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Essays on product trade-ins: Implications for consumer demand and retailer behavior

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Essays on product trade-ins: Implications for consumer demand and retailer behavior

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Content ESSAYS ON PRODUCT TRADE-INS: IMPLICATIONS FOR CONSUMER DEMAND AND RETAILER BEHAVIOR by Ohjin Kwon A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful¯llment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (BUSINESS ADMINISTRATION) May 2010 Copyright 2010 Ohjin Kwon Acknowledgements I would like to express my deepest gratitude to Professor Siddarth, my doctoral advisor,forhisinvaluableguidancewithoutwhichIcouldnothaveachievedwhat I was able to do in the doctoral program. It was my great honor and privilege to walkwithhimthroughoutthejourney. IcannotthankProfessorDukesenoughfor providing me with outstanding research advice as well as supportive mentoring. I also would like to thank Professor Luo and Professor Hsiao who have always been willing to provide me with excellent guidance for my research. My special thanks are reserved for my wife, Bohee, my parents, parents-in- law, brother, and sister for their unswerving trust in me. They did not stop encouraging me regardless of my situation. Finally, this statement would not be complete without acknowledging my fellow students in the doctoral program at Marshall School of Business. I shall not forget their support and encouragement. ii Table of Contents Acknowledgements ii List of Tables v List of Figures vi Abstract vii Chapter 1: Does a Consumer's Previous Purchase Predict Other Consumers' Choices? A Bayesian Probit Model with Spatial Correlation in Preference and Response 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Spatial Weight Matrix . . . . . . . . . . . . . . . . . . . . 6 1.2.1.1 Geographic Location . . . . . . . . . . . . . . . . 7 1.2.1.2 Previous Vehicle . . . . . . . . . . . . . . . . . . 8 1.2.2 Model Speci¯cation . . . . . . . . . . . . . . . . . . . . . . 9 1.2.2.1 Bayesian Preference Correlation Probit Model . . 10 1.2.2.2 Bayesian Response Correlation Probit Model . . 12 1.2.2.3 BayesianPreferenceandResponseCorrelationPro- bit Model . . . . . . . . . . . . . . . . . . . . . . 14 1.3 Data and Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.2 Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.4.1 Estimation Results . . . . . . . . . . . . . . . . . . . . . . 19 1.4.2 Demand Prediction in Other Markets . . . . . . . . . . . . 24 1.4.3 Elasticity Analysis . . . . . . . . . . . . . . . . . . . . . . 29 iii 1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Chapter 2: The Informational Role of Product Trade-Ins for Re- tailer Pricing 35 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.2 Theoretical Model of Retailer Pricing with Trade-Ins . . . . . . . 40 2.3 An Empirical Test of the Predictions from the Theoretical Model 47 2.3.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.3.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.3.3 Estimation Results . . . . . . . . . . . . . . . . . . . . . . 53 2.4 Automobile Choice Model with Trade-Ins . . . . . . . . . . . . . . 55 2.4.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.4.2 Model Estimation . . . . . . . . . . . . . . . . . . . . . . . 60 2.4.3 Estimation Results . . . . . . . . . . . . . . . . . . . . . . 62 2.4.4 Counterfactual Analysis . . . . . . . . . . . . . . . . . . . 62 2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Bibliography 70 Appendices 74 A MCMC Estimation for BPRCP Model . . . . . . . . . . . . . . . 75 A.1 Prior Speci¯cations . . . . . . . . . . . . . . . . . . . . . . 75 A.2 Conditional Posteriors . . . . . . . . . . . . . . . . . . . . 75 B Simulated Data Analysis of a BPRCP Model . . . . . . . . . . . . 79 C First Order Condition Derivation . . . . . . . . . . . . . . . . . . 82 D Proofs of Propositions . . . . . . . . . . . . . . . . . . . . . . . . 83 D.1 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . 83 D.2 Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . 84 E Dealer Pricing Based on Trade-In Information When Consumers Are Myopic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 iv List of Tables 1.1 Descriptive Statistics of the Data . . . . . . . . . . . . . . . . . . 17 1.2 Estimated Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.3 Parameter Estimates and Model Fit Statistics . . . . . . . . . . . 23 1.4 Demand Prediction in Other Markets . . . . . . . . . . . . . . . . 26 1.5 Demand Predictive Performance [MAD] in Other Markets . . . . 28 1.6 Own Price Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.1 Descriptive Statistics of Vehicle Models . . . . . . . . . . . . . . . 51 2.2 Summary Statistics of Hedonic Regression Model Variables . . . . 54 2.3 Hedonic Regression Estimation Results . . . . . . . . . . . . . . . 56 2.4 Choice Model Estimation Results . . . . . . . . . . . . . . . . . . 63 2.5 Percentage Change in Market Share . . . . . . . . . . . . . . . . . 65 2.6 Percentage Change in Revenue . . . . . . . . . . . . . . . . . . . . 66 v List of Figures 2.1 The Impact of Trade-in Similarity (t<t 0 ) on Equilibrium Price . 45 2.2 The Impact of Trade-in Event on Equilibrium Price . . . . . . . . 48 3 Posterior Distributions of ¯ 1 and ¯ 2 . . . . . . . . . . . . . . . . . 89 4 Histograms of Posterior Estimates of Ã 2 1 , Ã 2 2 , and ½ . . . . . . . . 90 vi Abstract Mydissertationresearchexaminesimplicationsofproducttrade-insforconsumer demandandretailerpricingbehavior. Althoughproducttrade-insareverypreva- lent in many durable goods markets, such as golf clubs, home appliances, and automobiles, there has been relatively little academic research examining this phenomenon. I examine how information provided by consumers' previous pur- chases can be leveraged to predict their future choices and its implications for retailer pricing decisions. In the ¯rst chapter, I propose a spatial autoregressive multinomial probit model in which the preferences and marketing mix responsiveness of di®erent consumers depend upon their relative proximity to each other. Unlike previous applications of spatial models in marketing that have focused on the impact of geographical proximity between consumers, I develop a contiguity metric which accounts for the similarity between consumer's previous purchases. I demon- strate that information about a consumer's previous purchase can be harnessed to predict the choices of other consumers for other products as well as simply to improve choice predictions of the same consumer for the same product, known in the marketing literature as structural state dependence. vii Iestimatetheproposedmodelusingtransactiondatafornewcarpurchasesin the midsize sedan market. The proposed model outperforms the commonly used random coe±cient probit model as well as other spatial models that are based solely on the geographic closeness between consumers or that only incorporate preference or response correlation individually, but not together. I show the spa- tial correlations in one market may be used to yield more accurate predictions of consumer demand in other markets. I also show that ignoring spatial correla- tion based on previous vehicle similarity is found to underestimate the elasticity di®erences between brand-loyal consumers and switchers. Building on this idea, in the second chapter, I investigate how retailers in- corporate consumer trade-in information in their pricing of new products, and test it in a ¯eld setting. First, I develop an analytical model of the phenomenon, and use it to derive the optimal new car prices with and without trade-in infor- mation. Second, I test the predictions of my theoretical model by estimating a hedonic regression model of new car prices obtained from transaction data in the midsize sedan market. Finally, I develop and estimate a structural choice model and conduct a series of counterfactual analysis to quantify the bene¯t of trade-in information to the dealer. The unique equilibrium solution of my theoretical model suggests that retail- ers charge a premium on new car when consumers trade in their used cars and that the premiums are even higher if the traded in vehicle is more similar to the new one. My empirical analysis supports my theory by showing that consumers who traded-in a used vehicle paid a higher price for the same new car than those viii who did not. Further, those consumers who traded in used cars that were of the same make and model of the new vehicle paid an even higher premium on their new car purchase. The structural model estimation results and counterfactual analysis show that price discrimination based on consumer trade-in information reduces market share but increases retailer pro¯ts because retailers end up leav- inglessmoneyonthetable. Thisdemonstratesthatthebetterinformationabout consumer preferences provided by trade-ins substantially impacts dealer pro¯ts. ix Chapter 1 Does a Consumer's Previous Purchase Predict Other Consumers' Choices? A Bayesian Probit Model with Spatial Correlation in Preference and Response 1.1 Introduction A vast literature in marketing has shown that a consumer exhibits an increased likelihood of re-purchasing an alternative that he or she has previously pur- chased. This phenomenon, termed structural state-dependence (e.g., Erdem, 1996;Seetharamanetal.,1999),linksaconsumer'spastpurchasestohisorherfu- turechoicesofthesameproduct. Inaddition,thenotionthatpastpurchasesmay also provide information about unobserved factors that a®ect consumer decision making has been relatively under-explored in marketing. For example, product purchasesmayrepresentspeci¯cvaluesthatconsumersseek(ReynoldsandJolly, 1 1980; Sheth et al., 1991), re°ect the self-image of the consumer (Sirgy, 1982), or convey some aspect of whom they want to be (Escalas and Bettman, 2003), es- pecially when these purchases are in publicly consumed product categories such as automobiles (Bourne, 1957; Grae®, 1988). Forasingleconsumermakingmultiplechoices,theimpactofsuchunobserved factors has sometimes been termed habit persistence in the choice modeling lit- erature, manifesting as serially correlated error terms in an individual's utility function (Roy et al., 1996). If the underlying factors that drive habit persistence for an individual consumer also impact other consumers in a similar fashion, or equivalently,ifdi®erentconsumerssharethesameunobservedfactors,thenutility canalsobecorrelatedacross consumers. Buildingonthisidea,Iproposeaspatial choice model that explicitly incorporates the correlation in consumer preferences and marketing mix responsiveness based upon their relative proximity. Spatial models provide a natural way to model the correlation between dif- ferent units of analysis based on how close they are to each other. In its most basic form, the model uses the spatial locations of these units on a map, or more precisely, the resulting proximity between them, to infer the correlation between them. Most previous applications of spatial models have focused on geographic contiguity. For example, LeSage (2003) develops a linear regression model which shows that house values in a particular region are negatively correlated with the crime rates in adjacent areas. In marketing, such models have been used to explain how brand shares in di®erent markets are correlated (Bronnenberg and Sismeiro, 2002; Bronnenberg and Mela, 2004) and to demonstrate how aisle 2 placement in a particular store can moderate the impact of a particular brand in one category on sales of the brand in a di®erent category (Bezawada et al., 2009). Duan and Mela (2009) ¯nd that housing prices are correlated based on apartment outlets' geographic location. Bronnenberg and Mahajan (2001) and van Dijk et al. (2004) show that explicitly modeling spatial correlation in retailer sales may attenuate bias due to endogeneity in estimating the impact of promo- tional variables on market share or sales. Mittal et al. (2004) and Hofstede et al. (2002) use survey data and the geographical contiguity between regions in which respondentslivetomodelthesimilarityintheirattitudestowardstoreimageand product quality, respectively. There has been relatively little research that examines spatial correlation in a discrete choice setting. Jank and Kannan (2005) use experimental data to esti- matealogitmodelofconsumerchoiceofproductforms-printorPDF-inwhich preferences and price sensitivities are spatially correlated across geographic re- gions. YangandAllenby(2003)estimateabinarychoicemodelinwhichconsumer preferencesforJapanesecarsarespatiallycorrelatedbasedonthegeographicdis- tance and demographic similarity between individual consumers. My proposed model adds to the existing literature in several important ways. First, in addition to spatial correlation in consumer preferences, my model also incorporates the spatial correlation in consumer responsiveness to the marketing mix. Second, in contrast to previous work which has focused on geographic proximity as a driver of consumer proximity, I demonstrate the important role played by the similarity in previous consumer purchases. From a substantive 3 standpoint, this permits me to go beyond state-dependence e®ect by showing how previous purchase information from consumers can be harnessed to predict better the choices of other consumers for other products. Third, the dependent variable in my study is a consumer's multinomial brand choice decision, which provides a more managerially relevant unit of analysis with direct implications for manufacturer promotional planning. Finally, my research contributes to the existingliteratureonconsumerheterogeneityandpriceandpromotionalplanning in the automobile industry by providing an alternative to a-priori geographic aggregationtocaptureconsumerheterogeneityintheautomarket. Thus,Bucklin etal.