Dynamic Demand for New and Used Durable Goods without Physical Depreciation: The Case of Japanese Video Games

Transcription

1 Dynamic Deman for New an Use Durable Goos without Physical Depreciation: The Case of Japanese Vieo Games Masakazu Ishihara Stern School of Business New York University Anrew Ching Rotman School of Management University of Toronto First raft: May 8, 21 This raft: Dec 15, 212 We have benefite from iscussions with Srihar Moorthy, Ron Borkovsky, Victor Aguirregabiria, Harikesh Nair, Avi Golfarb, Susumu Imai, Nitin Mehta, Mengze Shi, Tanjim Hossain, Davi Soberman, Ig Horstmann, Any Mitchell, Alon Eizenberg, Christos Genakos, Benjamin Shiller. We also thank seminar an conference participants at U of Toronto, Erasmus School of Economics, NYU, U of Michigan, U of Rochester, UT-Dallas, UBC, NUS, HKUST, Washington University-Saint Louis, OSU, UCLA, Columbia, Northwestern, UCSD, McMaster, UC Berkeley, Stanfor, Chicago, 29 Marketing Dynamics Conference, 21/212 IIOC, 212 CKGSB Marketing Research Forum, an 212 NBER Summer Institute Economics of IT an Digitization Workshop for their helpful comments. All remaining errors are ours. Please irect all corresponence to Masakazu Ishihara, Stern School of Business, New York University. mishihar@stern.nyu.eu. Electronic copy available at:

2 Dynamic Deman for New an Use Durable Goos without Physical Depreciation: The Case of Japanese Vieo Games Abstract For information/igital proucts, the use goos market has been viewe as a threat by proucers. However, it is not clear if this view is justifie because the use goos market also provies owners with an opportunity to sell their proucts. To investigate the impact of the use goos market on new goos sales, we collect a unique ata set from the Japanese vieo game market. Base on the ata, we evelop an estimate a new ynamic structural moel of consumers buying an selling ecisions. The estimation results show that the consumption value of owners epreciates much faster than that of potential buyers, an consumers are heterogeneous in transaction costs of buying an selling use copies. We also fin evience that new an use copies are not close substitutes, an consumers are forwar-looking. The latter suggests that the future resale opportunity coul increase consumers willingness-to-pay for new copies. Using the estimates, we quantify the impact of eliminating the use game market on publishers profits. We fin that this policy woul reuce the average profits per game by 1% if publishers o not ajust their prices. However, if they ajust prices optimally, it woul increase the average profits per game by 19%. Keywors: Information/Digital Proucts, Durable Goos, Use Goos Market, Deman Estimation, Dynamic Programming, Transaction Costs, Satiation, Discount Factor, Bayesian Estimation. Electronic copy available at:

3 1 Introuction The existence of use goos markets has been viewe as a serious problem by proucers in information/igital prouct categories such as books, CDs/DVDs, an vieo games. They argue that the competition from use goos significantly lowers their profits an reuce the incentive to evelop new proucts. For instance, book publishers an authors expresse their annoyance to Amazon over use books sol on its websites (Teeschi 24). Vieo game publishers in Japan attempte to kill off use vieo game retailing by suing use vieo game retailers (Hirayama 26). Their main argument is that proucts like books an vieo games physically epreciate negligibly, but owners consumption values can ecline very quickly ue to satiation. As a result, unlike proucts that physically epreciate more consierably (such as cars), proucers of information/igital proucts may face competition from use goos that appear to be almost ientical to new goos soon after the release of a new prouct. However, their argument focuses only on one aspect of use goos markets (substitution effect), an ignores the possibility that transaction costs of buying an selling use goos coul reuce the substitutability between new an use goos. Moreover, the existence of use goos markets provies consumers with a selling opportunity. If consumers are forwar-looking an account for the future resale value when making a buying ecision, the effective price consumers pay for a prouct will be lower than the price of the prouct (resale effect). This feature implies that the existence of use goos markets coul increase the sales of new goos. Thus, whether the existence of use goos markets hurts or benefits new-goo proucers is an empirical question, an the answer epens on which effect, substitution or resale effect, ominates. In light of these shortcomings, this paper contributes to the existing literature in two important imensions. First, we assemble a new ata set from the Japanese vieo game market, which inclues weekly aggregate level ata for 2 vieo game titles release in Japan between 24 an 28. The novel aspect of this ata set is that, in aition to the sales an prices of new an use goos, which are the main variables focuse in the previous works (e.g., Esteban an Shum 27, Chen et al. 211, Schirali 211), it inclues 1

