When Talk is Free : The Effect of Tariff Structure on Usage under Two- and Three-Part Tariffs

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1 0 When Talk s Free : The Effect of Tarff Structure on Usage under Two- and Three-Part Tarffs Eva Ascarza Ana Lambrecht Naufel Vlcassm July 2012 (Forthcomng at Journal of Marketng Research) Eva Ascarza s Assstant Professor of Marketng at Columba Unversty (emal: [email protected]). Ana Lambrecht s Assstant Professor n Marketng at London Busness School (emal: [email protected]). Naufel Vlcassm s Professor of Marketng at London Busness School (emal: [email protected]). The authors thank the London Busness School Centre for Marketng for fnancal support. They would lke to thank Raesh Chandy, Bruce Harde, Kamel Jedd, Carl Mela, Oded Netzer, Catarna Ssmero, Gonca Soysal, partcpants at the UTD FORMS, the 2009 Marketng Scence Conference, the 8 th Trennal Invtatonal Choce Symposum, the 2011 Four School Colloquum, The Psychology and Economcs of Scarce Attenton conference, and at semnars at INSEAD, Erasmus Unversty, HKUST, Northwestern Unversty, and Unversty of Rochester for ther helpful comments.

2 When Talk s Free : The Effect of Tarff Structure on Usage under Two- and Three-Part Tarffs 1 Abstract In many servce ndustres, frms ntroduce three-part tarffs to replace or complement exstng two-part tarffs. As opposed to two-part tarffs, three-part tarffs offer allowances, or free unts of the servce. Behavoral research suggests that the attrbutes of a prcng plan may affect behavor beyond ther drect cost mplcatons. There s evdence that customers value free unts above and beyond what would be expected based on the change to ther budget constrant. Nonlnear prcng research, however, has not consdered such an effect. The authors consder a market where three-part tarffs were ntroduced for the frst tme. They analyze tarff choce and usage behavor for customers who swtch from two-part to three-part tarffs. Ths study fnds that swtchers sgnfcantly over-use compared to ther pror two-part tarff usage. They attan a level of consumpton that cannot be explaned by a shft n the budget constrant. The authors estmate a dscrete-contnuous model of tarff choce and usage that accounts for the valuaton of free unts. Results show that 83.9% of three-part tarff users value mnutes on a three-part tarff more than they would on a two-part tarff. The authors derve recommendatons for how the provder can explot these nsghts to further ncrease revenues. Keywords: Prcng, Nonlnear Prcng, Dscrete / Contnuous Choce Model, Three-Part Tarffs, Uncertanty, Learnng, Free products.

3 2 Frms n varous sectors are complementng or replacng ther two-part tarffs wth three-part tarffs. For example, telecom provders offer plans wth free mnutes nstead of chargng for every mnute and banks offer a set number of free check-wrtng prvleges nstead of bllng per check. Two-part tarff customers pay a regular, often monthly, access prce and a usage prce for every unt of consumpton, whereas under a three-part tarff a usage prce apples only to consumpton n excess of the usage allowance. Wthn the allowance there s no usage charge; usage s free. Recent evdence llustrates that consumers generally respond to free products or servces dfferently from how they respond to the same good f the frm charged for t. Specfcally, when evaluatng free products or servces, consumers do not smply subtract costs from benefts but nstead perceve the benefts assocated wth free products as beng hgher than they would otherwse. Ths leads to ncreased demand (Shampaner, Mazar, and Arely 2007), whch has mportant mplcatons for frms. For example, when AOL replaced ther pay-per-use plans for dal-up nternet access wth flat-rate plans, demand at a zero usage prce was far greater than AOL had forecasted based on the ncome effect of the prce change alone (Cnet.com 1996; Messay 1998). 1 Behavoral research suggests that ths ncreased demand can be attrbuted to a postve affectve response to the offer of a zero usage prce a free component of the tarff. Ths affectve response ncreases usage above and beyond what would be predcted based on the change of the budget constrant alone (Shampaner, Mazar, and Arely 2007). Importantly, research demonstrates that ths postve affectve response may lkewse ncrease the valuaton of other, even unrelated products. For example, Isen et al. (1978) show that ndvduals who obtan a small free gft (notepad or nal clpper) subsequently evaluate the performance of unrelated products (ther own car and TV) as sgnfcantly hgher than ndvduals 1 As a result, AOL had to manage sgnfcant congeston and dssatsfed customers.

4 3 who do not obtan a free gft. Smlarly, feld data show that coupons can ncrease purchases beyond the expected ncome effect for other products than the coupon was ssued for (Helman, Nakamoto, and Rao 2002). 2 These nsghts go aganst standard economc theory that assumes that a change to a prce would affect demand only through a change n the budget constrant. In ths research we examne how consumer demand changes when consumers swtch from a two-part to a three-part tarff. We buld on Shampaner, Mazar, and Arely (2007) and argue that the free component of a three-part tarff leads to a postve affectve response. Ths postve affectve response ncreases the valuaton of the servce as such. Buldng on research that llustrates persstence of demand effects from postve affect across products, we argue that the postve affectve response to a tarff wth free unts perssts even after consumers have exceeded ther usage allowance. As a result, we propose that when consumers swtch from two-part to three-part tarffs, demand should ncrease beyond what would be predcted based on the change n the budget constrant alone. Ths demand effect should hold even for usage beyond the allowance. We use data on tarff choce and usage of customers of a moble phone company. An mportant feature of our data s the ntroducton of three-part tarffs n addton to the exstng two-part tarffs durng our observaton perod. Ths allows us to observe the same set of customers under two dfferent prcng regmes: frst, when only two-part tarffs were avalable, and then when customers were free to swtch to three-part tarffs. In ths market, the three-part tarffs were largely desgned to ncrease customer acquston. Thus, ther addton to the choce set for exstng customers s close to a natural experment. 2 The authors attrbute ths to elevated mood and addtonally propose that a psychologcal ncome effect from recevng an unexpected coupon could lead consumers to spendng more than the wndfall gan from the coupon. They do not test whch of the two explanatons s more relevant. Golden and Zmmer (1986), Sherman and Smth (1987) and Donovan et al. (1994) provde further evdence that postve affect ncreases product demand, even for products that dd not drectly stmulate the postve affect.

5 4 An ntal exploraton of the data shows that customers who swtched to a three-part tarff sgnfcantly over-use after swtchng: ther level of consumpton cannot easly be explaned by the change to the budget constrant only, or by other plausble alternatve explanatons. To dsentangle the effect of free mnutes on customers valuaton of the servce from the change n the budget constrant that arses from the new prcng structure, and from preferences at tarff choce, we ontly estmate each customer s tarff choce and usage decson condtonal on the chosen tarff. In the utlty functon, we explctly allow for greater demand on three-part tarffs. Snce three-part tarffs are new to ths market, customers are lkely to be ntally unaware that free mnutes mght affect ther demand beyond the budget constrant. Hence, we allow for the possblty that customers learn about ther three-part tarff usage whch means that they learn about ther valuaton of free mnutes. Our results ndcate that on three-part tarffs, 83.9% of customers use more than expected based on ther prevous usage. We nterpret ths as these customers havng a greater valuaton of the servce than under the two-part tarff. Ths effect ncreases the provder s revenue from threepart tarff customers by 19.7%. We fnd that by reducng the fee charged for swtchng between tarffs, the provder could ncrease total revenues by 3.9%, and even further f t dscontnued the opton to swtch to another two-part tarff. In both nstances, customers greater usage on threepart tarffs s key to any revenue ncrease. Our fndngs are managerally relevant from three perspectves. Frst, proectng customer usage based solely on observed usage under exstng two-part tarffs could lead frms to ncorrectly determne the optmal tarff structure and prces, wth potentally serous consequences for the frm s profts. Our analyss shows that frms may sgnfcantly underestmate the revenue effect from ntroducng three-part tarffs f they do not suffcently account for the effect on preferences arsng from the change n tarff structure. Second, our

6 5 fndngs show that gnorng the effect of a greater valuaton for free mnutes underestmates three-part tarff usage by 14.9%. Ths result suggests that, when changng ther tarff structure, frms may also need to adust ther servce capacty. Thrd, and more broadly, our results llustrate that the attrbutes of a prcng plan do not only change ts monetary value but also affect the perceved characterstcs of the servce. Our fndngs add to the nonlnear prcng lterature that has recognzed behavoral preferences at tarff choce: customers choose flat-rate or three-part tarffs wth large allowances even when these ental a greater bll than tarffs wth a lower allowance (Nunes 2000; DellaVgna and Malmender 2006; Lambrecht and Skera 2006; Lambrecht Sem, and Skera 2007). Our work confrms that such devatons from standard economc theory are not lmted to the choce of a product or servce but also affect ts usage. The present work lkewse complements a recent lterature on choce and consumpton under three-part tarffs (Jensen 2006; Bagh and Bhargava 2007; Iyengar, Ansar, and Gupta 2007; Grubb 2009; Grubb and Osborne 2011), whch has so far abstracted from potental effects of the tarff structure on usage. As an excepton, Iyengar et al. (2011) explore how tarff structure affects usage on two-part versus pay-per-use tarffs. They fnd that customers margnal utlty of consumpton s lower on a two-part tarff than on a pay-peruse tarff. More broadly our work contrbutes to research that explores behavoral effects of prcng. Ths ncludes the nsght that attrbutes of a prce or a prcng plan can affect behavor beyond ther drect cost mplcatons (Bertn and Watheu 2008), systematc effects of prce endngs on consumers' purchase decsons (Anderson and Smester 2003; Thomas and Morwtz 2005), or a valuaton of dscounts that goes beyond the change n prces (Darke and Dahl 2003). We next present our data, then provde evdence that customers over-use on three-part tarffs and dscuss possble explanatons. We then develop a ont model of tarff choce and

7 6 usage that allows for a greater valuaton of the servce on a three-part tarff, resultng n greater usage. We present the results of the estmaton and of our counterfactual analyses, and conclude wth a summary of fndngs and mplcatons of our work. DATA Our data ncludes a random sample of 5,831 ndvdual customers (.e., non-corporate) of a South Asan moble telephony provder. We observe customers for up to 12 months, commencng May The focal frm had 16% of the nstalled base. Moble phone servce penetraton was 35% n May On average, customers had been wth the frm for 23.5 months before the start of our observaton perod. The data contan nformaton on the tarff chosen and monthly usage of outgong calls. Durng the observaton perod, 3.7% of customers left the frm, resultng n a total of 69,878 monthly usage and tarff choce observatons. Durng the frst three months, customers were offered a choce of two-part tarffs (Tarff_2_1 to Tarff_2_4 n Table 1; we refer to ts currency as MU for monetary unts ). For each two-part tarff, the provder charges four dfferent per-mnute prces, all greater than zero, dependng on the tme of day and the call destnaton. Our data nclude the total number of mnutes used per month, but not by tme of day or destnaton. In addton, the frm provded us wth the number of mnutes used across all customers n each tarff by tme of day and call destnaton. As a result, we use the weghted average of usage prces per tarff as a measure of the usage prce. On average, a customer uses 297 mnutes a month and has a bll of MU (Table 1). Customers are able to check ther usage and bll by text-message, by phone or over the Internet. They are free to leave the provder at any tme there are no contractual oblgatons or to swtch to another tarff of the same provder. Customers can swtch tarffs by callng nto the frm s customer servce center, vstng one of the frm s retal outlets or through an authorzed agent. The provder charged MU 10 for swtchng to another tarff. Ths fee s hgh compared to

8 7 the two-part tarff access prces and represents a sgnfcant expendture n ths emergng market where customers are cash flow-constraned. We examne whether customers choose the ex post cost-mnmzng two-part tarff based on the average and standard devaton of ther usage n the frst three months of our data. We fnd that only 10.9% of customers would have pad less on a dfferent two-part tarff (see web appendx). Three months after the start of our observaton perod, the company added three three-part tarffs to the exstng two-part tarffs (Tarff_3_1 to Tarff_3_3 n Table 1). Under a three-part tarff, the margnal prce s zero for usage wthn the allowance. The provder charges a sngle prce for usage above the allowance. The new tarffs were heavly advertsed n prnt and on TV. The provder ntroduced three-part tarffs to dfferentate ts offerngs from ts compettors and to ncrease customer acquston, not as a recognton of lmtatons of two-part tarffs n sortng customers (Wlson 1993; Jensen 2006). Hence, for exstng customers, the ntroducton of threepart tarffs was close to a natural experment. The frm was unaware that a change n the tarff structure could potentally change demand above and beyond what would be expected from the change n the budget constrant. Our panel covers customers who were subscrbers of the frm before three-part tarffs were ntroduced but not newly acqured customers. Thus, we do not address market expanson effects. The two compettors offered smlar two-part tarffs as the focal frm but no three-part tarffs. DESCRIPTIVE ANALYSES Swtchng from two- to three-part tarffs Whle the focus of ths research les on three-part tarff usage, we also provde an overvew of tarff-swtchng behavor. In our data, 13.7% of customers swtched between tarffs: 5.8%

9 8 swtched to a two-part tarff and 7.9% swtched to one of the three-part tarffs, resultng n a total of 2,357 three-part tarff observatons. A key strength of our data s that we observe customers on a two-part tarff pror to the ntroducton of three-part tarffs and, subsequently, several months of usage behavor under three-part tarffs. Ths provdes us wth a hgh number of observatons per tarff and allows us to dentfy the effect of tarff structure on three-part tarff usage wthn ndvdual customers. As Table 2 llustrates, customers mostly swtched from any of the two-part tarffs to Tarff_3_1. We ask whether a customer s decson to swtch to a three-part tarff could have been predcted from her prevous consumpton. We fnd that of all customers that would have benefted from swtchng, 9.0% dd swtch, whereas among those customers that would not have benefted, only 4.7% swtched (see web appendx for detals). Ths s consstent wth generally low swtchng rates n telecom servces and lkely a result of the hgh swtchng fee that may have deterred customers from swtchng. 3 To assess whether the hgh swtchng fee mght have deterred customers from swtchng, we replcate the analyss above, now consderng a swtch to be benefcal only when savngs n the frst month would compensate for the swtchng fee. In ths case, a greater proporton of customers who would beneft from swtchng to a three-part tarff dd swtch (13.2% versus 9.0%). These results provde some ndcaton that whle customers behave optmally when choosng tarffs, the swtchng fee could have prevented customers from swtchng to three-part tarffs. Our econometrc model wll account for ths. 3 The share of customers swtchng to a three-part tarff s sgnfcantly lower than the share of customers that Grubb (2009) observes ntally choosng a three-part tarff. Multple factors lkely contrbute to ths dfference. Frst, our customers are requred to swtch to a three-part tarff, so swtchng costs may deter customers from swtchng. Second, our customers had a long-tme experence wth the servce so over-confdence, whch Grubb dentfes as an mportant factor n choce, may have been less mportant. Thrd, n our market three-part tarffs are new hence customers mght feel reluctant to try new plans.

