A Dyad Model of Calling Behavior with Tie Strength Dynamics #

Transcription

1 A Dyad Model of Calling Behavior with Tie Strength Dynamics # Mengze Shi 105 St. George Street Rotman School of Management University of Toronto Toronto, ON M5S 3E6, Canada Botao Yang Marshall School of Business University of Southern California 3660 Trousdale Parkway, ACC 306E Los Angeles, CA Jeongwen Chiang China Europe International Business School Shanghai, China October 2010 # We thank the NET Institute ( for financial support.

2 A Dyad Model of Calling Behavior with Tie Strength Dynamics Abstract In this study, we investigate the effect of social networks on wireless phone service consumption. We argue that, unlike other products and services, phone calls require two parties to jointly and simultaneously consume. As both parties pay the fees for communication, and as phone calls are a way of strengthening a relationship, the calling activity between two parties can be viewed as the optimal outcome of a cooperative decision. Using a large wireless telecommunication dataset, we estimate a dynamic model that encapsulates the evolving relationship between pairs of consumers. We find that the number of calls and the call duration between a pair of consumers are positively affected by the number of their common contacts. We also find that the reciprocity effect is prevalent in telecoms consumption. Calling is a two-way street the more one calls the other, the stronger the relationship becomes and, subsequently, the more the other will call back. We demonstrate the importance of accounting for these effects when assessing the returns on temporary call price cuts or the implications of new pricing schemes. Keywords: Social Network, Tie-strength, Reciprocity, Wireless Phone Service. 1

3 A Dyad Model of Calling Behavior with Tie Strength Dynamics 1. Introduction The cellular phone, once viewed as a gadget for the elite, has now become a ubiquitous communication device among the general public. A recent survey reports that nearly 5 billion people around the world use cellular phones, and among them 1.3 billion have signed long-term service contracts with their service providers (International Telecommunication Union, 2010). Although it is easier to buy better phones at affordable prices today, picking the right telecoms service plan remains a challenging task for most consumers. This is because there are many uncertain factors that a consumer cannot easily determine before signing a contract, including service quality, coverage range, future usage, and monthly expenses. Past research has examined how customers make decisions under these uncertain circumstances. For example, some studies have investigated consumer service usage under non-linear pricing schemes, whereas others have looked into service plan choice when future usage and service quality are both uncertain for customers (Lambrecht and Skiera 2006; Lambrecht, Seim, and Skiera 2007; Iyengar, Jedidi, and Kohli 2008; Huang 2008; Ascarza, Lambrecht, and Vilcassim 2009; Miravete 2003; Narayanan, Chintagunta, and Miravete 2007; Iyengar, Ansari, and Gupta 2007). None of these studies, however, take into account the unique aspect of telecommunications known as consumption externality. Unlike usual products and services, a phone call requires two parties to consume jointly and simultaneously. In other words, it takes two to tango. As it takes two parties to complete a call, how often one calls the other or how long a call lasts is not totally related to budgetary considerations. It also partly depends on the strength of the relationship between the two parties. As it is typical for telecoms service providers to charge 2

4 for both incoming and outgoing calls, they may try to entice customers to call more frequently or make longer calls. Intuitively, we know that calling more frequently or making longer calls should strengthen the social bond between two parties, which may in turn intensify their personal interaction and cause them to call each other more often. Hence, telecoms firms are likely to underestimate the effect of their marketing initiatives if their evaluation is limited only to the immediate change in consumption of targeted customers without taking into account this social network effect. To the best of our knowledge, no studies have examined the influence of social networks on telecoms consumption. This paper intends to fill that void. To that end, we have acquired a unique wireless telecoms panel dataset that contains detailed information on the numbers of callers and receivers, time of the call, duration of the call, outgoing call rate, incoming call rate, and the socio-demographics of all callers. We develop a conceptual model in which each pair of consumers works cooperatively to determine the number of calls and the duration of calls in each period. Following the social network literature, we consider the strength of a pair s social ties to be directional, asymmetric, dynamic, and reciprocal (as elaborated in the following section). We postulate that phone calls can enhance the strength of social ties, and that stronger ties mean more subsequent calls. We use the data to empirically test and validate our propositions. We show that the number of common social contacts shared by a pair of consumers is a good predictor of the strength of their social ties. Our results also validate the reciprocity effect, that is, that caller A s ties with caller B will strengthen with the duration of calls that A received from B in the previous period. We also find that the outgoing call rate matters more than the incoming call rate in determining the number of calls made. Based on our estimates, we further examine the managerial implications of price promotions through model simulation. First, we evaluate the effect of temporary price cuts on 3

