. In general the response in the GR model isabout 10% of the response in the static models. All threemodels reportgreater average responses, in similar proportions, from Fujifilm thanfrom Nikon. This probably reflects that Fujifilm is quite a bit smallerthan Nikon so removing Nikon's competition has a greater effect on itspricing than removing Fujifilm on Nikon's pricing. The fact that otherfirms do not change their prices or quantities very much is alsoconsistent with this. The merger does not matter that much for the

Table 4Pricing equations for three models.

Variable BLP model BLPWP model GR model

Parameter estimates Standard error Parameter estimates Standard error Parameter estimates Standard error

Ln (resolution) 0.360 0.437 0.259⁎⁎ 0.113 0.686⁎⁎⁎ 0.021Ln(LCD) 0.228⁎⁎⁎ 0.034 0.245 0.982 0.221⁎⁎⁎ 0.012Opt. zoom 0.063⁎⁎⁎ 0.021 0.085⁎⁎⁎ 0.023 0.534⁎⁎⁎ 0.025Ln(size) −0.411⁎⁎⁎ 0.051 −0.321⁎⁎⁎ 0.053 −0.279⁎⁎⁎ 0.020Ln(weight) 0.762⁎⁎⁎ 0.112 0.667⁎⁎⁎ 0.108 0.573⁎⁎⁎ 0.037Dig. zoom −0.239⁎⁎⁎ 0.034 −0.214⁎⁎⁎ 0.036 −0.529⁎⁎⁎ 0.034Trend −0.012⁎⁎⁎ 0.001 −0.011⁎⁎⁎ 0.001 −0.025⁎⁎⁎ 0.001Canon 1.688⁎⁎⁎ 0.216 2.827⁎⁎⁎ 0.297 3.843⁎⁎⁎ 0.065Fujifilm 1.842⁎⁎⁎ 0.184 2.861⁎⁎⁎ 0.267 3.644⁎⁎⁎ 0.059Kodak 1.750⁎⁎⁎ 0.193 2.785⁎⁎⁎ 0.275 3.651⁎⁎⁎ 0.059Nikon 1.985⁎⁎⁎ 0.185 3.028⁎⁎⁎ 0.268 3.936⁎⁎⁎ 0.056Olympus 1.852⁎⁎⁎ 0.191 2.901⁎⁎⁎ 0.272 3.767⁎⁎⁎ 0.057Sony 1.570⁎⁎⁎ 0.222 2.745⁎⁎⁎ 0.304 3.734⁎⁎⁎ 0.065

⁎⁎⁎ Denotes significant at the 1% level.⁎⁎ Denotes the 5% significance level.

Table 5Mark-ups and elasticities.

Mean Standard deviation Minimum Maximum

BLP modelOwn price elasticity −1.160 0.034 −1.103 −1.256Maximum crossprice elasticity

0.0094 0.0032 0.0035 0.0223

Markup 0.880 0.027 0.806 0.935

BLPWP modelOwn price elasticity −1.443 0.108 −1.2264 −1.699Maximum crossprice elasticity

0.0183 0.0056 0.0086 0.0392

Markup 0.720 0.054 0.606 0.854

GR modelOwn price elasticity −3.418 0.006 −3.387 −3.425Maximum crossprice elasticity

0.0563 0.0029 0.047 0.061

Markup 0.320 0.001 0.318 0.322

37W. Lou et al. / Int. J. Ind. Organ. 30 (2012) 30–40

market. Finally note that Fujifilm has little relative variation in theproportional responses compared with Nikon. This pattern of resultsis very similar to those found in Table 5 in Nevo (2000) — smallchanges for firms not involved in mergers, and much larger changesfor the smaller partners in a merger. Nevo (2000) tends to find muchlarger changes though.

To check whether the small magnitudes of changes in the mergerwere a result of merging two of the smaller firms, we also simulated amerger between the two largest firms, Canon and Sony. We againreport the results by the five price groups. The first thing we notice isthat as expected in all cases the effects of the merger are much largercompared with the results for the Fujifilm–Nikon merger. However,

Table 6Actual market shares by firm and by price group.