10 9 Fnally we examne subsequent tarff choces among customers who swtched to a threepart tarff. We fnd that 11.7% later swtched to another tarff: 8.3% swtched back to a two-part tarff and 3.4% swtched to a dfferent three-part tarff. In contrast, none of the customers who swtched to a two-part tarff n the frst place later swtched agan. The dfference n subsequent swtchng behavor between customers who swtch to two-part tarffs and those who swtch to three-part tarffs suggests they had dffculty predctng ther own usage under three-part tarffs but not under two-part tarffs. Furthermore, customers typcally do not swtch mmedately after ther frst three-part tarff choce. Rather, they spend on average 2.7 months on a three-part tarff before swtchng agan. Ths ndcates that customers learn about ther usage on three-part tarffs before adustng ther tarff choce. Our econometrc model wll ncorporate ths learnng process. Usage under three-part tarffs We turn to customers usage behavor after the ntroducton of the three-part tarffs. A unque aspect of our data s that we observe all customers on two-part tarffs before the three-part tarffs were ntroduced. Moreover, not all customers swtched to three-part tarffs after the ntroducton. We can therefore analyze whether swtchng to a tarff wth free mnutes affects consumpton. We compare the average monthly usage before the three-part tarff ntroducton to usage n the last month of our data. Customers who swtched to a three-part tarff ncreased ther usage by 15.1%, whle customers who remaned on a two-part tarff ncreased ther usage by.9% (Fgure 1(a)). Ths ndcates a change n usage of three-part tarff customers that goes beyond a general tme trend. Ths pattern s persstent over tme (see web appendx) and s consstent across all three-part tarffs: On Tarff_3_1, usage ncreased by an average of 15.5%, on Tarff_3_2 by 16.2% and on Tarff_3_3 by 19.2%. Furthermore, actual usage often sgnfcantly exceeds the allowance: 72% of three-part tarff observatons exceed the usage allowance, on average by 88.4%.

11 10 At frst glance, ths ncrease n usage could be a result of the change n tarffs margnal prces; a utlty-maxmzng customer may use more on a three-part tarff smply because of the change n the budget constrant. To explore whether the change to the budget constrant can explan the ncreased three-part tarff usage, we estmate a lnear demand model of monthly usage. Usng the observatons before the three-part tarff ntroducton, we estmate an ndvduallevel demand ntercept and a prce coeffcent for monthly consumpton. We then predct usage condtonal on the chosen tarff n the last month n our data, and compare these predctons wth the actual behavor. Ths approach accounts for changes to the budget constrant snce the predcton s based on prces and allowances of the tarff that each customer faces n the last month (see web appendx for detals of the analyss and results). Fgure 1(b) shows the actual and predcted average usage n the last perod. For customers who stayed on a two-part tarff predcted usage s 98.9% of observed usage. However, for customers who swtched to a three-part tarff, predcted usage s only 85.9% of actual usage. In other words, the demand model that accounts for the change n the budget constrant predcts two-part tarff usage very accurately, but underestmates three-part tarff usage by almost 15%. Ths result s consstent across all three-part tarffs, and s ndependent of the month n whch customers swtch to a three-part tarff. Ths ndcates that the effect perssts over tme (see web appendx). Moreover, ths result stll holds when we relax model assumptons that could lead us to systematcally over-predct usage. Frst, f demand was not lnear n prce but convex, then mposng a lnear demand specfcaton could possbly underestmate usage n regons where prce s very low (or zero), hence systematcally underestmatng three-part tarff usage. We relax the lnearty assumpton and fnd that non-lnear utlty specfcatons lead to qualtatvely the same results (see web appendx). Second, t s possble that customers who swtch to a three-part

12 11 tarff had dfferent usage prce senstvty than customers who do not swtch to a three-part tarff. As a consequence, the assumpton of homogenous usage prce senstvty could lead us to underor overestmate ther prce response and to under-predct three-part tarff usage. Smlar to exstng research on mult-part tarffs (Iyengar, Ansar, and Gupta 2007; Lambrecht, Sem, and Skera 2007; Narayanan, Chntagunta, and Mravete 2007), we cannot estmate an ndvduallevel prce coeffcent due to lack of ndvdual-level prce varaton n the data. We can check, however, whether the homogenety assumpton s drvng our results. We estmate a demand specfcaton n whch customers who swtched to a three-part tarff have a dfferent set of parameters than customers who dd not swtch to a three-part tarff. Agan, we obtan qualtatvely smlar results (see web appendx). In sum, the large ncrease n usage after swtchng to a tarff wth free mnutes cannot be explaned by the dfference n the budget constrant. It s consstent, however, wth prevous research that shows that free goods lead to a postve affectve response, hence ncrease the valuaton of the product or servce, and consequently, ts demand (Shampaner, Mazar, and Arely 2007). Furthermore, ths postve response towards free mnutes can ncrease customers valuaton of other goods (Isen et al. 1978; Helman, Nakamoto, and Rao 2002), thus affectng the entre consumpton experence. We therefore conclude that customers who swtch to a three-part tarff may assgn greater value to the mnutes of that tarff, ncludng those above the allowance. Our data support ths: 72% of three-part tarff observatons exceed the usage allowance, on average by 88.4%. In other words, we observe that most customers ncrease ther usage after swtchng to a three-part tarff, even when that mples that monthly consumpton exceeds the tarff allowance. Alternatve explanatons We acknowledge that other explanatons could plausbly lead to a smlar pattern of usage.

13 12 Rsk averson: Rsk averson mght lead customers to choose tarffs wth large allowances where greater usage may be optmal. Ths may then result n greater consumpton. However, rskaverse customers would also be more lkely to keep ther usage at or slghtly below the allowance, whch s not consstent wth our data: 72% of three-part tarff observatons exceed the usage allowance, on average by 88.4%, and 92% of three-part tarff customers exceed ther usage allowance at least once. Furthermore, we observe that for 61% of the three-part tarff customers, usage les above ther two-part tarff sataton level. Rsk averson would not be able to explan such a change to the sataton level. Regret avodance: On a three-part tarff, customers mght want to use ther money s worth,.e., entrely use ther allowance even f ths exceeds the optmal usage of a ratonal utlty-maxmzng consumer. However, ths explanaton s not consstent wth our data snce most three-part tarff customers exceed the allowance by a large amount (on average 88.4%). Wthn-day prce varaton: On the frm s two-part tarffs, usage prces vary wth the tme of day (peak and off-peak rates) and call destnaton (wthn and out of network). Snce we do not have access to usage data by call type or records of ndvdual calls, our prevous analyss reled on the average usage prce provded to us by the provder. However, n theory, all observed twopart tarff calls could have been made durng peak hours when a greater usage prce was charged, n whch case the prevous analyss may have overestmated the usage prce senstvty and hence under-predcted three-part tarff usage. As a robustness check, we re-estmate the model presented above, now assumng that all two-part tarff calls were made at the hghest margnal prce,.e. durng peak hours out of network. In dong so, we possbly underestmate customers prce senstvty and possbly overpredct, but would not under-predct, three-part tarff usage. Agan only 85.8% of usage of threepart tarff customers can be explaned by the shft n the budget constrant.

14 13 Self-selecton: Customers may have swtched to a three-part tarff because they antcpated greater usage n future perods. Econometrcally, self-selecton should lead to a hgh correlaton between factors that affect three-part tarff choce, above and beyond expected savngs, and factors that affect three-part tarff usage, beyond what would be predcted based on a consumer s demand parameters from two-part tarff usage. Investgatng whether such a correlaton exsts s not feasble n a purely descrptve way, or by lookng at demand alone. Ths can only be tested n a ont model of usage and tarff choce. We wll therefore check for such a correlaton when estmatng our full dscrete-contnuous choce model n our model secton. Alternatvely, self-selecton could arse f usage followed an autoregressve process. If ths were the case, customers who swtch to a three-part tarff because they had a postve usage shock n the last perod should also be more lkely to ncrease ther usage n future perods. We rule out ths possblty n two ways. Frst we check for seral correlaton among monthly usage shocks. Second, we nvestgate whether customers who get (hgher) postve usage shocks are ndeed more lkely to swtch. Nether of the analyses support that an autoregressve process leads to self-selecton n our data (see web appendx for detals). Tarff-specfc servces or marketng actvtes: Usage behavor could change f the three-part tarff offered other servces unavalable on the two-part tarff. For example, f text messages were offered for free on the two-part but not on the three-part tarff, three-part tarff customers may substtute calls for text messages. In our settng, text messages are rarely used because the language of conversaton s dfferent from the language scrpt on the handset and because nether callng plan s connected wth other servces that would lead to such an ncrease n usage. Smlarly, marketng actvtes amed at swtchng customers to three-part tarffs and smultaneously ncreasng usage on these tarffs could explan hgh three-part tarff usage, e.g., advertsng or the ntroducton of handsets wth new features that stmulate usage and were

15 14 lmted to three-part tarff users. We know from the provder that no such actvtes were undertaken n ths market. Awareness of usage: Customers mght over-use because they are unaware of ther usage level. There are several ndcatons, however, that suggest that over-usage s not due to a lack of awareness. Frst, customers had used the servce for, on average, 23.5 months before the start of our data and the frm provdes many possbltes for montorng usage. Hence, t seems unlkely that three-part tarff swtchers are completely unaware of ther usage level. Even f the avalablty of free mnutes ntally resulted n unntended over-usage, t seems reasonable to assume that customers would adust ther usage wthn the next months, a pattern not observed n the data (see web appendx). Second, our data show a mass pont of usage observatons at the allowance, provdng further support that customers track ther usage (see web appendx). Thrd, f over-usage was largely a result of a lack of awareness, customers should stop usng at ther sataton pont. However, 61.0% of customers use more than the sataton level we predct based on ther two-part tarff usage. Ths provdes further support that a lack of awareness s lkely not the man reason behnd the usage ncrease, but that nstead the sataton level changed. Stll we acknowledge that snce our data does not nclude nformaton on when or how often customers check ther usage levels we cannot fully rule out that a lack of awareness contrbuted to the ncrease n usage we observe. Intra-month usage uncertanty: On a three-part tarff, a customer s decson to make a call depends on her expected valuaton of future calls durng that month. For nstance, a customer would prefer to use the entre allowance today even f today s calls are of low value to her, as long as the expected value of tomorrow s calls are of even lower value. However, f tomorrow s calls are unexpectedly of greater value than the three-part tarff s usage prce, then the customer wll stll make these calls, possbly resultng n over-usage. As a consequence, ntra-month

16 15 usage uncertanty could lead to the over-usage we observe n the data. To nvestgate ths possblty, we analyze whether customers wth greater ntra-month usage uncertanty also show greater over-usage once they swtch to a three-part tarff. Snce our data s lmted to aggregate monthly usage and does not contan nformaton on ndvdual calls, we cannot measure the level of uncertanty wthn an ndvdual month. However, the level of usage varaton across months provdes a measure of the degree of uncertanty a consumer faces n her overall usage. We check whether the degree of usage varaton before the three-part tarffs were ntroduced s correlated wth over-usage after swtchng. We measure over-usage as the rato of actual to predcted three-part tarff usage. We fnd no correlaton between these two measures (correlaton=0.080, p-value=0.098). Alternatvely, we measure over-usage as the dfference between actual and predcted three-part tarff usage and correlate ths wth usage varaton. Agan, we fnd no correlaton wth the degree of usage varaton (correlaton=0.038, p-value=0.432). We conclude that the degree of ntramonth uncertanty s unlkely to explan the ncrease n usage we observe n the data. To conclude, even f we cannot smultaneously rule out all alternatve accounts, they can hardly explan the full extent of the ncrease n usage we observe. Instead, the ncrease n usage appears consstent wth the nterpretaton that customers have a greater valuaton when a tarff offers free mnutes. There are, however, dffcultes n precsely pnnng down the effect of free mnutes n the descrptve model presented so far. Frst, we cannot dentfy a systematc ncrease n usage separately from random usage shocks and tme-varyng demand shfters. As a result we are so far unable to precsely estmate by how much customers demand changes due to the change n tarff structure. Ths s mportant for frms who need to accurately forecast ther revenues and capacty needs. Second, modelng usage ndependently from tarff choce could lead to selecton bas (Dubn and McFadden 1984) and provde based estmates of demand

17 16 parameters. Snce the same set of parameters affects choce and usage, ontly modelng both should yeld unbased and more relable parameter estmates. Thrd, n order to conduct polcy smulatons, we need a consstent set of parameters that fully descrbes customers usage and tarff choce decsons and so need to ncorporate factors that affect tarff choce alone (e.g., swtchng costs, tarff preferences) whch have been overlooked so far. Fnally, only ontly modelng choce and usage wll allow us to conclusvely rule out self-selecton as an alternatve explanaton. As a consequence, we next buld a ont model of usage and tarff choce that enables us to estmate the effect of free mnutes and allows us to make nferences about customers behavor on three-part tarffs. MODEL DEVELOPMENT AND ESTIMATION Model set-up At the begnnng of each month, a customer chooses one of the avalable tarffs or leaves the provder based on her expected usage for that month. Condtonal on her tarff choce, she next determnes her monthly usage based on the utlty she derves from the servce. We capture ths behavor wth a dscrete/contnuous choce model (Hanemann 1984; Dubn and McFadden 1984). Buldng on our descrptve analyses, we ncorporate a factor n the utlty functon to capture the possblty of greater utlty f the tarff provdes free mnutes. Ths valuaton of the free mnutes affects three-part tarff usage drectly, and choce ndrectly, through expected usage. Snce three-part tarffs were completely new to ths market, we assume that a customer s ntally unaware of a possble effect of free mnutes on her consumpton, above and beyond what the change to her budget constrant would account for. 4 Only when she frst experences a three-part tarff does she become aware of her valuaton of free mnutes. Consstent wth tarff 4 The frm dd not expect any change to the usage from the ntroducton of three-part tarffs beyond what the change to the cost structure would ental.