(2008)andSilva-RissoandIonova(2008)estimatearandomcoe±cientlogit modelafteraggregatingtransactionstothezip-code,andDesignatedMarketArea (DMA) levels, respectively, which implicitly assumes that consumers in the same ZIP code or DMA share the same parameters. In contrast, my spatial model provides an alternative means of identifying a focal consumer's preference and response based on his or her proximity to other consumers. I apply the model to transaction data for new car purchases in the premium midsize sedan market, in which I also observe what vehicle was traded-in by the new car buyer. Model parameters are estimated using a Hierarchical Bayes approach. The proposed model outperforms the commonly used a random coef- ¯cient probit model as well as other spatial models that only include geographic closeness between consumers or only incorporate either preference or response correlation individually, but not together. 4 I demonstrate how parameter estimates obtained in one market may be used to improve demand predictions in other markets. The empirical performance of the proposed model is striking; in four out of ¯ve holdout markets the proposed model outperforms a random coe±cient probit model in which model parame- ters have been re-estimated on the holdout data. In other words, spatial model parameters estimated in Market A provide more precise predictions of consumer choices in Market B than a random coe±cient probit model whose parameters are directly estimated on Market B. I also compare estimated price elasticities for loyal consumers and switchers from the proposed model with those obtained from a random coe±cient probit model. Ignoring spatial correlation based on previous vehicle similarity is found to underestimate the elasticity di®erences be- tween these two groups of consumers. The results suggest that prices derived from a random coe±cient probit model, the current state-of-the-art promotional planning methods (Silva-Risso and Ionova, 2008), are biased downward [upward] for those who purchased a vehicle that is similar [dissimilar] vehicle to the one they traded-in. 1.2 Model I begin by describing the spatial weight matrix, which captures the similarity be- tweenconsumersandformsacriticalbuildingblockforalloftheproposedspatial choice models. I discuss how the weight matrices in my study are constructed basedon(i)thegeographicallocationofconsumersand(ii)thesimilarityintheir previously purchased vehicles. I introduce the Bayesian Preference Correlation 5 Probit model (BPCP), which incorporates the spatial correlation in consumer brand preferences, the Bayesian Response Correlation Probit model (BRCP), which incorporates spatial correlation in consumer response to the marketing mixbutignoresthecorrelationinconsumerpreferencesand,¯nally,theBayesian Preference and Response Correlation model (BPRCP), which incorporates both preference and response correlation and nests the BPCP and BRCP models as special cases. 1.2.1 Spatial Weight Matrix For a group of n consumers, each element of the n£n spatial matrix, W, repre- sents the closeness between a \row" consumer (say, consumer i) and a \column" consumer (say, consumer m). In my empirical application, W is based on one of two sources of information: the geographic location of the consumer or the characteristics of the vehicle previously owned by the consumer. 1 Next, I discuss how each of these matrices is operationalized in my study. 1 Yang and Allenby (2003) ¯nd that geographic distance plays a more signi¯cant role than demographic network in spatial correlation in consumer preferences for Japanese (vs. non- Japanese) vehicles. Furthermore, I do not have access to detailed information on consumer demographics such as income, ethnicity, or family size. Therefore, the spatial weight matrices used in my study are based on geographic distance and previous vehicle similarity, not on demographics. 6 1.2.1.1 Geographic Location Let d im represent the Euclidian geographic distance between the residential lo- cations of consumers i and m. Each element of the W matrix, which captures the geographic contiguity between two consumers, is calculated in a two-step approach. The ¯rst step involves developing a raw contiguity measure between these consumers as follows: w im = 1 exp(d im ) : (1.1) The formulation ensures that contiguity increases as the distance between the residential locations decreases. Second, the raw numbers in the matrix are nor- malized by dividing each element by the corresponding sum of the raw values in each row (Anselin, 1988; LeSage, 2000), yielding the elements: ~ w im = 1=exp(d im ) P n m=1 (1=exp(d im )) ; (1.2) and the ¯nal geographic contiguity matrix W = 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 ~ w 11 ¢¢¢ ¢¢¢ ~ w 1n . . . . . . ~ w im . . . ¢¢¢ . . . ¢¢¢ . . . . . . . . . ~ w n1 ¢¢¢ ¢¢¢ ~ w nn 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 : (1.3) 7 1.2.1.2 Previous Vehicle Basedona Lancasterianperspective, thepreviously-ownedvehicleofaconsumer may be represented as a vector of attributes. Speci¯cally, each traded-in vehi- cle is described by the following seven characteristics: manufacturer (e.g., GM, Honda.), name plate (e.g., Chevrolet, Acura.), model (e.g., Taurus, Accord.), body type (e.g., sedan, coupe.), manufacturer country of origin (e.g.,Japanese, American.), segment(e.g., midsizesedan, SUV.), andsubsegment(e.g., premium midsize sedan, compact SUV.). My proposed similarity measure is based upon c im ,thenumberofcharacteristicscommontothevehiclestraded-inbyconsumers i and m. For example, if consumer i traded in a Chevrolet Malibu sedan and consumer m traded in a Hyundai Sonata sedan, then, c im = 3 because these two vehicles share three common characteristics (body type, segment, and sub- segment). The raw similarity measure is calculated as exp(c im ), which in this example is exp(3). This operationalization implicitly assumes that all vehicle characteristics are equally important. The assumption reduces the number of parameters in the model and makes it more parsimonious (Ho and Chong, 2003). As before, the raw elements of the matrix are normalized so that the sum of the elements in each row is one. Thus, ~ w im = exp(c im ) P n m=1 (exp(c im )) : (1.4) The diagonal terms in the W matrix are di®erent depending upon whether it is used to model preference or response correlation. In the case of preference 8 correlation, the diagonal terms in the spatial weight matrix are set to zero, in ordertoexcludetheimpactofintrinsicpreferences,whicharemodeledseparately (Anselin, 1988). In contrast, the diagonal terms of W are set to be equal to the maximum value in each row, when correlation in individual response parameters is modeled. Thus, each consumer has the same weight as her closest neighbor (Bavaud, 1998). The formulation ensures that each consumer's responsiveness parameter is estimated based on his or her purchase history as well as other consumers' purchases. These points are discussed in greater detail in the model speci¯cation section. 1.2.2 Model Speci¯cation I model the probability that consumer i = 1;2;:::;n chooses vehicle model j = 1;2;:::;J, conditional on purchase in the product category using an ad- ditive random utility framework. A consumer chooses the alternative (y i ) that maximizes her unobserved latent utility (U i¢ ), i.e., y i = j ¤ if U ij ¤ >U ij 8j6=j ¤ : (1.5) 9 1.2.2.1 Bayesian Preference Correlation Probit Model IntheBayesianPreferenceCorrelation Probit(BPCP)model, spatialcorrelation pertainsonlytoconsumerpreferencesforthedi®erentalternatives,andthescaled utility of consumer i for alternative j is given as: u ij = U ij ¡U iJ = ® j +X ij ¯+µ ij +" ij = ® j +µ ij +X ij ¯+" ij ; (1.6) " i » N(0;§); (1.7) § = diag(¾ 2 1 ;¾ 2 2 ;:::;¾ 2 J¡1 ): (1.8) X ij is a matrix of alternative- and consumer-speci¯c variables. Consumer utility consists of a deterministic part, ® j +X ij ¯, and a stochastic component µ ij +" ij , the latter representing the impact of unobserved factors on consumer utility. Unlikeastandardprobitmodel, thestochasticcomponentofutilityintheBPCP model does not consist of single i:i:d: term, consists instead of two parts: a spatially correlated component, µ ij , and an independent random component, " ij . µ ij represents the correlated portion of consumer i's preference for alternative j. The random error term in the utility function, " i , is normally distributed with mean 0 and covariance matrix §, the ¯rst element of which, ¾ 2 1 , is set to be one for identi¯cation purposes. In equation (1.6), ® j represents consumer i's intrinsic preference for alternative j that is common to all consumers. In the absence 10 of spatially correlated preferences, the proposed model reduces to the standard probit model. Letµbeastackedvectorofthepreferencesofallconsumers,sothatµcontains the n£(J¡1) individual elements µ ij . I complete the speci¯cation of my model by specifying the following autoregressive structure for µ. µ = ½(WP I J¡1 )µ+»; (1.9) » i » N(0;ª); (1.10) ª = diag(Ã 2 1 ;Ã 2 2 ;:::;Ã 2 J¡1 ): (1.11) As previously discussed, the o®-diagonal elements of the n£ n spatial weight matrix for preference correlation, WP, in equation (1.9) contain normalized con- tiguity measures of the closeness between a \row" consumer and a \column" consumer, while the diagonal elements are set to be zero. Thus, equation (1.9) speci¯es consumer i's µ ij as a weighted average of the µ i 0 j of all other individuals, with the similarity between i and i 0 serving as the weight. For example, consider two consumers m and m 0 such that consumer i is more similar to consumer m than consumer m 0 , i.e., ~ w im 0 < ~ w im . In the averaging process, therefore, con- sumer i's preferences will be more highly correlated with consumer m than with consumer m 0 . The spatial autoregressive parameter, ½, captures the average in°uence of the preferences of neighboring or contiguous consumers on the preferences of a focal 11 consumer. Finally, the residuals (» i ) are normally distributed with mean 0 and variance ª. Solving for µ in terms of » yields the following expression for µ: µ » MN(0;¤); (1.12) ¤ = (I n ª) ¢ · ³ I n(J¡1) ¡½(WP I J¡1 ) ´ T ³ I n(J¡1) ¡½(WP I J¡1 ) ´ ¸ ¡1 :(1.13) In other words, µ follows a multivariate normal distribution with mean zero and the covariance matrix, ¤. I note that the o®-diagonal terms in the covariance matrix can take on non-zero values, so that µ ij is allowed to be correlated with µ i 0 j and µ i 0 j 0, where i6= i 0 and j 6= j 0 . Thus, each consumer's preference can be correlatedwithotherconsumer'preferences. Thecorrelationbetween µ i 0 j andµ i 0 j indicates preference correlation between consumer i and i 0 . 