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Vertical integration and two-sided market pricing: evidence from the video game industry
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Content
VERTICAL INTEGRATION AND TWO-SIDED MARKET PRICING:
EVIDENCE FROM THE VIDEO GAME INDUSTRY
by
Timothy P. Derdenger
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ECONOMICS)
December 2009
Copyright 2009 Timothy P. Derdenger
i
Dedication
To My Friend, My Love, My Wife
v Laura
ii
Acknowledgements
Finishingmydissertationwouldneverhavebeenpossiblewithouttheguidanceof
my committee members and the support from my friends, family and wife.
I would like to explicitly express my appreciation to my advisors Tom Gilligan,
Geert Ridder, Guofu Tan and Michelle Goeree for their questions, advice and guid-
ance. And to an anonymous industry insider for my data set and knowledge of the
video game industry. It is you who made this dissertation truly possible. For that
I am forever indebted to you.
I would also like to thank my parents, and brother and sister. They supported
me and encouraged me with their best wishes from the very start.
Finally, I would like to express my sincerest gratitude to my wife, Laura. She
pushedandmotivatedmetocompletethisdissertationwhilestandingbymethrough
my good days and bad.
iii
Table of Contents
Dedication i
Acknowledgements ii
List ofTables iv
List ofFigures vi
Abstract vii
ChapterI: Introduction 1
The 128 Bit Video Game Industry 6
Data 10
ChapterII: Console Demand Model 14
The EmpiricalModel 17
Structural Model Preferences 18
Econometric Specification 21
Video Game Specification 22
Console Specification 24
Estimation 31
Identification 35
Instruments 36
Estimation Results 39
ModelResults 39
Alternative Console Demand Model Results 44
HardwareSoftware Elasticities 52
Goodness of FitTest 53
ChapterIII: Console SupplyModel 56
Pricing 57
Implied Marginal Cost and Margins 64
Counterfactual Simulation 64
Console Supply 67
Counterfactual Results 70
SensitivityAnalysis 78
Market Structure 78
Video Game Heterogeneity 82
ChapterIV: Conclusion 88
References 92
iv
List of Tables
Table 1 First Party Game Statistics 9
Table 2 Summary Statistics 13
Table 3 Demand Results 39
Table 4 Demand Results-Console Fixed E¤ects 40
Table 5 First Stage Results-Logit Model 40
Table 6 Mean RCL Logit Console Elasticities 43
Table 7 Mean Logit Console Elasticities 43
Table 8 Demand Results-Alternative Model II 46
Table 9 Demand Results-Fixed E¤ects for Alternative Model II 47
Table 10Mean RCL Logit Console Elasticities-Model II 47
Table 11Mean Logit Console Elasticities-Model II 48
Table 12Demand Results-Alternative Model III 50
Table 13Demand Results-Fixed E¤ects for Alternative Model III 51
Table 14Mean RCL Logit Console Elasticities-Model III 52
Table 15Mean Logit Console Elasticities-Model III 52
Table 16Hardware Elasticities from Losing the Top Selling Software Title53
Table 17Goodness of Fit 55
Table 18Implied Marginal Cost and Markups 66
Table 19Counterfactual Results 72
Table 20Top 10 Video Game Titles 74
v
Table 21Counterfactual II Results 79
Table 22Price E¤ects with an Incorrect Supply Model 80
Table 23Implied Markups and MarginsIncorrect Supply Model 81
Table 24Implied Mean Marginal Cost and MarkupsIncorrect Supply Model81
Table 26Counterfactual Results-RCL Model III 84
Table 27Counterfactual Results-RCL Model II 86
vi
List of Figures
Figure 1Video Game Market Structure 8
Figure 2Console Quantities and Installed Base 11
Figure 3Software Quantities per Month 12
vii
Abstract
The focus of this dissertation is twofold. The rst objective is to construct an
empirical demand model for video game consoles which captures the complementary
nature between hardware and software while accounting for software heterogeneity
andcompetition. Thesecondobjectiveistodeterminethee¤ectsofverticalintegra-
tion on video game console price competition as well as consumer welfare and rm
pro ts.
These objectives are answered with data from the 128 bit video game industry
which consists of Nintendo Gamecube, Sony Playstation 2 and Microsoft Xbox. A
new methodology is formed to estimate the demand for video game consoles. In
order to understand how vertical integration impacts console price competition, my
analysisextendstheempiricalindustrialorganizationliteraturebyconstructinganew
methodologywhichallowsconsumerdemandforvideogameconsolestodependupon
the set of available video games rather than only the number of games. The estima-
tion technique di¤ers from prior research by incorporating video game heterogeneity
and software competition into the indirect network e¤ect.
Withtheimplementationofamodelwhichismoreexiblethanpriormodels,Ide-
termineverticalintegrationinthevideogameindustryincreasespricecompetitionas
wellasconsumerwelfareandconsolemanufacturerpro ts. Therearetwoimportant
trade-o¤s to vertical integration. The rst is a demand e¤ect which further di¤eren-
tiates consoles and forces prices higher. The second, a market structure e¤ect, drives
viii
prices lower. Since price competition increases, the demand e¤ect is thus dominated
by the market structure e¤ect which results in higher consumer welfare. Moreover,
the increase in price competition also bene ts console manufacturers. Lower prices
generate greater demand for consoles which leads to a rise in the number of video
games sold, where the "real" pro ts are made. I nd that console makers are thus
willing to set lower console prices in order to increase sales of their own developed
video games. Under a more restrictive model, however, prices rise leading to the
conclusion which is counter to what an industry insider would suspect. I determine
thatitisimportanttoproperlymodeltheconsolemanufacturerspro tfunctionsand
model the demand for video games well since console demand is derived from video
game demand. Without doing so, incorrect policy conclusions are made.
1
Chapter I
Introduction
There are many high tech industries in which consumers associate with a platform
in order to utilize its complements. For example, a consumer chooses between a HD-
DVDorBlu-RaymachineoraPlaystation2, MicrosoftXboxorNintendoGamecube
before he is able to use dvd titles or video games. Moreover, with a large portion
of complements available on multiple platforms the additional di¤erentiation they
create is quite minimal. There are complements, however, that are exclusive to one
platformtopurchasetheAppleiPhoneconsumersmustsubscribetoAT&TWireless
or to play Nintendos Super Mario Sunshine consumers need to own a Nintendo
Gamecube. Exclusivecomplementsbringaddeddi¤erentiationtoplatformsandthus
inuence an industrys competitive landscape.
Exclusive complements like those above can raise anticompetitive concerns. For
instance, in the mid 1980s Nintendo faced concerns over its exclusive dealings with
gamedevelopers. PriortothistimeAtarisgameconsolewastheindustryleader,but
inearly1985Nintendolaunchedanewplatformtoconsumers. UnlikeAtari,Nintendo
didnotpermitindependentthird party developerstocreategamesforbothconsoles.
1
Developers instead entered into exclusive contracts with Nintendo which restricted a
1
A third party developer is an independent company which produces video games but is not
a¢ liated with any console
2
games playability to Nintendo for the rst two years of its release. Accordingly, a
gamer who wished to play a particular Nintendo game was required to purchase a
Nintendo console.
ExclusivecontractswereonetoolNintendousedtoincreasedi¤erentiationbetween
themselvesanditscompetitorAtari. Nintendosverticalintegrationintothesoftware
market may have also played an integral role in creating greater di¤erentiation by
restricting the games it produced to its own platform. Vertical integration in this
situation and as will be de ned throughout the dissertation is a result of Nintendo
(or in general any other console manufacturer) electing to design, produce and sell
games themselves and not by acquiring a third party game developer.
2
There are numerous papers by many authors which study vertical integration.
3
Manyof these papers, however, focus onvertical integrationinmarkets whichdonot
possess similar characteristics as the above example. Only a relatively small number
of empirical papers exist as well. For example, in the video game industry indirect
network externalities exist.
4
The price structure associated with a two-sided market
like that of the video game industry also diverges from a traditional structure. In
order to properly study the e¤ects of vertical integration in two-sided markets one
must account for these di¤erences.
2
However, vertical integration via the purchase of a developement company does also occur. For
instances, Sonys recent purchase of ZIPPER INTERACTIVE and Microsofts talks to acquire Epic
Games
3
See i.e. Rasmusen, Ramseyer and Wiley (1991), Bernheim and Whinston (1998) or for an
overview Whinston (2006) and Rey and Tirole (2007)
4
See i.e. Church and Gandal (1993), Rysman (2004), Dube, Hitsch, Chintagunta, (2007) for a
few references of literature on network e¤ects
3
The focus of this dissertation is twofold. The rst objective is to construct an
empirical demand model for video game consoles which captures the complementary
nature between hardware and software while accounting for software heterogeneity
andcompetition. Thesecondobjectiveistodeterminethee¤ectsofverticalintegra-
tion on video game console price competition as well as consumer welfare and rm
pro t.
These objectives are answered with data from the 128 bit video game industry
which consists of Nintendo Gamecube, Sony Playstation 2 and Microsoft Xbox. A
new methodology is formed to estimate the demand for video game consoles. The
technique deviates from prior research by allowing the indirect network e¤ect to ac-
count for video game heterogeneity and competition among video game titles. The
methodology measures the externality by implementing an index which captures the
expected maximum utility of choosing from a set of video games as oppose to the
numberofavailablegames.
5
Employingthenumberofgamesimplicitlypresumesall
video games provide the same utility to each consumer, which is a nice approxima-
tion when consumers only care about product variety. However, in the case of the
video game industry where software heterogeneity is a distinguishing characteristic
it is rather important to allow consumers to di¤erentiate between games. Account-
ing for video game heterogeneity is an important aspect of console demand; a 2002
study by Forrester Research concluded 96% of people surveyed believed the quality
5
See i.e. Nair, Chintagunta and Dube (2004), Clements and Ohashi (2004), Prieger and Hu
(2007), Corts and Lederman (2007) and Dube, Hitsch and Chingtagunta (2007)
4
of video games was an important characteristic in choosing a game console. To un-
derstand how important software quality is in constructing console demand consider
the following: assume two competing consoles are identical with the exception of one
consolehavingtwomediocrehomogeneousvideogametitleswhilethesecondconsole
also has two titles but one is of equal quality of the titles on the competing console
and the other is of high quality. Under a demand model which only accounts for
the number of games compatible to a console, demand for each console would be
identical. A more exible model which accounts for software heterogeneity would
provide greater demand for console two than for console one, resulting in a di¤erent
equilibrium outcome from model one. It is essential to model the demand for video
games well given that console demand is derived from video game demand.
Even with the existence of a proper video game console demand model the ef-
fect of vertical integration on console price competition is unclear. There are two
important trade-o¤s to vertical integration. The rst is a demand or product di¤er-
entiation e¤ect. The production of a rst party game and its release exclusively for
theproducingconsolehasanapparentbene tsinceitsproductionincreasesthevalue
oftheconsolerelativetoothersthroughtheindirectnetworkexternality. Theadded
di¤erentiation consequently forces prices higher. One can also think of the demand
e¤ect as increasing a console makers market power. Since a rst party game is
always exclusive to the producing console maker it forecloses rival consoles from this
game. In order for a consumer to play a rst party title he has to rst purchase the
5
respective console. The exclusivity of the game increases the console manufacturers
market power which generates an incentive to raise console price.
There is also a market structure e¤ect. Integration increases price competition
among consoles. When a console manufacturer elects to design video games as well
asproduceconsolesitspricestructureadjuststoreectitsdecision. Withoutvertical
integration console prices are discounted by the pro t console manufacturers receive
from their interactions with developers when an additional consumer purchases a
console. With vertical integration a third pro t stream is created. Price is further
discounted by the pro t the console producer receives from designing, producing and
selling its own video games when one more console is sold. Vertical integration,
therefore, levies added pressure on price or generates an incentive for console manu-
facturerstolowerconsolepricesincelowerpricesleadtoanincreaseinthenumberof
consoles sold which generates greater demand for video games. This e¤ect can also
be interpreted as an e¢ ciency gain. Since video games and consoles are complemen-
tary products a vertically integrated rm can coordinate on video game and console
pricing and generate gains by internalizing the e¤ects that video games and consoles
have on each other.
The structure of this dissertation is as follows. First, I provide an overview of
the 128 bit video game industry and the data used in my analyses. Chapter 1
discusses the demand for video game consoles which includes a presentation of my
empirical model of console demand as well as previous models used in the literature,
6
the estimation methodology employed, and a comparison of the t of my empirical
modeltopastmodelsofconsoledemand. Afterdiscussingthedemandforvideogame
consoles in Chapter 2, Chapter 3 presents the supply side model, which illustrates
the e¤ects of vertical integration on console prices and discusses the results of the
vertical integration on console price competition. Chapter 4 concludes.
The 128 Bit Video Game Industry
During the early 2000s the video game industry saw three of the most revolutioniz-
ing consoles come to market, the Sony Playstation 2, Microsoft Xbox and Nintendo
Gamecube. Theseconsolesbroughtlargercomputingpower,morememory,enhanced
graphics,bettersoundandtheabilitytoplaydvdmovies. Inaddition,theproducing
rms each launched an expansive line of accessories to accompany their platform.
Sony enjoyed a yearlong rst mover advantage with its launch of Playstation 2
debuting in October 2000. Its success was attributed to moving rst but more
signi cantly was its large catalog of games which were exclusively produced for its
consolebyitsdevelopmentstudioandby third party developers. Manyofitsbiggest
software hits were exclusive to Playstation 2 but only one was Sony produced.
Microsoft Xbox launched in very late October 2001 and was by far the most
technologically advanced console. It was technically superior to the dominant Sony
Playstation 2 possessing faster processing speed and more memory. Microsoft, how-
ever, struggledtogainmarketshareasaresultoftheirinabilitytoattractdevelopers
7
toitsplatformtoproducesoftwaretitlesexclusivelyforXbox,inparticularthemany
prominent Japanese developers (Pachter and Woo). The inability to secure third
party exclusivegamesforcedMicrosofttodesignandproducevideogames internally.
NintendoGamecubelaunchedinNovemberof2001,withinweeksoftheMicrosoft
Xbox. The Gamecube was the least technically advanced of the three consoles. In-
stead of competing in technology with Sony and Microsoft, Nintendo targeted its
console to younger kids. "The Gamecubes appeal as a kiddie device was made
apparent given the fact that the device did not include a dvd player and its games
tilt[ed] towards an E rating" (Pachter and Woo). Gamecubes limited success was
a result of Nintendo leveraging its "internal development strength and target[ing] its
loyal fan base, composed of twenty somethings who grew up playing Nintendo games
and younger players who favored more family friendly games" (Pachter and Woo).
The structure of the video gaming industry is a prototypical two-sided platform
market where video game consoles act as platforms to two di¤erent end users, con-
sumers and game developers.
