Estimating The Effect Of Subscription based Streaming Services On The Demand For Game Consoles
aa r X i v : . [ ec on . GN ] D ec Estimating The Effect Of Subscription based Streaming ServicesOn The Demand For Game Consoles ∗ Chan Tung Yu Marco Zhang Yue Yeung Tsun Yi
Dec 30 2018
Abstract
In this paper, we attempt to estimate the effect of the implementation of subscrip-tion based streaming services on the demand of the associated game consoles. Wedo this by applying the BLP demand estimation model proposed by Berry (1994).This results in a linear demand specification which can be identified using conven-tional identification methods such as instrumental variables estimation and fixedeffects models. We find that given our dataset, the two-stage least squares (2SLS)regression provides us with convincing estimates that subscription-based streamingservices does have a positive effect on the demand of game consoles as proposed bythe general principle of complementary goods.
Subscription based business models have been around since the 17 th Century which were usedby publishers of books and periodicals (Clapp, 1931). We also see this in newspapers andmagazines, and more recently we are starting to see this being incorporated into digital mediaplatforms; a prime example being the American based media-services provider of TV shows andmovies Netflix. Glazer et al. (1982) shows that subscription services together with individualunit sales allow monopolists to implement price discrimination resulting in a increased profitsand net welfare gain.However, our topic of interest is investigating how a subscription based service will affectthe demand of a complementary good. In the years surrounding 2013, the leaders of the gamingindustry Sony, Microsoft and Nintendo released several game consoles, few of which are stillleading the game console markets to this day, the notable ones being XBox One (XBO) andPlayStation 4 (PS4). In 2014, Sony released a cloud gaming subscription service PlayStationNow (PS Now) for PlayStation 4 and PC players to pay for access to a selection of PlayStation2, PlayStation 3 and PlayStation 4 games through a monthly subscription . Similarly and more ∗ ECON 4114 Final Project, HKUST Fall Semester 2018-19 More precisely their hardware revised variants .The goal of this study is to investigate the effects of the introduction of such subscription-based streaming services on the demand of the associated game consoles. Using basic economicreasoning on the behaviour of complementary products, our prior would be that since thesesubscription streaming services are intended to offer a discount on games, then the increaseddemand due to the discount would have a spillover effect onto the demand on consoles associatedwith such streaming services. We will be investigating this empirically by estimating the demandfor each console where the presence of a subscription based service will be represented by adummy variable Subscribe . Thus, the coefficient on
Subscribe will ideally capture its effect onthe demand of the respective console.
We will be estimating demand using the BLP Discrete-Choice Demand Model (Berry, 1994). Weassume that the choice probabilities take a multinomial logit form, thus we have to incorporatethe
Independence of Irrelevant Alternatives (IIA) assumption . The objective is toobtain structural estimates for the demand function as a function of console characteristics,and hence obtain the coefficient on the dummy variable Subscribe jt in order to capture theeffect on demand after introducing a subscription-based streaming service. The data is in a panel data format with each console j and their product characteristics x jt ata given year t . There were a few simplifications that need to be made when constructing ourdataset due to a number of complications. Table 1 Below shows the definitions of the productcharacteristics used in the demand estimation.The data is obtained from various sources, mainly from different sites that track prices ofvideo game products for video game enthusiasts. The source of market share data is from thesite VGChartz (2018b) accessed through the online statistics portal Statista. Sources of dataon product characteristics include product comparison articles on Forbes and GameSpot .Data for the costs of components of consoles are obtained from online articles published by The ratio of the probability of choosing either of of the two alternatives are independent of the set ofalternatives available. Where ( Subscribe jt = 1 , If Subscription service is introduced for console j at time t . Subscribe jt = 0 , otherwise For example, the market share data for each console does not distinguish between different models of thesame console resulting from a number of hardware revisions. To have the regression run more smoothly, eachyear we assumed that the newer revised model replaces the older model and thus represents the aggregate marketshare for the year. Gordon Kelly (2016) Jimmy Thang (2017) Table 1: DefinitionsTrait DefinitionVol Volume of Game console in mm Alone Dummy variable for Standalone consolesgrams Weight in grams (g)Storage Storage space in Gigabytes (GB)
