Digital distribution and the prohibition of resale markets for information goods

Quant Mark Econ (2013) 11:403–435DOI 10.1007/s11129-013-9139-x

Digital distribution and the prohibition of resalemarkets for information goods

Benjamin Reed Shiller

Received: 20 January 2012 / Accepted: 29 August 2013 / Published online: 24 September 2013© Springer Science+Business Media New York 2013

Abstract An existing theoretical literature finds that frictionless resale markets can-not reduce profits of monopolist producers of perfectly durable goods. This paperstarts by presenting logical arguments suggesting this finding does not hold for goodsconsumers tire of with use, implying the impact of resale is an empirical ques-tion. The empirical impact is then estimated in the market for video games, one ofmany markets in which producers may soon legally prevent resale by distributingtheir products digitally as downloads or streamed rentals. Estimation proceeds in twosteps. First, demand parameters are estimated using a dynamic discrete choice modelin a market with allowed resale, using data on new sales and used trade-ins. Then,using these parameter estimates, prices, profits, and consumer welfare are simulatedunder counterfactual environments. When resale is allowed, firms are unable to pre-vent their goods from selling for low prices in later periods. The ability to do so byrestricting resale outright yields significant profit increases. Renting, however, doesnot raise profits as much due to a revenue extraction problem.

I owe much gratitude to Joel Waldfogel, Katja Seim, and Alon Eizenberg for numerous discussions,suggestions, advice, and generosity with their time. I also thank Ulrich Doraszelski and Lorin Hittfor their helpful input, and the editor and two anonymous referees for insightful comments andsuggestions. I also would like to thank Tim Derdenger, Shane Greenstein, Adam Isen, Phil Leslie,Andrew Paciorek, John Riley, David Rothschild, Kent Smetters, Rahul Telang, and JeremyTobacman for their suggestions, and Hamilton Chu, David Edery, and Marc Mondhaschen forimparting to me some of their wisdom on the video game industry. I am also grateful for supportreceived from the NBER program on digitization which is kindly funded by the Sloan Foundation.

Electronic supplementary material The online version of this article(doi:10.1007/s11129-013-9139-x) contains supplementary material, which is available toauthorized users.

B. R. Shiller (�)Sachar International Center, Brandeis University,415 South St., Waltham, MA 02453, USAe-mail: [email protected]

http://dx.doi.org/10.1007/s11129-013-9139-x

mailto:[email protected]

404 B.R. Shiller

Keywords Resale · Secondary market · Digital · Downloads · Renting · Streaming

JEL Classifications M30 · L00 · K19

1 Introduction

The standard theoretical model of perfectly durable goods finds that frictionlessresale does not lower monopolist profits, implying producers would welcome well-functioning resale markets for their products. The reasoning behind this finding isthat forward-looking consumers incorporate the expected resale price into initial will-ingness to pay, and the increase in revenue from higher initial prices offsets revenuelost from fewer sales. Since firms may earn the same revenues with fewer goodsproduced, profits may be higher when resale is allowed.

If one modifies the standard model of resale by allowing consumers to tire ofgoods, however, this finding no longer holds, implying the impact of resale on profitsis ambiguous. The intuition is as follows. Owners, having grown tired with use, reselltheir used products in later periods. These used goods fulfill some residual demand,clearing the market at a low price. Anticipating the low price and extant high qualityto someone that has not used it, forward-looking consumers are not willing to pay asmuch as they otherwise would initially.

The assumption that consumers tire of products with use is relevant for many typesof information goods. It clearly applies to books, movies, video games, and music,which together yield about $90 billion in sales in the U.S.1 It also applies to non-entertainment goods like learning software (e.g. languages) and any product elicitinggreater enjoyment during initial use.

For many such goods, resale markets exist not because they weakly raise producerprofits—nay, practitioners strongly believe otherwise—but because there has beenno legal way to prevent them. The U.S. first sale doctrine (17 U.S.C. section 109)guarantees consumers’ right to resell the original purchased copy of a durable good,even if copyrighted, so long as no copies were made.2

However, because transferring a digital file involves making a copy from the harddrive, and the first sale doctrine only applies to the original copy, the doctrine does not

1See Hurt (2009), Rich (2009), Digital Entertainment Group’s “Digital Entertainment Group Year-End2008 Home Entertainment Sales Figures,” and the International Federation of the Phonographic Industry’s“Recorded Music Sales 2008” report.2The first-sale doctrine dates back to an 1854 Supreme Court case, Stevens v. Royal Gladding, whichruled that a cartographer’s right to sole distribution ended at first sale. It was subsequently codified in1909, and updated in 1976. It has been unclear whether the first-sale doctrine applies to licensed goods. ADistrict Court judge decided in Vernor v. Autodesk in 2008 that permanent licenses constituted sales, andas a result were covered by the first-sale doctrine. In September 2010, the Ninth Circuit Court of Appealsreversed this ruling, determining that firms can legally prohibit resale in their licensing agreement even ifthey never intended for the good to be returned to them. In 2011, the ninth circuit took the opposite viewin Universal Group v. Augusto. Capital records v. ReDigi, currently ongoing, considers whether licenseddigital songs can be resold.

Digital distribution and the prohibition of resale markets 405

apply to digital downloads.3,4,5 Firms can also prevent resale indirectly by stream-ing rentals from places like Netflix and Spotify. Moreover, with the advent of highspeed Internet connections, digital distribution is becoming feasible. Resale has forpractical purposes been shut down for applications purchased on tablets or smart-phones. Traditional platforms may follow suit. Microsoft initially announced that allgames for their newest video game platform would be downloaded and publisherscould place restrictions on resale. However, they quickly reversed course followingcustomer threats to switch to a rival platform (Stuart 2013).

To investigate the empirical impact of shutting resale markets in the video gamemarket, I employ a two-step approach to estimate the impact on a sample of 14highly acclaimed games. First, demand parameters are estimated in a market whereresale exists, using a dynamic discrete choice structural model of the consumers’ pur-chase and resale decisions and a dataset containing new video game purchases andused game resales. Second, using the parameter estimates, profits are simulated incounterfactual environments.

I find that consumers tire quickly with use. High valuation consumers reduce theirvalue from $80 for the average game in the 1st month of use to just a couple ofdollars per month by the sixth month. As a result, resale markets put downward pres-sure on price. In counterfactual simulations, I find that optimal prices fall at a muchslower rate when resale markets are shut down, providing much less incentive todelay purchase. Selling non-resellable downloads is estimated to raise producer prof-its substantially, by 109 %. However, the magnitude of this finding is sensitive to theassumed market size. Preventing resale indirectly by exclusively renting only raisesprofits by at most 5 %.

This paper contributes to a sparse empirical literature on resale and monopolistprofits. Chen et al. (2011) find that resale would raise a monopolist car producer’sprofits by 15 %, but did not allow consumers to tire with use.6 A contemporaneouspaper by Ishihara and Ching (2011) allows for such tiring. To appropriately modelJapan, they assume novelty effects which cause usage values to also decline for con-sumers yet to play the game, but they do not allow for heterogeneous usage values.7

Despite using different assumptions, their results are qualitatively similar to the find-ings in this paper. Focusing on airline tickets, Lazarev (2012) also finds resale would

3To resell a downloaded good, one would need to sell the hard drive that contains it. In many cases,this would mean selling the entire device, along with all other information goods downloaded to it. See(Graham 2002; Hinkes 2006; Long 2007; Seringhaus 2009).4Firms can enforce prohibited resale with access control software, and following the Digital MillenniumCopyright Act (1998) can prosecute creators of software designed to circumvent copyright protectionsoftware.5In the Balance Act of 2003, Congress considered instituting a digital first-sale doctrine, allowing resaleof digital goods via the ”forward and delete” resale method. However, the bill did not pass.6For oligopolist producers, Chen et al. (2011) find resale lowers profits.7In Japan new game prices do not fall over time. In the U.S. prices fall by roughly half in the first yearfollowing release.

406 B.R. Shiller

lower profits, by 29 %.8 To my knowledge, no empirical papers investigate preventingresale via renting.

In the next section, I discuss the importance of the assumption of losing interestwith use and provide an industry background. Section 3 describes the data. Then,in Sections 4 and 5, the model of consumer demand and the estimation strategy aredetailed. Section 6 presents the results.

2 Background

2.1 Logic and prior theory

This subsection presents logical arguments illustrating why monopolist revenuesmay be higher if selling a non-resellable good, compared with renting or selling aresellable good. The intuition is then contrasted with the prior theoretical literature.

When forward-looking consumers tire of goods, selling a non-resellable good mayyield more revenue for a monopolist than renting does. To illustrate this point, sup-pose a single individual and a monopolist selling a non-resellable good. To maximizeprofits, the firm should set a price equal to the individual’s present discounted valuefrom use. If the individual buys, the firm extracts full surplus, leaving the consumerwith zero net surplus. If the individual cannot acquire the good for less later, i.e. thefirm commits to maintaining prices, then the individual is not able to increase netconsumer surplus by delaying purchase. Thus, the individual is indifferent betweenbuying and not, and is assumed to buy.