6
Consoles permit two end users to interact via its
platform creating externalities for each side of the market. Determining the size of
thesecrossgroupexternalitiesdependsonhowwelltheconsolesperforminattracting
the other side. On the gamersside of the market, consoles interact with players by
selling game consoles for a xed fee where as on the game developer side console pro-
ducers interact with developers by levying royalty payments for the right to produce
6
Seei.e. Kaiser(2002), RochetandTirole(2002),CaillaudandJullien(2003),KaiserandWright
(2005), Armstrong (2006), Hagiu (2006) and for general literature on two-sided platform markets
8
Figure 1: Video Game Market Structure
and sell games compatible with their console.
7
Figure 1 presents an illustration of
the discussed market structure.
Typically, third party vendors make games accessible to all consoles as a result
of the high xed costs of production where as rst party games are kept exclusive
to the gaming console. The average xed cost for a game on Nintendo Gamecube,
Sony Playstation 2 or Microsoft Xbox is roughly two and half to four million dollars
(Pachter and Woo). Even with the high costs associated with producing a video
game, consoles invest in the development of rst party games.
8
In Table 1, I illustrate the total units sold of rst party games for each console
in January of the reported years as well as the number of rst party games and a
"pseudo" HHI.
9
The HHI index measures the concentration of vertically integrated
7
Console manufacturers actually manufacture all video games themselves to ensure control over
the printing process
8
An e¤ect which is not studied in this paper but would be a valuable line of research is that
verticalintegrationisonemethodtosolvethechickenandeggproblemwhichcomes rst? Withthe
implementationofverticalintegrationconsolemakerscommittoprovidingvideogamestoconsumers
which then fosters the development of third party games
9
The HHI measure is calculated by summing the squared marketshares of each integrated game
9
Table 1: First Party Game Statistics
Platform Units Sold of First Party Games
2002 2003 2004
Gamecube 179,011 193,347 427,153
Playstation 2 267,545 925,290 546,351
Xbox 382,599 234,258 414,333
Number of First Party Games
Gamecube 5 12 21
Playstation 2 24 45 66
Xbox 10 20 38
Pseudo HHI of First Party Games
Gamecube 535.94 59.49 54.44
Playstation 2 10.28 55.29 8.02
Xbox 305.02 17.39 29.09
Note: Statistics calculated for January of the corresponding year.
gamesforeachconsole. Asmallindexindicates rst party gamesgarnerlittleimpact
on video game sales while a large number signi es the opposite. The HHI is a more
encompassingindexasopposetothenumberofgamesorthetotalunitsof rst party
gamessoldsinceeachofthetwoothermeasuresdonotinformoneofthequalityofthe
games while the lattermeasure also does not indicate the numberof games available.
The table shows the importance of vertically integrated games, in particular for Nin-
tendo and Microsoft. In January 2002 both Nintendos and Microsofts HHI are on
themagnitudeof 500and300timesthesizeof Sonys, respectively. InJanuary2004
the relative importance of vertically integrated games remained constant (Nintendo,
Microsoft and Sony), however, the magnitude was only ve and three times the size
of Sonys.
10
Data
The datausedinthis studyoriginates fromtwo independent sources, NPDFunworld
and TNS Media Intelligence. Data from the marketing group NPD Funworld tracks
sales and pricing for the video game industry and is collected using point-of-sale
scanners linked to over 65% of the consumer electronics retail stores in the United
States. NPD extrapolates the data to project sales for the entire country. Included
in the data are quantity sold and total revenue for Microsofts Xbox, Nintendos
Gamecube and Sonys Playstation 2.
The console demand model requires video game data in order to incorporate the
indirect network externality, which accounts for software heterogeneity and video
game competition. Unlike previous studies data on sales and total revenues for
over 1200 unique video games is available. The accessibility of this data allows
for the implementation of a less restrictive model that captures the expected utility
consumers garner from the consumption of compatible software.
Each data set covers 35 months starting in January 2002 and continuing through
November2004. Theterminaldatewasselectedforanimportantreason: Microsofts
release of its next generation console in November 2005. To ensure there is no bias
fromconsumerspostponingtheirconsumption, Iterminatethesampleoneyearprior
to the release of the new Xbox 360.
The second data set originates from TNS Media Intelligence; it collects informa-
tion on total advertising expenditures for each of the three consoles across 19 media
11
Figure 2: Console Quantities and Installed Base
channels within the United States.
General statistics of the video game industry are provided in Table 2. Below I
briey discuss two important stylized facts regarding the industry.
The rstimportantindustryfactis thatthevideogameindustryexhibitsalarge
degree of seasonality in both console and video game demand. Figures 2 and 3
illustrate the total number of consoles and video games sold in each month. Both of
whichincreaseconsiderablyinthemonthsofNovemberandDecember. Itistherefore
important to consider and account for the large degree of seasonality in estimation.
Secondly,videogamesareheterogeneousgoods. Thisheterogeneityisthedriving
factor for the construction of a new demand model for consoles. For instance, there
are over eleven genres of games which range from action to simulation. The largest
12
Figure 3: Software Quantities per Month
being action games with 24% of the market and simulation games the smallest with
only 1%. Video game sales for individual games also range in the number of units
sold. TherearelargehitssuchasGrandTheftAuto: ViceCitywhichhascumulative
sales of over six million on Playstation 2 and "busts" like F1 2002 which sold only
forty-eight thousand units on the same console.
13
Table 2: Summary Statistics
Gamecube Xbox Playstation 2
Release Date Nov. 2001 Oct. 2001 Oct. 2000
Hardware
Price
Average (over months) $133.18 $190.54 $240.10
Std. Dev. (over months) 34.27 42.56 54.97
Max 199.85 299.46 299.54
Min 92.37 146.92 180.66
Sales
Average (over months) 200,420 264,140 522,860
Std. Dev. (over months) 218,410 226,920 501,050
Max 1,158,200 1,079,400 2,686,300
Min 58,712 77,456 188,670
Installed Base (Nov. 2004) 8,223,000 10,657000 25,581,000
Software
Sales
Average (over months) 7,436 7,962 10,488
Std. Dev (over months) 23,410 32,803 44,973
Max 826,352 1,777,697 2,053,983
Min 3 1 3
Total Number of Games (Nov. 2004) 398 560 931
Average 210.54 272.4 550.29
Std. Dev 114.99 153.62 203.65
Max 398 560 931
Min 22 41 223
14
Chapter II
Console Demand Model
Chapter 2 discusses the demand for video game consoles which includes a presen-
tation of my empirical model of console demand as well as previous models used in
the literature, the estimation methodology employed, and a comparison of the t
of my empirical model to past models of console demand. Most importantly, how-
ever, is that it presents an empirical model of console demand which captures the
complementary nature between hardware and software while accounting for software
heterogeneity and competition.
Althoughtherearenumeroustheoreticalstudieswhichanalyzeexclusionarystrate-
giesandverticalintegration,alimitednumberofempiricalstudiesexist. Conversely,
theliteraturecoveringnetworke¤ectsisaburgeoningtopic. A2004paperfromNair,
Chintagunta, and Dube which measures the impact of indirect network e¤ects in the
PDA market has sparked a line a research that analyzes indirect network externali-
ties. Intheirpapertheauthorsconstructastructuralmodeltoestimatetheindirect
networke¤ect. Themodelcapturesthee¤ectwiththeuseofthenumberofsoftware
titles compatible with a given PDA. Papers by Clements and Ohashi (2004) and Hu
15
and Prieger (2007a, 2007b) follow the same methodology as is presented in Nair et
al. but with their focus on the video game industry. The use of the number of video
game titles as a measure of the indirect network e¤ect is quite restrictiveit does not
allow consumers to di¤erentiate between video games. Moreover, a study conducted
by Forrester Research Group in 2002 provides su¢ cient evidence to support the no-
tion that consumers nd the quality of games as equally important to the number of
gamesavailableonaconsole.IntheattempttoeasethisrestrictionLee(2008)allows
consumers to di¤erentiate between video games but in doing so he makes a strong
assumption regarding the nature of competition in the software market.
10
Hu and Prieger, and Lee all study the impact of exclusive titles in the video
game market and determine whether exclusive titles are anticompetitive. Hu and
Prieger (2007a; 2007b) employ a structural model to estimate the demand for video
game consolesidentical to that of Nair et. al.. As explained above, this method
is quite restrictive and does not allow for di¤erentiated video games. Nonetheless,
HuandPriegermoveforwardandruna"counterfactualexperiment"whichconcludes
exclusivegamesdonotalterthedemandforvideogameconsoles.
11
Moreimportantly
they nd exclusive video games are not anticompetitive or create signi cant barriers
to entry.
10
He makes such an assumption for computational purposes
11
They do not o¢ cially run a counterfactual experiment which nds a new equilibrium price
vector. Instead they take the approach of re-estimating the demand model without exclusive video
games
16
Lee (2008) addresses the same question as Hu and Priegerare exclusive titles
anticompetitive? Lee implements a methodology which simultaneously estimates
dynamic demands for software and hardware. He assumes software titles are neither
substitutes nor complements to each other; he e¤ectively places each title into a
market of its own and does not allow substitution to occur among video games. Lee
also abstracts away from the rmsdynamic pricing decision. He does not attempt
to model the dynamic price setting behavior for software or hardware rms. In
his counterfactual exercises he presumes all prices follow the same price path as is
observed in the data. However, he does endogenize the re-contracting of video game
developers (e.g. allow game developers to re-select which consoles its game will be
produced for, given rst party games are no longer produced). The counterfactual is
thus a partial counterfactual; it does not nd new equilibrium console prices.
In this study an empirical model is constructed which relaxes the simpli cations
made in the prior research by introducing software heterogeneity and competition
into the software market.
The empirical methodology presented in the sections below is closest to Nevo
(2001), Berry, Levinsohn and Pakes (1995) and Berry (1994). More speci cally,
console demand is estimated using a random coe¢ cient utility function to recover
parameters for use in counterfactual exercises.
A few recent and more prominent papers within the discrete choice literature are
those of the founder of discrete choice models Daniel McFadden (1973, 1978, 1981),
17
Berry (1994), Berry, Levinsohn and Pakes (1995) and Nevo (2001). Berry (1994)
constructed a procedure which enabled him to estimate demand for di¤erentiated
productsviaasimplelinearregressionfortwotypesofmodels, logitandnestedlogit.
He also provided theory for a thirdthe random coe¢ cient model. Berry Levinsohn
and Pakes (1995), hence forth BLP, derived an algorithm which enabled them to
estimate the demand and supply for di¤erentiated products via a random coe¢ cient
model. They applied their algorithm to the automobile market. The paper by Nevo
(2001) estimated price-cost margins for the ready-to-eat cereal industry. In doing so
heusedquarterlyscannerdata. The technique he employedis similartothat of BLP
but di¤ered in the manner of the employed instrumental variables and the ability to
control for unobserved product characteristics by using brand xed e¤ects.
The Empirical Model
Ineachperiodapotentialconsumerpurchasesavideogameconsoleorchoosesnotto.
After purchasing a console a consumer decides which game to purchase, if any, from
a set of available games. Once a consumer has purchased a video game console he
exitsthemarketforconsolesbutcontinuestopurchasevideogamesinfutureperiods.
A consumer derives utility when he purchases a given video game. This utility
must be accounted for in the utility he receives when consuming a speci c console.
Moreover, at the stage in which a consumer decides to purchase a console he is
uncertainabouttheutilityhereceivesfromvideogames. Theconsumeronlyrealizes
18
the utility after the purchase of a video game console. It is therefore important to
link the realized video game demand with the expected utility from video games in
console demand.
Given the sequential nature of the model and the model assumptions, a nested
logitstructureisemployedforconsoledemand. Theuseofthenestedlogitstructure
providesanaturalextensionfortheinclusivevaluetofunctionastheindirectnetwork
e¤ect in addition to it being consistent with the model assumptions. The formation
of the inclusive value is generated from the assumption that video game demand is a
discrete choice in each month and is of logit form. Employing the methodology of
Berry (1994) I am able to construct the inclusive value (video game index) without
parameterizingthedemandforvideogamesallthatisrequiredisdataonvideogame
sales and the potential market size.
Iwouldliketonotethatthesequentialinterpretationofmymodelisjustthat: an
interpretation. Thesamemodelalsosupportsamultinomiallogitmodelwherebuyers
simultaneously choose consoles and games. In this case the choice probabilities for
consoles have inclusive values and are interpreted as the indirect network externality.
Structural Model Preferences
The consumer decision process is as follows. In time t, each consumer makes a
discretechoicefromthesetofJ availableconsoles. Ifaconsumerselectstopurchase
consolej 2 (0;:::;J)where0istheoutsideoptionofnotpurchasing,hethenpurchases
complementaryvideogameswhicharecompatibletoconsolej: Inchoosingaconsole,
19
a consumer only considers the expected maximum utility generated from the set of
availablevideogamesinperiodtasaresultoftheconsumersuncertaintyoftheutility
each video game generates at the stage in which he elects to purchase a console. The
timing is as follows:
Stage 1: Consumers choose which console to purchasej 2J
Stage 2a: Consumers realize the utility video games generate
Stage 2b: Consumers purchase video games which are compatible to consolej.
A consumer who purchases consolej at timet will generate utility equal to
U
ijt
=U
j
("
ijt
;X
jt;
jt
;
jt
();
hw
)
where
jt
istheexpectedmaximumutilityfromthesetofavailablegamesonconsole
j inperiodt. DenoteX
jt
as product characteristics,
jt
unobservedproductcharac-
teristics and"
ijt
an idiosyncratic taste variable for individual i for consolej in time
t.
From the above utility function a consumer will purchase console j if and only
if the utility from console j is greater then the utility of all other consoles and the
outside option
U
j
("
ij
;X
j;
j
;
j
();
hw
)U
r
("
ir
;X
r;
r
;
r
();
hw
)8r 2J:
12
12
For the remainder of this section the time subscript will be omitted
20
Let
A
j
=f" :U
j
("
ij
;X
j;
j
;
j
();
hw
)U("
ir
;X
r;
r
;
r
();
hw
)8r 2Jg
denotethesetofvaluesof"
ij
whichinduceconsumerstopurchaseconsolej: Assume
a distribution ofF(") for" with the corresponding densityf(") than the probability
that a consumer purchases consolej is given by
s
j
(X;;;
hw
) =
R
A
j
f(")d":
I examine the utility a consumer receives from purchasing software in order to
de ne
j
(): Consider a consumer who purchases consolej: The indirect utility con-
sumeri receives when purchasing softwarek is
U
kj
(
ik
;x
k;
k
;
sw;j
)
where
ik
is an idiosyncratic taste variable for individual i for game k, x
k
are game
characteristics,
k
are unobserved product characteristics and
sw;j
are video game
demand parameters speci c to console j. Parameters vary by console to allow for
the possibility that consumer preferences di¤er across consoles. Unlike a model
wheresoftwaretitlesareneithersubstitutesnorcomplements,
13
aconsumermakeshis
decisionbaseduponthenotionthattitlesaresubstitutestoeachother. Consequently,
13
Which is in the spirit of a static version of Lees (2008) paper
21
a consumer purchases softwarek if and only if
U
kj
(
ik
;x
k
;
k
;
sw;j
)U
gj
(
ig
;x
g
;
g
;
sw;j
)8g 2K:
Similar to the above console model, denote the set of values of which induce con-
sumption of softwarek be de ned as
L
k
=f :U
kj
(
ik
;x
k
;
k
;
sw;j
)U
gj
(
ig
;x
g
;
g
;
sw;j
)8g 2Kg:
Withsoftwaretitlesbeingsubstitutesforoneanotherandconsumersknowingwhich
games are available on a console but not the utility a game provides at the console
selection stage, the consumer forms an expectation as to the utility he would receive
from video games. The expectation of software utility forms the indirect network
e¤ect and equals the expected maximumutility fromchoosing froma set of available
video games on consolej
j
=E(max
k2K
U
kj
):
Econometric Speci cation
I now describe the econometric speci cation and estimation procedure for the above
model. I follow the estimation techniques of Berry (1994) and Nevo (2001).
