Backward Compatibility in Two-Sided Markets

Transcription

1 Backward Compatblty n Two-Sded Markets Rchard T. Gretz Myongjn Km Suman Basuroy August, 2014 Prelmnary and Incomplete Please do not crculate Abstract Often new hardware s backward compatble wth software desgned for prevous generatons of hardware. For example, PlayStaton 2 can play games desgned for PlayStaton. Our study contrbutes to the growng lterature on dynamc dscrete choce- demand estmaton for consumer durables by ncorporatng backward compatblty nto a framework wth heterogeneous forward lookng consumer who can mult-home (purchase more than one pece of hardware). We apply t usng data from the home vdeo game ndustry on seven consoles and ther games spannng two product generatons from We use our estmates to obtan the margnal value of console backward compatblty on hardware share. Our results suggest backward compatblty offers hardware frms a sgnfcant advantage over non-backward compatble compettors. However, backward compatblty ncreases the cannbalzaton of the assocated prevous generaton hardware - an mportant factor for managers consderng proftablty throughout the hardware lfespan. Also, we assess the effect of backward compatblty on hardware adopton for dfferent consumer nventores. Interestngly, we fnd backward compatblty has the greatest effect on non-adopters of the prevous generaton hardware. Keywords: two-sded markets, backwards compatblty, dynamc demand, estmaton of network effects, vdeogame ndustry JEL: L13, L14, L42, L86 Rchard T. Gretz s the correspondng author. Bradley Unversty. Address: Department of Economcs, 209 Baker Hall 208, Peora, IL E-mal: rgretz@bradley.edu; webste: Unversty of Oklahoma. Address: Department of Economcs, Cate Center Drve, Norman, OK E-mal: mjkm@ou.edu; webste: Unversty of Oklahoma. Address: Prce College of Busness, Dvson of Marketng & Supply Chan Management 307 W. Brooks, Sute 3 Norman, Oklahoma E-mal: sumanbasuroy@ou.edu; webste:

2 1 Introducton For many consumer electroncs customers choose a product platform to consume the assocated product and servces, e.g. smart phones, TV set-top boxes or game consoles. Many provders thus target to lock consumers nto ther platform and make platform swtchng costly. A partcular mportant tme n the product lfe cycle s the release of a successor product. The hardware provder needs on the one hand a superor product n order to attract new customers but at the same tme needs to ensure that not too many exstng customer use the opportunty of a new product ntroducton to swtch platforms. Many manufacturers therefore allow ther successor product to be backward compatble to the prevous generaton product, a partcular example would be the Phone whch n each new teraton can run the software for the old Phone but also typcally ncludes new software features. However, manufacturers not always choose to make the product backward compatble. An ndustry n whch we observe both actons s the game console ndustry. Whle Sony choose to make the PlayStaton 2 backward compatble, Nntendo opted not to do so n the sxth generaton hardware (GameCube). Ths paper therefore studes the ratonal of allowng backward compatblty n the game console ndustry. The man contrbuton of our paper s to extend Lee (2013) by allowng for backward compatble hardware. Ths allows us to study the effects of backward compatblty on manufacturers profts and consumer welfare. We are able to dentfy ths by keepng track of consumer s nventory over tme. Specfcally, consumers purchase the backward compatble hardware even though they do not own the prevous generaton of the hardware. Ths offers a source of varaton that we use to dentfy the backward compatblty. We therefore allow that owners of a Playstaton 2 derve utlty from games avalable for the Playstaton 1. We therefore keep track of the consumers nventory over tme. Our goal n ths paper s to examne the benefts and costs to consumers, console makers, and game developers of backward compatblty n a varety of settngs. In the counterfactual we examne the effect of backward compatblty by studyng the mplcatons of a non-backward compatble PlayStaton 2. We fnd that the t s the non-adopters of Playstaton 1 that beneft the most from the backward compatblty. In partcular we fnd that Playstaton 2 would have fewer adopters a year after t s ntroducton f t was not backward compatble. However, ths comes wth the tradeoff that the Playstaton 1 would n fact have had more adopters one year after the PlayStaton 2 was ntroduced. Overall, consumer welfare ncreases through backward compatblty. In another counterfactual we study the effect of forcng all hardware to be backward compatble and the effect on both consumers and frms proft. Ths paper s related to the lterature on modelng demand for durable goods. Emprcally modelng demand for durable goods ncorporates several nterestng and challengng phenomena. In many ndustres t s approprate to assume consumers have heterogeneous preferences, are forward lookng and have ratonal expectatons over the expected utlty of future products, base ther decsons on ther current nventory of competng products, and may make repeat purchases. Indeed, not ncludng these realstc aspects of consumer demand can lead to based estmates (Conlon (2012); Gowrsankaran and Rysman (2009); Lee (2013)). Researchers have recently combned the technques developed by Berry (1994) and Berry, Levnsohn and Pakes (1995) wth the optmal stoppng lterature poneered by Rust (1987) to obtan emprcal estmatons ncorporatng these aspects of consumer demand. Gowrsankaran and Rysman (2009) estmate demand n the dgtal camcorder ndustry allowng for persstent consumer heterogenety, consumers who can delay 1