5 outgoing and incoming calls, respectively. Second, we show how much revenue may be underestimated when the social network effect is not accounted for. Third, we show the implications for a variety of discriminatory pricing schemes. For example, we find that waiving incoming call fees completely can be beneficial to service providers in situations in which the incoming call fee plays an influential role in calling activities. This paper contributes to the emerging literature on applying social network concepts to marketing. Iacobucci (1996) and more recently Van den Bulte and Wuyts (2007) review the important relation between social networks and marketing. Recent research in marketing has examined other issues such as new product diffusion, commercial World Wide Web structure, and social commerce from a social network perspective (Van den Bulte and Joshi 2007; Katona and Sarvary 2008; Stephen and Toubia 2009). To the best of our knowledge, this is the first empirical study to focus on social network-level consumer usage behaviour and offer marketing implications. The remainder of the paper is organized as follows. The model is presented in Section 2 and the data and analyses are given in Section 3. We report the estimation results and related discussion in Section 4. The simulations and their marketing implications are shown in Section 5. A conclusion and future research directions are offered in Section Model In this section, we develop a dyad model of calling behavior with dynamic tie strength. We first explain how the tie strength of a pair of consumers is measured and how it evolves over time. We then model calling behavior, and specifically the way in which the number of calls and call duration depend on tie strength and other characteristics. 4

6 2.1 Tie Strength and its Dynamics In Granovetter s seminal work (1973), tie strength was defined as a combination of the amount of time, the emotional intensity, the intimacy (mutual confiding) and reciprocal services which characterize the tie. We view the tie strength between a pair of consumers as a state variable that reflects the closeness and intensity of the social relationship in all its dimensions. Although social ties are multi-dimensional in nature, in this paper we use a single-dimensional composite measure of social ties with four essential characteristics: directional, asymmetric, reciprocal, and dynamic. Consider a pair of individuals denoted by i and j, respectively. We use to represent the tie strength of individual j to i in period t, and to represent the opposite. Thus, tie strength is directional. Second, and have different values, and hence tie strength is also asymmetric. They are reciprocal because the current tie strength depends on past interactions, which we will define shortly. Lastly, they are dynamic because these values evolve over time. Specifically, we assume that takes the following form., (1) where is the number of common contacts shared by individuals i and j in period t-1, is the duration of calls from j to i in period t-1, is the duration of calls from i to j in period t-1, is the total duration of all i s outgoing calls in period t-1, is the total duration of all i s incoming calls in period t-1, means individual j is in i s contact list, and is the lagged tie strength in period t-1. 5

7 Equation (1) captures several important properties of social ties. First, we use the number of common contacts in both individuals personal networks as a proxy for the overlap of their social circles. This follows the same approach as Alba and Kadushin (1976), who use the number of common contacts to measure the extent of overlap between social circles, which is assumed to be a predictor of social closeness. In a more recent study on the dynamics of communications within a major university, Kossinets and Watts (2006) find that people are more likely to interact when they share acquaintances. This is also consistent with the transitive property of social networks whereby a tie between individuals A and B and a tie between individuals B and C can often lead to a stronger tie between individuals A and C due to multiple transitivity (Wasserman and Faust 1994). We thus postulate that tie strength is positively affected by the number of shared acquaintances (c 1 >0). Second, the reciprocal nature of social ties has been widely documented in studies of social exchanges (e.g., Blau 1965; Macaulay 1963; Granovetter 1973 and 1985). Montgomery (1996) formalizes the idea of reciprocity in social exchange theory and demonstrates the importance of the reciprocity effect in achieving trust-building equilibrium. In this study, we hypothesize that individual j, by initiating phone calls to individual i, creates goodwill and subsequently strengthens the social ties with i. Furthermore, this goodwill effect should be in proportion to the portion of j s calls to i relative to all calls received by i. In other words, the more j called i in the previous period, the greater the tie strength between i and j in the current period. 1 Note that we use the share of calls rather than the number of calls, because the social effect of an incoming phone call should depend on the relative amount of attention the receiver has paid to the caller. We thus postulate a positive reciprocity effect (c 2 >0). 1 Alternatively, we could measure reciprocity as the proportion of j s calls to i in the previous period. However, this measure may suffer from an imperfect information problem, because caller i typically does not observe the total number of calls made by caller j. In equation (1), we thus use only the measures observable to caller i. 6