Titles Number of game titles for respective console in respective year Exclusive Number of exclusive game titles for respective console in respective year RAM RAM capacity of game console in Megabytes (MB)
CPU Clock rate of game console in Megahertz (Mhz)
GPU GPU processor clocking speed in Megahertz (Mhz)
Core Number of processor cores in the CPU
Subscribe Dummy variable for presence of Subscription-based Game streaming serviceslog Log differences in market share of j and outside alternative Price Console price CPU cost CPU component cost
RAM cost Memory component cost Aggregate data is retrieved from Wikipedia, with various individual sources. Gordon Kelly (2016), Forbes Steven Mather and Andrew Rassweiler (2013), IHS ; proxy estimate for New 3DS XL CPU. Steve Burk (2017) ;proxy estimate for PS Vita and PS Vita Slim CPU ; proxy estimate for Nintendo Switch CPU. VGChartz (2018a) VGChartz (2018b) Michael Passingham (2018) • We have T = 5 time periods starting from 2014 to 2018. • N t individual consumers at time t such that P Jj =1 q jt = N t . • We have J = 5 alternatives (PS4, Xbox One, Nintendo Switch, Nintendo 3DS, PlayStationVita). This is the case for a number of consoles (PS4, NN3DS XL, PS Vita, NS). We had to find substitute CPUprocessors from the same manufacturer of similar specifications. E.g. the PS4 uses the 2.1 GHz 8-core AMDcustom Jaguar. We use the price of the 3.3 GHz 8-core AMD FX-8300 CPU instead which is suggested as aperfect substitute. We have a K vector of characteristics for all consoles j at time t , x jt = ( x jt , ..., x jtK ).Note that Subscribe jt is an entry in this vector. • We have prices of console j at time t , p jt • We have empirical (observed) market shares ˆ s jt = q jt N t . We denote outside market share tobe ˆ s t to account for the difference (this should be the demand for gaming consoles otherthan the three alternatives in the same time period). • Unobserved market/product heterogeneity j at time t , ξ jt = ξ j + ξ t + ∆ ξ jt , where ξ j isconsole specific shock, ξ t is common shock at time t , ∆ ξ jt is non-fixed product/productunobserved shocks, specific to j and t . We first write our indirect random utility for individual i as: u ijt = x ′ jt β − αp jt + ξ jt + ε ijt ≡ δ jt + ε ijt (1)where δ jt = x ′ jt β − αp jt + ξ jt is the mean utility for console j at time t . By writing theindirect random utility in the form of (1), we are making two important assumptions.1. We assume ε ijt to be i.i.d type I extreme value distributed under the logit assumption.2. We assume that all consumer heterogeneity will be captured by the term ε ijt , resulting inthe homogenous parameters ( α, β ) which we are to estimate. Under these two assumptions we are able to obtain the closed form for estimated marketshare ˜ s jt as a function of ( δ t , ..., δ Jt ). (See Appendix A).˜ s jt ( δ t , ..., δ Jt ) = exp( δ jt )exp( δ t ) + ... + exp( δ Jt ) (2)Then for our estimation, we will be using the following moment conditions: ˆ s t = ˜ s t ( δ t , ..., δ Jt )...ˆ s Jt = ˜ s Jt ( δ t , ..., δ Jt ) (3)where we normalize δ t = 0. Then from the moment conditions (3) we can see that ˆ s jt islog-linear and we can write, E.g., unobserved characteristics of console, measurement error in price, demand shocks etc. This is opposed to the Random Coefficients Model where we estimate ( α i , β i ). We assume homogenousparameters to simplify our analysis. δ t = 0 δ t = log ˆ s t − log ˆ s t ... δ Jt = log ˆ s Jt − log ˆ s t (4)where log ˆ s t = − log(exp δ t + ... + exp δ Jt ). Now we have obtained a linear reduced formthat can be used for estimation, so we can run OLS on:log ˆ s jt − log ˆ s t = x jt β + αp jt + ξ jt (5)However, notice that by the definition of the error term ξ jt , it is reasonable to assume that cov ( p jt , ξ jt ) = 0. Hence to obtain consistent estimates for ( α, β ) we can either carry out IVestimation that requires valid instruments, or run a fixed effects model. We have the linear specification (5) to estimate:log ˆ s jt − log ˆ s t = x jt β + αp jt + ξ jt One method that is available to us for identification since we have a panel data format isto run a two-way fixed effects model on (5) to account for time and individual fixed effects.However this still requires that cov ( p jt , ∆ ξ jt ) = 0 in order to obtain consistent estimates. It isalso implicitly required that although T may be required to be small, J is required to be large.Since our panel data only consists of J = 5 alternatives, the estimates are shown to havevery high standard errors resulting in low levels of significance. Furthermore, as shown inspecification (4) in Table 2, the coefficient on Subscribe changes drastically compared to therest of the specifications showing a negative sign. Due to the small magnitude and insignificanceof most of the coefficients, these estimates are unlikely to be interpretable and no statisticalinference or insight can be made. It should also be noted that some of the specificationswere not permitted as the characteristic
Subscribe would be dropped due to high levels ofmulticollinearity with other product characteristics.