1.2.2.2 Bayesian Response Correlation Probit Model In the Bayesian Response Correlation Probit (BRCP) model the spatial con- tiguity between consumers in°uences the extent to which their marketing mix responsiveness is correlated. The overall model speci¯cation is as follows: u ij = U ij ¡U iJ = ® j +X ij ¯ i +" ij ; (1.14) (WR 1 2 i I J¡1 )u = (WR 1 2 i I J¡1 )(®+X¯ i )+" i ; (1.15) 12 " i » N(0;§); (1.16) § i = diag(¾ 2 i1 ;¾ 2 i2 ;:::;¾ 2 i;J¡1 ): (1.17) Unlike the standard probit and BPCP models, consumer response parameters, ¯ i , are heterogeneous and spatially correlated across consumers. Transforming equation (1.14) into equation (1.15) ensures that a consumer's response parame- ters are estimated with transactions of other contiguous consumers as well as of the focal consumers. Here, ® and " i are n£(J¡1) vectors. WR i is an n£n diagonalmatrix, whosediagonalelementsrepresentthenormalizedsimilaritybe- tween row and column consumers. In other words, the elements in the i th row of the spatial weight matrix WR become the diagonal terms in the matrix WR i . ¯ i = (~ w i1 I k ¢¢¢ ~ w in I k ) 0 B B B B B B @ ¯ 1 . . . ¯ n 1 C C C C C C A +´ i ; (1.18) ´ i » N(0; i ); (1.19) i = ± 2 (X T (I n § i )(WR i I J¡1 )X) ¡1 : (1.20) Equation (1.18) represents a parameter smoothing speci¯cation in which con- sumer i's response parameter vector, ¯ i , is a weighted linear average of the re- sponse parameters of all individuals, with the similarity between consumer i and any other individual j, ~ w ij , serving as a weight (LeSage, 2003). Thus, the extent 13 to which the marketing mix responsiveness of one consumer is correlated with that of another consumer depends upon how similar they are to each other. Combining equation (1.18) with equation (1.15) yields an analytical solution of the ¯ estimates (Theil and Goldberger, 1961). ^ ¯ i = h X T (WR i I J¡1 )X +X T (WR i I J¡1 )X=± 2 i ¡1 ¢ h X T (WR i I J¡1 )u+(X T (WR i I J¡1 )XA i °)=± 2 i , (1.21) where A i = (~ w i1 I k ¢¢¢ ~ w in I k ) and ° = (¯ 1 ;:::;¯ n ) T . Further details are provided in the Appendix A. 1.2.2.3 Bayesian Preference and Response Correlation Probit Model In the Bayesian Preference and Response Correlation Probit (BPRCP) model, bothconsumerpreferencesandmarketingmixresponsivenessarecorrelated. The model is speci¯ed as below: u ij = U ij ¡U iJ = ® j +X ij ¯ i +µ ij +" ij ; (1.22) (WR 1 2 i I J¡1 )u = (WR 1 2 i I J¡1 )(®+X¯ i )+µ i +" i ; (1.23) ¯ i = (~ w i1 I k ¢¢¢ ~ w in I k ) 0 B B B B B B @ ¯ 1 . . . ¯ n 1 C C C C C C A +´ i ; (1.24) µ = ½(WP I J¡1 )µ+»: (1.25) 14 Spatially correlated consumer preference parameters are estimated from the au- toregressive structure in equation (1.25), and consumer response parameters are heterogeneous and spatially correlated as in equations (1.23) and (1.24). The model incorporates two spatial weight matrices, one for preference correlation (WP) and the other for response correlation (WR), and does not require that thesematricesbeidentical. Thus,eachsimilaritymatrixcanbebasedonadi®er- ent measure. For example, WP may incorporate geographic contiguity and WR may be based on the similarity in previously owned vehicles. In my empirical application, I estimate di®erent versions of the model by changing the factors used to de¯ne the spatial weight matrices WP and WR. 1.3 Data and Estimation 1.3.1 Data Power Information Network (PIN), a division of J.D.Power and Associates, col- lects new vehicle transaction data from a large number of dealers electronically. Thedatausedinthisstudycomefromatransactionhistoryofnewcarpurchases in the midsize sedan category made by consumers in the Los Angeles Designated Market Area (DMA) during the ¯rst six months of 2007. 2 Since the four top-selling models accounted for about 93% of all transactions in this category, my analysis is restricted to predicting consumer choice among 2 All statistics are based on the observations in our data set. 15 these four models. Further, because I am interested in examining the impact of previously purchased vehicles, I restrict my sample to only those transactions in which a consumer purchasing a new car also traded-in another vehicle. Although consumersinmysamplepurchasedoneofthefourmidsizesedans,theirtraded-in vehicles represented a wide range of di®erent manufacturers and models. Specif- ically, the traded-in vehicles in my sample included 178 di®erent vehicle models from 37 manufacturers. The ¯nal data set consisted of a total of 1158 new car transactions over the six month period: 856 transactions from the ¯rst four months are used to cali- brate model parameters and the remaining transactions are held out for model validation. The data includes several details of each transaction including the price each individual consumer paid for the vehicle, the Annual Percentage Rate (APR) for ¯nance and lease contracts, the monthly payment amount, manufac- turer rebate (if any) and the residual value of the vehicle if it was leased. The data also contain the geo-coded location (i.e., precise latitude and longitude co- ordinates) of the consumer's residence as well as detailed attribute information for traded-in vehicles. Table 1.1 reports descriptive statistics for my sample in- cluding vehicle market shares expressed as a fraction of the 93% total share of all the vehicles together. The exogenous variables in the estimated model include the log of price and last make dummy variable. I standardized vehicle transaction price to con- struct baseline price net of vehicle options with a hedonic regression (see, e.g., 16 Table 1.1: Descriptive Statistics of the Data Honda Accord Nissan Altima Toyota Camry Volkswagen Passat Average Price 21,384 21,103 21,218 25,339 Average Rebate 0 1,520 554 203 Average APR 6.067% 9.183% 9.546% 5.200% Average Adjusted Price 21,267 19,583 21,216 24,696 Market Share 47.66% 17.41% 30.61% 4.32% 17 Zettelmeyer et al., 2006). I then constructed adjusted vehicle prices by sub- tracting manufacturer rebate, dollar amount of APR promotion, and trade-in over[under] allowance. I calculated the dollar amount of an APR promotion us- ing a 5% base APR level. Speci¯cally, for transactions with APR's less than 5%, the dollar amount corresponding to the APR subvention was treated as an APR promotion. APR's greater than 5% were considered non-promotional and the dollar amount of the promotion was set to zero. The data also include a ¯eld for Trade-in over[under] allowance, which represents the di®erence between the price the dealer pays to the consumer for the trade-in car and the wholesale value of the traded-in car. Paid prices are adjusted by the over[under] allowance to control the possibility that dealers may pay consumers a higher[lower] price for the traded-in vehicle and then charge them a lower[higher] price for the new car. The last make dummy variable takes the value 1 if the make of the new car purchased by the consumer is same as that of the traded-in vehicle, 0 otherwise. 1.3.2 Estimation IusedMarkovChainMonteCarlo(MCMC)methodstoestimatetheparameters of each model. Speci¯cally, Gibbs sampling steps are employed to make draws from the full conditional distributions of each parameter, except for ½ which re- quired the use of a Metropolis-Hastings algorithm because it does not have a posterior distribution with a closed form solution (Chib and Greenberg, 1995). I ran the sampler for 50,000 iterations, thinning it by retaining every 50th draw, and assessed convergence by monitoring the time-series plots of the parameter 18 draws. Idiscardedthe¯rst500retaineddrawsas\burn-in"andusedthelast500 draws to make inferences about the posterior distribution of the parameters. Be- foreestimatingthemodelonthetransactiondata, Iranaseriesofsimulationsto con¯rm that parameters were recovered properly. Details of the estimation pro- cedure, including the conditional distributions of each of the parameters appear inAppendixA.AdescriptionofthesimulationanalysisappearsintheAppendix B. 1.4 Results 1.4.1 Estimation Results To evaluate the performance of the proposed model, I estimated the seven di®er- ent models listed in Table 1.2. Two non-spatial models are estimated. Model 1, the standard probit model, does not incorporate any heterogeneity or spatial correlation in parameters. The random coe±cient probit model (Model 2) incorporates preference and response heterogeneity using the a-priori aggregation approach of Bucklin et al. (2008), with parameters aggregated to the three-digit ZIP code level. 3 3 Thedatasetcontains24three-digitZIPcodes,yieldinganaverageofabout48observations for each geographic unit. 19 Table 1.2: Estimated Models Spatial weight matrix Spatial weight matrix for response correlation for preference correlation Model 1 Standard Probit Model - - Model 2 Random Coe±cient Model - - Model 3 BRCP Model 1 geographic - Model 4 BRCP Model 2 vehicle - Model 5 BPCP Model 1 - geographic Model 6 BPCP Model 2 - vehicle Model 7 BPRCP vehicle vehicle 20 I estimated ¯ve di®erent spatial models. Models 3 and 4 represent two di®er- ent versions of the BRCP model in which consumers' marketing mix responsive- ness is spatially correlated. Model 3 used a spatial weight matrix WR based on geographic contiguity, while in Model 4 it is based on previous vehicle similarity. Similarly, I also estimated two versions of the BPCP model. Model 5 employs a spatial weight matrix, WP, based on geographic contiguity, while Model 6 used a spatial weight matrix based on the similarity of traded-in vehicles. Finally, Model 7 incorporates spatial correlation in both preference and re- sponse, and uses a spatial weight matrix based on the similarity of previously owned vehicles, not on geographical contiguity. 4 I follow previous research (e.g., Rossi and Allenby, 1993; Allenby et al., 1998), and use the log marginal density in the calibration sample (Newton and Raftery, 1994) , and the mean absolute deviation (MAD) in the holdout sample to evaluate model ¯t. Becauseconsumersinthecalibrationsampleandholdoutsamplearedi®erent, Ihadtogenerateindividual-levelparametersforconsumersintheholdoutsample, so as to calculate predicted probabilities of brand choice. These parameters includedmarketingmixresponsivenessparameters,¯,fortheBRCPandBPRCP models, and the preference correlation parameters, µ, for the BPCP and BPRCP models. 4 The superior empirical performance of models based on previous vehicle similarity (Model 4 and 6) over models based on geographic contiguity (Model 3 and 5) led me to use previous vehicle similarity only for Model 7. 21 I ¯rst constructed an augmented W matrix that included consumers in both calibrationandholdoutsamples. Thus,the856consumersinthecalibrationsam- pleandthe302consumersintheholdoutsampleresulted in a W withdimension 1158 by 1158. Then, using these elements if the W matrix that corresponded to the contiguity between calibration and holdout consumers as weight, I averaged across the estimated values for consumers in the calibration sample to produce the individual-level predictions. ¯ i = X m w im ¢ ^ ¯ m ; (1.26) µ ij = v u u t Ã 2 j Var(µ ¢j ) X m w im ¢ ^ µ mj : (1.27) In the equations (1.26) and (1.27), i denotes a holdout observation and m a calibration observation. The term r Ã 2 j Var(µ ¢j ) serves as a variance adjustment, whichmakesthevarianceofholdoutµequaltothatofcalibrationµ. Thevariance adjustment process ensures that the degree of preference correlation in holdout sample is same as that in calibration sample. The similarity between i and m, w im , is calculated in the same way as it was in the estimation sample, and either geographic distance based similarity or previous vehicle based similarity is used, depending upon the model. Parameter estimates and ¯t statistics for each model are reported in Table 1.3. Based on a 95 % posterior density interval, I see that the coe±cient for adjustedpriceisnegativeandsigni¯cantandthecoe±cientforlastmakedummy 22 Table 1.3: Parameter Estimates and Model Fit Statistics Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Accord 0.068 0.154 ¡0:014 ¡0:063 0.038 0.027 ¡0.272 Altima ¡0.519 ¡0.651 ¡0.733 ¡0.861 ¡0.977 ¡1.269 ¡1.429 Camry ¡0.214 ¡0.255 ¡0.321 ¡0.419 ¡0.518 ¡0.571 ¡0.753 Price ¡2.133 ¡2.470 ¡3.315 ¡2.706 ¡4.370 ¡4.744 ¡5.137 Last Make 1.207 1.431 1.397 1.463 2.155 2.429 2.801 ½ - - - - 0.385 0.504 0.429 Log Marginal Density a ¡750:92 ¡699:44 ¡713:80 ¡665:91 ¡541:94 ¡501:93 ¡439:66 Mean Absolute Deviation b 0.458 0.411 0.390 0.387 0.342 0.335 0.330 a In calibration sample b In holdout sample 23 is positive and signi¯cant in all models. The spatial autoregressive parameter, ½, is positive and signi¯cant for models in which preference correlation is modeled. Model 2 outperforms Model 1 in terms of both calibration and holdout ¯t statistics, which establishes that consumer heterogeneity plays a signi¯cant role in new car purchases. Among the models that capture spatial correlation in response, Model 4 provides a better ¯t than Model 3, which suggests that previ- ous vehicle similarity is a more important driver of the correlation in consumer responses to the marketing mix than is geographic closeness. The relative impor- tance of previous vehicle similarity is also evident in the relative performance of the two preference correlation models, Models 5 and 6. As previously discussed, I estimated a model that combines the correlation in preference and responsive- ness,Model7, usingW matricesbasedonpreviousvehiclesimilarity. Thismodel ¯ts the data best and forms the basis for my further analysis. 