Is the Video Games Industry Recession Proof?

UNIVERSITY OF TARTU Faculty of Social Sciences School of Economics and Business Administration Yesudassen Pillay Mauree “IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF?” Master’s Thesis Supervisor: Prof. Ricardo Alfredo Mendes Pereira Vicente Tartu, 2022 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? I have written this Research paper/Master’s Thesis independently. Any ideas or data taken from other authors or other sources have been fully referenced. IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? Abstract This master’s thesis investigates the relationship between GDP growth and video games revenues’ growth by testing for the presence of Granger-causal relationships between GDP growth rates and video game revenue growth rates through the application of VAR models, IRF curves, and the Toda-Yamamoto (1995) Granger Causality method; using Video Games Revenues’ annual Growth Rates (Total and by segment) and GDP Growth Rates of North America, Europe & Central Asia, East Asia Pacific, and South Asia from 1972 to 2019. Our analysis shows no general evidence of GDP growth rates Granger-causing Video Games Growth rates, except in the region of North America for the console segment and video games industry. We also find strong evidence that the mobile gaming revenue is granger-caused by GDP growth in Europe & Central Asia and South Asia. IRF curves further show a short-run inverse relationship between GDP-growth rates and video games growth rates across segments in North America, which points to the industry being recession-resistant in that area. Keywords: Video games, Recession-proof, Granger Causality, Vector Autoregressive Model, Toda-Yamamoto Causality Test. CERCS: S180 Acknowledgments I would like to express my heartfelt gratitude to my esteemed supervisor Prof. Ricardo Alfredo Mendes Pereira Vicente for his patience, expertise, and invaluable guidance. I am immensely thankful to Prof. Jaan Masso and Prof. Mustafa Hakan Eratalay for their feedback and knowledge which were instrumental in the writing of this paper. Additionally, I would like to thank the University of Tartu for allowing me the opportunity to undertake my master’s degree. I am also very grateful to my family for their emotional and mental support throughout the duration of this course. Finally, I would like to thank video games for being an ever-present source of inspiration. IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? Table of Contents 1. Introduction: A case for video games................................................................. 1 2. Literature review ................................................................................................. 3 2.1 A general overview ................................................................................................ 3 2.2 Gaming hours vs Labor hours ............................................................................. 6 2.3 The Lipstick Effect ................................................................................................ 6 2.4 The habit-forming nature of video games .......................................................... 7 2.5. Vice Industries & recession resilience ................................................................ 8 3. Data and Empirics ............................................................................................... 9 4. Methodology ....................................................................................................... 12 5. Results and Discussions ..................................................................................... 17 6. Conclusions ......................................................................................................... 26 7. References ........................................................................................................... 27 8. Appendix ............................................................................................................. 32 List of Figures Figure 1: Video Games Revenue over the years ....................................................... 1 Figure 2: IRF for Video Games Industry, arcade and handheld ......................... 19 Figure 3: IRF for Console, Mobile, and PC............................................................. 20 List of Tables Table 1. GDP Growth Rates ........................................................................... 10 Table 2. Video Games Revenue Growth Rates .............................................. 11 Table 3. ADF Test for Stationarity and max I(0) .......................................... 12 Table 4. lag selection as per FPE, AIC, HQIC, and SBIC ........................... 13 Table 5. Johansen Cointegration test results ................................................. 14 Table 6. Heteroskedasticity Tests ................................................................... 16 Table 7. Selected Results from Augmented VAR .............................................17 Table 8.1-8.9. Granger Causality Tests .............................................................. 22-23 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? 1. Introduction: A case for video games “We would like to convince you that there is indeed a market in which money can be made in the near future.” – Ralph Baer (The Father of Video Games), 1968 Video games are big business. While they were originally seen as a fad that would quickly die out when they were first introduced to the consumer market in the early 1970s, the video game industry boasted a whopping $159.3 Billion estimated revenue in 2020, dwarfing the Movie and Music industries by around 4 and 3 times respectively (Newzoo, 2020). Even more impressively, the latest DFC intelligence report (March 2022) estimates that around 40% of the world population (around 3 billion people) play some form of video game. These numbers are expected to increase further as the global covid-19 pandemic persists. The industry has also been growing rapidly for the past couple of decades, consistently and increasingly exceeding analyst expectations – 2016 estimates for 2020 revenue were 90 billion USD, while actual industry values in the said year were 76.8% higher. The industry is hence set to hit the 200 billion USD mark by 2023. (Statista, 2020). Figure 1: Video Games Revenue over the years Source: Bloomberg Finance 2019, Statista 2020 1 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? The historical importance of video games and their contributions to society therefore shouldn’t be overlooked. As video games become increasingly accepted as a form of art and entertainment in contemporary culture, it can be argued that their influence on society grows accordingly (Ivory, 2015). Since their inception, video games have generally been regarded as significant drivers of progress, often acting as catalysts for the development of numerous new technologies, from 3D graphics computing to game controllers routinely being repurposed for military and space exploration purposed by the US Army and NASA. Sherry (2015) explores the different ways in which video games can be used as an educational tool to promote learning