4 three new important variables which have not been stuie before: (i) the resale value of use goos, 1 (ii) the quantity of use goos retailers purchase from consumers, an (iii) the aggregate inventory level of use goos at retailers. They allow us to ocument new empirical regularities for the use vieo game market. Secon, base on this new ata set, we evelop an estimate a new structural moel of consumers buying an selling ecisions of urable goos which o not suffer from physical epreciation. To our knowlege, this is the first ynamic moel of forwar-looking consumers that incorporates all of the following features: (i) new an use goos buying ecisions, (ii) use goos selling ecision, (iii) consumer expectations about future prices of new an use goos an resale values of use goos, (iv) transaction costs of buying an selling use goos, (v) the impact of use goos availability on buying ecisions, an (vi) the epreciation of both owners an potential buyers consumption values. In our moel, the expecte iscounte value of future payoffs from buying a prouct is etermine by a ynamic consumer selling ecision problem, which epens on the epreciation rate of owners consumption values an future resale values. This moeling approach allows us to stuy the role of consumer expectation about future use-copy prices an resale values on current buying ecisions. It shoul be highlighte that we allow owners consumption values an potential buyers consumption values to epreciate ifferently over time. In the previous empirical literature, these two epreciation rates are always assume to be the same for owners an buyers (e.g., Esteban an Shum 27, Chen et al. 211, Schirali 211). However, this assumption will likely be violate in information/igital prouct categories such as CDs/DVDs an vieo games because for prouct owners, the epreciation of consumption values is mainly ue to satiation (satiation-base epreciation); but for potential buyers, it is mainly ue to how long a prouct has been release (freshness-base epreciation). Our new ata set, together with the structural moel, allow us to measure these two concepts of epreciation separately. To estimate the propose ynamic moel, we employ a new Bayesian Markov chain Monte Carlo (MCMC) algorithm first propose by Imai, Jain an Ching (29) (IJC algorithm), an is extene by 1 We efine resale value as the amount consumers receive when they sell their use vieo games to retailers. In Japan, retailers usually set a take-it-or-leave-it resale value for each game, an consumers sell their games at that resale value. Negotiation is uncommon. 2

5 Ishihara an Ching (212) to a non-stationary finite-horizon environment. As we will escribe in the moel section, our propose framework uses a non-stationary finite-horizon ynamic programming moel with stochastic continuous state variables. Ishihara an Ching (212) argue that their algorithm has the potential to reuce the computational buren of this class of moels. In this paper, we exten their algorithm further by combining it with the pseuo-policy function approach propose by Ching (21b), to aress the potential price enogeneity problem. The metho we propose augments unobserve aggregate shocks base on the joint-likelihoo of the eman-sie moel an the pseuo-policy functions. Compare to the GMM approach use in the previous literature (Berry et al. 1995, Gowrisankaran an Rysman 211), our approach oes not require using the contraction mapping proceure to recover the mean utility level from observe market shares. Also, since we use the Bayesian ata augmentation technique, unlike the simulate maximum likelihoo metho, we o not nee to integrate out the unobserve shocks uring the estimation. 2 We apply this new empirical framework to the Japanese vieo game market, an stuy the impact of the use vieo game market on the profitability of vieo game publishers. The estimation results show that the consumption value of owners epreciates much faster than that of potential buyers. We also fin evience that consumers are forwar-looking, suggesting that the future resale opportunity coul increase consumers willingness-to-pay for new copies. Consumers are heterogeneous in the transaction costs of buying an selling use copies in particular, those who have relatively higher costs of buying also ten to have lower costs of selling. Moreover, we fin that the transaction costs (both psychological costs an search costs) of buying a use copy reuce the substitutability between new an use copies in the Japanese vieo game market. Finally, we fin that the eman for use copies is sensitive to its availability, an that the elasticity of use-copy supply eclines over time. These finings might partly explain why the aggregate inventory of use-copy increases uring the early stage of the prouct lifecycle. Using the estimate moel, we quantify the impact of eliminating the use vieo game market on newcopy sales an profits by conucting a counterfactual experiment. The vieo game market has recently trie to move towars using igital ownloa as an alternative istribution channel. A complete switch to 2 Yang et al. (23) an Musalem et al. (29) evelope similar Bayesian algorithms for static moels. 3

6 igital ownloa woul essentially shut own the use vieo game market. Therefore, the results of this experiment coul she some light on this strategy. We first conuct the experiment by holing the prices of new copies at the observe level. On average, the elimination of the use vieo game market reuces consumers willingness-to-pay for new copies of vieo games in the earlier part of the prouct lifecycle this is mainly because the resale effect ominates the substitution effect. As a result, we fin that the average profits per game eclines by 1.3%. We then compute the optimal prices of new copies when there is no use game market, an quantify the change in profits. We fin that the optimal flat prices are on average 33% lower than the observe prices, an the elimination of the use vieo game market coul increase the average profits per game by 18.6%. The rest of the paper is organize as follows. Section 2 reviews the previous literature. Section 3 escribes the Japanese vieo game ata use in this paper an presents some empirical regularities that have not been ocumente in the previous literature. Section 4 escribes the ynamic iscrete choice moel of consumer buying an selling ecisions. Section 5 explains the estimation strategy an ientification. In Section 6, we iscuss the parameter estimates an the counterfactual experiment results. Section 7 conclues. 2 Literature Review Our research is closely relate to previous stuies on vieo game markets using the ynamic structural moeling approach (e.g., Nair 27, Dubè et al. 21, Liu 21). 3 In particular, Nair (27) stuies the intertemporal price iscrimination for new games in the U.S. vieo game inustry, an examines the role of consumer price expectation. However, none of these stuies accounts for the potential impact of the use goo market on the eman for new games. Previous empirical stuies on new an use urable goos have largely focuse on car (e.g., Esteban an Shum 27, Chen et al. 211, Schirali 211, Engers et al. 29, Purohit 1992) an housing markets (e.g., Tanaka 29). One common feature of the moels in these empirical stuies is that the epreciation rate of consumption values is assume to be common across 3 Our moeling framework is also relate to the previous literature on the ynamic purchase ecisions in other consumer urable goos markets (e.g., Melnikov 2, Song an Chintagunta 23, Goron 29, Goettler an Goron 211, Carranza 21, Gowrisankaran an Rysman 211). 4

