TUTOR BUSINESS MANAGEMENT A+ WORK, ON TIME, NO PLAGARIZING; ON TIME

RAND Journal of Economics Vol. 53, No. 2, Summer 2022 pp. 328–355

Prioritization vs. congestion on platforms: evidence from Amazon’s Twitch.tv

José Tudón∗

This article studies the efficient use of prioritizing certain content over others in Amazon’s Twitch.tv, a live streaming service, taking into account the trade-off between entry and conges- tion. I specify and estimate supply and demand models for live video, and a congestion model. Using technological shocks, I identify congestion costs for content providers and their consumers. Using shocks in prioritization, I identify its benefits. With estimated preferences and technologi- cal parameters, I construct counterfactuals. Without congestion, demand doubles. A supply-side Pigouvian tax on traffic is preferred to a demand-side one. Without prioritization, consumer wel- fare drops by 10%.

1. Introduction

� In many telecommunication networks, sending content, such as video, generates conges- tion externalities. During periods of congestion, network managers improve the performance of private networks by prioritizing time-sensitive data, for instance, by allowing videocall data through before email data. However, like internet bandwidth, priority is a scarce resource. This article studies the impact of prioritization on congestion, content provision, and consumer wel- fare. I focus on the trade-off between entry and congestion, and use data on Twitch.tv, a popular live-streaming video platform, to identify short-run supply and demand elasticities with respect to congestion.

Prioritization incentivizes entry from prioritized content providers, but this entry generates congestion. Thus, network managers must understand the magnitude of congestion externalities in order to address them, say, with a Pigouvian tax. However, quantifying congestion externalities and their effects on supply and demand remains an open question not only in economics, but also in the engineering sciences (Malone, Nevo, and Williams, 2017; Sundaresan et al., 2017). Moreover, in a two-sided market, a Pigouvian tax could have different outcomes depending on

∗ ITAM; [email protected]. Thanks to Ali Hortaçsu, Michael Dinerstein, Dennis Carlton, Brent Hickman, and Pietro Tebaldi for their guidance and support. Financial support from the NET Institute (www.netinst.org) and from the Becker Friedman Institute is gratefully acknowledged. I am also grateful to the members of the IO and applied micro working groups at the University of Chicago. Thanks to the editor and referees, and thanks to deiniel_, sori_slim, CantFoldThis, and the rest of the Twitch community who provided me with valuable insights into the platform. [email protected]

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which side of the market is levied (Rochet and Tirole, 2006). Furthermore, platforms might be interested in extracting rents from prioritized service (e.g., Comcast vs. Netflix, Facebook)1, or in prioritizing their own products and services (e.g., Google, Netflix, and Amazon have incentives to prioritize their own offerings by showing them first and more often to consumers who use their search engines). If congestion externalities are large, such discriminatory policies might even increase consumer welfare by decreasing content provision.

To address these questions, this article studies the world’s leader in live-streaming content of any kind, Twitch.tv. Bought by Amazon.com in 2014 for nearly $1 billion, Twitch is an inter- net platform where people broadcast live video and where people watch the broadcasts of other people, with video gaming content being the specialty of the platform. In February 2014, Twitch was the fourth-largest source of internet traffic during peak times in the United States, at 1.8% of total traffic, behind Netflix, Google, and Apple but ahead of Hulu and Facebook.2 Broadcasters streamed from 170 countries, spoke 43 different languages, and spanned 37 time zones. Cur- rently, Twitch has over 1.7 million unique broadcasters per month, and over 100 million unique viewers per month, consuming, on average, 106 min of video a day.3

The data feature the universe of stream-level metadata from Twitch collected at 10-min in- tervals during 90 days in 2014. Importantly, the data, described in Section 2, include viewership, video bitrates, and whether the stream has been prioritized with a transcoder, which allows view- ers with low-speed internet connections to watch high-bitrate videos. The high-frequency of the data allows me to construct a volatility measure of the bitrate. The demand for live videos is sen- sitive to such volatility, which increases with congestion and manifests as buffering, stuttering, and other anomalies.

In the first subsection of Section 3, I estimate a technological equation in which the volatil- ity of individual streams is a function of real-time aggregate traffic and idiosyncratic shocks. I identify the elasticity of volatility with respect to traffic by exploiting a software upgrade that ex- ogenously increased aggregate traffic. In the second subsection of Section 3, I estimate a static, discrete-choice model of demand in which viewers choose their preferred channel, given the in- dividual channels’ volatilities and their access to a transcoder. Upgrades in the platform’s infras- tructure provide exogenous variation to identify the demand elasticity for volatility. To identify the benefits of the transcoder, I exploit the high frequency of the data to recover unexpected pri- oritization allocations. In the third subsection of Section 3, I estimate a binary-choice model of supply in which content providers decide to be online as a function of their individual audience and of other suppliers’ decisions. The interaction between entry and congestion can be effectively studied, because I observe content providers turning on and off with high frequency.

The estimates, presented in Section 4, suggest that if traffic increases by 1%, the volatility of every stream increases by 0.7%. In addition, they suggest the elasticity of demand with respect to volatility is −2.5, and that cross-side network externalities exist, but aggregate supply is more responsive to aggregate demand than aggregate demand is to aggregate supply.

The structural estimation allows me to quantify the equilibrium effects of congestion and to consider counterfactual prioritization in Section 5. Congestion externalities are substantial and magnified by cross-side network effects; the platform could be twice as large if not for congestion. A small Pigouvian tax on the demand side decreases consumer surplus, whereas one on the supply side does not. If the platform allocates prioritization randomly, as opposed to prioritizing the most popular broadcasters, consumer welfare drops up to 10% in the worst-case

1 In 2014, Netflix agreed to pay Comcast to co-locate servers inside Comcast’s network (Greenstein, Peitz, and Valletti, 2016). Facebook offers free or subsidized, but restricted, internet access. In particular, Facebook’s Free Basics was banned from India in 2016 for violating net-neutrality rules, despite being used by millions of people. See timesofindia. indiatimes.com, about.fb.com, or facebook.com/connectivity. In this article, URLs are abbreviated in print, but their hyperlinks point to a saved version at archive.org or to the original source.

2 See The Wall Street Journal, www.wsj.com. 3 See twitch.tv/p/about.

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scenario. Prioritization also boosts the consumer welfare gains from increased heterogeneity of content providers.

This article is related to a literature that studies congestion externalities (Duranton and Turner, 2011), especially in telecommunications. Malone, Nevo, and Williams (2017) study congestion in broadband networks, and find that peak-use pricing, combined with local-cache technology, effectively reduces congestion. However, they assume congestion follows a day- to-day first-order Markov process. My contribution is to relax the assumption that conges- tion is independent of aggregate traffic. I rely on high-frequency data to estimate a 10-min- window congestion model that depends on the equilibrium level of traffic, which in turn responds to congestion.

This article is also related to a literature studying discriminatory platforms and two-sided markets. Zhu and Liu (2018) analyze Amazon’s entry into third-party sellers’ product spaces; Weeds (2016) studies the pay-TV case; and Genakos, Kühn, and Van Reenen (2018) explore Microsoft’s incentives to reduce interoperability. Also related is Lee (2013), who studies the US video-gaming industry and estimates cross-side network effects.

Finally, Section 6 concludes and discusses external validity and similarities with the net neutrality literature (Greenstein, Peitz, and Valletti, 2016; Nurski, 2012).

2. Empirical context and data

� Twitch.tv is the largest live streaming service in the world. It is an online platform where people can broadcast themselves and in which streamers and viewers are brought together in a two-sided market. Twitch specializes in broadcasting live video-game sessions and content, but other categories include entertainment, social, news, sports, animals, creativity, and poker. That is, a typical Twitch stream features a video gamer, live streaming their gaming session, and viewers around the world watching them play. Other examples include: people playing chess, or sportscasters performing live commentary on others’ live video games.

As The Economist reports, “e-sports, in which computer gamers compete before thou- sands of fans in person and millions more online, is on the rise,” attracting a global audience of almost 400 million in an industry worth $700 million annually.4 In 2014, Twitch already dominated the gaming video content market, broadly defined, with 43% of the market share, followed by YouTube at 36%. In 2021, Twitch remains the largely uncontested leader in live- streaming content of any kind, holding more than 70% of the video game streaming market, with competitors such as Microsoft’s Mixer, YouTube Gaming, and Facebook Gaming follow- ing far behind.5 Every major e-sports tournament in the world is broadcasted on Twitch.6 In 2021, the most popular streamers can earn up to 1 million USD a year on the platform.7 The five most popular games currently are Grand Theft Auto V, League of Legends, Fortnite, Val- orant, and Call of Duty: Warzone, and together amass a total of 140 million hours watched per week.8

The data used in this research are mainly from Pires and Simon (2015). The data consist of stream-level metadata for all Twitch channels, collected at roughly every 10 min from January 6, 2014, to April 6, 2014. The dataset contains more than 1 million unique broadcasters. Each panel follows a broadcaster and contains channel ids, session ids, time stamps, real-time number of viewers, video bitrates, creation date, country of origin, language, time zone, and other infor- mation. The data do not contain the actual content of the stream. To this dataset, I added account

4 See The Economist, (a) economist.com, (b) economist.com. 5 See nytimes.com/2019/12/15/business, blog.streamlabs.com, and qz.com. 6 See twitch.tv/directory/esports. 7 See nytimes.com/2021/03/18/style/ludwig-ahgren-twitch-livestream. 8 See twitchtracker.com/games/time-watched.