The analogous rental strategy involves the producer charging the individual herfull usage value each period, i.e. set a rental price for the tth period equal to the utilityreceived from her tth period of use. Since static usage utility declines with use, pricesunder this strategy would decline over time. Therein lies the problem. With fallingprices, a forward-looking consumer would prefer to wait. By delaying, the individualpays a lower price, but receives the same utility, since her usage value declines onlyafter she uses the product. By waiting to rent, the individual yields positive, ratherthan zero, consumer surplus. The firm thus cannot successfully charge rental pricesthat would extract full surplus from the individual, implying profits under renting arelower than profits from selling a non-resellable good.9

Similar logic applies to frictionless resale. When resale markets exist, an individ-ual can implicitly rent the product for any number of periods by buying and reselling.Because the supply of existing products is non-declining over time and the overalldemand for use falls as consumers own, use, and tire of the product, the market clear-ing implicit rental price should fall over time. The falling implicit rental price limitsthe amount of surplus a monopolist can extract, suggesting that preventing resalewould raise profits.

8Leslie and Sorensen (2011) also investigate impact of ticket resale on consumer welfare.9The firm can extract full surplus from a single individual by renting if it can condition the rental price onthe consumer’s past rental history.


By contrast, existing models of secondary markets for durables, which do notallow consumers to tire of goods, typically find that frictionless resale can raise, butnot lower, monopolist producer profits (Hendel and Lizzeri 1999; Rust 1986).10,11,12

The intuition is that the same stream of services might be provided with fewer pro-duced goods when goods change hands under resale and renting. Hence, the firmmay have equal or similar revenues when resale is allowed compared to when not,but lower costs when selling a resellable good.

The following reasoning helps clarify why two seemingly similar modelingassumptions, (i) consumers grow tired of a product and (ii) imperfect durability, havevery different implications. When consumers tire of non-depreciating goods, theycan obtain the full quality product for a lower price by waiting, reducing how muchthey are willing to pay initially. For goods that depreciate, however, waiting to buya used good entails obtaining a lower quality product, generally offsetting the gainfrom obtaining the product at a lower price, eliminating the incentive to wait.

The above logic and prior theory have conflicting implications for whether allow-ing resale raises or lowers profit, implying it is an empirical question, one investigatednext.

2.2 Industry background

When purchasing a game, consumers can generally choose between a new and usedcopy, and between online and offline sellers. The price a consumer pays for a usedcopy is close to the price of a new copy. The small price difference (about 10 %)is usually assumed to be due to risks involved in buying a used copy which maynot function, and negative feelings associated with buying a used copy experiencedat time of purchase. However, as long as the used game is not sufficiently damaged(such as having a bad scratch), it provides exactly the same service as a new copy.It also is typically assumed that the larger price difference between copies boughtin brick and mortar stores and via auction, both for new and used games, reflectsadditional costs borne by the buyer in an auction. Such costs include shipping fees,risk of being scammed, the cost of postponing gratification while the auction con-cludes and the game ships, etc. It seems reasonable to assume that the true totalcost of buying a copy of a game does not depend on the condition, new or used, orwhether bought online. Hence, consumers view these choices as roughly equivalent invalue.

Consumers, when they have tired of a game, have the option to resell their copyeither directly back to another consumer via auction, or to a retailer. It seems logical

10Bulow (1982), Hendel and Lizzeri (1999), Rust (1986) show that imperfect durability on its own maylower profits, because owners have the option of keeping a good they purchased earlier rather thanreturning to the market to buy a new product.11Resale can lower producer profits if resale transaction costs exceed primary market transaction costs, ordemand fluctuates substantially. See the hide/steers analogy in Benjamin and Kormendi (1974).12Papers finding resale lowers firm profits (Anderson and Ginsburgh 1994; Miller 1974) still find resaleweakly raises monopoly profits for producers of perfectly durable goods.

408 B.R. Shiller

that since these different mediums are competing for traded-in games, and consumerscan freely choose where to resell their games, that the price they receive for trade-insdoes not heavily depend on where they choose to resell it.

The used game market was generally considered concentrated, but the market fornew games was not. One company, GameStop, was and generally still is regarded asthe dominant buyer and seller of used games. The former director of used games atGameCrazy assured that GameStop’s used game market share was estimated to be80 % in 2010.13 GameStop also competed in the resale market with online auctionwebsites like eBay and niche online retailers. Sales of new games were less concen-trated. Based on calculations explained later, GameStop was estimated to accountfor approximately 25 % of new sales, and competitors such as Best Buy, Target, andWalmart also had substantial new game sales market share. While these major retailchains contemplated entering the used game market in earnest, none did until 2009,which is after the period investigated in this paper.

See Lee (2012a) for a more in-depth background and related literature.

3 Data

The data used in this paper were constructed from two datasets. The first dataset,from the NPD group, provides information on monthly sales and average prices ofnew copies of XBOX 360 video games by game in the U.S. from November 2005 toDecember 2008.14 The second dataset contains used game auctions from a popularonline marketplace over that same timespan. These latter data are a good indicatorof consumers’ decision to resell, and hence serve as a good proxy for the monthlyquantity of used games traded-in by consumers, i.e. resold by consumers to retailstores, which is how most games are resold. These data also contain prices consumersreceive for reselling.15 Because these auctions will proxy for trade-ins, I will sub-sequently refer to these data as the trade-ins data. Additionally, time-invariant gamecharacteristics were obtained from the NPD group and Game Informer Magazine’sreviews.

The trade-ins data, comprised of 691,722 used game auction sales, were aggre-gated to the month in order to match the new game sales data. Trade-in quantitieswere summed and trade-in prices averaged.16 Then, the trade-ins data were matched

13GameCrazy shared retail space with Hollywood Video. It closed when its parent company, MovieGallery, declared bankruptcy in 2010.14NPD observes over 80 % of point of sales transactions of video games and scales them up to the market.15Consumers had several outlets for reselling games, suggesting a competitive market price received forresold (traded-in) games16The standard deviation of trade-in prices around the average in the first year following release was $5.67,omitting outliers priced above $100 (0.25 % of observations). Differences in trade-in prices across copiesof the same game in the same month can have many causes, including market price changing over themonth, differences in the perceived quality of auction sellers and the condition of the item (e.g. whether itincludes instruction manual), and randomness in number of bidders participating in the auction.


to the new game sales data. In total, 326 games were successfully matched, yielding5020 game/month observations.

Since the trade-ins data are from a single firm, they must be scaled up to be con-sistent with the new copy sales data which represent the entire U.S. market. Thescale-up involved several steps. First, the expected number of used copy sales byretailers to consumers in the first two months following games’ releases is calcu-lated using industry statistics. Next, this figure is used to calculate the expectednumber of trade-ins by consumers to retailers in this same time frame, includingcopies remaining in retailers’ unsold inventories. This calculation uses the averagetime lag between trade-ins by consumers to retailers and subsequent resale of thesame copies from inventory back to consumers. Lastly, the appropriate scale-up fac-tor matches the trade-ins in the data with the expected number of trade-ins from thiscalculation.

The analysis in this paper also requires information on total sales of a game byretailers to consumers, including both new and used copies. The expected number ofused copy sales of each game is calculated from trade-ins, again using the averagetime a game remains in inventory. Such sales are added to new copy sales to yield anestimate of total sales by retailers to consumers.

The dataset using these imputed values for trade-ins quantities and quantitiesof used sales by retailers is used in the remainder of this paper unless otherwisespecified. Further details on the data construction are available in an ElectronicSupplementary Materials (Online Appendix).

3.1 Data consistency tests

A major concern, given the low share of the used market covered by the raw data, isthat the propensity to sell online may change as a game ages. This would imply theappropriate scale-up should change over a game’s life cycle.

The trade-ins data provide a simple check for this concern. Sellers whose ship-ments originated from zipcodes of the lowest population density quintile, averagedensity 114 people per square mile, likely have poor access to brick and mortarstores like GameStop, making offline trading-in impractical. Consumers in high pop-ulation density areas, however, should on average have much better access to brickand mortar stores to trade-in their used games. If the relative benefit of trading-in at GameStop changes with games’ ages, then consumers in high density areaswould likely shift their trade-ins from nearby to online, or vice versa, as games age.Consumers in low density areas, however, likely resell used games online regard-less. Therefore, if the appeal of trading-in at GameStop changes with a game’sage, then the fraction of used game auctions for a game occurring in the first sev-eral months of release, relative to later following release, should be different forrural and urban consumers. Figure 1 shows this does not occur, supporting the con-tention that the data are equally representative over game age, at least for the firstyear.