7 potential buyers an prouct owners. This assumption is motivate by two challenges: (i) when physical epreciation is present, it is ifficult to separately measure the ecline of owners consumption values ue to satiation from that ue to physical epreciation; (ii) even if researchers can control for physical epreciation, the consumption value epreciation for potential buyers (mainly ue to how fresh the prouct is) can still be ifferent from that for owners (mainly ue to satiation). The ata sets use in the previous stuies only inclue variation in sales an prices of new an use goos. It lacks information on the quantities of use goos sol by consumers to retailers an the associate resale values, which are crucial for isentangling these two consumption value epreciation. These challenges have force the previous stuies to assume that consumption value epreciation is ientical for prouct owners an potential buyers. In our stuy, we argue that by focusing on information/igital proucts (such as vieo games), we can rule out physical epreciation. Moreover, our new ata set, which contains information on the quantities of use copies supplie by owners over time, allows us to relax this assumption. Another important ifference between our stuy an the previous stuies is that we will estimate consumers iscount factor, instea of calibrating it accoring to the interest rate. As we will escribe, our moel implies that resale values of use copies provie exclusion restrictions that help ientify the iscount factor (Magnac an Thesmar 22, Fang an Wang 212). The intuition is that resale values o not affect consumers current utility for buying ecisions, but affect consumers expecte future payoffs. As a result, the observe correlation between sales of new vieo games an resale values can help recover the iscount factor. Our ientification strategy is similar to Chevalier an Goolsbee (29), who stuy whether stuents are forwar-looking in their textbook purchase ecision. However, since they o not observe when an whether stuents sell their textbooks, they assume that all of them will sell it at the en of the semester, an the textbook resale value affects all stuents utility for buying a new textbook if they are forwarlooking. While this assumption may be reasonable in the textbook market, the timing of selling use goos is enogenous in general. It shoul be highlighte that we enogenize the timing of selling use vieo game copies in this stuy. Furthermore, we observe how many owners sol their games to retailers an the cor- 5

8 responing resale value. This allows us to moel the expecte future payoff from buying a vieo game as a function of not only the future resale value, but also the value of keeping the vieo game in the future. As a result, we have a richer framework to control for the impact of the resale value on buying ecisions. Also, this is the first paper that separately estimates the transaction costs for buying an selling use goos. Previous stuies o not separately observe the quantities of use copies purchase an supplie by consumers an associate use-copy prices an resale values. Thus, they can estimate only one transaction cost (e.g., Chen et al. 211, Schirali 211). Our results show that these two transaction costs play ifferent roles in influencing ynamic consumer buying an selling ecisions. There is also a large boy of theoretical literature in economics an marketing. Theoretical papers in economics are mainly concerne with urability choice, pricing, the role of market frictions, etc. for urable goos monopolists (e.g., Swan 197, Rust 1986, Bulow 1986, Anerson an Ginsburgh 1994, Walman 1996, Henel an Lizzeri 1999, Johnson 211). In marketing, several papers examine a variety of marketing practices in new an use urable goos markets. These inclue leasing contracts (e.g., Desai an Purohit 1998, Desai an Purohit 1999), channel coorination (Desai et al. 24, Shulman an Coughlan 27), trae-ins (Rao et al. 29), an retail versus P2P use goos markets (Yin et al. 21). One common feature of these theoretical moels is that they assume a market-clearing conition for use goos markets in every perio. However, our ata show that this assumption is far from a goo approximation for the Japanese vieo game market we consistently observe excess supply of use goos. Thus, our ynamic structural eman moel will not impose a market-clearing conition. Instea, we will take avantage of the observe aggregate inventory of use copies an allow the transaction costs to epen on it (to capture the iea that it may reuce the search costs). When our research is well uner way, we learn another inepenent on-going work by Shiller (212), who also investigates the interaction between new an use goo eman, but in the U.S. vieo game inustry. Due to the limite availability of use vieo game ata in the U.S., he only examines online auction ata for use goos transactions an scales it up by a factor of approximately forty in orer to approximate the 6

9 entire use goos market. As a result, his moeling approach an counterfactual experiment are ifferent from ours in three important imensions: First, he assumes that the resale value is the same as the use-copy price. Therefore, unlike our stuy, his moel oes not have any exclusion restrictions that can help ientify the iscount factor, an hence he calibrates it accoring to the interest rate. Secon, since he oes not observe the eman for an the supply of use copies in the regular retail market, he assumes a completely frictionless use goo market, an that the use goo market clears every perio. In contrast, our ata come from use goos transactions at retailers, which account for about 8% of the entire use goos market in Japan uring our sample perio. When retailers act as a mileman for use goos transactions, it is crucial to unerstan the role of transactions costs for both buying an selling ecisions by using ata on both quantities emane an supplie for use goos, an the corresponing prices an resale values. In section 6, we will iscuss how transactions costs generate important ynamic patterns in both consumer buying an selling ecisions. Finally, the U.S. an Japanese vieo game markets have aopte ifferent pricing practices for new copies. As we will escribe in the next section, Japanese vieo game publishers have historically been using flat-pricing for new copies. However, in the U.S., price skimming has been a common practice. As a result, Shiller s paper an ours investigate the optimal pricing implication for ifferent pricing practices (price skimming versus flat pricing) in the counterfactual experiments where the use vieo game market is shut own. 4 3 Data 3.1 Japanese vieo game inustry Since mi-8s, the Japanese vieo game market has grown rapily. The size of the inustry in 29 has reache $5.5 billion on a revenue basis (incluing sales of harware, software, other equipments). This is about three times larger than the theatrical movie revenue in Japan, an it has become one of the most 4 There are two other working papers which also stuy the vieo game markets using the structural moeling approach. Lee (212) examines the impact of vertically integrate an exclusive software on inustry structure an welfare in the U.S. vieo game inustry. Zhou (212) proposes a framework for stuying ynamic pricing problems in a two-sie market, an applies it to the U.S. vieo game inustry; she extens the estimation metho propose by Ishihara an Ching (212) to estimate her moel. Both stuies abstract away the use vieo game market. 7