22
Video Game Speci cation
Aconsumersutilityforsoftwarekinperiodtconditionalonhavingpurchasedconsole
j is
u
ikt
=
sw;j
p
kt
+x
kt
sw;j
+
kt
+
ikt
kt
+
ikt
where p
kt
is software ks price, x
kt
is vector of game characteristics,
kt
are software
characteristics unobservable to the econometrician and
ikt
is a type one extreme
value distributed random variable which is independently and identically distributed
across individuals, software and time.
Demand for video games follows a multinomial logit structure. Consumers may
repurchase an already owned title. This assumption may not seem as far fetched
as one might think. Consumers are likely to repurchase a game after it has been
lost or damaged. Under such assumptions the software index is analytic and can
be determined without the parameterization of the demand model. Only monthly
quantity and potential market size data are needed.
The implementation of the standard logit utility function as oppose to a more
complexrandomcoe¢ cientfunctionallowsmetoconstructthesoftwareindexwithout
parameterizingthedemandmodel aslongastheindirectutilityfunctionforsoftware
is of a linear form. Yet, the ease of the technique has its drawbacks. For instance,
the above model does not allow one to determine how prices change as a result of a
merger among video game developers or the elimination of any games. To analyze
these questions I would need to the estimate the demand model for video games and
23
recover the model parameters.
In order to construct the software index I proceed by following the methodology
of Berry (1994).
LetS
kt
betheobservedprobabilitythatgamek ispurchasedinperiodtands
kt
be
themodelspredictedprobabilitythenthefollowingequationwillholdforpopulation
values of :
14
S
kt
=s
kt
() 8 k = 0:::K:
where 0 is the outside option of not purchasing a game. Given the logit distribu-
tion for unobserved consumer taste the above system of equations can be inverted
analytically. The mean utility (in vector form) is
=s
1
(S):
The mean utility is determined uniquely by the observed probabilities along with a
normalization of the outside goods utility to zero
ln
S
kt
S
ot
=
kt
:
14
Observed probabilities are constructed by dividing sales in period t by the potential market.
This is done for each game which leads to the probability that no purchase is made
S
ot
=1
J
X
j=1
S
jt
:
24
The software index for consolej in timet is
jt
=E(max
k2K
U
kj
) = ln
K
P
k=0
exp[
kt
]
+'
where ' is Eulers constant. The software index is of the familiar logit inclusive
value form and holds the same interpretation: the expected maximum utility for the
choice of video games in period t for console j. Again, note that the software index
is determined only with potential market size and sales datano parameterization is
required.
Console Speci cation
Demand
In every period t, each potential consumer makes a decision on whether or not to
purchase a game console. If a consumer purchases a console he exits the market.
Consumers are indexed by i, consoles by j and time by t. A consumers indirect
utility for consolej is characterized by a set of observed physical characteristicsX
jt
,
the software index
jt
, the year speci c mean unobserved (by the econometrician)
product characteristics
jy
, the console-month speci c deviation from the mean
jt
and an individual taste parameter "
ijt
; distributed i.i.d. type-1 extreme value across
i;j andt. A consumers indirect utility for consolej is
25
u
ijt
=
hw
P
jt
+X
jt
hw
+
jt
+
jy
+
jt
+"
ijt
u
ijt
=
jt
+"
ijt
where
jt
is the mean utility, common to all individuals. The model parameters
are
hw
= (
hw
1
).
hw
1
contains the linear parameters of the model (
hw
;
hw
;) .
15
Examples of physical characteristics are price, processing speed, graphics quality,
volume of the console, CPU bits, advertising expenditures and advertising expen-
ditures squared. Unobserved characteristics include other technical characteristics
and market speci c e¤ects of merchandising. I control for these unobserved product
characteristics as well as observed characteristics which do not vary over time with
theinclusionofbrandspeci c xede¤ects. Intheattempttocapturesomedynamic
aspects of the consumers valuation for consoles over time, I allow the console xed
e¤ects to be year speci c. I also control for the large seasonal spikes during holiday
months with quarterly dummy variables. Lastly, I assume consumers observe all
console characteristics and use them in their decision making.
Theaboveutilityfunctiondoes notallowconsumertastes towardconsolepriceto
di¤er among consumers. This function is associated with a logit model of demand.
Thestandardlogitmodelisquiterestrictiveinthatitpredictsunrealisticsubstitution
15
Software utility enters linearly into the utility function for consoles so the expected utility of
software is a su¢ cient statistic for calculating utility for hardware
26
patterns. To alleviate this problem I introduce additional consumer heterogeneity
and thus recovermore realistic substitution patterns which are not solely determined
byproductmarketshare.
16
Iintroduceconsumerheterogeneitybyallowingconsumer
tastestowardconsolepricetodi¤eramongpotentialconsolebuyersbutisunobserved
toaneconometrician. Iassumeconsumerpricesensitivitiesarenormallydistributed
with mean
hw
and variance
2
: By assuming a consumers taste toward price is
distributed normally I separate the heterogeneity into two parts a scaling parameter
which measures the standard deviation of consumer tastes toward prices about the
mean and an unobserved consumer speci c taste term v
i
vN(0;1):
17
Below is the
underlying consumer utility function associated with a more exible demand model
which is also know as a random coe¢ cient logit model of demand.
u
ijt
=
jt
(X
jt
;P
jt
;
jt
;
jt
;
hw
1
)+
ijt
(P
jt
;v
i
;
hw
2
)+"
ijt
jt
=
hw
P
jt
+X
jt
hw
+
jt
+
jy
+
jt
;
ijt
= P
jt
v
i
v
i
vN(0;1)
The model parameters for the above utility function are
hw
= (
hw
1
;
hw
2
) where
hw
2
= () is the nonlinear parameter and
hw
1
are the linear parameters.
jt
is the
mean utility common to all individuals, like that of the logit model, while u
ijt
+"
ijt
16
Formal derivation of console elasticities for the logit model of demand and a random coe¢ cient
logit model is found below
17
Note: I have tried to further decompose the unobserved consumer heterogeniety v
i
by includ-
ing income and other demographic variables but I was unable to identify any of these additional
parameters.
27
is the mean-zero heteroskedastic deviation from the mean utility. It is important to
note that the term u
ijt
+"
ijt
is what drives the more realistic substitution patterns
in a random coe¢ cient logit model and is a result of consumer tastesu
ijt
+"
ijt
being
correlatedacrossproducts. Consoleswithsimilarcharacteristicshavemorecorrelated
u
ijt
+"
ijt
while products with dissimilar characteristics do not. Consequently, cross-
price elasticities are higher between two products that are "closer" in characteristics.
Alternative Console Demand Models
Next,Idiscusstwoalternativemethodologiestolinkvideogameandconsoledemand,
speci cally two methods seen in previous research. As I have stated above the
literature implements two restrictive methods. The rst being that only the number
ofavailablegamesforagivenconsoledrivesconsolesaleswhilethesecondrelaxesthis
assumption but does so with the implementation of a strong assumption regarding
the nature of video game competition. I rst discuss the model most similar to my
approach above. This rst model allows consumers to di¤erentiate between video
games but does not allow games to compete against each other. I then review a
method which only employs the number of available video games.
Model II: Video game heterogeneity, no video game competition
For this alternative model I make the assumption that the model timing is iden-
tical to the model above. I also assume all console characteristics and consumer
heterogeneity associated with the model above remains with the exception of how
I form the indirect network e¤ect. The measure for gamma is quite di¤erent than
28
one which allows for video game competition and video game heterogeneity. This
alternative model assumes video games are in individual secluded markets. Thus,
the video game index is formed by deriving the expected utility from choosing each
individual game and then summing over the many game speci c inclusive values,
which takes the form
jt
=
K
P
k=1
E(max
k2G
U
kj
)
=
K
P
k=1
fln(1+exp[
kt
])+'g
jt
=
K
P
k=1
fln(1+exp[
kt
])g
'
| {z }
Differentiation term
+ K
jt
|{z}
Number of games
where' isEulersconstantandK
jt
isthetotalnumberofgamesavailableonconsole
j intimet. G represents the consumerchoice set whichconsists of avideogame and
the outside option of not purchasing. With simple arithmetic one sees that the index
is a function of the total number of available video games and a term which captures
the di¤erentiation among all video games. This approach can be interpreted as a
consumerwalkingintoavideogamestoreandlookingateachvideogameindividually
todeterminewhetherheshouldpurchaseeachspeci cgame. Myabovemodeldi¤ers
fromthisalternativeapproachbyhavingtheconsumerdecidewhichgametopurchase
from the set of available games rather than looking at each game individually.
Given the assumption regarding the lack of competition in the video game mar-
ket I re-estimate the demand for video games in order to recover the mean utilities
associated with each game. I employ the same technique used above to recover
kt
:
29
Yet, insteadoftheemployingamultinomial logitmodel Iuseabinomial logitmodel.
Under such a model consumers either purchase or do not purchase a speci c game.
The outside option of not purchasing is equal to 1S
kt
, rather than 1
K
P
k=1
S
kt
:
Model III: Number of games
Papers by Clements and Ohashi and Hu and Prieger use the number of available
videogamescompatiblewithconsolej intimettolinkvideogamedemandbackinto
console demand. The corresponding gamma in these respective papers are a simple
count of video games available for each console.
jt
=K
jt
This index implicitly assumes video games are homogenous and it is the most
restrictive index to implement.
Market Size
I conclude the discussion regarding the empirical model of console demand with a
short dialogue concerning the market de nition for video games and video game
consoles. In order to estimate video game console demand and identify the video
game index, measures of potential market size are required. The potential market
sizeisakeycomponentforestimatingdemandinthatitallowsproductmarketshares
to be formed as well as the outside alternative of not purchasing.
30
Insteadofusinganarbitrarynumberequaltothenumberofhouseholdsortelevi-
sions in the United States to form a potential market size for video game consoles I
let the data determine the size. I use an approach from Bass (1969) that illustrates
how to infer the initial potential market size of a product from its sales data. This
approach uses "an approximation to the discrete-time version of the model [that] im-
plies an estimation equation in which current sales are related linearly to cumulative
sales and (cumulative sales)
2
" (Nair 2004). Let w
t
and W
t
denote the aggregate
sales of all consoles in month t and cumulative sales up to and including month t
respectively. Let the below equation be the regression I estimate:
w =a+bW
t
+cW
2
t
+
t
:
Given the estimates, the Bass model implies the initial potential market size for all
consoles is
M =
a
f
; where f is the positive root of the equation f
2
+fb +ac = 0
and a is from the regression above. The predicted initial market size is 78,354,700
households. Thepotentialmarketinperiodt isM
t
=
_
Mcumulativeconsolesales
till month t:
18
The potential market size for video games is equal to the installed base of the
video game console which is equivalent to the installed base in period t1 and the
numberofconsolessoldinperiodt: Thepotentialmarketsizeforgamek compatible
18
The construction of the potential market size reects the idea that a consumer is a rst time
buyer and does not re-enter the market to purchase additional goods. Consequently, I do not
account for multihoming consumers.
31
with consolej is thus,
(IB
jt1
+M
t
S
jt
(P;X;;
hw
)
| {z }
Potential Market for game d=IB
jt
)
where IB
jt1
is the installed in period t 1; M
t
is the potential market size for
video game consoles and S
jt
(P;X;;
hw
) is the consumer choice probability that he
purchase consolej in periodt.
Estimation
Estimation of console demand for models without additional consumer heterogeneity
follows that of the Berry (1994). Let S
j
be the observed market share for console j
and s
j
be the models predicted market share then the following equation will hold
for true values of :
19
S
jt
=s
jt
() j = 0:::J
where
s
jt
() =
exp(
jt
)
P
J+1
r=0
exp(
kt
)
.
By assuming a logit distribution for unobserved consumer tastes the above system of
equations can be inverted analytically so that we may write mean utility (in vector
19
Observed market shares are constructed by dividing sales in market t by the potential market.
This is done for each console which leads to the outside market share of
s
o
=1
J
X
j=1
s
j
:
32
form) as
=
^
s
1
(S):
The mean utility is then determined uniquely by the observed market shares. Given
a logit distribution along with a normalization of the outside goods mean utility to
zero, I write the mean utility level of consolej as
s
jt
s
ot
=
jt
exp(
hw
P
jt
+X
jt
hw
+
jt
+
jy
+
jt
)
which implies
ln(
s
jt
s
ot
) =
jt
hw
P
jt
+X
jt
hw
+
jt
+
jy
+
jt
The above equation is linear in parameters
HW
1
and therefore can be estimated
via ordinary least squares by regressing mean utilities ln(
s
jt
sot
) =
jt
on covariates
(P
jt
;X
jt
;
jt
).
This procedure, however, results in biased coe¢ cients. The bias is a direct con-
sequenceofnotaccountingfortheendogeneityof consoleprices. Iemployaninstru-
mental variables approach to correct for such bias. Discussion of proper instruments
follows in the sections below.
The logit and instrumental variable logit model does not provide realistic substi-
tution patterns. Although the extreme value distributional assumption for "
ijt
and
the fact that all coe¢ cients enter market shares linearly produces a rather simple
33
solution for product elasticities; it nonetheless bears some consequences. The main
concern is with regard to the substitution patters for own and cross-price elasticities.
The price elasticities are
jkt
=
@s
jt
p
kt
@p
kt
s
jt
=
p
jt
(1s
jt
) if j =k
p
kt
s
kt
otherwise.
For the logit models the elasticities only depend on market shares. Any pair of
consoles which have the same market share will have the same cross-price elasticity
with any other console.