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creation dates with my own calls to the Twitch REST API.9 The following platform’s description applies to January–April 2014.

The platform’s main source of revenues is digital advertising. The platform sells ads to advertisers and shows them during streams. Streamers do not have a say in the platform’s ad policy. However, the platform pays popular streamers a share of the ad revenues they generate. Streamers also earn income from viewers’ donations. As streamers become (subjectively) better and more popular, their viewership increases, which also increases their income.

Twitch broadcasters manage one channel, registered to them when they join the platform. Twitch does not charge for signing up or requesting a channel. Signing up is easy (comparable with signing up on, say, Twitter). The opportunity cost of time is virtually the only marginal cost for streamers. As a fixed cost, some streamers purchase a webcam or a microphone, but this equipment is not necessary to stream. On the benefit side, apart from streaming as a pastime, streamers also enjoy fame and, if enough people are watching, some ad revenues. A channel can either be online at a given time, which means the uploader is broadcasting a live video, or offline. Streamers decide what to broadcast. No videos, live or otherwise, are available when the channel is offline. The number of viewers changes during streaming sessions, and the broadcaster observes the changes in real time.

Viewers enjoy watching professionals and more skillful players playing video games, just as in traditional sports viewers enjoy watching professional matches. Watching a stream is also free, except for the time spent watching ads. Viewers decide which channel to watch by search- ing and clicking a channel in a similar way to YouTube.10 Viewers can watch from any device: personal computers, mobile phones, tablets, gaming consoles, etc. Some channels are featured on the homepage of the website, which makes them salient. Viewers can change channels, or turn off, at any time. Some viewers donate to support the streamer when they enjoy their content. Twitch takes a cut from donations, if any, which amounts to a second-order source of income for the platform.

Besides deciding what to broadcast, the broadcaster also decides when to stream, how long, and at what average speed, measured in bits per second. Because the majority of channels stream video-game content, a chess match is a useful analogy. Rather than streaming for a fixed amount of time or a set schedule as in a soccer match, broadcasters stream, say, one or two chess matches, which take an unknown amount of time. If broadcasters expect a high viewership, they start their streams. If viewership is actually high, they play an extra match.

In practice, major broadcasters start their streams at a set schedule. They are not required to commit to any schedule, but consistency helps build viewership. However, scheduling is largely not strategic; broadcasters are motivated more by their live viewership and personal reasons (e.g., day job schedule) than by competition from similar content providers. Moreover, they are small; no broadcaster ever reaches a 1% market share. If we define professional streamers as being in the top 5% of popularity, Figure 1 shows the schedule distribution of pros versus amateurs. Schedules are similar. No evidence of, say, American streamers targeting European consumers exists; streamers on the east coast of the United States do not react to changes in the European daylight saving time. If one worries about aggregation effects, Figure 1 also shows the schedule distribution for the top 100 channels. Further disaggregation shows similar patterns. Finally, experienced streamers I interviewed confirm that, in 2014, almost no streamer was strategic: they only cared about their own viewership, and they chose their schedules exogenously.

The second decision—how long—depends on live viewership. All else equal, streamers are motivated to broadcast if they have a higher viewership. A minority of streamers, called partners,

9 Pires and Simon (2015) data can be found in https://doi.org/10.1145/2713168.2713195 or by request. The do files that I used to parse it, complement it, and analyze it are available upon request. REST API stands for REpresentational State Transfer Application Programming Interface. It is a communication method between the programmer and the platform and allows data requests.

10 In fact, the uninitiated reader might find it helpful to think of YouTube as a proxy for Twitch, except for videos being live on Twitch.

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FIGURE 1

PRO VERSUS AMATEUR SCHEDULES

Note: Histograms of chosen hours-of-week to broadcast. Local times, 60,571,499 observations.

have an extra financial motivation, because the platform shares ad revenues with them, which are proportional to viewership. In sum, all broadcasters respond to viewership.

The third decision—the bitrate—is not strategic. All else equal, a higher average bitrate implies a better quality, because it allows for a higher resolution. However, a viewer requires high-speed internet to be able to watch a live high-bitrate video. Otherwise, the viewer would ex- perience video buffering and delays. Therefore, the broadcaster faces a trade-off between “viewa- bility” and quality. Twitch guidelines and community suggest a target bitrate of 1.5 Mbps (sd video) to optimize viewership, which the data confirm.11

The platform gives preference to a minority of streams by transcoding their signal. A transcoder allows viewers to select the video quality that best suits their internet speeds. If a video is not transcoded, viewers must watch it at its original speed. Essentially, a transcoder al- lows content to reach viewers with low connection speeds. Users know when their streams are transcoded. At any given moment, less than 10% of live channels are transcoded, in contrast to YouTube, where all non-live videos are transcoded by default. A live transcoding server is a scarce resource because it uses specialized hardware to encode a single stream into several in real time. Reportedly, a transcoding server that costs about $1000 can provide transcoding to four live channels at once. A popular channel, broadcasting hd video to 250 viewers, would cost $2000 per hour using a third-party cloud-based transcoding service at current market rates.12 The effi- cient allocation of transcoders is a first-order problem for the platform. In this sense, the platform is not neutral, because it gives preference to a minority of channels.

If a channel is transcoded, the broadcaster does not face the viewability–quality trade-off, because all her viewers can dial down the source speed to match an appropriate bitrate to their

11 A standard-definition YouTube 480p video requires around a 1.5Mbps upload speed, whereas a high-definition 720p video requires around 2.5Mbps (support.google.com/youtube). In the first quarter of 2014, global average internet download speed was 3.9Mbps; a download speed of 3Mbps is recommended to watch sd video (webanalyticsworld.net, and lifewire.com).

12 See reddit.com/r/Twitch. For market prices, see amazon.com and zencoder.com.

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FIGURE 2

DATA FLOW WITH TRANSCODING VERSUS WITHOUT

Note: An (abstracted) example of a broadcast’s path from upload (↗) to download (↘). If the broadcast is transcoded, it reaches a transcode server that distributes the data at lower bitrates. If it is not, the broadcast is mirrored (→) at source speed. 1.5 Mbps ∼ sd video, 2.5 Mbps ∼ hd video.

connections. Thus, a transcoded channel will choose the maximum speed its connection can handle, which, on average, is 2.5 Mbps (hd video). For these reasons, I treat the choice of video bitrate as exogenous.

The video bitrate is one of two key dimensions of the objective quality of a stream. The second dimension is the volatility of the bitrate. Video encoding and decoding is CPU-intensive. To decode a stream, a computer expects consistency from the source, especially if the encoding protocol is “Constant BitRate,” which Twitch requires. Network congestion at any level creates variation in the streamed data due to lost data packets and bottlenecks. This bitrate volatility manifests as video buffering or stuttering. Evidence suggests delays and loss of data packets, such as those created by volatility, significantly decrease the end-users’ quality of experience while watching a video stream (Pankert, Faggiano, and Taga, 2014). All else equal, viewers prefer less volatility in their streams.

This article measures volatility with the noise-to-signal ratio of the stream’s video bitrate. The ratio is a form of coefficient of variation. Let bjt stand for the (upload) video bitrate of channel j at date t, and let bj be its mean over t. Then, the noise-to-signal ratio σ jt is defined as

σ jt ≡ ∣∣bjt − bj

∣∣ bj

.

Because Twitch enforces a constant bitrate protocol, in principle, bjt should be constant. Any deviations from bj correspond to noise caused by congestion. Note that bj is a consistent estimate of the target bitrate and that σ jt is dimensionless. All else equal, a low noise-to-signal ratio implies better quality and is largely beyond the control of the broadcasters.13

When content providers broadcast, the uploaded signal reaches a platform’s server, from which it is mirrored through the platform’s network and then distributed to edge servers, from which viewers download the stream; see Figure 2 for reference. At any leg of the journey, noise may be added to the signal due to congestion. Noise can be generated while uploading or down- loading and has both idiosyncratic and aggregate components. Also note that noise gets com- pounded downstream; that is, noise generated on the upload side is transmitted to all the viewers watching the broadcast. However, noise generated on the download side is idiosyncratic to each consumer and does not affect the upload side of the network or other downloads.

13 Different level of time aggregations are possible for bj . The results in this article do not change significantly if, for instance, I consider aggregation at the session level, but measurement error for the target bitrate increases. For applications of the noise-to-signal ratio in the engineering sciences, see Huynh-Thu and Ghanbari (2008) or Shivaldova, Winkelbauer, and Mecklenbrauker (2014). Huynh-Thu and Ghanbari (2008) discuss the scope of the noise-to-signal ratio to assess video quality. See also help.twitch.tv.

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FIGURE 3

NEW CHANNELS AND DAILY PARTICIPATION

Note: (a) Daily number of new broadcasting accounts created. (b) Daily number of unique channels in the data, and daily median of concurrent viewers in the data. Peaks correspond to weekends. The solid line signals the Xbox One broadcasting shock. Dashed lines signal the platform’s point-of-presence upgrades.