Number of models Share of best sellingmodel by brand

Share in thetop 6 brands

Share of price group within top 6 brands

b$100 $100–$200 $200–$300 $300–$400 N$400

Canon 31 5.85 31.0 15.5 19.7 31.5 53.8 58.0Fujifilm 14 1.76 5.2 0 9.2 2.4 2.3 0Kodak 28 1.75 15.1 77.2 23.0 11.0 1.5 0Nikon 18 4.37 14.6 0 24.4 5.1 13.5 0Olympus 24 2.07 11.6 7.3 14.2 10.9 9.8 1.4Sony 28 3.36 22.5 0 9.5 39.1 19.1 40.6Total 143 100 100 100 100 100 100Price group share oftotal sales

1.4 43.5 34.0 16.4 4.7

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0 5 10 15 20 25 0 5 10 15 20 25

CANON POWERSHOTA520 FUJIFILM FINEPIXA345

KODAK CX7430 NIKON COOLPIX3200

OLYMPUS D540 SONY DSCP72

GR BLP with Proxy BLP

age

Fig. 3. Relative markups over time for six top selling models. Note: The horizontal axis measures the number of months since the camera was first introduced into the market. Thevertical axis is the ratio of themarkup inmonth t to themarkup inmonth 0. For example, for the Olympus D540 inmonth 25 the BLPmodel estimates that markup was just 55% of themarkup when it was introduced.

38 W. Lou et al. / Int. J. Ind. Organ. 30 (2012) 30–40

there is a similar pattern of differences across the three models. TheBLPWP model returns the largest changes, followed by the BLP modeland the GR model.

Because Sony is larger in some submarkets and Canon larger inothers we report average changes across different submarkets to see ifthe quantity and price responses vary. In all except one of thesubmarkets, the three specifications return the same ranking of priceand quantity changes; the exception occurs in the one submarketwhereSony andCanonhave a similarmarket share. In general, as the smaller ofthe two firms, Sony returns the largest proportional increases in priceand decreases in quantity, except for the submarket of $300–$400.Indeed, for all of the mid-range segments in the BLPWP model theaverage price increases are substantial, ranging between 4.6% and 8.2%.It is interesting tonote that Sony's proportional price increases get largeras the market segment moves from more expensive to cheaper. Apossible explanation for this lies in the fact that before themerger, Sonyhad a very small share of the market below $200. This could haverestrained them from raising prices and losing business to other firms.After the merger, the merged firm has a larger share in the lower pricemarkets,whichwould havemade itmoreprofitable for cameras bearingthe Sony brand to have higher prices, because themerged company canpartially internalize the lost sales. Because Canon already had a

reasonable share of the low-price market, the effect on Canon wouldbe less significant as the results demonstrate.

In both mergers the BLP and BLPWP models yield results that aremore similar to each other than to the GR model. For the Fujifilm–

Nikonmerger all models suggest that any price effects would be small.For the merger between the two largest firms, Canon and Sony, theBLPWP and, to a lesser extent, BLP models do predict substantial (ifnot large across the board) price increases, which although theMerger Guidelines do not specify an upper bound on price effects fortoleratingmergers, would still be more likely to attract interest than ifthe predictions from the GR model were used.

5. Concluding remarks

While BLP style models have yielded satisfactory estimates in stableoligopolies like cars and breakfast cereals, they have yielded lesssatisfactory estimates in markets, like consumer electronics, wherethere are rapid technological changes and falling prices. A small set ofpapers, including GR has specified and estimated structural dynamicdemand models. It remains an open question though as to what is thegeneral effect of introducing dynamics into empirical oligopoly models.In this paperwe analyze theUS digital cameramarket using the BLP andGR models. In addition, we propose a semi-parametric approach toestimating the GR model and take a first step in implementing it byincluding an age proxy in the BLP model. While all three models yieldinitially plausible results the dynamic model suggests that demand ismore elastic and that the industry features lowermarkups.12 This resultis inconsistent with the predictions of the simulation analysis of Chenet al. (2008) although it is consistent with the results of econometricanalyses by GR and Conlon (2010). In general the markups implied bythe dynamic model seem more plausible. However, all three modelsyield declining markups over the products life consistent withintertemporal price discrimination and inconsistent with the Coaseconjecture. We also perform two merger simulations of two smallsellers in the top six brands, Nikon and Fujifilm, and two large firms,Sony and Canon. The BLP and BLPWP models tend to yield similarresults to each other, whereas the GR model implies the smallest priceincreases from each merger.

Despite the greater computational demands the evidence from theUS digital camera industry is that introducing dynamics as illustrated bythe GR model does make a difference. The dynamic GR model suggeststhat demand is more elastic, the market is more competitive andmergers have lower price increases than suggested by the staticeconometric models. Furthermore, some of the results from using anage proxy are suggestive that a semi-parametric approach may enablean analysis closer to a full dynamic analysis with less computationaldemands, particularly as it is possible that the conditions that createproblems for the static models are less acute in this particular case.