A second concern is that the market share of the raw used game data may changeover the time period analyzed, due to changing conditions, entry, or exit. This too iseasily checked. If this were to occur, then one would expect the ratio of trade-ins in

410 B.R. Shiller

0 2 4 6 8 10 120

0.02

0.04

0.06

0.08

0.1

0.12

0.14N

orm

aliz

ed Q

uant

ity S

old*

Age of Game (in Months)*Sales normalized to sum to one over the 1st year, separately by quintile

Lowest Pop Density

2nd Quintile

3rd Quintile

4th QuintileHighest Quintile

Fig. 1 Normalized used auction sales vs. time since release—by population density quintile of seller’szipcode

the raw data to total new game sales in the U.S. market to change over time. Figure 2shows no consistent trend of this sort, addressing this concern as well.

3.2 Summary statistics

The trends in the new game price data, shown in Table 1, suggest that the decisionsof when to buy and when to resell are non-trivial. If consumers buy a game rightafter it is released, they typically pay about $55 for the game. But, if they wait to buythe game, they can acquire the game for much less, since the price typically declinesrapidly. They can on average save 22 % by waiting 6 months, and almost 50 % bywaiting a full year to buy the game. The implied rental prices (the buying price minusthe amount received when reselling later) also typically decline over time. Since bothprices and implied rental prices decline over time, consumers must trade off betweenbuying and using the product immediately and paying less for it later.

The sales data, also summarized in Table 1, show that sales are more front-loadedthan in the classic diffusion model, in which sales start slowly and increase over time.This front-loading may be due to the firm’s response to competition from used sales.In the market for video games, on average about 40 % of total sales of a game inthe first year occur in the first 2 months. Not surprisingly, almost all of these games


Jan−06 Jan−07 Jan−08−9.5

−9

−8.5

−8

−7.5

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−6

−5.5

−5

−4.5Lo

g R

atio

of T

rade

−in

s to

New

Sal

es

Release Date

QTrade in

/ QNew

Fitted Line

Each circle denotes a game

Fig. 2 Ratio of trade-ins in raw data to new game sales in first two months following game release

are new, and the firm profits directly from these sales. As time progresses, whiletotal sales typically decline, the number of trade-ins initially increases, reaching apeak in the fifth month, and thereafter declines slightly before appearing to plateau.Used copy sales by retailers to consumers follow a similar pattern, with a slight lag,peaking in the 7th month following release. Since new copy sales continue to decline,the average proportion of game sales that are of used copies increases reaching over40 % a month one year after release. Hence, producers face steep competition fromused goods.

Sales are heavily skewed across games. New copy sales in the first year followingrelease ranged from 15,643 for “Fatal Inertia” to over five million for “Halo 3.” Thestandard deviation equals 642,768.

The data exhibit obvious seasonality, e.g. more sales around Christmas. Onemethod for controlling for seasonality is to add monthly demand shifters. However,Gowrisankaran and Rysman (2009) note the lack of intuition for why products wouldbe enjoyed so much more during the Christmas season, also noting that adding seasondummies to a dynamic model typically requires adding an additional state variable,substantially slowing estimation due to the curse of dimensionality. They show thatdeseasoning the data a priori yields similar results to traditional methods, suggestinga better alternative.

412 B.R. Shiller

Table 1 Average price and quantity patterns over time

Quantities (normalizeda) Prices

New copies Used trade-ins Used copy sales Purchase price Trade-in price

Age (in months) Mean SD Mean SD Mean SD Mean SD Mean SD

1 23.8 13.8 0.3 0.4 0.0 0.1 56.1 8.8 40.8 7.5

2 18.8 10.3 1.1 0.8 0.3 0.3 54.8 8.3 35.8 8.0

3 9.8 6.8 1.5 1.0 0.7 0.4 53.4 8.9 31.7 7.9

4 8.3 5.9 1.7 1.0 1.0 0.6 50.9 10.9 28.7 7.5

5 5.4 3.0 1.9 1.1 1.3 0.8 47.6 11.4 25.7 7.7

6 4.7 3.3 1.7 0.9 1.5 0.8 43.8 12.8 23.2 7.0

7 4.3 4.8 1.6 0.8 1.5 0.7 41.1 12.8 21.2 7.1

8 3.4 3.3 1.4 0.9 1.5 0.7 38.4 12.4 19.5 6.9

9 2.9 2.1 1.4 0.7 1.4 0.7 35.4 12.2 18.0 6.9

10 3.1 3.1 1.4 0.7 1.4 0.6 32.9 11.6 16.8 6.8

11 2.3 1.9 1.3 0.5 1.4 0.5 31.0 11.4 15.6 6.8

12 1.9 1.6 1.4 0.6 1.3 0.5 28.6 10.3 14.5 6.2

aNormalized by total game purchases in the first 12 months, by game. Reported values of used sales andtrade-ins are after scaling up to the market

Each monthly numerical variable in the dataset is deseasoned by running a regres-sion of its log on the composite critic review score and its square, age of gamedummies, and date fixed effects. Specifically:

Log(V art ) = α + β1 ∗ rev scorej + β2 ∗ rev scorej ˆ2 + λage(t) ∗ I (age(t))

+γt ∗ I (t) + εt (1)

The dependent variable is deseasoned by subtracting γt ∗ I (t) from the log of thedependent variable, and then exponentiating. This variable is then scaled up or downto the point where the sum of this seasonally adjusted variable equals the sum of thecorresponding raw (not deseasoned) variable.

3.3 Law of motion

An important component of any dynamic model of consumer demand is the specifi-cation of consumer expectations of payoff relevant state variables in future periods.A common method is to assume that consumers base expectations on reduced formregressions of current state variables on lagged variables and product characteristics(Gowrisankaran and Rysman 2009; Lee 2012b; Nair 2007). The underlying assump-tion is that the reduced form model well replicates heuristics that consumers havedeveloped with experience.

To see which observables predict future values of prices, they are regressed onlag prices and game characteristics. Recall two types of prices exist—purchase and


trade-in. The results for both are shown in Table 2. For purchase prices, including onelag alone yields an R2 of 0.90. However, no other variable, including additional lags,increases the R2 by more than 0.01. This suggests that while other variables maybe statistically significant, they are not meaningful to the consumers’ decisions. Therightmost columns in Table 2 repeats this exercise for trade-in prices of used games,yielding similar patterns.

4 Empirical model

4.1 Demand

The model of consumer demand is cast as a discrete choice problem, where at thebeginning of each period each consumer decides whether to be an owner of eachgame, independent of which other games they own. If, at the beginning of a timeperiod, they do not own the product in question, this framework requires that they

Table 2 Price path regressions

Dependent variable is

Purchase price Trade-in price

Lag of respective price 0.96 0.95 0.87 0.84

(0.02)** (0.01)** (0.01)** (0.01)**

Twice lagged price −0.01

(0.02)

2nd critic quintile −0.16 −0.05

(0.32) (0.21)

3rd critic quintile −0.11 0.50

(0.34) (0.22)*

4th critic quintile 0.16 0.75

(0.33) (0.21)**

Highest critic quintile 1.08 1.57

(0.38)** (0.25)**

Month fixed effects Y Y

[0.00]** [0.00]**

Genre fixed effects Y Y

[0.00]** [0.00]**

Constant −0.59 −0.49 0.93 0.80

(0.34) (0.52) (0.17)** (0.32)**

R2 0.90 0.91 0.89 0.90

N 2,202 2,346 2,145 2,108

Standard errors in parentheses. For group variables, F-statistics in brackets. *p < 0.05; ** p < 0.01

414 B.R. Shiller

decide between buying and not buying the product. If they do own the product, theyalternatively decide between keeping the product and selling it.

This setup implicitly makes several assumptions. First, it assumes consumers haveno use for a second copy. This seems reasonable given that the second copy doesnot provide any additional functionality. Second, this framework implies that gamesare not substitutable for one another. Nair (2007) argues this is true because gamesare fairly unique in their story and game play. They may be no closer substitutesfor each other than for other entertainment activities like watching movies. In theAppendix, I test this, finding no evidence that popular games are substitutable, sug-gesting the assumption is reasonable enough for the purpose of this paper. Third, thissetup implies that used and new games are perfect substitutes for one another. Sinceused games provide the same service as new games, it seems quite reasonable thatthis assumption would nearly hold. Any price discounts for used copies are assumedto exactly offset a one-time disutility of purchasing a used, as opposed to new, copy.Hence, it is assumed that the true price of buying a game, new or used, is the price ofa new copy. Lastly, this setup assumes consumers do not have the opportunity to rentgames through a third party seller. Rental companies did exist, but had very smallmarket share.17

In the remainder of this section, I present the specifics. Note that game subscriptsare omitted for parsimonious notation, since the described process is repeated foreach game during estimation.

4.1.1 Flow utility

There are four possible actions consumers can take at some point. They are buying,waiting to buy, keeping, and selling.