To relax this restriction the estimation methodology for the general console de-
mand model which includes additional consumer heterogeneity follows that of Nevo
(2001). In particular, simulated shares are matched to observed shares in order to
use a simulated method of moment procedure to estimate the model parameters.
Estimation for a random coe¢ cient model of demand is as follows. For given
hw
2
= () simulate ns "consumer" purchases and determine the average probability
ofconsumptionassociatedwitheachconsole. Then, performacontractionmapping,
the one proposed by BLP, to recover the mean utility
jt
linked to all individuals
h+1
t
=
h
t
+lnS
:t
ln
f
S
:t
t = 1:::T; h = 1:::H:
Follow with a regression of
jt
on covariatesX
jt
;P
jt
;
jt
to determine the linear esti-
34
mates of
hw
hw
and. Once the parameters are estimated calculate
jt
from
jt
=
jt
(X
jt
;
jt
;P
jt
;
hw
2
)
hw
p
jt
X
jt
hw
jt
jy
:
After computing
jt
generate a matrix of exogenous instrumentsZ and assume the
condition
E[jZ] = 0:
The unobservables are used to determine the sample analogue of the above orthogo-
nality condition
M
N
()
1
G
G
P
g=1
Z
g
g
and the simulated method of moment objective function
M
N
()
0
W
1
()M
N
()
whereGequalsthenumberofobservationsinthedatasetandW
1
()isaweighting
matrix that is a consistent estimate of [M
N
()M
N
()
0
]:
Foreachguessof
hw
2
repeattheestimationprocedureuntiltheobjectivefunction
is minimized. The weighting matrix in the above equation is computed using an
iterative approach.
In summary, the estimation procedure is
1. construct the video game index
35
2. given
hw
2
, simulate 5000 individualspurchases of video games consoles
3. perform a contraction mapping to invert out the structural error terms
4. compute the sample analogue, weighting matrix and the objective function
5. search for the parameter values that minimize the objective function
6. recalculatetheweightingmatrixgiventheparametervectorofthepriorminimization
iteration
7. repeat steps (2)-(6) until parameters do not vary
8. construct new weighting matrix with estimated parameters
9. iterate on steps (2)-(8) until optimal gmm estimators are recovered
Identi cation
The following is a short discussion on how the model parameters are identi ed.
With every console there is a mean utility found to match the observed and pre-
dictedpurchaseprobabilities. Ifweassumeconsumersareidenticalthenallvariation
in sales would be a result of variation in product characteristics. Thus, monthly
variationinproductcharacteristicswithmonthlyvariationinsharesaidsintheiden-
ti cation of the mean utility parameters such as price and software index.
Identi cation of pertains to how price sensitive households are and how they
substitute. Ifthepriceofoneproductchangesandsubstitutionoccurstootherprod-
ucts with a similar price then there are signs of consumer heterogeneity. Likewise,
36
if consumers substitute equally to all other goods then consumers are homogenous.
Changes in product characteristics therefore aid the identi cation of the nonlinear
parameter. For instance, assume console A and B are very similar in characteris-
tics, think of A and B as Playstation 2 and Xbox while console B and C, Xbox and
Gamecube, have the same purchase probabilities. Suppose we have sales and price
information for two periods and that the only change to occur is a reduction in the
price of console A. The logit model predicts purchase probability for B and C fall
byequalamountswhereastherandomcoe¢ cientlogitmodelpredictsconsoleB,the
console most similar in characteristics to console A, to fall by more than that of con-
soleC. Therefore, byobservingtheactualrelativechangesinpurchaseprobabilityof
consoles B and C I can determine whether the model is a logit or random coe¢ cient
logitmodelofdemand. Additionally, thedegreeofchangeallowstheparameterthat
determines the distribution of the random coe¢ cient to be identi ed.
20
Instruments
For both the instrumental variable logit and the random coe¢ cient logit models the
underlying assumption to estimate the models is
E[jZ] = 0
20
This example is a modi ed version of the example provided in Nevo (2000)
37
where the demand unobservables are mean independent of the set of instruments
Z: Since the unobservables are not observed by the econometrician but are by the
consumers, there exists an endogeneity issue. If price is positively correlated with
unobserved product characteristics the price coe¢ cient will be biased. I resolve this
correlation through the use of year speci c console dummy variables. Even with
the use of console dummy variables the proportion of the unobservable which is not
accounted for may still be correlated with price as a result of consumers and produc-
ers correctly observing and accounting for the deviation.
21
Under the assumption,
marketspeci cmarkupswillbeinuencedbythedeviationandwillbiastheestimate
of console price sensitivity. Instrumental variables correct this bias. Berry (1994)
and BLP both show that proper instruments for price are variables which shift cost.
In addition to console price being endogenous, one might suppose the software
index is as well. In order to properly identify the indirect network externality an
assumption regarding the autocorrelation of
jt
is made. I assume the residuals
of the structural error terms, the proportions which are not captured by the year
speci cconsole xede¤ects,areindependentofeachother. Thisassumptionnegates
any impact an aggregate demand shock in period t1 has on the software index in
periodt and therefore eliminates the need for instrumental variables.
Theinstrumentswhichcontrolfortheendogeneityofpricemustbecorrelatedwith
the underlying variable but independent of the unobserved error terms. Instruments
follow the logic of BLP. However, instead of using instruments constructed from ob-
21
See Nevo 2001 for futher explanation
38
servable product characteristics I employ variables which proxy for marginal cost. I
use the monthly producer price index for computers, the average monthly Japanese
toUSexchangerateandtheageofagivenconsole,whichhasbecomestandardinthe
video game literature (see Hu and Prieger (2007) and Clements and Ohashi (2004)).
Exchange rates are suitable since most of the manufacturing of consoles occurred in
Japan and would consequently e¤ect retail console price. Lastly, the producer price
index for computers is a nice proxy to console marginal cost since the internal hard-
wareofavideogameconsoleconsistsofitemsfoundindesktopcomputers. Thetime
variationwithintheexchangerateandproducerpriceindexassistsinidentifyingcon-
sole demand. Note though, these measures are industry aggregates and do not vary
byconsole. Inordertoconstructconsolespeci cinstrumentalvariablestheproducer
price index and exchange rates are interacted with console dummy variables.
22
The
intuition for interacting input prices and exchange rates with product dummies is to
alloweachtoentertheproductionfunctionof agivenconsoledi¤erently. Firststage
regression results are presented in Table 5 for the logit model of the above model,
a model which includes video game quality di¤erentiation but no video game sub-
stitution and a model which uses the number of video games as its measure for the
indirect networkexternalities. The large adjustedRsquaredandFstatistic indicate
the instruments have some power as seen in Table 5.
22
This method is similar to that of Villas Boas (2007)
39
Table 3: Demand Results
Demand Parameters Logit Logit-IV Random Coe¢ cient
(i) (ii) (iii)
Price -0.0041** -0.0140** -0.0288**
(0.0017) (0.0031) (0.0084)
Gamma 0.6815** 0.6971** 0.8664**
(0.0793) (0.1064) (0.1339)
Ad 0.1752 0.1550 0.2417**
(0.1434) (0.1022) (0.1071)
Ad
2
-0.0000 -0.0000 -0.0000*
(0.0000) (0.0000) (0.0000)
Sigma - - 0.0084**
(0.0030)
Q1 -0.5618** -0.1771 -0.0898
(0.1214) (0.2075) (0.1924)
Q2 -0.6494** -0.5241** -0.5061**
(0.1069) (0.1454) (0.1532)
Q3 -0.5570** -0.5100** -0.4831**
(0.1058) (0.1367) (0.1451)
GMM Objective 15.1251
Test Statistic-Over Identi cation
A
16.01
A
Test statistic at 97.5% con dence level
Estimation Results
Model Results
Estimates of the demand equation are found in the tables below. Multiple speci ca-
tionsareshown. Columnoneprovidesresultsfromestimatingalogitdemandmodel;
columntwointroducesinstrumentalvariableswhilecolumnthreeallowsforconsumer
heterogeneity. Below,inTable3,Ipresenttheestimatesforthedemandmodelwhich
accounts for video game heterogeneity and software competition. Alternative model
speci cations are also discussed, but follow below.
40
Table 4: Demand Results-Console Fixed E¤ects
Demand Parameters Logit Logit-IV Random Coe¢ cient
(ii) (iii)
Gamecube 2002 -5.408 -3.8752 -2.4163
(0.2981) (0.4814) (0.8391)
2003 -5.0531 -3.9357 -2.6829
(0.2356) (0.3863) (0.7425)
2004 -5.0083 -4.2028 -3.1609
(0.1898) (0.2826) (0.6607)
Playstation 2 2002 -3.5792 -0.7393 0.8958
(0.5069) (0.8928) (1.0943)
2003 -3.7247 -1.6474 -0.0773
(0.3795) (0.6817) (0.9546)
2004 -3.7597 -2.0590 -0.4983
(0.3199) (0.5312) (0.8718)
Xbox 2002 -4.9086 -2.7779 -1.1907
(0.3936) (0.6654) (0.9466)
2003 -4.6757 -3.0312 -1.4398
(0.3117) (0.5331) (0.8677)
2004 -4.1875 -2.8060 -1.3912
(0.2745) (0.4492) (0.7997)
Table 5: First Stage Results-Logit Model
Logit-IV Logit-IV Logit-IV
(1) (Binomial) (Number)
F-test 60.35 61.26 61.31
Adjusted R
2
0.9194 0.9206 0.9206
41
The non-linear set of parameters
hw
2
= fg is estimated and is found to be
signi cantatthe95%con dencelevel.
23
Theestimateofis0:084anddescribeshow
consumerpricesensitivityisdistributedamongindividuals. Apositiveandsigni cant
value indicates that the model of demand is identi ed as a random coe¢ cient logit
model where as an insigni cant measure of would indicate a logit demand model
without consumer heterogeneity.
Theestimatesofthelinearparameters
hw
1
=f;;gfollowbelow. Theparame-
terestimateof; themeanpricesensitivityof consumers, is0:0288 andsigni cant.
The bias associated with the endogeneity of price is quite evident when comparing
the ols estimate of the logit model to the price coe¢ cient under the iv-logit model.
The ols estimate is 0:0041 while the iv-logit estimate is 0:0140. A Hausman test
for endogeneity concludes price is endogenous.
The year speci c console xed e¤ects are found in Table 4. Fixed e¤ects de-
crease signaling consumers value consoles less over time.
24
The estimates of the
quarter dummy variables are all negative demonstrating that holiday periods bring
consumers larger increases in utility relative to the three other quarters. The para-
meter associated with the software index is 0:8664 and signi cant. The positive sign
indicates video games and consoles are complements. Lastly, the parameter asso-
ciated with advertising expenditures is 0:2417 and signi cant at the 95% con dence
23
Any future use of signi cance will be at the 95% con dence level
24
The above estimation does not consider Sony Playstation 2s large catalog of video games from
its previously produced console, the Playstation
42
level while advertising squared is 5:1025e008 and not signi cantly di¤erent from
zero at the conventional 95% level. The positive sign on the advertising expenditure
parameter illustrates an increase in consumer demand when advertising dollars are
spent.
AsinBLP,standarderrorsarecorrectedforsimulation. Iassumethepopulation
samplingerrorisnegligiblegiventhelargesamplesizeofover78;000;000households.
Simulation error, however, cannot be ignored as a result of the need to simulate the
integral which de nes console market shareS
jt
. Calculating the variance associated
with parameter estimates from simulation requires that I x () at its estimated
value and recalculate
hw
1
using 500 di¤erent simulation draws. Given the fact that
simulation error and standard sampling error are independent I simply aggregate the
e¤ects to determine the total standard errors.
One of the many bene ts of estimating a structural demand model is that it
suppliessu¢ cientinformationtodeterminepriceelasticities. Table6 belowprovides
average elasticities estimates for the given time period. Elasticity calculations are
below.
jrt
=
@S
jt
P
rt
@P
rt
S
jt
=
P
jt
S
jt
R
i
S
ijt
(1S
ijt
)dP
v
(v) if j =r
Prt
S
jt
R
i
S
ijt
S
irt
dP
v
(v) otherwise
Theaverageown-priceelasticitiesforthegiventimeperiod are2:6527;3:1972
and3:1401forGamecube,Playstation2andXbox,respectively. Estimatesofcross-
priceelasticitiesestablishSonysPlaystation2astheclosestsubstitutetoNintendos
43
Table 6: Mean RCL Logit Console Elasticities
Gamecube Playstation 2 Xbox
Gamecube -2.6527 0.1067 0.0374
(-2.1807 , -3.3906) (0.2763 ,0.0500) (0.0959 , 0.0167)
Playstation2 0.0201 -3.1972 0.0531
( 0.0530 , 0.0092) (-3.2444 , -3.9553) (0.1288 , 0.0196)
Xbox 0.0190 0.1436 -3.1401
(0.0492 , 0.0083) (0.3334 , 0.0512) (-3.1801 , -3.4382)
Note: Cell entry i, j, where i indexes row and j column, give the percent change in market share
of brand i with a one percent change in the price of j. 95% con dence intervals in parentheses
Table 7: Mean Logit Console Elasticities
Gamecube Playstation 2 Xbox
Gamecube -1.8548 0.0344 0.0136
(-1.0751 , -2.6502 ) (0.0491 , 0.0199) (0.0194 , 0.0079)
Playstation2 0.0068 -3.3218 0.0136
(0.0098 , 0.0040) (-1.9254 , -4.7461) (0.0194 , 0.0079)
Xbox 0.0068 0.0344 -2.6498
(0.0098 , 0.0040) (0.0491 , 0.0199) (-1.5359 , -3.7860)
Note: Cell entry i, j, where i indexes row and j column, give the percent change in market share
of brand i with a one percent change in the price of j. 95% con dence intervals in parentheses
Gamecube while the closest competitor to Microsofts Xbox and Sonys Playstation
2 are each other. As Table 6 illustrates the cross-price elasticities are not of the
logit form. The implementation of the random coe¢ cient utility function eliminates
the independent of irrelevant alternative (IIA) bias associated with the logit model
and provides more realistic substitution as a result. Furthermore, the estimated
cross-price elasticity measures are consistent with the beliefs of an industry insider
regarding the relative competition among video games consoles.
44
Alternative Console Demand Model Results
Model II: Video game heterogeneity, no video game competition
Estimates of the alternative demand model which does not account for video
game competition are found in the tables below. Multiple speci cations are shown.
Columnoneprovidesresultsfromestimatingalogitdemandmodel;columntwointro-
duces instrumental variables while column three allows for consumer heterogeneity.
The non-linear set of parameters
hw
2
= fg is estimated and is found to be
signi cant. The estimate of is 0:083 and describes how consumer price sensitivity
is distributed among individuals. A positive and signi cant value indicates that the
model of demand is identi ed as a random coe¢ cient logit model.