Appendix A. Estimates of the BLP and BLPWP with alternativeutility function

In order to analyze the robustness of our conclusions, we alsoattempted to estimate all three models using the same utility functionused in BLPwith price entering asαln(y−p) and random coefficients ofproduct characteristics, where y is household income. However, wewere not able to estimate the GRmodel with this utility function as theestimation routine failed to converge. Hence, we cannot state whether

12 Other results, including those reported in the appendix, from estimating the BLPand BLPWP models suggest that introducing more random coefficients may increasethe demand elasticities and reduce the markups but we were unable to obtainmatching results for the GR model to determine the relationship of these results to theGR model. This is discussed in more detail in the appendix.

Table 8Average price and quantity changes following two mergers.

BLP model BLPWP model GR model

Price Quantity Price Quantity Price Quantity

Fujifilm–Nikon merger (standard errors in parentheses)Fujifilm 1.534

(0.103)−1.747(0.072)

2.154(0.240)

−3.024(0.139)

0.148(0.002)

−0.632(0.010)

Nikon 0.420(0.133)

−0.463(0.164)

0.586(0.185)

−0.773(0.309)

0.039(0.015)

−0.155(0.065)

Canon–Sony mergerPre merger price $400 or more

Canon 3.008 −2.964 4.011 −4.295 0.276 −0.990Sony 2.519 −2.451 3.646 −3.792 0.203 −0.672

Pre merger price between $300 and $400Canon 2.895 −2.902 4.202 −4.594 0.278 −0.998Sony 3.199 −3.217 4.607 −5.123 0.269 −0.959

Pre merger price between $200 and $300Canon 2.792 −2.843 3.645 −4.289 0.270 −0.964Sony 4.326 −4.486 5.624 −6.872 0.377 −1.427

Pre merger price between $100 and $200Canon 2.536 −2.686 3.386 −4.252 0.272 −0.980Sony 6.450 −6.874 8.156 −10.661 0.616 −2.459

Pre merger price less than $100Canon 2.322 −2.545 2.930 −3.958 0.279 −1.024

Note: All changes are proportional.

Table 7Precision of estimates of predicted prices.

Mean Standard Deviation 95% Confidence Interval

BLP modelFuji FinePix E500 102.80 12.74 [77.84, 127.77]Fuji FinePix E900 355.23 51.46 [254.37, 456.09]Nikon CoolPix 4600 113.88 15.13 [84.22, 143.54]Nikon CoolPix P3 378.72 57.27 [266.47, 490.97]

BLPWP modelFuji FinePix E500 106.12 16.68 [73.42, 138.81]Fuji FinePix E900 367.17 90.58 [189.64, 544.70]Nikon CoolPix 4600 116.20 19.48 [78.03, 154.37]Nikon CoolPix P3 380.45 98.63 [187.13, 573.76]

GR modelFuji FinePix E500 102.58 0.03 [102.51, 102.64]Fuji FinePix E900 352.99 0.10 [352.79, 353.19]Nikon CoolPix 4600 113.18 0.04 [113.11, 113.26]Nikon CoolPix P3 374.93 0.08 [374.78, 375.07]

39W. Lou et al. / Int. J. Ind. Organ. 30 (2012) 30–40

the BLP or BLPWPmodelswith this utility function yield results closer tothe dynamicmodel through a comparison similar to that for Tables 3–5.It is possible that the BLP model is closer to the GR model than theBLPWPmodel. Nevertheless, we report themain results for the demandand pricing equations for BLP and BLPWP models in Tables A.1 and A.2

because they are somewhat different and consistent with the pre-dictions of Chen et al. (2008). First, note that the price responsiveness ofdemand is much lower in the BLPWP model than in the BLP model.Furthermore, though while most coefficients in the BLPWP model arerelatively smaller again it is the coefficients on size and weight thatchangemost substantially. It is also worth noting that the coefficient onthe random component of size is statistically significant in bothmodels,suggesting that it may be preferable to allow for more consumerheterogeneity when estimating the GR model. The brand coefficientsfrom the supply equation estimated for the BLPWPmodel are relativelysmall consistent with the lower price coefficient.

Looking at the elasticities, we note two features. First, the estimatesof demand elasticities from the BLPWPmodel are lower than those fromthe BLP model as are the cross-price elasticities. Second, the range ofelasticities calculated for both models is also, plausibly, much greaterthan in the text. However, both models include a few own-priceelasticities less than one. Both models predict declining markups overtime, consistent with intertemporal price discrimination, and the rangeofmarkups is also greater than in themodels in the text. It should alsobenoted that bothmodels suggest thatmarginal cost is decliningover time.See Lou et al. (2008) for a complete set of results and more discussion.