18 17 swtchng patterns n the data, we assume that a customer learns about her three-part tarff usage, and thus the value of consumng on a three-part tarff to her, over tme. Moble phone penetraton s ncreasng and the frm's customers have used the servce for a long tme, so we assume that a customer who leaves the provder swtches to a compettor rather than dsconnectng the servce. The compettors tarff offerngs dd not change durng the observaton perod, so explctly accountng for ther tarffs n estmaton would not dffer greatly from normalzng the prce of the outsde opton to one, whch we do for smplcty. We model a customer s tarff choce based on the expected utlty n the next perod only (Iyengar, Ansar, and Gupta 2007; Lambrecht, Sem, and Skera 2007; Narayanan, Chntagunta, and Mravete 2007). Alternatvely, we could assume that customers trade off current-perod swtchng cost aganst all future utlty gans (Goettler and Clay 2011). However, accountng for future perods would requre assumptons about the dscount rate and complcate the estmaton. Note that f consumers were n fact forward-lookng, a statc model mght potentally overestmate consumers swtchng costs but wll not bas our man parameter of nterest that captures the addtonal value of a three-part tarff. Utlty functon The customer chooses among a set of J tarffs. Each tarff s defned by a monthly access prce, denoted by F, an allowance measured n mnutes of usage, q ~, and a margnal prce, p, charged for each mnute that exceeds the tarff s monthly allowance. A hgher access prce s assocated wth a hgher usage allowance, so that F F' f q q'. A two-part tarff s smlar to a threepart tarff, but ts allowance, q ~, s by defnton set to zero. For each two-part tarff, a hgher access prce s assocated wth a lower usage prce so that p p f F F'. '

19 We assume that customer at tme t chooses the optmal tarff and consumpton levels for mnutes of calls, * q t, and the outsde good, q * 0t 18, to maxmze her utlty subect to the budget constrant. We choose a quadratc utlty functon as t allows for sataton (Iyengar, Ansar, and Gupta 2007, Lambrecht, Sem, and Skera 2007). Ths s mportant snce t reflects the behavor n our data where some customers use less than the allowance, the maxmum possble usage at a zero usage prce. It also assumes that customers are rsk-averse agents. Snce the utlty functon s lnear n q 0t, t does not capture nonlneartes n the outsde good. Utlty on tarff s represented by (1) U q d (, ),,, 0, t t t qt q 0t c dtq t q 0t t b c dt b 2 where c represents the margnal utlty of ncome and d t the sataton level,.e., demand at a zero usage prce. The demand slope, b, measures senstvty to the usage prce. The term t captures observable and unobservable characterstcs that affect tarff choce but not consumpton. Customer s budget constrant s gven by (2) y q 0 F ( q q ) I p, t t t q t q where the prce of the outsde good has been normalzed to one. Under a three-part tarff, the usage prce, p, s strctly postve only for qt q, nstances that we capture wth the ndcator varable I set to one f q q and zero otherwse. For two-part tarffs, q t s by defnton q t q set to zero, hence I s always one. q t q From Equatons (1) and (2), we derve the customer s optmal two-part tarff usage as (3) 0 f * d b p qt d b p f d b p t t t

20 19 and under a three-part tarff as (4) dt f dt q * qt dt b p f dt b p q q f dt b p q dt. The frst part of Equaton (4) reflects consumpton when usage s below the allowance. The second part determnes usage when consumpton exceeds the allowance and a strctly postve usage prce, p, apples. The last part accounts for stuatons where the optmal usage would exceed the allowance of q ~ at a margnal prce of zero, but falls short of the allowance at the postve margnal prce. Snce the ncremental value of usage beyond the allowance s not ustfed by the addtonal usage charges that accrue abruptly, * q t must be equal to Substtutng the optmal demand for the outsde good and usage nto the utlty functon yelds the condtonal ndrect utlty functon under a two-part tarff q ~. (5) and under a three-part tarff c y F q Vt ( yt, p, F ) bp c y F d p q 2 * t t f t 0 * t t t f t 0 (6) c y F f q q Vt ( yt, p, F ) bp c y F p q d p q q 2 * t t t * t t t f t. We decompose t nto three observed tarff preference shfters: () the cost of swtchng to another tarff of the same provder, () the cost of swtchng to the outsde opton (.e., churn) and () the preference for choosng a three-part as opposed to a two-part tarff, (7) SC I I I. T T P 3 pt t 1 2 t

21 20 The term T SC reflects the provder s fee for swtchng to one of ts own tarffs, 1 reflects the senstvty to ths swtchng cost, and T I s an ndcator for swtchng to another tarff of the same provder. P I s an ndcator for swtchng to another provder, and 2 captures non-monetary costs of swtchng to a provder other than the focal frm. The ndcator 3 pt I s one only under a three-part tarff, so captures unobserved factors that affect three-part tarff choce ndependent from usage expectatons. It determnes the ndvdual-specfc propensty to choose a three-part tarff. For customers who do not swtch to three-part tarffs, t may, for example, capture a preference for a famlar tarff structure, or averson to a hgh access prce. For swtchers to a three-part tarff t may capture a wllngness to experment wth new tarffs that domnates the cost of the swtchng fee. Thus, t s a factor that s known to customers, even though t s unobserved to the researcher. Importantly, ths s a preference that s reflected n choce, and explans swtchng to three-part tarffs, but not the changes n usage. We assume to be 2 normally dstrbuted across the populaton wth mean and varance,. The term t s an unobserved preference shfter that the customer knows at the tme of tarff choce. It s assumed to follow a Type 1 extreme value dstrbuton. Last, we specfy the factors that determne the sataton level d t. Our challenge s to model ncreased usage on a three-part versus a two-part tarff beyond what s due to the change n the budget constrant. Emprcally, only a change to the demand ntercept, d t, could explan the observed ncrease n usage at any level of consumpton. (A change to the demand slope could not explan a change n usage whle usage s below the allowance.) We specfy as the addtonal value from the servce when consumng on a three-part tarff. It s ndependent from the change of the budget constrant and measures a change n behavor condtonal on tarff choce. Note that

22 whle the parameter captures unobserved factors that lead to the choce of a three-part tarff, captures how the valuaton of free mnutes changes customers usage behavor. Snce three-part tarffs are new to ths market, customers are not yet aware of ther postve affectve response to the free allowance and ts subsequent effect on usage at ther ntal three-part tarff choce. Ths means that they do not yet know that access to free mnutes may change ther usage behavor. Therefore, does not affect the ntal three-part tarff choce 21 and enters the demand ntercept, d t, only after a customer ntally chooses a three-part tarff. Note that we would be unable to dentfy both and f the consumer was aware of at her ntal three-part tarff choce. The parameter s assumed to be normally dstrbuted across the populaton wth mean 2 and varance, and takes the same value for any three-part tarff. An ndvdual-specfc parameter captures dfferences among customers demand that are constant over tme and known to the customer but unknown to the econometrcan. It s assumed to be normally 2 dstrbuted wth mean and varance,. It s possble that smlar factors drve a customer s choce of a three-part tarff and her usage on a three-part tarff. Ths would nduce a correlaton between the three-part tarff choce preference,, and the valuaton of the three-part tarff s allowance that affects usage,. Such a correlaton could come from self-selecton of customers who swtch to a three-part tarff because they plan to use more, or from tarff-specfc marketng actvtes (e.g., handset subsdes), or dfferences n tarff-specfc servces (e.g., ncluded text messages). As we dscuss above, our conversatons wth the provder confrm that there are no such polces, and our analyses of the

23 data provde no support for self-selecton. Nevertheless, we revst ths possblty n the results secton and look at the correlaton between posteror estmates for parameters and. We allow for uncertanty over usage at the tme of tarff choce (Narayanan, Chntagunta, and Mravete 2007; Lambrecht, Sem, and Skera 2007). We model an unobserved usage shock t that reflects random usage varaton. We observe n our data that ndvdual-level usage varaton s correlated wth ndvdual average consumpton (correlaton=0.77 p-value<0.0001),.e., heavy users have a hgher varance of usage than lght users. Thus, we assume a multplcatve usage shock, t, whch s gamma dstrbuted wth equal shape and scale parameter r, hence wth mean 1, and varance 22 1 / r. At the moment of tarff choce, the customer knows ths shock only n dstrbuton. Followng the tarff choce but pror to makng her usage decson, she observes her usage shock and consumes accordngly. Unobserved tarff-specfc preferences, t, drve tarff choce, but do not affect the dstrbuton of demand. The two sets of unobservables, t and t, are assumed to be ndependent. Correlaton could arse from user- and plan-specfc advertsng or customer-specfc promotons but we know from the provder that such campagns were not present. To ensure a postve demand ntercept, we specfy d t n exponental form (8) d t t 3 pt ht a1 I e, where h t s a dummy for holday perods and a 1 s a parameter to be estmated. Note that even though the varance of the usage shock s homogeneous across customers, the effect of the shock on usage s heterogeneous because of ts multplcatve nteracton wth mean usage, e 3 pt ht a1 I.

24 23 Demand uncertanty and tarff choce A customer chooses the tarff that yelds the hghest expected ndrect utlty. Customers are experenced users of a two-part tarff: They know ther two-part tarff usage preferences and the dstrbuton of the usage shock, t, 5 but are uncertan about ts exact realzaton. In other words, at tarff choce, customers do not know ther exact usage on each tarff, * q t, snce the usage shock t has not been yet realzed. However, they know ther expected usage on each tarff, snce they know the dstrbuton of the usage shock. We obtan the expected ndrect utlty of a two-part tarff by takng expectatons over the unknown usage quantty n Equaton (5), that s over the dstrbuton of the uncertan shock t Sem, and Skera 2007; Goettler and Clay 2011) (see also Iyengar, Ansar, and Gupta 2007; Lambrecht, (9) * * * * [ Vt ] P( qt 0) [ Vt qt 0] P( qt 0) [ Vt qt 0] * * P( qt 0 ) c ( yt F ) P( qt 0) 1 2 ha t 1 * c yt F b p te qt 0 p t. 2 Smlarly we obtan the expected ndrect utlty of a three-part tarff by takng expectatons of the three-part tarff optmal usage over the unknown quantty. Whle our customers are experenced users of two-part tarffs, they do not have past experence on threepart tarffs. As such, when a customer experences a three-part tarff, she observes a realzaton of t e but cannot separate the effect of the usage shock, t, from that of the new tarff structure, In other words, her three-part tarff choce s guded by uncertanty about the usage shock, t, and the value of. Hence we obtan the expected ndrect utlty of a three-part tarff by takng expectatons of Equaton (6) wth respect to the dstrbuton of t e 5 Iyengar, Ansar, and Gupta 2007 fnd that consumers learn about ther usage uncertanty wthn nne months.