8 We also expect caller i to update tie strength based on the intensity of communications initiated by him or her to caller j in the most recent period, which is measured by. We hypothesize that c 3 >0. Finally, tie strength is expected to persist over time (e.g., Wellman, Wong, Tindall, and Nazer 1997; Blumstein and Kollock 1988), and thus we expect that r 1 >0. Our tie strength construct shares some resemblance with the brand loyalty construct in brand choice studies (e.g., Guadagni and Little 1983). Both constructs are associated with past purchase (in this case calling) behavior and are updated by more recent activity. However, unlike the brand loyalty measure, which depends solely on the consumer s own past brand choices, social tie strength depends on network characteristics, or the number of overlapping contacts shared by two people. Second, brand loyalty goes only one-way consumer to brand whereas social ties are a two-way measure individual i to j and vice versa which allows for asymmetric strength. Third, social tie strength is interactive, in that each side takes stock of the other side s calling initiatives and reciprocates in subsequent periods. We next propose a cooperative framework for deriving consumers calling behavior as a utility-maximizing outcome Number of Calls and Call Duration: A Cooperative Game Framework We investigate two key variables: number of calls and total call duration. We use to denote the number of calls that individual i made to individual j in period t, and to denote the total duration of these calls (in the estimation, we rescale to the logarithm of the total calling seconds from i to j in period t.) We adopt the quasi-linear utility framework in Shi (2003) and 7

9 assume the following quadratic utility function for individual i to initiate number of calls to individual j. subject to the budget constraint = ( ) (2.1) = +, (2.2) where y it denotes the total budget for i, the price of outside good q io,t is normalized to one, X i represents individual i s vector of characteristics, and is the unit variable price individual i pays for outgoing calls. Following Lambrecht, Seim, and Skiera (2007), we assume that = +, where is a pair-specific usage shock that caller i experienced before making the usage decision. However, note that this usage shock is unobservable to researchers. Similarly, we then assume that the utility that individual j derives from receiving number of calls from i is as follows. subject to the budget constraint = ( + β 1 + β 2 - β 3 + (3.1) = +, (3.2) 2 where y jt denotes the budget constraint, the price of outside good q jo,t is normalized to one, X j represents individual j s vector of characteristics, and is the unit variable price that individual j pays for incoming calls. We assume that = +, where is a pair-specific usage shock that caller j experienced before making the usage decision. Again, this usage shock is unobservable to researchers. 2 In both budget constraints (2.2) and (3.2), the fixed fees in the service contracts are not included explicitly, because when making quantity decisions they are already deducted from the budget y it for caller i and y jt for caller j. 8

10 Equations (2.1) and (3.1) reflect that the value for an individual of initiating and receiving calls depends on the strength of ties between callers and also on the callers characteristics. The decreasing marginal utility implied by the quadratic function is due to the opportunity cost of time spent on communication (Mitchell 1978). We assume that the equilibrium communication amount is determined by the two individuals in a cooperative fashion. 3 Specifically, we follow the cooperative game framework and determine the equilibrium amount of by maximizing + (1- ) given the caller s and recipient s budget constraints in (2.2) and (3.2), respectively. Note that 1 0 serves to capture the power of negotiation between the two individuals. We adopt this cooperative framework to reflect the fact that calling decisions are determined by both callers jointly: whereas caller i decides whether or not to initiate a call, caller j holds the option of not taking the call. The availability of caller ID service provides the receiver with perfect information on the caller. Once both sides are connected, the length of the call should also depend on both callers, as each can terminate the call unilaterally. Thus, both callers utilities must be considered jointly in the model. Our model nests the case where λ=1, which is the standard utility-maximizing model for caller i alone. The empirical estimate of λ is used to test the joint decision-making hypothesis. 4 After substituting the binding budget constraints (2.2) and (3.2), respectively, into the utility functions (2.1) and (3.1), we take the first-order condition of + (1- ) with respect to and obtain 3 Jeon, Laffont, and Tirole (2004) adopt a non-cooperative framework in which both individuals behave purely according to their own self-interest. In their model, each individual chooses an amount that maximizes his or her own utility. The equilibrium is the minimum of the two callers optimal volumes. 4 Note that each of the two callers in our cooperative framework can still act in their own best interests. We do not explicitly model how these two callers reach the equilibrium number of calls. This is similar to Nash bargaining models that provide the equilibrium bargaining outcomes but omit the bargaining process. 9

11 = , (4) where a 0 = and = 2 [ 3 + (1- ) 3 ]. By parameter transformation and allowing, we can obtain the econometric specification for the number of calls. (5) Note that the relative sizes of coefficients a 2 and a 3 in equation (5) reflect the caller and the receiver s power in determining the equilibrium amount of communication. Next, by replacing with, we can derive the econometric specification for the call duration within the same cooperative framework.. (6) Equations (5) and (6) postulate that, first, the amount of communication increases with the social tie strength ( ). The amount of communication with j that is initiated by consumer i should increase with the tie strength between consumer j and consumer i. As elaborated earlier, if a higher proportion of all i s incoming calls came from j in the previous period, then the tie strength between j and i will be stronger in the current period. This will in turn increase the number of calls that i makes to j in the current period, thus enhancing i s tie strength with j in the following period, which means that j will make more calls to i in the next period, and so on. Mathematically, a larger a stronger a larger a stronger a larger. This is how the reciprocity effect of calling occurs through the dynamic properties of tie strength. 10