On the upload side, the “production” of noise is composed of two factors: an individual factor and an aggregate factor. The individual factor is created by the broadcaster’s private inter- net connection, the quality of the connection, and shocks beyond the platform’s influence. The aggregate factor is common to all broadcasters and is rooted in the platform’s physical capacities. This aggregate factor is a function of aggregate participation and the manifestation of congestion externalities. Transcoding has no effect on the volatility of a stream.

Because the platform’s physical network has a fixed throughput capacity, one would expect the noise-to-signal ratio to increase as more viewers and broadcasters participate in the platform. Indeed, increasing the uploads and downloads worsens queuing delays, packet loss, and connec- tion blocking. However, its effect is confounded by selection, because viewers and broadcasters choose not to participate in the platform when it is congested (see the reduced form analysis in online Appendix Section A). The noise ratio is thus an endogenous variable: Less noise attracts more people, and more people creates more noise. The identification strategy is composed of a combination of instruments to disentangle the effect of noise over participation and vice versa.

Twitch users can broadcast their streams from their personal computers or video-game con- soles (e.g., PS4, Xbox One), and people can watch from any device. However, before March 11, 2014, viewers could watch broadcasts from the Xbox One, but broadcasters could not stream from it. On March 11, 2014, Twitch launched the complete app for the Xbox One, which allowed broadcasting.14 This introduction of a new technology is the source of an exogenous variation that affected the broadcasters, but not the viewers. Figure 3a shows the time series of new accounts for the list of channels that are found in the data, which peaks on the date when the Xbox One broadcasting became available.

According to the platform’s website, on March 11, 30% of broadcasters were streaming from the Xbox One, and within the first week, a total of 108,000 unique broadcasters were streaming from the Xbox One, accounting for 22% of Twitch’s broadcaster base.15 Figure 3b shows the time series of daily broadcasting and viewership. On Tuesday, March 11, broadcasting numbers jumped, confirming the press release from the platform.

14 See blog.twitch.tv, published February 25, 2014. Before March 11, 2014, Xbox One streamers had to broadcast from their PCs, which they connected to the Xbox One in a nontrivial way.

15 See blog.twitch.tv, published March 31, 2014.

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FIGURE 4

QUALITY OF SERVICE AND POINT-OF-PRESENCE UPGRADES

Note: Daily medians of noise-to-signal ratios. Dashed lines signal the platform’s point-of-presence upgrades. The solid line signals the Xbox One broadcasting shock.

Additionally, the platform expanded its infrastructure four times during the sample period by upgrading their points of presence (PoP).16 The expansion of PoPs increases the ingest capacity of the network and improves user experience in general. Effects are expected to be short-lived due to the “Iron Law of Congestion”: Improved capacity attracts more users, increasing noise (Duranton and Turner, 2011). The data show decreases in noise following each installment (see Figure 4, where the Xbox effect also is apparent).

Importantly, the Xbox One and PoP upgrades took months of planning and were released as soon as they were available.17 That is, Twitch follows a long-run business plan instead of reacting to the short term. For instance, the Xbox One upgrade was unveiled on a Tuesday, which is the second-least popular day to broadcast. Instead of being correlated with current traffic, the update was planned to coincide with the release of Titanfall, a video game.18

The platform incentivizes popular broadcasters through a partnership program. To join the program, the broadcaster needs to meet certain technical requirements, to be popular enough, and to be willing to join. Joining the partnership program is free, and its benefits include re- ceiving a share of ad revenue, the ability to accept donations from viewers in the form of a sub- scription, and, more importantly, guaranteed video transcoding. From the viewer’s perspective, beyond transcoding, the remaining perks of partnered channels, such as special chat interactions and “virtual badges,” do not offer substantial benefits.

To be a partner, broadcasters must apply through the platform’s website and be approved. Once they apply, broadcasters do not know if and when they will be approved. The platform approves partnerships on a rolling basis through an undisclosed method, which takes an unknown amount of time. From the broadcaster’s point of view, partnership comes unexpectedly. Non- partners do not have incentives to behave differently until they have been upgraded to partners. Once gained, partnerships are never lost. In the data, I observe more than 1600 partners, of whom more than 600 acquired partnerships during the sample period.

I do not observe partners’ financial incentives. However, these incentives are proportional to their viewership numbers. In practice, all else equal, partners stream more than non-partners but are less sensitive to viewership, partly because they have more viewers.

Because transcoding is guaranteed for partners, the platform has roughly enough transcod- ing servers for them. When not all the servers are being used, the excess capacity is allocated

16 See blog.twitch.tv, published March 28, 2014. 17 See reddit.com, blog.twitch.tv, or blog.twitch.tv. 18 See polygon.com.

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to non-partnered channels according to their current viewership. This excess allocation is never announced and comes as a surprise for viewers and streamers. Thus, viewers and non-partnered streamers do not have incentives to behave differently before they are allocated a transcoder.

Table 1 shows the main statistics of the streaming sessions. The average broadcasting ses- sion has 15 viewers, lasts 74 min, and streams at a video bitrate of 1.5 Mbps. Partnership plays a role as expected: Partners have much longer sessions, better viewership numbers, and higher video quality. The difference between a partnered broadcast and a non-partnered one is roughly that between hd and sd video.

After the Xbox shock, the number of gaming channels and viewers increased although the number of non-gaming channels and viewers decreased. The Xbox shock did not affect the non- gaming segment directly, which suggests the presence of a negative externality.

Notably, the data contain no prices, because joining the platform is free. In practice, viewers pay with “eyeballs,” because they have to watch ads to view the broadcasts. Moreover, this pric- ing and ad policy remained constant during the sampled time frame. When considering welfare implications, I focus on quantities.

Episodes when servers crash are excluded from the analysis. A notable case occurred in late March 2014, and the participation drop is apparent from Figure 3b.

The following section presents the structural models and identification arguments in detail.

3. The model

� The model has three components. In the congestion model, individual noise-to-signal ra- tios are determined by aggregate participation in the platform. In the demand model, individual consumers decide which channel to watch, given a set of online channels, their noise-to-signal ratios, and whether they have access to transcoding. In the supply model, individual streamers decide to be online, depending on their individual demands. The three model parts link to each other, because noise decreases demand, but demand increases supply, which increases noise.

The first subsection of Section 3 introduces the congestion model, the second subsection of Section 3 the demand model, and the third subsection of Section 3 the content-provision model. Each component is estimated separately in Section 4. The platform’s decisions are considered exogenous to the key elements of the model, as motivated by the fact that infrastructure changes take months of planning, whereas the economic agents in the model respond to short-run incen- tives, as advanced by the market description in the previous section.

� Congestion externalities. I assume the following model for channel j’s noise-to-signal ratio, σ jt :

log σ jt = μσ

0 t + ασ

1 log Bup t + βσ ′PoPt︸ ︷︷ ︸

aggregate component

+μσ

j + εσ

jt,︸ ︷︷ ︸ idiosyncratic component

(1)

where μσ 0 is a trend, Bup

t is the total video bitrate uploaded to the platform’s servers at time t, PoPt

is a vector of four indicators for the point of presence upgrades, and μσ j is a fixed effect, which

captures the streamer-level heterogeneity due to idiosyncrasies in, say, internet infrastructure. The parameter of interest is ασ

1 , which measures the elasticity of noise to traffic. In particular, μσ

0 t captures technological progress and updates that naturally reduce noise at the aggregate level. The time-step for t is 10 min.

The data constrain the congestion model to focus on the upload side. I implicitly assume total download video bitrate affects the noise-to-signal ratio in a way proportional to that of Bup

t . That is, I assume Bup

t is a proxy for total traffic. Second subsection of Section 3 discusses the implied assumptions and their relevance for the demand-side model.

Identification. Although individual channels are too small to have an effect on aggregate variables, individual noise and traffic are simultaneously determined. Traffic increases noise.

