A Dynamic Model of User Behavior in a Social Network Site∗ Dae-Yong Ahn School of Marketing University of Technology Sydney dae-yong.ahn@uts.edu.au Randal Watson Department of Economics University of Texas at Austin watson@eco.utexas.edu April 16, 2010 Abstract This paper estimates a dynamic model of user behavior in a social network site using unique data on the daily login activity of a sample of members of MySpace.com We view a social network as a stock of capital that yields a flow of utilities over time by creating interactions between the site user and her friends This capital stock can be maintained and expanded by logging in to the site and communicating with other members The user’s login decision is thus a forward-looking one, which we model in the framework of a dynamic discrete-choice model We allow for two sources of persistence in members’ login decisions: state dependence and unobserved heterogeneity We found two distinct types of consumers as regards utility, cost, and ∗ We are grateful to Susan Broniarczyk, Romana Khan, Vijay Mahajan, Om Narasimhan, Raghunath Rao, and Garrett Sonnier for their comments, suggestions, and corrections Electronic Electroniccopy copyavailable availableat: at:https://ssrn.com/abstract=1591102 http://ssrn.com/abstract=1591102 state transition Across types, real-time chat and messaging, features of MySpace.com, positively affect the usage decision We use our parameter estimates to perform counterfactual simulations with the goal of providing site managers with ways to enhance firm performance Keywords: dynamic discrete choice, online social networks, unobserved heterogeneity Electronic Electroniccopy copyavailable availableat: at:https://ssrn.com/abstract=1591102 http://ssrn.com/abstract=1591102 Introduction This paper structurally estimates a dynamic model of user behavior in a social network site using data from MySpace.com We view a social network as a stock of capital that yields a flow of utilities over time by creating social interactions between the owner and her friends Using a social network site may have two effects on this stock of capital: (1) maintaining the quality of interactions with an existing group of friends, and (2) expanding the quantity of interactions with the addition of new friends to the network Since both of these effects will yield a higher flow of utilities in the future, it is appropriate to analyze usage of a social network site with a model that takes into account consumers’ forward-looking behavior This is the task addressed here We use our model to measure how features of a social network site affect usage, and to evaluate counterfactual policies that are managerially relevant As their popularity grows among consumers, social network sites are attracting an increasing share of advertising expenditures Thirty-three percent of adult US internet users, and 70% of teenagers, logged in to a social network site at least monthly in 2007 A market research firm eMarketer projects that ‘50% of online adults and 84% of online teens in the US will use social networking by 2011’ To tap into this audience, marketers spent $1.2 billion on social network sites in 2007 and this figure is expected to climb to $3.6 billion by 2010 worldwide (eMarketer, December 2007) Industries that advertise in social network sites range from entertainment (25.2%), retail goods and services (17.6%), and telecommunications (16.2%) to financial services (6.3%) and automotive (5.1%) (Nielsen/NetRatings, September 2006).1 eMarketer reports that MySpace.com and Facebook.com, the two largest US social network sites, accounted for 72% of social network advertising spending in 2007 (Marketing News, July 15 2008) Media giants such as NBC and Warner Bros host sites on MySpace, while Coca-Cola, CBS, and Chase promote their products on Facebook On the other hand there is also a growing trend towards niche social network sites and marketer-sponsored sites that attract ‘a smaller, but passionate audience’ rather than the ‘diverse membership’ of MySpace and Facebook (CNN.com, April 16 2008) Examples include petside.com by Proctor & Gamble for its Iams pet foods and artofcookie.com by Campbell Soup Company for its Pepperidge Farm The numbers in parentheses are industries’ shares of the total advertising dollars spent on social network sites Electronic copy available at: https://ssrn.com/abstract=1591102 cookies Social network sites compete on features – instant messaging, video chat, etc – in order to attract more users and thereby bring in more advertising revenue.2 In this paper we assess the impact of two such features of the MySpace site – real-time chat, and a messaging or mailbox feature We estimate a single-agent, dynamic discrete-choice model in which usage is defined as a decision of whether or not to log in to the site This decision relates closely to the number of unique users that a site attracts, a benchmark used in the industry to rank sites Our estimates allow us to propose and evaluate other features that social network sites might adopt to enhance firm performance In particular we estimate the effects on site usage of policies designed to enhance