10 important sectors in the Japanese entertainment inustry. The existence of the use goo market has been a serious issue for vieo game publishers since 9s. In 29, the sales of use vieo games (software) alone amounts to $1. billion on a revenue basis. One reason for the large use vieo game market in Japan coul be that vieo game renting by thir-party companies is prohibite by law in Japan. 5 Another reason argue by Hirayama (26) is the flat-pricing strategy commonly aopte by vieo game publishers - the price of new games is maintaine at the initial level at least one year after the release. 6 This may provie an opportunity for use goos market to grow an capture the segment of consumers who o not min buying use goos. However, it can also be argue that the existence of the use market has inuce publishers to aopt the flat-pricing strategy. Liang (1999) uses a theoretical moel to show that when use goos markets are present, urable goos monopolists may be able to creibly commit to a high price (avoiing the Coase Conjecture). 7 While investigating the optimality of the flat-pricing strategy is interesting, we will leave this topic for future research. Instea, we will take the flat pricing strategy as given, an focus on unerstaning consumers ynamic buying an selling ecision problem. 3.2 Japanese vieo game ata We have collecte a ata set of 2 vieo games that were release in Japan between 24 an 28. The ata come from several sources. For each vieo game, weekly aggregate sales of new copies an its manufacturer suggeste retail price (MSRP) are obtaine from the weekly top 3 ranking publishe in Weekly Famitsu Magazine, a major weekly vieo game magazine in Japan publishe by Enterbrain, Inc. The average number of weeks observe across games is 19 weeks. In Japan, the sales of new copies sharply eclines after the release week (see Figure 1). In our ata set, the meian percentage of new game copies sol in the release week (relative to the total annual sales for the first year) is 54%, an the meian percentage of new game copies sol within the first month (4 weeks) after release is 82%. Thus, the sales of new copies is highly 5 In principle, vieo game publishers can run the rental business for their own vieo games. However, only one publisher attempte to operate it in the history an i not succee an exite. 6 Note that in Japan, resale price maintenance is illegal for vieo games although it is legal for books, magazines, newspapers an music. 7 The iea is similar to Ching (21a) an Frank an Salkever (1992), who argue that enogenous market segmentation can allow bran-name firms to sustain a high price when facing entry of generic proucts in the prescription rug market. 8

11 concentrate within the first month in Japan. In aition to the ata from the primary market, we collecte weekly aggregate traing volumes (both buying an selling) an the associate weekly average retail prices an resale values in the use market by game title. These are collecte from the Annual Vieo Game Inustry Report publishe by Meia Create Co., Lt. The average number of weeks observe across games is 36 weeks. Accoring to an annual inustry report by Enterbrain, Inc., about 8% of use vieo game traing occur at retailers uring our sample perio. Thus we o not consier the possibility such as online auctions for buying an selling use copies. We also collecte vieo game characteristics from Weekly Famitsu Magazine, incluing average critic an user rating, story-base game ummy, 8 an multi-player game ummy. Finally, the potential size of market for a vieo game is measure by the installe base of the platform in which the vieo game was release. The platforms of the 2 games inclue three consoles (PlayStation 2, PlayStation 3, Ninteno GameCube). We collecte the weekly sales of all three consoles above from their release week to calculate the cumulative sales. Table 1 shows the summary statistics. The average price of use copies across games an time is about two-thirs of the price of a new copy. The average retailer markup for use copies is large: 1,687.2 in JPY or 73.%. This number is in contrast to the average retailer markup for new copies, which is aroun 1% (Tachibana 26), an provies strong incentives for retailers to trae use copies. The average relative size of the use game market to the new game market, efine as the ratio of cumulative sales of use copies to that of new copies at the en of new-copy sales sample perio, is.11 with a maximum of.29 an a minimum of.2. These numbers might appear small, but this is mainly because of the length of our sample. We observe the sales of new copies on average for 19 weeks, an the sales of use copies typically lasts longer than that of new copies beyon 19 weeks. If we ha a longer time-series ata set, we woul expect the average ratio to be significantly larger than.11. However, our ata show that we have variation in the ratio. In particular, our ata set contains vieo games with a very small use game market (the 8 Story-base games (e.g., role-playing games) have an ening of the story, while non story-base games (e.g., sports games) have no clear efinition for ening. 9

12 minimum is 2%). Thus, our parameters will not be estimate by ata variation that are completely far from the counterfactual experiment situation, which is shutting own the use game market. 3.3 Some empirical regularities In this section, we will iscuss some new empirical regularities along three imensions: (i) the quantities of use goos emane an supplie over time, (ii) the inventory level of use goos over time, an (iii) the price an the resale value of use goos. Figure 2 plots the average quantities of use copies emane an supplie as well as the average inventory level of use copies over 15 weeks. The inventory level of use copies in week t for a game is efine as the ifference between the cumulative quantity of use copies supplie by consumers up to week t 1 an the cumulative quantity of use copies emane by consumers up to week t 1. First, both quantities of use copies emane an supplie sharply increase in the first few weeks after the opening of the use game market (secon week after release), reach their peaks, an graually ecrease afterwars. The initial increase is probably because it takes a few weeks for owners of a game to become satiate with their games. As the quantity of use copies supplie by owners increases, the sales of use copies also follows. Secon, on average, the inventory level of use copies carrie by retailers grows in the first 15 weeks. About half of the games in our ata set exhibit a ecline after some point uring the sample perio. It is clear that in the Japanese vieo game market, the use market oes not clear in every perio. As mentione earlier, unlike previous stuies which assume the use goos market clears in each perio, we will make use of this excess supply information when estimating our ynamic moel. Also note that although retailers accumulate use-copy inventory, their buy-early-sell-late strategy still allows them to make positive profits ue to a high markup. Thir, as shown in Figure 3, both the average price an resale value of use goos graually ecrease over time, an the resale value ecreases slightly faster. This suggests that both potential buyers an owners consumption values epreciate over time, an their epreciation rates coul be ifferent. We will 1