12 Equations (5) and (6) also indicate that the amount of communication depends on both the outgoing calling price ( ) and the incoming calling price ( ). Whereas the (expected) negative effect of i s outgoing price on the amount of communications is standard, the effect of receiver j s incoming price on the calling amount is unique to two-sided communication services. The receiver is more likely to disconnect the phone or terminate the call sooner when the incoming call price is higher. Finally, the amount of communication may also depend on sociodemographic variables. In summary, we construct a cooperative model in which two consumers collectively maximize their joint utility through phone communication. In the context of telecommunications, we provide an estimable model that explicitly takes into account both social networks and economic factors in determining the number and duration of calls. For completeness, we assume the following mean-variance structure to the error terms, as both variables are interrelated.. (7) Later, in section 4.4, we extend the model by allowing within-dyad correlations. 3. Data and Empirical Strategy Our data was collected from a large Chinese metropolitan market with the collaboration of a major cellular phone service operator. The data consists of 12 months of call records (May 2003 to April 2004) of approximately 38,000 VIP customers the entire membership list of the service provider s VIP club. From this original customer-level data, we examined all of the call records and identified 5,140 distinctive pairs formed by 6,290 distinctive customers. We selected 11

13 the pairs to ensure that there were at least two phone exchanges between paired customers and the communication history between the pair was at least eight months long. We discuss this limitation and potential selection bias in the conclusion. For the pairs identified, we aggregated the original data to form a composite monthly dataset. As all of the callers were located in the same city, our analysis focuses on local calls only. In total, the dataset contains 61,680 (5,140*12) pair-level observations. For practical purposes, we use the first two months of data to construct the lagged variables of tie strength. Hence, the data eventually used for the estimation covers 10 months of activity from July 2003 to April 2004, with 102,800 (5,140*2*10) individual-level observations. The descriptive statistics are presented in Table 1. Our data contains three caller characteristic variables: age, gender, and VIP status. The ages of the callers range from 19 to 93, 25% are female, and 65% are Silver members. There are four status levels: Diamond, Gold, Silver, and Value. So Vip i is a 3-by-1 vector that indicates individual i s VIP status. Specifically, if i is a Gold customer, then Vip i = (1, 0, 0), and if i is a Value customer, then Vip i = (0, 0, 0). On average, each pair shared 16.6 common contacts in the sample. On a monthly basis, each individual initiated an average of 12.0 calls with a total duration of 12.3 minutes each. At the time a typical price plan consists of a small monthly fee and a variable fee, possibly with some free minutes (it is more like a two-part tariff than a three-part tariff). For instance, one of the plans charged a fixed fee of RMB (Chinese Yuan) per month and 0.20 RMB for each minute of usage (the exchange rate was about 8.28 RMB to 1 USD during the data period). As our sample consists of subscribers to the same service provider, all of the calls occurred within the same wireless network. The average calling price per minute was slightly 12

14 less than 0.20 RMB, which was equivalent to USD at that time. There are two main sources of price variation. First, different consumers can subscribe to different plans. A plan with a higher fixed fee typically corresponds to a lower variable fee. 5 We note that very few consumers changed their price plan during the observation period. Second, the service provider can provide various forms of discounts. For example, the service provider in question designed different types of price plans and sometimes offered discounts to callers who chose the same type of plan. Some consumers received promotional discounts, such as a 20% discount on the variable fees for being a loyal customer for more than three years. The price variables in our estimation are the net price after deducting any promotional discounts. We jointly estimated equations (1), (5), (6), and (7) using the standard maximum likelihood method to derive the following likelihood function., (8) where for and, the probability is. For zero observations ( and ), as in a Tobit model, we use the cumulative normal distribution function. When the number of calls is zero, the duration of calls is necessarily also zero. Thus, the probability can be simplified from a bivariate normal CDF to a univariate normal CDF. 5 There may be an endogeneity problem here, as heavy users may choose plans with high fixed fees and low variable fees. As we do not model consumer tariff choice, we may mistakenly attribute high call volumes to low variable fees. We discuss this issue further in the section on robustness checks. 13