the networking experience while online, and to expand a user’s network Our data are observations on a random sample of college-aged members of MySpace We collected data from their webpages on a daily basis for four weeks, recording three types of variables for each member: usage behavior, social interactions, and the evolution of the social network For usage behavior we recorded whether or not one used MySpace for each member each day For social interactions we recorded real-time chat and messaging, two features of MySpace, for each member each day.3 We tracked changes in members’ social networks by recording the size of each member’s network each day Our estimation strategy is based on the MPEC (Mathematical Programming with Equilibrium Constraints) approach (Su and Judd 2008).4 This approach alleviates the computational burden in estimating a dynamic discretechoice model by formulating the NFXP (Nested Fixed Point) approach as a constrained optimization problem We allow for two sources of persistence in members’ login decisions: state dependence and unobserved heterogeneity To accommodate unobserved heterogeneity, we use a finite mixture model Advertising rates on these sites are set as fees per quantity of page views For example Merrill Lynch reports a rate of $1.83 per thousand views (BusinessWeek, November 2007) For real-time chat we actually measure a proxy, namely the number of friends online at the same time of each day See Rust (1987), Hotz and Miller (1993), Hotz, Miller, Sanders, and Smith (1994), Keane and Wolpin (1994), Magnac and Thesmar (2002), Aguirregabiria and Mira (2007), Bajari, Benkard, and Levin (2007), Pakes, Ostrovsky, and Berry (2007), Pesendorfer and Schmidt-Dengler (2007), Arcidiacono and Miller (2008), Imai, Jain, and Ching (2009) for estimation of dynamic discrete-choice models Electronic copy available at: https://ssrn.com/abstract=1591102 that incorporates members’ demographics into segment membership probabilities (Gupta and Chintagunta 1994, Erdem, Imai, and Keane 2003, Erdem, ¨ u, and Strebel 2005) Keane, Onc¨ We found that consumers can be classified into two distinct latent groups, according to their base rates of site usage Segment membership probability was most affected by a member’s age with a 47%/53% split between the two segments averaged across demographics – older members have lower rates of site usage on average Expected quantities of real-time chat, measured by the number of friends who are online, and messaging, measured by the number of incoming messages per day, both had positive effects on usage across segments All else equal, usage of the site was more likely on a weekday than on a weekend, although this effect is not statistically significant We used our estimates to analyze the potential effects of two counterfactual policies The first is designed to enhance the networking experience during online meetings An example of this type of policy is MySpace’s introduction of video chat using Skype in October 2007 The second policy is designed to assist in the acquisition of new friends, for example through the adoption of a collaborative filtering system such as that used by online retailers like Amazon.com, or survey techniques used by online dating services such as Eharmony.com or Match.com We found that these policies had varying dynamic effects on site traffic They had a similar initial effect on usage, but subsequently a gap between the two effects appears, with the second policy resulting in larger gains in site usage over time There is a growing empirical literature on the economics of social networks or social network websites Manski (1993) illustrated the difficulty of separating endogenous effects (social effects) in cross-sectional data from contextual and correlated effects Recent work by Graham (2008) exploits the specific nature of particular datasets to isolate social effects, separating these from group-level heterogeneity by, for example, using the random assignment of teachers and students to classes of different sizes Other studies have developed structural approaches that explicitly solve network coordination games among agents in static settings For example Hartmann (2008) developed a likelihood-based, game-theoretic approach to model the joint consumption decisions of golf players, while Bao, Gupta, and Kadiyali (2009) modelled social interactions in MBA students’ choices of summer internship applications Yet another group of studies identifies social interactions using reduced-form panel-data approaches Examples include Trusov, Bodapati, and Bucklin (2008), who investigated the determinants of influential network users, Nair, Electronic copy available at: https://ssrn.com/abstract=1591102 Manchanda, and Bhatia (2008), who examined the role of opinion leaders in physician prescription behavior, and Mayer and Puller (2008), who studied the effects of academic and demographic factors on links between college users of Facebook Our structural dynamic approach is related to that in Ryan and Tucker (2008), who use dynamic discrete-choice techniques to incorporate network effects into a model of new technology adoption They