at different ages. Likewise, Dale and Green (2015) investigate the claims that video games positively influence perceptual and cognitive measures and concluded that they did result in better spatial selective attention. Olson (2015) further writes about how educational video games geared towards health and medical purposes are useful in instructing users on nutrition, emergency health procedures, or managing illnesses, while persuasive games can help gamers be more productive and overcome addictions to substance. Considering the impact and growth of the industry, there have been numerous claims of the latter being immune to recessionary turmoil (as discussed in the literature review). However, there also seems to be a significant gap in the literature when it comes to the empirical study of the economics of video games, and the recessionary-resistant features it allegedly has. This paper aims to empirically determine whether the claim that the video games industry is unaffected by recessions is empirically sound. Hence, we set out to find if video game revenue growth is affected by GDP growth (considering that recessions are characterized by periods of negative GDP growth), and if this is the case for the industry as a whole or specific segments only (ie. Arcade, Handheld, Console, Mobile and PC gaming). We only consider direct video game revenue streams from the sale of hardware and software, and disregard indirect revenue from esports and merchandising. Furthermore, this study does not factor in Virtual Reality gaming due to its novelty and subsequent lack of data. The structure of this paper is as follows: the next section deals with the literature review on the video games industry’s wider economic impact, followed by an analysis of prior research pertaining to the effects of video games on the labor market, as well as theories regarding recession-resistant industries and habit-forming good. 2 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? We then move on to a presentation of the data used in our study and document the application of lag-augmented VAR models to test if GDP growth rates Granger-cause Video Games Revenue Growth Rates. We find evidence of counter-cyclicity in North America for the video games industry and the console segment, implying that the industry thrives during recessions. Our results overall support the general claim that the video games industry is recession-proof for the rest of the segments and geographical areas, except for the mobile game industry in Europe & Central Asia and South Asia. We end our analysis by discussing our results and drawing parallels with prior papers and existing economic theory relating to recession-proof industries. 2. Literature review 2.1 A general overview: From philosophers to science-fiction writers, the virtual experiences offered by video games have often been regarded as having the potential to drastically change the way humans interact inside and outside of the virtual space. Søraker (2010) explores the question of how activities in Massively Multiplayer Online games such as Second Life and World of Warcraft affect how people act, communicate, and overall exist in the real world, by analyzing how multiplayer games influence the gamer’s philosophical concept of well-being, while also drawing on psychological research regarding arbitrary concepts of wellness. In his 2011 novel Ready Player One, Cline imagines a world ravaged by climate change, pollution, and overpopulation where humanity retreats into an alternate reality in the form of an ultra-realistic Virtual Reality online game, complete with its own economy and societal system. While seemingly whimsical, such works of fiction remind us that as technology evolves and video games become more realistic, the potential effects of video games on humans as a species grow past what we presently may deem rational. With the advent of the metaverse and the move towards WEB 3.0, numerous business and tech analysts, JP Morgan (2022) predict that this vision of the future grows ever more into an eventuality. More recently, politician Alexandria Ocasio-Cortez broadcasted herself playing the video game “Among Us” with popular internet personalities on the streaming platform “Twitch” during the 2020 US presidential elections campaign. While unconventional, this can be seen as a novel way for politicians to interact and cultivate relatability with their target demographics. 3 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? The event ended up being watched by around 439,000 users concurrently, leaving Cortez with the title of third most-watched twitch individual streamer as of October 2020. Analysts have qualified this event as significant in the outcome of the elections, encouraging many youths to cast their votes for the democratic party (The Guardian, 2020). Indeed, it can be argued that Gaming Streamers and Youtubers are the new ‘rockstars’. Youtube gaming has roughly doubled in size from 2018 to 2020, with around 100 billion hours of gaming-related content being watched on the website in the last year, 10 billion of which were from live-streaming from gamers (Wyatt, 2020). Other platforms such as Twitch and Mixer offer highly skilled competitive gamers a platform to transform themselves into internet entertainers rather than only competing in e-sports tournaments. Forbes 2020 estimates for the top-earning pro-gamers showcase figures as high as $17 million with Tyler Blevins (a.k.a “Ninja”) at the top spot, followed by the likes of PewDiePie ($15 million) and Preston Arsement ($14 million). Therefore, it is evident how much influence these gaming entertainers have on ever-growing crowds of gaming fans; and the significant economic and political power that such popularity entails. Speaking of pro-gamers and esports- while esports figures are not considered in the Pelham Smithers data presented earlier, the esports gaming industry is growing rapidly together with the video games industry, with a revenue of around $1.06 billion in 2020 (Statista, 2020). I chose not to include esports data for the sake of caution, but it is to be noted that the use of conservative figures undervalues the enormity of the video game industry by excluding brand deals, licensed movie spin-offs, merchandising, and so on. Hence, considering that the video games industry has experienced consistently positive growth figures since as far back as 1995 regardless of recessionary years (Bloomberg, 2019), as well as the aforementioned discussion about its tremendous potential and impacts on the economy and society as a whole: is it unsurprising that news outlets and industry analysts have frequently put out sensationalist headlines about the video games industry being recession-proof. 