25 24 * * * * [ Vt ] P( qt q ) [ Vt qt q ] P( qt q ) [ Vt qt q ] (10) * * P( qt q ) c ( yt F ) P( qt q ) ha t 1 * c y F p q b p e q q p. t t t t Note that the expected ndrect utlty of an ntal three-part tarff choce s slghtly dfferent snce, as dscussed earler n ths secton, does not affect a customer's ntal threepart tarff choce. As a consequence, when computng the expected ndrect utlty of a three-part tarff for customers who have not yet experenced t, delta drops from Equaton (10) and hence we take expectatons over the shock t. In the appendx we derve the close form expressons for the expected ndrect utlty n all three cases: a two-part tarff, an ntal three-part tarff, and subsequent three-part tarff choces. Fnally, f a customer decdes to leave the provder, her expected ndrect utlty s (11) [ V 0t ] c yt 0t. Summarzng, a customer evaluates the expected ndrect utlty of each avalable opton and chooses the opton wth the hghest expected ndrect utlty. When evaluatng a two-part tarff, a customer knows her preferences and the dstrbuton of the shocks that affect future demand, but not the exact consumpton next perod. The same consderatons affect her ntal three-part tarff choce. Once a customer has experenced a three-part tarff, she evaluates subsequent three-part tarff choces takng nto account her belefs about her three-part tarff usage, that s her belefs about her own valuaton of free mnutes. We next explan how customers learn about that value over tme. Learnng At the start of our data perod, customers have been wth the provder for on average 23.5 months, exclusvely on two-part tarffs. Consstent wth pror research that has found that

26 customers learn about ther usage wthn approxmately 9 months (Iyengar, Ansar, and Gupta 2007), we assume that by the tme we observe them customers have already learned about ther two-part tarff usage. However, once they swtch to a three-part tarff, customers usage behavor changes and customers cannot easly nfer ther three-part tarff usage from pror two-part tarff consumpton. Two mechansms could descrbe the process by whch customers become aware of ther three-part tarff usage. Ether, customers become nstantly knowledgeable as they make ther frst usage decson on a three-part tarff, or they learn gradually as they observe ther usage behavor. Our data shows that customers who swtch from three-part tarffs do so after an average of 2.7 usage perods, whch suggests that they learn about three-part tarff usage over tme. We therefore extend our model to accommodate customers learnng. Specfcally, we allow customers to learn about how ther usage on a three-part tarff dffers from ther usage on a two-part tarff. Ths corresponds to learnng about ther preference for free mnutes, and thus about the parameter whch captures the dfferental usage. We assume a Bayesan learnng process (Erdem and Keane 1996). A customer learns about her true value of usng her own usage as the sgnal of her preferences. Econometrcally, a customer knows that the unknown usage quantty on a three-part tarff, 25 t e, s gammadstrbuted wth parameters r, where r e. 6 The customer knows r snce 1 r s the varance of the usage shock. Thus, learnng about translates nto fndng the true value of the scale parameter. After frst swtchng to a three-part tarff, she forms a belef about the true value of. We denote the tme-varyng ndvdual belefs by t. At the end of a perod she 6 X wth 1, 2 0. Ths result follows from the propertes of the gamma dstrbuton: Let be ~ gamma 1, 2 For any k 0, kx ~ gamma, / k. 1 2

27 observes her three-part tarff usage and updates the belef. Fgure 5 summarzes the decson process. We assume that the ntal belefs are gamma-dstrbuted. Ths s a less restrctve specfcaton than the commonly used normal dstrbuton, snce the gamma dstrbuton allows for non-symmetry n the dstrbuton of the unknown usage quantty. In our multplcatve settng, normally dstrbuted belefs would not be easly tractable. Snce the nose that affects the learnng process (usage shock) s not normally, but gamma-dstrbuted, normal belefs would not be conugate prors. Moreover, the gamma specfcaton allows customers to learn at dfferent rates n a relatvely parsmonous model snce a customer s varance of the belef, and thus her speed of learnng, depends on her own sgnal (Equaton (16). More generally, whereas most learnng models reflect learnng about an addtve shock or shft, we suggest an approach that allows customers to learn about a shock wth multplcatve nature. Followng the customer s swtch to a three-part tarff, she forms an ntal belef over the dstrbuton of such that 26 (12) ~ gamma, The customer knows the tarffs characterstcs ( p, q ), her preferences a 1 and that affect her demand ntercept, and her demand slope, b. At the end of the frst perod on a threepart tarff, 1, she observes her consumpton q and receves the sgnal * 1 s 1 (13) s 1 * q 1 ha t 1 e q b p e * 1 ha t 1 f q f q * 1 * 1 q, q

28 whch she knows s gamma-dstrbuted, wth known shape parameter r and scale parameter She updates her pror belef about, 1, whch then enters the next perod s tarff choce, (14) 1 ~ gamma 0 r, 0 s. More generally, a customer who has spent n perods on a three-part tarff has the followng belef about the scale parameter 1 (15) wth mean and varance n ~ gamma 0, n nr 0 s t, t1 0 nr 0 nr (16) E( ) Var( ) n n n n 0 s t 0 s t t1 t1 2. Snce customers are unaware of the value of free mnutes before experencng the threepart tarffs, we set 0 r0. Ths leads to an expected value of the ntal belef of r and reduces Equaton (15) to Equaton (16). The varance of the ntal belef s r. For any value of the 0 0, 0, the expected value of the belef converges to the true value and the varance goes to zero as the customer gets more experence on a three-part tarff (see web Appendx for proof). Identfcaton and estmaton There are three groups of parameters: () preferences for usage and senstvty to the usage prce (, b, ), () preferences for tarffs, margnal utlty of ncome, and swtchng costs (, c, 1, 2 ), and () parameters capturng the dstrbuton of uncertanty ncludng belefs 7 If a customer s usage s zero or equal to the allowance, q, there s not a one-to-one relatonshp between the shock and realzed usage so the customer cannot nfer the sgnal s t. We have no observatons of zero usage under three-part tarffs. In 11 nstances, we observe usage equal to the allowance, resultng n a many-to-one mappng between t and q. We assume that customers do not update ther belefs n such cases. * t

29 ( 0 ) and usage shocks ( r ). For each customer we observe tarff choce and usage. Usage s governed by the preference for mnutes, the prce senstvty and the dstrbuton of the usage shock, whle tarff choce s governed by expected usage (determned by known preferences and belefs about the unknowns) and tarff choce specfc parameters. For 13.7% of customers we observe usage on at least two dfferent tarffs. Gven that many customers stay on the same tarff for the entre observaton perod (.e., they face the same margnal prce), we cannot dentfy unobserved ndvdual-level heterogenety 28 n both and b. As a consequence, we estmate wth unobserved ndvdual-level heterogenety whch we dentfy from dfferences n usage across customers, whle we specfy the prce coeffcent b as a lnear functon of ndvdual-level (gender and locaton) and dstrct-level (labor and lteracy levels) demographc varables. That s, b b a2d, where d s a vector contanng demographc nformaton and b and a 2 are parameters to be estmated. We dentfy the prce coeffcent from dfferences n usage prces across customers, that s the dfferent usage prces across tarffs (rangng from MU 0 to.079), and wthn customers, that s the change n usage prce when a customer swtches between tarffs (13.7% of customers are on at least two tarffs) and the dfferent margnal prces on a three-part tarff (MU 0 for usage below and MU.050 for usage beyond the allowance). Observng usage under a varety of dfferent usage prces allows us to precsely pn down the prce coeffcent. Prevous research was restrcted to a much lesser degree of prce varaton, even across customers (Iyengar, Ansar, and Gupta 2007; Lambrecht, Sem, and Skera 2007; Narayanan, Chntagunta, and Mravete 2007). We can dsentangle and snce we observe both tarff choce and usage behavors: does not enter the usage decson, and does not affect the ntal three-part tarff choce. We dentfy on an ndvdual-level from observed choces between two-part and three-part tarffs

30 because we observe that customers who are otherwse smlar n ther parameter values have a dfferent propensty to swtch to a three-part tarff. For swtchers to a three-part tarff, we dentfy from the ndvdual-level dfferences n usage levels on two-part versus three-part tarffs that are not explaned by changes to the budget constrant. Note that we can separate from for all three-part tarff swtchers snce we observe the same set of customers on both prcng regmes: frst on a two-part tarff and then on a three-part tarff. Churn s not promnent, so we are unable to dentfy the margnal utlty of ncome, c, whch we set to 1 (Narayanan, Chntagunta, and Mravete 2007). We dentfy the senstvty to swtchng costs, 1, from dfferences n the propensty to swtch between customers wth otherwse smlar parameters. We can dentfy the senstvty to swtchng cost, 1, separately from the three-part tarff preference, only. 29, snce some customers swtch between two-part tarffs The parameter 0 reflects the varablty of the ntal belef about. It s dentfed from dfferences n choce after havng swtched to a three-part tarff (11.7% of the three-part tarff swtchers later swtch to a dfferent tarff), that s from varablty across (whether they swtch agan) and wthn three-part tarff customers (when they swtch). We dentfy the parameter r, whch drves usage uncertanty, from tarff choce and usage varaton across people and perods. The expresson of the lkelhood functon s derved n the appendx. It entals the ont probablty of tarff choce and usage decsons. The model s estmated n a Herarchcal Bayes framework. We use a data augmentaton approach to model the unobserved ndvdual-level parameters as well as the tme-varant belefs (see web appendx) In addton to the full model ust descrbed (denoted by Model 3 hereafter), we also estmate two restrcted versons: Model 1, whch assumes that customers do not value three-part

31 tarff mnutes any dfferently from two-part tarff mnutes and so the same parameter set governs behavor on two-part and three-part tarffs, and Model 2, whch accounts for a greater valuaton of mnutes on a three-part tarff but assumes that, after swtchng to a three-part tarff, customers mmedately acqure full knowledge about ther value of. 30 RESULTS Estmaton results Table 3 summarzes the posteror dstrbutons of the parameter estmates of the three models lad out n the prevous secton (Model 1 where s set to zero, Model 2 whch ncludes but no learnng, and Model 3 whch accounts for ndvdual-level learnng about ). Usng each set of estmates, we predct usage levels for all customers n our data (Table 4). Predcted two-part tarff usage of 282 mnutes n Model 3 compares to observed usage of 294 mnutes. The predcted three-part tarff usage of 434 mnutes very accurately reflects the observed three-part tarff usage of 434 mnutes. In contrast, Models 1 and 2 predct consderably lower three-part tarff usage (369 and 410 mnutes respectvely). Smlarly, ft measures suggest that Model 3 best reflects usage behavor (Table 5). Compared to Model 1, Model 3 reduces the Mean Squared Error (MSE) for usage, condtonal on observed tarff choce, by 3.0%. If we consder three-part tarff observatons only, the MSE reduces by 72.1%. By contrast, Model 2 reduces the MSE by 1.3% for all observatons and by 21.5% for three-part tarff observatons relatve to Model 1. The Mean Absolute Percentage Error (MAPE) confrms that Model 3 performs better than ether Model 1 or Model 2. The percentage of correctly predcted choces (ht rate) ndcates that all three models predct choce well. All ft measures confrm that Model 3 captures customers tarff choce and usage behavor better than Models 1 and 2.

32 We next turn to the parameter estmates of Model 3 n more detal. The ndvdual-level preference for free mnutes, 31, has a mean of.218 and a standard devaton of.384. It s postve for 83.9% of three-part tarff customers, ndcatng that a large maorty of customers value the free mnutes beyond ther drect cost mplcatons. Smlarly, Model 2 fnds a postve valuaton for 84.8% of customers. The varance of the usage shock, r, has a posteror mean of.205, whch translates nto a sgnfcant effect on usage volatlty. For example, a value of the usage shock that s equal to ts standard devaton shfts the average two-part tarff usage by 45.3%. The negatve coeffcent for the senstvty to swtchng costs between tarffs, 1, ndcates that the swtchng fee notably reduces swtchng. Smlarly, the negatve coeffcent for the senstvty to cost of swtchng to other provders, 2, shows that customers also have hgh non-pecunary costs of leavng the provder. The parameter o relates to the learnng process: the varance of customers ntal belef, r / o, reflects the extent of over- or underestmaton of the true value of when a customer frst swtches to a three-part tarff. For the sample of 247 customers who were observed on a threepart tarff for at least four perods, we compute the ndvdual-level devaton between the true value of r/ e and the belef, t. In perod 1, the devaton s 32.8% and t reduces to 25.5% after experencng the three-part tarff for 3 months. Ths result ndcates that customers learn about ther three-part tarff usage over tme. Not surprsngly, estmaton of the learnng process leads to a slghtly lower varance of the usage shock, 1/r, than n Model 2. Varaton n usage that was prevously attrbuted to the usage shock s now partly captured by learnng about. Fnally, we look at the correlaton between the posteror means of the ndvdual-level parameters and (Fgure 2). The addtonal valuaton of consumng on a three-part tarff s uncorrelated wth the customer s choce preference for three-part tarffs (correlaton=0.004 p-

33 value=0.930). As a robustness check, we compute the correlaton between the posteror means of and consderng only customers for whom we observe at least 5, 6 or 7 perods on a three-part tarff. 8 In all cases we fnd the correlaton to be small and nsgnfcant (Table 6). In sum, our results provde strong evdence that accountng for the value of free mnutes explans behavor sgnfcantly better than gnorng such an effect. We show that the large maorty of customers value free unts above ther costs mplcatons, and that customers learn about ths valuaton over tme. 32 Customer senstvty to prces and allowances We evaluate the senstvty of customers behavor wth respect to tarff attrbutes. Based on the estmates of Model 3, we compute the elastcty of choce and usage to changes of prces and allowances (Table 7). The two-part tarff s choce elastcty wth respect to changes n the access prce s The three-part tarff s choce elastcty wth respect to the access prce s That s comparable to prevously estmated three-part tarff elastctes of up to (Lambrecht, Sem, and Skera 2007). These estmates reflect that the elastcty ncreases n the access prce and mply that the access prce elastcty s, on average, about four tmes larger for the three-part tarff relatve to a two-part tarff. For the two-part tarff we fnd a partcularly hgh choce elastcty wth respect to the usage prce of Ths s lkely a result of the structure of the two-part tarff menu where the ndvdual usage prces are relatvely comparable. Threepart tarff choce s less elastc to the usage prce ( 5.05). Its elastcty to changes n the usage allowance s 4.30, reflectng that the allowance plays an mportant role n consumer tarff choce. We now turn to the effect on usage. Smlarly to prevous results (Park, Wetzel, and Mtchell 1983), two-part tarff usage s relatvely nelastc to changes n the usage prce (.10). 8 By dong so we confrm that the absence of correlaton s not drven by the pror assumpton of ndependence, snce we exclude customers whose ndvdual-level estmates would mostly rely on the pror dstrbuton.

34 33 Usage s even less elastc on three-part tarffs (.03) as not every usage observaton les above the usage allowance. The elastcty of usage wth respect to the allowance s.84. Overall, the prces and allowances are more mportant n determnng choce than usage condtonal on choce. Impact of the free mnutes to the provder s forecasts and revenues Our results so far show clear evdence for the addtonal value of free mnutes. A frm benefts from knowng that customers value usage on a three-part tarff more than on a two-part tarff along several dmensons. Frst, f a frm was not aware of such greater usage, t would under-estmate usage under a three-part tarff, wth lkely sgnfcant mpact on capacty plannng. As Table 4 llustrates, a model gnorng the effect of a greater valuaton for free mnutes (Model 1), underestmates three-part tarff usage by 14.9%. If a provder s operatng close to ts capacty lmts, such predcton error may easly cause a drop n call qualty and customer satsfacton, whch eventually could lead to hgher churn. Fnally, systematc errors n usage predctons wll lead to msleadng revenue forecasts. Ths would have a negatve mpact on management decsons such as budgetng, customer resource allocaton (based, for example, on customer lfetme value calculatons) or targetng. To measure the effect of for our provder s revenue, we smulate three-part tarff revenue based on the ndvdual-level estmates of the full model (Model 3) and compare t to the revenue the company would obtan f customers dd not attach greater value to the free mnutes.e., we set to zero. We fnd that the mean expected revenue per three-part tarff customer decreases from MU 21.3 to MU 17.1, whch mples that the preference for free mnutes,, accounts for 19.7% of the revenues obtaned from three-part tarff customers and so represents a sgnfcant fracton of a frm s three-part tarff revenues.