3 purchases based on ratonal expectatons of the evoluton of product characterstcs, and repeat purchases by consumers. Lee (2013) extends ths methodology wth hs study of the vdeo game console ndustry and ntroduces a new fxed pont routne whch smultaneously recovers hardware and software utltes. Ths paper proceeds as follows: We descrbe the vdeo game data set n secton 2. In secton 3, we descrbe a dynamc model for software and hardware demand and buld up a method for ncorporatng backward compatblty. Then we dscuss computaton and the specfcs of the MPEC technques employed on the software sde of the problem n secton 4. We descrbe nstruments and dentfcaton strategy n secton 5. The dynamc estmaton results are presented n secton 6. Usng the estmated parameters, we recover theoretcal polcy functons for hypothetcal counterfactuals n secton 7. Then we conclude n the last secton. 2 Data and Industry Background The game ndustry has a (surprsngly) long hstory. Each generaton of gamng console hardware s essentally a sgnfcant mprovement over the prevous generaton n the hardware qualty. Before we provde detals on the 5th and 6th generaton hardware that are underlyng ths paper we brefly revew the hstory of gamng consoles that starts n the 1970s. The frst generaton was created n the early 1970s wth Atar beng one of the leadng producers of arcade vdeo games. One of the frst successful games was a smple table tenns game called Pong n The frst generaton typcally had the game hardwred nto mcrochps. The second generaton mproved upon ths by allowng dfferent software to run on the same hard. Both the frst and second generaton vdeo game consoles were frequently arcade games that were con operated and present n many shoppng malls. The 3rd generaton gamng console arrved n consumers homes n larger numbers than prevous generatons and arcade games slowly started ther declne thereafter. The 3rd generaton s represented n partcular by the Nntendo Entertanment System (NES) and ended wth the dscontnuaton of the NES. The fourth generaton ncluded Mega Drve/Geness and Super NES and started roughly n The fourth generaton also came along wth a contnued declne n the popularty of arcades and an ncreasng penetraton of handheld gamng consoles such as the Gameboy. The ffth generaton ncluded the Sony Playstaton, Sega Saturn and Nntendo 64. The ffth generaton s noteworthy for ts transton to 3D graphcs and use of CDs. Fnally, the sxth generaton started n the early 2000s and ncludes the Sega Dreamcast, Sony Playstaton 2 and Nntendo Gamecube. Moreover, Mcrosoft entered the game console ndustry wth the ntroducton of the Xbox Our study examnes the ffth and sxth product generaton of the home vdeo game ndustry from May 1995 through October The data set does not nclude the next generaton of consoles (seventh) whch s ntroduced n November Our data source s the NPD Group, a market research frm wth pont of sale data from approxmately 65% of U.S. retalers. We have observatons on console and game quantty sold and average prce over that tmeframe. We should note the ffth generaton began n 1993 wth the ntroducton of the 3DO and Atar Jaguar, however these consoles were short lved and exted the market rather quckly. The majorty of sales n the ffth product generaton are generated by the consoles that we nclude n our study: Sega Saturn ntroduced n May 1995, the Sony PlayStaton ntroduced n September 1995, and Nntendo 64 ntroduced n September We also nclude all sxth generaton consoles: Sega Dreamcast ntroduced n September 1999, Sony PlayStaton 2 ntroduced n October 2000, and Nntendo GameCube and Mcrosoft Xbox both ntroduced n November 2

4 2001. In total, we observe 7 consoles over the tmeframe (3 n the ffth generaton, 4 n the sxth). However, only 4 consoles survve through from the ffth generaton and 3 from the sxth generaton; Sega Saturn, Nntendo 64, and Sega Dreamcast ext n August 1999, December 2003, and February 2002, respectvely. Each console s techncal characterstcs reman unchanged over tme, however, new product generatons are marked by the ntroducton of new consoles wth a dstnct shft n performance ablty. For example, the majorty of consoles n the 3rd generaton feature 32-bt central processng unts (CPUs); 128-bt CPUs are the norm for the 4th generaton. In general, new vdeo game console generatons are ntroduced every 5-7 years. Table 4 summarzes the above ponts whle Table 5 dsplays descrptve statstcs by console, by generaton, and n total for the NPD data. Table 1: Entry and Ext of Ffth and Sxth Generaton Consoles Ffth Generaton Processor bt sze Entrance Date Ext Date (f applcable) Sega Saturn 32 May 1995 August 1999 Sony PlayStaton 32 September 1995 Nntendo September 1996 December 2003 Sxth Generaton Processor bt sze Entrance Date Ext Date (f applcable) Sega Dreamcast 128 September 1999 February 2002 Sony PlayStaton October 2000 Mcrosoft Xbox 128 November 2001 Nntendo GameCube 128 November 2001 Notes: In the market through October 2005 Our study concerns the effect of backward compatblty on adopton and game avalablty. The ffth and the sxth product generatons are deal canddates for our purposes. Each console n the ffth generaton has a successor n the sxth: Sega Saturn - Sega Dreamcast, Sony PlayStaton - Sony PlayStaton 2, and Nntendo 64 - Nntendo GameCube. However, only the Sony PlayStaton 2 had the ablty to play games for the orgnal Sony PlayStaton. In that sense, Sony PlayStaton 2 was backward compatble wth Sony PlayStaton. In sum, we observe two console makers (Nntendo and Sega) who ntroduce consoles n both the ffth and sxth generaton and eschew backward compatblty, one console maker (Sony) who ntroduces consoles n both the ffth and sxth generaton and embraces backward compatblty, and one console maker, Mcrosoft wth the Mcrosoft Xbox, that s a new entrant to the ndustry n the sxth generaton. These dynamcs allow us to consder counterfactuals concernng the effect of backward compatblty on the backward compatble console and ts predecessor, ncumbent compettors, and new entrants. There are some stylzed facts about the ndustry we should menton before we move forward. Frst, there s sgnfcant consumer heterogenety around preference for gamng. 1 Second, 1 As noted n Lee (2013), 20% of game players account for 75% of all vdeo game usage. 3

5 Table 2: Descrptve Statstcs on Monthly Console and Game Prces and Quanttes Console Varable Average St. Dev. Mn Max Monthly Console Prce $ $74.44 $20.51 $ Sega Saturn Monthly Console Quantty Average Monthly Game Prce $15.68 $9.91 $0.30 $51.67 Average Monthly Game Quantty Monthly Console Prce $69.96 $44.42 $26.29 $ Sony PlayStaton Monthly Console Quantty Average Monthly Game Prce $11.04 $7.10 $0.01 $92.33 Average Monthly Game Quantty Monthly Console Prce $64.15 $28.81 $13.64 $ Nntendo 64 Monthly Console Quantty Average Monthly Game Prce $17.07 $8.94 $0.54 $48.49 Average Monthly Game Quantty Console Generaton Varable Average St. Dev. Mn Max Monthly Console Prce $76.28 $50.90 $13.64 $ Ffth Generaton Monthly Console Quantty Average Monthly Game Prce $12.28 $8.01 $0.01 $92.33 Average Monthly Game Quantty Console Varable Average St. Dev. Mn Max Monthly Console Prce $82.67 $31.87 $30.64 $ Sega Dreamcast Monthly Console Quantty Average Monthly Game Prce $14.62 $7.10 $2.41 $31.74 Average Monthly Game Quantty Monthly Console Prce $ $38.17 $74.40 $ Sony PlayStaton 2 Monthly Console Quantty Average Monthly Game Prce $13.02 $7.05 $0.01 $68.11 Average Monthly Game Quantty Monthly Console Prce $ $28.70 $74.97 $ Mcrosoft Xbox Monthly Console Quantty Average Monthly Game Prce $12.66 $7.74 $0.00 $ Average Monthly Game Quantty Monthly Console Prce $69.25 $21.83 $46.45 $ Nntendo GameCube Monthly Console Quantty Average Monthly Game Prce $12.79 $6.46 $0.68 $45.39 Average Monthly Game Quantty Console Generaton Varable Average St. Dev. Mn Max Monthly Console Prce $95.03 $36.35 $30.64 $ Sxth Generaton Monthly Console Quantty Average Monthly Game Prce $13.00 $7.15 $0.00 $ Average Monthly Game Quantty Monthly Console Prce $84.09 $46.30 $13.64 $ Total Monthly Console Quantty Average Monthly Game Prce $12.57 $7.67 $0.00 $ Average Monthly Game4Quantty Notes: All prces corrected for nflaton usng the Consumer Prce Index (1982 = 100).