analyze one-time adoption as a stopping problem, whereas we focus on an on-going usage problem Our decision to model social effects in a single-agent framework also resembles the approaches by Blume (1993) and Brock and Durlauf (2001, 2002) who modeled individual choices in the presence of social interactions while assuming that payoffs are affected only by the aggregate behavior of the group Section describes the data Section describes the model Section describes the estimation method Section discusses the results of the estimation Section describes the policy experiments and discusses the results Section concludes Data 2.1 Data description We randomly selected a group of college-aged members of MySpace (aged 19-23) and tracked their websites daily for four weeks from mid-January to mid-February of 2008 Our sample comprised only non-business members, excluding artists or companies who used the site for promotional or business purposes Privacy restrictions forced us to confine our sample to members whose profiles were open to the public.5 About 15% of members in the initial sample were dropped from the final sample according to the following criteria First, we dropped members who switched their profiles from public to private during the data collection period Second, we dropped members who had less than 51 or more than 200 friends This was due to the scarcity of observations outside this range In addition, this criterion allows us to reduce the size of state space Finally, we dropped members who exhibited extreme behavior, defined as losing or This may give rise to some selection issues Hence our inferences only apply to members whose profiles are open to the public Electronic copy available at: https://ssrn.com/abstract=1591102 gaining more than 10 friends on any given day The final data set consists of 111 members Three types of variables were recorded daily for each member of our sample: usage behavior, social interactions, and the evolution of the social network Usage behavior is defined as one’s daily decision to use a site This definition closely relates to the advertising revenue of social network sites and thus is of direct managerial relevance Since MySpace automatically updates the last time that a member used the site on a real-time basis, this variable is collected with high accuracy Social interactions comprise real-time chat and messaging, the ways through which members can interact with each other on MySpace Real-time chat is a system that allows for the back-and-forth exchange of text messages among members who are currently online Messaging is similar to electronic mail in that it allows members to post messages to friends’ webpages Unlike chat, messaging does not require members to be simultaneously online in order to exchange messages Since we not observe real-time chat directly, in our empirical work we proxy for this variable with the number of friends online at the time of login Hence we will often use the terms ‘real-time chat’ and ‘number of friends online’ interchangeably To measure messaging activity we counted the number of incoming messages for each member, which serves as a proxy for messaging activities as a whole.6 We tracked the evolution of the social network by recording the number of friends for each member each day of the sample period The social network may grow or shrink over time as the member gains or loses friends.7 2.2 Descriptive statistics Tables and give definitions of, and summary statistics for, demographic and state variables used in our paper Over the time period of our sample, an average member was 21 years of age, and had about a 50% probability of being female, or of coming from outside the US.8 On average, a member of our sample had about 120 friends on MySpace Tables and give definitions Outgoing messages of the members in our sample were posted on their friends’ webpages, some of which were kept private preventing us from collecting this variable Thus we implicitly assume that the number of incoming messages is proportional to that of outgoing messages All data were recorded at the same time of each day so as to minimize any noise from time-of-day effects Most non-US users in our sample are from Australia and the UK Electronic copy available at: https://ssrn.com/abstract=1591102 of, and summary statistics for, our measures of site usage, social interactions, and network evolution The average rate of daily usage in our sample was about 52%, and the average number of friends who were online at the time of data collection was about four Members only received an average of about 0.26 messages per day on their webpages This low number may be due to the availability of other ways of exchanging messages such as electronic mails On average, daily changes in social networks were small: 90% of daily network changes were either or 1, and the mean daily change was close to zero Table shows the evolution of social networks for the members of our sample after about weeks The median of monthly changes in network size was still zero and the mean was a gain of less than two friends However, there were substantial individual differences in network