15 The log likelihood function can then be written as Finally, c 1, c 2, r 1 in equation (1) cannot be separately identified from a 1 in equation (5) or b 1 in equation (6). Hence, we tried nine specifications with r 1 =0.1, 0.2, The specification with r 1 =0.3 gave the best model fit, and we thus normalize r 1 to 0.3, which then forms an implicit condition in the results reported in the following section. 4. Estimation Results In Table 2, we present the estimation results for equation (1) regarding the dynamics of tie strength. Tables 3 and 4 present the results of equations (5) and (6), respectively, regarding the number of calls and call duration. Overall, the results are strongly consistent with our hypotheses. Note that we obtain our results after controlling for the correlation between two unobserved error terms in equations (5) and (6), that is, = Tie Strength Dynamics Table 2 shows the estimated results for the dynamics of tie strength. The estimate for c 1 is positive and statistically significant, indicating that the number of overlapping contacts serves as a good predictor of tie strength. This result supports the transitivity theory that the greater the number of common contacts that two individuals share, the better they tend to know each other, the closer their relationship tends to be, and the stronger their social ties with each other. 14

16 Second, the estimate for c 2 is also positive and statistically significant, indicating that our results confirm the reciprocity effect. All other things being equal, if caller A initiates more calls to caller B in a particular month, then caller B s tie strength with caller A will increase in the following month, thereby increasing caller B s marginal utility of calling A. As a result, in the next month caller B will make more calls to caller A, possibly both in frequency and duration. This will in turn increase the strength of A s ties with B in the subsequent month, which will lead to more calls from A to B, and so on. The prediction in the opposite direction of the dynamic reciprocity effect is that, all other things being equal, if A reduces the number of calls to B in the current period, then B will make fewer phone calls to A in the next period. If A does not initiate additional phone calls to B, then their relationship will be weakened in the long run. 4.2 Number of Calls Table 3 presents the results for the dependence of the number of calls on tie strength, price, and the callers characteristics. First, the estimates for and are positive and statistically significant, indicating that people in the sample made more phone calls to individuals with whom they had stronger ties. Although a large part of the population has access to telecommunication services, each individual consumer s usage is concentrated within a limited section of the consumer s social circle. This concept is similar to the 80/20 rule: our results show that people make most of their phone calls ( 80% ) to a very small proportion ( 20% ) of their contacts. Second, the estimates for both a 2 and a 3 are negative and statistically significant. Thus, both the incoming and outgoing call rates matter in determining the number of calls from caller A to caller B. We also find that the absolute value of the estimate for a 2 is much larger than that 15

17 for a 3, with a 2 /a 3 =3.04. This implies that the outgoing price has a stronger influence than the incoming price on the number of calls. In relation to the cooperative utility framework described earlier, these results imply that both the initiating and the receiving caller s communication values are weighted positively when determining the number of calls. However, a higher weight is assigned to the initiating caller s value of communications. One of the implications of this is that the calling behavior of a pair of consumers is asymmetric. For example, suppose that caller A s service plan has a higher outgoing call price than caller B s plan. All other things being equal, caller B should initiate more calls to A than A to B. As a result, B will have a higher outgoing/incoming call ratio than A. Although the negative effect of price on the number of calls has been well documented, the literature has not distinguished the effects of outgoing and incoming call prices. To the best of our knowledge, ours is the first study to empirically demonstrate the differential effects of outgoing and incoming prices on the number of calls. Third, the number of calls depends on the callers characteristics. The results show that older customers made more calls but did not receive more calls. This implies that the outgoing/incoming call ratio is higher for older callers. The results also show that, on average, female customers received 0.44 more calls than male customers in each month. However, the effect of gender on the number of outgoing calls was not significant. Finally, higher VIP-status customers generally made more calls. On average, gold, silver, and diamond customers made 2.89, 2.57, and 2.16 more phone calls every month, respectively, than value class customers. 4.3 Call Duration The results for the duration of calls are very similar to the results for the number of calls. First, the estimates for and are positive and statistically significant, indicating that people in the 16

18 sample spent more minutes calling the individuals with whom they had strong ties. Second, the estimates for both b 2 and b 3 are negative and statistically significant, indicating that the total call duration was lower when the initiating caller s outgoing price was higher or the receiving caller s incoming call price was higher. Interestingly, the magnitudes of b 2 and b 3 are similar. Third, again similar to the results for the number of calls, older customers made longer calls but received shorter calls. Thus, the ratio of outgoing to incoming call minutes was higher among older customers than younger customers, and an asymmetrically large flow of phone calls was initiated by older callers. Gender is another personal characteristic that affected the amount of call time, with more calling minutes both made and received by female customers, all other things being equal. Overall, female customers spent more time talking on the phone. Finally, customers with a higher VIP status generally made longer calls. 4.4 Robustness Checks Heterogeneity: Making the intercepts in equations (5) and (6) random coefficients Different consumers may have different rates of diminishing returns from the number or duration of calls. To accommodate this unobserved heterogeneity, we allowed the intercepts in equations (5) and (6) to be normally distributed random coefficients 6, as follows.,. We then re-estimated the model with the random coefficients specification. As reported in Tables A1-A3 in the appendix, the earlier results remain quite robust. 6 To keep the model parsimonious, we only allow the intercepts to be random coefficients. This is sufficient to guarantee that different consumers have different rates of diminishing returns. 17

