Measuring the Marketing-Mix Effects in
the Video Game Console Market.
A Model for Competing Brands.
Author: Joaquin Iglesias Turina (11086300)
Supervisor: Prof. dr. J.C.M. van Ophem
Second Reader: Prof. dr. K.J. van Garderen
Master Thesis
Statement of Originality
This document is written by Student Joaquin Iglesias Turina who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of
Aknowledgements
I would like to thank my supervisor Hans van Ophem for all his support and guidance while writing this thesis. To my colleagues and friends Sara, Jan, Wouter, Verena, Janelle, Andres and Miguel, thank you all for your comments and criticisms. Finalmente me gustar´ıa dar de todo coraz´on las gracias a mi padres, Pedro y Araceli, por toda su ayuda y apoyo.
Abstract
This thesis studies the effects of the marketing mix variables (i.e. prices and number of available software) in the video game industry. One of the main differences with previous liter-ature of this nliter-ature is the distinction between types of games. Games that can only be played in a given console are found to have a positive effect in sales, while standard cross-platform games have a statistically insignificant effect. The flexible semiparametric specification and the availability of brand level data allows to test whether there is heterogeneity among the firms sales functions. While the effects of the variables of the marketing mix are found to be constant across firms, evidence was found that there is some degree of heterogeneity in the sales functions.
Contents
1 Introduction 5
2 Previous Literature and Theory 6
2.1 Marketing Literature . . . 6
2.2 Industrial Organization Literature . . . 6
2.3 Theory and Bass Model Literature . . . 7
2.3.1 Theory . . . 7
2.3.2 Bass Model Literature . . . 9
3 Econometric Specification 11 4 Data 14 5 Results 19 5.1 Base Model . . . 20
5.2 Marginal Effects . . . 22
5.2.1 Short Term Marginal Effects . . . 23
5.2.2 Long Term Marginal Effects . . . 25
5.3 Controlling for endogenous variables . . . 25
5.4 Models with varying hazards . . . 27
6 Conclusions 30
A First Stage Regressions Full Results 32
1
Introduction
The video game industry is one of the biggest entertainment industries world wide. In the US alone, it was valuated at 25 billion dollars in 2010, and around that same period, about 80 million consoles were sold. The relevance of this industry lies not only on its size, but also on the business practices, which have managed to attract scholars’ attention, mainly from the fields of Marketing and Industrial Organization. Several studies put special interest in vertical integration and the obvious relation to the regulation and competition. Another topic of interest are the network effects inherent to technological products. Some of these studies are reviewed in the next section.
The data are for the seventh generation of video game consoles. These data were taken from the NPD survey, which was published in several media outlets. This generation was started by Microsoft’s Xbox360 console in late 2005, and it also includes Sony’s PlayStation3 and Nintendo’s Wii, introduced in 2006. Previous studies (Shankar and Bayus, 2003; Chintagunta et al. 2009) found prices and available games to be the main drivers of sales, and measured the effects of these two variables (defined as the marketing mix) on the sales of video game consoles. This thesis aims to update (using more recent data) and expand these studies by exploring the effects once brand level data is used, as well as introducing some of the findings of the more recent Industrial Orga-nization literature into this analysis of the marketing mix effects. Specifically, hardware vendors have the chance to integrate vertically with software developers to produce exclusive games, which can only be played in the console produced by the hardware vendor. This thesis differentiates between regular games and exclusive games in the marketing mix variables. With this distinction, the effect that regular games have on sales was found to be statistically insignificant.
This thesis uses the representation of the Bass Model presented by Chintagunta et al. (2009). This model is in turn based on the Proportional Hazard Model framework. The use of brand level data allows to examine whether the hazard functions are different for each console. The results show that the baseline hazard functions are different.
Other common issue studied is the endogeneity of the variables of the marketing mix. No relevant instrument was found for either exclusive games or prices. It was, however, found that both the prices of consoles and the prices of the components used to build such consoles are both non-stationary. This should serve as caution for future research on technological products.
This thesis is structured as follows. The next section covers the previous literature in Marketing and Industrial Organization, the theory related to the Proportional Hazard Model and the litera-ture on the Bass Model. Sections 3 and 5 present the data and the estimation results. The thesis closes with the conclusions as well as further research and criticisms to this dissertation.
2
Previous Literature and Theory
This section covers the previous literature. First I present the research covering the marketing ori-ented literature, which has the main focus of defining and estimating the effects of the marketing mix in the video game console market. Then the industrial organization literature, more focused on the structure of the industry is presented. This industrial organization proposes new questions that extensions of the marketing literature could answer. The last part discusses the theory of the methods used in this thesis, as well as commenting on some of the most relevant research done on the Bass Model.
2.1
Marketing Literature
Shankar and Bayus (2003) analyzed the network effects in the video game console market. They modeled the demand as a Cobb-Douglas function, taking as inputs the prices and level of adver-tising of the different brands in the market. The model coefficients are linearly dependent on the size and strength of the networks for the different brands. This demand is then used to compute the profit function for the different firms. Their main findings after estimating this model were: asymmetry in the network effects for the different brands (which helps explain the changes in market shares during the period of study) and that the main drivers of sales were prices and avail-able software for the consoles, these are the variavail-ables of the marketing mix that concern this thesis.
This last result was used by Chintagunta et al. (2009). They used the effect of the marketing mix variables in the diffusion of the video game consoles. To do so they used a semiparametric specification of the Bass diffusion model in order to ensure flexibility (further details in Section 2.3.1). Their findings are in line with Shankar and Bayus (2003): prices and available software have a significant effect on hardware adoption. Furthermore they found that the effects of these variables change over time: at the beginning of the product’s life cycle, the effect of prices is greater, and it decreases over time. For the available games, the effect evolves in the opposite direction as time evolves.
2.2
Industrial Organization Literature
Lee (2013) carries out an in depth analysis of the video game industry, with special interest on vertical integration practices. The main finding is that vertical integration allows for market en-trance, which in turn fosters competition. A great effort was put by the author into controlling for different kinds of games (sports, adventure, etc.) This allowed him to model the demand and
supply functions in great detail, accounting for the heterogeneous preferences of the individuals consuming these products.
Lee (2013) also explains some of the practices of the industry. The insight provided about pric-ing practices contributes relevant information when it comes to issues of endogeneity. The paper states that consoles are being sold at or below cost, and the benefits for the hardware vendors come from selling the right to game developers to develop games for the platform. Chintagunta
et al. (2009) controlled for price endogeneity, which in the light of Lee’s (2013) claims might not
be the most relevant endogenous variable. On the other hand, games, and specially exclusive games can be used to attract consumers into the platform. This increases the pool of potential consumers for game developers if they were to make games for that console. Chintagunta et al. argue that games take time to be developed and have fixed release dates, then games should be considered exogenous. Clements and Ohashi (2005) (another study on the network effects in the video game industry) instrument the number of available games. Despite their different approach, both Chintagunta et al. (2009) and Clements and Ohashi (2005) find similar estimates for their estimations with and without endogenous variables, and little or none information on the first stage of their 2SLS estimations is given.