The flow utility of buying a game is given by:

ubuy

(δi , αi, ξt , Pt , εi,t

) = δi + ξt − αiPt + εi,t = ubuy

(δi , αi, ξt , Pt

) + εi,t (2)

where δi is the mean flow utility of the product to individual i at first use, ξt is a tran-sient utility shock in period t common across individuals, αi is the price sensitivityof consumer i, Pt is the price at which the game can be bought, and εi,t is an individ-ual specific shock. The function ubuy

(δi , αi, ξt , Pt

)equals the flow utility of buying

minus εi,t , and will be used subsequently for notational purposes.The mean flow utility of owning, assuming purchased previously, is given by:

uown

(δi , ξt , hi,t , εi,t

) = (δi + ξt )B(hi,t ) + εi,t = uown

(δi , ξt , hi,t

) + εi,t (3)

where B(hi,t

)is a function that reflects the decrease in value due to length of

previous ownership hi,t .

17Rental revenues in 2011 in the U.S. were approximately $330 million (http://www.ibisworld.com/industry/default.aspx?indid=1370). Total industry revenues from the U.S. were $16.6 billion(https://www.npd.com/wps/portal/npd/us/news/press-releases/pr120116/).

http://www.ibisworld.com/industry/default.aspx?indid=1370

http://www.ibisworld.com/industry/default.aspx?indid=1370

https://www.npd.com/wps/portal/npd/us/news/press-releases/pr120116/


For several reasons, it is assumed that the rate at which consumers lose interest isthe same across games. First, it seems unlikely that consumers anticipate the game-specific rate of boredom. Rather it is learned with experience as they play the game.Second, Game Informer reviews’ “Replay Value” scores, which purportedly informconsumers of how quickly they will bore of a game, did not predict differences acrossgames in the rate of price declines or the timing of sales. This suggests differencesacross games are not large. Third, this assumption reduces the number of parametersto be estimated.

The function B(hi,t

)is parameterized as B

(hi,t

) = (1 − λ1) exp(λ2hi,t

) − λ1,where 0 ≤ λ1 ≤ 1, λ2 ≤ 0. I assume that hi,t is capped at H = 12, i.e. subsequentownership periods beyond H do not change the value of the B () function. Moreflexible specifications were tested, such as combining an exponential and linear func-tional form, relaxing the assumption that monthly value with use plateaus. They didnot meaningfully improve fit or change the shape of the estimated boredom function.

The mean flow utility of the outside good equals:

uwait

(ε0i,t

)= ω + ε0

i,t = uwait + ε0i,t (4)

where ω is the value of the outside good and ε0i,t is an individual specific shock. ω

is normalized to a positive constant large enough to ensure that(δi + ξt

)is positive

in every instance. As long as this holds, the actual value of ω is inconsequential. If(δi + ξt

)were less than zero, the model would nonsensically imply that tiring with

use increases valuation for the good.The mean flow utility of selling is given by:

usell

(P T I

t , αi, ζt , ε0i,t

)= ω+αi

(P T I

t + ζt

)+ε0

i,t = usell

(P T I

t , αi, ζt

)+ε0

i,t (5)

where P T It is the price at which owners can resell the product, i.e. the trade-in price,

and αi is the same as in the buying equation. ζt , a transaction cost shock commonacross individuals, is similar to the demand shock ξt , but is experienced only bycurrent owners.

4.1.2 Heterogeneity

Managers have noted the video game market consists of two groups of consumers,“hard-core gamers” and the “mass market.”18 I use a latent class approximation to thebimodal distribution of valuations (Kamakura and Russell 1989). Following earlierpapers focusing on the market for video games (Liu 2010; Nair 2007) I assume thereare two types, denoted by k. The low type has intrinsic value of ownership equalto δk = δ, and the high type has intrinsic value equal to δk = δ + β. The pricesensitivity is also estimated separately by type. The fraction of high types amongst

18See Nair (2007).

416 B.R. Shiller

the population is estimated asexp

(γ1+γ2∗AP

j,t

)

1+exp(γ1+γ2∗AP

j,t

) , where APj,t is the age of platform at

the time of game j’s release. The parameter γ2 accounts for the changes in the initialcomposition of consumers, i.e. fraction that are high types, in the market for the gameas the platform matures. Lee (2012b) noted the importance of controlling for changesin the installed base of potential buyers in the context of video games. The fractionof non-owners that are high types is allowed to change endogenously over time in themodel, since high-type consumers are more likely to purchase thus removing themfrom the pool of potential buyers for that game.

4.1.3 State and control space

While there is only one control variable, ownership, there are several other relevantstate variables. They are the price (Pt ), trade-in price

(P T I

t

), previous periods of

ownership (hi,t ), demand shock (ξt ), transaction cost shock (ζt ), and individual spe-cific utility shocks (εi,t and ε0

i,t ). Ownership status and previous periods of ownershipare deterministic. The remaining state variables are stochastic from the perspectiveof consumers.

Evidence presented in Section 3.3 supports the assumption that purchase pricesand trade-in prices follow a first order Markov process. Accordingly, I assume thatfrom the perspective of consumers, purchase prices for the highest quintile of gamesfollow the random process described in Eq. 6 below.

Pt+1 = g(Pt ) + ηt+1 (6)

where g(P) is the function estimated from the data, and ηt is the component ofthe change in price unpredictable to consumers. Similarly, I assume consumerexpectations of trade-in prices are given by:

P T It+1 = f

(P T I

t

)+ ηT I

t+1 (7)

where f(P T I

t

)is the function estimated from the data, and ηT I

t is the component oftrade-in prices unanticipated by consumers.

Following Nair (2007), I allow consumers to incorporate the correlation betweenprice shocks ηt and demand shocks ξt in their expectations.19 Specifically, I assumeηt and ξt are distributed jointly normal with correlation ρξ,η to be estimated, butare uncorrelated with other state variables. Since they are also not persistent, theseshocks follow Rust’s conditional independence assumption (Rust 1987).

Each of the remaining stochastic state variables(ζt , εi,t , ε0

i,t

)are assumed to

be independently distributed across time, and hence are uncorrelated with all otherstate variables, present and future. This implies that they too follow Rust’s condi-tional independence assumption. I assume ζt are distributed normally, and εi,t and

19These assumptions imply that the firm can condition on the current value of the component of demandnot observed by the econometrician, ξt , but not future ones, when setting prices.


ε0i,t follow the type 1 extreme value distribution with location parameter equal to the

negative of Euler’s constant and scale parameter equal to one.

4.1.4 Value functions

The ownership control variable is binary. Hence, for presentation purposes, the valuefunction can be broken into two value functions, each conditional on ownershipstatus.

For both value functions, one can yield a simplified Bellman equation on areduced state space without the variables that satisfy Rust’s conditional independenceassumptions (ξt ,ζt ,ηt ,ηT I

t ,εi,t , and ε0i,t ) by integrating these states out of the value

function. This results in the expected value of the value function before any of thesevariables are known. The states εi,t and ε0

i,t can be integrated over analytically.20

However ζt , ξt , ηt , and ηT It , must be integrated out numerically.

I specify the “alternative specific” (i.e. choice specific) value functions so thatthey provide the expected maximum discounted future utility.21 The equation forthe ”alternative specific” value function of owning (excluding current flow utility),equals:

WO(St ) =∫

ln

{exp (uown(St+1, ξt+1) + ϕWO(St+1))

+ exp(usell(St+1, ζt+1) + ϕ ω

1−ϕ

)}

df (St+1, ξt+1, ζt+1|St )

(8)where the state variables St = {

δk, αk, P T It , hi,t

}, ϕ is the discount factor, and

ϕ ω1−ϕ

gives the expected discounted value of using the outside product for allfuture periods. This formula defines the expected future utility as the expected max-imum utility from the consumer’s two choices in the next period, assuming thatthe consumer owns the product at the end of the current period. If, next period,the consumer again keeps the product, they obtain flow utility from using it, plusthe expected discounted utility from continuing to own it going forward. If, nextperiod, they sell the product, they obtain utility from money received from sell-ing it, plus the discounted expected utility of using the outside good for all futureperiods.

20When ε1 and ε2 follow the type 1 extreme value distribution with location parameter equal to the negativeof Euler’s constant, and scale parameter equal to one: E [max (A + ε1, B + ε2)] = ln

(eA + eB

). See Rust

(1987), equation 4.12.21Note that this is a nontraditional specification of the value function. It (1) does not include the currentflow utility, and (2) is specified as the expected maximum utility from next period’s options. Neitherdifference, however, precludes contraction—one can verify that this function satisfies the monotonicityand discounting sufficient conditions in Blackwell’s Theorem. While one could specify the value functionin the traditional way for this problem, doing so would slow estimation considerably because it requiresξt be included as a state variable in order to account for its correlation with ηt . This is because ξt cannotbe integrated out without knowledge of ηt , which requires knowledge of Pt−1 as well as Pt . Hence laggedprice, or the price shock, would need to be included as a state variable too in order to integrate out ξt .

418 B.R. Shiller

Likewise, the equation for the alternative specific value function for the futurevalue of not having owned the product, WNO , can be written as:

WNO(St ) =∫

ln

{exp(ubuy(St+1, ξt+1) + ϕWO(St+1))

+ exp(uwait + ϕWNO(St+1))

}df (St+1, ξt+1|St ) (9)

where in this equation the state variables St = {δk, αk, Pt, P T I

t , hi,t

}. This equa-

tion equals the expected maximum utility of the consumer’s two choices in the nextperiod, assuming the consumer does not own the product at the end of the currentperiod. To reduce the computational burden of including several continuous statevariables, I assume, for the above equation only, consumers use the purchase price toapproximate the trade-in price. Anecdotal evidence suggests consumers do not payattention to the trade-in price when deciding whether to buy a game, but rather useheuristics based on past experiences.