19 4.4.2 Dyad dependence: Allowing,,,and in equations (5) and (6) to be correlated In equation (7), we only allow and (similarly, and ) to be correlated. That is, we allow the unobserved factor in the number of calls from i to j and the unobserved factor in the duration of calls from i to j to be correlated. To account for possible within-dyad dependence, we further specify a more flexible error term structure.,. (7 ) The estimation becomes more difficult with the new error term structure, because the main model is now a multivariate Tobit model. Depending on whether >0 and >0, our likelihood function takes one of four forms. 1. >0, >0 This is the simplest case. We can use the PDF of a multivariate normal distribution to define the likelihood. 2. >0, =0. 18

20 The likelihood can be defined sequentially as the probability of observing >0 times the probability of observing =0 conditional on >0., where,,. 3. =0, >0 Case 3 is similar to case 2. We omit the equations to avoid repetition. 4. =0, =0, 19

21 where The probability is given by a bivariate normal CDF, which cannot be directly obtained. We thus simulate bivariate normal distributions using the GHK simulator to calculate the probability for this case. We jointly estimate equations (1), (5), (6), and (7 ). The results are reported in Tables A4-A6 in the appendix. Qualitatively, the results are largely similar. We do find any significant and positive correlations between the unobserved factors within a dyad (all of the s are significant and positive) Adding individual-level fixed effects to the duration of calls regression It is likely that heavy users may choose a plan that has a high fixed fee but low variable fees to save money. This is a typical self-selection or endogeneity problem that we must address or mitigate in the estimation, otherwise we might mistakenly attribute a high calling volume to low variable fees when, in fact, the negative correlation between price and calling volume may be simply an outcome of tariff plan choice. To address this issue, we estimate two fixed-effects models, one with the caller as the panel variable and the other with receiver as the panel variable. 7 By eliminating unobserved individual heterogeneity (including the cross-sectional variation in price plan selection), we can test, conditional on the price plan chosen, whether consumers are indeed sensitive to price changes. The results are reported in Tables A7-A8 in the appendix. After adding a fixed effect to the caller, both the outgoing and the incoming call price coefficients remain statistically 7 Here, we do not add fixed effects at the pair level because the price plan is chosen by individuals after considering their social contacts, and is thus not a dyad-level decision. 20

22 significant and negative. These results indicate that the caller is indeed responsive to the outgoing call price, and also cares about the receiver s incoming call price. Similarly, after adding a fixed effect to the receiver, both the incoming call and outgoing call price coefficients remain statistically significant and negative. These results imply that the receiver is not only sensitive to the incoming call price, but also cares about the caller s outgoing call price. These combined results support the notion that calling is a joint decision made by both parties. The fixed-effect models also confirm that consumers are responsive to price changes the negative relationship is not simply driven by endogenous tariff choice Caller identity: Adding dummies for individuals who appeared in multiple pairs Among the 6,290 distinctive consumers in our data (5,140 dyads), 2,208 consumers appeared in more than one dyad, either as a caller or as a receiver. If the same consumer is included in multiple pairs, then there might be cross-dyad dependence. To check whether our results are robust to such cross-dyad dependence, we estimate two reduced-form specifications with respect to the number of calls. In the first specification, we modify equation (5) by replacing tie strength with the number of common contacts and estimate the following single equation.. In the second specification, we add 2,208 dummies to this equation for the 2,208 consumers who appeared in multiple dyads. We also estimate two similar specifications with respect to the duration of calls,. 21

23 The results are reported in Table A9. With 2,208 dummies, it is conceivable that the coefficient estimates would change, but the qualitative properties of the results still hold. We did not add 2,208 dummies to our main empirical specification for the following three reasons. First, is not directly observed, so we cannot add the dummies to equation (1). Second, our model is a simultaneous equation model estimated by maximum likelihood. Even if we add dummies only to equations (5) and (6), we will have more than 4,416 (2,208*2) parameters. Technically, it is very difficult to get accurate estimates of such a huge number of parameters via maximum likelihood. Third, our main empirical specification is derived from a cooperative utility framework. The model coefficients have clear economic meanings and we need them to calculate firm revenues and conduct counter-factual experiments. Adding these dummies would make it difficult to interpret the economic meanings of our model coefficients Reduced-form model: Estimating alternative reduced-form models and comparing the model fit To test whether modeling dynamic tie strength improves the fit, we estimate three reduced-form specifications and compare the model fit. Typical benchmark models are models with similar specifications but without the theoretical structure. For example, dynamic choice models are often compared with choice models with similar specifications but without consumer foresight (e.g., Erdem and Keane 1996, Gonul and Shi 1998). Similarly, in a study of umbrella branding, Erdem (1998) uses a benchmark model without a cross-category quality association. Most of these studies compare the model fit using the log-likelihood (LL), AIC, and BIC criteria. 22