1.4.2 Demand Prediction in Other Markets In this section, I show how parameter estimates from the best-¯tting BPRCP in one market can be used to predict consumer choices in another target market. Such predictions require that I ¯rst specify the individual level parameters for consumers in the target market. To this end, I adopt the same approach that I used to calculate the predictive performance in the holdout sample. Therefore, I construct a spatial weight matrix, W, for consumers in both markets based on the similarity in previously owned vehicles. These values are used to weight the estimates obtained in the calibration sample and to impute parameter values for 24 consumers in the holdout sample. Note that this procedure only requires that we have information on the previous vehicle ownership pattern of consumers in the new market instead of the actual transactions made by these consumers. For example, I predict the preference and responsiveness of consumers in New York, based on how similar their traded-in vehicles are to the Los Angeles consumers who formed out calibration sample. I assess the predictive performance of the proposed BPRCP model estimated with Los Angeles data using the mean absolute deviation (MAD) criterion. I compare the performance of my model to the performance of two other non- spatial competing models. The benchmark models include the standard probit model and the random coe±cient probit model, both of which are re-estimated using the transaction data of the prediction market, i.e., the New York market in the example above. Table 1.4 summarizes the models estimated and the data that each model uses. The key point to note is that the spatial model relies on Los Angeles data to make prediction, while the other two models use parameters thathavebeenre-estimatedwithtransactiondatafromthenewmarket. Overall, this represents a very severe test of the model. I selected seven other regional markets in the U.S. for this forecasting exer- cise. 5 TheseconsistofoneWestcoastregionalmarket(NorthernCalifornia), two markets on the East coast (New York and Baltimore/Washington D.C.), two in the Midwest (Illinois/Indiana, Minnesota), and one in the South (South Texas, 5 I used the de¯nition of regions de¯ned by J.D. Power and Associates. 25 Table 1.4: Demand Prediction in Other Markets Model Data used to estimate parameters Prediction 1 Standard Probit Model Prediction market data Prediction 2 Random Coe±cient Model Prediction market data Prediction 3 BPRCP model Los Angeles data 26 Miami). Demand parameters for the competing models were estimated using transaction data from January to April 2007, and transactions from the period May and June 2007 in each market were used to evaluate model performance. I note that automobile demand hinges on regional market-speci¯c characteristics, including the dealer distribution intensity for each manufacturer, climate, and the general preference for Japanese vehicles. While re-estimation ensures that the competing prediction methods (Prediction 1 and 2) can take advantage of these regional market characteristics, the prediction from the proposed spatial model (Prediction 3) does not leverage such information. Despite this handicap, as reported in Table 1.5, the mean absolute deviation (MAD) of the proposed model (Prediction 3) is smaller than those for the com- peting methods. Speci¯cally, the proposed model provides more precise forecasts than the standard probit model in each of the seven regional markets, and more impressively, also outperforms the random coe±cient probit model with three- digit zip code heterogeneity (Prediction 2) in six out of seven markets. These results highlight the importance of capturing spatial correlation in preference and responsiveness based on previous vehicle similarity and the persistent role it plays in predicting demand di®erent geographic markets, in spite of market- speci¯c conditions that keep preferences and response of consumers in di®erent markets from being similar to each other. 27 Table 1.5: Demand Predictive Performance [MAD] in Other Markets Area Market Prediction 1 Prediction 2 Prediction 3 West Northern California 0.437 0.380 0.338 East New York 0.501 0.403 0.389 Baltimore and D.C. 0.530 0.447 0.414 Midwest Illinois and Indiana 0.513 0.419 0.497 Minnesota 0.586 0.569 0.521 South South Texas 0.505 0.447 0.446 Miami 0.532 0.500 0.473 28 1.4.3 Elasticity Analysis In this section, I compare the market structure derived from some of the bench- mark models with that derived from the proposed model. For each model, I calculated the base choice probability of each alternative by averaging across the predicted probabilities derived from each of 5;000 draws from the posterior dis- tributionofthemodelparameters(i.e.,®'s,¯'s,andµ's). Summingtheseaverage probabilities across the sample provided the baseline market shares. I then re- peated this process after changing the price of a target alternative by 10% to obtain the new market share of each alternative (Manchanda et al., 1996), and calculate the corresponding price elasticity. Table 1.6 reports the average own price elasticities obtained from a random coe±cient probit model (Model 2) and a BPRCP model (Model 7). 6 Consumers who purchased a particular vehicle were divided into two groups: for whom the manufacturer of their traded-in vehicle was the same as for the new vehicle [loyal consumers], and the remaining consumers for whom the new and traded-in vehicles had di®erent manufacturers [switchers]. Using the same approachdescribedabove, Icalculatedpriceelasticitiesforeachgroupseparately and found that the price elasticities for loyal consumers were lower (in magni- tude) than the price elasticities of the switchers. The key di®erence between Model 7 and Model 2 is pronounced in the di®erence in price elasticity between 6 I also compared Model 1 (standard probit model) to ¯nd little di®erence between Model 1 and Model 2 in terms of elasticity. 29 Table 1.6: Own Price Elasticity Honda Accord Nissan Altima Toyota Camry Volkswagen Passat Model 2 Loyal consumers ¡0:539 ¡1:048 ¡0:741 ¡2:057 Switchers ¡1:700 ¡2:707 ¡2:164 ¡4:812 Model 7 Loyal consumers ¡0:219 ¡0:926 ¡0:626 ¡1:787 Switchers ¡2:408 ¡4:974 ¡3:905 ¡7:275 30 the two groups. Elasticity estimates from the spatial model [Model 7] indicate that switchers were about six times more price elastic than loyal consumers. In contrast, Model 2, which only accounts for state dependence, estimates the ratio to be about 3.4. Therefore,apromotionalplanningmodelthatignoresspatialcorrelationwould under-utilize the information contained in consumers' previously owned vehicle, providing larger than optimal discounts to the loyal consumers and smaller than optimaldiscountstotheswitchergroup. Thisdi®erencebetweenloyalconsumers and switchers provides important implications for managers and dealers. Dealers canadaptthisresultintheirpricenegotiationtoestimateconsumers'willingness to pay for a new vehicle. They can increase sales and pro¯t by o®ering higher price for loyal consumers and lower price for switchers, based on consumers' pre- vious vehicle information. 1.5 Conclusion I develop and estimate a new Bayesian spatial choice model that permits pref- erence and marketing mix responsiveness to be correlated among consumers. I apply the model to transaction data from the U.S. automobile market and ¯nd that the proposed model ¯ts the data better than both standard probit and random coe±cient probit models. While previous applications of spatial models have highlighted the role of geographic contiguity, I show that the correlation in consumer preferences and response are explained better by the extent to which consumers' previously purchased vehicles are similar. Therefore, in addition to 31 structural state dependence which enables one to make better predictions of a particularconsumer'sfuturechoicesofthesameproduct,Ishowhowinformation about previous purchases can be used to make better predictions of how other consumers choose other products. Idemonstratehowparametersoftheproposedmodelestimatedinonemarket can be used to make consumer choice predictions in other markets when only in- formationontrade-invehiclesisavailableinthenewmarket. Ialsoshowthatthe proposed model provides a very di®erent picture of market segmentation based on price elasticity, as compared with a random coe±cient model. The empir- ical results suggest that promotional planning methods that ignore the spatial correlation in consumer preferences and response would be suboptimal; o®ering a larger than optimal discount to loyal consumers and a smaller than optimal discount to the switcher group. Limitationsofthisresearchincludethefollowing. First,theproposeddemand model does not explicitly incorporate strategic production and pricing decisions made by manufacturers or retailers. The demand only model may have endo- geneity issue (i.e., correlation between explanatory variables and the error term), as supply side decisions can be made based on consumer demand (Villas-Boas and Winer, 1999). However, production and pricing decisions in the automobile industry are not as °exible as other industries, which may attenuate the poten- tial endogeneity bias in the proposed model (Silva-Risso and Ionova, 2008). In addition, previous research shows that incorporating spatial correlation in un- observed factors may reduce endogeneity bias in estimating model parameters. 32 I acknowledge that these provide a partial solution to this problem, and future research should further investigate how to address the endogeneity problem in the proposed model. Second, I incorporate geographic distance and previous vehicle information in a spatial weight matrix. Other variables can be used to measure the sim- ilarity between consumers, if they are relevant to consumer brand preferences and response to marketing mix. For example, some demographic information can serve to identify spatial correlation among consumers. Consumers of similar income level may exhibit similar price sensitivity, and ethnicity, age and gender might explain intrinsic preferences for particular brands. Future research may also incorporate multiple spatial weight matrices in a model, and estimate op- timal mixture of the matrices. For example, one might be interested in ¯nding relative importance of geographic distance, demographic information and previ- ous vehicle similarity. Although I partially answer this question by comparing model ¯t measures of econometric models that incorporate single information, future research can provide optimal mixture of each set of information. Third, in addition to spatial correlation between consumers, future research may incorporate spatial correlation among alternatives. I show that similar con- sumers are likely to make similar choice decisions. A choice model with spatial correlation in alternatives would show that a particular consumer is more likely to choose an alternative similar to what he or she purchased in the past. Duan and Mela (2009) develop a spatial demand model in which geographic distance 33 between alternatives (outlet location) serves as an identi¯cation source of con- sumer preferences. Future research may incorporate spatial correlations both in consumers and in alternatives so that it utilizes both of the similarity structures simultaneously. 