35 RECOMMENDATIONS TO THE FIRM Our results ndcate that three-part tarffs can ncrease customers usage and a frm s revenues. We next explore whether and how the frm can explot ths nsght by encouragng swtchng to three-part tarffs. We nvestgate the mpact of lowerng the swtchng fee on frm s revenues, whether the frm can ncrease revenues by ncreasng customers choce preferences for three-part tarffs and whether the frm would beneft from elmnatng two-part tarffs. Snce we do not have data about customer acquston we restrct our analyss to the current set of customers. 34 Lowerng the swtchng fee Our estmates show that the swtchng fee strongly affects swtchng ( ). To check whether the frm could further ncrease ts revenues by reducng the swtchng fee, we smulate revenues n the perod followng our observaton wndow under dfferent levels of the swtchng fee usng the estmates from Model 3. Fgure 3 shows that the frm would maxmze ts revenues f t reduced the swtchng fee from the current level of MU 10 to MU 3.6. We fnd that ths change would ncrease the frm s revenues by 3.9% (95% posteror nterval [1.9%, 5.8%]). 9 We next examne what share of ths revenue ncrease s due to the effect of. We compute expected revenues usng the same model estmates but now set to zero. Fgure 3 (a) llustrates that the revenue ncrease from lowerng the swtchng fee s largely due to customers preference for free mnutes. Fgure 3(b) llustrates that at the optmal level of the swtchng fee of MU 3.6, ths effect s sgnfcantly dfferent from zero. In the absence of, reducng the swtchng fee to MU 3.6 would not sgnfcantly ncrease revenues snce the posteror mean of the revenue ncrease s 1.5% wth a 95% posteror nterval of [.2%, 3.3%] (Fgure 3(c)). In concluson, the ncrease n revenue obtaned by reducng the swtchng fee hence encouragng 9 An ncrease n revenue may not fully translate nto an ncrease n profts f the frm does not have excess capacty. However, n ths case the company s network was not operatng at or close to capacty constrants.

36 customers to swtch to three-part tarffs s manly drven by customers greater valuaton for three-part tarff mnutes Adustng the tarff structure A frm mght further consder removng two-part tarffs from ther product offerng whle allowng current two-part tarff customers to reman on ther tarff. We nvestgate whether such a decson would be benefcal f the frm also lowered the swtchng fee. We fnd an optmal swtchng fee of MU 2.2, whch mples an expected revenue ncrease of 4.1% (95% posteror nterval [1.8%, 6.4%]) and an average ncrease n customer surplus of.4% (95% posteror nterval [.2%,.6%]). The revenue effect would be neglgble, and even negatve, f customers dd not have a preference for free mnutes (Fgure 4). Ths result hghlghts the rsk for a frm to msalgn ts prcng structure f t were to abstract from the value of free mnutes to consumers. Interestngly, the optmal level of the swtchng fee s lower than the optmal swtchng fee f the frm contnued to offer two-part tarffs. Ths dfference s drven by customers who prevously would have swtched to a dfferent two-part tarff, provded the swtchng fee was suffcently low. Now, snce two-part tarffs are no longer avalable, these customers ether reman on ther current tarff, keepng ther revenues constant, or swtch to a three-part tarff where ther revenue s lkely to ncrease due to the preference for free mnutes. Snce consumers may apprecate a smplfcaton of a provder s prcng offerng, we lastly examne the consequences of elmnatng the swtchng fee entrely. If, as llustrated n Fgure 4, the frm elmnated the swtchng fee and also removed the two-part tarffs, expected revenue would ncrease by 4.0% (95% posteror nterval [1.5%, 6.5%]) only slghtly less than at 10 Note that our econometrc model assumes that customers choce decsons are based on the next perod only. If customers were n fact forward-lookng, our model would potentally over-estmate customers senstvty to swtchng costs and the effect of lowerng the swtchng fee on provder revenues may be lower than predcted here. We run a senstvty analyss n whch we decrease the estmate for customers senstvty to the swtchng fee,, by 5%, 10%, and 20%. Our fndngs are very robust to those changes (see web appendx). 1

37 36 the optmal level of the swtchng fee and customer surplus would ncrease by.6% (95% posteror nterval [.5%,.8%]). In contrast, f two-part tarffs were stll on offer, elmnatng the swtchng fee would lead to a revenue loss for the frm snce consumers would be more lkely to swtch to two-part than to three-part tarffs (Fgure 3). CONCLUSION Compared to two-part tarffs, three-part tarffs ntroduce free unts of consumpton. Behavoral research suggests that free products affect customers behavor beyond what the change to the budget constrant would predct. In ths research we examne how consumer demand changes when consumers swtch from a two-part to a three-part tarff. We argue that the free component of a three-part tarff leads to a postve affectve response ncreasng the valuaton of the servce, an effect that perssts even after consumers have exceeded ther usage allowance. To dentfy the effect of tarff structure separately from the shft to the budget constrant, we ontly estmate tarff choce and usage. We explctly model the effect of the usage allowance on the valuaton of a three-part tarff. Our results confrm that the structure of the three-part tarff affects behavor. They ndcate that the large maorty of customers value free unts beyond the change to ther cost structure, sgnfcantly ncreasng frm s revenue. The addtonal valuaton of free mnutes accounts for 19.7% of the revenue generated from three-part tarff customers. We provde evdence that after swtchng to a three-part tarff, customers learn about ther valuaton over tme. We fnd that the provder would beneft from reducng the swtchng fee whch would lead more customers to swtch to three-part tarffs, and from dscontnung the opton to swtch to two-part tarffs. Customers valuaton for free unts s always key to any revenue ncrease. Our fndngs have mportant mplcatons. Frst, they suggest that companes should conduct feld tests of new tarff structures to better understand how new tarffs affect customer behavor. Ths s mportant to set optmal prces and swtchng fees. Second, t may be benefcal

38 37 for provders to advertse free mnutes more ntensely snce these are hghly valued by consumers. Thrd, companes that face capacty constrants should take nto account that changng the tarff structure could lead to greater than expected usage of current capacty. More broadly, our results pont to a dual role of a nonlnear prcng plan: It not only determnes the cost to the customer but also alters the perceved characterstcs of the servce, and so nfluences customers choce and usage. Overall, our fndngs add a new dmenson to nonlnear prcng research that typcally assumes that the dfference n tarff structure affects usage exclusvely through the budget constrant. Our results motvate a more extensve study of how dfferent tarff structures affect usage. A lmtaton of our study s that the data only spans customers who were wth the frm before three-part tarffs were ntroduced. Future work could address customer acquston and market expanson effects of ntroducng three-part tarffs and could examne how a frm can optmally combne three- and two-part tarffs. Furthermore, future research should nvestgate behavor when customers swtch back to two-part tarffs. Snce we have few perods n whch we observe customers swtchng back, our data do not speak to whether usage declnes beyond what a change to the budget constrant would predct, or whether greater usage alters preferences to such an extend that t becomes persstent, even once a customer leaves a three-part tarff. Addtonally, whle we have run multple robustness checks and senstvty analyses, we cannot conclusvely rule out that other factors contrbute to the phenomenon we observe. Future research could address ths ssue wth expermental data, where all alternatve accounts can be controlled for at the same tme. Fnally, future research could examne the effect of other tarff structures, such as bucket prcng that strctly lmt consumpton to the usage allowance (Schlereth and Skera 2012), on consumers valuaton of a servce.

39 38 REFERENCES Anderson, Erc and Duncan Smester (2003), "Effect of $9 Prce Endngs on Retal Sales: Evdence from Feld Experments," Quanttatve Marketng and Economcs, 1 (1), Bagh, Adb and Hemant K. Bhargava (2007), "Dong More wth Less: Prce Dscrmnaton wth Three-Part vs. Two-Part Tarffs," Unversty of Calforna, Davs. Bertn, Marco and Luc Watheu (2008), "Research Note - Attenton Arousal Through Prce Parttonng " Marketng Scence, 27 (2 ), Cnet.com (1996), "New usage plan swamps AOL," Darke, Peter R. and Darren W. Dahl (2003), "Farness and Dscounts: The Subectve Value of a Bargan," Journal of Consumer Psychology, 13 (3), DellaVgna, Stefano and Ulrke Malmender (2006), "Payng Not to Go to the Gym," Amercan Economc Revew, 96, Donovan, Robert J., John R. Rosster, Glan Marcoolyn, and Andrew Nesdale (1994), "Store Atmosphere and Purchasng Behavor," Journal of Retalng, 70 (3), Dubn, Jeffrey A. and Danel L. McFadden (1984), "An Econometrc Analyss of Resdental Electrc Applance Holdngs and Consumpton," Econometrca, 52 (2), Erdem, Tüln and Mchael P. Keane (1996), "Decson-Makng Under Uncertanty: Capturng Dynamc Brand Choce Processes n Turbulent Consumer Goods Markets," Marketng Scence, 15 (1), Golden, Lnda and Mary R. Zmmer (1986), "Relatonshp Between Affect, Patronage, Frequency and Amount of Money Spent wth a Comment on Affect Scalng and Measurement," Advances n Consumer Research, 13,

40 39 Goettler, Ronald L. and Karen. B. Clay (2011), "Tarff Choce wth Consumer Learnng and Swtchng Costs," Journal of Marketng Research, 48 (4), 633{652. Grubb, Mchael D. (2009), Sellng to Overconfdent Consumers," Amercan Economc Revew, 2009, 99 (5), Grubb, Mchael and Matthew Osborne (2011), "Tarff choce, usage uncertanty, based belefs, and learnng," Workng paper. Hanemann, W.Mchael (1984), "Dscrete/Contnuous Models of Consumer Demand," Econometrca, 52 (3), Helman, Carre M., Kent Nakamoto, and Ambar G. Rao (2002), "Pleasant Surprse: Consumer Response to Unexpected In-Store Coupons," Journal of Marketng Research, 39 (May), Isen, Alce M., Margaret Clark, Thomas E. Shalker, and Lynn Karp (1978), "Affect, Accessblty of Materal n Memory, and Behavor: A Cogntve Loop?," Journal of Personalty and Socal Psychology, 36 (1), Iyengar, Raghuram, Kamel Jedd, Skander Essegaer, and Peter J. Danaher (2011), "The Impact of Tarff Structure on Customer Retenton, Usage and Proftablty of Access Servces," Marketng Scence, 30 (5), Iyengar, Raghuram, Asm Ansar, and Sunl Gupta (2007), "A Model of Consumer Learnng for Servce Qualty and Usage," Journal of Marketng Research, 44 (4), Jensen, Sssel (2006), "Implementaton of Compettve Nonlnear Prcng: Tarffs wth Inclusve Consumpton," Revew of Economc Desgn, 10, Lambrecht, Ana, Kata Sem, and Bernd Skera (2007), "Does Uncertanty Matter? Consumer Behavor under Three-Part Tarffs," Marketng Scence, 26 (5),

41 40 Lambrecht, Ana and Bernd Skera (2006), "Payng Too Much and Beng Happy About It: Exstence, Causes and Consequences of Tarff-Choce Bases," Journal of Marketng Research, 43 (May), Messay, Cade. (1998), "Amerca Onlne," mmeo. Narayanan, Srdhar, Pradeep K. Chntagunta, and Eugeno J. Mravete (2007), "The Role of Self Selecton and Usage Uncertanty n the Demand for Local Telephone Servce," Quanttatve Marketng and Economcs, March (5), Nunes, Joseph C. (2000), "A Cogntve Model of People's Usage Estmatons," Journal of Marketng Research, 37 (November), Park, Rolla Edward, B.M. Wetzel, and B.M. Mtchell (1983), "Prce Elastctes for Local Telephone Calls," Econometrca, 51 (6), Schlereth Chrstan and B. Skera (2012), "Measurement of Consumer Preferences for Bucket Prcng Plans wth Dfferent Servce Attrbutes," Internatonal Journal of Research n Marketng. Forthcomng. Shampaner, Krstna, Nna Mazar, and Dan Arely (2007), "Zero as a Specal Prce: The True Value of Free Products," Marketng Scence, 26 (6), Sherman, Elane and Ruth B. Smth (1987), "Mood States of Shoppers and Store Image: Promsng Interactons and Possble Behavoral Effects," Advances n Consumer Research, 14, Thomas, Mano and Vcky Morwtz (2005), "Penny wse and pound foolsh: The left-dgt effect n prce cognton," Journal of Consumer Research, 32 (1), Wlson, Robert (1993), Nonlnear Prcng. New York: Oxford Unversty Press.