The topic of vertical integration was further explored by Gil and Warzynski (2015). They consider two different kinds of vertical integration. One type is developer-publisher integration. Under these vertical integration scheme, the authors found that vertical integration leads to better economic performance of the game. This was mainly due to better marketing practices, as well as publish timing, making sure that the game was not published to close to another title. The second type of vertical integration is developer-hardware vendor integration. Games published under these scheme are called exclusive games, and can only be played in the publishing hardware vendor’s console. The authors found that these games sell less units and generate smaller revenue. This rises the question of whether exclusive games are used to attract consumers to the platform.
2.3
Theory and Bass Model Literature
2.3.1 Theory
The base model for this thesis is the Bass (2004) model, which in turn is based on the Proportional Hazard Model (PHM) framework. This type of framework is used to study the transition between two states (e.g. employed and unemployed in labor economics) and how long do these states last, this is called spell. In this thesis, the two states are no purchase and purchase. The main research is to measure how the variables of the marketing mix affect the transition between these two states, or in layman terms, how do the marketing mix variables affect the purchase decision.
To do so, the Bass Model will be used. This model is derived from the assumption that the sales at a given time equal the size of the market times the probability of purchase at that time (this is the regular probability density function evaluated at the time of interest).
Under the Proportional Hazard Model framework, the instantaneous probability of purchase (the probability of purchase at time t given no purchase has been made yet), also known as the hazard rate is defined as
λ(t, Z) = f (t, Z)
1− F (t, Z)=−
d ln(1− F (t, Z))
dt ,
where f (t, Z) is the probability function and F (t, Z) is the density function. In order to get a solution to F (t, Z), it is possible to integrate and take exponential on the hazard function above:
1− F (t, Z) = exp(− ∫ t
0
λ(u, Z)du).
The above specification is based on continuous time, and the data available for this thesis is monthly data. Then it is necessary to have a discrete time version of that model.
λ(ti−1, ti) = F (ti, Z)− F (ti−1, Z) 1− F (ti−1, Z) = 1− exp(− ∫ ti ti−1 λ(u, Z)du).
Under a proportional hazard model, the hazard rate λ(t, Z) can be factorized into two different functions,
λ(t, Z) = λ0(t, αt)ϕ(Z, γ)
λ0(t, αt) is the baseline hazard, and it is a function of time alone. ϕ(Z, γ) is a function of Z. Since
λ(u, Z) must be always positive, we can write
λ0(t, ατ) = exp(αt); ϕ(Z, γ) = exp(Zγ).
With these results, and assuming that the covariates Zti are kept fixed during each of the time
periods, the hazard rate function in discrete time could be written as
λ(ti−1, ti) = 1− exp(− exp(αti+ Ztiγ)).
Within this framework, Bass (2004) developed his model. Setting the accumulated sales at time
t,Xt as the sum monthly sales (St) up to time t, and knowing that f (t, Z) is the probability of
purchase, so sales in month t, St= mf (t, Z), where m is the total size of the market,
Xt= ∫ ti 0 Sudu = m ∫ ti 0 f (u)du = mF (ti).
Then, taking differences, and using the definition of the hazard rate such that f (t, Z) = λ(t, Z)(1−
F (t, Z)):
Sti= mf (ti) = mλ(ti−1, ti)(1− F (ti)) = (m− Xt,i−1)λ(ti−1, ti),
this is the specification used by Chintagunta et al. (2009), and is the model estimated in this thesis.
2.3.2 Bass Model Literature
The Bass model has different representations, as shown in Bass et al. (2000). Bass’ (2004) original representation of the model had a different direction. His specification was based on a theoretical framework for the diffusion of durable goods, where there where two types of consumers, innovators and imitators. The former make their purchase decision at the beginning of the product’s life cycle, with little external influence. Then this external influence, such as marketing or mouth-to-mouth communication will attract the imitators to purchase the product. To accommodate this theory, the hazard rate could be written as
λ(t, Z) = p + qF (t, Z),
where p is fraction of innovators and q is that of the imitators. Thus, the results shown above could be written in terms of these p and q. Then the sales equation would become
St= pm + (q− p)Xt−
q mX
2
t.
This equation describes the behavioral assumptions of the model: Both innovators and imitators make initial purchases of the product, the main difference is the external influence. Innovators have no external influence in their purchase decision, while imitators are influenced by marketing, mouth-to-mouth, etc. Overtime, the amount of the innovators’ purchases decreases.
This representation of the model also gives a close form solution for the cumulative density func-tion:
f (t, Z) = dF (t, Z)
dt = (p + (p− q)F (t, Z) − qF (t, Z)
2. (1)
By solving this differential equation, there is a solution to F (t, Z), which in turn allows to get a formula for the sales,
F (t, Z) = (q− p exp(−(t + C)(p + q))) q(1 + exp(−(t + C)(p + q))) =
(1− exp(−t(p + q)))
q/p exp(−t(p + q)) + 1),
his model to sales data for different products, such as black and white televisions or refrigerators, and found that the data was in accordance with the model, however, the predicted sales followed a smoother pattern than the actual data.
It should be noted that the model presented by Bass (2004) includes no explanatory variables. Fur-ther research done in Bass et al. (1994) modifies this model to include explanatory variables using the proportional hazard framework explained above. In this generalization, λ(t, Z) = p + qF (t, Z) is kept as the baseline hazard, and then this is multiplied by a function of the marketing effort at a given time. Again, the model was tested against sales of color televisions and air condition units, and the researches found that the predictions are in accordance with the actual data. However, once explanatory variables were accounted for, the model picked up more of the irregularities of the data.
Further generalization of the Bass model was done by Boswijk and Franses (2005) by making (1) a stochastic differential equation. From this different representation, the authors develop the model
Xt− Xt−1= m(F (t, Z)− F (t − 1, Z)) + ui.
Through Monte Carlo simulations, it is shown that this model allows for consistent estimation of the parameters of interest, as well as proving that the t-tests follow the expected standard normal distribution. However, using the Bass’ (2004) representation, they find that the model is very sensitive to omitted variable bias and heterokedasticity. These issues become less relevant as the data is more aggregated, this is, yearly data should be less problematic than monthly data.