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TABLE 1 Summary Statistics

Mean Std p10 p25 p50 p75 p90 Before After

All Sessions: Duration (min) 73 242 0 0 22 80 177 74 71 Mean Viewers 14.9 436.3 0.0 1.0 1.5 3.0 7.7 15 14 Max Viewers 22 686 0 1 2 4 11 22 21 Bitrate (kbps) 1486 1132 379 708 1148 2092 3026 1460 1545 Noise-to-Signal (%) 17 22 3 5 8 21 47 17 18 Transcoded (%) 2 13 0 0 0 0 0 2 2 Avg online channels 5,594 5,930 Avg online viewers 324,265 325,862 Observations 11,614,965 Broadcasters 1,520,406 Partner: Duration (min) 223 305 20 80 170 299 450 223 224 Mean Viewers 798.4 2450.4 30.0 79.7 212.2 582.9 1549.5 850 696 Max Viewers 1164 3577 40 107 294 824 2245 1239 1016 Bitrate (kbps) 2330 1061 1022 1585 2261 3066 3559 2317 2357 Noise-to-Signal (%) 12 14 4 5 7 11 26 12 12 Transcoded (%) 100 0 100 100 100 100 100 100 100 Avg online channels 144 176 Avg online viewers 178,282 169,670 Observations 97,775 Broadcasters 1,736 Non-Partner: Duration (min) 72 241 0 0 22 79 172 73 69 Mean Viewers 8.2 368.4 0.0 1.0 1.5 2.9 7.0 8 8 Max Viewers 12 595 0 1 2 4 10 12 12 Bitrate (kbps) 1479 1130 377 704 1143 2086 3016 1453 1538 Noise-to-Signal (%) 18 22 3 5 8 21 47 17 18 Transcoded (%) 1 9 0 0 0 0 0 1 1 Avg online channels 5,449 5,754 Avg online viewers 145,983 156,192 Observations 11,517,190 Broadcasters 1,519,351 Gaming: Duration (min) 63 128 0 0 22 78 169 63 62 Mean Viewers 14.8 448.0 0.0 1.0 1.5 2.9 7.0 15 14 Max Viewers 22 704 0 1 2 4 10 22 21 Bitrate (kbps) 1535 1132 432 762 1192 2118 3053 1510 1588 Noise-to-Signal (%) 17 22 3 5 8 20 46 17 18 Transcoded (%) 1 12 0 0 0 0 0 1 1 Avg online channels 4,873 5,291 Avg online viewers 298,596 302,459 Observations 10,986,716 Broadcasters 1,467,585 Non-Gaming: Duration (min) 252 870 0 0 35 139 533 254 248 Mean Viewers 16.5 99.5 0.0 0.1 1.5 6.5 37.2 17 16 Max Viewers 24 157 0 1 2 9 48 24 23 Bitrate (kbps) 641 738 70 197 439 857 1358 626 679 Noise-to-Signal (%) 23 25 4 7 14 30 51 23 23 Transcoded (%) 4 20 0 0 0 0 0 4 5 Avg online channels 721 639 Avg online viewers 25,669 23,403 Observations 628,249 Broadcasters 53,353

Note: Data collected at 5-min intervals. Duration in minutes with a 5 min margin of error. Video bitrate in kbps. Before and after with respect to the Xbox One shock on March 11, 2014.

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However, if noise is too high, channels turn off, which reduces total traffic. I use the Xbox One shock as an instrument for log Bup

t because the shock increased the number of broadcasters, which increased the upload traffic.

A threat to identification comes from the possibility that the Xbox One substantially changes demand or if it attracts noisier channels. However, the channels attracted by the Xbox One shock mostly have low or no viewership; for the next few days after the Xbox shock, the number of viewers per channel is below trend due to an increase in the number of channels. Moreover, I can perform the estimation only for the professional channels (those in the top 5% of popu- larity), which are arguably not changing their behavior because of the Xbox One broadcasting availability. Results are similar in this subsample.

Finally, I include fixed effects in this estimation because no cross-sectional variation exists over Bup

t . The fixed effects also control for unobserved channel characteristics such as location, internet connection, or hardware. Peak hours and weekend dummies are also included.

Formally,

Assumption 1. log Bup t ⊥ εσ

jt |Xboxt, PoPt , μσ j , t.

All estimation results are presented in Section 4. Selection from noisy channels turning off is also considered, but its discussion parallels the selection correction discussion on the demand side in the next subsection.

� Viewers (demand). Each period t, a representative consumer i decides which channel to watch according to a discrete-choice model with a nested structure (Berry, 1994; McFadden, 1974). Let J be the set of all channels that have an account on the platform. The set J exoge- nously grows over time as new channels sign up; no new notation is introduced to account for this fact. Let Jt ⊂ J be the set of online channels at time t, and it always includes the outside option, which is watching nothing. The consumer’s outside option has a normalized utility of εi0t , whereas the payoff for tuning into channel j is ui jt ≡ δ jt + εi jt . To allow for more flexible substitution patterns, four nests are defined: (1) the outside option; (2) non-gaming channels; (3) amateur gaming channels; (4) pro gaming channels. The subscript g = 1, . . . , 4, labels nests.

Let σi jt be the final noise-to-signal ratio experienced by consumer i watching channel j at time t. I assume

log σi jt = log σ jt + ηi jt,

for some unobservable ηi jt , with ηi jt ⊥ log σ jt . In other words, I assume the final noise-to-signal ratio can be decomposed into the “upload” side noise, log σ jt , plus an idiosyncratic shock for consumer i, ηi jt , which captures individual-level heterogeneity and is absorbed by εi jt . Because noise is compounded downstream, this assumption is close to reality.

The consumer solves max j∈Jt ui jt and, assuming type-1 extreme-value errors, the market- share equation becomes

log

( s jt

s0t

) = δ jt ≡ μ j + α1 log σ jt + α2τ jt + α3 log s jt|g + β′x jt + ξ jt, (2)

where μ j is a fixed effect, σ jt is the noise-to-signal ratio of channel j, τ jt indicates whether channel j’s broadcast is transcoded, s jt|g is the market share of channel j as a fraction of group g (Berry, 1994; Cardell, 1997), and ξ jt is unobservable. Channel j characteristics, x jt , include the following: indicators for partnership, for a channel being featured on the platform’s homepage, for weekends, and for peak hours (between 6 pm and 1 am local time); the log of tenure in the platform (as a proxy for experience, quality, and fan-base size); and the log of uptime.

The quality of a stream can be divided into subjective and objective qualities. The unob- served subjective quality of a video (how good the content is) is absorbed by μ j and ξ jt and may be regarded as a horizontal attribute. As a vertical attribute, the objective quality is composed of

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three parts: the video bitrate, the noise-to-signal ratio, and whether the stream is transcoded. The video bitrate is absorbed by the fixed effect, because, in principle, the bitrate should be constant conditional on whether the channel is transcoded. All else equal, I expect a high noise-to-signal ratio to decrease the demand for a channel, and a transcoded stream to have more viewers.

Let Mt be the market size at time t; then, s0tMt viewers tune out of the platform at t. There- fore, quasi-demand is (1 − s0t )Mt and quasi-supply is #Jt (Rochet and Tirole, 2006). Streamers compete for viewers with a Twitch account. The relevant market size is then the number of Twitch viewers. In February 2014, Twitch.tv had about 45 million unique viewers each month. By the end of 2014, the number had reached 100 million. Assuming linear growth, by the end of April 2014, the platform would have grown to around 50 million viewers. The platform also reports that each viewer watches an average of 106 min per day. I assume viewers have 2 hours available per day to watch videos. The data span 90 days. Assuming a uniform distribution over the day, I define the market size at date d = 1, . . . , 90 as Md = 45(2/24) + 5(2/24)(d/90) million view- ers available at date d. Thus, Mt = Md if time t is part of day d. The results are not sensitive to this assumption. Demand equation (2) does not include a time trend, because platform growth is already embedded in Mt .

Identification. First, as an equilibrium outcome, noise is simultaneously determined with de- mand: Noise decreases demand, but demand increases supply, which increases noise. Also, noise could be correlated with the error term through selection, because noisier channels go offline. Yet another concern is measurement error, because σ jt is constructed using the average bitrate as a proxy for the target bitrate.

To mitigate these concerns, the regression includes a fixed effect for channel j; moreover, I use two sets of instruments for log σ jt ; and, finally, I correct for selection. The first set of instru- ments are the PoP upgrades, which improved the network infrastructure and decreased noise all over the platform. These upgrades should not increase viewership directly but only through noise reduction. A second instrument comes from the introduction of the Xbox One broadcasting abil- ity, which increased upload video bitrate. The spike in traffic increased the noise-to-signal ratio across the platform. Importantly, the Xbox shock attracted fringe channels with low viewership: Channels created after March 11, 2014, have 2.1 viewers on average, whereas the 90th percentile is 2.5 viewers, compared with 15 and 7.7, respectively, for the whole sample. Thus, consideration sets are virtually unchanged after the shock.

A more serious threat to identification comes from the possibility of the platform reacting strategically to viewership when it deployed the PoP and Xbox upgrades. However, as argued in Section 2, these upgrades require months of planning, rather than days or weeks.

The instruments do not contain cross-sectional variation. I address selection separately using a control function based on Heckman (1979) and Olsen (1980). In a first step, the decision of channel j to be online at t is modeled as a function of a channel fixed effect, whether the stream was interrupted, viewership, and other observables at t − 1. In a second step, a control function is included in the regression to deal with the fact that noisier channels choose to turn off.

Equation (2) includes no random coefficients that allow for more flexible substitution pat- terns. However, the logic that applies to common price elasticities does not translate directly into noise elasticities. A classic problem in a BLP-type model is that own-price elasticities are roughly constant (when the model includes log prices), which implies similar markups even for products with different prices (Berry, Levinsohn, and Pakes, 1995). An additional problem is that cross-price elasticities are proportional to market shares. However, back to this setting, channels do not choose their noise-to-signal ratio. Therefore, we have no a priori reason to discard con- stant own-noise elasticities. More importantly, the relevant substitution direction is toward the outside option. The reason the nested logit is favored over a random-coefficients approach is a practical one. Because viewers can watch any channel around the world, at any given time, 5000 “products” are available in about 13,000 “markets” t.

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Second, transcoder allocation is correlated with quality. Identification of the transcoder ef- fect comes from comparing non-partnered channels before and after receiving a transcoder. For non-partners, transcoders come as a surprise. Formally, I assume transcoders are orthogonal to the error conditional on fixed effects. That is, conditional on quality, the allocation of transcoders is as good as random. A possible threat to identification comes from the fact that receiving a transcoder means fewer partnered channels are online, which means less competition. The es- timation could be picking up the effect of less competition, instead of the causal effect of a transcoder, and could bias the target coefficient upward. To mitigate this concern, I include con- trols such as weekend and peak-hour dummies. The results are also robust to the inclusion of day-of-week and hour-of-day fixed effects.