13 incorporate these features into our moel. 4 Moel In this section, we present our ynamic iscrete choice moel of consumer buying an selling ecisions for urable goos without physical epreciation. To make our presentation more concrete, we will escribe our moel in terms vieo games, as this is the market which we will stuy. We assume that consumers make buying an selling ecisions separately for each game. 9 Let i inexes consumers, g inexes games, an t inexes time. To capture consumer heterogeneity, we allow iscrete consumer types. At the beginning of the initial perio t = 1 (i.e., the perio in which the new game is release), no consumers own game g an use games are not available yet. Thus, consumers ecision problem is to ecie whether to buy a new goo or not to buy at all in t = 1. In perio t > 1, consumers who have not bought the game up to t 1 observe the prices of new an use copies, the resale value an inventory level of use copies at retailers, an ecie whether to buy a new or use goo, or not to buy anything. Let j =, 1, 2 enote no purchase option, new goo purchase, an use goo purchase, respectively. If consumers have alreay bought game g prior to time t an have not sol it yet, then they ecie whether or not to keep the game given the resale value in perio t. Let k =, 1 enote keeping an selling options, respectively. If consumers sell their game, they exit the market. Since vieo games will eventually become outate, we assume a terminal perio t = T after which consumers can neither buy nor sell. The state space of the consumer ecision moel consists of the following variables: (1) price of new an use goos (p 1, p 2 ); (2) resale value (r); (3) inventory level of use copies at retailers (Y ), which controls for the impact of the availability of use copies on consumer buying ecisions; (4) time since release (t), which characterizes the single-perio consumption value to potential buyers; (5) time since purchase (τ), which affects the single-perio consumption value to owners; (6) unobserve eman shocks for new an 9 We o not explicitly moel the choice among ifferent games because our focus is to stuy the choice between new an use copies of the same game title. We control for the impact of the availability of other games on the purchase ecision of the focal game by incluing the cumulative number of other newly introuce games since game g s release. Note that Nair (27) fins evience that the substitutability between two ifferent vieo games is very low in the US market, an consequently, he also oes not moel the choice among ifferent games. 11

14 use copies (ξ 1, ξ 2 ); (7) unobserve supply shocks for use copies (ξ s ); (8) cumulative number of newly introuce games since the release of the focal game (C). As we will escribe later, (1), (6), an (8) appear only in the consumer buying ecision problem, (5) an (7) appear only in the consumer selling ecision problem, an (2), (3) an (4) appear in both consumer buying an selling ecision problems. We assume that consumers make their buying an selling ecisions to maximize their total iscounte expecte utility for each game. We will first escribe the single-perio utility functions for buying an selling ecisions, an then move to the escription of the value functions. 4.1 Single-perio utility functions In each perio, consumers erive a value from owning game g (consumption values). We assume that once consumers buy a game, they will erive the same consumption value regarless of whether it is a new copy or a use copy. This assumption is to capture the iea that the goos consiere in this research have no physical epreciation. However, the ecision to buy a use copy may be influence by other factors such as the availability of use copies at retailers, psychological costs for using pre-owne goos, 1 etc. Let v g (t, τ) be a consumer s single-perio consumption value of owning game g at time t if he has owne game g for τ perios prior to time t. Note that if a consumer buys game g at time t, he will receive v g (t, ); if he/she keeps it at time t + 1, he will receive v g (t + 1, 1). Later in this section, we will escribe how we allow the two types of epreciation, freshness-base an satiation-base, to affect the consumption value over time. Finally, note that we assume that all consumers share a common consumption value. Suppose that a consumer has not bought game g up to time t > 1. Consumer i s single-perio utility for buying ecisions at time t is given by: v g (t, ) αp g u g 1t + ξg 1t + ρdg t + ϵg i1t if buying a new copy (j = 1) ijt = v g (t, ) αp g 2t l Y (Y g t ; λ i) + ρd g t + ξg 2t + ϵg i2t if buying a use copy (j = 2) l C (C g t ; π) + ϵg it if no purchase (j = ), (1) where p g 1t (pg 2t ) is the price of new (use) copies of game g at time t; ξg 1t (ξg 2t ) is the unobserve eman 1 Our assumption here is that once consumers overcome this psychological costs at the time of making a buying ecision, then the consumption value they receive in subsequent perios is not affecte by the psychological costs. 12