The estimates of the linear parameters
hw
1
= f;;g follow. The parameter
estimate of ; the mean price sensitivity of consumers, is 0:0296 and signi cant.
The bias associated with the endogeneity of price is quite evident when comparing
the ols estimate of the logit model to the price coe¢ cient under the iv-logit model.
The ols estimate is 0:0040 while the iv-logit estimate is 0:0153. A Hausman test
for endogeneity concludes price is endogenous.
Theyearspeci cconsole xede¤ectsarefoundinTable9. Fixede¤ectsdecrease
signaling consumers value consoles less over time. The estimates of the quarter
dummy variables are positive for quarter one and quarter two. However, the para-
meter associated with quarter 2 is insigni cant. The sign of these quarter dummy
variables are certainly not intuitive and thus I cannot construct a reason to explain
45
sucharesult. Thecoe¢ cientforthevariablequarterthreedoesholdthepropersign,
negative, demonstrating that this period bring consumers smaller increases in utility
relativetotheholidayquarter. Butdonotethisparameterisinsigni cantlydi¤erent
from zero. The parameter associated with the software index is 0:0193 and is sig-
ni cant which indicates video games provide additional utility to consumers leading
to the conclusion that consoles and games are complementary products. Lastly, the
parameter associated with advertising expenditures is 0:0309 but insigni cant while
advertisingsquaredisnotsigni cantlydi¤erentfromzeroattheconventional95%as
well.
Standard errors are calculated in the identical manner as the model presented
above.
Theaverageown-priceelasticitiesforthegiventimeperiod are2:7517;3:3580
and3:2804forGamecube,Playstation2andXbox,respectively. Estimatesofcross-
priceelasticitiesestablishSonysPlaystation2astheclosestsubstituteforNintendos
Gamecube while the closest competitor to Microsofts Xbox is Sonys Playstation
2 and vice versa. As Table 10 illustrates the estimated cross-price elasticities are
consistent with the beliefs of an industry insider regarding the relative competition
among the three console makers.
46
Table 8: Demand Results-Alternative Model II
Demand Parameters Logit Logit-IV Random Coe¢ cient-II
(i) (ii) (iv)
Price -0.0040** -0.0153** -0.0296**
(0.0020) (0.0043) (0.0146)
Gamma 0.0131** 0.0139** 0.0193**
(0.0034) (0.0040) (0.0060)
Ad 0.0139 -0.0141 0.0309
(0.1785) (0.1528) (0.1504)
Ad
2
0.0000 0.0000 0.0000
(0.0000) (0.0000) (0.0000)
Sigma - - 0.0083*
(0.0049)
Q1 0.1400** 0.6329 1.0627**
(0.3113) (0.3979) (0.4743)
Q2 -0.2319** -0.0510 0.2424
(0.2481) (0.2957) (0.3229)
Q3 -0.4125** -0.3372 -0.1401
(0.1873) (0.2267) (0.2322)
GMM Objective 13.7264
Test Statistic-Over Identi cation
A
16.01
A
Test statistic at 97.5% con dence level
47
Table 9: Demand Results-Fixed E¤ects for Alternative Model II
Logit Logit-IV Random Coe¢ cient II
(ii) (iv)
Gamecube 2002 -5.8263 -4.1221 -3.1032
(0.4644) (0.6984) (1.2931)
2003 -6.7127 -5.5459 -5.2298
(0.6550) (0.8403) (1.0399)
2004 -7.7886 -7.0386 -7.3114
(0.8693) (1.0247) (1.0811)
Playstation 2 2002 -5.8523 -2.7470 -2.3030
(0.9887) (1.4411) (1.5852)
2003 -8.0257 -5.9044 -6.4803
(1.3183) (1.6834) (1.7442)
2004 -9.9375 -8.3550 -9.5208
(1.7560) (2.0428) (2.2461)
Xbox 2002 -5.4921 -3.1043 -2.0519
(0.5876) (0.9869) (1.4875)
2003 -6.7495 -5.0000 -4.4591
(0.7820) (1.0234) (1.2152)
2004 -7.7468 -6.3833 -6.6334
(1.1115) (1.3245) (1.3804)
Table 10: Mean RCL Logit Console Elasticities-Model II
Gamecube Playstation 2 Xbox
Gamecube -2.7517 0.1145 0.0396
(-2.2011 , -3.9548 ) (0.4482 , 0.0331) (0.1727 , 0.0136)
Playstation2 0.0215 -3.3580 0.0577
(0.0893 , 0.0069) (-3.6789 , -4.0582) (0.2700 , 0.0169)
Xbox 0.0202 0.1565 -3.2804
(0.0898 , 0.0068) (0.6760 , 0.0402) (-3.2338 , -4.1510)
Note: Cell entry i, j, where i indexes row and j column, give the percent change in market share
of brand i with a one percent change in the price of j. 95% con dence intervals in parentheses
48
Table 11: Mean Logit Console Elasticities-Model II
Gamecube Playstation 2 Xbox
Gamecube -2.0272 0.0376 0.0149
(-0.9231 , -3.1323 ) (0.0581 , 0.0171) (0.0230 , 0.0068)
Playstation2 0.0075 -3.6304 0.0149
(0.0116 , 0.0034) (-1.6531 , -5.6095) (0.0230 , 0.0068)
Xbox 0.0075 0.0376 -2.8960
(0.0116 , 0.0034) (0.0581 , 0.0171) (-1.3187 , -4.4748)
Note: Cell entry i, j, where i indexes row and j column, give the percent change in market share
of brand i with a one percent change in the price of j. 95% con dence intervals in parentheses
Model III: Number of games
The estimates for the second alternative model of demand equation are found in
the tables 12- below. Like each of the above two models, multiple speci cations
are shown. Column one provides results from estimating a logit demand model;
columntwointroducesinstrumentalvariableswhilecolumnthreeallowsforconsumer
heterogeneity.
The non-linear set of parameters
hw
2
= fg is estimated and is found to be
signi cant at the 90% con dence level. The estimate of is 0:084 which identi es
the demand model as a random coe¢ cient logit model.
Theestimatesofthelinearparameters
hw
1
=f;;garebelow. Theparameter
estimate of ; the mean price sensitivity of consumers, is 0:0297 and signi cant.
The bias associated with the endogeneity of price is quite evident when comparing
the ols estimate of the logit model to the price coe¢ cient under the iv-logit model.
The ols estimate is 0:0040 while the iv-logit estimate is 0:0154. A Hausman test
for endogeneity concludes price is endogenous.
49
The year speci c console xed e¤ects are found in Table 9-15. Fixed e¤ects
decrease signaling consumers value consoles less over time. The estimates of the
quarter dummy variables are positive for quarter one and quarter two. However,
the parameter associated with quarter 2 is insigni cant. The sign of these quarter
dummy variables are certainly not intuitive and thus I cannot construct a reason to
explain such. The coe¢ cient for the variable quarter three does hold the proper
sign, negative, demonstrating that this period bring consumers smaller increases in
utility relative to the holiday quarter. But do note this parameter is insigni cantly
di¤erent from zero. The parameter associated with the software index is 0:0111 and
signi cant which indicates video games and consoles are complements. Lastly, the
parameter associated with advertising expenditures is 0:0317 but insigni cant while
advertising squared is not signi cantly di¤erent from zero at the conventional 95%.
Standard errors are calculated in the identical manner as each of the two models
presented above.
Theaverageown-priceelasticitiesforthegiventimeperiod are2:6527;3:1972
and 3:1401 for Gamecube, Playstation 2 and Xbox, respectively. Estimates of
cross-price elasticities establish Sonys Playstation 2 as the closest substitute for the
Nintendos Gamecube while the closest competitor to Microsofts Xbox is Sonys
Playstation 2 and vice versa. Again, like above, Table 14 illustrates the estimated
elasticitymeasuresareconsistentwiththebeliefsofanindustryinsiderregardingthe
50
Table 12: Demand Results-Alternative Model III
Demand Parameters Logit Logit-IV Random Coe¢ cient-III
(i) (ii) (v)
Price -0.0040** -0.0154** -0.0297**
(0.0021) (0.0043) (0.0147)
Gamma 0.0075** 0.0079** 0.0111**
(0.0034) (0.0023) (0.0035)
Ad -0.0149 -0.0149 0.0317
(0.1530) (0.1530) (0.1506)
Ad
2
0.0000 0.0000 0.0000
(0.0000) (0.0000) (0.0000)
Sigma - - 0.0084*
(0.0049)
Q1 0.6245 -0.0607 1.0565**
(0.3999) (0.3999) (0.4772)
Q2 -0.0607 -0.3449 0.2343
(0.2969) (0.2969) (0.3240)
Q3 -0.3449 -0.0149 -0.1464
(0.2275) (0.2275) (0.2327)
GMM Objective 13.7929
Test Statistic-Over Identi cation
A
16.01
A
Test statistic at 97.5% con dence level
51
Table 13: Demand Results-Fixed E¤ects for Alternative Model III
Logit Logit-IV Random Coe¢ cient II
(ii) (iv)
Gamecube 2002 -5.8085 -4.0901 -3.0711
(0.4652) (0.7039) (1.3060)
2003 -6.6852 -5.5084 -5.1921
(0.6575) (0.8458) (1.0481)
2004 -7.7538 -6.9971 -7.2703
(0.8739) (1.0309) (1.0859)
Playstation 2 2002 -5.8184 -2.6875 -2.2471
(0.9925) (1.4523) (1.5975)
2003 -7.9766 -5.8374 -6.4165
(1.3256) (1.6950) (1.7520)
2004 -9.8717 -8.2752 -9.4434
(1.7668) (2.0570) (2.2554)
Xbox 2002 -5.4726 -3.0652 -2.0141
(0.5887) (0.9943) (1.5024)
2003 -6.7192 -4.9550 -4.4145
(0.7853) (1.0310) (1.2244)
2004 -7.7031 -6.3278 -6.5787
(1.1174) (1.3332) (1.3864)
52
Table 14: Mean RCL Logit Console Elasticities-Model III
Gamecube Playstation 2 Xbox
Gamecube -2.7612 0.1153 0.0399
(-2.2049 , 3.9658 ) (0.4493 , 0.0329) (0.1732 , 0.0136)
Playstation2 0.0216 -3.3699 0.0583
(0.0895 , 0.0068) (-3.6933 , -4.0691) (0.2710 , 0.0168)
Xbox 0.0203 0.1579 -3.2922
(0.0901 , 0.0068) (0.6789 , 0.0399) (-3.2438 , -4.1725)
Note: Cell entry i, j, where i indexes row and j column, give the percent change in market share
of brand i with a one percent change in the price of j. 95% con dence intervals in parentheses
Table 15: Mean Logit Console Elasticities-Model III
Gamecube Playstation 2 Xbox
Gamecube -2.0380 0.0378 0.0150
(-0.8906 , -3.1713 ) (0.0588 , 0.0165) (0.0233 , 0.0065)
Playstation2 0.0075 -3.6499 0.0150
(0.0117 , 0.0033) (-1.9254 , -4.7461) (0.0233 , 0.0065)
Xbox 0.0075 0.0378 -2.9115
(0.0117, 0.0033) (0.0588 , 0.0165) (-1.5359 , -3.7860)
Note: Cell entry i, j, where i indexes row and j column, give the percent change in market share
of brand i with a one percent change in the price of j. 95% con dence intervals in parentheses
relative competition among the three console makers.
Hardware-Software Elasticities
Theestimationofastructuraldemandmodelforvideogameconsolesallowsonetonot
onlyestimateconsolepriceelasticitiesbutallowthemarginale¤ectofaconsoleloosing
a video game title. Table 16 below illustrates the signi cant di¤erence between the
threediscusseddemandmodelsindeterminingtheimpactofloosingeachconsolestop
sellingvideogametitleinthe rstmonthofitsrelease. Themodelwhichaccountsfor
53
Table 16: Hardware-Software Elasticities from Losing the Top Selling Software Title
Random Coe¢ cient Logit Model I
Gamecube Playstation 2 Xbox
Gamecube -6.4485 0.0431 0.1111
Playstation2 0.2339 -0.7242 0.2334
Xbox 0.2178 0.0905 -5.6783
Random Coe¢ cient Logit Model II
Gamecube -0.1486 0.0010 0.0025
Playstation2 0.0054 -0.0162 0.0053
Xbox 0.0050 0.0020 -0.1303
Random Coe¢ cient Logit Model III
Gamecube -1.0772 0.0586 0.0207
Playstation2 0.0391 -0.9819 0.0435
Xbox 0.0364 0.1229 -1.0605
videogameheterogeneityandsoftwarecompetitionpredictsthetopselling rst party
video game to have a substantial impact on console shares while the two alternative
models predict minimal degree of substitution or di¤erences across consoles.
Goodness of Fit Test
In this section I test the t of the above model as well as the two alternative demand
modelsone which does incorporate video game di¤erentiation but omits competi-
tion and another which assumes all video games are homogeneous. I conclude my
methodologywhichmodelsvideogamedemandasamultinomiallogitperformsbetter
at tting the data than the alternative models.
The rst goodness-of- t test I implement is one which determines whether or not
54
allthemomentconditionsaresatis ed-atestofoveridenti cation. Theteststatistic
is theGMMobjectivefunctionandis aWaldstatistic.
25
It is distributedchi-squared
with degrees of freedom equal to number of moment restrictions minus the number
of estimated parameters. I nd all three models are not rejected at a con dence of
97.5%.
Ialsowouldliketotesttherelative toftheabovemodeltothemodelspresented
in the previous literature parametrically in order to determine which demand model
ts the data best; however, a formal test of a non-nested hypothesis requires addi-
tionalassumptionsonthedistributionoftheconsole-monthdeviation,
jt
,fromthe
meanunobservedproductcharacteristics. Withthegivendatasuggestingnonatural
assumption for the error distribution there are other methods in which I am able to
compare the above model to the two alternative models. One natural approach is to
look at the role unobservedproduct characteristics play. In each of the three models
the mean utility is chosen in order to match predicted market shares and observed
market shares. While there is no explicit role for video game heterogeneity in the
model which only employs the number of video games for the indirect network exter-
nality, I interpret the unobserved product characteristics terms (
jt
) as containing
this information. In order to gain insight into the importance of these unobserved
product characteristics as well as indicate how well the model ts the market shares
based solely on observables I restrict
jt
to zero and recalculate the predicted mar-
ket shares. I compare how close the "pseudo" market shares are to the observed in
25
Test statistic is the gmm objective function for optimal gmm estimators
55
Table 17: Goodness of Fit
Percent Difference from Observed Shares
Random Coe¢ cient Random Coe¢ cient II Random Coe¢ cient III
Gamecube 19.14% 27.41% 27.50%
Playstation 2 38.00% 40.85% 40.85%
Xbox 21.81% 27.17% 27.39%
Total 26.32% 31.81% 31.91%
Sum of Squared Errors
14.9382 23.3435 23.5254
Notes: Predicted market shares are evaluated at parameter estimates with unobserved product attributes restricted to zero
order to determine whether the model employing the number of video games ts the
data better than a model which accounts for video game heterogeneity. The results
of the closeness measure are presented in Table 17. The homogeneous video game
model does not predict market shares nearly as well as a methodology which incor-
porates video game heterogeneity and software competition. It is no surprise
jt
plays a larger role in the homogeneous setting given the fact there is survey support
to conclude consumers do indeed value video game quality. An alternative method
is to look at a statistic such as the sum of the squared errors across each model.