Third, by construction, log s jt|g is an endogenous regressor. Following Berry (1994), I in- strument it with the characteristics of other channels in the group. Namely, I instrument log s jt|g with the number of channels: in English, from the United States, with transcoders, featured, and partnered, as percentages of group g, excluding j, at time t. The characteristics of other chan- nels in the group should not affect directly the market share of channel j but should shift the within-group shares.

Although the data set is poor on channel characteristics, it is rich in the time dimension. Channel fixed effects control for important but unobserved attributes such as content, subjec- tive quality, and other horizontal characteristics. The following summarizes the identification assumptions.

Assumption 2.

(a) log σ jt ⊥ ξ jt |Xboxt, PoPt, μ j, x jt ; (b) τ jt ⊥ ξ jt |μ j, x jt ; (c) log s jt|g ⊥ ξ jt |μ j, x jt, English%− jt|g, US%− jt|g, Transcoder%− jt|g, Featured%− jt|g,

Partner%− jt|g

� Content providers (supply). Broadcasters are strategic. Each period t, they play a simul- taneous game in which each broadcaster j ∈ J decides to be online or not. Let yjt indicate if channel j is online at t. Let uC

jt be the utility of broadcasting at t. That is, the payoffs are {uC

jt (yjt, y− jt )} j∈J , which depend on own strategies (yjt) and on others’ strategies (y− jt), and are defined below. The utility of not broadcasting is normalized to zero. Thus, broadcasters solve a static problem: max{0, uC

jt}. Lemma 1 in the online Appendix ensures a Nash equilibrium exists for this game.

Payoffs uC jt depend on the information available at t. In particular, the decision depends on

the number of viewers watching j. However, this information is not available when channel j is offline. I thus separate broadcasters’ decisions by their information sets.

I assume the broadcaster’s static problem is divided into an extensive and an intensive mar- gin: (1) When the channel is offline, the broadcaster decides whether to Turn On. (2) If the broadcaster has decided to be online, this decision will be followed by the decision to Keep On or not, in the following periods.

First, when the channel is offline, the channel does not know exactly how many viewers it could have if it were online, but it can make an educated guess. I model this decision as a function of a fixed effect, and observables such as the aggregate number of viewers and channels, which proxy as potential market and competition. Importantly, a deciding factor is the promise of a transcoder, which is only guaranteed for partners. Time effects are included to account for schedules.

Second, given that the channel is already online at time t, the number of viewers is realized and the channel decides whether to Keep On given this information. Thus, being online at t + 1 is decided at t with information at t.

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Specifically, channel j observes the state of the world and decides whether to Turn On at the beginning of period t, according to a utility associated with each decision. Let uIO

jt be the (expected) utility of Turning On, and let 0 be the utility of staying offline. Thus, channel j Turns On iff uIO

jt > 0. That is, I assume

yj,t+1 = 1 | yjt = 0 ⇐⇒ uIO jt > 0,

uIO jt ≡ μIO

j + αIO 1 1{Partner jt} + βIO′

xIO jt + εIO

jt , (3)

where μIO j is a fixed effect, and 1{Partner jt} is an indicator for partnership. The controls, xIO

jt , include information available before the transmission starts: an indicator of the Xbox One broad- casting availability, its interaction with a gaming dummy, indicators for weekend and for peak hours, and the log of tenure in the platform, as a proxy for experience or for developing a fan base. Channel j perfectly observes uIO

jt . The fixed effects μIO j and the error εIO

jt are unobservable to the researcher.

All else equal, one would expect partners to be more willing to broadcast, because they know they will have a transcoder, which will increase their viewership.

Given that the channel decided to Turn On at t, the viewers of channel j are realized and observed by j at t. With this information, at the end of period t, the channel decides whether to Keep On or to Turn Off at t + 1. Let uB

jt be the utility of Keeping On, and let 0 be the utility of Turning Off. Thus, channel j Keeps On iff uB

jt > 0:

yj,t+1 = 1 | yjt = 1 ⇐⇒ uB jt > 0,

uB jt ≡ μB

j + αB 1 log nV,Partner

jt + αB 2 log nV,NonPartner

jt + αB 3 1{Partner jt} + βB ′xB

jt + εB jt, (4)

where μB j is a fixed effect, nV

jt is the number of viewers watching j at t, and it is interacted with the partnership dummy. The controls, xB

jt , include the following: indicators for Xbox broadcasting availability, for weekends, and for peak hours; the log of tenure; and yjt . Channel j perfectly observes uB

jt . The fixed effects μB j and the error εB

jt are unobservable to the researcher. Because only information sets change between equations (3) and (4), I impose equal fixed

effects in both equations, μIO j = μB

j . These fixed effects reflect channel j’s unconditional ex- pectation of viewership. The effect of own viewership, nV

jt , is separated between partners and non-partners to allow different marginal valuations.

At this point, the likelihood of observing a given history of a channel can be written. Let T s

j define the set of periods when channel j had its s-th broadcasting session. That is, T s j ≡

{ts 1 j, . . . , ts

end, j}, where the channel was offline at time ts 1 j − 1, Turned On at ts

1 j and was online until ts end, j, when it decided to Turn Off. That is, the typical s-th session is {yjt}t∈T s

j = {1, 1, . . . , 1, 1, 0}.

Any channel j could have Sj of such broadcasting sessions. The likelihood of session s is

Ls j

( θIO

0 , θB 0

) = P [ yjts

1 j = 1

∣∣ yj,ts 1 j−1 = 0, θIO

0

]⎡⎣ts end, j−2∏ t=ts

1 j

P [ yj,t+1 = 1

∣∣ yjt = 1, θB 0

]⎤⎦ × P

[ yj,ts

end, j = 0

∣∣ yj,ts end, j−1 = 1, θB

0

] ,

where θIO 0 and θB

0 are the vectors of parameters from the decisions of Turning On and Keeping On. This likelihood is conditional on the fact that (by definition) the channel was offline before

the session starts. To wrap up the likelihood of the data, define T off j ≡ T \ ⋃S j

s=1 T s j as the inter-

session periods when the channel was offline, and where T is the set of periods in the data. Then,

Lj

( θIO

0

∣∣yj0

) = ∏

t∈T off j

P [ yjt = 0

∣∣ yj,t−1 = 0, θIO 0

]

is the likelihood of observing channel j being offline in the inter-session periods, conditional on the starting value yj0.

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FIGURE 5

COMPARISON OF DOWNTIME AND UPTIME

Note: Downtime and uptime comparison. Kaplan–Meier survival estimates and a fitted exponential curve.

Finally, the likelihood of the data can then be written by considering all sessions for all channels:

L ( θIO

0 , θB 0

) = ∏ j∈J

Lj

( θIO

0

∣∣yj0

) S j∏ s=1

Ls j

( θIO

0 , θB 0

) . (5)

In particular, this model is consistent with a survival model with exponential decay, in which each period the broadcaster can change state. Figure 5 presents non-parametric Kaplan–Meier survival estimates for downtime, where Turning On is the change of state, and for uptime, where Turning Off is the change of state. The figure also shows a simple exponential curve, with no covariates, approximating the Kaplan–Meier curve.

I focus on modelling the extensive margin of when to broadcast rather than the margin of when to join the platform, because entry is free, in the sense that no investment is necessary. Therefore, streamers who have not joined the platform can be considered as offline, until they decide to be online. If this is the case, we can reinterpret the results through the lens of a selected sample of streamers that were observed to be online at some point in a 90-day period. Because an entry model would also be consistent with Figure 5, but harder to identify, I favor the simpler model of this article, which already accounts for the most important incentives: namely, the opportunity cost of streaming, and the effect of viewership on supply.

Identification. A simplifying assumption is implicit in (5): I assume equations (3) and (4) are independent of each other. That is, the working assumption is that the errors from equations (3) and (4) are independent.

The potential problem with this assumption is that a shock that pushes a channel to Turn On could be correlated with the shocks a channel experiences once it is online. That is, the errors could be correlated across time. I do not consider this issue to be a major setback, because I include individual effects on both equations and I allow for panels in the likelihood. I also in- clude tenure data, which allows me to control for unobserved dynamics. Moreover, the likelihood conditions on the outcome of the previous period, and the presence of autocorrelation does not bias the estimates. Dynamic considerations are even less important if one assumes channels can predict their viewers in the next 10 min by observing their current number of viewers.

Because the likelihoods are separable, the parameters can be estimated with a stacked logit. The advantage is that I can include channel fixed effects in both equations, which allows me to control for unobserved but important attributes such as content, quality, or ability that may be correlated with partnership or viewership. Because the time series is long for each panel, the

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incidental parameters’ problem is a minor issue. Alternatively, one could estimate a conditional logit in which the channel fixed effects drop out, so they are never actually estimated. However, the conditional logit is impractical.

Finally, consider the problem of estimating the effect of the number of viewers, nV jt . Viewer-

ship could be correlated with the error term for a number of reasons. First, endogenous schedul- ing could dampen the elasticity of supply to viewership. Second, demand and supply are simul- taneously determined. Third, unobserved quality could have a positive effect on the utility of the broadcaster. Fourth, dynamic considerations, such as inertia of viewers, could imply lagged variables or differences are omitted variables.