4.1.5 Policy functions

An owner will sell the product if the expected discounted utility of selling exceedsthe expected discounted utility of keeping. Specifically, the optimal policy is sellingif and only if:

usell(St , ζt ) + ϕω

1 − ϕ+ ε0

i,t > uown(St , ξt ) + ϕWO(St ) + εi,t (10)

Since the error terms εi,t and ε0i,t follow the type 1 extreme value distribution, the

probability of selling for owner i of type k with h previous ownership periods can bewritten analytically as:

sk,sell(St , ξt , ζt ) =exp

(usell(St , ζt ) + ϕ ω

1−ϕ

)

exp(usell(St , ζt ) + ϕ ω

1−ϕ

)+ exp(uown(St , ξt ) + ϕWO(St ))

(11)Following analogous steps, the probability of buying for non-owner i of type k canbe written as:

sk,buy(St , ξt ) = exp(ubuy(St , ξt ) + ϕWO(St ))

exp(ubuy(St , ξt ) + ϕWO(St )) + exp(uwait + ϕWNO(St ))(12)

5 Estimation

The model is estimated by maximum likelihood. The likelihood function equals:

L(θ) =∏

j,t

L(Pj,t , P T I

j,t , Qj,t , QT Ij,t ; θ

)(13)

where Q is the quantity purchased, including used game purchases, QT I is thequantity of trade-ins, and the parameter vector θ = (

λ, α, β, γ, δj, σξ , ση, σηT I ,


σζ , ρξ,η, ϕ). Prior literature has noted that the discount factor (ϕ) is not identi-

fied in dynamic models of aggregate demand without substitution across products(Aguirregabiria and Nevo 2013) or, in the monopoly case, without observed variationin the expected continuation values of owning the product (Chevalier and Goolsbee2009). In cases without such variation, its value is often assumed. Following Nair(2007), I assume ϕ = 0.975. This falls between recent estimates of 0.93 (Lee 2012b),and close to 1 (Chevalier and Goolsbee 2009). The standard deviation of the priceshocks, ση and σηT I , can be estimated a priori.

After a change of variables transformation, the likelihood can be written in termsof the price, demand, and transaction cost shocks, as:

L(η, ξ, ζ ; θ) =∏

j,t

f (ηj,t , ξj,t ; θ)f (ζj,t ; θ)||J || (14)

where ||J || is the Jacobian determinant. The derivation of the Jacobian is shown in anOnline Appendix. The price shocks η are estimated a priori from the data, accordingto Eq. 6. The demand and transaction cost shocks (ξ and ζ ) are recovered within eachiteration, by the method described in the next subsection.

5.1 Recovering error terms

To compute the values of the demand and transaction cost shocks, ξ and ζ , foreach product and period, I follow recent models (Gowrisankaran and Rysman 2009;Nair 2007). In each iteration in the maximization procedure, the value functions arecomputed first. Then, the shocks are computed as explained below.

For each game j, the values of ξ are found sequentially using contraction mappingfrom Berry et al. (1995) to find the value of ξj,t which equalizes the observed andmodel’s predicted aggregate share buying.22 The formula for the model’s predictedmarket share buying is:

sbuy(Sj,t , ξj,t ) =∑

k

Mj,k,t ∗ sk,buy(Sj,t , ξj,t )

∑

k

Mj,k,t

(15)

where Mj,k,t equals the mass of non-owners of type k in the market for game j at thebeginning of period t.

The mass of non-owners in the first period equals the installed base of potentialconsumers in that period. In subsequent periods, it is updated to reflect buyers, whohave exited the market, and incoming potential consumers who were not in the marketfor the game in the previous period, for example because they had not yet joinedthe platform, i.e. bought the console. The fraction of entering consumers of a giventype then equals the total amount of entering consumers multiplied by the fractionof consumers that are of that type, implied by the γ parameters. The formula for

22When ξ follows Rust’s conditional independence assumption, the value function is independent of ξ ,and the contraction mapping still holds.

420 B.R. Shiller

updating the masses of non-owners in each period after the game is released is givenbelow:

Mj,k,t+1 = Mj,k,t ∗ (1 − sk,buy

(Sj,t , ξj,t

)) + Mnewj,k (16)

where Mnewj,k is the incoming group of potential consumers of type k entering each

period.The transaction cost shocks ζ can be found through a similar method. In each

period beyond the first, ζj,t is found by equalizing the actual and model’s predictedshare of owners selling, using the same contraction mapping. The predicted shareselling is:

ssell(Sj,t , ξj,t , ζj,t ) =∑

k,h

Rh,j,k,t ∗ sk,sell(Sj,t , ξj,t , ζj,t )

∑

k,h

Rh,j,k,t

(17)

where Rh,j,k,t is the mass of owners of type k with h previous ownership periods ofgame j at the beginning of period t.

The mass of owners of each type and previous ownership length Rh,j,k,t evolvessimilarly to masses of non-owners. Before the product is introduced, there are noowners. After the good is released, the masses of owners are updated each period by:

Rh,j,k,t+1 ={

Mj,k,t ∗ sk,buy(Sj,t , ξj,t ) f or h = 1Rh−1,j,k,t ∗ (

1 − sk,sell(Sj,t , ξj,t , ζj,t ))

f or h > 1

}(18)

Hence the number of owners of game j of discrete type k with one period of previousownership equals the mass of buyers of type k in the previous period. The mass ofowners of type k with h > 1 previous periods of ownership of game j equals the massof individuals of type k, who in the previous period had h − 1 previous ownershipperiods and decided not to sell.

5.2 Market size

It is common in studies of video games (Lee 2012b; Nair 2007) to assume the mar-ket size is comprised of initial consumers present when the game is released, andincoming consumers arriving each period.

It is easiest to assume all platform owners are in the market for a game. However,some platform owners may have no value for specific games, irrespective of quality,implying that they are not for practical purposes in the market for those games. Forexample, an adult male may have no interest in a game designed for young girls, evenif it has exceedingly high quality.

Previous research supports this assertion. Shiller and Waldfogel (2011) foundusing stated valuations that, for songs on iTunes top 50, on average about a third ofindividuals attribute zero value to the song. However, which individuals had zero val-uations depended on which song. Moreover, the zero valuations could not reasonablybe explained as being the censored tail of the distribution of valuations.


The video game data seem to display similar features. Even among games fromthe top quintile of critic review scores, average shares of platform owners buying aspecific game vary greatly in the first year, from about 0.8 % to 55.3 %, nearly a twoorder difference in magnitude.

Falsely attributing differences in sales to quality levels could lead to odd resultsin models of resale markets. Under such assumptions, games with low sales wouldbe estimated to have low quality. This would in turn imply that most purchaseswere due to transient utility shocks, and therefore owners would be keen on quicklyreselling these games soon after purchase. The model would have trouble explain-ing why they do not, and may lead to biased estimates of the rate of lost interest forgames.

Heterogeneity, depending on the form, may be able to absorb incorrect assump-tions on market sizes common across games. But, it cannot explain differences acrossgames unless heterogeneity is allowed to vary by game, which is not feasible—heterogeneity is not separately identified by game. Moreover, differing heterogeneityacross games may merely be compensating for incorrect market size assumptions,suggesting a simpler and feasible approach.

I assume that the size of incoming potential consumers for a game, Mnewj,k , is

constant, and that after prices stabilize some fraction κ buy upon entering, explain-ing all sales that period. This assumption seems logical, because once the price hasstabilized, there is no incentive to delay purchase. So, κ ∗ Mnew

j,k can be observeddirectly late in a game’s life cycle. Therefore, I restrict the sample to games releasedearly enough to observe sales after prices plateau—the data suggest 24 months issufficiently long. Potential consumers also include those present at game launch. Afraction κ of them would be willing to purchase once prices stabilized at lower lev-els, or before then. Hence, κ times total potential consumers at game launch can becalculated by subtracting from total cumulative sales the total cumulative sales dueto potential consumers entering after launch. Last, I find the level of κ such that thegame with the highest proportion of console owners consuming it has market sizeequal to the installed base of platform owners.

5.3 Controlling for endogeneity

A worry with this estimation approach is that firms have more information on thedemand shock ξ than the econometrician does, which would give rise to a biasedestimate of the price coefficient. Controlling for endogeneity is difficult in this con-text. A valid instrument would be a shock to costs or competitive conditions. It isdifficult to find Bresnahan style instruments (Bresnahan 1981, 1987) for competitiveconditions, since games are not very substitutable statistically (shown in Appendix).It is also difficult to find strong Hausman style instruments for cost shocks (Hausmanand McFadden 1984; Hausman 1996), since marginal production costs are very low(about $1.50).