6 game sales are drven by ht ttles (Gretz and Basuroy (2014); Lee (2013); Bnken and Stremersch (2009)). Smlar to moves (Basuroy, Chatterjee and Ravd (2003)), the majorty of games released sell relatvely lttle compared to a few superstars or kller applcatons. Fgure 1 shows hstograms for each console where y-axs s the number of games and the x-axs s total sales. Notce the hstograms each dsplay smlar patterns - few games wth many unts sold, many games wth few unts sold. Thrd, most of the games are exclusve to a sngle console. Ths means that gamers may multhome (.e. purchase more than one console) to obtan access to ttles they cannot get from consoles already n ther nventory. Table 3 provdes data on the number of games and number of exclusve games released for each console. Table 3: Installed Base and Number of Games per Console Console Months Number of Number of Generaton Console Installed on the Games Released Exclusve Base Market for Each Console Games Sega Saturn Ffth Generaton Sony PlayStaton Nntendo Sega Dreamcast Sxth Generaton Sony PlayStaton Mcrosoft Xbox Nntendo GameCube Notes: Fgures based on observatons through October Sony PlayStaton, Sony PlayStaton 2, Mcrosoft Xbox, and Nntendo GameCube stll on market at the end of the sample tmeframe. Importantly, backward compatblty gves anyone who purchases the next generaton console access to all games avalable on the related prevous generaton console. Ths means that purchasers of the prevous generaton console have access to all ther prevous generaton games and non-purchasers of the prevous generaton console have access to a large number of (exclusve) games that were not n ther prevous nventory. The mportance of backward compatblty to the vdeo game ndustry s up for debate - and s the focus of ths study. Anecdotal evdence suggests consumers desre the ablty to play prevous generaton games on new systems. An example from the ntroducton of the most recent generaton of vdeo game consoles, Keth Stuart from the Guardan laments [t]he new consoles from Sony and Mcrosoft are sellng n ther mllons, but customers hopng to play ther old games wll be dsapponted (Stuart (2013)). Interestngly, smlar evdence suggests developers desre backward compatblty as well. Guseppe Nelva n the ndustry publcaton DualSHOCKERS dscusses a promnent game developer s negatve reacton 2 upon learnng new generaton consoles wll not be backward compatble and notes t s funny to see a promnent game developer so surprsed consderng the radcal dfference n archtecture between the two generatons. 2 The developer, Hdek Kamya, called the lack of backward compatblty for PlayStaton 4 malcous (Nelva (2014)). 5

7 (a) Sega Saturn - Ffth Generaton Console (b) Sony Play Staton - Ffth Generaton Console (c) Nntendo 64 - Ffth Generaton Console (d) Sega Dreamcast - Sxth Generaton Console (e) Sony Play Staton2 - Sxth Generaton Console (f) Mcrosoft Xbox - Sxth Generaton Console (g) Nntendo GameCube - Sxth Generaton Console 6 Fgure 1: Total Sale per Console Type

8 Another example shows the concerns of smaller game producers and devlopers, [t]he lack of backwards compatblty really affects more then consumers. It affects the small and ndependent, developers and publshers as well (Pearman (2013)). However, console makers may face sgnfcant costs, ether fnancally or n crpplng the new technology, by ncludng the ablty to play prevous generaton games n ther new generaton consoles. In a recent Wall Street Journal ntervew, the head of Mcrosoft s nteractve entertanment busness, Don Mattrck, made ths pont, Compatblty between software and hardware s also a challenge. For example, nether the PlayStaton 4 nor the Xbox One can play game dsks made for ther predecessors... Mcrosoft s Mattrck says If you are backwards compatble, you are really backwards (Sherr (2013)). 3 Model Our model bulds on Lee (2013) and modfes the fxed pont routne to ncorporate overlappng product generatons and backward compatblty. That s, current generaton hardware may have the ablty to use software desgned for prevous generatons. Also, we employ an MPEC (Mathematcal Programmng wth Equlbrum Constrants) type technque derved from by Su and Judd (2012) and Dubé, Fox and Su (2012) on the software sde of the problem to speed up computaton. Both Su and Judd (2012) and Dubé, Fox and Su (2012) show sgnfcant speed mprovements wth MPEC over the tradtonal fxed pont approach n several settngs ncludng logt demand models smlar to the one we present below. 3.1 Software demand Our man contrbuton les wth the ncluson of multple product generatons of hardware and backward compatblty. It s mportant to note n ths subsecton we focus on software desgned for a unt of hardware whch ncludes all software orgnally released specfcally to be used wth that unt of hardware. For example, PlayStaton 2 games were orgnally desgned to be played on PlayStaton 2. However, PlayStaton 2 s backward compatble and can play games desgned for PlayStaton. 3 We ncorporate backward compatblty n the next subsecton. Our goals for ths subsecton are to fnd the expected opton value for a unt of software desgned for hardware j. We employ the same assumpton as Lee (2013) where consumers consder software purchase decsons ndependently (.e. software are not substtutes for each other). Several mportant ndustry features are ncorporated nto the software demand sde of the problem. Frst, software must be consumed together wth hardware n order to provde utlty. In other words, a consumer wll only consder purchasng a pece of software f they own the approprate hardware. Second, consumers face a dscrete-choce problem of whether to purchase a pece of software or not. Whereas software s a durable good, consumers never return to the market for a pece of software they have purchased prevously. Thrd, consumers are forward lookng and have ratonal expectatons regardng the evoluton of software characterstcs. That s, they compare the present value of purchasng the unt of software n perod t to the expected value of watng untl the next perod to reconsder purchase. We assume consumers have ratonal expectatons over the expected value of watng untl the next perod. Fourth, we assume consumers are heterogeneous wth respect to ther taste for software and ther senstvty to software prce. 3 PlayStaton 2 s Sony s next generaton follow up to the PlayStaton. 7