34 Chapter 2 The Informational Role of Product Trade-Ins for Retailer Pricing 2.1 Introduction In durable goods markets, retailers often accept trade-ins of used products from consumers who buy a new product from them. Consumers bene¯t by not incur- ring the cost of selling the used product on their own, and by receiving credit towardpurchaseofthenewgood. Retailers,inturn,cangainbyaddingamarkup and by reselling traded-in products either in auction markets or directly to other consumers. Ishowthat,inadditiontothepro¯tfromsucharbitragetransactions, trade-ins provide retailers with information about consumer brand preferences, helping them to make better pricing decisions. This information is particularly valuable in durable goods markets such as automobiles that are characterized by negotiated prices and in which dealers have the ability to quote speci¯c prices based on an assessment of an individual consumers' willingness to pay. 35 Previousresearchhasshownthatproducttrade-insprovideinformationabout consumers' price sensitivity for new product purchases, so that retailers can seg- mentmarketsbasedonit. vanAckereandReyniers(1995)showthatamonopoly ¯rmcanusediscountsontrade-instopricediscriminatebetween¯rsttimebuyers and those who have previously purchased a product in that category. In their two-period analytical model, the monopolist sets an initial price level for the ¯rst period, and then uses the trade-in programs to price discriminate between consumers who purchased in the ¯rst period and those who did not. More re- cently, Rao et al. (2009) argue that retailers should o®er a lower new car price to consumers who trade in their used products. Onecrucialassumptioninthisworkisthatconsumerswhoownausedvehicle can do one of two things: continue to use the used car or trade it in to the dealer when they buy a new vehicle. This assumption ignores the private transaction market for used cars in which consumers can directly sell their used vehicles to otherconsumers. However,whileconsumerscantypicallyselltheircaratahigher price in a private sale, they also have to incur costs, such as advertising expenses or time costs in organizing test-drives for interestedpotentialbuyers. Consumers musttradeo®thesebene¯tsandcostsinordertodecidewhetherornottotrade- in their vehicle to the dealer. Thus, an analysis ignoring the existence of private selling used car market may overestimate optimal level of trade-in incentives for dealers to o®er to consumers. My analysis explicitly recognizes that consumers decide on whether or not to trade-in the used product based on the tradeo®s 36 between private selling and trading in that are characterized by di®erent costs and bene¯ts. Some empirical and experimental studies that do not rely on the \no private selling market" assumption ¯nd that consumers who trade-in used vehicle pay a higher price for a new car than those who do not, which contradicts the ¯ndings of Rao et al. (2009). Putsis and Srinivasan (1994) and Goldberg (1996) examine survey data on new car purchases and ¯nd that consumers who traded in their used car received smaller dealer discounts relative to those who did not. Purohit (1995)andZhuetal.(2008)conductexperimentstoexplainwhyconsumerswith trade-inspayhigherpriceforanewgood. Basedonthementalaccountingtheory, theyarguethatretailerscanchargehighernewcarpricestoconsumerswhotrade in their used car, because these consumers focus more on getting a higher price for their used car than on a lower price on the new one. Though previous research identi¯es a behavioral rationale for why the price of a new car should depend upon whether a consumer does or does not trade in another vehicle, it overlooks the potential e®ect of the trade-in characteristics. I provide an alternative, economic, rationale for both these e®ects building on the idea that a traded in vehicle provides information about consumer brand prefer- encesandmarketingmixresponsivenessthathelpsthedealerbetterestimatethe consumer's purchase probability and willingness to pay for a new vehicle. Previ- ousresearchbyRayetal.(2005)showthattheleveloftrade-inrebateso®eredby a¯rmshouldvarywiththevintageofthetraded-inproducts, becauseconsumers who replace used products more frequently are likely to be less sensitive to price. 37 In my work, I focus on the information provided by a match between the make and model of the traded-in vehicle and the new one, as previous research has shown that consumers tend to repurchase the same make and/or same vehicle model(Bucklinetal.,2008;Silva-RissoandIonova,2008). Forexample, aHonda dealer may charge a higher new car price to a consumer trading in a Honda if owning a Honda reveals a high preference and a higher willingness to pay for Honda. Myresearchmakesthefollowingthreecontributions. First,Idevelopamicro- theoretic model of the consumer's trade-in decision and of the retailer's new car pricing decision. In this model, both the consumer's decision to trade in a used car and the characteristics of the traded in product help the dealer assess the consumer's opportunity cost of time and preferences for the new vehicle more accurately. If opportunity cost is correlated with willingness to pay, then con- sumers who trade in used cars may be willing to pay a higher price for a new vehicle than those who do not. Conditional on a trade-in, I show how observing the characteristics of the traded in vehicle enable the dealership to update its assessment of the consumer's preferences for the new vehicle and derive the opti- mal prices for both trade-in and non trade-in conditions. Speci¯cally, the model predicts that dealers will charge consumers higher prices if they trade in vehicles that are more similar to the new one. Second,Iprovideanempiricaltestofthesepredictionsbyestimatingahedonic regressionmodelofpricesobtainedfromalargesetofnewcartransactionsinthe premium midsize sedan market. I show that new car transaction prices depend 38 not only on whether or not a consumer traded in his or her existing car to the dealer but also upon which brand and model was traded in. Finally, I examine the implications of product trade-ins for retailers' market shares and pro¯t, by quantifying the bene¯t of trade-ins for retailers. To this end, I use the transaction data to estimate the parameters of an automobile choice model in which dealers adjust new car prices based on consumer trade- in information. I conduct a series of counterfactual analyses to quantify the informational value of consumer trade-ins to the dealers. The results show that pricediscriminationbasedonconsumertrade-ininformationreducesmarketshare but increases retailer pro¯ts because retailers end up leaving less money on the table. The results also show that if dealers of any particular vehicle discontinued their trade-in programs, it would decrease not only the pro¯t of that dealer, but also that of all the other competitors. Theremainderofthechapterisorganizedasfollows. Section2introducesmy theoretical model of consumer trade-ins and of retailer pricing of new products. Section 3 discusses the hedonic regression analysis that empirically tests the pre- dictions of the theoretical model. Section 4 describes the structural choice model that incorporates consumer trade-in information and the results of the counter- factual analysis used to quantify the value of consumer trade-in information to retailers. Section 5 concludes and discusses the managerial implications of this research. 39 2.2 Theoretical Model of Retailer Pricing with Trade-Ins In this section, I develop a generic model of dealer pricing that illustrates the informational role played by the buyer's decision on whether or not to trade in a used vehicle and of the characteristics of the traded in vehicle. The model shows how a retailer can utilize this information to increase price if the new good, and delineatesthepreciseconditionsunderwhichtrade-insleadtohighernewproduct prices. The model describes the actions of two players: a new car buyer and a car dealer. The buyer initially possesses a used car, which he or she can either sell on the used car market or trade in to the dealer. Let (V;T;C) be a vector that characterizesthenewcarbuyer. V ¸0isthevaluethataconsumerderivesfrom anewcar(i.e.,willingnesstopay),T ¸0isanindexofthesimilaritybetweenthe new car and the consumer's used car, with larger values of the index indicating a greater similarity, and C > 0 is the transaction cost of privately selling the used car. I assume that (V;T;C) is a random vector with joint distribution function F(V;T;C) and corresponding density function f(V;T;C). Central to my model are the relationships between the pairs of random vari- ables (V;C) and (V;T). First, I assume that higher values of C imply higher values of V. In other words, a higher cost of selling the used car on the private market indicates a higher opportunity cost of time. If higher opportunity cost is 40 positively linked with the consumer's wage, then he or she has a higher willing- ness to pay for the new car (V). Second, the more similar the used car is to the newcar,themoreloyaltheconsumeristothattypeofcar. Forexample,ifacon- sumerwhopreviouslypurchasedmodel X intendsto repurchasethesame model, then he or she has a higher willingness to pay for the new car. I operataionalize these relationships in the following assumption: ASSUMPTION 1 The random variables V, T and C are a±liated. This assumption implies that V and T as well as V and C are positively correlated. I also assume that all marginal distributions of V are regular, in the sense that they have non-decreasing hazard functions. ASSUMPTION 2 ForallrelevantmarginaldistributionsofV,theinversehaz- ard function ©(p)= 1¡Fv(p) f v (p) is non-increasing in p. Assumption A2 states that the marginal probability of a consumer's purchase at a given price does not increase with p. The assumption ensures that consumer demand does not increase as price increases. In this section I assume that a consumer is fully rational and anticipates that the retailer utilizes trade-in information in assessing the consumer's willingness to pay for a new car. 1 The consumer brings his or her used car as a trade-in, if and only if, the convenience bene¯t of going through the dealer exceeds the 1 It can be shown the basic results hold when the consumer is myopic and therefore unable to anticipate the dealer's use of trade-in information. See Appendix E. 41 premium he or she could obtain by selling the used vehicle in the private market. Mathematically, s´k+(p TI ¡p NTI ): (2.1) s is the threshold level of transaction cost such that transaction cost above it implies that a consumer trades in his or her vehicle to the dealer. p TI and p NTI represent the new car prices for the trade-in (TI) and no trade-in (NTI) conditions, and k > 0 denotes the ¯nancial premium that the buyer can realize by selling the used car privately. 2 I start by analyzing the case in which the consumer brings in a used car as a trade-in. This implies that the transaction cost is greater than the trade-in bene¯t, i.e.: C >s: (2.2) The dealer observes the similarity of the used and new cars T = t and chooses p TI to maximize expected pro¯t: (p TI ¡w)¢[1¡F v (p TI jT =t;C >s)]; (2.3) 2 While it is theoretically possible that a dealer pays a consumer more than what the con- sumer would get in the private market, this is highly unlikely. Dealers typically o®er a trade-in credit which is much lower than the private selling market value of the traded-in product, and common information sources about prices in the dealer and private markets (e.g., Kelley Blue Book) are consistent with this assertion. 42 whereF v denotesthedistributionfunctionofV conditionalon(2.2),andw isthe dealer's wholesale price. The ¯rst term, (p TI ¡w) is the margin for the product, and the second term, [1¡F v (p TI jT =t;C >s)], represents the probability that a consumer who brings in a trade-in is willing to buy the product at price p TI . Themaximizingpricewithobservedtrade-inmustsatisfythefollowing¯rstorder condition: (p TI ¡w)¢ " 1+ (@F v =@s)(@s=@p TI ) f v (p TI jT =t;C >s) # = [1¡F v (p TI jT =t;C >s)] f v (p TI jT =t;C >s) : (2.4) This condition re°ects the dealer's trade-o® when marginally raising price. To understand this trade-o®, note that right-hand side of (2.4) is the marginal prob- ability of the consumer accepting the dealer's price, which, by assumption A2, is decreasing in p TI . The left-hand side of (2.4) represents the marginal impact of raising price. The ¯rst term, p TI ¡w, represents the foregone margin. This loss is muted somewhat by the second additive term in the bracketed part of the left-hand side of (2.4), which is negative because @F v =@s< 0 (based on assump- tion A1) and @s=@p TI = 1 from (2.1). The negative sign of this term re°ects the fact that, as the dealer increases new car price, it raises the threshold for the consumer's trade-in decision (2.2). If a consumer with a higher threshold for private selling transaction cost, C, brings a trade-in, the dealer infers higher V. My assumptions imply that there exists a unique solution, p ¤ TI to (2.4), which is the optimal price for a new car when the consumer brings a trade-in. 43 To see how similarity of the trade-in, T, a®ects this optimal price, I ¯rst de¯ne the right-hand side of (2.4) as © TI (p;t;k). The a±liation assumption, A1, implies that © TI (p;t;k) is increasing in t and thus leads to the following result: PROPOSITION 1 Under A1 and A2, when the consumer brings a trade-in, the dealers' optimal new car price p ¤ TI is increasing in similarity t. Figure 2.1 graphically characterizes Propositions 1. An upward line and a downward curve represent the left-hand side and the right-hand side of (2.4), respectively. Asthesimilaritybetweenatradedinvehicleandanewcarincreases from t to t 0 , the downward curve shifts from © TI (p;t;k) to © TI (p;t 0 ;k), which increases the equilibrium price from p ¤ TI (t) to p ¤ TI (t 0 ). Now I examine the condition in which the consumer does not trade in his or her old vehicle. In this case, the only inference the dealer can make is that the cost of selling the consumer's used car does not exceed the premium of selling it privately, i.e., C <s: (2.5) The dealer then chooses new car price p NTI to maximize the expected pro¯t: (p NTI ¡w)¢[1¡F v (p NTI jC <s)]; (2.6) which leads to the following ¯rst order condition: (p NTI ¡w)¢ " 1+ (@F v =@s)(@s=@p NTI ) f v (p NTI jT =t;C <s) # = [1¡F v (p NTI jT =t;C <s)] f v (p NTI jT =t;C <s) : (2.7) 44 Figure 2.1: The Impact of Trade-in Similarity (t<t 0 ) on Equilibrium Price 45 Theinterpretationof(2.7)issimilartothatof(2.4). Incontrasttothetrade- in case, however, the second term in the bracketed expression on the left hand side of (2.7) is greater than unity since @s=@p TI =¡1, while @F v =@s is negative by assumption A1, as in the trade-in case. Thus, in contrast to the trade-in case (2.4), an increase in new car price p NTI only encourages consumers with lower C to sell their used car privately. This lowers the optimal level of p NTI because the absence of a trade-in makes the dealer infer that the consumer has a very low C and, therefore, a low V. My assumptions ensure that a unique solution to the ¯rst-order condition exists, which I denote as p ¤ NTI . Now I examine the condition under which trading in a used car leads to a higher price for a new vehicle. Let © NTI (p;k) denote the right-hand side of (2.7), which is non-increasing in p by A2. Comparing (2.4) and (2.7), we see that p ¤ NTI < p ¤ TI if © NTI (p;k) < © TI (p;t;k) for all p. To compare these two functions we must specify an additional property on the marginal distributions of V conditional on T =t. This property is given in assumption A3. ASSUMPTION 3 The conditional inverse hazard function 1¡F v (pjT=t;C<s) f v (pjT=t;C<s) is non-convex in t. Intuitively, the condition in assumption A3 states that for a consumer who does not trade in a used vehicle (C <s), increasing similarity between a used vehicle and a new one has a decreasing impact on the pricing power of the dealer. In other words, if the dealer had knowledge of the used vehicle that had not been traded in, the impact of its similarity to the new one on pricing power would be positive, but at a diminishing rate. 46 PROPOSITION 2 UnderA1,A2,andA3,thedealerhasauniqueequilibrium pricing strategy characterized by (p ¤ NTI ;p ¤ TI ) and the following property. When the consumer brings a trade-in with t > ¹ T, the new car price is higher than with no trade-in: p ¤ NTI <p ¤ TI . This proposition states that if the trade-in vehicle is above the (unconditional) average similarity of the focal vehicle, then the dealer's price will be higher than without the trade-in. Figure 2.2 demonstrates Propositions 2. If a consumer does not bring in a used vehicle as a trade-in, the equilibrium price is set at p ¤ NTI by equation (2.7) In contrast, the equilibrium price for consumers who trade in a used car is set at p ¤ TI (t) by equation (2.4), which is greater than p ¤ NTI . 2.3 An Empirical Test of the Predictions from the Theoretical Model In this section, I test the implications of my theoretical propositions via hedo- nic regression analysis. Speci¯cally, I test whether and how much transaction prices in the automobile market increase with the presence of a trade-in and the similarity between the traded in and new product. 47 Figure 2.2: The Impact of Trade-in Event on Equilibrium Price 48 2.3.1 Model I ¯rst specify a hedonic regression model for p ij , price paid by consumer i for vehicle j as: p ij = ® j +X ij ¯+TRD i (¸ 1 +¸ 2 TMAKE i +¸ 3 TMODEL i )+" i : (2.8) X ij represent a vector of vehicle j's characteristics, and consumer i's demograph- ics that may a®ect car price. TRD i , TMAKE i , and TMODEL i are indicator variables that represent whether or not consumer i traded-in a used car, whether consumer i's traded in car was the same make as the new car, and whether the traded in and purchased vehicle were the same model, respectively. 2.3.2 Data Power Information Network (PIN), a division of J.D.Power and Associates, col- lects new vehicle transaction data from a large number of dealers. It acquires information on details of transactions from participating dealers electronically, and cleans the information, decodes it, and removes any con¯dential informa- tion. The data used in this study come from a transaction history of new car purchasesinthepremiummidsizesedancategorymadebyconsumersinSouthern 49 California in 2004. 3 Our data set consists of a total of 41,592 new car transac- tions for one of the twelve top-selling premium midsize sedans which together accounted for 93% of transactions in this category. The data captures several details of each transaction including the price each individual consumer paid for the vehicle, the Annual Percentage Rate (APR) for ¯nance and lease contracts, the monthly payment amount, manufacturer rebate (if any) and the residual value of the vehicle if it was leased. Table 2.1 reports descriptive statistics for the data in our sample including market shares for each vehicle. Inadditiontomarketing-mixandtrade-inrelatedvariables,Iincludetwosets of variables to control for other factors that may a®ect new car prices. First, I include vehicle characteristics to capture variations in prices due to changes in characteristics within each vehicle model. Previous research ¯nds that consumer demographics play a signi¯cant role in explaining bargaining power in new car price negotiations (Chen et al., 2008), and consumer information search behav- ior on the internet for better negotiation of vehicle transaction prices (Ratchford et al., 2003). Therefore, second, I also include consumer demographics in my analysis to control for consumer speci¯c factors that might impact the transac- tion prices (Scott-Morton et al., 2003). To do this, I link each transaction with census data at the census-block level (Scott-Morton et al., 2001; Silva-Risso and Ionova, 2008), which permits me to connect each transaction to the demographic 3 All statistics are based on the observations in our data set. 50 Table 2.1: Descriptive Statistics of Vehicle Models Make and Model Mean Price($) Mean Rebate($) Mean APR Market Share Honda Accord 21,920 0 4.74 % 27.41 % Nissan Altima 21,115 674 6.80 % 26.72 % Toyota Camry 20,545 457 6.02 % 24.51 % Nissan Maxima 29,306 361 5.28 % 6.20 % Volvo S40 25,369 17 5.25 % 3.39 % Volkswagen Passat 24,647 304 3.12 % 2.87 % Mazda 6 22,765 1451 5.37 % 2.29 % Subaru Outback 26,727 377 3.72 % 1.69 % Toyota Avalon 29,178 14 6.04 % 1.36 % Dodge Magnum 31,119 679 7.80 % 1.27 % Chevrolet Impala 23,681 3544 6.72 % 1.24 % Ford Taurus 20,562 2930 7.22 % 1.04 % 51 characteristics of each census-block. The following variables represent the vehicle characteristics included in my anal- ysis. COUPE j =1 if the body type of vehicle j is coupe, 0 otherwise. MANUAL j =1 if the transmission of vehicle j is manual, 0 otherwise. CYL6 j =1 if vehicle j is a 6 cylinder vehicle, 0 otherwise. MY2005 j =1 if vehicle j is of 2005 vehicle, 0 otherwise. The following demographic variables were included in the analysis. FEMALE i =1 if consumer i is female, 0 otherwise. RBLACK i is ratio of the number of African-Americans to the total number of residents in the census block where consumer i lives. RASIAN i is ratio of the number of Asians to the total number of residents in the census block where consumer i lives. RHISP i is ratio of the number of Hispanics to the total number of residents in the census block where consumer i lives. RLOWED i is ratio of the number of people who did not ¯nish high school to the total number of residents in the census block where consumer i lives. 52 MHHINC i is the median income of households in thousands of dollars in the census block where consumer i lives. Summary statistics for these variables derived from the data are reported in Table 2.2. Each variable takes a wide range of values which should help in identifying the correlation with vehicle transaction prices. The mean values of thethreetrade-inrelatedvariables(TRD i ,TMAKE i ,andTMODEL i )indicate that 29.60% of consumers in our sample traded in a used car, and that 12.24% of consumers, or 41.35% of those who traded in a used car purchased the same make car as their trade-ins, and 5.82% of consumers, or 47.55% of those who traded in a car purchased a new car of the same vehicle as their trade-ins. 2.3.3 Estimation Results I estimated the model using ordinary least squares. I conducted regression diag- nosticstoensurethevalidityandrobustnessoftheestimatedparameters. First,I testedtheindependenceofresidualsbyDurbin-Watsontest(DurbinandWatson, 1950). The Durbin-Watsonstatistic forthe estimated model is1.9815 (p-value= 0.7603), which indicates that the residuals of the estimated model are indepen- dent. Second,IconductedaHarrison-McCabetesttocheckwhetherthevariances of residuals are equal for all observations (i.e., homoscedasticity) (Harrison and McCabe,1979). Thestatisticvalueis0.5083(p-value=0.981), whichshowsthat residual variances are not statistically di®erent across observations. 53 Table 2.2: Summary Statistics of Hedonic Regression Model Variables Variable Mean Std. Dev. Min. Med. Max. COUPE 0.1191 0.3239 0 0 1 MANUAL 0.0217 0.1457 0 0 1 CYL6 0.3294 0.4700 0 0 1 MY2005 0.3944 0.4887 0 0 1 FEMALE 0.4397 0.4964 0 0 1 RBLACK 0.0667 0.1268 0 0.0244 0.9377 RASIAN 0.1372 0.1431 0 0.0878 0.8712 RHISP 0.3564 0.2834 0 0.2521 1 RLOWED 0.1944 0.1804 0 0.1282 1 MHHINC 64,643 30,371 7,500 59,249 398,345 TRD 0.2960 0.4565 0 0 1 TMAKE 0.1224 0.3278 0 0 1 TMODEL 0.0582 0.2341 0 0 1 54 The estimation results appear in Table 2.3. The results show that parameter estimates associated with the three trade-in variables (i.e., TRD i , TMAKE i , andTMODEL i )are allpositiveandstatistically signi¯cant, after controllingfor vehicle characteristics and consumer demographics. Compared with consumers who do not trade in a vehicle, those who do trade-in pay a premium of $98.60, those who purchase a new vehicle of the same make as their trade-in pay $218.15 more, and those who purchase a new vehicle of the same model as their trade-in pay $376.24 more. These results are consistent with the predictions from the theoretical model. 2.4 Automobile Choice Model with Trade-Ins Building on the previously described theoretical model and empirical ¯ndings, I quantify the impact of trade-in information on retailers' market shares and pro¯t. I ¯rst develop and estimate a new car choice model in which consumers face di®erent prices depending on their trade-in information. I use the estimated parameters to conduct a series of counterfactual analyses that provide insights into seven di®erent scenarios, in which dealers of a particular brand either incor- porate or ignore trade-in information in their new car pricing decisions. 