The difficulty in finding valid instruments motivates use of an alternative methodto control for endogeneity, one often used in marketing (Jiang et al. 2009; Nair 2007;Villas-Boas and Winer 1999). The method involves first estimating a reduced formregression of price on an instrument for price, often lagged price, and recording the

422 B.R. Shiller

residuals. Price can then be split into two parts, an exogenous component and theseresiduals which contain the endogenous component of price. The correlation betweenthese price residuals and the unobserved demand shocks can then be estimated withinthe model, and explicitly accounted for in the likelihood function.

Without the correlation parameter, exogenous and endogenous price shocks wouldelicit the same response in the share buying in the model. The correlation parameterexplains the extent to which share buying responds less to endogenous price shocksthan to exogenous price shocks. This muted response thus no longer loads on theprice parameter, limiting the extent of bias. At first glance it might appear that thereis not the cross-sectional variation in the exogenous component of price requiredfor identification, since prices for games in estimation follow the same 1st orderMarkov process. However, because higher order Markov processes were empiricallyruled out, endogenous price shocks in the current period carry forward and providecross-sectional variation in the exogenous component of price in future periods. Jianget al. (2009) show using simulations that this approach in a Bayesian model typicallyyields lower mean square error and bias, compared to the GMM method outlined byBerry et al. (1995). As an added benefit in dynamic models, this approach facilitatesincorporation of the correlation between price and demand shocks into consumers’expectations.

5.4 Identification

Heterogeneity in intrinsic valuations (β, γ ) is identified by the average trends inprices and in the share of non-owners buying. I borrow an argument from Nair (2007).Both the price and implicit rental cost decline on average over time, but quality onaverage remains the same. Hence, the expected gain from buying and probability ofpurchase typically increases over time for any one type of individual. With hetero-geneity, the share of non-owners that are low-valuation types increases over time,which can explain the trends in share buying, even if decreasing as price falls. Thegreater the heterogeneity, the less the share buying increases as prices fall. Differ-ences across games released at different stages in the console’s life cycle identifiesthe impact of console’s age on the composition of types k.

The mean price sensitivity is identified by cross-sectional variation in prices andshare of non-owners buying. Heterogeneity in price sensitivities is identified by thedifferential impacts of price shocks on sales early in the product’s life cycle, and laterin the life cycle when a greater share of non-owners are of the low-valuation type andthe low-valuation types are the marginal buyers. This logic is similar to identificationarguments from Lazarev (2012).

The coefficient of lost interest (λ) generates the time pattern of used sales overtime. Higher boredom implies consumers are more likely to sell the product soonafter purchase, which translates into a more active resale market.

The coefficient of lost interest and heterogeneity parameters are separately iden-tified. While an infinite number of sets of rates of lost interest and initial valuationscan result in an individual wanting to sell a game after h periods but not after h − 1periods, given prices, they cannot explain the individual’s choice of when to buy. Herfirst h uses must in expectation be valued at least high enough to justify buying when


she did, but not high enough to justify buying earlier when prices were higher. Aseries of inequalities like these separately identifies these parameters.

5.5 Computation of counterfactuals

Counterfactual simulations using the parameters from demand estimation allow com-parison of prices, profits, and welfare under alternative environments. Specifically,I compare the status quo environment where resale is allowed with hypotheticalenvironments where the firm sells only non-resellable goods, or where the firm exclu-sively rents goods directly to consumers. I do not consider the case of combiningselling and renting, nor allow third party firms like Blockbuster to rent games toconsumers.

Calculation of dynamic equilibrium prices in counterfactuals requires that pricepaths and levels be allowed to differ from those occurring in the status quo environ-ment, and also that consumers have correct expectations. I assume consumers knowthe firm’s policy function and observe all relevant information. It seems reasonableto assume that the firm sets prices based on a set of demand conditions. Demand con-ditions for non-resellable goods can be characterized by the mass of non-owners ofthe good by consumer type (two variables). When resale is allowed, however, condi-tions for the supply of used goods, which compete with new goods, are relevant forpricing. Thus the masses of owners by type and ownership length, 24 variables intotal, must also be included as continuous state variables. The same is true for rent-ing, because demand to rent depends on the length of time different consumers haveused the product.

While a method from Nair (2007) can be used to calculate the Markov perfectequilibrium prices when resale is prohibited, the large number of variables charac-terizing market conditions in the other cases, which need to be included as statevariables, pose a challenge for estimation. I circumvent this problem for the case ofallowed resale by taking observed prices and quantities sold from the data. By doingso, I am implicitly assuming that the observed prices would result from an equilib-rium simulated by the model, were such a simulation feasible. To allow simulationof the rental counterfactual, I make some strong assumptions, all of which shouldbias profits upwards. Thus, this simulations yields an upper bound estimate of rentalprofits.

5.5.1 Non-resellable goods

To find the price paths arising from a Markov Perfect rational expectations equi-librium game between firms and consumers when resale markets are shut down,I use a policy function iteration procedure similar to Nair (2007).23 The resultingpolicy functions for each player account for their own impact on the evolution of

23Nair notes that the the equilibrium is not guaranteed to be unique. However, we both found that multiplestarting values converged to the same equilibrium.

424 B.R. Shiller

states, and are optimal given the calculated policy functions of other players in thegame.

The profit-maximizing firm’s policy function follows from the static profit func-tion and the evolution of states. The static profit function is:

π(SF

j,t , Pj,t

)= (Pj,t − MC) ∗ Q

(SF

j,t , Pj,t

)(19)

where Q(SF , P

), the quantity purchased, is given by the product of the shares buy-

ing, and the market sizes of each type, denoted by SF . The change in notation of thestate variables, to SF , highlights that the firm’s state variables omit some variablesin the set of consumers’ state variables S. Nair (2007) notes the marginal cost for acopy of a game equals about $11.50; $1.50 in production costs plus $10 in fees paidto the platform. The firm’s value function equals:

VFirm

(SF

j,t

)= max

Pj,t

{π

(SF

j,t , Pj,t

)+ ϕVFirm

(SF

j,t+1|SFj,t , Pj,t

)}(20)

where SF evolve analogously to the masses of non-owners according to Eq. 16. Thefirm’s policy function is the profit maximizing price at each state:

P(SF

j,t

)= arg max

SFj,t

{π

(SF

j,t , Pj,t

)+ ϕVFirm

(SF

j,t+1|SFj,t , Pj,t

)}(21)

The consumer policy functions used in these simulations are similar to the onesspecified in the model section, with an important change. In the counterfactual, Ino longer assume consumers base future price expectation on current prices as I doduring estimation. Rather, I assume consumers base future price expectations on thesame state variables firms use to set prices in the counterfactual simulations, i.e.masses of non-owners by type. So consumer expectations are correct.

The numerical procedure proceeds by four steps, separately for each game. Thefirst step is simply to guess at both the consumers’ policy functions, sk,buy(S), andtheir expectations for the evolution of the state variables, Mj,t+1(sk,buy(S)). The sec-ond step calculates an updated guess at the the firm’s value and policy functions,VFirm(S) and P(S), conditioning on the most recent guess of the consumers’ policyfunctions, sk,buy(S). The third step iterates on two substeps. The first substep is cal-culating the next period states, Mj,t+1(sk,buy(S)), as a function of current states andthe most recent guess at the consumers’ policy functions, sk,buy(S). Then in the nextsubstep the consumers’ policy functions, sk,buy(S), are recomputed using the updatedguess of consumers expectations, Mj,t+1(sk,buy(S)). These two substeps are repeateduntil the total absolute difference in the consumers’ policy functions between itera-tions on the substeps is sufficiently small. This concludes the third step, yielding thenext guess of the consumers’ policy functions, sk,buy(S). The fourth step iterates onsteps two and three repeatedly until the total absolute difference in the firm’s policyfunction betweens iterations is smaller than some arbitrary value, at which time theprocedure stops.


5.5.2 Rented goods

Many information goods are now “streamed”, whereby the firm sells the right touse the digital product over the Internet for a short length of time, without grantingownership. In this case, consumers lose access to the product at the end of the period,and must rent the product again if they wish to continue to have access to it. Thisstrategy is commonly employed for movies (e.g. Netflix, Amazon Prime) and music(e.g. Spotify).

To circumvent issues arising when simulating rentals, four different assumptionsare chosen for the rental simulations. Each assumption should bias rental profitsupwards, yielding an upper bound estimate of rental profits. First, fully characteriz-ing demand would require too many state variables to feasibly simulate a Markovequilibrium, so I allow the firm to set flat rental prices. Second, the licensing fees theplatform charges content producers, currently charged per physical copy produced,would likely be different for digital rentals. To address this, I assume zero marginalcosts of renting, but assume an additional fixed cost equal to the total marginal costincurred when resale is allowed.24 Third, I assume zero transactions costs for return-ing or acquiring a rental and allow consumers to rent again after they had stoppedrenting. Fourth, consumers incorporate expected future value into their willingnessto pay when purchasing a game, implying that profits from outright sales during anylength of time reflect consumers’ use beyond that time. This would not be true, how-ever, for short rentals. I therefore allow the firm to earn profits from renting over amuch longer period, two years as opposed to one when goods are sold. However, tobe consistent, I only allow new consumers to enter during the first year followingrelease.