9 The lfe-tme utlty for consumer who owns hardware j and purchases software k at tme t s: u j,k,t = α sw + α sw,c c j,k,t + α sw,pp j,k,t + η j,k,t + ε j,k,t. (3.1) Consumer s software preference parameter, coeffcent on software prce, and dosyncratc utlty shock for software k at tme t are gven by αsw, αsw,p, and ε j,k,t, respectvely. Importantly, we assume ε j,k,t s IID from the type I extreme value dstrbuton. Software k s observed characterstcs, unobserved (to the econometrcan) characterstcs, and prce at tme t are gven by c j,k,t, η j,k,t, and P j,k,t. 4 Gong forward t s useful to dstngush the dosyncratc utlty shock from the rest of the consumer s lfe-tme utlty and rewrte (3.1) as u j,k,t = ζ j,k,t + ε j,k,t where ζ j,k,t = α sw + α sw,c c j,k,t + αsw,pp j,k,t + η j,k,t s nterpreted as consumer s mean lfe-tme utlty of purchasng software k at tme t. Alternatvely, consumer may choose to not purchase software k at tme t and receve utlty u j,0,t = ε j,0,t (.e. mean lfe-tme utlty of not purchasng, ζj,0,t, s normalzed to zero). Consumer who does not purchase software k at tme t returns to the market at tme t + 1 to reconsder the purchase. Therefore, consumer faces an optmal stoppng problem (Rust (1987)) where the consumer has to consder when to make a purchase (.e. stop comng back to the market). The soluton to the optmal stoppng problem s descrbed by the polcy functon W (Ω t, ε j,k,t) = max{u j,k,t, u j,0,t + βe[w (Ω t+1, ε j,k,t+1) Ω t]} (3.2) where Ω t contans all the relevant nformaton (prces, product attrbutes, etc.) to predct the expected value of returnng to the market next perod. It s necessary to make some assumptons about Ω t n order for the state space to be tractable. Lee (2013) followng Gowrsankaran and Rysman (2009) and Melnkov (2013) take the followng approach. Frst, Ω t evolves accordng to a frst order Markov process 5, G j(ζj,k,t+1 Ω t), where G j s consumer and hardware specfc (.e. G j does not dffer for software desgned for hardware j). Second, Ω t evolves smlarly for unts of software wth the same the mean lfe-tme utlty. In other words, ζj,k,t and the evoluton of ζ j,k,t are suffcent statstcs for consumers to solve ther dynamc optmzaton problem. 6 Ths means the state can be descrbed by two varables: whether or not software k was prevously purchased and ζj,k,t. Ths smplfes from ncludng prces and other product attrbutes n the state space. Lee (2013) also ncludes month of the year, m(t), as an addtonal state space varable snce vdeo game software and hardware sales are hghly seasonal, or formally G j(ζj,k,t+1 ζ j,k,t, m(t)). Thrd, t s necessary to descrbe belefs over the evoluton of ζj,k,t. Followng Assumpton II.2 n Lee (2013), we assume consumers expectatons of ζ j,k,t+1 are 4 The coeffcent on observed characterstcs, α sw,c, s assumed to be consumer, tme, console, and software ndependent. 5 Lee (2013) ponts out that the frst order process may not accurately reflect the underlyng process but t s a useful smplfcaton that eases the computatonal burden of the problem. Further, Hendel and Nevo (2006) show that t mght be a reasonable approxmaton of consumer memory and expectatons. 6 Ths s smlar to the Inclusve Value Suffcency assumpton (Assumpton 1) n Gowrsankaran and Rysman (2009). 8

10 descrbed as: ζ j,k,t+1 = γ j,0 + γ j,1ζ j,k,t + γ j,2(ζ j,k,t) m=1 γ j,m+2χ m(t) + ν j,k,t (3.3) where the frst term s a constant, the second and thrd terms are the lnear and quadratc effects of ζj,k,t, the summaton represents month dummes, and the last term s an error. Wth these assumptons, we can analytcally ntegrate 3.2 over all ε j,k,t to obtan consumer s expected opton value of beng able to purchase software desgned for hardware j wth mean lfe-tme utlty ζj,k,t n month m(t): EWj (ζj,k,t, m(t)) = W (ζj,k,t, m(t), ε j,k,t)f(ε) ε j,k,t ) = ln (e ζ j,k,t + e βe[ewj (ζ j,k,t+1,m(t+1)) ζ j,k,t,m(t)] where β < 1 s a dscount parameter and E[g] s the expectaton operator (we leave out the constant of ntegraton snce t does not affect consumer purchasng decsons). 3.2 Software benefts on hardware j and backward compatblty In ths subsecton we dscuss the software avalable on hardware j for whch the consumer values the opton to purchase, we ncorporate the benefts of the opton to purchase backward compatble software, we descrbe consumer belefs and values over future software release, and fnally our goal, we defne the expected dscounted beneft consumer obtans from havng the opton to purchase all relevant current and future software avalable on hardware j. Importantly, ths beneft depends on the hardware unts already n the consumer s nventory. Consumer s nventory s gven by ι I 1 I 2 where I 1 and I 2 represent the nventory states of frst and second generaton hardware, respectvely. For our problem, I 1 {0, 1} 3 represents nventory states for N64, PlayStaton, and Saturn (0 for not purchased, 1 for purchased) n the frst hardware generaton and I 2 {0, 1} 4 represents nventory states for Dreamcast, GameCube, PlayStaton 2, and Xbox n the second hardware generaton. In all, there are 128 (= 2 7 ) possble nvent states gven 7 unts of hardware. It s helpful to group hardware n consumer nventory nto smlar product generatons n order to compare wth hardware not n the nventory. Let ι j and ι j be the hardware n nventory ι n the same and dfferent generaton as hardware j, respectvely. We assume that consumers value the opton to purchase two types of software avalable for hardware j gven ther exstng nventory. Frst, consumers value unque software, or formally, let K j,t (ι) be the set of software avalable for hardware j and not avalable on any other hardware n nventory ι. Ths assumpton follows Lee (2013) where consumers only value software optons that are not already avalable n ther current nventory. Second, for any nventory ι consumers value software avalable on hardware j that s not avalable on any other same generaton hardware n ther nventory (ι j ) but s avalable on dfferent product generaton hardware n ther nventory (ι j ). Ths s a modfcaton of Lee (2013) that takes nto account software competton across product generatons. The underlyng assumpton s that there s suffcent dfferentaton between hardware product generatons for consumers to value the opton of purchasng software avalable for hardware j that s also avalable for dfferent product generaton hardware n ther nventory. 9 (3.4)