To identify the effects of nV jt , first, I include peak-hour and weekend dummies. If schedule

choice is endogenous, supply’s elasticity to viewership would be underestimated, especially for larger channels, because larger channels would not change their broadcasting decisions as much, because they are predetermined by their schedules. Online Appendix Section B.1 defines a two- stage game, where streamers choose schedules in a first stage and choose to keep online in a second stage. The upshot is that a Nash equilibrium exists and that the two-stage game can be approximated by the benchmark if we control for scheduling.

Second, I use the demand-side model to derive exogenous variation in viewership. Specifi- cally, in a first stage, I instrument log nV

jt with the noise-to-signal ratio, a dummy for transcoding, and a dummy for being featured, and I construct a control function (Petrin and Train, 2010). That is, I estimate

log nV jt = μF

j + αF 1 log σ jt + αF

2 τ jt + αF 2 1{Featured jt} + βF ′xF

jt + η jt,

where η jt and εB jt are correlated with each other. I then construct η̂ jt and include it as an additional

regressor in (4). The following summarizes the assumptions.

Assumption 3.

(a) εIO jt , εB

jt are iid; (b) the error εB

jt can be decomposed into the part that can be explained by a general function of an error η jt and a residual: εB

jt ≡ CF(η) + ε̃B jt ;

(c) log nV jt ⊥ εB

jt |μB j , xB

jt, η̂ jt .

In practice, for computational concerns, I separate the estimation of the supply decision by partners and non-partners. Moreover, a separate estimation allows partners and non-partners to have different marginal valuations of viewership.

Although the counterfactuals do not require the identification of a causal effect of the part- nership status, data on partners identify the effect of a partnership change. Being a partner is endogenous, because partners are expected to have a higher quality and to be the most popular channels. However, identification comes from non-partnered channels that suddenly (and surpris- ingly to them) are upgraded to partners. Thus, the effect of partnership has a causal interpretation, once we include channel fixed effects. This effect is likely underestimated if a high investment is necessary to become a high-skilled streamer, but, to a degree, the tenure of the channel controls for growth in quality or in the fan base over time. In any case, if one is willing to additionally assume

(d) 1{Partner jt} ⊥ εIO jt |μIO

j , xIO jt ;

(e) 1{Partner jt} ⊥ εB jt |μB

j , xB jt ;

then, we have a causal interpretation of 1{Partner jt}, which opens the door to further counterfac- tuals.

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TABLE 2 Noise Estimations

Models

Dep var: log σ jt (1) (2) (3) (4) (5)

log BU pload t −0.005 0.959*** 0.544 0.775*** 0.738***

(0.003) (0.144) (0.362) (0.081) (0.075) PoP1 −0.062*** −0.060*** −0.042** −0.050*** −0.052***

(0.004) (0.007) (0.018) (0.004) (0.004) PoP2 0.021*** 0.015** 0.022 0.021*** 0.022***

(0.004) (0.006) (0.018) (0.004) (0.003) PoP3 0.029*** −0.012** 0.000 −0.007* −0.006

(0.003) (0.006) (0.015) (0.004) (0.004) PoP4 0.050*** 0.01x6* 0.024 0.009* 0.016***

(0.003) (0.010) (0.025) (0.005) (0.005) Trend −0.001*** −0.002*** −0.002*** −0.002*** −0.002***

(0.000) (0.000) (0.001) (0.000) (0.000) Heckman −0.451***

(0.034) cons −2.305*** −17.662*** −10.818* −14.727*** −14.174***

(0.050) (2.285) (5.758) (1.291) (1.198) Channel FE yes yes yes yes yes

Peak Hours FE Yes Yes Yes Yes Yes

2SLS . yes yes yes yes

Subsample of . Pros NonGaming . . Obs 38,283,191 15,861,549 2,649,865 38,283,191 38,283,191

Note: Standard errors in parenthesis, clustered at channel id. Time series of 10-mine windows. Bup t is the aggregate,

upload video bitrate, which is being instrumented with the Xbox One shock in the 2SLS columns. “Peak Hours FE” indicates the inclusion of peak hours and weekend dummies. “Pros only” refers to a restricted sample of channels in the top 5% of popularity. “Heckman” indicates the inclusion of a control function, based on Heckman (1979) and Olsen (1980), which controls for selection, with excluded variables: partner, transcoding, featured, interrupted, log tenure, log uptime, log viewers. First stages, for both selection-correction and 2SLS, are shown in Table 3. Bootstrapped standard errors in last column with 500 replications. Stars: *** significant at the 1% level; ** at 5%; * at 10%.

4. Estimation results

� Congestion externalities. Table 2 shows the estimation results of the noise equation (1). Column 1 shows an OLS. Columns 2 to 5 instrument Bup

t with an Xbox One dummy; first stages can be found in Table 3. Column 2 restricts the sample to pro channels (defined by being in the top 5% of popularity), and column 3 restricts it for non-gaming channels. These subsamples should not be affected by the Xbox shock directly under any circumstance. They are only affected by congestion externalities. Finally, column 5 corrects for selection.

The coefficients of the PoP upgrades loosely align with the relative importance of these upgrades, even if we only establish correlations. Although precise numbers were not released, the first upgrade was the largest, followed by the third, followed by the second. No information is available on the relative size of the fourth upgrade.19

The results imply increasing the aggregate, upload video bitrate by 1% will increase the noise-to-signal ratio of every channel by about 0.7%. An increase of 10% in Bup

t would translate into an increase of 7% in the noise-to-signal ratio of every channel. In a single day, Bup

t can fluctuate by up to 50%.

� Demand-side results. Table 4 shows the estimation results of the demand equation (2). Column 1 shows an OLS. Columns 2 and 3 instrument log σ jt and log s jt|g. Column 3 controls for selection. First stages are reported in Table B1 in the online Appendix B.

19 See blog.twitch.tv.

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TABLE 3 Noise Estimations, First Stages

Models

(1) (2) (3) (4) (5) Dep var: Online j,t+1 = 1 log BU pload

t log BU pload t log BU pload

t log BU pload t

Xbox Available −0.003*** 0.041*** 0.045*** 0.045*** 0.044***

(0.000) (0.000) (0.001) (0.000) (0.000) PoP1 −0.003*** −0.011*** −0.006*** −0.012*** −0.013***

(0.000) (0.000) (0.001) (0.000) (0.000) PoP2 0.002*** 0.006*** 0.008*** 0.004*** 0.004***

(0.000) (0.000) (0.001) (0.000) (0.000) PoP3 0.002*** 0.011*** 0.005*** 0.009*** 0.010***

(0.000) (0.000) (0.001) (0.000) (0.000) PoP4 0.013*** 0.053*** 0.052*** 0.050*** 0.052***

(0.000) (0.000) (0.001) (0.000) (0.000) Trend 0.000*** 0.001*** 0.001*** 0.001*** 0.001***

(0.000) (0.000) (0.000) (0.000) (0.000) Weekend −0.008*** 0.001** 0.021*** 0.004*** 0.003***

(0.000) (0.000) (0.001) (0.000) (0.000) After 6 pm −0.016*** 0.039*** 0.011*** 0.040*** 0.038***

(0.000) (0.001) (0.003) (0.000) (0.000) log nV

jt (Partner) 0.010***

(0.000) log nV

jt (Non-Partner) 0.031***

(0.000) Partner 0.113***

(0.002) Transcoder −0.014***

(0.000) Featured −0.052***

(0.010) Interrupted −0.028***

(0.000) log Tenure 0.004***

(0.000) log Uptime −0.004***

(0.000) Heckman −0.168***

(0.004) cons 0.854*** 15.922*** 15.913*** 15.922*** 15.907***

(0.001) (0.001) (0.001) (0.000) (0.001) Channel FE yes yes yes yes yes

Subsample of . Pros NonGaming . . R2

a 0.12 0.20 0.16 0.19 0.19 F -stat 14,934 32,151 7,989 75,259 65,958 Obs 48,570,885 15,861,549 2,649,865 38,283,191 38,283,191

Note: Standard errors in parenthesis, clustered at channel id. Time series of 10-min windows. First column predicts channel j keeping online at time t + 1; predictions used to construct a control function to correct for selection bias, based on Heckman (1979) and Olsen (1980). Bup

t is the aggregate, upload video bitrate. “Pros only” refers to a restricted sample of channels in the top 5% of popularity. “Heckman” indicates the inclusion of the control function derived from column 1, which controls for selection. Bootstrapped standard errors in last column with 500 replications. Stars: *** significant at the 1% level; ** at 5%; * at 10%.