4 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? “Is the video game industry recession-proof?” - NBC News, March 2008 “Analyze This: Is the Video Game Industry Recession-Proof?” - Gamasutra, 2008 “Play on -Video games have proved to be recession-proof—so far, at least” - The Economist, 2008 “Pandemic Video-Game Boom Sends Sales Forecasts Soaring” - Bloomberg, 2020 “Is Gaming Recession-Proof? Record Revenue For $160 Billion Industry With 2.7 billion Players” - Forbes, 2020 “Fully Charged - The Video Game Industry Is Consolidating” - Bloomberg, 2021 “Gaming Industry Sees Big Growth While People Stay Home” - Forbes, 2021 These are but a few of the hundreds of news headlines that have popped up over the years, especially during times of economic downturn. And understandably so- despite recessionary events, video game revenue seems to showcase an ever-positive trend. It is hence surprising that despite the question of whether video games are recession-proof is so often asked- there seems to be a significant gap in the literature on the topic in the field of academia. Huntemann (2010) briefly depicts the discourse around the video game industry in the period 2000-2010 and argues that when it comes to the industry’s resilience to a recession, it is mostly hits-driven (that is, the industry performance depends on the quality of the products it churns out, and recessionary years have potentially coincidentally also been hit-years). Furthermore, they conclude that while video game revenue has mostly resisted the economic downturn at the end of the decade, it still experienced a deep fragmentation of its demographic and market segments. While a plethora of academic papers exists on in-game video game economies such as the works of Castronova (2002), Hamidi (2018) & Bilir (2020), a lack of research on real-life video game economics is very much observed, and the inner workings of the video game industry from an economics perspective are still relatively unexplored. For the sake of this paper, the use of economic research on recession-proof industries and recession-related concepts is hence necessary, as these may apply to the video games context. 5 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? 2.2 Gaming hours vs Labor hours Using Engel leisure curves, Aguiar et al. (2017) found that over the years, younger male workers significantly decreased their amount of labor hours supplied compared to older male workers or female workers due to an increase in leisure hours directly attributed to video gaming consumption. Furthermore, as innovations in video games increased the quality of the product, the fall in labor hours increased steeply compared to other demographics. Likewise, Pasharov and Paklina (2019) found a positive relationship between video games' popularity and unemployment rates, despite the subsequent fall in the income of gamers. This dynamic between labor and gaming hours can arguably happen the other way around: during recessions, layoffs and falls in wages result in a fall in labor hours supplied and a rise in unemployment. It is hence reasonable to infer that this increase in free time or leisure hours is likely to drive up the demand for leisure and entertainment in the form of video games, despite the expected fall in income. 2.3 The Lipstick Effect Economic theory tells us that economic recessions are often associated with a relative increase in consumer spending on inferior goods (such as lower quality staples), and morale boosters (such as the consumption of uplifting media during a time of economic turmoil.) In this regard, the “Lipstick Effect” was coined by the honorary chairman of cosmetic company Esteé Lauder, who remarked that the sales of lipstick increased significantly during the 2001 recession, especially after the 9/11 attacks on the World Trade Centre. Lauder later brought up that a similar upward shift in lipstick consumption occurred following the 2008 recession. (Chan 2021) As such, the lipstick effect stipulates that those affordable luxuries experience an increase in demand compared to less affordable luxuries, due to the “feel good” or “morale-boosting” factor that they provide. Using real-world data and five different experiments studying the dynamics of unemployment and consumer spending priorities, the psychological impacts of recessions on mating preferences, and the comparison of the impact on beauty products versus inferior goods (lowcost indulgences), Hill et al (2012) argue that women's spending on beauty product can be seen 6 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? as an indicator of economic recessions. Similarly, Finuras (2017) argues that the increase in demand for lipstick is more significant than other types of cosmetics due to lipsticks being relatively more efficient in “beautifying and attracting” compared to other beauty products. While the lipstick effect has mostly been used when considering beauty products, Tajtakova et al. (2020) show that hedonic consumption in the face of recessions as stipulated by the theory can also be applied to other goods and services; by demonstrating through empirical analysis the increased consumption of Outdoor Cultural events (theatre, cinema, and similar forms of entertainment) in Slovakia during recessionary times, potentially due to the escapism that such consumption items offer. This is a particularly interesting argument in the case of video games (assuming these can be considered to be affordable luxuries compared to expensive holidays or theatre plays, and morale-boosting due to their entertainment nature), as it may account for the general claim that video games tend to be more recession-resistant. 2.4 The habit-forming nature of video games “Gaming Disorders” is listed by the WHO (2018) as “gaming behavior ... characterized by impaired control over gaming, increasing priority given to gaming over other activities to the extent that gaming takes precedence over other interests and daily activities, and continuation or escalation of gaming despite the occurrence of negative consequences.” Looking at the field of psychology, there is plenty of literature regarding the addictiveness of video games. Rooji (2010) explores how gamers can exhibit the behavior of addiction which disrupts other facets of their school, work, and social life. An interesting comparison is made between the gambling industry and gambling addiction despite the latter being much more regulated than the video games industry. Adding to the research on gaming addictions, Sigerson et al. (2017) empirically test the validity of the Chinese Internet Gaming Disorder Scale (C-IGDS) and provide the reader with an indepth picture of how extensive the degree of addiction to online video gaming can be. Saquib et al. (2017) demonstrated through survey data that a significant proportion of students (16%) suffered from psychological distress associated with video game addiction. 7 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? This is further reflected by Gros et al. (2020), who provide an in-depth dive into the literature surrounding video game addiction and the confusion between gratification and happiness that comes from addictive video gaming behavior. The paper also investigates the relationship between different psychological indicators across study groups and provides many insights into how video game addiction can substantially affect video gamers that become too enthralled by the virtual world. After considering the habit-forming and sometimes addictive nature of video games, it is sensible to consider the literature on how industries with addictive products fare during recessions. 