11 For example, smlar games (.e. same ttle, software developer, plot, characters, player nteracton, etc.) can be released on N64 (frst generaton hardware) and GameCube (second generaton hardware). The game on GameCube s lkely more ntrcate, has more features, and s vsually more appealng than the smlar release on the prevous generaton hardware; the game on N64 s lkely avalable for a dscount compared to the enhanced game on the next generaton hardware. In ether case, gven the games are not perfect substtutes, we assume consumers value these purchase optons when consderng ther hardware decsons. For convenence, we call ths ntergeneratonal software. Formally, let K j,t (ι j ) be the set of ntergeneratonal software - software avalable on hardware j at tme t, n the nventory of dfferent generaton hardware ι j, and not n the nventory of same generaton hardware. We want to ncorporate the opton values of backward compatble software - software desgned for a prevous generaton system that can be used on a current generaton system. Ths ncludes two more sets of software smlar to K j,t (ι) and K j,t (ι j ) but modfed for backward compatblty - essentally we fnd consumer beneft for the opton to purchase software, k, desgned for a prevous generaton hardware, j, whch can be used on hardware j. 7 For backward compatble hardware j consumers wll also value K j,t(ι j) and K j,t(ι j j). The frst term s the set of unque software on hardware j - software not avalable n the nventory or hardware j. The second term s the set of ntergeneratonal software on hardware j - software avalable on hardware j, n the nventory of hardware n a dfferent generaton than j (note ths nventory ncludes j), and not n the nventory of same generaton hardware as j. Note, K j,t(ι j) and K j,t(ι j j) are empty sets f hardware j s not backward compatble. The opton values assocated wth exstng software n K j,t (ι), K j,t (ι j ), K j,t(ι j), and K j,t(ι j j) make up the total utlty receved from purchasng hardware j. We assume consumers receve utlty from software avalable at tme t as well as expected future software releases. We let the utlty from software avalable at tme t for hardware j, Λ C, j,t,ι, be the sum of the opton values at tme t where C Λ j,t,ι = EWj,k(Ω t) + ϖ EWj,k(Ω t) (3.5a) k K j,t (ι) k K j,t (ι j ) for non-backward compatble hardware j and C Λ j,t,ι = k K j,t (ι) EWj,k(Ω t) + ϖ k K j,t (ι j ) EWj,k(Ω t) + φ C Λ j,t,ι j (3.5b) C for backward compatble hardware j. Note Λ j,t,ι j n (3.5b) s smply a restatement of (3.5a) for hardware j ncludng hardware j n the nventory. The frst summaton n (3.5a) and (3.5b) aggregates the opton values for unque software on hardware j whle the second summaton totals the opton values for ntergeneratonal software on hardware j. Smply put, backward compatble hardware provdes the expected utlty of a non-backward compatble hardware plus the opton value of usng the software of the prevous generaton. We ncorporate the scalars ϖ and φ to 7 Note our model can be easly modfed to crcumstances where not all the software on j can be used on hardware j. Ths s not a concern n our dataset so we restrct the theory we dsplay for brevty. 10

12 allow for dfferng effects of ntergeneratonal and backward compatble software, respectvely. The utlty from future software releases s F T t Λ j,t,ι = (β Γ ) τ T t + ϖ (β Γ ) τ EWj,k(Ω t+τ) (3.6a) τ=1 k K R j,t+τ (ι) EW j,k(ω t+τ) for non-backward compatble hardware j and F T t Λ j,t,ι = (β Γ ) τ T t + ϖ (β Γ ) τ τ=1 k K R j,t+τ (ι) EW j,k(ω t+τ) τ=1 τ=1 k K R j,t+τ (ι j) k K R j,t+τ (ι j) EW j,k(ω t+τ) + φ F Λ j,t,ι j (3.6b) F for backward compatble hardware j. Λ j,t,ι j s a restatement of (3.6a) for hardware j ncludng hardware j n the nventory. Kj,t(ι) R and Kj,t(ι R j ) denote the sets of unque software and ntergeneratonal software, respectvely, on hardware j released at tme t. For each of the double sum terms n (3.6a) and (3.6b) the nsde sum aggregates the opton values of software released n a future perod after t. Ths value s dscounted by β Γ. The outsde sum totals the dscounted future release opton values from tme t + 1 to some termnal tme T (.e. the date after whch no new software s released for hardware j). The frst double summaton s for unque future releases on hardware j whle the second s for ntergeneratonal future releases on hardware j. Smlar to the case of exstng software, the expected beneft from future software for backward compatble hardware s the same as for non-backward compatble hardware plus the expected beneft of future software release for a prevous generaton hardware. Wth (3.5a), (3.5b), (3.6a), and (3.6b) we can obtan consumer s expected present value for purchasng all avalable software for hardware j at tme t gven nventory ι, Γ j: C F Γ j,t(αsw, αsw,p; ι) = Λ j,t,ι + E( Λ j,t,ι Ω t). (3.7) Note, (3.7) depends on the expected value of future software releases. We assume consumers have ratonal expectatons over future software utlty and obtan the second term by regressng (3.6a) and (3.6b) on (3.5a) and (3.5b), among other varables, for each consumer. Specfcally, we mpose the followng functonal form on consumer belefs: F Λ j,t+1,ι = ς0,ιχ ι + ςj Λ j,t,ι + C 11 m=1 ς 0,0,mχ m(t) + ς ΛX Λ + µ j,t (3.8) where the frst term s an nventory specfc constant; the second term s the effect of utlty from software avalable at tme t for hardware j gven nventory ι; the summaton ndcates month dummes; the fourth term ndcates other observables ncludng hardware age, age squared, the number of avalable games on hardware j, and hardware nstalled base n levels and logs; the last term s an error. Note the coeffcent on utlty from software avalable at tme t, ς j, s ndependent of nventory - nventory effects are captured by a constant. We estmate (3.8) separately for each consumer by stackng observatons for every possble 11