As expected, an increase in the noise-to-signal ratio decreases demand. Because market shares are small, (1 − α3s jt|g − (1 − α3)s jt ) ≈ 1, then α1/(1 − α3) can be interpreted as the elas- ticity of own noise-to-signal ratio, where α1 and α3 are the coefficients of log σ jt and log s jt|g. In other words, if σ jt increases by 1%, demand decreases approximately 2.5%. Demand is elastic to

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TABLE 4 Demand Estimations

Models

Dep var: log(s jt/s0t ) (1) (2) (3)

log σ jt −0.001*** 0.166*** −1.677***

(0.000) (0.041) (0.125) Transcoder −0.051*** 0.328*** 0.291***

(0.004) (0.011) (0.014) Partner 0.052*** −0.188*** −0.266***

(0.009) (0.034) (0.046) Featured 0.346*** 1.837*** 1.085***

(0.048) (0.312) (0.235) log Tenure −0.018*** 0.029*** −0.184***

(0.002) (0.006) (0.012) Weekend 0.132*** 0.054*** 0.174***

(0.001) (0.001) (0.002) After 6pm 0.082*** 0.050*** 0.308***

(0.002) (0.002) (0.005) log s jt|g 0.807*** −0.048*** 0.320***

(0.001) (0.007) (0.010) Heckman 16.661***

(0.253) cons −5.284*** −13.718*** −11.874***

(0.015) (0.116) (0.332) Channel FE Yes Yes Yes

2SLS No Yes Yes

Obs 38,283,191 38,283,191 38,283,191

Note: Standard errors in parentheses, clustered at channel id. Time series of 10-min windows. “Heckman” indicates the inclusion of a control function, based on Heckman (1979) and Olsen (1980), which controls for selection. First stages, for both selection-correction and 2SLS, are shown in Table B1 in online Appendix B. Instruments for log σ jt : Xbox One broadcasting availability, PoP server upgrades. Instruments for log s jt|g: channels in English, from the United States, with transcoders, featured, and partnered, as percentages of group g, excluding j. Excluded variables for Heckman correction: if a channel was interrupted, and log nV

jt for partners and non-partners. Bootstrapped standard errors in last column with 500 replications. Stars: *** significant at the 1% level; ** at 5%; * at 10%.

noise. The partial-equilibrium effect of a 10% increase in Bup t translates into an increase of 7% in

σ jt , which in turn implies a 18% reduction in demand. Transcoding increases demand in a significant way, approximately by 25%. As expected,

conditional on transcoding, features, and a fixed effect, a channel’s partnership status does not increase viewership, because the remaining perks of partnered channels are trivial for viewers.

Finally, it can be shown that increasing the number of online channels by 1 increases viewer- ship by (s0 − s+

0 )/(1 − s0) percent in expectation, where s0 is the share of the outside option and s+

0 is the share of the outside option when the extra channel is online. Translated into elasticities, increasing the number of channels by 1% increases the number of viewers by 0.12%.

� Supply-side results. Results are in Table 5. Both columns show logit models. Translated into probabilities, a 1% increase in viewership increases the probability of keeping on by about 0.9% for partners, and by about 1% for non-partners. That is, partners’ supply is less elastic to viewership than non-partners’, even after controlling for scheduling. Because partners have many more viewers than non-partners, a lower marginal valuation is expected. Gaining partnership increases the probability of starting a stream at any given t by about 0.2% from a baseline of about 0.7%. Partners are more likely to start a broadcast because the promise of a transcoder increases expected viewership, and because viewers bring about monetary compensation.

In sum, for both partners and non-partners, the elasticity of supply with respect to viewers is about 1; a 1% increase in viewers increases the number of online channels by about 1%.

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TABLE 5 Supply Estimations

Models

Dep var: Online j,t+1 = 1 (1) (2)

log nV jt (Non-Partner) 0.311*** 0.084**

(0.046) (0.033) log nV

jt (Partner) 0.230***

(0.019) Partner1 0.517**

(0.212) Partner0 0.308***

(0.035) log Tenure1 −0.548*** −0.442***

(0.044) (0.025) log Tenure0 −0.605*** −0.623***

(0.028) (0.023) Weekend1 0.035*** −0.015

(0.009) (0.029) Weekend0 0.011 0.150***

(0.014) (0.022) Peak Hours1 −0.122*** −0.069*

(0.025) (0.038) Peak Hours0 0.708*** 0.638***

(0.035) (0.037) Online jt 6.219*** 6.667***

(0.333) (0.124) Xbox1 0.039*** 0.415*

(0.013) (0.230) Xbox0 −0.030* −0.880***

(0.017) (0.230) Xbox, gaming1 −0.218

(0.231) Xbox, gaming0 0.904***

(0.227) Control F., non partner −0.067*** 0.183***

(0.017) (0.025) Control F., partner −0.103***

(0.015) Channel FE Yes Yes

Model Logit Logit

Sample of Partners NonPartners

Obs 20,134,391 20,650,762

Note: Bootstrapped standard errors in parentheses with 200 replications, panel defined at channel id. Time series of 10- min windows. Logit models for j’s decision to be online at t. Variables “X 1” refer to Xjt when j is online; “X 0” refer to Xjt when j is offline. The control function is the residual of a regression of log nV

jt on log σ jt , indicators for transcoding and features, fixed effects, and the second-stage covariates; first stages are shown in Table B2 in online Appendix B. Sample of Partners refers to all broadcasters that eventually were partnered; NonPartners refers to a random sample of the rest. Coefficients already rescaled to achieve a standard logit’s variance (Guevara and Ben-Akiva, 2012). Stars: *** significant at the 1% level; ** at 5%; * at 10%.

Together with the demand-side results, the estimation implies the broadcaster side is more elastic to viewers than the viewer side is to broadcasters. Therefore, for platform growth, efforts to attract viewers have more impact than efforts to attract broadcasters.

5. Counterfactuals

� With estimated preferences and technology parameters, we can explore counterfactual allo- cations of transcoders and differential pricing. This section begins by quantifying the gains from

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the efficient use of transcoders, compared to a counterfactual random allocation. Next, I measure the effects of congestion externalities and explore a Pigouvian tax on each side of the market. I also simulate a counterfactual monopolistic platform and analyze the possibility of extracting rents from content providers and its implied equilibrium effects. Finally, I consider the role of supply heterogeneity in the platform. Because the model is static, these counterfactuals should be interpreted as short-run equilibrium responses to changes in the environment.

The counterfactuals consist of three regimes: neutral, preferential, and preferential with a rent-extractive platform. In the neutral regime, transcoders are allocated randomly through the population.

In the preferential regime, which represents the platform’s status quo, channels will be ranked by their quality and transcoders will be given to the highest-ranked channels. As a proxy for quality, I use the residual of a regression of the estimated fixed effects from the demand-side model on the observable time-invariant characteristics of the channel: average bitrate, average log noise-to-signal ratio, average viewers, log tenure, cost of internet in home country, and dum- mies for the gaming category, English language, US country, eventually becoming a partner, and being in the pro category.

Finally, in the preferential regime with a rent-extractive platform, transcoders will also be given to the highest-ranked channels, but the platform will charge them just enough to offset the benefits accrued from transcoding. I assume the platform has perfect information for it to be able to set this charge, and that the platform is a monopoly with all the bargaining power, arguably the worst-case scenario for content providers.

� Simulations details. For a given regime, label as c the counterfactual of guaranteeing enough transcoders for c% of the population. For example, the platform could have resources to guarantee transcoders to c = 1% of the population. I consider c ∈ {0, 1, . . . , 100}.

Online Appendix Section B defines the equilibrium and ensures a mixed-strategy Nash equi- librium exists, when streamers’ strategies are to be online or not. I do not impose an equilibrium- selection mechanism. Instead, I randomly select starting points, and then find a local fixed point by iterating on the equilibrium conditions. I draw 10,000 different starting points for each coun- terfactual c.

For each regime and for each counterfactual c, the algorithm to find the equilibrium outcome is as follows. Take a random sample J ⊂ J of channels. For each simulation s = 1, . . . , S:

1. Allocate transcoders to c% of J according to the given regime. 2. Given observed probabilities of being online, simulate a starting point of initial online/offline

status, {ys j0} . Simulate relevant covariates taken from observed distributions. Simulate struc-

tural, random shocks εIO,s j , εB,s

j and εσ,s j , ∀ j ∈ J .

(a) Given two of {Demand, Supply, Congestion}, predict the third one and update. That is, given {ys

j0, σ s j }, shocks, and covariates, predict {nV,s

j }. Then, given {nV,s j , σ s

j }, predict {ys j}.

Then, given {nV,s j , ys

j}, predict {σ s j }.

(b) Repeat 5 until convergence.

For each s, I calculate the consumer surplus, total channels online, total viewers online, the average noise-to-signal ratio, and the average quality of online channels. I perform S = 10, 000 simulations per counterfactual c, and I draw a random sample of #J = 50, 000 channels from the population for the simulations. I assume each channel has a weight of 20 for the total population size to be 1,000,000.

� Benchmark comparison: neutrality versus status quo. Figure 6 shows the results for the baseline comparison between the neutral and the preferential regime. The x-axis shows the estimated cost of purchasing enough transcoders to guarantee one for c% of the population, up to $250 million, the face-value cost of acquiring 1,000,000 transcoders, which is a worst-case

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FIGURE 6

NEUTRAL VERSUS PREFERENTIAL REGIMES

Note: Fractional polynomial curves fitted over averages of counterfactual simulations. Averages computed from 10,000 equilibrium simulations.

cost scenario. For clarity, all figures show a lowess fit that runs through 101 points; each point represents a different counterfactual c ∈ {0, 1, . . . , 100}. The platform’s infrastructure in 2014 is approximately c = 10.