42 Average usage (mnutes Average usage (mnutes Fgure 1: USAGE BEFORE AND AFTER THE INTRODUCTION OF THE THREE-PART TARIFFS 41 Actual usage, customers who stayed on 2-part tarff Actual usage, customers who swtched to 3-part tarff redcted usage % % % Before Before 3-part tarff ntroducton ast After perod of data Before Before 3-part tarff ntroducton ast perod After of data Fgure 2: CORRELATION AMONG THE POSTERIOR INDIVIDUAL-LEVEL ESTIMATES FOR AND

43 Revenue change Surplus change Revenue change 42 Fgure 3: CHANGE IN REVENUE AND SURPLUS DUE TO REDUCTION OF THE SWITCHING FEE (a) Posteror mean for revenue change (b) Posteror nterval for Model 3 6% 4% 2% 0% 6% 4% 2% 0% -2% -4% -6% (c) Posteror nterval for Delta set to zero -2% -4% -6% Delta set to zero Model Swtchng fee (n MUs) 6% 4% 2% 0% -2% -4% -6% Swtchng fee (n MUs) Fgure 4: CHANGE IN REVENUE AND SURPLUS DUE TO CHANGES IN SWITCHING FEE AND TARIFF OFFERINGS (a) Posteror mean for revenue change (b) Posteror mean for surplus change 6% 1% Delta set to zero Model 3 4% 0.8% 2% 0.6% 0% -2% 0.4% -4% 0.2% -6% Delta set to zero Model 3 0% Swtchng fee (n MUs) Swtchng fee (n MUs)

44 \ 43 Fgure 5: SEQUENCE OF MODEL DECISIONS Table 1: TARIFF CHARACTERISTICS Access Package Prce (MU) Allowance (mnutes) Usage Prce (MU) Average Usage (Mnutes) Average Bll (MU) Observatons (Number) Customers Aprl 2007 (Number) Tarff_2_1 1 _ 0 _ _ 766_. Tarff_2_2 2 _ 0 _ _ 752_. Tarff_2_3 3 _ 0 _ Tarff_2_4 5 _ 0 _ Tarff_3_1 10 _ 200 _ _ 321_ Tarff_3_2 20 _ 500 _ Tarff_3_3 30 _ 900 _ _ MU refers to the local currency Table 2: TARIFF SWITCHING MATRIX Swtchng to. Tarff_2_1 Tarff_2_2 Tarff_2_3 Tarff_2_4 Tarff_3_1 Tarff_3_2 Tarff_3_3 Tarff_2_1 87.3%.0% 3.2% 2.8% 6.5%.1%.1% Tarff_2_2.0% 91.1% 3.2% 1.8% 3.8%.1%.0% Swtchng from. Tarff_2_3 Tarff_2_4.1%.2%.1%.0% 85.6% 1.3% 6.0% 89.0% 7.1% 4.4%.6% 2.2%.6% 2.8% *For customers who swtched more than once, only the frst swtch s consdered

45 Table 3: POSTERIOR DISTRIBUTIONS OF PARAMETER ESTIMATES Model 1 Model 2 Model 3 Mean 95% Interval Mean 95% Interval Mean 95% Interval Demand ntercept Indvdual-level ntercept Mean, µ η Std. dev., σ η Dummy for holday season Demand slope, b Intercept Female Dstrct-level lteracy rate Dstrct-level employment rate Dstrct s captal dstrct Varance of usage shock, 1/r Varance of ntal belef, r/β Valuaton of free unts Mean, µ δ Std. dev., σ δ Preferences n tarff choce, ζ t SC bw. tarffs, ρ SC to other provder, ρ Preference for the three-part tarff Mean, µ λ Std. dev., σ λ Log Margnal Densty N = 5,831 customers, 63,449 usage and 63,616 choce observatons 44 Table 4: (IN-SAMPLE) PREDICTED VS. ACTUAL USAGE LEVELS (IN MINUTES) Model 1 Predcton Model 2 - Predcton Model 3 - Predcton Observed - Two-part tarffs Tarff_2_ Tarff_2_ Tarff_2_ Tarff_2_ Three-part tarffs Tarff_3_ Tarff_3_ Tarff_3_

46 45 Table 5: INDIVIDUAL-LEVEL FIT MEASURES MSE ('000) Model 1 Model 2 %Dff* Model 3 %Dff* Full sample Sample of two-part tarff usage Sample of three-part tarff usage MAPE Full sample Sample of two-part tarff usage Sample of three-part tarff usage Ht rate (%)** * Percent change compared to Model 1 ** We compare actual and predcted ndvdual tarff choce n each perod and report the average across all observatons. Table 6: CORRELATION BETWEEN AND Number of three-part tarff observatons per customer Correlaton P-value Number of customers Table 7: SUMMARY OF ELASTICITIES Model 3 Elastcty of Wth respect to All tarffs 2-part tarffs 3-part tarffs Tarff choce Access prce Tarff choce Usage prce Tarff choce Allowance Usage Usage prce Usage Allowance.843

47 46 APPENDIX In ths appendx we derve n greater detal the expresson of the expected ndrect utlty for two- and three-part tarffs as well as the overall lkelhood functon. Expected ndrect utlty: Equaton (9) shows the expected ndrect utlty of choosng a two-part tarff. In the estmaton, we evaluate the probablty of consumng zero mnutes and takng expectatons over the dstrbuton of t. From the demand Equaton (3), t follows that the probablty of zero usage s P( d ) P bp t b p t ha t 1 e, whch corresponds to the cumulatve dstrbuton functon (CDF) of a gamma dstrbuton wth parameters rr, evaluated at e bp ha t 1. To smplfy notaton, hereafter we denote G( x 1, 2) as the CDF of a gamma dstrbuton of shape parameter 1 and scale parameter 2, evaluated at x, and g( x, ) as the PDF of a gamma dstrbuton defned as g(, ) 1 x x x e / The probablty of observng zero usage s therefore bp r r. The term e * P( qt 0) G, ha t 1 bp t t follows a truncated gamma ha t 1 e dstrbuton. We therefore can express the expected value of the demand ntercept on a two-part ha t 1 tarff, e t, condtonal on usage greater than zero, as bp 1G r1, r ha t 1 ht a1 * ht a1 e te qt 0 e. bp 1 G rr, ha t 1 e We substtute the above equatons nto (9) and obtan the expected ndrect utlty of a two-part tarff whch determnes a customer s twopart tarff choce,

48 47 (App-1) b p b p [ Vt ] G r, r c ( yt F ) 1 G r, r ht a1 ht a1 e e bp 1G r1, r ha t ha t 1 e t t 2 bp 1 G rr, ha t 1 c y F b p e p e. Smlarly, we derve the expresson of the expected ndrect utlty of choosng a threepart tarff (from Equaton 10). Substtutng Equaton ((8) nto Equaton ((4), we obtan that P( q q )= P e * t t ha t 1 q e b p. Thus, the probablty that a customer s three-part tarff usage s equal to or below the allowance s * q b p P( qt q ) G r, ha t 1. The term e q b p e follows a truncated gamma dstrbuton wth parameters r te te ha t 1,. We express the expected ndrect utlty of a three-part tarff as (App-2) q b p q b p [ Vt ] G r, c ( yt F ) 1 G r, h ta1 ht a1 e e q b p G ha t e c yt F p q b p 2 q b p G ha t 1 e q b p 1G r 1, ha t 1 ha t 1 r e e p t. q b p 1 G r, ha t 1 e A customer who has not yet swtched to a three-part tarff s not aware of ts addtonal value so her choce s unaffected by. Hence, at her ntal three-part tarff choce, does not enter her expected ndrect utlty of a three-part tarff. She therefore takes expectatons over the shock t, and the expected ndrect utlty of a three-part tarff smplfes to

49 48 (App-3) q b p q b p [ Vt ] G r, r c ( yt F ) 1 G r, r ht a1 ht a1 e e q b p G ha t e c yt F p q b p 2 q bp G ha t 1 e e ha t 1 q b p 1G r1, r ha t 1 e p t. q b p 1 G rr, hta1 e Lkelhood functon: For every customer and tme t we observe usage, q t, and tarff choce, k t, whch are outcomes of the customer and tme-specfc covarates, Z { h, d }, the tarff-specfc characterstcs, X p, F, q t t, the populaton parameters, b,,,, a, a,exp( r) ndvdual parameters,,, , the tme-nvarant, and the ndvdual-specfc tme-varant belefs t. Lkelhood of usage: For a consumer on a two-part tarff, the probablty of observng a partcular usage level, gven the tarff choce, s f q k Z X P q q k Z X * ( t t,,, t, ) ( t t t,,, t, ) (App-4) q 0 ha q 0 * t * t 1 P( q 0) I + P( q e b p ) I t t t t bp bp G rr, ha t 1 t g r, r I ha t 1 e e q q t where the frst term corresponds to the probablty of observng zero usage, expressed as the CDF bp of a gamma dstrbuton wth shape and scale parameter r, evaluated at. The term ha t 1 e A I s the ndcator functon that takes value 1 f statement A s true, zero otherwse. The second term s

50 dvded nto two parts, the Jacoban of the transformaton from PDF of t, whch s dstrbuted Gamma rr,. qt to t, t e 1 ha t 1 49, and the For a consumer on a three-part tarff, the probablty of observng a partcular usage level s f q k Z X P q q k Z X * ( t t,,, t, ) ( t t t,,, t, ) * za t qt q * qt q P( q e ) I + P( q q ) I t t t + P( q * t e t zt a b p ) I qt q (App-5) q t g r, r I ha t 1 e qt q q b p q G r, r G r, r ht a1 ht a1 I e e q b p qt q t g r, r I, ha t 1 e qt q where 1 t s the Jacoban of the transformaton from q ha t 1 t to t. e Lkelhood of tarff choce: The tarff-specfc shock t s assumed to follow a Type 1 extreme value dstrbuton. Therefore, the probablty of choosng a partcular tarff s gven by (App-6) J t e f ( kt,,, Z, ) (,,,, ), t t X P kt Z t t X J 0 Vgt e g0 V where the term V t denotes the expected ndrect utlty of each tarff. We obtan the lkelhood functon by ntegratng the customer s tarff choce and usage decsons: (App-7) I T t t t t t t. 1 t1 L [ f ( q k,,, Z, X ) f ( k,,, Z, X )]

51 1 When Talk s Free : The Effect of Tarff Structure on Usage under Two- and Three-Part Tarffs Eva Ascarza, Ana Lambrecht, and Naufel Vlcassm Web Appendx In ths appendx, we present a detaled descrpton of the analyses performed to obtan certan results dscussed n the man manuscrpt. DESCRIPTIVE ANALYSES Analyss of tarff choce We analyze whether customers blls would have been lower on another than ther chosen tarff at the tme that three-part tarffs were ntroduced. Based on the three avalable usage perods pror to the three-part tarff ntroducton, we compute the ndvdual-level average usage and standard devaton. For smplcty, we exclude customers who have swtched more than once as well as the 1.1% of customers who swtched wthn these three months. To account for devatons from average usage due to random usage shocks, we then compute the bll for the usage level of [average usage +/ 1 standard devaton] under the current tarff, and the bll for the average usage under each of the remanng tarffs. We conclude that a customer would have had a lower bll on a dfferent tarff f the bll for ther average usage on a Web Appendx tarff other than the chosen tarff was below the lower bound of the bll-nterval that accounts for varaton n usage on the chosen tarff. Note that ths analyss focuses on potental savngs and does not account for the fact that customers may, on the same bll, be able to use more on a dfferent tarff. The next secton wll dscuss ths aspect n detal.

52 2 Table A1 llustrates that based on ther average usage and standard devaton of usage before the ntroducton of three-part tarffs, the large maorty of customers chose the tarff that mnmzes ther bll. In total, 26.2% of customers would pay less on a dfferent tarff. For customers that would pay less on a dfferent tarff average savngs were between MU 4.1 and MU 7.7. As a result, t would take customers more than one perod on average to amortze the swtchng fee of MU 10. We then exclude three-part tarffs from ths analyss and lmt the analyss to whether customers would have pad less on a dfferent two-part tarff. We fnd that only 10.9% of customers would have pad less on a dfferent two-part tarff. Ths further confrms that two-part tarff customers largely chose the bll-mnmzng tarff. Table A1: Potental savngs when three-part tarffs were ntroduced Tarff wth lowest bll (n %) Avg. savngs Chosen tarff T_2_1 T_2_2 T_2_3 T_2_4 T_3_1 T_3_2 T_3_3 N (n MU)* Tarff_2_ Tarff_2_ Tarff_2_ , Tarff_2_ , Excludng customers who swtched wthn the frst 3 months of our data and customers that n our data swtch more than once * Average savngs on tarff wth lowest bll, computed only for customers that would have had a lower bll on a dfferent tarff Detaled analyss of swtchng from two- to three-part tarffs Web Appendx The prevous secton focused on whether customers would have pad less on a dfferent tarff. We now focus on three-part tarffs and analyze n more detal whether customers would beneft from swtchng to a three-part tarff, accountng for both whether customers would have pad less on a dfferent tarff and whether they would have been able to use more for the same bll. Fgure A1 llustrates n whch stuatons a customer should or should not swtch to a threepart tarff. We abstract from swtchng costs and assume that a customer knows her optmal usage

53 3 under a two- and a three-part tarff. We assume a utlty functon whch s quadratc n usage (bold curve; the Model secton of the man paper ustfes the choce of utlty functon). The bll on a two-part tarff (straght lne) ncreases n the customer s usage. The bll on a three-part tarff (dashed lne) remans flat as long as usage remans wthn the allowance and then ncreases lnearly n usage. The maxmum dstance between the utlty functon and the bll ndcates a customer s surplus on that tarff. A ratonal customer should swtch to a three-part tarff f that entals a greater surplus than on a two-part tarff. The vertcal (horzontal) arrows ndcate how such a swtch would affect a customer s bll (usage). A customer should swtch to a three-part tarff f for the same optmal usage, she pays less on a three- than on a two-part tarff (II), for the same bll, her optmal usage s greater on a three- than on a two-part tarff (IV), or f she can ncrease her optmal usage and stll pay less on a three-part tarff (I). A customer should not swtch f for the same bll, her optmal usage on a three-part tarff would decrease (VI), for the same optmal usage her bll would ncrease (VIII) or f her bll would ncrease whle decreasng optmal usage (IX). She s ndfferent f the same optmal usage entals the same bll (V). If under a three-part tarff, both optmal usage and the bll would decrease (III) or ncrease (VII), swtchng may or may not be benefcal, dependng on the curvature of the utlty functon. To determne whch customers n our sample should or should not swtch to a three-part Web Appendx tarff, we compare actual usage and expendtures on a two-part tarff to (a) how much a customer could use under a three-part tarff for the same bll and (b) how much she would pay under a three-part tarff for the same usage (Fgure A1). To account for devatons from average usage due to random usage shocks, the nterval of [average usage +/ 1 standard devaton] and the nterval of the bll of [average usage +/ 1 standard devaton] serve as a reference pont. For