13 nventory where j can be purchased. We use nventory dummes and restrct coeffcents on software utlty, month dummes, and other observables to be the same for each nventory. Ths has the beneft of drastcally decreasng the computatonal burden. Also, there are several nventores where nventory specfc coeffcents on the predctors cannot be dentfed due to a lack of observatons. Ths occurs n our data set as a new hardware unt enters the market shortly before another hardware unt leaves; lttle overlap translates nto few observatons where the new hardware s n the consumer s nventory and the extng hardware s not. When consderng purchasng hardware j consumers wth more hardware n ther nventory wll lkely have a lower value of Γ j,t(g), ceters parbus, gven only unque software on j s ncluded along wth ntergeneratonal software when calculatng Γ j,t(g). Crtcally, the value of Γ j,t(g) for backward compatble hardware depends on whether or not the relevant prevous generaton hardware s already n the consumer s nventory. For consumers who do not own the prevous generaton hardware we calculate Γ j,t(g) usng (3.5b) and (a predcton of) (3.6b). For consumers who own the prevous generaton hardware we could ether calculate Γ j,t(g) usng (3.5b) and (3.6b) or use (3.5a) and (3.6a). Usng the latter mples the consumer only consders beneft from hardware j as hardware j s already n ther nventory - the underlyng assumpton s that the consumer wll use software k on hardware j and not on hardware j. The former mples the consumer consders benefts of upgradng from hardware j to hardware j - here we assume the consumer wll use software k on hardware j and not on hardware j. Essentally, usng the former mples a consumer who purchases hardware j elmnates hardware j from ther nventory and s never on the market for j agan. We use the former methodology n our estmatons below. 8 Ths was done for two reasons. Frst, we beleve t s closer approxmaton to the realty of ndustres wth backward compatble hardware. A man reason a hardware frm nvests n backward compatblty s so consumers who own the prevous generaton hardware can use ther exstng nventory of software on the new hardware. A common complant leved by consumers on hardware that eschew backward compatblty s the nablty to use ther exstng software lbrary on the new system. 9 Second, t allows rcher hypotheses tests concernng the mportance of backward compatblty to consumers who own and those who do not own the prevous generaton hardware. Otherwse, the value of backward compatblty s essentally restrcted to those who do not own the prevous generaton hardware. For example, a consumer who owns the prevous generaton system wll not take nto account backward compatblty when weghng a purchase of backward compatble hardware versus non-backward compatble hardware. Wth (3.7) we can relate the benefts of software to the hardware sde of the problem and move on to hardware demand. 3.3 Hardware demand Our goal for ths subsecton s to fnd the expected opton value of beng on the market wth any nventory and hardware avalable for purchase. We have several mportant assumptons smlar to the software sde of the problem whch echo ndustry features. Frst, consumers face a dscrete-choce problem of whether to purchase a pece of hardware 8 It s mportant to note we ran our estmatons usng both methodologes. Our parameter estmates were not qualtatvely dfferent. 9...The bggest complant s the lack of backward-compatblty wth PlayStaton 2 and PlayStaton 3 games, a possble deal breaker for some... as stated n the artcle Upgrade select PS3 games for use on the PS4, November 12,

14 or not. Lke software, hardware s a durable good. In each perod consumers can purchase any hardware they have not purchased prevously. However, we modfy ths to account for backward compatblty. Consumers who purchase any hardware that s backward compatble wth another unt of hardware wll never return to the market for ether. For example, a consumer who purchases PlayStaton 2 has no need to purchase PlayStaton gven the former can play all the games desgned for the latter. Second, consumers are forward lookng and have ratonal expectatons regardng the evoluton of hardware characterstcs condtonal on ther current nventory. That s, consumers compare the present value of purchasng hardware and returnng to the market n the next perod wth ther new nventory to the expected value of watng untl the next perod and returnng to the market wth the same nventory. We assume consumers have ratonal expectatons over the expected value of watng untl the next perod. Thrd, we assume consumers are heterogeneous wth respect to ther senstvty to hardware prce. Fnally, for smplcty we assume consumers can purchase at most one unt of hardware per perod. The lfe-tme expected utlty consumer wth nventory ι receves from purchasng hardware j / ι at tme t s: u j,t,ι = α hw,c c j,t + α hw,pp j,t + α Γ Γ j,t(α sw, α sw,p; ι) + D 1,2 (ι) + D 2 (ι) + ξ j,t + ε j,t,ι. (2.9) Observed product characterstcs, prces, and unobserved (to the econometrcan) characterstcs are gven by c j,t, P j,t, and ξ j,t. Coeffcents on observed hardware characterstcs, α hw,c, are ndependent of consumer type whle the coeffcent on prce, αhw,p, s consumer specfc. The expected present value for purchasng all avalable software for hardware j, Γ j,t(αsw, αsw,p; ι), s gven by (3.7) and depends on consumer s preference for software, senstvty to software prce, and nventory. The coeffcent on expected present value for purchasng all avalable software, α Γ, can also be thought of as a scalar whch ads n the comparson of hardware and software utlty (Tran (n.d.); Lee (2013)). We nclude dummy varables to assess complementartes of hardware n each generaton where D 1,2 (ι) = D 1,2, a constant, f consumer has any hardware n ther nventory, 0 otherwse. Smlarly, D 2 (ι) = D 2 f consumer has any second generaton hardware n ther nventory, 0 otherwse. The effect of ownng any frst generaton hardware s gven by D 1,2 and the effect of ownng any second generaton hardware s gven by D 1,2 + D 2 ; postve values ndcate the consumer s more lkely to purchase hardware f they already own hardware, negatve values ndcate they are less lkely to purchase hardware. Fnally, ε j,t,ι s an dosyncratc utlty shock for consumer purchasng hardware j at tme t not currently n nventory ι. Agan, as wth the software sde of the problem, we assume ε j,t,ι s IID from the type I extreme value dstrbuton. Smlar to the software sde, t s useful to dstngush the dosyncratc utlty shock from the rest of (2.9) and defne the mean expected lfe-tme utlty consumer receves from purchasng hardware j at tme t gven nventory ι as δ j,t,ι = α hw,c c j,t + α hw,pp j,t + α Γ Γ j,t(α sw, α sw,p; ι) + D 1,2 (ι) + D 2 (ι) + ξ j,t. Also, the consumer can choose to not purchase any hardware and receve u 0,t,ι = ε 0,t,ι. Consumer faces an optmal stoppng problem where the choce s to purchase one unt of hardware not already n ther nventory or not purchase any new hardware - n ether case, the 13