2.5 Vice Industries & recession resilience Vice industries can be defined as those industries that are generally regarded as of questionable morality, addictive, and/or harmful to society, such as alcohol, gambling, weaponry, pornography, and other such industries. In their financial textbook, Latane & Tuttle (1970) argue that investing in “sin” stocks during recessions is a viable way of diversifying portfolios, since, in their own words `smokers, eaters and drinkers continue to smoke, drink and eat, no matter what . . . which is why the stocks of companies supplying these demands are usually described as ``defensive’’. Ahrens (2004) wrote about the financial ingenuity of investing in firms involved in these activities, which bear a certain social stigma due to ethical grey areas and often harmful societal spillover effects. Despite being generally frowned upon, Ahren argues that these industries tend to feature robust anti-recessionary behavior. From a more empirical viewpoint, Freeman (2001) uses an error-corrected VAR model to test for Granger causality between beer consumption and macroeconomic indicators relating to economic activity and finds significant support for the claim that beer sales are relatively unaffected by economic cycles, and hence arguably “recession-proof”. Furthermore, cointegration among the variables suggests the existence of long-term stability in this equilibrium. 8 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? In the same vein, Richey (2020) uses an EGARCH model to model the volatility of select Sin portfolios (funds consisting of stocks of companies in the Alcohol, Tobacco, Gambling & Defense industries.) against barometers such as the S&P500, BAB, and T-bill. Hence, it is shown that Vice-related stocks have less systematic risk than the market index (beta <1) while outperforming the S&P500 in terms of mean returns. Through variance modeling, Sin stocks are also shown to not be subject to high volatility for long periods, following negative shocks. Richey concludes that positive shocks have a greater impact on the volatility of sin-stocks than negative shocks do. Hence these studies paint a general picture of how “vice” industries, through their habit-forming nature, often display relatively more resilience and stability during recessions than non-vice industries. Considering how video games industries have shown addictive tendencies similar to those of “vice” industries, it thus makes sense to contrast the behavior of said industries using the same methodologies. Hence Freeman's (2001) methodology was used as a baseline for our study. 3. Data and empirics Due to Real GDP figures being in trillions, and Real Video Game Revenue values being in billions, our two main sets of variables were converted into their continuous growth rates to facilitate comparison. This was achieved by taking the difference in the log of each series, which leaves us with Real GDP Growth (by geographical area) and Real Revenue growth (for the total industry, and by segment), The Real Gross Domestic Product was procured from the World Bank database and consists of annual real GDP segmented by geographical area. Considering that the bulk of video game revenue comes from North America (25.1%), Europe (18.6%), and Asia (49.2%), the real GDP for North America, Europe, and Central Asia, East Asia & Pacific, and South Asia were included. A full list of all individual countries included in these segments can be found on the World Bank database website. Latin America and Africa were omitted due to contributing only around 7% of total video game revenue, for the sake of simplicity (Newzoo 2021). 9 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? Furthermore, Aggregate World GDP was dropped after testing for high multicollinearity with the other GDP variables. Multicollinearity Tests were carried out with the remaining GDP variables by running linear regressions with their respective Industry segments and generating Variance Influence Factor values. (Appendix 1), leaving us with our chosen GDP Growth Rates variables by geographical area. Table 1 GDP Growth Rates Descriptive Statistics (1972 – 2019) GDP Growth Rates North America East Asia Pacific Europe & Central Asia South Asia Mean 0.0276 0.0485 0.0215 0.0517 Standard Error 0.0028 0.0020 0.0024 0.0031 Median 0.0290 0.0488 0.0229 0.0570 Standard Deviation 0.0192 0.0140 0.0167 0.0216 Sample Variance 0.0004 0.0002 0.0003 0.0005 Kurtosis 0.7675 2.2419 4.3536 4.1878 Skewness -0.6764 -0.7519 -1.2309 -1.7503 Range 0.0959 0.0697 0.1032 0.1073 Minimum -0.0260 0.0043 -0.0448 -0.0268 Maximum 0.0698 0.0740 0.0585 0.0806 Sum 1.3229 2.3265 1.0308 2.4833 Count 48 48 48 48 Annual Nominal Video Games Industry Revenue, originally compiled by Pelham Smithers, was web scraped from Bloomberg (2019). The original data consists of the annual total video games industry revenue as well as global revenues by segment (Arcade, Personal Computer (PC), Handheld, Consoles). Being in nominal terms, these series were deflated using CPI data from the World Bank database to convert them to real values and enable comparison with the Real GDP data (at 2015 base values). It is to be noted that the dataset also included Virtual Reality revenue values. These were dropped as VR, being fairly new, offered only 5 data observations. This set of data was converted into growth rates as shown in Table 2. 10 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? The values for video game revenue for 2020 were dropped due to being unconfirmed estimates. Furthermore, while news outlets report unprecedented growth in the industry, it is to be noted that, unlike prior recessions, the covid-19 pandemic forced people indoors and thus, pushed consumers towards indoor entertainment. Considering the unique set of circumstances involved, including these estimates is likely to push for biased results, hence the omission. Table 2: Video Games Revenue Growth Rates Descriptive Statistics Revenue Growth Rates Video Games Industry Arcade Console PC handheld mobile Mean 0.0714 -0.0168 0.0457 0.0745 -0.0372 0.1680 Standard Error 0.0357 0.0358 0.0683 0.0422 0.0622 0.0293 Median 0.0575 -0.0220 0.0648 0.0560 0.0214 0.1532 Standard Deviation 0.2472 0.2482 0.4584 0.2567 0.3405 0.1407 Sample Variance 0.0611 0.0616 0.2101 0.0659 0.1159 0.0198 Kurtosis 3.0395 1.0892 5.7422 6.1754 4.6140 8.0006 Skewness 0.3522 0.5777 -0.6121 1.5755 -0.9122 2.3547 Range 1.4779 1.1928 3.1614 1.4968 1.8816 0.7037 Minimum -0.6502 -0.5420 -1.6406 -0.4366 -1.2217 -0.0217 Maximum 0.8277 0.6508 1.5209 1.0602 0.6599 0.6820 Sum 3.4288 -0.8073 2.0549 2.7565 -1.1153 3.8647 Count 48 48 45 37 30 23 Time-period 1972 2019 1972 2019 1975 2019 1983 2019 1990 2019 1997 2019 It is to be noted that one significant limitation of this paper is the restrictive dataset. Unfortunately, there appears to be a lack of data on the video games industry. Other than the Pelham-Smithers dataset, firm-level data was deemed too difficult to obtain since 1) Historical data for firms was often locked behind corporate secrecy, and 2) it is difficult to identify specific video game revenue in diversified companies like Sony (PlayStation) and Microsoft (X-box). 