Optimal profits are simulated by searching over the flat rental price to maximizeprofits. For each rental price, the consumer policy functions are calculated, assumingthey expect rental prices to remain flat.

6 Results

The model was estimated using the sample of 14 games in the top critic quintile thatare observed for a long enough period to construct market sizes.25 The parameterestimates and their standard errors are reported in Table 3. Context is provided below.

The two curves in Fig. 3, one for each consumer type, show the consumers’ aver-age monthly values for owning a game conditional on how many periods they haveowned that game previously. The “hardcore gamers,” i.e. high types, value a monthof use of an average game at about $80 if they have not owned it previously, about

24The sum of marginal costs equals about $140 million, however 87 % of these costs are licensing fees.25The result for highly acclaimed games may not generalize to other games. Such games had higher salesand smaller price declines, compared to less highly acclaimed games. However, since highly acclaimedgames had a disproportionate share of sales, they might better reflect the overall impact.

426 B.R. Shiller

Table 3 Estimation results

Value Standard error

Rate of tiring coef 1 λ1 −1.10 0.16

Rate of tiring coef 2 λ2 0.81 0.01

Hard-core gamers add. value β 6.07 0.19

Heterogeneity parameter 1 γ1 0.16 0.03

Heterogeneity parameter 2 γ2 −0.28 0.04

Price sensitivity low type α(1) 0.37 0.05

Price sensitivity high type α(2) 0.31 0.04

Stand. dev. (demand shock) σ (ξ) 1.90 0.23

Stand. dev. (trans. cost shock) σ (ζ ) 5.80 0.41

Corr. btw. dem. and sup. shocks ρξ,η 0.16 0.03

Game fixed effects, not reported above, averaged about 19.3 above ω. Their point estimates have a standarddeviation of 3.2. Standard errors computed from the Hessian

$30 more than the low types. Both types tire quickly with use. The high types, forexample, lower their value for a month’s use of an average game from about $80 forthe first month they own it to about $4 per month after having owned it for 6 months.About 90 % of this decline occurs in the first two months following purchase.

The fraction of consumers in the market that have high intrinsic value for a game,as opposed to low intrinsic value, is implied by the parameters γ . For games releasedat the same time as the platform was released, it is estimated that about half of theconsumers in the market for the game are of the high valuation type. For gamesreleased 6 months later, however, only about 20 % are. This reflects the endogenousadoption decision shown in Lee (2012b) and found in Liu (2010). Consumers withhigh valuations for games presumably are more likely to buy the console early on,even before many games have been developed for it. Later, lower valuation typescomprise a larger share of consumers.

The price elasticities over time are shown in Table 4. Static (one-period) elas-ticities and dynamic elasticities are reported. For both types of elasticities, I allowexpectations of future prices to change with the current price change. The average ofthe static elasticities, −2.16, is quite close to the average elasticity estimated in Nair(2007), also −2. The dynamic elasticities, which report the percent change in thenext 3 month’s sales following a one percent change in price in the current month,are similar.

The estimated values of the standard deviations of ξ and ζ are both relativelysmall. The standard deviation of the demand shock ξ equals about $4 for the hightype, roughly 5 % of a high type’s typical initial one-period valuation for a game. Thestandard deviation of the transaction cost shock, ζ , is $15 for a high type, roughly15 % of the high type’s typical initial static valuation for the good. The correlationbetween the demand and price shocks is estimated to be 0.24.


0 2 4 6 8 10 12−10

0

10

20

30

40

50

60

70

80

90D

olla

r U

sage

Val

ue

Previous Ownership Periods

Low Type (Mass Market)High Type (Hardcore)

Fig. 3 Static (one-period) dollar value from usage against length of previous use

6.1 Counterfactual results

The main findings are shown in Table 5. Profits from selling non-resellable gamesare about twice as high as the corresponding profits from resellable games, in thefirst year following a game’s release. This is true even before accounting for the fixedcosts of developing the game.26 There is substantial variation across games. Thestandard deviation of the percent increase in profits is 75 %, although each simulatedgame is estimated to yield higher profits under prohibited resale. The overall profitdifference is due to the facts that (i) when resale is not allowed the firm sells morecopies and (ii) they sell for higher prices in later periods. Some of the differencein quantities sold is due to new sales being displaced by used copies when resaleis allowed and some to the fact that consumers delay purchase beyond a year whenresale is allowed and prices fall quickly. These latter sales are not captured in thiscomparison. Most individuals buying later when resale is allowed, however, buy usedgames if available, or buy the game at a price close to marginal costs, so the firm

26Average development costs for XBOX360/PS3/PC-based games for one major producer, Ubisoft,average between $18.8 million and $28.2 million. (http://www.gamasutra.com/php-bin/news index.php?story=18389, accessed Nov 28, 2011).

http://www.gamasutra.com/php-bin/news_index.php?story=18389

http://www.gamasutra.com/php-bin/news_index.php?story=18389

428 B.R. Shiller

Table 4 Mean price elasticity estimates

Age of game Elasticities

Static Dynamic (3 month)

1 −2.40(0.68) −3.13(14.20)

2 −2.53(0.90) −2.40(4.51)

3 −2.24(0.67) −1.48(0.45)

4 −2.19(0.68) −1.79(1.01)

5 −2.02(0.64) −2.04(3.20)

6 −1.91(0.60) −1.74(1.49)

7 −2.06(0.65) −1.53(0.64)

8 −2.15(0.73) −2.23(3.20)

9 −2.01(0.81) −0.90(1.06)

Standard deviations of point estimates across games in parentheses. Both types of elasticities allow con-sumers to update beliefs of future prices. The dynamic elasticities show the percent change in the quantitybought in the subsequent 3 months for a percent change in the current price

earns little profits on later sales when resale is allowed. Hence ignoring later saleshas negligible impact.27

The rental simulations yield an upper bound estimate of profits that is barelyhigher than profits from selling a resellable good, not significantly different. Rentalprofits are still much lower than profits from selling a non-resellable good, about halfas much.

The average equilibrium price paths under each distribution strategy are shownin Fig. 4. When resale is prohibited, optimal prices decline very slowly over time,falling by a few dollars over the first year. As a result, consumers do not have muchincentive to wait. However, when resale is allowed, prices fall sharply over time. Theprices decline for this group of games by about $30 over the first year on average, andimplied rental prices fall too.28 Consumers in the model anticipate the falling prices,and fewer are willing to buy in the first few months when prices are high, despite thefact that the good is worth more to them when resale is allowed, since they then havethe option to resell the good. Figure 5 verifies this, showing the increase in monthlysales from preventing resale is highest early on. By the end of the first year, monthlysales of resellable copies are close to monthly sales under prevented resale.

27For the 17 games released in the first two months of the dataset, 92 % of profits (in the first 3 years) occurin the first year, on average. Assuming that this holds for all games, then profits from resellable goods areunderestimated by about 8 %, not enough to explain the difference in profits when resale is shut down.28There are multiple possible definitions for implied rental prices. If it is defined by the cost of buyingminus the amount received from selling the product one period later, rental prices decline by about 80 %over the first year.


Table 5 Counterfactual results (total across 14 games)a

Goods that are

Resellableb Rented Non-resellable

Producer profits (in millions) $495 $522 $1,037

– (29.9) (40.2)

Q. new sales (in millions) 12.2 83.7c 29.3

– (3.9) (0.1)

Q. used sales (in millions) 2.2 – –

– – –

Standard errors, shown in in parentheses, computed via the delta methodaFirst twelve months post releasebNumbers for allowed resale are computed using observed salescEquals number times rented

The difference in prices across counterfactuals is logical. When resale is allowed,lowering price reduces the number of traded-in games. Fewer trade-ins in the currentperiod imply lower inventory levels of used games at retailers. Hence, by droppingprice in the current period, the seller reduces competition from used copies in laterperiods. This dynamic effect provides additional motivation to lower prices whenresale is allowed.

A related question is what impact resale markets have on consumer welfare, afteraccounting for the firm’s response. I calculate the exact net consumer welfare gainfrom resale markets using Small and Rosen’s (1981) formula for Hick’s equivalentvariation. The net consumer welfare gain/loss from allowing resale to an individualof type k, in dollars, equals:

EVk = WNO,YR(k, 1) − WNO,NR(k, 1)

αk

(22)

where αk is the price sensitivity, and WNO,YR(k, 1) and WNO,NR(k, 1) are the valuefunctions at game release, conditional on not owning the good, when resale is andis not allowed, respectively. I find that only distributing non-resellable goods wouldlower welfare by $23.80 on average for each low-type individual, but raise welfare by$11.87 on average per high-type individual, for an aggregate loss of $21 million onaverage across games.29 High-type individuals are better off because they can acquirethe game for less. Low types, however, yield positive utility from use of the productfor fewer periods. Losing the ability to resell the game is therefore quite costly tothem.