15 shocks to new (use) copies; α is the price-sensitivity. As justifie by the stylize facts iscusse earlier, we assume that the price of new copies is constant over time, i.e., p g 1t = pg 1 for all t, in our application to the Japanese vieo game market. We assume that ξ g 1t (ξg 2t ) is i.i.. across time an game, an is normally istribute with zero mean an the stanar eviation σ ξj for j = 1, 2; Y g t is the inventory level of use copies for game g at retailers at the beginning of perio t. l Y (Y g t ; λ i) is the one-time transaction cost that consumers incur when buying a use goo (search costs, psychological costs for pre-owne games, etc.), an λ i is a vector of parameters. In our empirical specification, we specify l Y (Y g t ; λ i) = λ i + λ 1 exp( λ 2 Y g t ) (2) to capture the ieas that (i) consumers might be heterogeneous in psychological costs for pre-owne games (λ i ) an (ii) search costs may epen on the availability of use copies capture by (λ 1, λ 2 ). The heterogeneity in λ i is motivate by a consumer survey conucte by Enterbrain, Inc., which shows that about 15% of consumers never inten to purchase a use copy. 11 This suggests that there is a segment of consumers who have high psychological costs of buying a use copy. This reuce form specification implies that when no use copies are available at the beginning of a perio (i.e., Y g t = ), 12 the cost is λ i + λ 1. As the availability of use copies increases to infinity, the cost approaches λ i (if λ 2 > ). Thus, if λ 1 an λ 2 are positive, the cost ecreases as Y g t increases; D g t is a vector of seasonal ummies an ρ captures the seasonal effects. 13 C g t is the cumulative number of newly introuce games at time t since the introuction of game g (incluing the games release in the same week as game g); l C (C g t ; π) captures the competitive effect from other newly introuce games. In our application, it is specifie as l C (C g t ; π) = π + π 1 ln(c g t ). (3) We assume that iiosyncratic errors, ϵ g ijt, are i.i.. across consumers an time, but allow it to be correlate across options j. We moel the correlation in a neste logit framework. Let ϵ g ijt = ζg iht +(1 η)υg ijt 11 Famitsu Game Hakusho 26, page Note that Y g t = oes not mean that there are no use copies available for purchase in perio t because some owners woul sell their copies to the market uring the perio. 13 We inclue this variable only to control for the seasonal variation in sales an o not inten to stuy its impact on consumers ynamic ecision making. Thus, it is not inclue as a state variable. 13

16 where ζ g iht an υg ijt are extreme value istribute, h inexes nest an takes two possible values: h = 1 groups the buying options (i.e., buying a new or use copy), an h = is the no purchase option. Thus, the consumer buying ecision problem here is equivalent to a two-stage ecision making where consumers first ecie whether or not to buy, an if buying, then consumers choose a new or use copy. In this setup, the parameter η [, 1) measures the within-nest correlation. Next, consier consumers selling ecisions. Suppose that a consumer has bought game g an kept it for τ perios. Consumer i s single-perio utility for selling ecisions at time t is given by w g ikt (τ) = { αr g t µ i + ξ g st + eg i1t if selling to a retailer (k = 1) v g (t, τ) + e g it if keeping the game (k = ) (4) where r g t is the resale value of game g at time t; µ i captures any aitional cost of selling (transaction costs, enowment effects, etc.) an is allowe to epen on consumer type. This is again motivate by the same consumer survey by Enterbrain, Inc. which inicates that not all consumers sell their games; ξ g st is an i.i.. unobserve shock to owners for selling ecisions at time t. We assume it is normally istribute with zero mean an the stanar eviation, σ ξs ; e g ikt is an iiosyncratic error, an we assume it is i.i.. extreme value istribute across consumers an time. For the single-perio consumption value, v g (t, τ), we will assume the following evolution over time. In the release perio, we set v g (1, ) = γ g, where γ g is a game-specific constant. To capture the epreciation of potential buyers consumption values ue to the aging of a game (freshness-base epreciation), we allow v g (t, ) to ecay as a function of t. Specifically, we moel the epreciation rate as: v g (t + 1, ) = (1 φ(t))v g (t, ), where φ(t) is a function of time tren. In our empirical application, we specify it as φ(t) = exp(ϕ 1I(t = 1) + (ϕ 2 + ϕ 3 ln(t 1))I(t > 1)) 1 + exp(ϕ 1 I(t = 1) + (ϕ 2 + ϕ 3 ln(t 1))I(t > 1)), (5) where I( ) is an inicator function. Note that we treat the epreciation from the first perio to the secon perio ifferently from the rest of the perios. This is motivate by the observations that the sales of new copies from the release week to the secon week usually suffers from a largest ecline in the vieo game market. Next, we capture the epreciation of owners consumption values ue to satiation by moeling the 14

17 epreciation rate as a function of prouct characteristics an the uration of ownership: v g (t + 1, τ + 1) = (1 κ(x gτ ))v g (t, τ), where κ(x gτ ) is a function of observe prouct characteristics an the uration of ownership. In the application, we use the following functional form: κ(x gτ ) = exp(x gτ δ) 1 + exp(x gτ δ), (6) where X gτ inclues observe prouct characteristics of game g (ummies for story-base games an multiplayer games, an average critic an user ratings) an the uration of ownership (τ). Finally, we emphasize that our propose moel allows for consumer heterogeneity in the costs of buying (λ i ) an selling (µ i ) a use copy. In aition, game owners are heterogeneous with respect to (t, τ): owners consumption value epens on when they bought the game an how long they have kept it. In general, we coul allow for consumer heterogeneity in other preference parameters such as price-sensitivity, initial consumption value, etc. We have experimente several aitional specifications an foun that after controlling for consumer heterogeneity in (λ i, µ i ), heterogeneity in other preference parameters oes not play a significant role in explaining the observe sales pattern. We iscuss some of those aitional specifications as robustness checks in Section 6.2 an Appenix A Value functions Since the ynamic consumer selling ecision is neste within the ynamic consumer buying ecision through the expecte future payoff, we start off by escribing the ynamic consumer selling ecision, an then escribe the ynamic buying ecision. To simplify the notation, we will rop g superscript. Also, let ξ = (ξ 1, ξ 2 ) be the unobserve eman shocks (as oppose to ξ s, the unobserve shocks for selling ecisions), an β be the iscount factor common across consumers. Let s t,τ = (r t, Y t, ξ st, t, τ) be the vector of state variables relevant to the selling ecision problem. Note that other state variables (p 1t, p 2t, C t, ξ t ) will not enter here. The inventory level, Y t, is inclue since it coul affect the istribution of the future resale value. Let W i (s t,τ ) be the integrate value function (or Emax function) of the selling ecision problem for consumer i, an W ik (s t,τ ) be the corresponing 15