The choice of the baseline hazards also deserves some comment. The options are to estimate the baseline hazards semiparametrically (as done by Chintagunta et al. 2009), by including time fixed effects, or parametrically (Boswijk and Franses 2005, Bass 2000, Bass 2004, Bass et al. 1994) , defining a function for the baseline hazards. The main advantage of the former is its flexibility, since it allows for irregular patterns in the data to be picked up by the time fixed effects. The semiparametric approach fails when the main purpose is forecasting, since there is no estimate for unobserved time periods. The parametric approach allows for forecasting, but imposes additional assumptions on the model. Since the objective of this thesis is to measure the effects of the mar-keting mix, then we can expect the baseline hazards to control for unobserved effects, enabling the estimation of the effects of the variables of interest.
3
Econometric Specification
The model estimated by Chintagunta’s (2009) is:
Sti= (m− Xt,i−1)λ(ti−1, ti).
where m is the market size, and Xt,i−1 is the cumulative lagged sales. One important
modifi-cation with respect to the theoretical model presented before is that, given that it infeasible to estimate one α parameter for each month, αt for t = 1, 2, ..., T must be replaced with ατ for
τ = 1, 2, ..., Γ; Γ < T . Now each interval τ has several months. In the case of these thesis, these intervals are six months long.
The first thing that needs to be changed for a multiple brand model is the changes in the market size as consumers buy other consoles. Then it is important that the covariates of the hazard function control for the prices and available software for competing products, which have an expected positive and negative sign on the hazard function. Then, for a 3 goods model we can write: S1,ti = (m− 3 ∑ c=1 Xc,t,i−1)λ1(ti−1, ti) = (m− 3 ∑ c=1
Xc,t,i−1)(1− exp(− exp(ατ ji+ W1,tiβ + ϵ1,ti))),
S2,ti= (m− 3 ∑ c=1 Xc,t,i−1)λ2(ti−1, ti), = (m− 3 ∑ c=1
Xc,t,i−1)(1− exp(− exp(ατ ji+ W2,tiβ + ϵ2,ti))), S3,ti= (m− 3 ∑ c=1 Xc,t,i−1)λ3(ti−1, ti), = (m− 3 ∑ c=1
Xc,t,i−1)(1− exp(− exp(ατ ji+ W3,tiβ + ϵ3,ti))).
Where Wc now also includes the prices and available software for the competing consoles.
This base model has the advantage that, after a logarithmic transformation the model can be estimated via OLS, 2SLS or SURE:
ln [ − ln [ 1− S1,ti (m−∑3c=1Xc,t,i−1) ]] = ατ j+ W1,tiβ + ϵ1,ti,
ln [ − ln [ 1− S2,ti (m−∑3c=1Xc,t,i−1) ]] = ατ j+ W2,tiβ + ϵ2,ti, ln [ − ln [ 1− S3,ti (m−∑3c=1Xc,t,i−1) ]] = ατ j+ W3,tiβ + ϵ3,ti.
Since prices are included among the explanatory variables, it is possible that this leads to an endogeneity issue. Then 2SLS is necessary to correct for possible price and sales simultaneity. There is a second potential source of endogeneity: the number of available exclusive games. As mentioned by Lee (2013), prices need not be endogenous in the video game industry, and exclusive games may be the main factor to attract new consumers, hence its potential endogeneity.
Other issue arising from this specification is that m is an unknown parameter. This was solved by Chintagunta et al. (2009) using the EM algorithm. This is, the regression is estimated using different fixed values for m, and the one which minimizes the sum of squared residuals is kept. Robust standard errors should be used.
A slight modification of this system allows for NLS estimation of the model:
S1,ti= (m− 3 ∑ c=1 Xc,t,i−1)λ1(ti−1, ti) + η1,ti S2,ti= (m− 3 ∑ c=1 Xc,t,i−1)λ2(ti−1, ti) + η2,ti, S3,ti= (m− 3 ∑ c=1 Xc,t,i−1)λ3(ti−1, ti) + η3,ti.
Now, the η term represent some sort of measurement error, rather than unobserved variables with a direct effect on the hazard. Under this specification, m can be estimated by NLS, and there is no need to use the EM algorithm. The main downside of this specification is that it does not allow for instrumentation.
The model presented above is however limited: the hazards for the different consoles only change with the explanatory variables. This assumes that the hazard function is the same for the different consoles. However, it is possible that different consoles have different hazard functions, specially since Shankar and Bayus (2003) found the different network effects for different consoles. There are several ways to overcome this limitation.
The first approach would be to relax the assumption that the baseline hazards, that is, the α terms, are the same for the different consoles. This model could be estimated by NLS, and the baseline hazards are allowed to vary proportionally between consoles through a multiplicative
term:
λc(ti−1, ti) = (1− exp(− exp(αcτ ji+ Wc,tiβ)))ηc,ti,
λc(t, Zc) = λ0(t, αcτϕ(Wc, γ) = λ0(t, κcατ)ϕ(Wc, γ),
and one of the κc terms should be kept fixed equal to one, in order to avoid identifiability issues.
This solution could be extended so it allows for different hazard functions. This could be thought as some sort of filter, that dampens or amplifies the hazard depending on some console-specific factor (i.e. brand loyalty or different target consumers for different brands), while the hazard function is kept constant across products.
S1,ti= (m− 3 ∑ c=1 Xc,t,i−1)λ1(ti−1, ti) + η1,ti= (m− 3 ∑ c=1 Xc,t,i−1)λ(ti−1, ti)ν1+ η1,ti, S2,ti= (m− 3 ∑ c=1 Xc,t,i−1)λ2(ti−1, ti) + η2,ti= (m− 3 ∑ c=1 Xc,t,i−1)λ(ti−1, ti)ν2+ η2,ti, S3,ti= (m− 3 ∑ c=1 Xc,t,i−1)λ3(ti−1, ti) + η3,ti= (m− 3 ∑ c=1 Xc,t,i−1)λ(ti−1, ti)ν3+ η3,ti. νc should be always positive, in order to prevent negative sales, so we can write
λc(ti−1, ti) = λ(ti−1, ti)νc= λ(ti−1, ti) exp(ξc).
This model could be estimated by NLS. While it is not as informative as the model previously mentioned, but it only involves 3 extra parameters, which are the only ones needed to test the whether the hazard functions are different between consoles.
A different solution would be to allow the β terms to be different for each of the competing consoles.
S1,ti= (m− 3
∑
c=1
Xc,t,i−1)(1− exp(− exp(ατ ji+ Wtiβ1+ ϵ3,ti))), S2,ti= (m−
3
∑
c=1
Xc,t,i−1)(1− exp(− exp(ατ ji+ Wtiβ2+ ϵ2,ti))), S3,ti= (m−
3
∑
c=1
Xc,t,i−1)(1− exp(− exp(ατ ji+ Wtiβ3+ ϵ3,ti))).