Another way to obtain consistent estimates for (5) is to run a 2SLS using valid instruments.Such instruments z , ..., z m are valid if they satisfy the following assumptions: Condition 1 (Instrument Relevance) . The instrument has a sufficiently high correlation withthe endogenous regressor. log ˆ s t is interpreted as the log of the ‘outside market share’, so the market share of products not includedin the analysis. .e. cov ( z jt , p jt ) = 0 (2) Condition 2 (Instrument Exogeneity) . The instrument is uncorrelated with the error term ξ jt .i.e. cov ( z jt , ξ jt ) = 0 (2)Berry (1994) suggests using cost shifters (i.e. Supply shifters), as they should be indepen-dent of unobservable market/product characteristics that may affect a consumer’s utility.The instruments that we will be using are the cost of the CPU and RAM components of theconsoles. Because these are cost factors, it should be reasonable to claim that cov ( CPU cost , CPU ) =0, cov ( CPU cost , Core ) = 0 and cov ( RAM cost , RAM ) = 0 for the relevance condition. We empir-ically test these conditions in the next section.Looking at the estimates in Table 3, all specifications show to have highly significant esti-mates for Subscribe as well as being similar in value and having an intuitive positive sign.Out of the four specifications, specification (1) is the only one with a significant coefficient on P rice at the 95% confidence level as well as having an intuitive negative sign. Furthermore,all coefficients are shown to be highly significant. Overall, the estimates from Table 3 make aconvincing case that the estimates on the coefficient for
Subscribe may be robust; as well asspecification (1) being the best estimate for the linear demand form (5).
To further confirm the validity of the estimates provided by specification (1) we proceed to testthe two conditions of instrument validity. The relevance condition can be empirically tested bythe conditional F test on the null H : π = π = 0. Tables 4 to 7 show the conditional F testsof all four specification from Table 3. We see that none of the specifications are able to satisfythe rule of thumb requirement of F ≥ (Stock et al., 2003), although the specificationsclosest to satisfying this requirement are specification (1) that yields F = 8 .
712 and (4) thatyields F = 9 . We continue to test the instrument exogeneity condition on specification (1). We do this byrunning Sargan’s J test (Sargan, 1958). To run Sargan’s J test , we run the following regressionusing the 2SLS residuals:ˆ u SLS = β + β CPU cost + β RAM cost + β x + ... + β K x K + e (6) All estimates are significant at the 99% level. Where π , π are the first stage coefficients of instruments CPU cost and
RAM cost respectively This may be an indication of weak instruments which may result in severely biased estimates depending onthe severity. Note that Sargan’s J test can only be implemented if the 2SLS model is over-identified, that is m > k for m instruments and k endogenous regressors. F statistic from Table 8, the J statistic is defined to be J = mF ,therefore J = 0 .
63. Because J ∼ χ ( m − k ), we have that the 95% critical value for χ (1) is0 . The data used in this study involved J = 5 alternatives for game consoles across T = 5 yearsof observations, totalling 22 observations. After obtaining the linear specification as specifiedfrom the BLP demand estimation model, we employed both two-way Fixed effects (FE) modeland two-stage least squares (2SLS) using Instrumental Variables to attempt identify the effectof
Subscription on the demand for consoles. The estimates from the FE model that attemptedto control for unobserved individual and time heterogeneity were uninterpretable most likelydue to the small number of observations of the panel data.The 2SLS estimates on the other hand yielded significant estimates which were convincinglyrobust as they varied little across specifications as well as having intuitive signs. Although theSargan J test supports the exogeneity of specification (1) from Table 3, the F statistic for testinginstrument relevance did not meet the F ≥
10 cut-off although it is still reasonably close. If wewere to interpret the positive coefficient of 1 .