18 alternative-specific value function of action k. The Bellman equation can be written recursively as: W i (s t,τ ) = E e max k {,1} {W ik(s t,τ ) + e ikt }, = ln{ k {,1} exp(w ik (s t,τ ))}, (7) where the secon equality follows from the assumption that e is type 1 extreme value istribute, an W ik (s t,τ ) = { αr t µ i + ξ st if selling (k = 1), v(t, τ) + βe[w i (s t+1,τ+1 ) s t,τ ] if keeping (k = ). (8) The expectation in E[W i (s t+1,τ+1 ) s t,τ ] is taken with respect to the future resale value (r t+1 ), inventory level (Y t+1 ), unobserve shock for selling ecision (ξ st+1 ). The probability of selling the game by consumer i at s t,τ is given by Pr(k = 1 s t,τ ; i) = exp(w i1 (s t,τ )) 1 k = exp(w ik (s t,τ )). (9) Next, consier the ynamic consumer buying ecision. Let b t = (p 1t, p 2t, r t, Y t, C t, ξ t, t) be the vector of state variables relevant to the buying ecision problem. Let V i (b t ) be the integrate value function for consumer i who has not bought the game prior to time t, an V ij (b t ) be the corresponing alternative-specific value functions of action j. The Bellman equation is given by V i (b t ) = E ϵ max j {,1,2} {V ij(b t ) + ϵ ijt } = ln{ j {,1,2} exp(v ij (b t ))} (1) where v(t, ) αp 1t + ξ 1t + βe[w i (s t+1,τ=1 ) s t,τ= ] new copy (j = 1), V ij (b t ) = v(t, ) αp 2t + ξ 2t l Y (Y t ; λ i ) + βe[w i (s t+1,τ=1 ) s t,τ= ] use copy (j = 2), l C (C t ; π) + βe[v i (b t+1 ) b t ] no purchase (j = ). (11) The expectation in E[V i (b t+1 ) b t ] is taken with respect to the future prices of new an use copies (p 1t+1, p 2t+1 ), resale value (r t+1 ), inventory level (Y t+1 ), cumulative number of competing games (C t+1 ), an unobserve shocks for buying ecisions (ξ t+1 ). It shoul be highlighte that the value function of the selling problem is embee into the value function of the buying problem Note that the bellman equations state here applies to t > 1. The expecte future payoffs component nees to be slightly moifie for t = 1 because p 2,t=1 an r 2,t=1 o not exist. We will iscuss how to specify consumers expectation about these state variables in the next section. 16

19 The choice probability for option j by consumer i at b t is given by Pr(j b t ; i) = Pr(h = 1 b t ; i) Pr(j h = 1, b t ; i), (12) where Pr(h = 1 b t ; i) = Pr(j h = 1, b t ; i) = [ 2 j =1 exp ( Vij 1 η )] 1 η [ 2 ( exp(v i ) + j =1 exp Vij 1 η ) exp ( Vij 1 η 2 j =1 exp ( Vij 1 η )] 1 η, (13) ). (14) Given a finite time horizon, the value functions for both buying an selling ecisions can be compute by backwar inuction from the terminal perio, T. We assume that after the terminal perio, consumers can neither buy or sell, but can continue enjoying the game if they have bought by the terminal perio. We thus assume that consumers who own the game at the en of t = T erive a terminal value equal to the present iscounte value of future consumption values, taking satiation-base epreciation into account. In the empirical application, we approximate it by the present iscounte value of consumption values for another 1 perios beyon the terminal perio, an we set T = Aggregate sales Let ψ l be the population proportion of type-l consumers an L l=1 ψ l = 1. In orer to erive the aggregate eman for new an use copies, an aggregate volume of use copies sol to retailers by owners, we nee to erive the evolution of the size of each consumer type. Let Mlt be the size of type-l consumers who have not bought the vieo game. It evolves accoring to M lt+1 = M lt (1 2 Pr(j b t ; l)) + N lt+1, (15) j=1 where N lt+1 is the size of new type-l consumers who enter the market at time t + 1. We assume that the proportion of new type-l consumers follows the population proportion, ψ l Therefore, we can use the total installe base of the corresponing game console in the release week to calibrate N l,t=1. For t > 1, N lt can be calibrate base on the weekly sales of the corresponing game console. 17