This model could be estimated by SURE with identical regressors. The main advantage of this solution is that provides exact information on how each of the variables affect each of the sales functions. The main downside it introduces the large increase in the number of parameters. This would be relevant when testing the differences between the parameters.
4
Data
The data used in this thesis are for the seventh generation of video-game consoles. Particularly the data set contains the US monthly sales from the PlaySation3, Xbox360 and Wii from November of 2006 to December of 2011. This generation of consoles was started by Microsoft, introducing the Xbox360 in November 2005, and Sony and Nintendo introduced the consoles PlayStation3 and Wii a year later, in November 2006.
The main covariates used for the analysis are the prices and the number of available software titles (including both the total number of games and the number of exclusive games, developed only to be played in a particular console) for each console.
Figure 1 presents both the sales and the cumulative sales for the three consoles. In the monthly sales it is notable the peaks that occur during December, related to the Christmas season. But there are other peaks in the sales, corresponding mainly to price cuts and the release of critically acclaimed/highly expected titles for the given platform.
The maximum in sales is for the Wii platform, in December 2009. This is most likely related to the price cut of $50 that the console experienced in September of that year, since there was no particularly relevant new title published around that date. The maximum sales for the PS3 also took place on December 2009, and its again likely related to the $100 price cut of that year. For the Xbox360, the maximum sales took place a year later, on December 2010, in this case, the peak in sales could possibly related to the publication of several highly anticipated or critically acclaimed games around that time.
In general the sales present a high variance, as can be noted in Table 1, being the standard deviation around one time the mean. However, it must be noted that most of this variance its upwards. Further evidence of this is Figure 2, which presents the histogram of all the console sales. Out of the 180 observations, over 100 lie around the mean, with around 10 being smaller than the mean, and the rest lie above the mean. Thus, the skewness of the sales data is 3.44.
Looking at the cumulative sales in the second panel of Figure 1, it is easy to see the expected diffusion patterns of durable goods. For all consoles, there is a constant slope in growth, with significant steps corresponding to the peaks of the Christmas season mentioned above. These steps seem to grow up until they reach their maximum size in the 3 and 4 year, and then growth
Mean Std Deviation Min Max Xbox 480.37 419.68 155 1860 PS3 322.20 259.37 82 1360 Wii 624.82 612.99 172 3816 Total 461.57 457.63 82 3810 Table 1: Descriptive Statistics Sales (in Thousand Units)
decreases.
Figure 2: Sales Histogram
Regarding the prices, one of the main characteristics of the seventh generation of consoles is the introduction of multiple models for the PlayStation3 and the Xbox360, with slightly different technical specifications. Namely, hard drives with varying amount of memory. Wii presented only one model, while Xbox360 and PS3 presented three and four tiers of the console respectively. For the actual estimations, the mean of the available prices is used. Note that in the graph, a price of zero means that a given model was discontinued.
In Figure 3 we can see the price cuts for the different tiers of the consoles. The prices are numbered relative to the tier of the hardware it corresponds, then price1 relates to the cheapest version of the console, with the smallest hard drive space, price2 is the second cheapest model, reaching up to price3 for Xbox360 and price4 for PlayStation3. The models where classified in tiers, but sometimes the technical specifications of the model within the tiers changed. Such is the case in the second tier of the Xbox360, we can see that in the twentieth month, the price went down, just to go up again. This corresponds to a change in the specification of the second tier console. First there was a drop in price, then the current second tier model got discontinued, and a new model
was introduced, with more hard disk space. Prices of zero are given to times where the tier is not available, either discontinued or not yet introduced. For both PS3 and Xbox360, there are price cuts for the first 35 moths of life of the product, and then the prices remain stable until the end of our time period. The prices cuts of these two brands are not far apart from each other. This is clear evidence for the different markets the consoles were trying to appeal. Nintendo marketed Wii as a family friendly and casual oriented product, while Sony and Microsoft competed for the
core gamers, a more mature audience1. The price cuts were mostly of $100, but sometimes $50.
Figure 3: Price cuts
Figure 4 shows the evolution of the total games and the exclusive games available for each con-sole. We can see how the number of games follows a very similar pattern for each console, as most published games are multi-platform. The main differences between consoles in the top left plot
can be traced to the top right plot, the plot of the games exclusive for each console. In this second graph, the differences between consoles are bigger, but there is still a common trend. Namely, there are more games published right before the Christmas season.
The bottom graph of this figure presents the cumulative games and exclusive games. Again the main differences are found in the exclusive games graph on the bottom right. We see how Wii accrued the most exclusive games during this time period. It should be considered however that Wii has a completely different controller than Xbox360 and PS3. Then games developed for Wii are not easily ported to other platforms, while most games made for PS3 can be easily ported to Xbox360 and vice versa.
Given the small differences between the number of games published for the different consoles, the explanatory variables used will be the number of available games and exclusive games for the given console, as well as the number of available games for the competing consoles. The number of regular games available for the competing consoles will not be included.
Table 2 presents the descriptive statistics for the monthly published games. The means are close to each other, and the standard deviation is quite high. It can then be concluded that the volatility of the games and exclusive games is quite high.
Mean Std Deviation Min Max Xbox Games 12.82 8.29 2 35 PS3 Games 9.983 7.12 0 29 Wii Games 11.48 9.59 1 38 Total Games 11.43 8.43 0 38 Xbox Exclusives 1.370 1.62 0 7 PS3 Exclusives 1.322 1.56 0 8 Wii Exclusives 2.387 1.99 0 8 Total Exclusives 1.693 1.79 0 8
Table 2: Descriptive Statistics Games
As mentioned before, there is a potential endogeneity issue with the prices/ exclusive games and sales. In order to control for this, 2SLS is used with costs of hard drive space and memory as instruments for price, and the average age of the available exclusive games and the stock price of the console manufacturer company as instruments for exclusive games. The rationale behind using the stock price as an instrument for games is the following: for these firms take part in diverse industries, both Sony and Nintendo produce a wider variety of consumer electronics, and Microsoft’s main product is software. Then the stock price might be a good proxy for the state of the business, and a well performing business might invest into developing more exclusive games. As for the age of the games, it could be expected that hardware vendors want to keep new games
Figure 4: Games
being published in order to attract more consumers.
The top two plots in Figure 5 present the consumer prices of these two components. These values are then multiplied by the amount of each component that the console uses to get the relevant instrument. The bottom two plots of 5 present the instruments used for exclusive games.
5
Results
First, I present the results regarding the base model, as well as the implications derived from these results. Then are displayed both the marginal effects as well as the marginal effects over time.