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Table A.1The BLP and BLPWP demand models with alternative utility function and a full set ofrandom coefficients.

Variable Parameterestimate

Standarderror

Parameterestimate

Standarderror

BLP BLPWP

Alpha: term on priceln(y−p) 0.671⁎⁎⁎ (0.070) 0.324⁎⁎ (0.116)

Beta: mean coefficientConstant −8.084⁎⁎⁎ (0.628) −7.428⁎⁎⁎ (0.596)Resolution 0.797⁎⁎⁎ (0.067) 0.383⁎⁎⁎ (0.119)LCD 0.504 (0.431) 0.247⁎⁎ (0.143)Opt. zoom 0.413⁎⁎⁎ (0.020) 0.249⁎⁎⁎ (0.030)Size 0.093 (0.123) −0.258⁎⁎⁎ (0.125)Weight −0.280⁎⁎⁎ (0.033) 0.023 (0.062)Dig. zoom 1.486⁎⁎⁎ (0.314) 1.523⁎⁎⁎ (0.574)Age −0.225⁎⁎⁎ (0.013)Sony 0.729⁎⁎⁎ (0.065) 0.528⁎⁎⁎ (0.063)Canon 0.520⁎⁎⁎ (0.057) 0.240⁎⁎⁎ (0.062)Nikon −0.120 (0.082) 0.098 (0.086)Olympus −0.500⁎⁎⁎ (0.060) −0.232⁎⁎⁎ (0.057)Kodak −0.264⁎⁎⁎ (0.069) −0.307⁎⁎⁎ (0.071)Fujifilm −1.202⁎⁎⁎ (0.080) −0.826⁎⁎⁎ (0.088)

Sigma: standard deviation on beta coefficientsConstant 0.838 (0.666) 0.842 (1.105)Resolution 0.066 (0.150) 0.037 (0.362)LCD 1.020⁎⁎⁎ (0.303) 0.292 (0.203)Opt. zoom 0.026 (0.052) 0.005 (0.099)Size 0.246⁎⁎⁎ (0.070) 0.181⁎ (0.104)Weight 0.023 (0.023) 0.077 (0.053)Dig. zoom 0.917 (1.015) 1.524⁎⁎⁎ (0.502)Age 0.095⁎⁎⁎ (0.006)

⁎⁎ Denotes the 5% significance level.⁎⁎⁎ Denotes significant at the 1% level.

Table A.2The BLP and BLPWP pricing equations, elasticities and markups with alternative utilityfunction and a full set of random coefficients.

Variable Parameterestimate

Standarderror

Parameterestimate

Standarderror

BLP BLPWP

Pricing equationTrend −0.020⁎⁎⁎,⁎⁎ (0.001) −0.012⁎⁎⁎ (0.002)Canon 3.007⁎⁎⁎ (0.120) 1.774⁎⁎⁎ (0.213)Fujifilm 2.956⁎⁎⁎ (0.118) 1.795⁎⁎⁎ (0.210)Kodak 2.929⁎⁎⁎ (0.116) 1.716⁎⁎⁎ (0.213)Nikon 3.272⁎⁎⁎ (0.111) 2.147⁎⁎⁎ (0.201)Olympus 3.067⁎⁎⁎ (0.115) 1.911⁎⁎⁎ (0.212)Sony 2.867⁎⁎⁎ (0.124) 1.683⁎⁎⁎ (0.222)Ln(resolution) 0.649⁎⁎⁎ (0.032) 0.433⁎⁎⁎ (0.096)Ln(LCD) 0.611⁎⁎⁎ (0.056) 0.419⁎⁎⁎ (0.046)Opt. zoom 0.047⁎⁎⁎ (0.007) 0.019⁎⁎⁎ (0.008)Ln(size) −0.567⁎⁎⁎ (0.030) −0.660⁎⁎⁎ (0.039)Ln(weight) 0.960⁎⁎⁎ (0.059) 1.423⁎⁎⁎ (0.079)Dig. zoom −0.485⁎⁎⁎ (0.077) −0.011 (0.162)

Elasticities Average Maximum–

minimumAverage Maximum–

minimumOwn-price −3.531 −0.425 to

−12.347−2.581 −0.438 to

−8.904Maximumcross-price

0.312 0.285

Markups 0.426 0.345–0.679 0.552 0.348–0.700

⁎⁎ Denotes the 5% significance level.⁎⁎⁎ Denotes significant at the 1% level.

40 W. Lou et al. / Int. J. Ind. Organ. 30 (2012) 30–40