evolution across the members About 5% of the members gained more than 10 friends after weeks, whereas some lost friends during that period The dispersion of network evolution across members demonstrates that our model must account for idiosyncratic time paths of individuals’ social networks The central notion of our paper is that members can maintain and invest in social networks now so that they yield larger social interactions in future Members perceive social networks as a stock of social capital, the ‘dividends’ of which are the expectation of chat and messaging activities upon login To this end we test whether members’ login decisions last period and the sizes of social networks – state variables that serve as proxies for maintenance of, and cumulative investment in, social capital – positively affect real-time chat and messaging Tables and show the results from Poisson regressions of the components of per-period utility – real-time chat and messaging – on state variables In the chat regression of table all effects are statistically significant at the 5% level or better Chat is increasing in the member’s network size – this is to be expected since chat itself is measured as the number of friends online It is also increasing in last period’s login decision, suggesting that a member’s stock of social capital depreciates if he or she does not log in frequently Moreover this effect is quite strong in a relative sense – whereas adding an extra person to one’s network increases the expected number of friends online on any given day by just one percent, a login last period increases the mean by around 14% Finally, the number of friends online is lower on weekends – perhaps reflecting the alternative activities available to members at those times Electronic copy available at: https://ssrn.com/abstract=1591102 Broadly similar effects are seen in the messaging regression of table Messaging shows a statistically significant response to network size and last period’s login While the former effect is quite small in magnitude, with an additional friend raising the expected number of daily messages by less than half a percent, the last-login effect is much larger, by a couple of orders of magnitude The dynamic considerations in the consumer’s choice problem, inherent in depreciation of the ‘capital stock’ if she does not log in, are thus clearly illustrated Model We propose a dynamic model of a member’s usage of a social network site (henceforth, a ‘site’) Consumers derive utility from interacting with other members of the site Enjoyment of these benefits requires the member to make costly login efforts so as to manage existing contacts and build new ones Managing contacts averts depreciation, which would be visible in our model as the negative effect on the expected amounts of chat and messaging if the member failed to log in last period Acquisition of new capital will be apparent in the effect of a login this period on the expected network size next period, and in the flow-on effects of a bigger network on social interactions in future periods A dynamic model allows us to incorporate expectations about these future effects into consumers’ login decisions 3.1 Member types We assume a finite number of latent types for consumers as regards utility, cost, and state transition Some members may be more social than others leading to variation in preferences towards the site Different lifestyles (e.g., indoorsy vs outdoorsy) may affect the cost of using the site Finally, some members may make friends more easily than others Allowing for such heterogeneity is important since the users in our sample show wide variations in daily login propensities and network evolutions, which are not obviously explained by their observed characteristics Furthermore our state space includes the lagged action as a variable conditioning current actions As is well known, coefficients on such lagged actions may be incorrectly estimated if unobserved time-constant heterogeneity is not also allowed for Electronic copy available at: https://ssrn.com/abstract=1591102 3.2 Per-period utility Let ait = 1, or 0, as consumer i does, or does not, log in at time t By using the site at time t she derives per-period utility uit , and incurs a login cost of cit The per-period utility from not logging in is normalized to zero, plus a random i.i.d error Let x1it and x2it respectively denote the amounts of real-time chat and messaging that member i engages in at time t We assume that, after logging in, member i of type j’s realized per-period utility takes the form: uit = θj1 + x1it θj2 + x2it θj3 (1) Here θj = (θj1 , θj2 , θj3 ) is a vector of type-specific parameters to be estimated Realized values of x1it and x2it will depend on factors that are somewhat uncertain prior to login, i.e., the number of friends online and the messaging activity This implies that a member’s login decision is based on expectations of x1it and x2it , conditional on all information available prior to login We assume that this information consists of variables that are observable to the econometrician, collected in a finite state space S, and of unobservable