20 Next, let Mlt s (τ) be the size of type-l consumers who have bought an owne the game for τ perios at time t. It evolves accoring to {M Mlt+1 s 2 (τ) = lt j=1 Pr(j b t; l) if τ = 1, Mlt s(τ 1) Pr(k = s t,τ 1; l)) if 1 < τ t. (16) The aggregate observe eman at state b t is then Q j (b t ) = L Mlt Pr(j b t; l) + ε jt (17) l=1 where j = 1 is new copies an j = 2 is use copies, an ε jt represents a measurement error. The aggregate observe quantity supplie to retailers by consumers at state s t = s t,τ \{τ} is given by Q s (s t ) = L t 1 Mlt s (τ) Pr(k = 1 s t,τ ; l) + ε st, (18) l=1 τ=1 where ε st represents a measurement error. 5 Estimation Strategy The estimation of consumer preference parameters is carrie out in two steps (e.g., Rust 1987, Henel an Nevo 26, Erem et al. 23). In the first step, we recover the evolution processes of use game prices, resale values, inventory levels, an cumulative number of newly introuce games from the ata. 16 In the secon step, these estimate processes will be use to form consumers expectation about future price of use goos, resale value, inventory level, cumulative number of newly introuce games, an then we estimate the rest of the structural parameters. In the first step, we estimate the consumer expectation processes as follows. For t > 2, we moel the processes of the price of use goos an the resale value to be a function of own lagge value, the lagge inventory level an game characteristics; we also moel the processes of the inventory level to be functions of its lagge value an game characteristics; For t = 2, this approach cannot be applie because the lagge values of use price an resale value o not exist (recall that t = 1 is the initial perio). We therefore assume that the initial price an resale value of use copies are functions of the price of new copies an 16 We assume that consumers expect the price of new copies to remain constant over time. 18

21 game characteristics. We shoul also note that Y t=1 = Y t=2 =. Finally, we assume that the cumulative number of newly introuce games to be a function of its lagge value. The estimation results base on all 2 vieo games are reporte in Tables 2 an In the secon step, we estimate the ynamic iscrete choice moel with a finite time horizon. Notice that the price of use goos an resale value may be correlate with unobserve shocks. We employ a new Bayesian MCMC algorithm for non-stationary finite-horizon DDP moels propose by Ishihara an Ching (212), an combine it with the pseuo-policy function approach in Ching (21b) to control for the potential enogeneity problems. 5.1 Bayesian Dynamic Programming Algorithm Recently, Imai et al. (29) evelop a new Bayesian estimation algorithm which has the potential to significantly cut own the computational buren of estimating stationary iscrete choice ynamic programming (DDP) problems. 18 The key innovation of the IJC algorithm is that instea of fully solving for the fixe point of the Bellman operator in each outer loop, it graually solves for it by applying the Bellman operator only once per outer loop iteration, an uses the set of partially-solve value functions (pseuo-value functions) from the past outer loop iterations for nonparametrically approximating expecte value functions. Ishihara an Ching (212) argue that if the ynamic moel has multiple continuous state variables, IJC s iea for estimating DDP moels with continuous state variables (see Section 3.2 of Imai et al. 29) can be extene to help reuce the computational buren of computing the expecte future payoffs even for non-stationary finite-horizon DDP moels. The main iea behin their algorithm for continuous state variables is to compute pseuo-value functions at one ranomly rawn state in each iteration an store them. The set of past pseuo-value functions use in approximating the expecte future payoffs will then be evaluate at ifferent state points. Thus, one can simply ajust the weight given to each of the past pseuo-value function by the transition ensity from the current state to the state at which the past pseuo-value function is evaluate. 17 We estimate the process for the cumulative number of newly introuce games separately for each of the 2 games. The results are not reporte here, but are available upon request. 18 Ching et al. (212) provie a step-by-step guie for implementing the IJC algorithm. 19

22 The new algorithm propose by Ishihara an Ching (212) has three main features: (1) pseuo-value functions are compute an store for each time perio, (2) in each MCMC iteration an in each time perio, pseuo-value functions are compute only at one ranomly rawn vector of continuous state variables by backwar inuction, an (3) expecte value functions at time t are approximate using the set of pseuovalue functions at time t + 1. Unlike other approximation approaches (e.g., Keane an Wolpin 1994, Rust 1997), in which value functions nee to be compute at a set of pre-etermine gri points in all perios, the new algorithm computes pseuo-value functions at only one ranomly rawn state point in each perio an the expectation of the future payoffs with respect to the continuous state variables can simply be one by the weighte average of past pseuo-value functions. Thus, it reuces the per iteration computational time ramatically, an has the potential to reuce the overall estimation buren. We escribe the etails of the estimation proceure for our moel in Appenix A Pseuo-policy function approach The price an resale value of use games coul be enogenous. To aress this issue, we follow the pseuopolicy function (PPF) approach propose by Ching (21b). This approach is similar to other limite information approaches (e.g., Villas-Boas an Winer 1999, Park an Gupta 29, Petrin an Train 21), but iffers in that it approximates the pricing policy as a function of observe an unobserve state variables of the equilibrium moel. This has the potential of generating a more flexible joint istribution of (p, q). 19 In our moel, the state space of the equilibrium moel inclues unobserve shocks (ξ 1t, ξ 2t, ξ st ), consumption values (v(t, τ)), inventory level (Y t ), cumulative number of newly introuce games (C t ), the size of potential buyers (Mlt ), an the size of owners for each each uration of ownership (M lt s (τ)). Furthermore, we inclue seasonal ummies for Golen Week (D 1t ) an Christmas (D 2t ). 2 After experimenting several functional 19 This approach can also be applie to control for the potential enogeneity of avertising/etailing (e.g., Ching an Ishihara 21; 212b), an iniviual retailers pricing (e.g., Gu an Yang 211). 2 Golen Week in Japan refers to a week in late April an early May that involves multiple public holiays. 2