In this benchmark case, neutrality yields a lower consumer surplus by construction. Because transcoders are scarce, their random allocation must yield a less efficient outcome than an allo- cation that favors the most proficient channels. However, this benchmark is useful to quantify a drop of up to 10% in consumer surplus, measured in utils, caused by an immediate shift to neutrality. Assuming an opportunity cost for viewers of 7.25 USD/hour, 30 seconds of ads cost viewers about 6 cents. On average, 10 min of streaming imply 30 seconds of ads. We can thus assume viewers are willing to pay at least 6 cents for 10 min. Up to 40,000 viewers may drop due to an immediate shift to neutrality. Thus, consumer welfare decreases by about 2400 USD each 10 min in the worst-case scenario.

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FIGURE 7

PREFERENTIAL REGIME WITH AND WITHOUT CONGESTION EXTERNALITIES

Under the preferential regime, the first transcoders are allocated to the channels with higher quality. The largest gains are here, because those channels make the best use of transcoders by reaching more viewers. These initial gains offset the congestion externalities from increased traffic. However, as the platform expands its transcoding infrastructure, and transcoders become less scarce, the relative efficiency gains shrink, because the marginal channel’s quality starts to decrease whereas the noise-to-signal ratio keeps increasing. In effect, the congestion externality increases the opportunity cost of transcoders.

Finally, note that ad revenues are proportional to viewership. Figure 6 shows that the plat- form’s short-run incentives to expand its infrastructure are eroded with a neutral allocation.

The counterfactual exercises have two main caveats. First, the nested logit model might overestimate gains from variety. Therefore, viewership and consumer-welfare estimations should be interpreted as an upper bound, especially for the neutral regime, where the number of broad- casters is higher. Second, for the preferential regime, my allocation of transcoders is based on a quality proxy. In reality, the platform has better information and can thus allocate transcoders optimally. Therefore, the preferential regime should be interpreted as a lower bound on consumer welfare and viewership.

� Effects of congestion. Congestion externalities play a major role in the growth of the platform because their impact is magnified by network effects. Figure 7 compares the preferential regime with and without congestion externalities. When the externality is turned off, the noise- to-signal ratio is assumed to be constant and equal to its 10th percentile in the data, regardless of aggregate traffic. The exercise shows that if not for congestion, participation in the platform would be significantly higher.

Interestingly, viewership, which is directly affected by the congestion externality, increases substantially without congestion, up to 100%. However, supply slightly decreases, by about 3%. Thus, with congestion, demand is inefficiently drawn toward those channels that are less valuable but that have a lower noise-to-signal ratio, prompting an over-supply of said channels. In contrast to Berry, Eizenberg, and Waldfogel (2016), where excessive entry occurs in radio markets (with no congestion externalities); here, excessive entry has a high opportunity cost due to congestion.

� Pigouvian taxation on the demand side. Assuming perfect information, the platform can tax viewers to offset the congestion externality, say, by increasing the number of ads in each stream by ai percent. With perfect information, the platform knows the level of ai that is equivalent to any tax level τi. That is, the platform can decrease the channel’s unobservable utility term uniformly across all channels in order to achieve any desired level of aggregate

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FIGURE 8

PREFERENTIAL REGIME WITH AND WITHOUT PIGOUVIAN TAXATION ON VIEWERS

FIGURE 9

PREFERENTIAL REGIME VERSUS PREFERENTIAL REGIME WITH RENT-EXTRACTIVE PLATFORM

demand decrease. As an example, Figure 8 compares the equilibria with and without a consumer’s Pigouvian tax, ai, which would result in a (partial-equilibrium) reduction of 5% in demand. To be clear, in each round of the simulation procedure, the platform is simulated to tax the demand side.

In equilibrium, viewership decreases, supply increases, but congestion is at similar levels. Content providers are better off, but viewers are not. Note, however, that uploaded traffic that is never consumed is a significant source of congestion. Taxing consumers would not alleviate this channel. Also, the two-sided structure matters: A dollar taxed on the consumer side does not have the same effect as a dollar taxed on the producer side. In particular, the estimations imply cross- side network externalities are larger for viewers than for broadcasters. That is, the platform’s size decreases by less if broadcasters rather than viewers are taxed.

� Pigouvian taxation on the supply side. To the extent that the platform can charge broad- casters differentially, it might be interested in the effects of a supply-side Pigouvian tax. The rent-extractive regime can be reinterpreted as a platform that taxes popular channels and thereby the largest sources of traffic.

Figure 9 shows that compared with the status quo, taxing the most popular channels (by an amount equivalent to the rents of transcoding) has virtually no effect on participation on either side of the market, at low levels of infrastructure. This is because the tax falls on the market side

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FIGURE 10

NEUTRAL REGIME VERSUS PREFERENTIAL REGIME WITH RENT-EXTRACTIVE PLATFORM

with lower cross-side network externalities. In this case, the platform is better off, because tax revenues are positive.

� Rent-extractive platform versus neutrality. Figure 10 compares rent extraction with a neutral allocation. As expected, neutrality encourages content provision. However, in equilib- rium, congestion is higher with neutrality. When transcoders are scarce, larger gains accrue from the efficient use of the infrastructure, but when transcoders become less scarce, they in- centivize over-supply.

� Heterogeneity. The internet at large features more heterogeneous content providers than Twitch. To explore the effects of heterogeneity, I consider a mean-preserving spread of quality. By adding a mean-zero shock, I double the variance of the content providers’ quality. Then, I compute the counterfactual equilibrium outcomes, and I compare the results with the outcomes of the neutral regime and the rent-extractive platform regime.

Figure 11 shows the results. Each line represents the difference between: (1) the equilib- rium with a mean-preserving spread of quality and (2) the equilibrium with the baseline quality. Increasing heterogeneity increases viewership under both neutral and preferential regimes. How- ever, the preferential regime achieves that outcome not because of more content providers, but because of the increase in the quality of online channels. Intuitively, when heterogeneity on the supply-side increases, the preferential regime allocates transcoders more efficiently, taking ad- vantage of the fatter tails of the distribution. Therefore, if heterogeneity among content providers is pronounced, as in this extreme example, we would expect the benefits of prioritization to increase.

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FIGURE 11

EFFECTS OF INCREASING QUALITY HETEROGENEITY

6. Concluding remarks

� Twitch offers a setting that features important trade-offs that parallel those faced by inter- net users. In particular, prioritization is important in the net neutrality debate. Net neutrality is the principle that internet service providers (ISPs) and governments should treat all data on the internet the same, not prioritizing traffic, charging differentially by priority status, or imposing congestion charges.20 Proponents of net neutrality argue prioritization risks being concentrated over larger firms, which will decrease the variety of content provision and thus decrease con- sumer welfare. Proponents of net neutrality also worry about ISPs using second-degree price discrimination as a device to extract rents from innovators and content providers.

However, although net neutrality encourages entry, it also creates congestion externalities from the increase in data traffic. Critics of net neutrality argue antitrust enforcement or more lim- ited regulatory mechanisms provide a better framework for addressing competitive concerns. See Becker, Carlton, and Sider (2010). Moreover, by differentiating between types of traffic, network managers can avoid congestion and improve utilization and quality of high-bandwidth services. Thus, even without a formal pricing system, prioritization can boost the quality of service, which will encourage content provision and investment in innovations that take advantage of improved network performance. Finally, if ISPs can extract rents from content providers in exchange for a “fast lane,” they would have a greater incentive to invest in higher-quality infrastructure, thus providing faster and more reliable internet service.

In recent years, policymakers and the general public have escalated the debate about net neutrality. The FCC’s website has received more than 23 million comments since April 2017.21

Europe’s telecommunications regulator held a public consultation in 2016 and gathered more than 500,000 comments in six weeks—the previous record was less than 100.22 Published on August 30, 2016, its final guidelines strongly protect net neutrality in the European Union.23

The theoretical literature emphasizes four lines of net-neutrality research: (1) congestion, See Choi and Kim (2010), Economides and Hermalin (2012). (2) the two-sided structure of the internet, See Economides and Tåg (2012), Caves (2012), Greenstein, Peitz, and Valletti (2016). (3) the heterogeneity of consumers and content providers, See Greenstein, Peitz, and Valletti (2016). and (4) investment. See Bourreau, Kourandi, and Valletti (2015), Choi and Kim (2010).

20 See Lee and Wu (2009) and the Federal Communications Commission’s website, fcc.gov. 21 Docket 17-108, “Restoring Internet Freedom,” fcc.gov. Around 150,000 of those comments were received within

24 hours after HBO’s John Oliver urged his viewers to intervene (usatoday.com). Shortly thereafter, the FCC’s website was subject to a distributed denial-of-service attack (cnbc.com).

22 See berec.europa.eu, medium.com. 23 See savetheinternet.eu.

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The structural model explicitly includes points 1–3, though it lacks point 4. Therefore, to the extent that an analogy of Twitch as an ISP holds, and if the counterfactuals are interpreted as short-run equilibrium responses, this article can inform the debate. Indeed, if prioritization is of first-order in evaluating a net neutrality policy, and if transcoding can be understood as a form of prioritization, we conclude prioritization is used more efficiently when it is not neutrally allocated, even in the presence of market power.

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Supporting information

Additional supporting information may be found online in the Supporting Information section at the end of the article.

Table A1: Reduced form: broadcasters and viewers Table B1: Demand estimations, first stages Table B2: Supply estimations, first stages

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