24 Following this tradition, we specify three sets of reduced-form models and summarize the results in Table A10-A12. In the first set of reduced-form regressions, we directly estimate equations (5) and (6) without adding tie strengths. The results are presented in Table A10. In the second set of reduced-form regressions, we use the number of common contacts to replace tie strengths and then estimate equations (5) and (6) as follows.. The results are presented in Table A11. In the third set of reduced-form regressions, we also add and to equations (5) and (6). The results for this model are presented in Table A12. We then compare the model fit between the three models and our main specification, as characterized by equations (1), (5), (6), and (7). Both the AIC and BIC suggest that our main specification performs better than the three reduced-form models. 23

25 Table A10 Table A11 Table A12 Table 3 -LL 537, , , ,765.7 AIC 1,074,207 1,064,238 1,038,993 1,029,603 BIC 1,074,294 1,064,332 1,039,099 1,029, Marketing Implications As mentioned, an important and unique feature of telecommunication is consumption externality. This makes any marketing initiatives to generate sales more complex. For example, a price discount on, say, laundry detergents would be likely to generate purchase accelerations in the target households. However, a price discount on cellular phone services affects not only the target customers (those making more calls) but also their social contacts. This possibly results in an additional source of revenue from incoming calls, because their contacts need to pay for the calls too. More importantly, phone interactions strengthen social ties, resulting in more calls in the future and thus more revenue for the service provider. Clearly, in the telecoms business, any initiatives to stimulate the market will have a significant and longlasting impact because of these ripple effects. In what follows, we use the numbers to demonstrate these effects. Before we start, it is important to note that as Equations (5) and (6) are the maximization outcomes of a joint utility model, the parameters estimated are transformed micro-parameters. This structural characteristic of the model allows us to conduct counterfactual experiments through a customer optimization process to assess the effects of marketing initiatives. 5.1 Evaluating the Return on a Temporary Price Promotion: Outgoing and Incoming Calls 24

26 To demonstrate how much revenue would be overlooked if service providers focus only on outgoing calls, we conduct the following counterfactual experiments based on the estimation results given in Tables 2-4. Consider a scenario of a one-time price promotion on outgoing calls in month three applied to all of our panel consumers. We first compute the revenue change for months three to twelve, but only from additional outgoing calls. We then compute the revenue change from additional outgoing and incoming calls. The difference is the overlooked revenue, if we treat additional telecoms consumption as if it were detergent. In Table 5, we provide the detailed results on different price promotion scenarios. For example, with a 90% discount on both the outgoing call price and incoming call price, we would miss 1.94% of the total revenue from increased incoming calls if we were to focus on outgoing calls only. Similarly, we estimate how much revenue would be overlooked if we were to focus solely on incoming calls (as the service provider can choose to promote either or both outgoing and incoming calls). We provide the detailed results in Table 6 for different levels of promotion. For example, for a 90% discount on both the incoming call price and the outgoing call price, we would miss 2.2% of the total revenue from increased outgoing calls if we were to ignore the revenue from outgoing calls. These counterfactual exercises show that the returns on price promotions can be underestimated if the externality effect is not taken into account. Given the size of cellular phone service subscriptions today, this may result in a huge miscalculation of marketing return on investment. 5.2 Evaluating the Long-Term Return on a Temporary Price Promotion: the Reciprocity Effect 25

27 The second-order effect comes from reciprocity, as described in Equation (1). Specifically, for a pair of individuals i and j, if the service provider runs a price promotion in period t-1 on j s outgoing call price or i s incoming call price, then j will call i more (as reflected by larger and ) in. Then, larger stronger larger stronger larger Again, to demonstrate the implications of this reciprocity effect, we consider a one-time price promotion offered in month three. Following the same logic and computational steps as before, we compute the promotional outcomes both with and without reciprocity, and then calculate the difference. The results are shown in Table 7. In contrast to the previous cases, the total revenue would be even further underestimated if we were to ignore the dynamic reciprocity effect. For example, for a 90% discount on both the outgoing and incoming call price, the promotional effect on the total revenue for months four to twelve would be underestimated by 5.98% if the reciprocity effect were to be ignored. The reciprocity effect highlights a new source of long-term effects of price promotions. In the packaged goods market, a price promotion may have long-term effects on sales through repeat purchases. Such long-term effects are typically driven by changes in consumer brand awareness, and by loyalty and switching costs (e.g., Blattberg, Briesch, and Fox 1995). In contrast, in the mobile telecoms market, what changes with the reciprocity effect is consumers relationship with their social contacts, rather than their relationship with the brand. The longterm sales effects resulting from the reciprocity factor are realized through consumption externality and the dynamic aspect of reciprocity. 5.3 Optimal two-sided Pay Scheme: Incoming Call and Outgoing Call Prices 26