Figure 5: Instruments
These have implications on the timing of applying the different variables of the marketing mix. Subsequently are presented the results of the model extensions shown before: First the control of possibly endogenous variables, and lastly the models that allow for heterogeneous hazard functions.
5.1
Base Model
In Table 3 we can find the parameter estimates and the standard errors for the OLS, SURE and NLS estimation. The market size was estimated using the EM algorithm for the OLS estimation, then it was kept fixed for the SURE estimation for comparability, in the NLS case, the market size was estimated directly by minimizing the NLS loss function. Then the NLS results should not be directly compared with the OLS and SURE results. While running the EM algorithm, it was note that the model was fairly insensitive to the market size estimate. The sum of squared errors decreased from about 41 to 40 as the market size values went from 100 to the actually estimated 129 million. While this estimate might seem high. It should be noted however, that the United States population is about 300 million people, 129 million accounts for roughly every teenager and young adult in the US and also that some individuals will buy more than one console. Then, it
OLS SURE NLS
Variable Estimate Std Error Estimate Std Error Estimate Std Error WNLS Std Error Exclusives 0.0315 0.0040 0.0319 0.0051 0.0340 0.118 0.0011 Mprice -0.0025 0.0010 -0.0024 0.0017 -0.0027 0.0023 0.0001 oexclusives 0.0666 0.0073 0.0670 0.0101 0.0675 0.0142 0.0013 oprice 0.0019 0.0020 0.0016 0.0033 0.0029 0.0033 0.0015 Games 0.0004 0.0008 0.0003 0.0005 0.0019 0.0014 0.0022 alpha1 -5.7108 1.1820 -5.5883 1.9584 -5.7107 2.1580 0.6962 alpha2 -7.0016 1.2587 -6.9115 2.0408 -7.0015 2.3458 0.8201 alpha3 -7.2397 1.2442 -7.1370 2.0209 -7.2396 2.5036 0.8171 alpha4 -8.6528 1.3069 -8.6094 2.0942 -8.6527 2.7042 0.9145 alpha5 -9.3617 1.3070 -9.2984 2.0299 -9.3615 2.8031 1.0109 alpha6 -11.0697 1.3648 -11.0094 2.0839 -11.696 2.9728 1.2530 alpha7 -11.5541 1.3530 -11.5182 2.0738 -11.5539 2.8887 1.1515 alpha8 -12.9146 1.4624 -12.8698 2.1810 -12.9145 3.2562 1.4027 alpha9 -13.4470 1.5258 -13.3724 2.3086 -13.4468 3.4499 1.5112 alpha10 -14.3876 1.5993 -14.3186 2.3471 -14.3874 3.5552 2.0140 alpha11 -14.7188 1.5990 -14.6402 2.3515 -14.7186 3.5645 2.1917 Market Size 129 million 129 million 86 million
Table 3: Base Model
can be concluded that this estimate is within the reasonable range for the US console market size. It is nevertheless in stark contrast with the NLS estimate, a much more conservative figure of 86 million estimated by NLS. While estimating m through EM algorithm, the decrease in the sum of squared errors between m = 129 and m = 86 was from 60 to 40, a significant amount compared with the decrease from m = 100 to m = 129.
Exclusives and Games are the number of titles available for a given platform, Mprice is the average
price for the console across different models, while oexclusives and oprice are average number in a given month of exclusive titles and the price for the competing consoles. Across the three different estimation methods used, the estimates for oprice, and Games are found to be insignificant, and only Games is found insignificant when computing the standard error is estimated via Weighted Non Linear Least Squares (WNLS) using a heterokedasticity robust working error covariance ma-trix. In general, all the estimations have the expected signs from economic theory: the more titles available the probability of purchase increases (since the value of the purchase is increased by more game alternatives), the higher the price, the less sales should be expected and the price of the competing consoles has a negative effect (since consoles are a normal good in a competitive market). There is no control for the competing consoles regular games,since as explained above, the amount of available games are too similar for the different consoles, and for the most part, non exclusive games are the same games for all platforms. While the sign of the other exclusives might seem surprising at first, it becomes clear once we account for how competitive this market was. Namely, we would expect companies to react to exclusive game publications of the
compet-ing firms by publishcompet-ing more exclusive games of their own. Then, even if a negative sign of this variable will be expected, a positive sign is found.
The baseline hazards are characterized by the alphas. These are bi-annual fixed effects. However, the observations for two months and five years, then there is another fixed effect for this two month period, alpha1. These parameters decline overtime. The actual baseline hazards 1−exp(− exp(αt))
are displayed in Figure 6. The baseline hazards decrease rapidly, then stall around period 3. Then, the baseline follows a slower decline. This is consistent with the theory of adoption and diffusion presented by Bass (2004). In the early stages of a product’s life, the innovators, has less weight, and external factors become relatively more relevant, the baseline hazards for OLS and NLS are not different enough to be noticed in Figure 6. The OLS estimates were used as the starting values for the NLS estimation process, hence the similarity between the estimates for the baseline hazards.
The standard errors of the NLS estimation are notably greater than the ones found using linear methods (almost twice the OLS estimates). In order to increase the efficiency of the estimates, WNLS was used, using a working error covariance matrix robust to heterokedasticity, following Cameron and Trivedi (2005). It is also possible that there are some issues with autocorrelation of the errors, which would be solved using the working error covariance matrix proposed by Newey and West (1987). However, the efficiency gains controlling only for heterokedasticity seem to be enough, leaving only Games insignificant. The NLS results were used as starting values for the WNLS optimization procedure, and WNLS did not lead to different estimates.
Since the estimates from the three different methods (OLS, SURE and NLS) are quite similar, it is interesting to test whether they are statistically different from each other. To do so, a t-tests were used to check whether each of the estimates was statistically equal to their counterparts estimated by other method (OLS vs SURE, OLS vs NLS, etc). The estimates were statistically different from each other for Exclusives, Mprice, oexclusives, oprice and Games. Despite these differences being statistically significant, the actual impact on sales should be quite similar, this is, the differences have little economic significance. For the alpha parameters, no differences were found.
5.2
Marginal Effects
In the section are presented first the short term elasticities and marginal effects, and later the long term elasticities. I refer as short term elasticities and marginal effects the standard meaning of those terms, the change in the dependent variable as the dependent variables change by 1% or 1 unit respectively. This results can be misleading using the Bass Model. As sales increase
Figure 6: Estimated Baseline Hazards
or decrease during a given month, the pool of potential consumers for the following months also changes, accounting for this difference in the consumer pool is then important to understand the long term effects of changes in the marketing mix variables.