The conclusions from this method are consistent to those presented with the prior
testdescribedabovethemodelwhichallowsforvideogamecompetitionandproduct
di¤erentiation ts the data better than either of the alternative models.
56
Chapter III
Console Supply Model
InthischapterIinvestigatetheimpactofverticalintegrationwithtwocounterfactual
simulationsusingtheestimatesofthedemandparametersfoundinthepreviouschap-
ter. Thetwocounterfactualsimulationsarei)all rst party gamesareprohibitedand
ii) rst party games become independent exclusive third party titles.
26
Furthermore,
I study the importance of incorporating video game heterogeneity and software com-
petition into the indirect network externality as well as a two-sided market structure
by simulating the same counterfactual experiment using previous research methods.
Iconcludeitisessentialtomodelthedemandforvideogameswellgiventhatconsole
demandisderivedfromvideogamedemand. Theintroductionofaconsolemanufac-
turespro tfunctionisnecessaryinordertoperformanycounterfactualsexperiment
and thus to study the importance of properly modeling the video game industry . I
discuss the pro t function below along with all assumptions.
26
Note: a rst party title is a game which is produced by a console manufacturer ie: Nintendo,
Microsoft or Sony
57
Pricing
Each console producer sets price in order to maximize pro ts. Moreover, makers
of consoles act myopically. The pro t function of a console manufacturer di¤ers
from that of a standard single product rm. Console rms face three streams of
pro ts (selling consoles, selling video games and licensing the right to produce a
game to game developers) and take each into consideration when setting console
price. Assumeconsoleproducersfaceamarginalcostoftwodollarswheninteracting
with game developers (this cost is associated with the production and packaging of
video games).
27
Additionally, a developers marginal cost for a game equals the
royalty rate charge by a console and is set at ten dollars per game.
Assumption 1: Console producers, game developers and consumers all act my-
opically
Assumption2: Console rmsfaceamarginalcostoftwodollarswheninteracting
with game developers
Assumption 3: Developer s marginal cost equals the royalty rates charged by
console manufacturer and is set at ten dollars per game.
28
27
Game developers do not actually create the physical disk which is sold to consumers. Instead,
the console manufacturer stamps all video games for quality control purposes
28
Assumptions two and three are made from inside knowledge regarding the industry
58
Console makerj
0
s pro t function in timet is
jt
= (P
jt
mc
jt
)M
t
S
jt
(P;X;;
hw
)
+
P
d
(IB
jt1
+M
t
S
jt
(P;X;;
hw
)
| {z }
Potential Market for game d=IB
jt
)S
dt
()(p
dt
c)
+
P
k
(IB
jt1
+M
t
S
jt
(P;X;;
hw
)
| {z }
Potential Market for game k=IB
jt
)S
kt
()(rc)
whereP
jt
istheconsoleprice,mc
jt
theconsolemarginalcost,M
t
thepotentialmarket
for consoles, S
jt
is the average probability consumers purchases console j; IB
jt1
is
the number ofj consoles sold up to and including periodt1,S
dt
is the probability
game d, which is produced by the console manufacturer, is purchased by consumers
and S
kt
is the probability consumers purchase game k, a third party game. Lastly,
IB
jt
is the installed base of consolej and the potential market size for a video game.
The above pro t function di¤ers from a standard single product pro t function
in that there are two additional pro t streams. The rst term is the usual single
productpro t. Thesecondandthirdtermsarepro tstheconsolemakerreceivesfrom
interacting with game developers and selling its own games. Speci cally, the second
termisthepro taconsolemakergarnersfromcreatingandsellingitsowngamesand
thethirdtermisthepro titreceivesfrom third party developers. Theresulting rst
order condition with respect to console price for the above pro t function in matrix
59
notation is
S(P)
1
+P mc+
= 0:
jt
=diag
@S
jt
()
@P
j
t
jt
=
P
d
S
dt
()(p
dt
c)+
P
k
S
kt
()(rc)
where
is the pro t a console producer receives from third party developers and
selling rst party games when one additional console is sold.
Although I do not simultaneously estimate the price equation with the demand
model, I use the above rst order conditions to infer marginal cost. Rewriting the
rst order conditions, marginal cost equals:
mc =P +S(P)
1
+
:
From the rst order conditions the impact of vertical integration is evident (by
rearranging the rst order condition for price P =mcS(P;X;;
hw
)
1
the
e¤ectbecomesmoreclear). Therearetwoopposingtrade-o¤s. The rstisademand
or di¤erentiation e¤ect while the second is a market structure e¤ect. In order to
see these e¤ects mathematically allow consolej to design and produce one vertically
integratedgamedandinteractwithaportfolioofthirdparty developerswhilebanning
all other console makers from designing any rst party games. Suppose the utility
associated with game d increases,
d
. What are the e¤ects? The utility for console
60
j increases through the indirect network externality creating greater di¤erentiation
between consoles. This e¤ect is the demand e¤ect. The second trade-o¤ is a
market structure e¤ect. With producer of console j designing and selling game d;
the pro t adjusts to reex the fact that gamed
0
s attractiveness increases. Designate
this pressure on price as the market structure e¤ect.
Proposition 1 There are two console price e¤ects given an increase in
d
- a demand
and a market structure
Proof. For a logit demand model (the results hold for a random coe¢ cient logit
demand model)
@P
j
@
d
=
@S
j
(P)
@
j
@
j
@
d
1
j
S
j
(P)
@
1
j
@S
j
(P)
@S
j
(P)
@
j
@
j
@
d
@S
d
()
@
d
(p
d
c)
X
k
@S
k
()
@
d
(rc)
@P
j
@
d
=
@S
j
(P)
@
j
@
j
@
d
S
j
(P)
@
1
j
@S
j
(P)
1
j
!
@S
d
()
@
d
(p
d
c)+
X
k
@S
k
()
@
d
(rc)
!
@P
j
@
d
=S
j
(1S
j
)S
d
S
j
2S
j
fS
j
(1S
j
)g
2
1
S
j
(1S
j
)
!
| {z }
Demand E¤ect
S
d
(1S
d
)(p
d
c)
X
k
S
d
S
k
(rc)
!
| {z }
Market Structure E¤ect
The last equation in the above proof illustrates the two e¤ects that a change in
the attractiveness of game d has on console price. The rst half of the equation is
the demand e¤ect or the impact a change in the attractiveness of game d brings to
the standard product margin. The second half is the market structure e¤ect or the
impactanincreasein
d
hasonmarginalrevenuefromdesigningandproducinggame
daswellasinteractingwiththirdparty developers. Furthermore,themarketstructure
61
e¤ectcanbedecomposedintotwoe¤ects,S
d
(1S
d
)(p
d
c)and
P
k
S
d
S
k
(rc): The
rst term represents the additional pro t console maker receive from its rst party
game when its attractiveness increases. The increase leads to a greater probability
thataconsumerpurchasesgamed: Nonetheless,suchanincreasecomesatacostthe
probability that a consumer purchases any third party game decreases. The console
makers expected pro t from interacting with third party developers thus decreases,
which is represented by the second term. In the following two propositions I show
that both the demand and market structure e¤ects are positive.
Proposition 2 Given an increase in
d
andS
j
<
1
2
the demand e¤ect will increase
console price
Proof.
S
j
(1S
j
)S
d
S
j
12S
j
fS
j
(1S
j
)g
2
1
S
j
(1S
j
)
!
>0
S
d
S
j
12S
j
2
S
j
(1S
j
)
1
>0
S
j
12S
j
2
S
j
(1S
j
)
>
1
12S
j
1S
j
>
S
j
<
1
2
62
Proposition 3 Given an increase in
d
the market structure e¤ect will decrease con-
sole price
Proof.
S
d
(1S
d
)(p
d
c)
X
k
S
d
S
k
(rc)> 0
(p
d
c)
(rc)
>
P
k
S
k
(1S
d
)
by assumption of the magnitude of r;c; and
(p
d
c)
(rc)
1
P
k
S
k
(1S
d
)
< 1
S
d
+
X
k
S
k
< 1
By de nitionS
d
+
X
k
S
k
< 1
sinceS
d
+
X
k
S
k
+S
0
= 1
ThepresentedexperimentisanalogoustoasituationwhereIallowaconsoleman-
ufacturer to add one new rst party game. However, I employ the above scenario
in order to show both the demand and market structure e¤ect in the same scale. A
console is able to generate a demand e¤ect by vertically integrating since the games
which are produced by the console maker are always exclusive to the console. Like-
wise, if a game is not on a given console and a consumer wants to play this game he
must purchase the respective console which therefore increases the demand for the
63
consoleanditsmarketpower. Donotethatindirectnetworke¤ectsarepresentwith-
out vertical integration but if all games which are not produced by console makers
areavailableonallconsolesthantheindirectnetworke¤ectdoesnotprovideanyad-
ditionaldi¤erentiation. Itisverticalintegrationwithexclusivitythatcreatesfurther
di¤erentiation. In conclusion, the above propositions demonstrate that determining
the e¤ect of vertical integration on console price is an empirical question.
Theabovediscussiondirectsitsanalysistowardthecounterfactualwhichlooksat
theimpactofcompletelyeliminating rst party games. Theanalysischangesslightly
when studying the counterfactual which converts rst party games to exclusive third
party games. Under "what if" scenario two, I assume there is no reduction in the
number of video games available during a given time period. What were once verti-
cally integrated video games are now independent exclusive third party video games.
Consequently, there is no demand e¤ect. The only e¤ect is the market structure,
whichcanalsobedescribedasadoublemarginalizatione¤ect. Thedoublemarginal-
ization e¤ect is present since console manufacturers and video game developers are
forcedtobeindependentfromeachotherwhichconsequentlyeliminatesanye¢ ciency
derivedfromcoordinatinginprice. Put di¤erently, when rms become disintegrated
thereisaneliminationofane¢ ciencygainfromasingleintegrated rminternalizing
the e¤ects that console and video game pricing has on each other causing prices of
consoles to increase.
29
This can be see from the rms rst order condition with
29
Speci cally both priecs of consoles and games will adjust but for the counterfactual exercise I
hold video game prices xed
64
respect to console price.
S(P)
1
+P mc+
= 0:
jt
=diag
@S
jt
()
@P
jt
jt
=
P
d
S
dt
()(p
dt
c)+
P
k
S
kt
()(rc)
When rms disintegratethereis areductionin
jt
: Underthis scenario
jt
nolonger
is a function of pro t from rst party games and third party software but instead
is only made up of pro t from third party developers. Note that this is not exactly
identical to the meaning of double marginalization in the theoretical industrial orga-
nizationliteratureonverticalintegrationdotoconsolesandvideogamesnotliterally
being vertical to each other. I also do not refer to the above market structure e¤ect
associated under counterfactual experiment one as a double marginalization e¤ect to
remain consistent with the economic literature. Given that all rst party games are
eliminated there is an additional supply side e¤ect in addition to a double marginal-
ization e¤ect.
Supply Model for Alternative Models:
Model 2: Video game heterogeneity, no video game competition
The price structure associated with this model is identical to the above model.
65
The rst order condition with respect to console price is
S(P)
1
+P mc+
= 0:
jt
=diag
@S
jt
()
@P
jt
jt
=
P
d
S
dt
()(p
dt
c)+
P
k
S
kt
()(rc):
Model 3: Number of games
Unlike the previous two models, the associated indirect network e¤ect is a simple
count of video games available on each console. Implementing the counterfactual ex-
periment requires a console pro t function which di¤ers from the ones above. The
function is identical to the one employed above but with the elimination of the addi-
tional revenue the console receives from interacting with game developers and selling
its own games. I use this pro t function as a result of it being standard practice in
thecurrent literature onindirect networke¤ects (e.g. Clements andOhasi &Huand
Prieger). The pro t for consolej is
jt
= (P
jt
mc
jt
)M
t
S
jt
(P;X;;
hw
)
with the rst order condition equal to, in matrix notation,
S(P)
1
+(P mc) = 0:
66
Table 18: Implied Marginal Cost and Markups
Mean Marginal Cost Mean Markup (%)
Gamecube 92.7074 31.00
Playstation2 175.0610 28.64
Xbox 136.5501 27.38
Implied Marginal Cost and Margins
In Table 18 I present the mean marginal cost and percent markup associated with
the rst demand model and a pro t function which includes all pro t streams. By
employing the rms rst order condition and knowledge of the estimated demand
parameters I recover the implied marginal cost and rm markups. I nd contrary
to popular belief, consoles do indeed generate variable pro ts for console makers.
However, the implied markups consist of rm and retail markups. Taking into
account a retailers margin of roughly 10% console makers receive less than a twenty
percent markup on each console sold. In a section below I discuss how the estimated
marginal costs and markups di¤er across demand and supply models and how they
impact predicting the e¤ects of vertical integration.
Counterfactual Simulation
Determiningthee¤ectsfromverticalintegrationrequirestheimplementationofcoun-
terfactual exercises. Since the data in hand permits vertical integration to occur I
assume two "what if" situation in which all rst party games are removed from their
67
respective consoles and are not produced and a second scenario which transfers rst
party games to an independent third party game developer which has an exclusive
contract with the respective console. These two counterfactual experiments pro-
vide an upper and lower bound as to the e¤ects the industry would see if a policy
eliminating vertical integration was implemented.
Determiningtheimpactofverticalintegrationusingacounterfactualmethodology
requiresafewassumptionsregardingthepricingofvideogames. The rstassumption
is that video game prices do not adjust to changes in competitive environments.
30
And the second is that console manufacturers issue the same royalty rates to all
games and do not vary across console producers.
31
Console Supply
With the above assumptions along with estimated demand parameters and marginal
costsofconsolesconsolemakerj
0
spro tfunctionunderthecounterfactualexperiment
where consoles are unable to produce video games is
jt
=(
b
P
jt
mc
jt
)M
t
S
jt
(
b
P;X;
b
;
hw
)+
P
k
(IB
t1
+M
t
S
jt
(
b
P;X;
b
;
hw
))
b
S
kt
()(rc)
30
The di¤erence between the average price of a rst party and third party games is roughly sixty-
ve cents. I thus infer that any change in price as a result of change in who sets video game price
would be minimal
31
The last assumption is supported by knowledge from an industry insider
68
where
b
P
jt
;
b
;
b
S
kt
are new equilibrium prices, new video game index and new equilib-
riumgamepurchaseprobabilities,respectively. Itisquiteevidentthattheadditional
pro t stream from selling rst party games is omitted under the counterfactual sce-
nario.