components of the login cost cit that are private information to the member Since we assume that the private login costs are in fact uncorrelated with the same-period values of x1it and x2it , only the observable states in S need condition the member’s expectations Where sit denotes a vector of state variables from S, we can define member i’s of type j’s expected per-period utility at the beginning of period t as: uit ≡ E[uit |sit ] = θj1 + E[x1it |sit ]θj2 + E[x2it |sit ]θj3 = θj1 + x1it θj2 + x2it θj3 (2) Here x˜it = (x1it , x2it ) denotes a vector of expected chat and messaging activities upon login conditional on sit 3.3 State space Our specification of S includes as state variables the members’ histories of login activity and size of social network The member’s login history is represented by a binary indicator of whether or not she logged in last period.9 The members engage in other activities such as sending messages to friends during login sessions We not have this type of information in our data To the extent that other activities are conditional on the member’s login decision, the login histories serve as a gross proxy for the activities after login Electronic copy available at: https://ssrn.com/abstract=1591102 false causality Since we include day of the week in the state space, any time-varying shared unobservables that follow a regular cycle (e.g., sporting fixtures, popular TV shows, etc.) are already accounted for That is, since the value function Vk may vary over the week, consumer choice behavior may also vary over this cycle, independently of expected chat and messaging Another factor working in our favor is that we measure responses to both messaging and number of friends online A positive response to messaging, for a given number of friends online, suggests that this factor induces more logins even after controlling for any shared unobservables that cause more friends to use their PC’s Furthermore our framework assumes that user i’s action responds to friends’ expected current-period activity, not to actual activity (which is not known prior to login) In turn these expectations are conditioned on state variables (last login and network size) that are determined by actions in previous periods With respect to user i’s action the potential endogeneity problem is thus one of serial correlation between εi and previous values of any shared unobservables The hope is that by incorporating the latent time-constant user types we have controlled for most sources of such serial correlation.12 Our counterfactual simulations inherit the assumptions of our model, and therefore suppose that the systematic part of login behavior is all driven by time-of-week, personal characteristics, and expectations of chat, messaging, and network evolution We suppose that a site manager’s strategic tools (the introduction of new site features and so on) affect the latter expectations Even if some shared unobservables (not on a weekly schedule) remain in the model, our estimates and methodology might still be of interest as providing an upper bound to what managers might achieve with enhancements to the networking experience If the manager believes that in fact some common unobservables are affecting login behavior then he may want to scale back the simulated impacts derived from a model of the present type Under the above assumptions the model infers the parameters governing the dynamics of consumer behavior from observed login responses to changes in network size and changes in presumed expectations of chat and messag12 Our construction of expected chat and messaging effectively assumes that friends not observe i’s contemporaneous private costs εit when making their own login decisions For if they did, then i would presumably be aware of this, in which case εit would become part of the ‘public’ state and would need to condition i’s expectations of current-period chat and messaging activity 16 Electronic copy available at: https://ssrn.com/abstract=1591102 ing activity In general the discount factor β is not identified in dynamic discrete-choice models (Rust 1987, 1994) Hence we set β = 0.98 The utility parameters (including the constant and coefficients on chat and messaging) and the weekend premium are identified by the variation in the member’s login propensity across states, conditional on the transition probabilities and associated future expectations State transition parameters (including cutoff points) are identified by the variation in network evolution across actions and states Segment membership probabilities are identified by the correlation across consumers between time-averaged login propensities and demographic variables Results We estimated our model for up to segments and chose a 2-segment model based on Bayesian Information Criterion (BIC) Table presents the estimates of per-period utility The coefficients for real-time chat and weekend premium were restricted to be the same across the two segments; allowing them to be different does not improve the model fit The most pronounced difference between the two segments appears in the base rates of login with estimated constants of −2.1520 