11 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? Ideally, access to higher frequency data would make the models more robust. However, considering that only annual data is available and that certain segments of the video game industry were introduced as recently as the mid-90s (notably Mobile-phone gaming), certain compromises had to be made when it came to specifying the models (especially when choosing lags) to keep them stable. 4. Methodology Building on the methodology used by Freeman (2001) in his analysis of Beer and the Business Cycle, this paper uses a VAR framework to test for Granger causality between the growth rates of the video game industry revenues (total and by segment) and the growth rates of the GDP of select geographical blocks. The first step was to test for stationarity in the series. An augmented dickey fuller test was run, and the following results were obtained when using 2 lags. (Experiments with more and fewer lags were run, resulting in the same conclusions) Table 3: Augmented Dickey-Fuller Test for Stationarity and maximum order of Integration growth rates p-values VGI Revenue North America GDP East Asia Pacific GDP Europe & Central Asia South Asia Arcade Revenue North America GDP East Asia Pacific GDP Europe & Central Asia South Asia growth 0.0009 0.0008 0.0052 0.0043 0.0009 0.006 0.0008 0.0052 0.0043 0.0009 Max I(x) 0 0 0 0 0 0 0 0 0 0 growth rates p-values Handheld Revenue North America GDP East Asia Pacific GDP Europe & Central Asia South Asia Mobile Revenue North America GDP East Asia Pacific GDP Europe & Central Asia South Asia level 0.7312 0.2486 0.1678 0.082 0.0226 0.0000 0.0601 0.0997 0.1519 0.1132 1st diff 0.0275 0.0066 0.0012 0.0104 0.0182 0.0142 0.0052 0.0007 0.0119 Max I(x) 1 1 1 1 1 0 1 1 1 1 Console Revenue North America GDP East Asia Pacific GDP Europe & Central Asia South Asia 0.0000 0.0016 0.0266 0.0083 0.0244 0 0 0 0 0 PC Revenue North America GDP East Asia Pacific GDP Europe & Central Asia South Asia 0.0000 0.0601 0.0997 0.1519 0.1132 0.0142 0.0052 0.0007 0.0119 0 1 1 1 1 Since H0 in the Dickey-Fuller test is that the variable exhibits a unit root; we reject the null hypothesis when the p-value is less than 0.05 (at 5% significance levels) 12 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? Hence, we find out that all variables are stationary for the Revenue Growth of the Total Video Game Industry, Arcade, and Console. However, For Handheld, Mobile and PC, the variables are not stationary at level but have a maximum integration of order 1. The optimum number of lags overall is determined to be one (t*=1) as per FPE, AIC, HQIC, and SBIC criteria. This is consistent with the literature since we are using annual data, hence no seasonality comes into play, and congruent with our limited dataset. Extra lags are later added to the appropriate models, as discussed further down. Table 4: lag selection as per FPE, AIC, HQIC, and SBIC lag LL LR df p FPE AIC HQIC SBIC 8.40E-17 -22.8234 -22.4582 -22.6226* Arcade 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 518.526 545.411 53.771 25 0.001 7.8e-17* -22.9072* -22.7485* -21.7027 565.266 39.709 25 0.031 1.00E-16 -22.6785 -21.8553 -20.4703 2.50E-21 -30.4162 -30.3252 -30.1679* Console 456.989 485.443 56.908 36 0 1.3e-21* -31.111 -30.4741* -29.3733 511.483 52.08 36 0 1.30E-21 -31.2027* -30.0199 -27.9756 7.60E-17 -22.9211 -22.8484 -22.6832* Handheld 325.896 366.106 80.42 25 0 2.7e-17* -24.0076* -23.5712* -22.5802 387.034 41.856* 25 0.019 4.30E-17 -23.7167 -22.9167 -21.0999 1.90E-24 -37.6052 -37.5405 -37.3068 Mobile 400.855 459.539 117.37 36 0 2.50E-25 -39.7656 -39.3123 -37.6766 520.848 122.62* 36 0 6.8e-26* -42.176* -41.334* -38.2963* 1.90E-17 -24.3018 -24.2252 -24.0773* PC 418.13 460.006 83.752 25 0 7.3e-18* -25.2945* -24.8352* -23.9477 476.681 33.349 25 0.123 1.30E-17 -24.8047 -23.9627 -22.3356 13 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? Video Games Industry 0 1 2 519.173 8.20E-17 -22.8522 -22.6727 -22.6514* 550.238 62.13 25 0 6.3e-17* -23.1217* -22.7773* -21.9173 574.326 48.176 25 0.004 6.80E-17 -23.0812 -22.258 -20.873 It is to be noted that the Mobile segment required 2 lags: however, I chose to use only one because the dataset for mobile is small (n=21), resulting in an unstable model if too many lags are taken. This is later remedied by using the augmented-lag model. Next, the Johansen Cointegration test was run to determine the number of cointegrating equations, which would point to whether a Vector Error Correction Model would be needed. The following results were obtained: Table 5: Johansen Cointegration test results. Johansen Cointegration Test Video Games Industry Revenue Arcade Revenue Console Revenue handheld Revenue Mobile Revenue PC Revenue Cointegration rank 0 0 0 2 2 3 Cointegration equations were found in all handheld, Mobile, and PC Revenue growth models. This implies the potential existence of long-term stable relationships between the variables of the models and warrants further testing of Granger Causality. Generally, this would entail the need for a VEC Model to be specified to incorporate Cointegration Equations. However, attempting to do so with our small sample results in unstable models with autocorrelations in the residuals, eigenvalues exceeding 1, and residuals being not normally distributed when going through the post-diagnostics (Especially in smaller datasets like Mobile). 14 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? As an alternative to the use of VECs, the Toda-Yamamoto (1995) Granger-causality method is used instead, whereby a lag-augmented VAR (in levels) is instead specified to account for the cointegration. As proven by Toda-Yamamoto, adding an extra number of lags equal to the maximum order of integration (dmax) to a VAR’s optimum lag (t*) allows for the added lags to capture the cointegration elements. This causes a notable loss of prediction power of the coefficients of the VAR model: however, if one’s aim is not to interpret the model but to test for Granger Causality between the variables (as in the case of this paper), then running Grangercausality tests post-estimation factoring in only the optimum lags, allows for a reliable method to test for Granger causality. Furthermore, empirical tests of the Toda Yamamoto method have shown that the loss in power of the VAR is often negligible, hence allowing for prediction despite the truncated model (Clarke & Mirza 2006). As such, the following set of equations is specified. 