268 on
Subscription from Table 3, this representsthe positive change as a result of implementing a subscription based streaming service on thedemand of game consoles in terms of the log differences of market shares as defined by the BLPdemand model.To further improve this study, increasing the number of alternatives in the model as well asincreasing the number of years (or frequency) of observation may allow for a fixed effects modelto run smoothly where estimates can then be compared with IV estimates. Implementing therandom coefficient model as mentioned in Section 2.4 may also yield more structurally robustestimates as the homogenous parameter assumption is relaxed. If the null were rejected, that would indicate that there is at least one endogenous instrument. Nintendo Switch only started to appear in 2017 Tables
Table 2: Fixed Effects model, Two ways
Dependent variable: log(1) (2) (3) (4)Vol − − − − − − − − − − − − − − − − − − − − − Note: ∗ p < ∗∗ p < ∗∗∗ p < Dependent variable: log(1) (2) (3) (4)Price − ∗∗ − − ∗∗∗ ∗∗ ∗∗∗ (0.001) (0.001) (0.001) (0.001)RAM − ∗∗∗ − ∗∗∗ − ∗∗∗ − ∗∗∗ (0.0001) (0.0001) (0.0001) (0.0001)GPU 0.007 ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (0.001) (0.001) (0.001) (0.001)Titles − ∗∗∗ − − ∗∗∗ (0.006)Storage 0.001 ∗ ∗∗ (0.001) (0.001)Core − ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (0.140) (0.250) (0.229) (0.209)Constant − ∗∗∗ − ∗∗∗ − ∗∗∗ − ∗∗∗ (0.354) (0.299) (0.186) (0.312)Observations 22 22 22 22R Note: ∗ p < ∗∗ p < ∗∗∗ p < The robust.se function was used from the ivpack R package to obtain heteroskedastic robust standarderrors for instrumental variable analysis. i.e. These are the Huber-White standard errors for instrumentalvariable analysis as described in White (1982). (Jiang & Small, 2014) F test for (1) from Table 3Statistic N Mean St. Dev. Min Pctl(25) Pctl(75) MaxRes.Df 2 16.000 1.414 15 15.5 16.5 17Df 1 − − − − − > F) 1 0.003 0.003 0.003 0.003 0.003Table 5: Conditional F test for (2) from Table 3Statistic N Mean St. Dev. Min Pctl(25) Pctl(75) MaxRes.Df 2 14.000 1.414 13 13.5 14.5 15Df 1 − − − − − > F) 1 0.005 0.005 0.005 0.005 0.005Table 6: Conditional F test for (3) from Table 3Statistic N Mean St. Dev. Min Pctl(25) Pctl(75) MaxRes.Df 2 12.000 1.414 11 11.5 12.5 13Df 1 − − − − − > F) 1 0.125 0.125 0.125 0.125 0.125Table 7: Conditional F test for (4) from Table 3Statistic N Mean St. Dev. Min Pctl(25) Pctl(75) MaxRes.Df 2 15.000 1.414 14 14.5 15.5 16Df 1 − − − − − > F) 1 0.003 0.003 0.003 0.003 0.00310able 8: Residual Regression
Dependent variable: res.IV1CPU cost 0.005(0.004)RAM cost − − − − − Note: ∗ p < ∗∗ p < ∗∗∗ p < ppendix A Logit model for probabilistic choice
First we define ˜ ε ≡ ε ij ′ t − ε ijt . Where ˜ ε will follow a logistic CDF by assumption 1. in Section2.4. Given the indirect random utility from (1),Pr(Consumer chooses j ) = Pr( δ jt + ε ijt > δ j ′ t + ε ij ′ t )= Pr( ε ij ′ t − ε ijt < δ jt − δ j ′ t )= Pr(˜ ε < δ jt − δ j ′ t )= exp δ jt exp δ jt + exp δ j ′ t (7) B Dataset
Dataset and code can be accessed via. https://github.com/ctymarco/gamepass/tree/10c6983afdf08ba8123cecf162f34fd218b76e61 eferences Berry, S. T. (1994). Estimating discrete-choice models of product differentiation.
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