54 4 example, we classfy a customer as beng ndfferent between swtchng to a three-part tarff and stayng on a two-part tarff (Case V) f the same optmal usage entals a bll n the same nterval on a two- and a three-part tarff. Web Appendx

55 Bll ncreases Bll stays constant Bll decreases Bll Bll Usage Usage Usage Utlty VII VIII IX Better Off Worse Off Utlty Utlty 5 Fgure A1: Predcted swtchng from two- to three-part tarffs IV V VI II III Better Off Worse Off Bll Utlty Usage Usage Usage Usage IV I Bll Usage Utlty Bll Bll Usage Usage Usage ncreases Usage stays constant Usage decreases The maxmum dstance between the utlty functon and a tarff s bll ndcates maxmum surplus. The vertcal dotted lne represents the optmal level of usage on a two-part tarff. Note: Margnal utlty and the prce of the outsde good are set to 1, so utlty represents wllngness to pay. II Utlty Utlty Bll Bll Bll Usage Utlty Utlty Web Appendx

56 6 Table A2 summarzes the results of ths analyss. The frst four columns correspond to the results when the swtchng fee s not taken nto consderaton. They ndcate that customers who, accordng to our analyss, should swtch to a three-part tarff were far more lkely to swtch to a three-part tarff than customers who accordng to our analyss should not swtch to a three-part tarff. The next set of results accounts for the fee the customer has to pay for swtchng. Here we consder a swtch to be benefcal f savngs n the frst month would compensate for the swtchng fee. Snce the fee ncreases the bll, the share of customers classfed as unknown,.e., those for whom both optmal usage and the bll would ncrease on a three-part tarff, s larger than when abstractng from the swtchng fee. Table A2: Predcted and actual swtchng behavor Category No. of customers Not consderng swtchng fee % of sample % of total % of customers swtchers n that group belongng who swtched to category No. of customers Consderng swtchng fee % of sample % of total % of customers swtchers n that group belongng who swtched to category Should swtch 3, %0 8.95% 71.7% %0 13.2% %0 Should not swtch %0 4.71% 0.9% %0 6.4% %0 Indfferent (a) %0 7.19% 11.9% %0 10.4% %0 Unknown (b) %0 5.66% 15.6% %0 6.8% %0 (a) (b) A customer s ndfferent f the same optmal usage entals the same bll on a two- and a three-part tarff. If under a three-part tarff, both optmal usage and the bll would decrease or ncrease, swtchng may or may not be benefcal dependng on the curvature of the utlty functon. Persstence of three-part tarff usage over tme Web Appendx We next check whether the ncrease n three-part tarff usage perssts over tme. We focus on customers for whom we observe at least sx months of three-part tarff usage and plot the aggregate three-part tarff usage over tme. Fgure A2 llustrates that, apart from the holday seasons n months 5 and 7 after the ntroducton of the three-part tarffs, there are no clear trends of ncreasng or decreasng three-part tarff usage.

57 Mnutes Mnutes 7 Fgure A2: Monthly average usage after swtchng to a three-part tarff Months after three-part tarff ntroducton Second, we compare average usage before and after the three-part tarff ntroducton, as we do n the Descrptve Analyss secton of the man manuscrpt, but now analyze dfferences by cohorts (.e., groups of customers who swtched to a three-part tarff n the same month). Fgure A3 shows, for each cohort, the average usage before the three-part tarffs were ntroduced and the average usage n the last perod of our data and compares t to customers who dd not swtch to a three-part tarff. We observe a consstent ncrement n usage among three-part tarff swtchers, regardless of how long customers have been on a three-part tarff. Fgure A3: Average usage before and after the ntroducton of three-part tarffs, by cohorts Before Last perod Web Appendx Non-swtchers 5 months 6 months 7 months 8 months # perods on a three-part tarff

58 Fracton.1.15 Fracton Fracton.1 Fracton Further detals on three-part tarff usage behavor We summarze nformaton on customers usage behavor on three-part tarffs. Frst, we analyze the dstrbuton of usage as percentage of the allowance (Fgure A4). Across all three-part tarffs, we observe a mass pont of usage observatons when usage s approxmately equal to the allowance. Ths mass pont results from the type of budget constrant mposed by a three-part tarff that mples bunchng of usage observatons at 100% of the allowance (see equaton (4) n the man manuscrpt). It s reassurng that we ndeed fnd such a mass pont n our data snce t provdes addtonal evdence that customers are aware of ther usage behavor. Fgure A4 also llustrates that many customers use more than ther usage allowance. Ths s n lne wth the behavoral motvaton that leads to greater three-part tarff usage as dscussed n the man paper. It outlnes that the postve effect from a three-part tarff should persst when consumers have exceeded ther allowance. Fgure A4: Usage as a percent of allowance All tarffs Usage/Allowance rato Tarff_3_2 Tarff_3_ Usage/Allowance rato Web Appendx Tarff_3_ Usage/Allowance rato Usage/Allowance rato

59 Second, we analyze whether three-part tarff customers had chosen the ex-post bllmnmzng tarff based on ther frst three months of three-part tarff usage. As n the frst secton of ths web appendx, we rely on the bll for the usage level of [average usage +/- 1 standard devaton] under the current tarff, and the bll for the average usage under each avalable tarff. Table A3 llustrates that overall 86.8% of customers chose the three-part tarff that mnmzes ther bll based on ther ex post usage. Snce the dfferences between access prces and allowances between the three-part tarffs are large, even customers that use more than ther allowance are largely n the bll-mnmzng tarff. Table A3: Optmalty of chosen three-part tarff (based on frst three perods on a three-part tarff) Tarff wth lowest bll (n %) Chosen tarff Two-part tarff T_3_1 T_3_2 T_3_3 N Tarff_3_ Tarff_3_ Tarff_3_ Includes all customers wth at least three perods on a three-part tarff, excludes customers who swtched agan n ther frst three perods on a three-part tarff DEMAND ESTIMATION Lnear demand estmaton of three-part tarff usage We compare actual usage on two- and three-part tarffs to predcted usage for the last month n our data. We estmate a lnear demand functon for two-part tarff usage, qt dt bp, where Web Appendx q t denotes the number of mnutes that ndvdual consumes on tarff at tme t, d t denotes the sataton level, or demand ntercept, b refers to the prce coeffcent and 9 p s the usage prce of tarff. Snce we have lttle wthn-customer varaton of the usage prce, the prce coeffcent s assumed to be homogenous across customers. We ncorporate an ndvdual-level preference,, and a multplcatve shock, t, nto the demand ntercept, d t te. We assume that follows

60 0 t 1 2 r 2 a normal dstrbuton wth mean and varance, and that t s dstrbuted lognormal wth 2 2 parameters 0.5,, such that E( t ) 1. We use MCMC methods to estmate the model. We choose dffuse hyperprors for b,,,and 10. We burn-n 90,000 teratons and use the next 10,000 to sample from the posteror dstrbutons of the parameters of nterest and to predct consumpton n the last perod of data. The parameters estmates are shown n Table A4. Table A4: Estmaton Results (Homogeneous prce coeffcent) Mean 95% Interval b For customers who remaned on a two-part tarff, we predct consumpton n the last perod of the data as: q * t 0 f dt bp dt bp f dt bp. For customers who have swtched to a three-part tarff, we predct consumpton n the last perod of the data as q * t dt f dt q Max( q, dt bp ) f dt q Fgure A5 llustrates that the model accurately predcts usage for customers who reman on a two-part tarff whle notably underpredctng consumpton for customers who swtch to a three-part tarff. In other words, the model does not capture the ncrement n usage observed for three-part tarff customers. Web Appendx

61 11 Fgure A5: Usage predctons usng lnear model (all customers) 450 Actual Predcted Non_swtchers Swtchers Persstence of over-usage over tme We next check whether the unpredcted ncrease n three-part tarff usage perssts over tme. We use the estmates obtaned n the analyss presented n the prevous secton but now analyze threepart tarff customers n cohorts of customers who swtched to a three-part tarff n the same month. For each cohort, we predct usage n the last month of the data and compare t wth actual usage n that month. The model under-predcts three-part tarff usage regardless of how long customers have been on a three-part tarff. Specfcally, we under-predct usage by 22.1% for the fve-month cohort, by 12.7% for the sx-month cohort, by 19.8% for the seven-month cohort, and by 12.1% for the eght-month cohort. Robustness to non-lnear demand specfcatons Web Appendx If customers usage followed a convex demand functon, our lnear demand model n the prevous secton would predct demand accurately n the area of usage prces smlar to those of the twopart tarffs,.e., MU, but would possbly underpredct usage at a zero prce. As a consequence, the over-usage we fnd n the descrptve analyss presented n the man manuscrpt

62 could smply be due to the specfcaton of the demand functon. We rule out ths possblty by estmatng two addtonal demand specfcatons. Frst, we use a polynomal specfcaton (as a Taylor approxmaton to the true demand functon) to estmate demand. We buld on the demand functon presented n the prevous secton, qt dt bp, and nclude a quadratc term, as 2 3 t t bp, and a cubc term bp. We estmate demand q d b p b p b p. If the quadratc and cubc terms do not sgnfcantly dffer from zero, that would support the choce of a lnear demand functon. We replcate the analyss presented n the man manuscrpt. The results show that the quadratc and cubc terms of the demand functon are not sgnfcantly dfferent from zero (Table A5). We next use the parameter estmates to predct usage n the last perod. Fgure A6 dsplays the results. Smlarly to our man specfcaton, predcted usage of customers who swtched to a three-part tarff s only 86.4% of ther actual usage whle the model predcts 98.9% of actual usage for customers who reman on a two-part tarff. Ths provdes evdence that the ncrease n usage s not due to the specfc form of the demand functon. Table A5: Estmaton results (quadratc and cubc terms) Mean 95% Posteror Interval b b b Web Appendx

63 13 Fgure A6: Usage predctons usng quadratc and cubc terms q t e p Actual Predcted Non_swtchers Swtchers Second, we estmate an addtonal model specfcaton that allows for convex demand: t. Ths demand specfcaton s obtaned by maxmzng the utlty functon U ( q, q ) log( q ) q q t t 0t t t 0t outsde good, when ts prce s beng normalzed to 1., wth, 0 and 0. The term q 0 t denotes the To emprcally dsentangle and, the data needs to have ndvdual-level varaton of the usage prce. However, n our data there s lttle tarff swtchng before the three-part tarffs were ntroduced. An alternatve s to fx the value of at a reasonable level and estmate the remanng parameters based on the frst two perods and predct usage for the last perod. We proceed n three steps: Web Appendx 1. To avod havng to arbtrarly set, we estmate the demand model usng all observatons from the frst sx perods of data. We obtan an estmate of (-0.049). 1 1 We conduct two sets of robustness checks to our estmate of. Frst, we estmate based on a dfferent number of perods (4 and 6 perods). Second, we estmate based on a random subsample of 50% of the customers n our dataset. We fnd that our estmate of s robust to these alternatve specfcatons.

64 2. We then set and estmate the remanng parameters, ncludng, usng two-part tarff usage observatons pror to the three-part tarff ntroducton. 3. We then use the set of estmated parameters to predct usage n the last perod of our data. Fgure A7 llustrates predcted versus actual usage. Consstent wth the results obtaned n the prevous secton, we under-predct three-part tarff usage by 19.2% whle predctng two-part tarff usage very accurately (under-predcton of only 0.9%). Ths provdes further evdence that the assumpton of lnear demand does not lead us to artfcally under-predct three-part tarff usage. Fgure A7: Usage predcton convex demand functon actual predcted Non_swtchers Robustness to non-homogeneous prce senstvty Swtchers It s possble that customers who swtch to a three-part tarff dffer n ther usage prce senstvty Web Appendx from customers who reman on a two-part tarff. Gven the lmted wthn-customer prce varaton n our data, we cannot estmate a model wth an ndvdual-level prce coeffcent, b. Nevertheless, we conduct an ad hoc analyss n whch we allow for a dfferent set of parameters for swtchers to a three-part tarff compared to all other customers. We then test whether ths specfcaton stll under-predcts three-part tarff usage. 14

65 As n the Descrptve Analyss secton n the man manuscrpt, we estmate a demand model usng the two-part tarff perods pror to the three-part tarff ntroducton and then predct usage n the last perod of our data. We now estmate two sets of coeffcents, one for customers who remaned on a two-part tarff and one for customers who swtched to a three-part tarff. The same dffuse prors were chosen for both sets of parameters. Table A6 summarzes the posteror dstrbutons and Fgure A8 shows the model predctons. The model wth heterogenety n prce senstvty under-predcts three-part tarff usage by 9.8% whle two-part tarff usage s predcted very accurately. We conclude that whle heterogenety n usage prce senstvty may possbly contrbute to greater three-part tarff usage, t does not explan the large ncrease n usage we observe n the data. To capture some degree of heterogenety n usage prce senstvty, our full model specfcaton (the Model secton of the man manuscrpt) ncorporates observed heterogenety n the usage prce senstvty. Table A6: Estmaton results (heterogeneous prce coeffcent) Customers who do not swtch to a three-part tarff Customers who swtch to a three-part tarff Mean 95% Interval Mean 95% Interval b Web Appendx 15