𝑔𝑉 = 𝛼 + 𝛽 𝑔𝑉 + +𝑈 ( ) 𝜓 𝑔𝑁𝐴 + 𝜂 𝑔𝐸𝐴𝑃 + 𝜃 𝑔𝐸𝑈𝐶𝐴 + Where gVZt is the growth rate of the video games industry revenue of segment Z 𝑉𝑖𝑑𝑒𝑜 𝐺𝑎𝑚𝑒𝑠 𝐼𝑛𝑑𝑢𝑠𝑡𝑟𝑦 𝐴𝑟𝑐𝑎𝑑𝑒 ⎛ 𝐻𝑎𝑛𝑑ℎ𝑒𝑙𝑑 And VZ =⎜ 𝐶𝑜𝑛𝑠𝑜𝑙𝑒 ⎜ 𝑀𝑜𝑏𝑖𝑙𝑒 𝑃𝐶 ⎝ ⎞ ⎟ ⎟ 𝜑 𝑔𝑆𝑂𝐴 (1) (2) ⎠ gNA is the growth rate of North America GDP gEAP is the growth rate of East Asia Pacific GDP gEUCA is the growth rate of Europe & Central Asia GDP gSOA is the growth rate of the South Asia GDP Uc is an error term that captures the residuals in the model t = augmented lag, whereby t = t* + dmax (3) ; t*= optimal lag length ; dmax = maximum order of integration 15 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? It is to be noted that ‘g’ is not a parameter in this case but is used as a notation to denote the use of the growth rate. Hence, six distinct equations are obtained for each component of V t, resulting in six lag-augmented var models in levels (still computed using the growth rates of the variables). Since the maximum order of integration was found to be 0 for Video Games Industry, Arcade, and Consoles, and 1 for Handheld, Mobile, and PC, this extra lag is added to the previous optimum lag chosen (t*+dmax), resulting in a lag augmented models consisting of t=1 and t=2 for each set of equations respectively. The results are discussed in the next section (Table 7) Table 6: Heteroskedasticity Tests Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance ; Variables: fitted values of squares of residuals Video Games Industry Arcade Handheld Console Mobile PC Chi2 8.54 18.45 23.79 7.15 4.09 30.06 Prob > chi2 0.0035 0 0 0.0075 0.043 0 P<0.05; presence of heteroskedasticity warrants the use of robust errors Due to the presence of heteroskedasticity as per the Breusch-Pagan / Cook-Weisberg test in Table 7 (whereby p<0.05), the use of robust errors instead of standard errors was implemented to solve the issue and avoid overestimating the significance of the variables. Post-estimation diagnostics for the lag-augmented VAR models can be found in the Appendix (Appendix 2.1– 2.6), to support the validity of the model. All the equations fulfill the VAR stability criteria, since all eigenvalues lie within the unit circle. All the models also pass the Lagrange Multiplier Test, except for mobile due to the latter’s small sample size, which made taking more lags impractical. This leaves us with some autocorrelation in the mobile model, which could make the estimators less efficient. The main issue in our model is seen in the Jarque Bera Test, which shows that our errors are not normally distributed. This was partly fixed by using robust errors and small-sample degrees-of-freedom adjustments when running the var. However, the problem persists and may affect the efficiency of our models. 16 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? 5. Results and Discussions Considering that the focus of this paper is analyzing the unilateral relationships between GDP growth rates and Revenue Growth rates, only results about these are extracted from the 6 VAR results. Table 7: Selected Results from Augmented VARs G G G G G G Video Games Arcade Handheld Console Mobile PC G Industry 0.410** 0.392** 1.077* 0.205 0.279* 0.455** Segment [β] L1 (0.193) (0.185) (0.550) (0.261) (0.131) (0.173) Coefficients G Industry -0.409 0.0158 -0.341 Segment [β] L2 (0.448) (0.140) (0.203) G North -3.715* -1.096 -6.784 -10.41* -3.204 -3.308 America [ψ] L1 (2.878) (2.800) (6.610) (5.787) (2.311) (2.888) G North 8.921 -2.805 -0.289 America [ψ] L2 (8.459) (3.276) (2.626) G East Asia -0.703 0.0667 3.641 -0.909 -3.262 1.034 Pacific [η] L1 (2.489) (2.454) (4.324) (4.369) (2.265) (2.276) G East Asia 1.033 0.648 1.122 Pacific [η] L2 (2.874) (1.566) (2.613) G Europe& 4.714* 2.228 5.806 8.855* 5.072** 1.290 Central Asia [θ] L1 (2.561) (1.230) (5.174) (5.250) (2.215) (2.784) G Europe & -5.407 1.766 0.635 Central Asia [θ] L2 (7.389) (1.887) (2.248) G South Asia -0.604 -1.885 1.209 1.661 3.337* 0.657 [φ] L1 (0.997) -1.432 (2.965) (2.611) (1.730) (1.984) G South Asia -9.122 -1.757 -1.057 [φ] L2 (7.414) (2.087) (1.780) Constant 0.0969 0.0487 0.116 0.0624 0.130 0.0119 [α] (0.145) (0.138) (0.364) (0.193) (0.100) (0.158) Observations 47 47 28 44 21 35 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 17 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? It is to be noted that the term “G Industry Segment [β] Lx” refers to the respective model’s industry’s own xth lagged variable, L being the lag operator. While the focus of the paper is the Granger Causality results, it is still useful to interpret the significance of the results of the lag-augmented VAR models. Looking at relationships between industry segments and geographical areas, the coefficients for North America and Europe & Central Asia in both the Video Games Industry and Console equations are found to be statistically significant at the 10% level. We also find significant coefficients for Europe & Central Asia and South Asia in the mobile equation at the 5% and 10% levels respectively. This points to the existence of relationships between GDP growth rates in these specific geographical areas and the Revenue Growth of the Video Games Industry, Console, and Mobile segments. The rest of the coefficients, as well as all coefficients for Arcade, Handheld, and PC, are not statistically significant, pointing towards Revenue Growth Rates for these segments not being affected by GDP growth rates. Most interestingly, we find negative coefficients across North America for all segments, for which the total video games industry and Console segments are significant. These are mirrored when looking at the Impulse Response Functions (Figures 2 and 3) which show the Responses of the Revenue Growths rates in response to a one standard deviation Impulse (or shock) in GDP growth rates. Overall, we see that Revenue growth rates across segments tend to stabilize in the long run (4 periods) after a brief initial increase in the short run when faced with an increase in GDP growth rates of one standard deviation for all geographical areas except for North America (gna). The latter features a negative impulse response in the short run, which points toward the existence of an inverse relationship between GDP growth rates and Revenue Growth rates in North America. 18 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? Figure 2: Impulse Response Functions for the Video Games Industry, Arcade, and Handheld. 19 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? Figure 3: Impulse Response Functions for Console, Mobile, and PC segments. 20 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? The Granger Causality test can be run normally for the Video Games Industry, Arcade, and Console models since dmax for these was 0, hence no lags were added. For the Handheld, Mobile, and PC models, however, individual Wald tests were computed taking only into consideration t*=1 and disregarding the added augmented lag; as per the Toda-Yamamoto method. Hence, we conduct the following hypothesis tests, whereby H0 implies non-causality, If the p-value is less than 0.05, it means that we can reject the null hypothesis at the 5% level. If the p-value is less than 0.10, it means that we can reject the null hypothesis at the 10% level. Only unilateral Granger causality is taken into consideration since whether the video games industry Granger-causes economic growth is not the interest of this paper. The results of the tests can be found in Tables 8.1-8.6. We find evidence of North America GDP growth Granger-causing Revenue Growth for the Video Games Industry and Console segment, at the 10% and 5% levels respectively. There is no evidence of GDP growth Granger-causing Video Games Industry and Console Revenue Growth for East Asia Pacific, Europe & Central Asia, and South Asia. There is also no evidence of the collective GDP growth rates of all the geographical areas jointly Grangercausing Revenue Growth for these two segments. We also find evidence of Europe & Central Asia and South Asia GDP growth rates granger-causing Mobile Revenue Growth at the 5% level. There is no evidence of such Granger Causality for mobile for North America, East Asia Pacific, and all geographical regions jointly taken together. Overall, we find no evidence of any GDP growth rates (jointly or area-specific) Granger-causing Revenue Growth for the Arcade, Handheld, and PC segments at any level of significance. 