29The welfare calculation does not include a third group, used video game retailers, whose profits wouldincrease welfare when resale is allowed. Their profits cannot be estimated because their cost functions arenot known.

430 B.R. Shiller

1 2 3 4 5 6 7 8 9 10 11 120

10

20

30

40

50

60

Time (Months) Since Release

Pric

eResellableNon−ResellableRental

Fig. 4 Simulated price paths

Using an analogous equation for consumer welfare changes, I find that rent-ing as opposed to selling resellable goods lowers aggregate consumer welfare by$75 million for the average game. This loss arises from the fact that consumersforgo using the product when their valuations are between zero and the rentalprice.

In a related paper, Ishihara and Ching (2011) find less of a difference in prof-its, possibly due to differences across these markets. In Japan, new games pricesdo not fall over time. This stands in stark contrast to other countries. Addition-ally, the Japanese market seems to highly value novelty. Accordingly, they allowfor novelty effects, i.e. for perceived quality to decline to non-owners as well.They did not, however, allow for heterogeneous usage values, since heterogeneoususage values are not separately identified from novelty effects. In their judgment,novelty was the more important feature to include when studying the Japanesemarket.

If novelty is an important feature in the U.S. market, then the findings in this papermay overstate the true impact of resale. Recall that the rapid price declines which arepresent only when resale markets exist make waiting to buy an attractive substitute forbuying immediately. This substitute reduces extractable surplus when resale marketsexist. However, the value to a consumer of waiting until later to buy is reduced whennovelty matters, since in later periods the good will inherently be valued less due to


0 2 4 6 8 10 120

2

4

6

8

10

12x 10

6

Time (Months) Since Release

Qua

ntity

Sol

d/R

ente

d

ResellableNon−ResellableRental

Fig. 5 Simulated sales trends

novelty effects. As a result, firms can extract more revenue from consumers in thepresence of resale when novelty effects exist, possibly implying a smaller profit gainfrom preventing resale. However, the profit gain should not disappear. Even assumingthe other extreme—novelty effects but no heterogeneous usage values—Ishihara andChing (2011) still find that preventing resale would meaningfully raise profits inJapan.

6.2 Robustness checks

The standard approach for comparing profits between the status quo and counterfac-tual policies is to simulate both scenarios using the estimated parameters. For rentalsand non-resellable goods, this was feasible. However, for reasons described earlier,it is not feasible to fully simulate the case where resale is allowed. This leads to theconcern that a poorly specified model might be driving the finding that preventingresale raises profits.

This subsection tests whether any of several modeling assumptions drives the mainresult. One at a time, each assumption is changed, and the estimation model andcounterfactual simulations are repeated. The results are shown in Table 6.

432 B.R. Shiller

Table 6 Robustness checks profits (in Millions)

Main results Robustness checks

Market size

Smaller used market DF 0.95 25 % Lower 50 % Lower

Resellable goodsa 495 495 474 495 495

– – – – –

Rented goods 522 548 373 371 213

(29.9) (29.2) (34.1) (22.2) (17.1)

Non-resellable goods 1,037 1,002 991 778 484

(40.2) (40.4) (62.7) (26.5) (19.3)

Standard errors, shown in parentheses, computed via the delta methodaObserved in data

Neither reducing the monthly discount from 0.975 to 0.95 nor reducing the num-ber of games traded-in by 25 % changes the results qualitatively.30 Note that byconstruction, profits from resellable goods are unchanged.

The assumed market size magnitude does seem to matter, however. The main spec-ification assumed that the most popular game had a market size equal to the installedbase of platform owners. Reducing the market size by 25 % for all games reducesnon-resellable good profits by 25 % and rental profits by 29 %. This is likely dueto the fact that reducing the market size reduces the number of unserved consumersin the status quo case, who may be served and thus contribute to revenues in coun-terfactual environments. Reducing the market size further, by 50 %, implies nearlyeveryone in the market for a game buys it within the first two years. In this case, thedifference in profits between non-resellable and resellable goods was not statisticallysignificant. However, a drastically different market size assumption was required toreach this result.

The observed relationship between rental profits and resellable good profits can beused to provide credibility to the main model. Because buying and selling a resellablegood is logically similar to renting, as explained in Section 2.1, we might expectprofits from renting to be similar to profits from resellable goods. This provides acheck—are rental and resellable good profits in fact similar? In the main model theywere: 522 vs. 495 million, close enough that the difference was not significant. Inrobustness checks yielding different qualitative findings, they were not. Moreover,the relationship between non-resellable good profits and rental profits is more sta-ble; their percent difference ranged from 83 % to 165 % across robustness tests. Sothe two environments which could be simulated did demonstrate a robust qualitative

30A greater share of revenues are obtained later under the rental pricing strategy, compared with otherstrategies. Hence, profits under renting decline faster as the discount factor is reduced.


result. We might expect a similar result for the impact of eliminating resale directly,and did so in the main model, thus providing some ex-post support for it.

7 Discussion and conclusion

Firms can or may soon be able to circumvent the first sale doctrine and legally pre-vent resale outright in the U.S. by selling non-resellable digital downloads or bystreaming rentals. The results in this paper show that profits from selling video gameswould be much higher for non-resellable goods, over 100 % higher in the base speci-fication. However, the exact size of the increase was sensitive to the assumed marketsize. Throughout all robustness checks, non-resellable good profits were substantialyhigher than rental profits, at leat 83 %.

These findings stand in contrast to most previous empirical and theoretical papersfocusing on monopolists producing goods for which consumers do not lose interest.The different results, along with the logic put forth in Section 2.1, suggest the rate atwhich consumers lose interest might be important in determining the impact of resaleon producer profits. This may interest managers and policy makers, since the typesof goods obviously satisfying this assumption, entertainment information products,are the types of goods easily distributed as non-resellable downloads.

Appendix

Evidence that games are not substitutes

Nair (2007) argued that because “each game is fairly unique, having its own dis-tinct features, characters and idiosyncrasies,” they are likely not substitutes for oneanother. Empirical results showed (1) that there are no statistically significant cross-price effects within genre, (2) neither sales nor prices are significantly impacted byhit game releases in the same genre, and (3) that concentration in a genre does notsignificantly impact the rate at which prices decline. However, Derdenger (2011)yielded opposing results when investigating other 6th generation consoles.

To test whether XBOX 360 video games in the data are substitutes, I employ astatic nested logit regression similar to previous papers (Nair 2007; Derdenger 2011),where genre determines the nest. Following their specification, I regress:

ln(sjt /s0t ) = αj + ωt + λ(t − rj ) + βPjt + σ ln(sjt |g) + ϕjt (23)

where sjt and s0t are the shares of game j and the outside good in period t, respec-tively, αj and ωt are game and month fixed effects, rj is the release date of gamej, Pjt is the price, sjt |g is game j’s share of genre g sales, and ϕj,t is an error term.Following earlier papers (Derdenger 2011; Nair 2007), I set the market size to thecumulative installed base of XBOX 360 console owners. The value of the parame-ter σ determines the extent to which games are substitutes for one another. A valueclose to zero, rather than a higher positive number close to 1, denotes that the nestsare largely irrelevant and hence games are not substitutes for one another.

434 B.R. Shiller

Table 7 Nested logit estimation of substitutability

Dependent variable is log(sj t /s0t )

OLS 2SLS

Age(t − rj

) −0.194 −0.317 −0.400 −0.363 −0.624 −0.947

(0.007) (0.015) (0.036) (0.019) (0.036) (0.07)

Ageˆ2 0.009 0.025 0.018 0.072

(0.001) (0.006) (0.001) (0.009)

Ageˆ3 −0.001 −0.003

(0.000) (0.000)

Price −0.012 −0.013 −0.013 −0.033 −0.034 −0.031

(0.002) (0.002) (0.002) (0.003) (0.003) (0.003)

Within genre share (σ ) 0.623 0.602 0.602 −0.05 −0.068 −0.071

(0.014) (0.014) (0.014) (0.07) (0.068) (0.067)

Observations 2875 2875 2875 2594 2594 2594

R-squared 0.93 0.93 0.93 0.93 0.94 0.94

Standard errors in parentheses. Game and month fixed effects are included in all specifications. Regressionrestricted to observations where the game’s age (t − rj ) ≤ 12. Regressions of endogenous variableson instrument matrix—prices: (Rsquare = 0.92, F = 27, 975), within genre share: (Rsquare = 0.55,F = 3220)

Two right-hand size variables in Eq. 23 above, price (Pjt ) and the within-genreshare of sales (sjt |g), are likely endogenous. To address this concern, I instrument forthem using the lagged price and the number of games in the genre.

The results are shown in Table 7. The sample is restricted to games with the highestquintile of critic scores. The first three columns in Table 7 employ OLS, and thesecond three employ 2SLS. Note that once the instruments are included, the estimatedvalues of σ are negative and insignificant, strongly suggesting that games are notsubstitutable for one another.

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