and −0.1149 for segments and respectively This translates into an average difference across states in predicted login probabilities of about 55% between the two segments; the minimum predicted login probabilities are 14.2% and 63.1% for segments and respectively Based on this substantial difference the need for a model that allows for unobserved latent login propensities is clear Both segments show per-period utility significantly increasing in chat (the expected number of friends online) and messaging Interestingly the response to messaging is considerably higher in segment 2, the group with the higher latent login propensity, than in segment It is also interesting to note that the estimated effect on per-period utility of one extra incoming message is much larger than that of an extra online friend This suggests that, although a member may have friends online when she logs in, on average they not necessarily chat all that much Instead, social network sites are used as online scrapbooks, where users share personal lives with friends by exchanging messages The login cost is estimated to be higher on weekends, although it is not statistically significant at the 10% level The negative sign of the weekend premium implies that some users may have limited internet access on the 17 Electronic copy available at: https://ssrn.com/abstract=1591102 weekend Alternatively, site usage may be an inferior good with respect to the time constraint, leading users to substitute toward other activities when they have more leisure Table presents the estimated network evolution or state transition probabilities We allowed the cutoffs of the ordered logit probabilities to differ between ait = and ait = The magnitudes of the cutoffs seem quite intuitive The probability of gaining friends increases by nearly two percentage points averaged across states and segments if a member logs in than not Not many parameters are statistically significant, except for the network-size parameter in segment Relative to segment 1, members of segment seem to be ‘social butterflies’ who attract more and more friends as they engage in social networking Table 10 presents the estimation results for segment membership probabilities The constant for segment is estimated to be negative and statistically significant at the 10% level, implying that all else equal segment is smaller in size than segment Across all demographics, the membership probabilities are 47.3% and 52.7% for segments and respectively Age has a positive and statistically significant effect on a member’s probability of belonging to segment 1: older members are less active in site usage and make fewer friends than younger ones Supposing that most of our sample are college students, this suggests that it is on average harder for a site manager to get upper-year students to log in, perhaps because they are busy looking for jobs and preparing for graduation Policy experiment Parameter estimates are used to perform two counterfactual simulations, with the goal of providing managers with policies that increase site traffic The first policy is designed to enhance the intensity of a user’s online experience with a given set of friends We exogenously raise the coefficient on real-time chat and simulate the effects on the user’s login behavior, and on the size of the user’s social network The second policy fixes the coefficients in perperiod utility at the existing levels, and exogenously raises the propensity to acquire new friends This may not have an immediate effect on the member’s login behavior, but bigger networks may feed back into enhanced utility from social networking The first policy might be implemented via technology aimed at enhancing 18 Electronic copy available at: https://ssrn.com/abstract=1591102 the networking experience during online meetings An example of this is MySpace’s decision to allow for video chat by incorporating Skype into its internet messenger system in October of 2007 We simulate such a policy by exogenously raising by 10% the coefficient on real-time chat in per-period utility, which is common to both segments For our second policy simulation we increase the propensity to acquire new friends by 5% for both segments A manager seeking to implement such a network expansion could for example adopt collaborative filtering mechanisms or survey techniques to match members based on common traits Many online retailers like Amazon.com use collaborative filtering systems to recommend products to customers based on their purchase histories, and online dating services like Match.com and Eharmony.com use detailed surveys to match members Both policy experiments were performed by simulating paths of actions and states at the observed demographics-states combinations We simulated ten 365-day sequences per demographics-states combination and then averaged the results over all time paths Note that our policy experiments are inherently partial equilibrium in nature After adjusting the relevant parameter (for utility of online meetings, or for network evolution) we not solve for a new equilibrium of the whole coordination game between user i and her friends Instead