21 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? Table 8.1 Granger Causality Tests for Video Games Industry Video Games Industry: Granger Causality test H0: North America GDP growth does not Granger-Cause Video Games Industry Revenue Growth H0: East Asia Pacific GDP growth does not Granger-Cause Video Games Industry Revenue Growth H0: Europe & Central Asia GDP growth does not Granger-Cause Video Games Industry Revenue Growth H0: South Asia GDP growth does not Granger-Cause Video Games Industry Revenue Growth H0: ALL GDP growth does not jointly Granger-Cause Video Games Industry Revenue Growth F 2.8872 Prob > chi2 0.0969 * 0.08463 0.7726 3.3155 0.0759 0.17814 0.6752 1.0674 0.3849 Table 8.2 Granger Causality Tests for Arcade Arcade: Granger Causality test H0: North America GDP growth does not Granger-Cause Arcade Revenue Growth H0: East Asia Pacific GDP growth does not Granger-Cause Arcade Revenue Growth H0: Europe & Central Asia GDP growth does not Granger-Cause Arcade Revenue Growth H0: South Asia GDP growth does not Granger-Cause Arcade Revenue Growth H0: ALL GDP growth does not jointly Granger-Cause Arcade Revenue Growth 0.23198 Prob > chi2 0.6326 0.00072 0.9788 0.71157 0.4038 1.5113 0.226 0.71261 0.5881 F Table 8.3 Granger Causality Tests for Handheld Handheld: Granger Causality test H0: North America GDP growth does not Granger-Cause Handheld Revenue Growth H0: East Asia Pacific GDP growth does not Granger-Cause Handheld Revenue Growth H0: Europe & Central Asia GDP growth does not Granger-Cause Handheld Revenue Growth H0: South Asia GDP growth does not Granger-Cause Handheld Revenue Growth H0: ALL GDP growth does not jointly Granger-Cause Handheld Revenue Growth 1.1997 Prob > chi2 0.3255 0.21959 0.8051 0.59059 0.565 1.1405 0.3429 0.4348 0.8839 F 22 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? Table 8.4 Granger Causality Tests for Console 0.02753 Prob > chi2 0.0195 ** 0.8691 2.8257 0.101 0.28953 0.5937 1.5121 0.2181 F Prob > chi2 1.64 0.2288 H0: East Asia Pacific GDP growth does not Granger-Cause Mobile Revenue Growth 1.73 0.2175 H0: Europe & Central Asia GDP growth does not Granger-Cause Mobile Revenue Growth 5.20 0.0458 ** 5.96 0.0348 ** 2.00 0.1701 F Prob > chi2 1.39 0.2494 0.12 0.7316 0.15 0.7017 0.11 0.7465 0.41 0.7999 Console: Granger Causality test H0: North America GDP growth does not Granger-Cause Console Revenue Growth H0: East Asia Pacific GDP growth does not Granger-Cause Console Revenue Growth H0: Europe & Central Asia GDP growth does not Granger-Cause Console Revenue Growth H0: South Asia GDP growth does not Granger-Cause Console Revenue Growth H0: ALL GDP growth does not jointly Granger-Cause Console Revenue Growth F 5.9488 Table 8.5 Granger Causality Tests for Mobile Mobile: Granger Causality test H0: North America GDP growth does not Granger-Cause Mobile Revenue Growth H0: South Asia GDP growth does not Granger-Cause Mobile Revenue Growth H0: ALL GDP growth does not jointly Granger-Cause Mobile Revenue Growth Table 8.6 Granger Causality Tests for PC PC: Granger Causality test H0: North America GDP growth does not Granger-Cause PC Revenue Growth H0: East Asia Pacific GDP growth does not Granger-Cause PC Revenue Growth H0: Europe & Central Asia GDP growth does not Granger-Cause PC Revenue Growth H0: South Asia GDP growth does not Granger-Cause PC Revenue Growth H0: ALL GDP growth does not jointly Granger-Cause PC Revenue Growth *** p<0.01, ** p<0.05, * p<0.1 23 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? Factoring in the results from the VAR models, IRF graphs, and Granger-causality Tests, we can put forward some interesting claims about the video game industry’s resilience in the face of recessionary pressures. First of all, insignificant coefficients in the equations for VAR models of Arcade, Handheld, and PC, and no evidence of Granger Causality being found in these segments of the video games industry point to these segments’ revenues not being granger-caused by GDP growth: implying that they are recession-resistant. Furthermore, East Asia Pacific GDP Growth Rate does not Granger-cause any Industry Revenue Growth, implying that the video games industry and its different segments are unaffected by recessions in East Asia Pacific countries. Negative and significant coefficients for North America GDP Growth for the video games industry and console equations; and evidence of the GDP growth Granger-causing video games and console Revenue growth in the North American Market has the interesting implication that while video games industry and console revenue growth are affected by North America GDP growth rates: it is an inverse relationship, whereby a negative North America GDP growth would result in a subsequent increase in the video games industry and console revenue growth (Which stabilizes after 2 periods, according to the IRF). This adds weight to the claim that the video games industry, particularly the console segment, thrives during recessions by being counter-cyclical in the North America area. An attempt can be made to explain this phenomenon using the lipstick effect as discussed in the literature review. The World Bank’s International Comparison Program (2017) shows that the median Purchasing Power Parity of consumers in the North America area is higher than those in the other geographical areas in this model. Considering that video game pricing is fairly consistent over the world (Wirtz, 2022) and that the lipstick effect is a theory of affordable luxuries, we can argue that video games are relatively more affordable in North America compared to other geographical areas, hence making it more likely to be treated as an affordable luxury during recessions. The same effect is hence less pronounced in the other geographical areas for all the other segments except mobile and reflected in the non-significant VAR coefficients and no evidence of Granger causality in these segments. This implies that video games in these areas are still seen as affordable luxuries; but not as affordable as in North America. The positive and significant coefficients in the mobile equation, and evidence of South Asia and Europe and Central Asia GDP growth Granger-causing mobile revenue growth further supports this theory, as South Asia and Central Asia have relatively low PPPs, hence 24 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? consumers might not consider mobile gaming to be as affordable as consumers from other areas do: which leads to a lessened lipstick effect and mobile revenue growth contracting when GDP growth falls. Our findings also follow mirror of those of Freeman’s (2001) beer study, whose methodology was partly the basis of the one used in our paper. Considering the literature on video game addiction, and our overall findings that the industry and its different segments’ revenue growths are