5.2.1 Short Term Marginal Effects
OLS SURE NLS Exclusives 12913.58 13003.16 15078.40 Mprice -1007.46 -998.80 -1182.93 oexclusives 27293.94 27314.42 29923.98 oprice 770.46 659.14 1306.43 Games 158.75 110.03 834.83
Table 4: Mean Marginal Effects
In Table 4 are presented the mean marginal effects, this is, the change in sales as one of the covari-ates changes by one. As mentioned above, while the differences in the estimcovari-ates are statistically significant, they correspond at most to around 100 units difference between SURE and OLS in the marginal effect, being the economic significance of the difference between these two estimators negligible. The NLS estimates present an economically significant greater marginal effects. E.g. in the case of the exclusives, with 2000 units difference with the OLS or SURE counterparts. The main changes in sales are driven by the exclusive games, attracting about 13000 new consumers with each exclusive, thus even if these kind of games do not yield the same direct revenue, as stated by Gil and Warzynski (2015), they might be still profitable for the hardware vendors, given they are the main system sellers. Then we can see that an increase in price of $1 in the console is met with around 1000 less purchases, while if the competition increases their prices by the same amount, 700 new consumers are expected.
peri-Marginal Effects Over Time
OLS SURE NLS
Mprice Exclusives Mprice Exclusives Mprice Exclusives Period 1 -1335.3488 17116.393 -1356.7610 17663.348 -1437.5222 18323.459 Period 2 -553.7563 7098.003 -543.2336 7072.228 -619.8623 7901.110 Period 3 -1177.1072 15088.065 -1182.8417 15399.135 -1393.6671 17764.456 Period 4 -843.2487 10808.694 -802.3405 10445.479 -1057.1345 13474.824 Period 5 -1430.5101 18336.162 -1410.1002 18357.758 -1895.7631 24164.452 Period 6 -716.1173 9179.134 -706.1103 9192.682 -972.9890 12402.259 Period 7 -1300.9462 16675.423 -1261.7210 16426.045 -1878.3973 23943.098 Period 8 -792.3479 10156.251 -776.4528 10108.453 -1054.4362 13440.430 Period 9 -1242.7921 15930.008 -1254.2801 16329.173 -1623.8659 20698.699 Period10 -776.8447 9957.532 -779.9622 10154.142 -679.0895 8656.052 Period11 -1131.6675 14505.622 -1151.6565 14993.142 -569.3278 7256.969
Elasticities Over Time
OLS SURE NLS
Mprice Exclusives Mprice Exclusives Mprice Exclusives Period 1 -0.9384 0.1205 -0.9348 0.1220 -1.01782 0.1300 Period 2 -0.9708 0.2571 -0.9671 0.2602 -1.05340 0.2774 Period 3 -0.9239 0.5519 -0.9204 0.5584 -1.00168 0.5946 Period 4 -0.9061 0.9509 -0.9027 0.9622 -0.98236 1.0247 Period 5 -0.8155 1.3177 -0.8124 1.3333 -0.88264 1.4168 Period 6 -0.7750 1.7201 -0.7721 1.7405 -0.83956 1.8522 Period 7 -0.7057 2.0454 -0.7031 2.0698 -0.76224 2.1942 Period 8 -0.6927 2.3970 -0.6901 2.4254 -0.74874 2.5746 Period 9 -0.6916 2.7191 -0.6890 2.7512 -0.74393 2.9045 Period10 -0.6651 2.9364 -0.6625 2.9711 -0.71639 3.1409 Period11 -0.6095 3.1655 -0.6072 3.2026 -0.65232 3.3569
Table 5: Mean Marginal Effects and Elasticities
ods for which there is a different alpha. It is noticeable that the marginal effects follow a different pattern in the even and odd periods. The odd periods match the second half of the year and the holiday season. For both prices and exclusive games, the marginal effects are noticeable stronger during the second part of the year. However, these odd-period marginal effects tend to become smaller over time, while the even-period marginal effects do not have a so clear cut pattern. This is evidence for diminishing returns of the variables of the marketing mix.
Turning the attention to elasticities, it is noticeable that the price elasticities decline over time. At the beginning of the product’s life, the price is high as the market has its biggest size. During this time frame price cuts have greater effect. However, over time the market decreases size, and new price cuts have smaller effect. It is also worth noticing that, with an elasticity smaller than one, it can be concluded that the market is not very elastic with respect to price. On the other hand, the elasticity with respect to exclusive games increases over time, reaching three in the later periods. As time goes by, we can expect more loyal consumers to buy early, while consumers with smaller interest in the product will delay their purchase. These consumers are more likely to make a decision based on external factors, as outlined by Bass’ (2004) theory of adoption and diffusion,
and this is captured in the increasing elasticity for exclusive games. It is also possible,that once a system is more established, the exclusive games that are published will take advantage of the features of the console, becoming more significant system-sellers.
Finally, Table 5 gives insight on when to apply different changes in the marketing mix. Early in the life of the product, price cuts tend to have a greater effect, while later in the life of the product, the investments should go into developing games for the platform.
5.2.2 Long Term Marginal Effects
It is important to note that a change in the short term sales has a long term effect, since the pool of potential consumers changes. These dynamics are presented in Table 6. Under the column
Current Month is presented the average change in units sold during that as the variable increases
by 1%. In the column Average Future Months the average of the changes in units sold in all remaining months. Using a specific example, for a 1% increase of the price during month 1: Each of the firms increase the price of the products 1%. The average change in units sold is−5459.11. The next entry on the table, 21.03 is the average of the changes in units sold over the remaining months for all of the three brands, accounting for the fact that over 15000 did not make a purchase during the first month. The economic interpretation would be that on average 21 new consumers will buy each of the consoles in the next 61 months after a 1% increase in prices in the first month. Table 6 further illustrates how the elasticities of the variables Mprice and Exclusives change over time: The changes in prices are quite stable over time, specially compared with the effects for exclusive games, which have an increasing magnitude in the long term effects.
5.3
Controlling for endogenous variables
Table 7 presents the 2SLS results, considering the price of the consoles to be endogenous in the left hand side, and the exclusive games available on the right hand side of the table. The first stage estimates for the alphas have been omitted, the full results are presented on the Appendix A.
On the left hand side of the table, with endogenous prices, the effects of the exclusives, prices and games have a smaller magnitude compared to the OLS and SURE results of the base model. The price for the competing consoles now is significant, and the sign is changed, in contradiction with common economic theory, which would lead us to expect the price of the competing products to have a positive effect on sales. It is also noticeable that the some alphas become positive, but they keep the decreasing pattern seen before.