Given a pure-strategy Bertrand-Nash equilibrium in prices and that the prices
that support the equilibrium are strictly positive, then the new equilibrium price
vector must satisfy the rst-order conditions
S(
b
P;
b
)
1
+
b
P mc+
b
= 0
jt
=diag
@S
jt
()
@P
jt
c
jt
=
P
k
b
S
kt
()(rc):
Dissimilartothescenarioinwhichamanufacturecanproducevideogamesacon-
soles markupis afunctionof the inverse price derivative, the probabilitya consumer
purchases console j and the additional pro t associated with interacting with third
party game developers when on more console is sold.
Counterfactual Supply Model for Alternative Models:
Model 2: Video game heterogeneity, no video game competition
With video games placed into individual markets there exists no competition
amongvideogames. Thus,unlikemodelonewhichallowsforvideogamecompetition
and for third party games to partially o¤set the impact of eliminating rst party
69
games this model does not. The purchase probability for third party video games,
consequently, does not change when rst party games are banned. The rst order
condition with respect to console price under this model with vertical integration
prohibited is
S(
b
P;
b
)
1
+
b
P mc+
b
= 0:
jt
=diag
@S
jt
()
@P
jt
c
jt
=
P
k
S
kt
()(rc)
and is identical in structure to the counterfactual supply model presented previously.
Model 3: Number of games
With the number of games acting as the measure of the indirect network exter-
nality and a pro t function which only includes the pro t from selling video game
consoles,the rstorderconditionwhen third party gamesaresolelyproducedchanges
only when video games are completely eliminated. Thus, the new equilibrium prices
aredrivenbythedemande¤ect, nomarketstructuree¤ectsexistandisevidentfrom
the rst order condition below.
S(
b
P;
b
)
1
+(
b
Pmc) = 0:
Solving for New Equilibrium Prices
Solvingfornewequilibriumpricesrequirestheuseofanumericalalgorithm. The
70
algorithm nds the new equilibrium price vector which solves the FOC under the
counterfactual experiment given the estimated demand parameters and console char-
acteristics. In solving for new prices I generate new marginal revenues from video
games when one additional console is sold. Moreover, the formulation of the mar-
ginal revenues associated with the counterfactual experiment allows new equilibrium
sharesforvideogamestobedetermined. Theseshares, however, arecalculatedwith
video game prices remaining unchanged. The algorithm used is the nonlinear system
of equations solver in Mathlab, fsolve.
Counterfactual Results
The results of counterfactual simulation one are presented in Table 19 while coun-
terfactual two are in Table 21.
32
The outcome from vertical integration is clear:
console price competition increases. Moreover, rst party games bene t Microsoft
and Nintendo. The rst counterfactual predicts Nintendos price for Gamecube to
increases on average 5:36 percent while Microsofts Xbox price rises an average of
2:32 percent and Sonys price by 1 percent when rst party games are eliminated.
The increase in price provides support to conclude the market structure dominates
the demand e¤ect. I also compute new console shares. The increase in the price of
Xbox and Gamecube decrease their respective shares by an average of two and three
quarter and three quarters percentage points which leads to an increase in industry
32
All results are calulated as a weighted average. The weight is the proportion of sales in each
month relative to aggregate sales.
71
concentration. One explanation as to why prices increase more for Microsoft and
Nintendo than for Sony is a result of these two console makers producing "hit" rst
party games. Similarly, the production of rst party games for Sonys Playstation
2 results in an increase in price but by a lesser amount than its competitors, roughly
onepercentandariseinthemeanmarketsharebythreeandahalfpercentagepoints.
The result is a consequence of the fact that the model accounts for fewer "hit" rst
party gamesforSonythanMicrosoftandNintendo,aresultofSonysdecreaseinmar-
ginal revenue from video games under the policy banning rst party software being
substantially smaller than those of its competitors.
Table 20 shows the ten leading titles on each platform for the given time period,
nine of which are rst party titles for Nintendo and four for Microsoft. The banning
of these top selling games in addition to all other rst party titles homogenizes the
consoles as well as forces consoles to be less attractive since gamma, the expected
utilityfromchoosingfromasetofavailablevideogames,issmallerwhichdrivesprice
lower via the demand e¤ect. In particular, the e¤ect is substantially larger for Nin-
tendo and Microsoft since nine out of Nintendo s top ten games are rst party titles
while four of Microsofts top games are designed in house. However, the additional
pro t console makers receive from developers when one more console is sold is now
only a function of its interactions with third party developers and not its rst party
games. This reduction consequently increases price relative to a scenario which per-
72
Table 19: Counterfactual Results
w/o VI w/ VI
Mean Price Gamecube $138.70 $131.66
Playstation 2 $246.97 $244.44
Xbox $191.74 $187.36
Mean Price E¤ect Gamecube 5.36%
Playstation 2 0.98%
Xbox 2.32%
Mean % Market Share Gamecube 17.45% 20.30%
Playstation 2 56.52% 52.95%
Xbox 26.02% 26.75%
Mean Number of Consoles Sold Gamecube 267,160 378,660
Playstation 2 908,560 958,260
Xbox 396,140 461,540
Total Number of Consoles Sold (M) 31.555 34.55942
Mean Variable Pro t (M) Gamecube $25.890 $60.590
Playstation 2 $134.120 $166.230
Xbox $41.730 $68.270
Mean Variable Pro t From Games (M) Gamecube $14.557 $48.080
Playstation 2 $69.728 $101.360
Xbox $21.515 $47.210
Mean Compensating Variation (M) $22.080
73
mitsverticalintegration. I ndthatthemarketstructuree¤ecto¤setsandovercomes
the demand e¤ect.
In addition to illustrating that Nintendo and Microsoft are quite reliable on its
production of hit rst party games through a list of top ten video games, my model
can also show the bene t each game brings to its respective console. In Table 16
above I provide console elasticities from losing the consoles top selling rst party
video game. The elasticities show the change in console share in the rst month in
whichthe"hit"gamewasreleased. Ialsoshowhowcompetingconsolesbene twhen
a competing console loses a "hit" title. The table illustrates the sizable impact the
loss of such games have on Gamecubes and Xboxs console share.
After establishing the market structure e¤ect dominates the demand e¤ect I ana-
lyze console manufacturer pro ts. I determine the pro t manufacturers receive from
sellingconsolesunderthepolicywhichbansverticalintegrationissmallerthanunder
a policy which allows vertical integration. The intuition is that although console
prices rise when vertical integration is prohibited the percentage reduction in the
number of consoles sold is larger than the increase in price. Furthermore, the reduc-
tion in the number of consoles sold consequently decreases the demand for software
and thus reduces the pro t manufacturers receive from video games. Average total
console pro ts decrease when vertical integration is banned. Or alternatively put,
when vertical integration is permitted it drives console prices lower which in turn
74
Table 20: Top 10 Video Game Titles
Console Title Publisher Quantity
Gamecube MARIO KART: DOUBLE NINTENDO 1,731,903
SUPER SMASH BROTHER MELEE NINTENDO 1,028,343
ANIMAL CROSSING NINTENDO 799,842
MARIO PARTY 5 NINTENDO 774,623
SOUL CALIBUR II NAMCO 718,395
LUIGIS MANSION NINTENDO 702,401
POKEMON COLOSSEUM NINTENDO 698,449
SUPER MARIO SUNSHINE NINTENDO 600,091
ZELDA: THE WIND WAKER NINTENDO 547,067
METROID PRIME NINTENDO 499,929
Playstation 2 GRAND THEFT AUTO:VICE CITY TAKE 2 INTERACTIVE 6,315,099
GRAND THEFT AUTO 3 TAKE 2 INTERACTIVE 5,194,262
GRAND THEFT: ANDREAS TAKE 2 INTERACTIVE 3,590,284
MADDEN NFL 2004 ELECTRONIC ARTS 3,419,157
GRAN TURISMO 3:A-SPEC SONY 2,781,235
MADDEN NFL 2003 ELECTRONIC ARTS 2,727,112
FINAL FANTASY X SQUARE ENIX USA 2,192,461
MEDAL HONOR FRONTLINE ELECTRONIC ARTS 2,185,916
KINGDOM HEARTS SQUARE ENIX USA 2,120,314
NEED SPEED: UNDERGROUND ELECTRONIC ARTS 2,111,249
Xbox HALO MICROSOFT 3,789,232
HALO 2 MICROSOFT 1,777,697
HALO 2 LIMITED ED MICROSOFT 1,489,406
T.CLANCYS SPLINTER UBISOFT 1,483,843
GRAND THEFT AUTO PACK TAKE 2 INTERACTIVE 1,200,618
PROJECT GOTHAM RACING MICROSOFT 1,188,976
T.CLANCYS GHOST RECON UBISOFT 965,620
ESPN NFL 2K5 TAKE 2 INTERACTIVE 938,203
DEAD OR ALIVE 3
STAR WARS: KNIGHTS
TECMO
LUCASARTS
885,781
881,740
75
raises console sales and thus increases video game demand. Console makers there-
fore use vertical integration in order to drive sales of video games, in particular their
own rst party games, where the "real" pro ts are made.
The bene t of estimating a structural model is the ability to analyze consumer
welfare. I quantify the change in consumer welfare using compensating variation.
Forthe presentedmodel the compensating variation quanti es the amount of income
necessary to maintain a consumers utility at levels associated with vertical integra-
tion. It equals
CV
i
=
1
hw
i
CS
i
CS
0
i
CS
i
=ln
(
1+
J
P
j=1
exp[
hw
i
p
jt
+X
jt
hw
+
jt
+
jt
]
)
CS
0
i
=ln
(
1+
J
P
j=1
exp[
hw
i
p
0
jt
+X
jt
hw
+
0
jt
+
jt
]
)
per individual or
M
R
CV
i
dP
v
(v)
for the mean compensating variation in the population. The mean compensating
variation needed to hold the populationsutility at the level associated with verti-
cal integration is on average $22:08 million dollars. Vertical integration enhances
consumer welfare.
76
In summary, the market structure dominates the demand e¤ect for all consoles.
Pricesof consoleswithalargerdegreeof concentrationinverticallyintegratedgames
fall more than consoles with less when vertical integration is permitted. As a result,
consumer welfare increases an average $22:08 million dollars per month. Likewise,
pro ts increase.
Thesecondcounterfactualdi¤ersfromtheoneabovebyallowing rst party games
tostillbeproduced. InsteadofeliminatingthesegamesIallowthemtobecomethird
party exclusive video games. In doing so, the associated demand e¤ect disappears
while the market structure e¤ect remains. Consequently, video game console prices
will rise when rst party games are banned. This is a direct result of
diminishing
under such a scenario relative to the circumstance in which all console manufactured
games are produced. Or put di¤erently, the elimination of console manufacturers
internalizing the e¤ects that its console pricing decision has on its own rst party
games. I nd console price competition decreases when vertical integration is pro-
hibited. Console prices rise on average 4:7901; 0:7094; 1:9800 percent for Nintendo,
Sony, and Microsoft, respectively. However, these increases in price are not as large
as those presented above.
Theresultsofeachcounterfactualareinterpretedasboundsforwhatwouldlikely
occur in practice, a number of rst party games being completely eliminated while
others are produced. Similar to the rst counterfactual scenario, the increase in the
price of Xbox and Gamecube in the second scenario decrease their respective shares
77
which leads to an increase in industry concentration. The explanation as to why
prices increase more for Microsoft and Nintendo than for Sony in the rst exercise
also holds here. These two console makers produce more "hit" rst party games,
relative to Sony. The production of rst party games for Sonys Playstation 2
likewise results in an increase in price but by a lesser amount than its competitors
and a rise in the mean market share. The result is due to the fact that the model
accounts for fewer "hit" rst party games for Sony than Microsoft and Nintendo.
Sonys decrease in video game marginal revenue when an additional console is sold
under the policy banning rst party software is substantially smaller than those of
its competitors. Also note, under the second counterfactual scenario there is no
substitution to third party games when rst party games are eliminated which would
partially o¤set the impact of the market structure e¤ect. Instead, the additional
pro t a console maker receives from rst party games is the same royalty payment
it levies on third party titles. Table 20 above shows the ten leading titles on each
platform for the given time period, nine of which were rst party titles for Nintendo,
four for Microsoft and one for Sony. The switching of these top selling games in
addition to all other rst party titles to third party games eliminates the substantial
premium console developers receive from selling their own games. Thus, console
manufacturer pro ts are smaller than when vertical integration is permitted.
Likethe rstcounterfactualexerciseIestimatethecompensatingvariationneeded
toholdconsumerwelfareconstantunderthesecondregime. I ndthemeancompen-
78
sating variation to be smaller under counterfactual two than for scenario one. The
estimated mean compensating variation is 7:7548 million dollars. The intuition for
this is quite simple. It is a result of the smaller increase in price associated with the
counterfactualregimeandtheomissionofdecreasedutilityfromreducingthenumber
of available video games associated with a console in a given time period. Regardless
ofhowonede nesthebasepointinwhichtocomparetheresultofverticalintegration
to, it is quite evident that console price competition and consumer welfare increases.
Sensitivity Analysis
Market Structure
I now test the importance of properly modeling the console supply model, which
includes the multiproduct pricing associated with the industry. When a console
manufacturer optimally sets console price, console prices not only e¤ect console de-
mand but also aggregate video game demand and the revenue the manufacturer can
receive from video game developers. For this sensitivity test I eliminate the market
structure e¤ect and impose a traditional pricing equation, which results in a new
margin estimate. To be speci c, a substantially larger margin estimate. As is seen
in the equations below the pro t function as well as the product margin no longer
includes the expected pro t from video games when one more console is sold.
79
Table 21: Counterfactual II Results
w/o VI w/ VI
Mean Price Gamecube $137.95 $131.66
Playstation 2 $246.21 $244.44
Xbox $191.09 $187.36
Mean Price E¤ect Gamecube 4.79%
Playstation 2 0.71%
Xbox 1.98%
Mean % Market Share Gamecube 18.88% 20.30%
Playstation 2 54.65% 52.95%
Xbox 26.47% 26.75%
Mean Number of Consoles Sold per Month Gamecube 323,110 378,660
Playstation 2 943,920 958,260
Xbox 433,940 461,540
Total Number of Consoles Sold (M) 33.311 34.55942
Mean Variable Pro t per Month (M) Gamecube $32.150 $60.590
Playstation 2 $140.840 $166.230
Xbox $47.180 $68.270
Mean Variable Pro t From Games per Month (M) Gamecube $18.707 $48.080
Playstation 2 $74.552 $101.360
Xbox $25.331 $47.210
Mean Compensating Variation per Month (M) $7.7548
80
Table 22: Price E¤ects with an Incorrect Supply Model
w/o VI w/ VI
Mean Price Gamecube $129.94 $131.66
Playstation 2 $244.37 $244.44
Xbox $185.77 $187.36
Mean Price Effect Gamecube -1.178%
Playstation 2 -0.023%
Xbox -0.703%
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The test results are drastically di¤erent from the above counterfactual. Console
prices are no longer higher under the scenario in which rst party games are elimi-
nated. Nintendos and Microsofts prices fall by 1.18 and .70 percent while Sonys
price falls by .02 percent. It is clear from this analysis that imposing the proper
supply equation, which accounts for the multiproduct price is necessary to recover
proper estimates of the e¤ects from eliminating all rst party games.