28 Our model has useful implications for the optimal design of pay schemes with differential prices for incoming and outgoing calls. Incoming calls are typically free for fixed-line services but are often charged in the cellular phone service industry in many parts of the world. Analytical research has been conducted to study the welfare implications of the receiver-pay principle (e.g., Jeon, Laffont, and Tirole 2004). To illustrate the implications of our model for the design of pricing plans, we conduct two simulation exercises. First, we search for the optimal third-period prices that maximize the service provider s revenue from the sample consumers. Second, we search for a revenue-neutral solution under a free incoming calls scenario. For the former, we consider a set of price deviations from the actual outgoing call and incoming call prices in the third month. Based on the results in Tables 2 to 4, we simulate the effects of these price changes on the total revenue from the entire sample in months three to twelve. Figure 1 displays the predicted total revenue as a function of the outgoing call price change and incoming call price change. The revenue-maximizing prices are positive and higher than the actual prices for both incoming and outgoing calls. There are two possible explanations for this. First, our model does not consider the competition between service providers. Second, our sample consists of only VIP customers, who are not very price sensitive. The optimal prices might well be lower if the dataset contained more low-volume customers, who tend to be more price sensitive. For the latter, to find situations in which a service provider might provide free incoming calls, we increase the coefficients of the outgoing call price ( and ) by 200% and the coefficients of the incoming call price ( and ) by 500%. As illustrated in Figure 2, the shape of the revenue function becomes quite different from that in Figure 1. The optimal pricing strategy to maximize revenue from months three to twelve is now to increase the outgoing call 27

29 price by % while giving customers free incoming calls. Interestingly, as the receiver s incoming call price becomes sufficiently important in determining the number of calls, the no receiver-pay principle may become optimal. When consumers really care about the receiving caller s costs, then giving consumers free incoming calls could cause them to call each other more often, which would bring higher revenues. 6. Conclusion This paper investigates consumers cellular phone calling behavior from the social network perspective. We propose an economic framework in which two consumers decide their calling activity collaboratively to maximize their joint communication utility. We concentrate on the number and duration of calls between a pair of consumers with dynamic social tie strength. We derive the demand equations based on the optimization principle. Using a unique telecoms panel dataset, we test and validate our propositions. Our empirical results show that, first, tie strength increases with the number of common contacts. Second, people initiate more calls and spend more time talking to the individuals with whom they have strong ties. Third, the reciprocity effect is strong in the telecoms market. In terms of marketing implications, we find that outgoing call prices have a much stronger influence on the number of calls than incoming call prices. Thus, the initiating caller s value function weighs more than the receiving caller s value function in determining the number of calls. Using simulations to evaluate the effects of temporal price promotions and a calling plan with free incoming calls, we find that failing to account for the social network effect could results in the underestimation of both the short-term and long-term returns on a price promotion. We also find that when the receiving consumer s communications value enjoys a greater weight 28

30 in determining the calling activity, service providers may find it optimal to offer free incoming calls. Despite its merits, our paper is subject to the sample selection issue. That is, the sample that we used for the estimation may be biased, because we did not include unrealized ties, or ties where communication could have potentially occurred but did not. There are reasons why we did not correct this selection bias. First, our network has 38,000 nodes, and thus 1,444/2 million pairs of customers. It is technically beyond our capability to deal with such a large sample. Second, although it is theoretically possible that any two consumers can be connected, in reality each consumer communicates with only a very small subset of this potentially large set (the whole society, if cellular phone penetration is 100%). We are confident in asserting that the ties between most of those 1,442/2 million pairs would never be realized. Third, previous research shows that only focusing on realized ties does not substantially reduce the statistical power (e.g., Coslett, 1981; Imbens, 1992; Sorenson and Stuart, 2008). Fourth, the main focus of our paper is to show that it is important to incorporate social network characteristics in the study of telecommunications markets. We do not intend to generalize our quantitative results beyond their original illustrative purposes. To some extent, one could view our study as focusing on heavy users only. However, this is important, because most firms earn their revenues primarily from heavy users, which in the telecoms industry means pairs of individuals that engage in frequent conversations. Any social network-based marketing schemes would only target pairs with strong ties anyway. Our paper is the first empirical attempt to examine wireless telecoms consumption from the social network perspective. Future research could extend the framework from the dyad level to multiple-player networks. This extension would generate additional insights into network 29

31 dynamics and their implications. Another direction of future research would be to study the relations among all ties. This extension would give us a better understanding of, for example, how consumers use different means of communication to contact different people within their social circle. 30

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