OLS
Mprice Exclusives
Current Month Average Future Months Current Month Average Future Months
Month 1 -5459.11 21.03 4128.66 -1.55 Month 11 -2660.42 10.93 3560.51 -5.50 Month 21 -1955.41 5.35 4263.27 -6.88 Month 31 -2489.74 12.57 8320.41 -32.21 Month 41 -2048.05 11.01 8863.89 -40.22 Month 51 -4217.20 10.39 5979.01 -42.91 Month 61 -3142.39 58.89 9328.54 -261.88 NLS Mprice Exclusives
Current Month Average Future Months Current Month Average Future Months
Month 1 -6203.13 33.85 5041.88 -2.49 Month 11 -3160.82 22.79 4395.56 -11.45 Month 21 -2601.69 15.23 5975.74 -19.55 Month 31 -3261.22 49.48 11328.12 -126.62 Month 41 -2155.77 54.08 9447.52 -197.41 Month 51 -5072.85 48.75 7171.94 -201.08 Month 61 -2940.75 155.42 7368.57 -689.93
Table 6: Average Long Term Elasticities
The second panel of Table 7 presents the first stage of the 2SLS regression. It is surprising to notice the different signs of the instruments for price, considering that both the cost of hard drive and the cost of memory have consistently gone down over time, as well as prices. However, most companies present a spike in the variable Mprice as models with larger hard drive capacity are introduced in the market. This pattern is followed by the hard drive cost, but not by memory costs.
Despite this incongruence, the instruments seem to be valid and relevant, as hinted by the F- and Sargan tests presented in Table 7. It should be noted however, that the variable HardDrive is not stationary (with a p-value of 0.3 in the augmented Dicky-Fuller test), which increases the chances of spurious correlation.
Furthermore, in the console market prices might not be endogenous. As stated in Lee (2013), consoles are being sold at or below cost, and console vendors make their profits by selling game developers the right to sell games for their hardware. Then price cuts are used to minimize losses through price discrimination, and might be little influenced by sales performance. Given these characteristics of the industry, it might be more relevant to study the endogeneity of exclusive games
Regarding the endogeneity of exclusive games, we can see that the instruments chosen are not not only non relevant but also weak instruments. In contrast with the results for endogenous prices, these estimates are not to different from those found for the base model.
2SLS
Endogenous Prices Endogenous Exclusives Variable Estimate Std Error Variable Estimate Std Error Exclusives 0.0160 0.0057 Exclusives 0.0299 0.0061 Mprice -0.0144 0.0026 Mprice -0.0026 0.0012 oexclusives 0.0408 0.0097 oexclusives 0.0639 0.0110 oprice -0.0192 0.0048 oprice 0.0015 0.0023 Games -0.0001 0.0010 Games 0.0004 0.0007 alpha1 7.0918 2.8132 alpha1 -5.4834 1.3890 alpha2 6.4104 2.9599 alpha2 -6.7502 1.5005 alpha3 5.9643 2.8814 alpha3 -6.9632 1.5335 alpha4 4.8585 2.9431 alpha4 -8.3322 1.6759 alpha5 3.4624 2.7817 alpha5 -9.0182 1.7231 alpha6 1.7597 2.8063 alpha6 -10.6887 1.8494 alpha7 0.8264 2.7211 alpha7 -11.1514 1.9000 alpha8 -0.2264 2.7985 alpha8 -12.4741 2.0645 alpha9 -0.2958 2.9137 alpha9 -12.9688 2.1862 alpha10 -1.2858 2.9193 alpha10 -13.8933 2.2952 alpha11 -2.0114 2.8443 alpha11 -14.2109 2.3248 First Stage
Endogenous Prices Endogenous Exclusives
Variable Estimate Std Error Variable Estimate Std Error HardDrive 5.6563 0.7782 Age 9.1518 20.2514 Memory -1.0283 0.3731 Stock 0.0341 0.1604 Exclusives -0.8655 0.2114 Mprice -0.1009 0.3226 oexclusives -1.4015 0.4174 oexclusives -2.1177 1.4450 oprice -1.4434 0.0704 oprice -0.2074 0.6005 Games -0.2125 0.0511 Games 0.0616 0.2491 Market Size 129 million Market Size 129 million
Sargan Test 0.5081 Sargan Test 29.6805 First Stage F-test 48.4435 First Stage F-test 0.0582
Table 7: 2SLS
5.4
Models with varying hazards
Table 8 shows the results of the NLS estimation, with different baseline hazards for the different consoles. The estimates are similar to those found for the base NLS model, with the exception of oprice, which more than doubles. The κ terms show that there is a difference in the baseline hazards of the different brands. A t-test shows that these two estimates are different from each other, as well as different than one, the value for which κW (the value for the Wii console) was
kept fixed. This result is the in line with the findings of Shankar and Bayus (2003), as we can expect these terms to pick differences in brand loyalty, which will in turn lead to different network effects for each of the competing companies. These baseline hazards are plotted in Figure 7.
parame-NLS
Variable Estimate Std Error WNLS Std Error κX 1.0996 0.0025 0.0034 κP 0.9010 0.000002 0.0000 Exclusives 0.0374 0.0181 0.0394 Mprice -0.0066 0.0063 0.0048 oexclus 0.0652 0.0989 0.1629 oprice 0.0048 0.0052 0.0017 Games 0.0028 0.0188 0.0347 alpha1 -5.5883 0.9953 1.1036 alpha2 -6.9115 0.5526 0.7850 alpha3 -7.1370 0.5299 0.0872 alpha4 -8.6094 0.4771 0.7432 alpha5 -9.2984 0.6851 0.8161 alpha6 -11.0094 0.5447 0.9367 alpha7 -11.5182 0.4427 0.6935 alpha8 -12.8698 0.2965 0.6259 alpha9 -13.3724 0.4844 0.2974 alpha10 -14.3186 0.6760 0.9344 alpha11 -14.6401 1.0142 1.2213 Market Size 86 million
Table 8: NLS with varying alphas
Figure 7: Heterogeneous Baseline Hazards
ters are quite close to each other, and their difference is not significant. In general the estimators are close to the ones found for the previous NLS results, but this model is however less efficient.
For the results shown in Table 8 and Table 9, the results for the NLS estimation were used as starting values for the WNLS estimation, which produced no different estimates.