In order to further illustrate the impact of incorrectly modeling the supply model
Ipresentthemeanandmedianestimatesoftheconsolemarginsandmarkupsundera
proper and improper supply equation in Table 23. The estimates of console margins
81
Table 23: Implied Markups and MarginsIncorrect Supply Model
Correct Supply Model Incorrect Supply Model
$ % $ %
Median 54.05 30.57 58.63 32.62
Mean 56.33 30.95 61.50 34.04
% of Estimated Marginal Cost <0 0 0
Table 24: Implied Mean Marginal Cost and MarkupsIncorrect Supply Model
Correct Supply Model Incorrect Supply Model
Marginal Cost Markup (%) Marginal Cost Markup (%)
Gamecube 92.7074 31.00 83.3365 38.27
Playstation2 175.0610 28.64 170.0506 30.70
Xbox 136.5501 27.38 129.5441 31.14
and markups are substantially smaller under the correct supply model. Signally
again, the importance of incorporating all console pro t streams.
Table 24 provides marginal cost and markup estimates predicted under a proper
supplysidedmodelandonewhichdoesnotincludepro tsfrominteractingwithvideo
game developers and selling rst party games. As the table illustrates the marginal
cost estimates associated with the correct supply model are larger than those for
incorrect model. The marginal cost estimates for an incorrect model are equal to
the marginal costs measures from a correctly speci ed pro t function less the pro t
a console maker receives from selling its own video games and interacting with third
party game developer when one additional console is sold (
):
82
With the implementation of these sensitivity tests, I determine that correctly
modelingthe rmspro tfunctionandthustheconsolepricestructureisanimportant
issue in order to predict unbiased e¤ects from vertical integration. Without the
inclusion of multiproduct pricing associated with a two-sided market, predictions
regarding the impact from producing rst party games on console price competition
will be understated.
Video Game Heterogeneity
Below I present counterfactual results for the two alternative models which look at
the importance of video game heterogeneity in determining the impact on console
price competition. I compare the simulation results in Table 19 to those employing
the number of available video games as the indirect network e¤ect and a traditional
"one-sided" market structure in addition to a model which incorporates video game
heterogeneity and a two-sided market structure but does not allow for software com-
petition as robustness checks. Implementing a methodology which does not account
for video game heterogeneity nor the two-sided nature of the industry consequently
results in a decrease in price when vertical integration is banneda result counter
to the those found above. The mean decrease in console prices is 0:63 percent for
Gamecube, 0:27 forXboxand 0:15 percent forPlaystation 2. Market shares forcon-
soles change appreciably; they become more compressed with Playstation 2s share
fallingfromroughly52:95%to45:17%,whileXboxandGamecubegainroughlythree,
and ve percentage points, respectively. The average number of consoles sold per
83
month for each manufacturer decreasesalmost 314 thousand units for Sony, twenty-
ve thousand for Nintendo and eighty thousand for Microsoft. The cause of the
decrease in consoles sold is the elimination of rst party games. Some consumers
substitute to an alternative console in the counterfactual simulation, while a large
number of consumers elect not to purchase a console as a result of their decreased
attractiveness. Nintendo, Microsoft and Sony all see similar results but Nintendo
and Microsoft are impacted less than Sony, a consequence of each having a smaller
number of rst party games than Sony.
33
Counterfactual results for this model are presented in Table 25.
I next analyze a model which does not allow consumers to substitute between
video games but does account for game quality di¤erences and the two-sided market
structure. Given the assumptions of this model, the impact on console pricing is
largerthanthee¤ectpredictedbythemodelwhichallowsforvideogamesubstitution.
This model over estimates the e¤ect on price compared to my more exible model.
The overestimation of the price e¤ect is a direct result of howvideo game demandis
linked to console demand. Moreover, since there is no video game competition third
party games are unable to partially o¤set the impact of eliminating all rst party
games via consumer substitution. Given this alternative model, consumers only
substitute to the outside product of not purchasing. Prices rise by 6:46, 1:38, 3:18
33
See Table 1 for review of the number of rst party games in January of 2002, 2003 and 2004
84
Table 25: Counterfactual Results-Random Coe¢ cient Logit Model III
Counterfactual I w/ VI
Mean Price Gamecube $130.60 $131.66
Playstation 2 $244.13 $244.44
Xbox $186.42 $187.36
Mean Price E¤ect Gamecube -0.63%
Playstation 2 -0.15%
Xbox -0.27%
Mean % Market Share Gamecube 25.18% 20.30%
Playstation 2 45.17% 52.95%
Xbox 29.65% 26.75%
Mean Number of Consoles Sold per Month Gamecube 350,570 378,660
Playstation 2 644,960 958,260
Xbox 382,050 461,540
Total Number of Consoles Sold per Month (M) 29.145 34.559
Mean Variable Console Pro t per Month (M) Gamecube $15.703 $16.820
Playstation 2 $47.116 $68.621
Xbox $20.436 $24.306
Mean Compensating Variation per Month (M) $22.293
85
percentforNintendoGamecube,SonyPlaystation2andMicrosoftXbox,respectively.
The model also predicts consumer welfare to decreases an average of $66:964 million
dollars when vertical integration is prohibited, an amount three times the size of the
model above. Average console market shares are calculated and determined to move
intheoppositedirectionasseeninmymoreexiblemodelabove. Consolesharesfall
drastically for Sony Playstation 2 and rise substantially for Nintendo and Microsoft
for this model , roughly ve and half, three, and two and half percentage points for
Sony,NintendoandMicrosoft,respectively. Asaresult,theindustryconcentrationis
reduced. Likethemodelwhichemploysthenumberofgames,theaveragenumberof
monthly consoles sold for each manufacturer decreases. I nd the decline is roughly
335 thousand units for Sony, 113 thousand for Nintendo and ninety-four thousand
for Microsoft, all larger than what the model using only the number of video games
predicts. The cause of the decrease is a consequence of the higher prices but also the
elimination of the rst party games. Although the formulation of the inclusive value
doesaccountforvideogameheterogeneityitdoesnotsubstantiallydi¤erentiateitself
fromusingthenumberofvideogamesaconsequenceofnotpermittingconsumersto
substitutebetweenvideogames. Withbothmeasurescloselyrelateditisnosurprise
toseethemeanmarketshareforeachconsoleonlyslightlydi¤erentthanthoseunder
a model which assumes video games are homogeneous.
86
Table 26: Counterfactual Results-Random Coe¢ cient Logit Model II
Counterfactual I Counterfactual II w/ VI
Mean Price Gamecube $140.10 138.64 $131.66
Playstation 2 $257.95 247.32 $244.44
Xbox $193.35 192.35 $187.36
Mean Price E¤ect Gamecube 6.46% 5.31%
Playstation 2 1.38% 1.13%
Xbox 3.18% 2.64%
Mean % Market Share Gamecube 23.13% 23.44% 20.30%
Playstation 2 47.56% 47.21% 52.95%
Xbox 29.31% 29.35% 26.75%
Mean Number of Consoles Gamecube 283,900 295,030 378,660
Sold per Month Playstation 2 623,620 629,130 958,260
Xbox 348,630 355,060 461,540
Total Number of Consoles Sold (M) 24.403 24.710 34.5594
Mean Variable Pro t per Month (M) Gamecube $23.903 $29.740 $60.010
Playstation 2 $97.356 $104.820 $163.010
Xbox $35.245 $40.060 $67.310
Mean Variable Pro t From Gamecube $11.714 $17.670 $48.080
Games per Month (M) Playstation 2 $53.839 $61.516 $101.360
Xbox $17.466 $22.405 $47.210
Mean Compensating Variation $66.964 65.401
per Month (M)
87
In comparing the two alternative models to the more exible model above, I nd
both video game heterogeneity and competition to be important aspects to capture.
Models used in the previous literature are unable to su¢ ciently account for the con-
centration(success) of verticallyintegratedgames forNintendoandMicrosoft. Video
game heterogeneity, software competition and a two-sided market structure are thus
industry characteristics which need to be accounted for in order to properly model
the industry. Any model which does not correctly incorporate these characteristics
will over estimate the impact of console demand on Sony and under estimate the ef-
fect on Nintendo. Additional consequences are the formulation of conclusions which
i) over predicts the change in price competition and foresees a reduction of industry
concentrationorii)predictspricecompetitionandindustryconcentrationtodecrease
when vertically integration is prohibited, both of which are counter to what a more
exible and structurally consistent model calculates. It is thus extremely important
to correctly model the industry for policy reasons.
88
Chapter IV
Conclusion
This dissertation analyzes the impact of vertical integration on console price com-
petition. I conclude vertical integration in the video game industry increases price
competition as well as consumer welfare and console manufacturer pro ts. With
the implementation of a less restrictive model, which includes a two-sided market
structure and accounts for video game heterogeneity and software competition, ver-
tical integration is pro-competitive. However, under a more restrictive model, which
does not allow for the two-sided market structure nor software heterogeneity, prices
rise leading to an anticompetitive conclusion. It is thus important to model the de-
mandforvideogameswellsinceconsoledemandisderivedfromvideogamedemand.
Moreover, incorporatingthetwo-sidednatureof themarketalsois equallyimportant
when studying competition in the video game industry.
In order to understand how vertical integration impacts console price competi-
tion, the above analysis extends the empirical industrial organization literature by
constructing a newmethodology which allows consumer demand for video game con-
solestodependuponthesetof availablevideogames ratherthanonlythenumberof
games. The estimation technique di¤ers from prior research by incorporating video
game heterogeneity and software competition into the indirect network e¤ect.
After the construction of an empirical model, the e¤ects of vertical integration
89
on console prices are investigated with the implementation of two counterfactual
simulationsi)whereall rstparty gamesareprohibitedandii)where rstparty games
become independent exclusive third party titles. In the rst counterfactual scenario
there are two important trade-o¤s to vertical integration. The rst is a demand
e¤ect and the second a market structure e¤ect. The counterfactual experiment
determines the market structure e¤ect dominates the demand e¤ect for all consoles.
When vertical integration is permitted aggregate consumer welfare increases by an
average of $22:08 million dollars and prices fall by 5:36;2:32 and 1:00 percent for
Nintendo Gamecube, Microsoft Xbox and Sony Playstation 2, respectively. The rise
in price competition is bene cial to console manufacturers. Lower prices lead to
an increase in the number of consoles sold which generates greater demand for video
games where the "real" pro ts are made. Console makers are thus willing to set
lower console prices in order to increase video game sales, in particular their own
rst party games. Under "what if" scenario two, I assume there is no reduction in
the number of video games available during a give time period. What were once
vertically integrated video games are now independent exclusive third party video
game. Consequently, there is no demand e¤ect. The only present e¤ect is the
marketstructuree¤ect,whichcanalsobedescribedasadoublemarginalizatione¤ect
for this speci c counterfactual. The double marginalization e¤ect is present since
console manufacturers and video game developers are forced to be independent from
each other which consequently eliminates any e¢ ciency derived from coordinating in
90
price. Or put di¤erently, when rms become disintegrated there is an elimination of
an e¢ ciency gain from a single integrated rm internalizing the e¤ects that console
and video game pricing has on each other causing prices of consoles to increase.
Console prices rise on average 4:7901; 0:7094; 1:9800 percent for Nintendo, Sony, and
Microsoft, respectively. However, these increases in price are not as substantial as
those presented in scenario one. Consequently, the mean compensating variation is
smaller than in counterfactual one with an amount equal to roughly 7:7548 million
dollars per month. The results of each counterfactual are interpreted as bounds
for what would likely occur in practice, with a number of rst party games being
completely eliminated while others remain in production.
Lastly, the more exible demand model provides a better t to the data than
the two previous models found in the literature. The results and conclusions found
using these alternative methodologies provide inaccurate predictions to the supposed
impactfromverticalintegration; Amodelwhichallowsforvideogameheterogeneity
butdoesnotincorporatevideogamecompetitionoverpredictsthepricee¤ectrelative
mymodelabovewhileamodelwhichdoesnotaccountforsoftwareheterogeneitynor
the two-sided nature of the industry predicts results counter to my more exible
model. It is thus extremely important to correctly model the video game industry.
Without doing so, incorrect policy conclusions are made.
The work associated with this dissertation has led to the investigation of several
other closely related topics. One subsequent paper studies the video game industry
91
using data on the handheld console market. In this paper my coauthor and I study
theoreticallyandempiricallytheimpactofmixbundlinginatwo-sidedmarketsetting.
Mixed bundling is found to be a form of price discrimination as well as a method to
produce greater console di¤erentiation, both of which increase the demand for video
game consoles. The increase in console demand consequently leads to a raise in the
numberofuniquelydesignedvideogames. Themethodofmixedbundlingthusassists
incoordinatingthe participation of consumers and game developers whichallows the
consoleproducertoextractlargerrentsfromthem. Anothersubsequentpaperfocuses
on how a divestiture or spin-o¤of an integrated design studio impacts console price
competition. Similarly,athirdpaperstudieshowamergeramongsoftwaredevelopers
impacts the complementary console market. In order to study these two relevant
questionsIextendtheabovemodeltoincludetheparameterizationofthevideogame
demand model as well as introduce a software supply model. Such an introduction
doesnotprovideanysubstantialempiricalhurdlesandisquitefeasibletoimplement.
92
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Abstract (if available)
Abstract
The focus of this dissertation is twofold. The first objective is to construct an empirical demand model for video game consoles which captures the complementary nature between hardware and software while accounting for software heterogeneity and competition. The second objective is to determine the effects of vertical integration on video game console price competition as well as consumer welfare and firm profits.
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Asset Metadata
Creator
Derdenger, Timothy P.
(author)
Core Title
Vertical integration and two-sided market pricing: evidence from the video game industry
School
College of Letters, Arts and Sciences
Degree
Doctor of Philosophy
Degree Program
Economics
Publication Date
09/11/2009
Defense Date
05/07/2009
Publisher
University of Southern California
(original),
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Tag
OAI-PMH Harvest,Pricing,two-sided markets,vertical integration,video game industry
Language
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Ridder, Geert (
committee chair
), Goeree, Michelle (
committee member
), Tan, Guofu (
committee member
), Zhu, Feng (
committee member
)
Creator Email
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