66 16 Fgure A8: Usage predctons for heterogenety n prce senstvty (lnear model) 450 Actual Predcted Non_swtchers Swtchers Analyss of autocorrelaton n the usage process leadng to self-selecton As dscussed n the man manuscrpt, autocorrelaton n the usage process could be a possble explanaton for the usage ncrease we observe. If usage followed an autoregressve process and customers swtched to a three-part tarff after havng receved a postve usage shock, then we would expect that customers ncrease ther consumpton after swtchng to a three-part tarff. However, we fnd that ths pattern of behavor s not consstent wth our data. We frst nvestgate the level of autocorrelaton among the usage shocks. Gven that our demand s specfed wth multplcatve usage shocks n the demand coeffcent, shocks do not Web Appendx enter n a lnear way. Hence, we cannot run smple autocorrelaton tests usng usage observatons. To solate the usage shocks, one would need to take logs of the quantty q t bp, whch s not feasble snce b s one of the parameters to be estmated. To overcome ths ssue, we consder sub-samples of customers for whch p does not vary, reducng the term pb to a constant, and then estmate the degree of autocorrelaton n each sub-sample. We do so by successvely lmtng

67 17 the sample to customers who are on the same tarff and do not swtch to a dfferent tarff. Then we run a fxed effect lnear regresson for the whole hstory of each set of customers, usng log t q as dependent varable and ts lagged value as ndependent varable. 2 For each of the subset of customers, we fnd no evdence of strong autocorrelaton among the usage shocks (ρ ranges from 0.16 to 0.35 across all tarffs). We then perform further analyses to ensure that the weak seral correlaton we fnd does not bas our model estmates. We frst smulate tarff choce and usage behavor for a synthetc panel of customers where we use the estmated parameters from our man model as the data generatng process. We ncorporate weak autocorrelaton (values of 0.2, 0.3 and 0.4) nto the usage process through autocorrelated usage shocks. We estmate all parameters usng our man model. We fnd that n all cases the smulated values lay wthn the posteror nterval of the estmated parameters. Ths provdes further confrmaton that our results are not affected by a possble weak autocorrelaton. Second, we nvestgate whether past usage shocks affect swtchng behavor. We estmate a logstc regresson wth swtchng to a three-part tarff as dependent varable. 3 As ndependent varables, we use past usage, dummy varables for the current two-part tarff, and the rato of usage n the last perod to usage n the perod before last. The latter varable serves as a proxy for Web Appendx the usage shock receved n the prevous perod. If past usage shocks affected swtchng to threepart tarffs, then the shock varable should be sgnfcant. We fnd that ths s not the case. Table A7 summarzes the results of three dfferent specfcatons. In the frst specfcaton, we nclude the usage shock n the last perod as a predctor for swtchng behavor, controllng for 2 We use the method proposed by Blundell and Bond (1998) to correct for the Nckell bas nduced by the fxed effect.

68 the chosen tarff. In the second specfcaton, we also control for the average usage level prevous to the three-part tarff ntroducton, and n the thrd specfcaton, we add a quadratc term for average usage. 4 In all specfcatons, the proxy for a past usage shock s not sgnfcant. We therefore conclude that autocorrelaton does not explan the over-usage we observe n the data. Table A7: Logstc regresson results for swtchng to three-part tarffs Varable Coeffcent p-value Coeffcent p-value Coeffcent p-value Constant Prevous usage (avg.) Prevous usage (avg.) ^ Past usage shock Dummy for prevous tarff 2_ Dummy for prevous tarff 2_ Dummy for prevous tarff 2_ Asymptotc propertes of the learnng model MODEL We show that for any value of the ntal parameters 0, 0, the expected value of the belef converges to the true value,, and ts varance goes to zero as the consumer gets more experence on a three-part tarff (.e., the number of perods on a three part tarff goes to nfnty). We compute the lmt of the mean and the varance of the belefs, as shown n equaton (22), when n goes to nfnty: Web Appendx 18 3 We estmate tarff choce n the fourth month of data. As a robustness check we also estmate the same model usng months 5, 6, etc. and n all cases, obtan qualtatvely the same results. 4 We perform the same analyss usng (1) current usage, and (2) lagged usage. We obtan the same qualtatve results.

69 0 nr lm E( ) lm n n n n s (A1) 0 r lm n. n n 0 1 s t n n We know from equaton (19), that r, r / e t. Thus, as n, we know that 0 t1 t t1 s s gamma-dstrbuted wth shape and scale parameters n 1 lm s e. n t n r Therefore, substtutng ths result nto (A1), we obtan that lm E( ) n n e. t1 0 nr lm Var( ) lm n n n n 0 s t1 0 r (A2) lm n n n 0 1 n s n n t1 Posteror dstrbutons for the full model 0. The model s estmated usng a Bayesan framework. We obtan estmates of all model Web Appendx parameters by drawng from the margnal posteror dstrbutons. Gven the nonlneartes of our lkelhood functon and the complexty of the herarchy n the parameters, most condtonal dstrbutons do not have conugate posterors. We use the Metropols-Hastng (MH) algorthm to draw from these condtonal posteror dstrbutons. We use a data augmentaton approach to nclude the unobserved ndvdual-level parameters as well as the tme-varant belefs. t 2 t 2 19

70 20 We denote as all parameters n our model, ncludng the populaton parameters b,,,, a, a,exp( r), the ndvdual-level parameters,, mxng parameters,,,,,, the, and the ndvdual specfc tme-varant belefs t. The full ont posteror dstrbuton can be wrtten as: f ( Data) L( Data ) f ( ) I T 1 t1 f ( q k,,,, Z, X ) t t t f ( k,,,,, Z, X ) t t t f ( t,, 0, Zt ) f (, ) f (, ) f (, ) f ( ) f ( ) f ( ) f ( ) f ( ) f ( ) f ( ). where f ( q k,,,, Z, X ), f ( k,,,,, Z, X ), and f(,, Z ) are the t t t t t t t t expressons derved n the appendx, (App-1), (App-2), and equaton (21) n the man paper. Expressons (, ), (, ), and (, ) correspond to the mxng f f f dstrbuton for the populaton parameters, as specfed n the Model secton. We choose dffuse pror dstrbutons for all populaton parameters. We use a normal dstrbuton wth mean and standard devaton (0,100) for,,, and nverse-gamma wth shape and scale parameters (1, 10 ) for,, Web Appendx. We assume that b,,,, a, a,exp( r) follows a multvarate normal dstrbuton wth parameters and dag( ) 100 I,1 n 1,3, where n s the dmenson of, n 1 s a 1n vector of zeros, and I n s the dentty matrx of dmensons n1

71 n n. (The values of and were chosen to ensure unnformatve prors n the transformed space.) We draw recursvely from the followng posteror dstrbutons: 1. (Gbbs) Parameters,,,,, are obtaned by samplng from the followng dstrbutons: f 2 1 (, ) Normal, I 1 I 2 I I 1 f (, ) Inverse Gamma 1, We proceed smlarly for parameters,,,. 2. (MH) Draws for are obtaned by samplng from I 2 (,,, t,data) exp.5 P(data, t, ) 1 f 3. (MH) Draws for are obtaned by samplng from: 2 f(,,,,, t,data) exp.5 P(data,, ) 2 t We proceed smlarly for. Web Appendx 4. (MH) Draws for t are obtaned by samplng from: (,,,,data), (data,,, ), n f t t g t r0 nr 0 s P t t t1 n where g t r0 nr, 0 s t s the gamma pdf as derved n (21). t1. 21

72 Snce there s no closed-form expresson for the posteror dstrbutons of and, we use a Gaussan random-walk Metropols-Hastng algorthm to draw from these dstrbutons. Followng the Metropols-Hastng procedure proposed by Atchade (2006), for each teraton, s, we draw a ( s) proposal vector of parameters (ether for and ): ~ Normal,, ( l ) ( l 1) ( l 1) ( l 1) and then accept the vector usng the Metropols-Hastngs acceptance rato. The tunng parameters ( l 1) ( l 1) and are adapted n each teraton to get an acceptance rate of approxmately 20%. We ran the smulaton for 30,000 teratons. The frst 20,000 teratons were used as a ``burn-n'' perod, and the last 10,000 teratons were used to estmate the condtonal posteror dstrbutons. Fgure A9 and Fgure A10 show the posteror draws obtaned n the smulaton. Fgure A9: Posteror draws for the populaton parameters (MH steps) b rho2 x beta0 x x r rho1 x Web Appendx x

73 23 Fgure A10: Posteror draws for mxng ndvdual-level parameters (Gbbs) mu eta sgma eta mu delta x mu lambda x x sgma delta x sgma lambda FURTHER ROBUSTNESS CHECKS x Senstvty analyss for the effect of swtchng costs on counterfactual analyses Our econometrc model assumes that customers choce decsons are based on the next perod only. Ths assumpton does not affect the estmates of our man varable of nterest,, but could potentally lead us to overestmate consumers senstvty to the swtchng fee, 1. If ths were the case, the effect of lowerng the swtchng fee on provder revenues could be lower than what our results about recommendatons to the frm suggest. We run a senstvty analyss to measure whether the effect of reducng the swtchng fee, as presented n n the man manuscrp, Web Appendx s robust to lower levels of 1. We reduce the estmate of 1 by 5%, 10%, and 20%. Fgure A11, Fgure A12 and Fgure A13 replcate the results obtaned n the man manuscrpt (see Fgure 3 of the man manuscrpt) for lower levels of 1. We fnd that the revenue mpact from lowerng the swtchng fee s very robust to lower levels of 1. In an addtonal analyss, we smlarly vary the level of the senstvty to cost of swtchng to a dfferent provder, x 10 4

74 Revenue change Revenue change 2. We fnd that whle a lower senstvty to cost of leavng the provder affects the level of provder revenues, t does not change the optmal level of the swtchng fee. Hence, we are confdent that the assumpton that customers make tarff choce decsons takng nto account ther usage n the next perod only does not sgnfcantly bas our polcy smulatons. Fgure A11: Change n revenue due to reducton of the swtchng fee f 1 s reduced by 5% 6% 4% 2% 0% -2% -4% -6% (a) Posteror mean for revenue change Delta set to zero Model Swtchng fee (n MUs) 6% 4% 2% 0% -2% -4% -6% 6% 4% 2% 0% -2% -4% -6% (b) Posteror nterval for Model (c) Posteror nterval for Delta set to zero Swtchng fee (n MUs) Fgure A12: Change n revenue due to reducton of the swtchng fee f 1 s reduced by 10% 6% 4% 2% 0% -2% -4% -6% (a) Posteror mean for revenue change Delta set to zero Model 3 6% 4% 2% 0% -2% -4% -6% (b) Posteror nterval for Model Web Appendx 6% 4% 2% 0% -2% -4% -6% (c) Posteror nterval for Delta set to zero Swtchng fee (n MUs) Swtchng fee (n MUs)

75 Revenue change 25 Fgure A13: Change n revenue due to reducton of the swtchng fee f 1 s reduced by 20% (a) Posteror mean for revenue change (b) Posteror nterval for Model 3 6% 4% 2% 0% -2% -4% -6% Delta set to zero Model Swtchng fee (n MUs) Alternatve model specfcaton: Addtonal value for free mnutes only 6% 4% 2% 0% -2% -4% -6% 6% 4% 2% 0% -2% -4% -6% (c) Posteror nterval for Delta set to zero Swtchng fee (n MUs) An alternatve way to buld our model would be to assume that three-part tarff customers assgn greater value only to mnutes strctly below the allowance, and not to all three-part tarff mnutes. In our data, three-part tarff usage mostly les beyond the allowance: 72% of three-part tarff observatons exceed the usage allowance, by an average of 88.4%. As a consequence, a behavoral theory that lmts the effect of free mnutes to usage below the allowance seems, n prncple, unable to explan the pattern n our data. To further confrm ths clam, we re-estmate Model 2 as presented n the man manuscrpt but allow the effect of free mnutes,, to apply to mnutes wthn the allowance only. We fnd that Web Appendx such a model does not reflect the phenomenon we observe well. Frst, the ft s worse than that of Models 2 and 3 (Model secton of the man manuscrpt) that assume that the addtonal valuaton apples to all three-part tarff mnutes. The MSE of the alternatve model s versus a MSE of n Model 2 and n Model 3. In the alternatve model we obtan a MAPE of versus a MAPE of 72.4 n Model 2 and of n Model 3. Second, we obtan a negatve

76 posteror mean of the varable relatng to the value of free mnutes. Ths estmate s negatve because n our sample customers generally consume above the allowance. As a consequence, a model that only estmates from mnutes wthn the allowance would overestmate the sataton level for customers who swtch to a three-part tarff and often consume above the allowance (.e., the maorty of our three-part tarff customers). Then, n the perods n whch these customers consume wthn the allowance, needs to be negatve to compensate for the overestmaton of ther sataton level. A negatve delta cannot explan the usage ncrease observed n the data and documented n the man manuscrpt, and t s not consstent wth prevous lterature ndcatng that free would lead to ncreased valuaton of the good. We conclude that ths model specfcaton s not a good representaton of the phenomenon we observe. Table A8: Posteror dstrbuton of parameter estmates for model where apples to free mnutes wthn the allowance only Model 2 free mnutes only Mean 95% Interval Demand ntercept Mean, µ η Std. dev., σ η Demand slope, b Varance of usage shock, 1/r Valuaton of free unts Mean, µ δ Std. dev., σ δ Preferences n tarff choce, ζ t SC bw. tarffs, ρ SC to other provder, ρ Web Appendx Preference for the three-part tarff Mean, µ λ Std. dev., σ λ Log Margnal Densty MSE ( 000) MAPE N=5,831 customers, 63,449 usage and 63,616 choce observatons Demographc shfters of the demand slope ncluded but not reported for readablty. 26

77 27 REFERENCES Atchade, Yves F. (2006), An adaptve verson for the Metropols adusted Langevn algorthm wth a truncated drft, Methodology and Computng n Appled Probablty, 8, Blundell, Rchard, and Stephen Bond. (1998). "Intal Condtons and Moment Restrctons n Dynamc Panel Data Models," Journal of Econometrcs 87, Roodman Davd (2009) "How to do xtabond2: An ntroducton to dfference and system GMM n Stata," Stata J.,9, Web Appendx