15 consumer returns to the market the next perod. Wth ε t representng the set of dosyncratc shocks from hardware purchases or non - purchases n each possble nventory state, the soluton to the optmal stoppng problem s descrbed by the polcy functon V ( { ) { ι, Ω t, ε t = max u 0,t,ι + βe[w (ι, Ω t+1, ε t+1) Ω t], max u {j},t,ι + βe[v (ι {j}, Ω t+1, ε t+1) Ω t] }} j / ι (2.10) and {j} represents a hardware unt purchased n perod t. The frst term represents consumer purchasng the best hardware avalable n perod t and returnng to the market n perod t+1 wth ther new nventory, the second term represents consumer not purchasng hardware n perod t and returnng to the market n perod t + 1 wth the same nventory. Smlar to the software sde, Ω t contans all the relevant nformaton (prces, product attrbutes, etc.) to predct the expected value of returnng to the market next perod. Agan, we use some assumptons to make the state space tractable. Ω t evolves accordng to a frst order Markov process, F j (δ j,t+1,ι Ω t), where F j s consumer and hardware specfc. We assume Ω t ncludes nformaton on hardware mean utltes for all hardware avalable at tme t not ncluded n the consumer s nventory, {δ j,t,ι} j / ι, the set of hardware avalable for purchase at tme t, J t, the consumer s nventory state ι, and month of the year. Specfcally, we use the functonal form δ j,t+1,ι = ϑ 0,ιχ ι + (j / ι) J t ϑ jδ j,t + 11 m=1 ϑ 0,0,mχ m(t) + ψ j,t (2.11) where the frst term s an nventory specfc constant effect, the frst summaton represents the effect of current mean lfe-tme utltes of hardware not n the consumer s nventory but avalable for purchase at tme t, the second summaton represents the effect of month dummes, and the last term s an error. Smlar to (3.8), we estmate (2.11) by stackng each nventory where hardware j s avalable for purchase and restrctng the coeffcents on hardware utlty and month dummes to be the same for each nventory. Ths dramatcally reduces the computatonal burden of the problem. Also, we accommodate stuatons where hardware optons change for a gven nventory by zerong out δj n (2.11) when hardware j s not avalable. As wth our dscusson of (3.8), ths occurs n our data set as hardware unts enter and leave the market at dfferent ponts over tme (.e. a consumer wth the same nventory may have dfferent hardware choces over tme). Wth these assumptons, we can analytcally ntegrate (2.10) over all ε t and obtan our goal for ths subsecton, consumer s expected opton value of beng on the market to purchase avalable hardware wth any nventory ι at tme t: EV (ι, { ) δj,t,ι }(j, m(t) = / ι) (j J t) = ln + e βe ( V (ι, { } ) δj,t,ι, m(t), (j / ι) (j J ε t) t f(ε) ε t ( { } ) ]) e δ j,t,ι [EV +βe ι j, δ,m(t+1) ι,{δ ĵ,t+1,ι j (ĵ / (ι j)) (ĵ J t+1 j,t,ι},m(t) ) (j / ι) (j Jt ) (j / ι) (j J t) [EV (ι,{δ j,t+1,ι} ),m(t+1) ι,{δ j,t,ι} ]),m(t) (j / ι) (j Jt+1) (j / ι) (j Jt). (2.12) 14

16 The summaton shows the value of beng on the market depends on whch hardware unts are avalable for purchase at tme t and not currently n a consumer s nventory. The frst term n the summaton represents the present value of purchasng console j whle the second term n the summaton represents the opton value of comng back to the market next perod wth console j n consumer s nventory. The last term represents the opton value of comng back to the market to the market wth the same nventory next perod. 3.4 State Space The assumptons outlned n the above subsectons drastcally reduce the state space of the problem. Smlar to Lee (2013), n each perod consumer wll condton ther hardware and software purchase decsons on hardware utltes, software utltes, ther hardware nventory, ther software nventory, and the month. As mentoned above, we modfy hardware nventory to take nto account backward compatblty. Consumers who purchase any hardware that s backward compatble wth another unt of hardware wll never return to the market for ether. 3.5 Other Assumptons We should note that we smply from several potentally strategc concerns. Frst, consumers and frms have perfect nformaton regardng hardware ext and entry. Also, ext and entry decsons by hardware and software frms are taken as exogenous and are not strategc. Fnally, software frm s platform decsons (.e. whch hardware does a software frm release ther software on) s also exogenous. In the next secton we estmate our model by fndng the parameter set that mnmzes an objectve functon constructed from these unobservables. 4 Estmaton The goal of ths secton s to descrbe the computaton algorthm used to ratonalze predcted market shares wth actual market shares and recover the sets of product unobservables for all software, {η j,k,t }, and all hardware, {ξ j,t }, for a gven set of parameters. We start by dscussng our approach to ncorporatng consumer heterogenety. Then we lay a general roadmap of the algorthm and proceed to move nto subsectons whch delve nto greater detal for portons of the computaton. In turn we look at the software sde of the problem, the hardware sde of the problem, and the nterface between the two. When lookng at the software and hardware sde, we show how the expected value functons n (3.4) and (2.12) are used to construct the probablty that a consumer wll purchase software and hardware, respectvely, n each perod. When dscussng the nterface between the two, we show how market shares on the hardware sde effect the avalable market on the software sde. Importantly, we also ncorporate backward compatblty nto the hardware and software nterface. Fnally we construct the objectve functon. The detals of the computatonal algorthm are provded n the Appendx. 4.1 Consumer heterogenety In the model consumers are heterogeneous wth respect to ther taste for software and ther senstvty to software prce. We assume consumer tastes for software are ndependent and normally dstrbuted wth mean zero and standard devaton σ sw. 10 We assume prce senstvty s a functon of ncome level and mpose the functonal form αr,p = α r,p σ r,p y where y s consumer s 10 In our estmatons we nclude software specfc constants to capture the effect of software qualty. Ths effect cannot be separately dentfed from mean software preference so we assume the later s zero. 15