Table 10 shows the results of the SURE using identical regressors keeping the market size fixed at 129 million for comparison with the previously shown OLS and SURE results, the variable names include the suffixes X,P,W signaling their relevant console, Xbox, PlayStation or Wii. Other than
NLS
Variable Estimate Std Error WNLS Std Error ξX 0.9451 0.5457 0.6740 ξP 1.2911 1.1431 1.2516 Exclusives 0.0386 0.0355 0.1980 Mprice -0.0049 0.0246 0.0355 oexclus 0.0718 0.0151 0.0110 oprice 0.0012 0.0484 0.0069 Games 0.0005 0.0136 0.0058 alpha1 -5.5934 0.0123 0.0042 alpha2 -6.9127 8.3978 0.4242 alpha3 -7.1378 8.3535 0.5695 alpha4 -8.6067 7.5359 0.5069 alpha5 -9.2789 6.8311 0.2603 alpha6 -11.0057 5.6801 0.0847 alpha7 -11.5020 4.5279 0.3764 alpha8 -12.8684 3.9078 0.5958 alpha9 -13.3848 2.8850 0.7309 alpha10 -14.3218 3.1023 0.4144 alpha11 -14.6498 1.1649 0.3657 Market Size 86 million
Table 9: NLS with heterogeneous term
Xbox360 PS3 Wii
Variable Estimate Std Error Estimate Std Error Estimate Std Error GamesX -0.0177 0.0145 -0.0214 0.0151 -0.0197 0.0152 GamesP -0.0030 0.0150 -0.0163 0.0156 -0.0068 0.0157 GamesW 0.0314 0.0087 0.0382 0.0091 0.0410 0.0092 PriceX -0.0096 0.0052 -0.0042 0.0054 0.0008 0.0054 PriceP 0.0037 0.0037 0.0003 0.0038 0.0000 0.0039 PriceW 0.0030 0.0033 0.0028 0.0035 0.0028 0.0035 ExclusivesX 0.0459 0.0300 0.0042 0.0313 -0.0123 0.0315 ExclusivesP 0.0733 0.0395 0.1015 0.0412 0.0607 0.0415 ExclusivesW -0.0300 0.0274 0.0068 0.0286 0.0042 0.0288 alpha1 -5.0177 1.7575 -5.9216 1.8367 -6.8654 1.8485 alpha2 -6.1843 1.8379 -6.6394 1.9207 -7.1483 1.9331 alpha3 -5.6445 1.8417 -6.1751 1.9247 -6.7970 1.9371 alpha4 -7.0131 1.9155 -6.5974 2.0018 -7.7492 2.0147 alpha5 -7.5701 1.8777 -7.3115 1.9624 -8.1367 1.9750 alpha6 -9.4162 1.9580 -8.7350 2.0462 -10.1102 2.0594 alpha7 -9.7340 1.9229 -8.8184 2.0095 -11.0233 2.0225 alpha8 -10.5567 2.0116 -9.8220 2.1023 -12.3296 2.1158 alpha9 -10.6133 2.1175 -10.1378 2.2129 -13.1508 2.2272 alpha10 -12.0575 2.1143 -11.3060 2.2096 -14.8964 2.2238 alpha11 -12.0745 2.1220 -11.1256 2.2177 -14.9933 2.2320
Table 10: SURE with identical regressors
the alphas, only the number of exclusives for PlayStation (ExclusivesP ) and the number of games for Wii (GamesW ) are significant. However, this results are relevant in order to test whether the parameters differ between consoles. The only significant difference at the 95% significance level is
found between the Xbox and Wii estimates for PriceX and ExclusivesX. This is, 0.03% of the 63 test rejected the null hypothesis.
Despite the results in Table 10 and 9, it can be stated that there exists a difference between the hazard functions corresponding to each brand. This difference lies in the baseline hazards, and the effects of the marketing mix are constant for all consoles. Again, the linkage with the theoretical diffusion model presented in Bass (2004) is that Sony managed to attract the most innovators to purchase the PlayStation3, while Nintendo and Microsoft felt behind.
6
Conclusions
This thesis estimates the effects of the marketing mix variables in the console video game market. Previous research in the topic did not account for the difference between regular games and exclu-sive games. The number of available excluexclu-sive games to a given consoles were found to be the main system sellers, while the effect of the regular games was found to be statistically insignificant. The magnitude of the effects found in this thesis is greater than those found in the previous literature. It should be considered that previous studies were carried out using data from previous console generations. These main results were used to compute the marginal effects and elasticities of the exclusive games and prices. Over time, the elasticity to prices decreased, while the elasticity to exclusive games increased.
The flexible semiparametric specification of the baseline hazards used in this thesis replicates the theory presented by Bass (2004) on the diffusion of durable goods. There is a group of consumers that will purchase the good independently of external factors. Over time, this kind of consumers represent a smaller fraction of the sales. Evidence was found that these baseline hazards are dif-ferent for the different consoles. This is in line with the results obtained by Shankar and Bayus (2003), and showcases that the differences between consoles appeal to different sorts of consumers.
While the efforts to instrument some of the potentially endogenous variables were unsuccessful, some of the pitfalls when modeling endogeneity in technological products were illustrated. Mainly, that the costs of technology will tend to go down. Then using costs as an instrument might lead to spurious relations.
Further research should aim to find relevant instruments for both games and prices, as well as considering a parametric specification of the baseline hazards. The study carried by Chintagunta
same way. As mentioned before, the main advantage of a predictive analysis would be to allow for prediction, but a specification such as the one presented by Bass (2004) would also inform on the shares of innovators and imitators in the pool of consumers.
Finally, the main limitation of this study is the quality of the sales data. The sales data comes from the highly renowned NPD survey. In the case of the seventh generation of video games, the data was presented to different media outlets, and I took the data from said outlets (where it is easily accessible) and not directly from NPD (which sells the data for a profit). Since the data was taken from a third party source rather than directly from the original source, the chances increase of having some type of measurement error, such as a typo.
A
First Stage Regressions Full Results
Table presents the full output of the first stage regression for the 2SLS estimation presented in Section 5.3.
First Stage
Endogenous Prices Endogenous Exclusives
Variable Estimate Std Error Variable Estimate Std Error HardDrive 5.6563 0.7782 Age 9.1518 20.2514 Memory -1.0283 0.3731 Stock 0.0342 0.1604 Exclusives -0.8655 0.2114 Mprice -0.1009 0.3227 oexclusives -1.4015 0.4174 oexclusives -2.1177 1.4450 oprice -1.4434 0.0704 oprice -0.2074 0.6005 Games -0.2125 0.0511 Games 0.0617 0.2491 alpha1 939.6624 33.3552 alpha1 124.2922 343.8708 alpha2 957.7990 34.9721 alpha2 125.9924 356.2628 alpha3 927.3205 36.1845 alpha3 126.3341 348.9882 alpha4 948.6546 38.9437 alpha4 145.5541 351.3716 alpha5 910.8256 39.2654 alpha5 149.9231 332.5665 alpha6 924.3496 42.1705 alpha6 164.8193 331.8543 alpha7 899.8315 44.6898 alpha7 166.0184 327.7535 alpha8 926.5494 49.3938 alpha8 176.0271 343.3677 alpha9 970.3514 53.5945 alpha9 186.2234 364.2374 alpha10 974.3344 55.5954 alpha10 181.6367 379.8202 alpha11 948.1963 58.1283 alpha11 176.0967 390.4904
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