2.4.1 Model I model the probability that consumer i = 1;2;:::;n chooses vehicle model j = 1;2;:::;J at time t, conditional on purchase in the product category using an 55 Table 2.3: Hedonic Regression Estimation Results Variable Parameter Estimate Standard Error t-value Intercept 16213 146.15 110.94 Honda Accord 3742.93 135.69 27.59 Nissan Altima 3566.36 138.46 25.76 Toyota Camry 2697.34 136.76 19.72 Nissan Maxima 8154.73 140.99 57.84 Volvo S40 8805.57 152.61 57.70 Volkswagen Passat 6940.59 153.38 45.25 Mazda 6 2819.87 157.70 17.88 Subaru Outback 7221.34 172.39 41.89 Toyota Avalon 8120.96 178.52 45.49 Dodge Magnum 8227.53 170.17 48.35 Chevrolet Impala 2653.33 172.18 15.41 COUPE 1470.93 48.79 30.15 MANUAL ¡969.49 87.59 -11.07 CYL6 4497.33 33.53 134.12 MY2005 563.62 30.54 18.46 FEMALE 172.09 26.29 6.55 RBLACK 922.76 110.61 8.34 RASIAN ¡852.21 101.83 -8.37 RHISP 327.43 105.85 3.09 RLOWED 32.28 166.80 0.19 MMHHINC 1.47 0.56 2.60 TRD 98.60 34.12 2.89 TMAKE 119.55 58.51 2.04 TMODEL 158.09 72.35 2.18 F-Value 2598.01 Adjusted R 2 0.65 56 additiverandomutilityframework. Aconsumerchoosesthealternative(y it )that maximizes his or her unobserved latent utility (u i¢t ), i.e., y it = j ¤ if u ij ¤ t >u ijt 8j6=j ¤ : (2.9) Consumeri=1;2;:::;nderivesthefollowingscaledutilityfromvehiclemodel j =1;2;:::;J at time t. 4 u ijt = ® ij +X ijt ¯ i +» jt +" ijt ; (2.10) whereu ijt representsconsumeri'slatentutilityforalternativej attimet,relative to the baseline alternative J, X ijt includes marketing mix variables consumer i faces regarding alternative j at timet. The variables in the X matrix include the log of price and a last-make dummy variable. » jt captures time-varying demand shock or vehicle characteristics that are observed to dealers but unobserved to researchers, and " ijt is a stochastic error term assumed to have a Type I ex- treme value distribution. Thus, the probability that consumer i purchases brand alternative j at time t is given by the logit expression: P ijt = exp(® ij +X ijt ¯ i +» jt ) P k exp(® ik +X ikt ¯ i +» kt ) : (2.11) 4 I do not consider competitive behavior between dealers who deal with the same manufac- turer's vehicles. In order to incorporate such dealer behavior, we can have alternative sets at vehicle model - dealer level (j =1;2;:::;J, and r =1;2;:::;R) 57 I construct the price variable to make it correspond to my theoretical model and empirical ¯ndings, I ¯rst standardized vehicle transaction price to construct a baseline price, net of vehicle options and the e®ect of consumer characteristics, using the hedonic regression described in the previous section. Based on the esti- mates from this model, I then simulated the higher prices paid by consumer who tradeinacar,whopurchaseanewcarofthesamemakeasthetrade-in,andwho purchase a new car model that is the same as the trade-in. The prices for these transactions were $98.60, $119.55, and $158.09 higher, respectively. The idea is that consumers face di®erent prices depending on their trade-in information, because dealers identify consumers' willingness to pay for a vehicle and adjust their pricing decisions accordingly. I then constructed adjusted vehicle prices by subtracting manufacturer re- bate, dollar amount of APR promotion, and trade-in over-[under-] allowance. I calculated dollar amount APR promotion based on 5% as a base level APR. Speci¯cally, ifatransactionwasmadeatanAPRlessthan5%, wecalculatedthe corresponding dollar amount and treated it as an APR promotion, while APR's greater than 5% were considered to be non-promotional with the dollar amount of the promotion set to be zero. The data also include a ¯eld for Trade-in over- [under-] allowance, which represents the di®erence between the price the dealer paystotheconsumerforthetrade-incarandthewholesalevalueofthetraded-in car estimated by the dealer. The adjustment of trade-in over-[under-] allowance controlsforthepossibilitythatadealermaypayaconsumerahigher[lower]price 58 for the traded-in car and then charge a correspondingly lower[higher] price for the new car. I note that retailer pricing decisions can be made based on market condi- tions or vehicle characteristics that are observed to retailers but unobserved to researchers. The unobserved factors may result in correlation between price vari- ables and the error term, causing price endogeneity. The potential existence of endogeneity suggests that I should correct for it to avoid bias in estimation of a price coe±cient (Villas-Boas and Winer, 1999). I address potential endogeneity using the control function approach developed by Petrin and Train (2010). The control function approach leverages extra variables to control for the demand shock or vehicle characteristics that are observed to dealers but unobserved to researchers. The ¯rst step is to ¯lter out potentially endogenous price variable with observable instrument variables. I specify this procedure as below: p jt = °Z jt +¹ jt : (2.12) I use wholesale price (i.e., price that a dealer pays for a car to a manufacturer) for an instrument, Z jt , as I believe it is highly correlated with retail price but unlikely to be correlated with unobserved market conditions a®ecting retailer pricing decisions. Consumer utility is then speci¯ed as below: u ijt = ® ij +X ijt ¯ i +» jt +" ijt (2.13) = ® ij +X ijt ¯ i +¸ i ¹ jt +[» jt ¡¸ i ¹ jt ]+" ijt (2.14) = ® ij +X ijt ¯ i +¸ i ¹ jt +¾ i ´ jt +" ijt : (2.15) 59 ¹ jt , a residual term from Equation (2.12), is a part of price that is not explained bywholesaleprice,andrepresentsunobservedmarketconditionsa®ectingretailer pricing. ´ jt is a random variable with a standard normal distribution. Thus, I decompose the error term in the utility function, » jt +" ijt , into three parts: a partexplainedbythecontrolfunction,¸ i ¹ jt ,anormallydistributedrandomerror component, » jt ¡¸ i ¹ jt , and the residuals, " ijt . I use Equation (2.15) instead of (2.13) in the choice model estimation, in order to correct for price endogeneity. 2.4.2 Model Estimation I restrict my analysis to predicting consumer choice among the seven top-selling models, which account for about 87% of all transactions in this category: Honda Accord, Nissan Altima, Toyota Camry, Nissan Maxima, Volvo S40, Volkswagen Passat, and Mazda 6. 5 Thus, the ¯nal data set consists of a total of 38,845 new car transactions. 5 I restrict my sample to only those vehicle models with 2% or above market share (see, e.g., Silva-Risso and Ionova, 2008), which eliminates ¯ve vehicle models from the hedonic regression analysis in previous section: Outback, Avalon, Magnum, Impala, and Taurus. I include more vehiclemodelsinthehedonicregressionanalysistoobtainmoreaccurateestimateoftheimpact that each vehicle option or consumer demographics has on new car prices. 60 I use a Hierarchical Bayesian approach to specify the zip code level heteroge- neous model parameters, and make the following distributional assumptions. 6 (® zj ;¯ z ;¸ z ;¾ z ) » MVN(¹;§): (2.16) I specify the hyperprior distributions as below: ¹ » MVN(´;C); (2.17) § ¡1 » MVN((½R) ¡1 ;½): (2.18) I used Markov Chain Monte Carlo (MCMC) methods to estimate the model parameters. Speci¯cally, Gibbs sampling steps are employed to draw ¹ and § estimates, and a random-walk Metropolis-Hastings algorithm is used to draw the zip code level model parameters (® zj ;¯ z ;¸ z ;¾ z ) (Chib and Greenberg, 1995). I ran the MCMC for 100,000 iterations, thinning it by retaining every 50th draw, and assessed convergence by monitoring the time-series plots of the parameter draws. I discarded the ¯rst 1,000 retained draws as \burn-in" and used the last 1,000drawstomakeinferencesabouttheposteriordistributionoftheparameters. 6 There are 725 distinct zip codes in our sample, and the average number of purchase obser- vations per zip code is 53.58 61 2.4.3 Estimation Results Parameter estimates with 95% posterior intervals are reported in Table 2.4. The results show that the coe±cient for LOGPRICE is negative and signi¯cant and the coe±cient for TMAKE is positive and signi¯cant. 7 The coe±cient for RESIDUALS is positive and signi¯cant, which indicates that the product con- tains desirable attributes that are unobserved by researchers and thus omitted from the model. 2.4.4 Counterfactual Analysis In this section, I quantify the informational value of product trade-ins to dealers, by examining its impact on market shares and pro¯ts under the scenarios that retailers discontinue their trade-in programs, using the following procedure. First, I use the estimated parameters to calculate baseline or status quo mar- ket shares and pro¯ts based on the market conditions represented by the data. Inthebaselinecase,alldealersincorporateconsumertrade-ininformationinnew car pricing, that is, charge di®erent transaction prices based on whether or not a consumer trades in a used car and the characteristics of the traded in car. I then re-calculate market shares and pro¯ts conditioning on the counterfactual scenarios and compare these two metrics with the baseline market condition. I examinesevendi®erentscenarios: sixscenariosinwhicheachofthesixbrands,in 7 I estimated a model without endogeneity correction, and ¯nd that the model without control function yields lower (in magnitude) price coe±cient (-0.7766). 62 Table 2.4: Choice Model Estimation Results Variable Mean Value Posterior Interval (2:5%, 97:5%) Honda Accord 2.7519 (2.6500, 2.8539) Nissan Altima 2.6330 (2.5276, 2.7530) Toyota Camry 2.6577 (2.5540, 2.7790) Nissan Maxima 1.4803 (1.3201, 1.6450) Volvo S40 0.6854 (0.5493, 0.8244) Volkswagen Passat 0.1697 (0.0278, 0.3263) LOGPRICE ¡0.9457 (¡1.3737,¡0.5493) RESIDUALS 0.0444 (0.0130, 0.0831) ERROR 0.0049 (¡0.0074, 0.0174) TMAKE 1.7324 (1.6733, 1.7903) 63 turn, does not incorporate trade-in information in pricing of new cars while oth- ers do, and one scenario in which all six brands ignore the information provided by consumer decisions on trade-in and characteristics of traded in vehicles. Tables 2.5 and 2.6 show the impact of discontinuing trade-in programs on marketshareandtotalrevenue, respectively. Eachrowinthetwotablescontains the percentage change in market share and total revenue, respectively. For ex- ample, the ¯rst row of each table reports the percentage change in market share and total revenue when Honda dealers do not incorporate consumer trade-in in- formation in new car pricing but all the other dealers do. Honda market share increases by 0.14%, but revenues decrease by 0.17%, which corresponds to a loss of about $295,000. Honda's market share increases because it draws potential consumers from other brands by lowering new car prices for trade-in consumers. The discontinuation of a trade-in program for one brand a®ects the market shares and pro¯ts of other brands as well, as seen by the o®-diagonal terms in Tables2.5and2.6. ConsiderthecaseinwhichToyotadealersdecidenottoaccept trade-ins while other dealers continue to incorporate the trade-in information in new car pricing decisions, represented by the row labeled Toyota in the tables above. This strategy decreases market shares of the other brands: Honda by 0.04%, Nissan Altima by 0.04%, Nissan Maxima by 0.04%, Volvo by 0.03%, Volkswagen by 0.04%, and Mazda by 0.04%, and decreases the revenue: Honda by 0.04%, Nissan Altima by 0.04%, Nissan Maxima by 0.04%, Volvo by 0.03%, Volkswagen by 0.04%, and Mazda by 0.04%. The intuition for this result is that Toyota's lower new car prices draw in more potential consumers, increasing 64 Table 2.5: Percentage Change in Market Share No Trade-In Brand Accord Altima Camry Maxima S40 Passat 6 Honda 0:1372 ¡0:0367 ¡0:0386 ¡0:0369 ¡0:0340 ¡0:0425 ¡0:0382 Nissan ¡0:0592 0:0751 ¡0:0618 0:0147 ¡0:0442 ¡0:0609 ¡0:0504 Toyota ¡0:0415 ¡0:0409 0:1368 ¡0:0404 ¡0:0347 ¡0:0418 ¡0:0391 Volvo ¡0:0028 ¡0:0020 ¡0:0027 ¡0:0021 0:0748 ¡0:0029 ¡0:0028 Volkswagen ¡0:0027 ¡0:0023 ¡0:0025 ¡0:0023 ¡0:0023 0:1035 ¡0:0026 Mazda ¡0:0017 ¡0:0013 ¡0:0016 ¡0:0013 ¡0:0016 ¡0:0018 0:1114 All 0:0292 0:0090 0:0295 ¡0:0910 ¡0:0423 ¡0:0467 ¡0:0222 65 Table 2.6: Percentage Change in Revenue No Trade-In Brand Accord Altima Camry Maxima S40 Passat 6 Honda ¡0:1682 ¡0:0369 ¡0:0387 ¡0:0370 ¡0:0341 ¡0:0426 ¡0:0384 Nissan ¡0:0594 ¡0:1495 ¡0:0622 ¡0:1516 ¡0:0442 ¡0:0611 ¡0:0506 Toyota ¡0:0417 ¡0:0411 ¡0:1555 ¡0:0405 ¡0:0349 ¡0:0419 ¡0:0392 Volvo ¡0:0028 ¡0:0020 ¡0:0027 ¡0:0021 ¡0:0275 ¡0:0029 ¡0:0029 Volkswagen ¡0:0027 ¡0:0023 ¡0:0025 ¡0:0023 ¡0:0023 ¡0:0212 ¡0:0026 Mazda ¡0:0017 ¡0:0013 ¡0:0016 ¡0:0013 ¡0:0016 ¡0:0018 ¡0:0277 All ¡0:2760 ¡0:2335 ¡0:2625 ¡0:2351 ¡0:1444 ¡0:1712 ¡0:1611 66 its market share, while decreasing its revenues and the revenue of all the other brands. Speci¯cally, Toyota's revenue declines by $267,000 while the revenue of the other brand dealers also declines by $257,000. The loss of automobile dealers is absorbed by car consumers who pay lower prices for new cars because dealers ignore trade-in information in pricing. The collective consumer surplus increases a total of $1,912,000 when no brands consider trade-in information in pricing of new cars. 2.5 Conclusions The purpose of this research is to propose a theory for how retailers incorporate consumer trade-in information in their pricing of new products, and how to test it in a ¯eld setting. I develop a theoretical model of retailer pricing with trade- ins and ¯nd empirical support of the propositions derived from the proposed model with the U.S. automobile transaction data. While previous research has highlighted the role of trade-ins in retailer pricing of new products, I show that retailers incorporate in pricing both consumer decisions on whether or not to trade in used products and characteristics of trade-in products. I also conduct a series of counterfactual analyses to demonstrate that a retailer may decide to discontinue trade-in programs in order to win competitors' market shares, the decision results in revenue decrease of all the brands in the market. Limitations and future research directions of this research include the follow- ing. First, the proposed model requires an assumption that each consumer who purchases a new car currently has a used car, and that each consumer in my 67 model chooses between trading-in and private selling his or her used car. This assumption is very likely to hold because the premium midsize sedan market used in the empirical analysis that typically targets replacement buyers rather than ¯rst-time buyers, for whom the entry-level compact segment is more attrac- tive. Future researchmay extend thesemodelsbyincorporating ¯rst time buyers in the modeling framework and further di®erentiating ¯rst time consumers and consumers who sell their used car privately. Second, I do not empirically examine consumers' decision on whether or not to trade in their used vehicle. Future research should seek to ¯nd factors that drive consumers' trade-in decision, which may help dealers promote car trade-ins moree®ectivelysothatthedealersincreasetheinformationalbene¯toftrade-ins. Third, I ¯nd that consumers who purchase the same make car as their trade- inspayahigherprice forthe new car. Futureresearchmaytake afurtherstep to examine other possible brand e®ects in new car pricing for trade-in consumers. Suppose two consumers purchasing brand A trade-in brand B and C, respec- tively. Brand A dealer may inference on the two consumers' brand preference and willingness to pay, based on the similarity, substitutability, and other com- petitive factors between brand A and the other two brands. The incorporation of such brand e®ect will provide a more detailed picture of the impact of trade-in information in dealer pricing. Fourth,mycounterfactualscenariosrequiremetosimulatenewcarpricesthat prevail when one dealer does not incorporate trade-in information in the pricing of new cars. Strictly speaking, in this case the dealer should charge the same 68 price (p) to those consumers who trade in a used car and to those who do not. In the simulations, however, I operationalize this price by setting the trade-in, same-make, and same-model dummies to zero in the hedonic regression, which yields p NTI , the price that a dealer would charge to consumers who do not trade intheirused cars. 