we hold friends’ strategies (their state-conditional action distributions) fixed, at the levels estimated for the original equilibrium (which is that observed in the data), and just allow i to adjust her own best response Were we to solve for a new equilibrium (or, more likely, equilibria), it is certainly possible that the friends would raise their own login and messaging activity, creating feedback effects that lead to network sizes still larger than those seen below We use two metrics to compare the effectiveness of the two policies with that of the baseline policy – the status quo of MySpace First, we divide 52 weeks into four quarters and compute the average daily site traffic for each quarter Second, we compute average individual network size for each quarter The first metric is directly related to the benchmark that ranks the sizes of social network sites – number of unique users per month The second metric measures an aspect of members’ well-being, because social network sites are in part used to make new friends Table 11 shows average daily usage rates for the three policies – status quo, enhanced utility for real-time chat, and bigger network Not surprisingly the two counterfactuals both better than the status quo in daily site usage 19 Electronic copy available at: https://ssrn.com/abstract=1591102 after 52 weeks However the usage trends over time show some differences between the two counterfactual policies Whereas the two counterfactual policies have a similar effect on the usage rate upon adoption, the second has the higher rate of increase in site usage after one year One can observe a widening gap in site usage between the first and second policies over time Table 12 shows average network sizes under the two policies, with the counterfactuals naturally leading to larger networks than the status quo Note that the effect of the first policy on network sizes is purely indirect: enhanced utility in real-time chat with friends leads a member to spend more time online, which in turn causes them to make new friends The two counterfactual policies have markedly different effects on network size over time Whereas the average network size of the first policy is nearly identical to that of status quo over time, the second policy has about an 8% bigger network size than the status quo by the fourth quarter Conclusions This paper structurally estimates a dynamic model of usage behavior and network effects in social network sites using data from MySpace Our goal is to estimate the effects of site features – real-time chat and messaging – on the usage behavior of members and to provide managers with business policies that may enhance firm performance The framework could easily be extended to incorporate other site features as data on these become available We found that (1) there are distinct types of consumers as regards utility, cost, and state transition, but (2) features of MySpace positively affect site traffic across all segments Using the parameter estimates, we performed policy experiments to simulate the effects of two counterfactual policies – enhanced utility for real-time chat at any given network size, and increased propensity to expand one’s network The two policies yield distinct time paths of usage rates and network sizes In addition to studying other site features, future research might focus on linking the dynamics of login behavior to other current topics in social networks One such topic is the question of how consumers in social networks share information about products they have purchased To study this question rigorously it is important to know the fundamental incentives that drive social networking – the model presented here might be one ingredient in such an analysis Another current topic relates to the role of influential members 20 Electronic copy available at: https://ssrn.com/abstract=1591102 in social networks To the extent that such members think about their roles in a forward-looking manner, the model here might again contribute to a richer empirical understanding of the structure of social networks and how managers can best exploit these structures 21 Electronic copy available at: https://ssrn.com/abstract=1591102 Reference Ackerberg, Daniel A (2001), ‘A new use of importance sampling to reduce computational burden in simulation estimation’, mimeo, UCLA Aguirregabiria, Victor, & Pedro Mira (2007), ‘Sequential estimation of dynamic discrete games’, Econometrica, 75, 1, 1-53 Arcidiacono, Peter, & Robert A Miller (2008), ‘CCP estimation of dynamic discrete choice models with unobserved heterogeneity’, mimeo, Carnegie Mellon University Bajari, Patrick, Lanier Benkard, & Jonathan Levin (2007), ‘Estimating dynamic models of imperfect competition’, Econometrica, 75, 5, 1331-1370 Bao, Tony, 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state variables Variable Age Gender Country of residence Network size Last period’s action Weekend status Mean StdDev 21.108 0.500 0.505 1.365 0.595 0.491 120.522 38.677 0.535 0.499 0.308 0.462 Min 19 0 53 0 Max 23 1 200 1 Note: Weekend status is if weekend, otherwise 25 Electronic copy available at: https://ssrn.com/abstract=1591102 