17 ncome, α r,p and σ r,p are the mean and standard devaton for prce senstvty, and r = hw, sw for hardware and software respectvely. We follow Berry, Levnsohn and Pakes (1995) and draw y from an ndependent and log normal dstrbuton wth the frst and second moments from the March 2001 Current Populaton Survey. In practce we dscretze the dstrbutons of consumer preferences. Lee (2013) followng Judd (1992) and Hess and Wnschel (2008) uses ndependent (wth respect to software preference and prce senstvty) Gauss-Hermte quadrature to determne ntal populaton shares of each type of consumer. We do the same and obtan 9 values of αsw = αsw,quad σ sw, where αsw,quad s a quadrature pont, and 7 values of y for sets of {αhw,p, α sw,p} for 63 dfferent consumer types, ndexed by, n our estmaton. 4.2 The Recovery of Unobservables and The Objectve Functon Our goal s to mnmze an objectve functon constructed from the hardware and software unobservables wth respect to the model s parameters. We adopt the approach of Lee (2013) and construct the objectve functon from the nnovatons n the unobservables rather than the unobservables themselves (the assumpton s that the nnovatons n unobservables can be descrbed by an AR(1) process wth mean zero ndependent errors). Ths approach s robust to software and hardware releases beng strategcally tmed and correlatons between observable and unobservable characterstcs. We defne the nnovatons n unobservables as ν j,t = ξ j,t ρ hw ξ j,t 1 and w j,k,t = η j,k,t ρ sw η j,t 1, for hardware and software respectvely where ρ hw and ρ sw are parameters to be estmated. Frst, we fnd the estmates α hw,c and α sw,c va a regresson of δ j,t α hw,p P j,t α Γ Γ j,t (0, α sw,p ; ι = 0) D 1,2 D 2 and ζ j,k,t α sw,p P j,k,t on observed hardware and software characterstcs ( c j,t and c j,k,t ), respectvely. 11 Wth estmates of α hw,c and α sw,c we construct nnovatons n hardware and software unobservables as follows: and ν j,t = ξ j,t ρ hw ξ j,t 1 = δ j,t ρ hw δ j,t 1 α hw,c (c j,t ρ hw c j,t 1 ) α hw,p (P j,t ρ hw P j,t 1 ) α Γ (Γ j,t (0, α sw,p ; ι = 0) ρ hw Γ j,t 1 (0, α sw,p ; ι = 0)) D 1,2 (1 ρ hw ) D 2 (1 ρ hw ) (4.1) w j,k,t = η j,k,t ρ sw η j,k,t 1 (4.2) = ζ j,k,t ρ sw ζ j,k,t 1 α sw,c (c j,k,t ρ sw c j,k,t 1 ) α sw,p (P j,k,t ρ sw P j,k,t 1 ). We should note that the ncluson of (D 1,2 and D 2 ) alters the nterpretaton of these coeffcents from the orgnal stated n (2.9). (D 1,2 and D 2 ) as well as D 1,2 are ncluded when we calculate (4.1) for generaton 1 and 2 hardware, respectvely. Therefore, D 1,2 captures the effect of purchasng frst generaton hardware whle D 1,2 and D 2 (summed) captures the effect of purchasng second generaton hardware gven a consumer does not own any hardware. Postve effects for (D 1,2 and D 2 ) ndcate an ncreased beneft of purchase f no other hardware s owned (.e. hardware s substtutable) whle negatve effects for (D 1,2 and D 2 ) ndcate the opposte (.e. hardware s complementary). 11 We use a GMM estmaton for both hardware and software separately where the nstruments are descrbed n the next subsecton. 16

18 We construct the condtonal moments wth nstruments for both hardware and software, Zj,t hw and Zj,k,t sw, dscussed below. The condtonal moments are: E[Z hw j,t ν j,t ] = 0, (4.3) E[(Z hw j,t Z hw j,t 1)(ν j,t ν j,t 1 )] = 0, (4.4) and E[Z sw j,k,tw j,k,t ] = 0, (4.5) E[(Z sw j,k,t Z sw j,k,t 1)(w j,k,t w j,k,t 1 )] = 0. (4.6) We nclude (4.4) and (4.6) as condtonal moments n addton to (4.3) and (4.5) as n Lee (2013) because ths approach has been shown to mprove estmaton results (Arelleno and Bover (1995); Blundell and Bond (1998)). The GMM estmator s: arg mn θ G(θ) (Z Z) 1 G(θ), where Z = (Z hw j,t Zj,t hw 0 Zj,t 1) hw 0 0 Z sw j,k,t 0 (Z sw j,k,t Zsw j,k,t 1 ) and θ = {θ 1, θ 2, θ 3 }. We do not constran parameters to be the same for each generaton and so the non-lnear parameters are gven by θ 1 = {β, β g Γ, σg hw,p, σg sw,p, σ g sw, α g Γ, φ, ϖ} and θ 2 = {α g hw,p, ρg hw, D 1,2, D 2, α g sw,p, ρ g sw} for generaton, g = 1, 2 whle the lnear parameters are: θ 3 = {α hw,c, α sw,c }. They are a functon of the non-lnear parameters. Our mnmzaton algorthm proceeds by fndng the Gradant of G(θ) (Z Z) 1 G(θ) usng fnte dfferences and mnmzng. 12 Wth ths approach, t s useful to dstngush θ 1 as t ncludes all of the parameters that enter the Hardware and Software Interface Loop. We hghlght these parameters because the Hardware Software Interface Loop takes a long tme to converge - more parameters n ths set dramatcally ncreases the tme to calculate the Gradant. Ths s why we manpulated several functons wthn the loops n order to dmnsh the number of parameters n ths set (.e. we are able to move α hw,p, α sw,p, D 1,2, and D 2 nto θ 2 ), though ths resulted n slghtly 12 We constran the search range to reasonable possble values for certan parameters (e.g. postve varances, postve dscount factors, etc.) n order to ncrease the speed wth whch the algorthm fnds a mnmum. 17