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Zhu, Rui (Juliet), Xinlei (Jack) Chen, Srabana Dasgupta. 2008. Can trade-ins hurt you?: Exploring the e®ect of a trade-in on consumer's willingness to pay for a new product. Journal of Marketing Research 45(2) 159{170. 74 Appendices A MCMC Estimation for BPRCP Model A.1 Prior Speci¯cations 1. ¾ 2 i »Inverted Gamma(a (¾) 0 ;b (¾) 0 ) a (¾) 0 =5; b (¾) 0 =0:05 2. ± 2 i »Inverted Gamma(a (±) 0 ;b (±) 0 ) a (±) 0 =5; b (±) 0 =0:05 3. Ã 2 i »Inverted Gamma(a (Ã) 0 ;b (Ã) 0 ) a (Ã) 0 =5; b (Ã) 0 =0:05 A.2 Conditional Posteriors 1. u i jy i ;¯ i ;°;µ;½;§;ª;;±, u i »truncated normal (X i ¯ i +µ i ;§), where the truncation is that if y i =j then u ij >y ik ;8k6=j . 75 Appendix A continued 2. ¾ 2 i ju;¯ i ;°;µ;½;ª;;± , ¾ 2 i »Inverted Gamma (a (¾) ;b (¾) ) , a (¾) =a (¾) 0 + n 2 , b (¾) = h (~ u i ¡ ~ X i ¯ i ) T (~ u i ¡ ~ X i ¯ i )+2=b (¾) 0 i =2 , ~ u i =WR 1 2 i u , ~ X i =WR 1 2 i X . 3. ¯ i ju;°;µ;½;§;ª;;± , ¯ i »N( ^ ¯ i ;©) , ^ ¯ i =© h X T (WR i I J¡1 )(u¡µ)+(X T (WR i I J¡1 )XA i °)=± 2 i , ©= h X T (WR i I J¡1 )X +X T (WR i I J¡1 )X=± 2 i ¡1 , A i =(w i1 I k ¢¢¢w in I k ), ° = 0 B B B B B B B B B @ ¯ 1 . . . ¯ n 1 C C C C C C C C C A . 4. Update ° with new draws of ¯ i 's . 5. ±ju;¯ i ;°;µ;½;§;ª; , ± 2 »Inverted Gamma (a (±) ;b (±) ) , a (±) =a (±) 0 + n£k 2 , 76 Appendix A continued b (±) = h P n i=1 (¯ i ¡A i °) T (X T (WR i I J¡1 )X) ¡1 (¯ i ¡A i °)+2=b (±) 0 i =2 . 6. µju;¯ i ;°;µ;½;§;ª;;± , µ»N(P;Q) , P =Q¢" , Q=(I¡Ã ¡2 R T R) ¡1 , "=(u 1 ¡X 1 ¯ 1 ;:::;u n ¡X n ¯ n ) T , R =(I¡½(WP I J¡1 )) . 7. Ã 2 j ju;¯ i ;°;µ;½;§;;± , Ã 2 j »Inverted Gamma (a (Ã) j ;b (Ã) j ) , a (Ã) j =a (Ã) 0 + n 2 , b (Ã) j = h µ T j (I¡½WP) T (I¡½WP)µ j +2=b (Ã) 0 i =2 . 8. ½ju;¯ i ;°;µ;½;§;ª;;± . I used a random walk Metropolis-Hastings algorithm to draw ½, as it does not have a closed form solution. (Chib and Greenberg, 1995) ½ new =½ old +¢ , 77 ¢»N(0;0:005 2 ): acceptance probability = min h jR(½ new )jexp(¡0:5(1=Ã 2 )µ T R(½ new ) T R(½ new )µ) jR(½ old )jexp(¡0:5(1=Ã 2 )µ T R(½ old ) T R(½ old )µ) ;1 i . 78 B Simulated Data Analysis of a BPRCP Model I simulated a data set of 300 individuals. Each individual (i = 1;2;:::300) is assumed to choose an alternative (j =1;2; or 3) that maximizes her unobserved latent utility. u ij = ® j +X ij ¯ i +µ ij +" ij ; µ = ½(WP I J¡1 )µ+»; " i » N(0;§); » i » N(0;ª): I generated two covariates for X matrix a stochastic random utility term ("), eachofwhichfromastandardnormaldistribution. Iassumethat½=0:5,§=I, and ª=3I. ¯ i¢ 's are assigned to each individual as below. ¯ ik = 8 > > > > > > > > > < > > > > > > > > > : 1:4 i=1;:::90 1:4+0:01¢(i¡90) i=91;:::210 2:6 i=211;:::300 ;k =1;2: 79 Appendix B continued A spatial weight matrix for preference correlation is constructed in a way that eachindividualiscorrelatedwithhisorher60closestneighbors,withanassump- tion that the individuals are connected circularly. For example, individual 31 is correlatedwithindividual1to30and32to61. Similarly, individual280iscorre- latedwithindividual250to279, 281to300, and1to10. Aspatialweightmatrix for response correlation is constructed in a way that each individual's true ¯ is a weightedaverageofhercorrelatedneighbors. Speci¯cally, individual1to90have the same value of ¯(= 1:4), and they are correlated with each other. Similarly, individual 211 to 300 are correlated with each other and share the same value of ¯(= 2:6). For individual 91 to 210, a correlation structure is imposed so that each individual is correlated with his or her 60 closest neighbors. I used Markov Chain Monte Carlo (MCMC) methods for 50;000 iterations, thinned the chain by keeping every 50th draw, to estimate a BPCP model with thesimulateddata. Ideletedthe¯rst500drawsoutof1;000retaineddrawsfrom the thinned chain, and used the last 500 draws to calculate posterior average of the parameters. Figure 3 displays two plots of true value and estimated posterior distribution of¯ 1 and¯ 2 ,respectively. Ineachoftheplots, asolidlineindicatestruevaluesof ¯, dots represent point estimates of the parameter provided by a BPCP model, and a shaded area shows 2:5% to 97:5%, or 95% range of posterior distribution of each individual's ¯. The results show that my proposed model recovers true 80 ¯ parameters of the model with simulated data. Figure 4 contains histograms of posteriorestimatesof Ã 2 1 , Ã 2 2 , and½. Eachofthehistogramsshowsthatposterior estimates are distributed around the true value. 81 C First Order Condition Derivation The expected pro¯t of dealer for trade-in case is as below: (p TI ¡w)¢[1¡F v (p TI jT =t;C >s)]: (19) Taking derivative with respect to p TI , I obtain the following: (p TI ¡w) h ¡f v (p TI jT =t;C >s)+ Ã ¡ @F v @s ¢ @s @p ! i + h 1¡F v (p TI jT =t;C >s) i =0; (20) which is equal to the following ¯rst order condition: (p TI ¡w)¢ " 1+ (@F v =@s)(@s=@p TI ) f v (p TI jT =t;C >s) # = [1¡F v (p TI jT =t;C >s)] f v (p TI jT =t;C >s) : (21) 82 D Proofs of Propositions D.1 Proof of Proposition 1 For all p 0 ·p 1 and t 0 ·t 1 , by de¯nition of a±liation, f(p 0 ;t 1 )f(p 1 ;t 0 )·f(p 0 ;t 0 )f(p 1 ;t 1 ); (22) or, equivalently, f(p 0 ;t 1 ) f(p 0 ;t 0 ) · f(p 1 ;t 1 ) f(p 1 ;t 0 ) ; (23) which, by a conditional distribution representation of joint density function, can be written as: f(p 1 jt 0 )f(t 0 ) f(p 0 jt 0 )f(t 0 ) · f(p 1 jt 1 )f(t 1 ) f(p 0 jt 1 )f(t 1 ) ; (24) or, equivalently, f(p 1 jt 0 ) f(p 0 jt 0 ) · f(p 1 jt 1 ) f(p 0 jt 1 ) : (25) Thus, for all p and t, Z z p 0 f(p 1 jt 0 ) f(p 0 jt 0 ) dp 1 · Z z p 0 f(p 1 jt 1 ) f(p 0 jt 1 ) dp 1 ; (26) 83 Appendix D continued or, equivalently, 1¡F(p 0 jt 0 ) f(p 0 jt 0 ) · 1¡F(p 0 jt 1 ) f(p 0 jt 1 ) : (27) [Q.E.D.] D.2 Proof of Proposition 2 An equilibrium pricing strategy for the dealer is a pair of prices simultaneously satisfying (2.2), (2.4), (2.5), and (2.7). It was shown that p ¤ NTI and p ¤ TI satisfy (2.4) and (2.7). The pair of prices satisfy (2.2) and (2.5) if p ¤ NTI < p ¤ TI . This is now shown. Note that the unconditional inverse hazard function © NTI (p;k) can be written as the expectation of the conditional over T. Therefore, © NTI (p;k) = [1¡F v (pjC <k)] f v (pjC <k) = E T " [1¡F v (pjT;C <k)] f v (pjT;C <k) # · h 1¡F v (pjT = ¹ T;C <k) i f v (pjT = ¹ T;C <k) · [1¡F v (pjT =t;C <k)] f v (pjT =t;C <k) = © TI (p;t;k); (28) 84 Appendix D continued where the ¯rst inequality follows from assumption A3 and Jensen's inequality and the second inequality follows from the fact that t > ¹ T and assumption A1. [Q.E.D.] 85 E DealerPricingBasedonTrade-InInformation When Consumers Are Myopic Supposeamyopicconsumerwhoisnotabletoanticipateadealer'suseoftrade-in information. The consumer brings her used car as a trade-in, if and only if, the convenience bene¯t of going through the dealer exceeds the premium he or she could obtain by selling the used vehicle in the private market. Mathematically, s´k: (29) Notethatequation(29)isdi®erentfromequation(2.1)inthatamyopicconsumer does not consider p TI ¡p NTI when he or she decides on whether or not to trade in a used vehicle. Istartwithaconsumerwhobringshisorherusedvehicleasatrade-in,which implies the following: C >s: (30) The dealer chooses p TI to maximize expected pro¯t: (p¡w)¢[1¡F v (pjT =t;C >s)]; (31) with the corresponding ¯rst order condition as below: (p¡w)= [1¡F v (pjT =t;C >s)] f v (pjT =t;C >s) : (32) 86 Appendix E continued Thus, the right-hand side of equation (32) is same as that of equation (2.4). The left-hand side of equation (32) increases in p, and the right-hand side of it decreases in p but increases in T. Therefore, Proposition 1 holds for a myopic consumer. Now I examine the condition in which the consumer does not trade in his or her old vehicle. In this case, the only inference the dealer can make is that the cost of selling the consumer's used car does not exceed the premium of selling it privately, i.e., C <s: (33) The dealer then chooses new car price p NTI to maximize the expected pro¯t: (p¡w)¢[1¡F v (pjC <s)]; (34) which leads to the following ¯rst order condition: (p¡w)= [1¡F v (pjT =t;C <s)] f v (pjT =t;C <s) : (35) Thus, the right-hand side of equation (35) is same as that of equation (2.7). In addition, the left-hand side of equation (35) is same as that of equation (32), which implies that it does not depend on a consumer's decision on whether or not to trade in a used car. The left-hand side of equation (35) increases in p, 87 Appendix E continued and the right-hand side of it decreases in p. Further, © NTI (p;k) < © TI (p;t;k). Therefore, Proposition 2 holds for a myopic consumer. 88 Figure 3: Posterior Distributions of ¯ 1 and ¯ 2 50 100 150 200 250 300 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 observation beta 1 50 100 150 200 250 300 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 observation beta 2 89 Figure 4: Histograms of Posterior Estimates of Ã 2 1 , Ã 2 2 , and ½ psi_1 squared Mean = 3.256 Frequency 1 2 3 4 5 6 7 8 0 10 20 30 40 50 60 70 psi_2 squared Mean = 2.731 Frequency 1 2 3 4 5 6 7 8 0 10 20 30 40 50 60 70 rho Mean = 0.516 Frequency 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0 5 10 15 20 25 30 35 90

Abstract (if available)

Abstract My dissertation research examines implications of product trade-ins for consumer demand and retailer pricing behavior. Although product trade-ins are very prevalent in many durable goods markets, such as golf clubs, home appliances, and automobiles, there has been relatively little academic research examining this phenomenon. I examine how information provided by consumers' previous purchases can be leveraged to predict their future choices and its implications for retailer pricing decisions.

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Creator Kwon, Ohjin (author)

Core Title Essays on product trade-ins: Implications for consumer demand and retailer behavior

School Marshall School of Business

Degree Doctor of Philosophy

Degree Program Business Administration

Publication Date 04/14/2012

Defense Date 03/15/2010

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag OAI-PMH Harvest,Product trade-ins

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Siddarth, Sivaramakrishnan (committee chair), Dukes, Anthony J. (committee member), Hsiao, Cheng (committee member), Luo, Lan (committee member)

Creator Email Ohjin.Kwon.2010@marshall.usc.edu,ohjin337@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m2913

Unique identifier UC176810

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Legacy Identifier etd-Kwon-3538.pdf

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Document Type Dissertation

Rights Kwon, Ohjin

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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Repository Location Los Angeles, California

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