Table 3: Definitions of site usage, social interactions, and network evolution Variable Site usage Definition if used a social network site on a given day, otherwise Real-time chat Number of friends online Messaging Number of incoming messages Network evolution Gain/loss of friends between two consecutive days Table 4: Summary statistics on site usage, social interactions, and network evolution Variable Mean Site usage 0.527 Real-time chat 3.634 Messaging 0.257 Network evolution 0.042 StdDev 0.499 3.241 0.753 0.456 Min 0 −6 Max 27 11 Notes: N = 111 × 26 = 2886 individuals-periods The numbers for social interactions are observed values, not expected ones 26 Electronic copy available at: https://ssrn.com/abstract=1591102 Table 5: Network evolution after about weeks Network evolution −4 −3 −2 −1 10 11 12 13 18 Frequency 15 23 16 1 1 1 Percent 2.70 5.41 8.11 13.51 20.72 14.41 5.41 6.31 3.60 4.50 1.80 0.90 0.90 0.90 0.90 1.80 0.90 0.90 0.90 Cumulative percent 2.70 8.11 16.22 29.73 50.45 61.26 75.68 81.98 85.59 90.09 91.89 92.79 93.69 94.59 95.50 97.30 98.20 99.10 100.00 Notes: N = 111 individuals Mean = 1.39 Standard deviation = 3.708 Table 6: Poisson regression of real-time chat on state variables Dependent variable: Number of friends online RHS variable Estimate Std Error Network size 0.0101∗∗ 0.0003 ∗∗ Last period’s action 0.1404 0.0200 Weekend status −0.0547∗ 0.0214 ∗∗ Constant 0.4375 0.0263 Log-likelihood = −7179.5593 N = 111 × 26 = 2886 Notes: (∗∗) significant at 1% level (∗) significant at 5% level (‡) significant at 10% level 27 Electronic copy available at: https://ssrn.com/abstract=1591102 Table 7: Poisson regression of messaging on state variables Dependent variable: Number of incoming messages RHS variable Estimate Std Error Network size 0.0032∗∗ 0.0010 Last period’s action 0.9833∗∗ 0.0943 ‡ Weekend status −0.1509 0.0906 ∗∗ Constant −2.3716 0.1123 Log-likelihood = −1587.9333 N = 111 × 26 = 2886 Notes: (∗∗) significant at 1% level (∗) significant at 5% level (‡) significant at 10% level Table 8: Estimation results of per-period utility Dependent variable: Daily site usage Segment Segment RHS variable Estimate Std Error Estimate Std Error Real-time chat 0.1435∗ 0.0679 Same as in segment ∗ Messaging 1.5973 0.7696 2.2858∗ 0.9366 Weekend premium −0.1797 0.1250 Same as in segment Constant −2.1520∗∗ 0.2956 −0.1149 0.2783 Log-likelihood = −3003.22 N = 111 × 26 = 2886 Notes: (∗∗) significant at 1% level (∗) significant at 5% level (‡) significant at 10% level Real-time chat and messaging are expected values conditional on state variables 28 Electronic copy available at: https://ssrn.com/abstract=1591102 Table 9: Estimation results of network evolution Dependent variable: Daily change in network size RHS variable log(Network size/10) Last period’s action Weekend status Cutoff(1) for ait = Cutoff(2) for ait = Cutoff(3) for ait = Cutoff(4) for ait = Cutoff(1) for ait = Cutoff(2) for ait = Cutoff(3) for ait = Cutoff(4) for ait = Segment Estimate Std Error −0.1860 0.1489 −0.1026 0.2301 −0.1104 0.1785 −4.8183∗∗ 0.4635 −3.4196∗∗ 0.2909 2.6380∗∗ 0.2384 4.0696∗∗ 0.3093 ∗∗ −5.2188 0.3591 −3.0191∗∗ 0.1839 ∗∗ 2.3628 0.2032 ∗∗ 4.1057 0.2562 Segment Estimate Std Error 0.2098‡ 0.1160 −0.1978 0.1915 0.1995 0.1360 Same as in segment Notes: (∗∗) significant at 1% level (∗) significant at 5% level (‡) significant at 10% level Table 10: Estimation results of segment membership probabilities RHS variable Age Country of residence Gender Constant Segment Estimate Std Error 0.3693∗ 0.1587 −0.4371 0.4019 −0.2345 0.3802 ‡ −0.8894 0.4918 Segment Estimate Std Error Normalized to zero Notes: (∗∗) significant at 1% level (∗) significant at 5% level (‡) significant at 10% level Real-time chat and messaging are expected values conditional on state variables 29 Electronic copy available at: https://ssrn.com/abstract=1591102 Table 11: The effects of counterfactual policies on daily site usage Policy Qtr1 Qtr2 Qtr3 Qtr4 Status quo 50.19% 50.72% 51.23% 51.56% Enhanced utility for real-time chat 50.39% 50.85% 51.29% 51.68% Bigger network 50.32% 51.02% 51.74% 52.52% Notes The numbers in cells are the rates of daily site usage in percentage Each quarter consists of thirteen weeks Table 12: The effects of counterfactual policies on network size Policy Qtr1 Status quo 71.86 Enhanced utility for real-time chat 71.90 Bigger network 72.93 Qtr2 76.30 76.32 79.50 Qtr3 80.59 80.53 85.64 Qtr4 84.45 84.41 91.38 Note The numbers in cells are average network sizes in number of friends 30 Electronic copy available at: https://ssrn.com/abstract=1591102 ... evaluate counterfactual policies that are managerially relevant As their popularity grows among consumers, social network sites are attracting an increasing share of advertising expenditures... demonstrates that our model must account for idiosyncratic time paths of individuals’ social networks The central notion of our paper is that members can maintain and invest in social networks... copy available at: https://ssrn.com/abstract=1591102 Table 3: Definitions of site usage, social interactions, and network evolution Variable Site usage Definition if used a social network site