generally not Granger-caused by GDP growth rates (and in the case of North America, even show counter-cyclical behavior), this draws an economic picture of a habit-forming industry and can be used to argue that there is a pattern of addiction to video games in general- most prominently in North America to Console games; and that there is less addiction in South Asia and Europe & Central Asia to mobile games. However, this is beyond the scope of this paper and would require further studies from a more qualitative and perhaps psychological approach. The observed counter-cyclical behavior of the industry in North America can also bear a lot of interest to investors when it comes to recession-proofing their portfolios Supplementary to our findings, using Richey’s (2020) EGARCH methodology and modeling the volatility of Video Game Stocks relative to industry benchmarks such as the S&P500 or the CBOE Volatility Index (VIX) topic would potentially be a good addition to the literature as it would give us a more financial perspective on the analysis of whether the video games industry is recessionproof. Considering the relative lack of data on the video games industry while the existing historical data points to the video games industry being relatively recession-resistant, and the immense potential of the said industry in the upcoming future factoring in market predictions and the advent of the multiverse: our preliminary findings aspire to act as a call to data analysts to collect higher frequency data for future research. With more data, the expansion of our model could include variables such as game scores and consumer behavior patterns to better paint a portrait of the economics of video games, and further expand on the literature. 25 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? 6. Conclusions This paper uses the Toda-Yamamoto lag-augmented VAR model to ascertain the presence of unilateral Granger-causality between GDP growth (by geographical area) and the video-games industry revenue growth (industry-wide and by segment). In doing so, we find that the video games industry and console segment are countercyclical and actually thrive during recessions in North America. No evidence of GDP Growth rates Granger-causing Arcade, Handheld, and PC Revenue Growth Rates was found. Only mobile revenue growths were granger caused by Europe & Central Asia and South Asia GDP Growth Rates; however, the mobile segment was unaffected by any other area’s GDP growth. The main limitations of our study come from the lack of data on the topic due to the study of video game economics being arguable minimal so far. As such, some of our models (notably mobile) suffer from small sample sizes and the presence of some heteroskedasticity in the result disturbances. Our paper also does not factor in the very promising VR industry and ignores significant streams of revenues from esports and merchandising to prioritize a conservative approach and avoid overestimations. To summarize our results: We find no evidence of the video games industry being negatively affected by recessions, except for mobile gaming when faced with recessionary pressures from East Asia Pacific and South Asia. 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Appendix Appendix 1: Multicollinearity tests in Variables: VGI geuca gna geap gsoa Mean VIF VIF 1/VIF 2.12 0.47189 1.85 0.54038 1.38 0.72204 1.09 0.915032 1.61 Arcade geuca gna geap gsoa Mean VIF VIF 1/VIF 2.12 0.47189 1.85 0.54038 1.38 0.72204 1.09 0.915032 1.61 Handheld geuca gna geap gsoa Mean VIF VIF 2.11 1.92 1.37 1.21 1.65 1/VIF 0.474078 0.519904 0.731395 0.828474 Console VIF 1/VIF PC VIF 1/VIF mobile VIF 1/VIF geuca 2.09 0.479355 geuca 1.96 0.509083 geuca 4.57 0.218611 gna 1.75 0.570021 gna 1.66 0.602284 gna 3.93 0.254766 geap 1.32 0.756703 geap 1.36 0.737297 geap 1.71 0.584872 gsoa 1.06 0.939109 gsoa 1.1 0.91014 gsoa 1.32 0.758418 Mean 1.56 Mean 1.52 Mean 2.88 VIF VIF VIF After dropping world GDP data, all VIF values are <10, indicating no/low multicollinearity. Appendix 2.1: ‘Video Games Industry Model Post-estimation diagnostics: Jarque Bera test Equation chi2 gvgi 0.297 gna 2.079 geap 9.265 geuca 1.34 gsoa 5.656 ALL 18.637 varlmar: Lagrange-multiplier test lag chi2 df Prob > chi2 1 37.5934 25 0.05066 2 30.4490 25 0.20792 H0: no autocorrelation at lag order df 2 2 2 2 2 10 Prob > chi2 0.8618 0.35358 0.00973 0.51173 0.05914 0.04512 1 Roots of the companion matrix .5 All the eigenvalues lie inside the Imaginary 0 unit circle. VAR satisfies stability -1 -.5 conditions. -1 -.5 0 Real .5 1 32 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? Appendix 2.2: Arcade Post-estimation diagnostics Lagrange-multiplier test lag chi2 df Prob > chi2 1 28.5497 25 0.28318 H0: no autocorrelation at lag order Jarque Bera test Equation chi2 garcade 0.077 gna 1.587 geap 11.336 geuca 1.288 gsoa 7.422 ALL 21.709 df 2 2 2 2 2 10 Prob > chi2 0.96227 0.45235 0.00345 0.5253 0.02446 0.01666 1 Roots of the companion matrix Imaginary 0 .5 All the eigenvalues lie inside the unit -1 -.5 circle. VAR satisfies stability conditions. -1 -.5 0 Real .5 1 Appendix 2.3: Console Post-estimation diagnostics Lagrange-multiplier test lag chi2 df Prob > chi2 1 31.7215 25 0.16623 2 31.3952 25 0.17626 H0: no autocorrelation at lag order Jarque Bera test Equation chi2 gconsole 1.785 gna 3.034 geap 9.203 geuca 2.081 gsoa 24.367 ALL 40.471 df 2 2 2 2 2 10 Prob > chi2 0.40958 0.21941 0.01003 0.35331 0.00001 0.00001 .5 1 Roots of the companion matrix Imaginary 0 All the eigenvalues lie inside the unit circle. -1 -.5 VAR satisfies stability conditions. -1 -.5 0 Real .5 1 33 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? Appendix 2.4: Handheld : Post-estimation diagnostics Lagrange-multiplier test lag chi2 df Prob > chi2 1 28.5145 25 0.28472 2 23.9769 25 0.52071 H0: no autocorrelation at lag order Jarque Bera test Equation chi2 df ghandheld gna geap geuca gsoa ALL 2 2 2 2 2 10 2.406 3.916 4.351 4.729 4.214 19.616 Prob > chi2 0.30036 0.14113 0.11355 0.094 0.12159 0.0331 .5 1 Roots of the companion matrix Imaginary 0 All the eigenvalues lie inside the unit circle. -1 -.5 VAR satisfies stability conditions. -1 -.5 0 Real .5 1 Appendix 2.5: Mobile Post-estimation diagnostics Lagrange-multiplier test lag chi2 df Prob > chi2 Jarques Bera test Equation chi2 df 1 2 gmobile gna geap geuca gsoa ALL 2 2 2 2 2 10 88.7023 25 30.4096 25 0 0.20932 H0: no autocorrelation at lag order 5.008 4.058 3.206 5.23 4.589 22.091 Prob > chi2 0.08174 0.13148 0.20129 0.07316 0.10081 0.01465 .5 1 Roots of the companion matrix Imaginary 0 All the eigenvalues lie inside the unit circle. -1 -.5 VAR satisfies stability conditions. -1 -.5 0 Real .5 1 34 IS THE VIDEO GAMES INDUSTRY RECESSION-PROOF? Appendix 2.6 : PC Post-estimation diagnostics Lagrange-multiplier test lag chi2 df Prob > chi2 1 37.1624 36 0.41527 2 26.2877 36 0.88238 H0: no autocorrelation at lag order Jarque Bera test Equation chi2 df gpc gna geap geuca gsoa ALL 2 2 2 2 2 10 28.944 4.986 4.105 0.741 2.41 41.188 Prob > chi2 0 0.08266 0.12838 0.69027 0.29966 0.00001 -1 -.5 Imaginary 0 .5 1 Roots of the companion matrix -1 -.5 0 Real .5 1 All the eigenvalues lie inside the unit circle. VAR satisfies stability conditions. 35