Cellular Service Demand: Biased Beliefs, Learning, and Bill Shock

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1 Cellular Servce Demand: Based Belefs, Learnng, and Bll Shock Mchael D. Grubb and Matthew Osborne July 10, 2013 Abstract As of Aprl 2013, the FCC s recent bll-shock agreement wh cellular carrers requres consumers be notfed when exceedng usage allowances. Wll the agreement help or hurt consumers? We estmate a model of consumer plan choce, usage, and learnng usng a panel of cellular blls from Our model predcts that had the polcy been mplemented n , average consumer welfare would have been $33 per year lower because frms would have changed fees to mantan profs whle consumer choces became less effcent. Our approach s based on novel evdence that consumers are nattentve to past usage (meanng that bll-shock alerts are nformatve) and advances structural modelng of demand n suatons where multpart tarffs nduce margnal-prce uncertanty. Addonally, our model estmates are consstent wh the average consumer underestmatng both the mean and varance of future callng. These bases cost consumers $91 per year at prces. Moreover, absent bas, the bll-shock agreement would have ltle to no effect. A prevous verson crculated under the tle Cellular Servce Demand: Tarff Choce, Usage Uncertanty, Based Belefs, and Learnng. We thank Parker Sheppard and Mengje Dng for research assstance and Katja Sem, Panle Ja, Eugeno Mravete, Catherne Tucker, Greg Lews, Chrs Kntel, Ron Goettler, Tavneet Sur, and S. Srram for careful readng and feedback on early drafts. We also thank Ted O Donoghue and semnar audences at Duke, Cornell, Chcago, and Rochester for useful feedback. Fnally we thank three anonymous referees for many helpful suggestons. Massachusetts Instute of Technology, Sloan School of Management. mgrubb@gmal.com. Unversy of Toronto, Rotman School of Management. matthew.osborne@gmal.com.

2 1 Introducton Cellular phone companes frequently offer consumers contracts wh ncluded allowances of voce mnutes, text messages, and data usage that are followed by overage charges for hgher usage. Consumers are often unaware that they are ncurrng overage charges durng the month, whch leads to bll shock at the end of the month. On October 17 th, 2011 Presdent Barack Obama declared: Far too many Amercans know what s lke to open up ther cell-phone bll and be shocked by hundreds or even thousands of dollars n unexpected fees and charges. But we can put an end to that wh a smple step: an alert warnng consumers that they re about to h ther lm before fees and charges add up (CTIA - The Wreless Assocaton 2011a). 1 Presdent Obama made ths statement at the announcement of a new bll-shock agreement between the FCC and cellular frms. As of Aprl 2013, ths agreement comms cellular servce provders to nform consumers when they approach and exceed ther ncluded voce, text, and data allowances (CTIA - The Wreless Assocaton 2011a). Pror to the agreement, the FCC had proposed a smlar regulaton whch was strongly supported by consumer groups but opposed by the ndustry (Deloney, Sherry, Grant, Desa, Rley, Wood, Breyault, Gonzalez and Lennett 2011, Altschul, Guttman-McCabe and Josef 2011). 2 Wll the new bll-shock agreement help or hurt consumers? If frms held ther prces fxed after mplementng the agreement then would weakly help consumers. Such prces-fxed logc lkely les behnd consumer groups strong advocacy for bll-shock alerts. However, the bll-shock agreement could hurt consumers once endogenous prce changes are taken nto account. Moreover, complementary theoretcal work by Grubb (2012) shows that the answer s theoretcally ambguous. 3 Whle our data are mperfect to drectly resolve the polcy queston today, we use them to predct what effect the polcy would have had durng Ths was a perod when 1 Only 8 ndvduals (0.5%) n our sample ncur a monthly bll n excess of $1,000 and these blls are due to roamng fees. Our study focuses on overage charges whch are typcally smaller but stll often hundreds of dollars. In our sample 19% of ndvduals ncur an overage over $100, 8% ncur an overage over $200, and 3% ncur an overage over $300. Consumer surveys suggest that 34 percent of cell-phone users responsble for payng ther own bll experence bll shock (GAO 2009) and 17 percent of all cell-phone users experence bll shock (Horrgan and Satterwhe 2010). 2 The wreless ndustry trade group, C.T.I.A. - The Wreless Assocaton, argued that proposed bll-shock regulaton volates carrers Frst Amendment protectons.... aganst government compelled speech (Altschul et al. 2011). 3 Bll-shock alerts do not drectly affect market power so ther effect on profs s unclear. If profs change ltle then consumers benef when socal surplus ncreases. Thus whether consumer surplus rses or falls may depend on whether or not consumer choces become more closely algned wh frm costs, somethng that s unclear a pror. 1

3 people used cellular phones to talk to each other. Whle we do not address the effect of the polcy on text or data plans prevalent today, an advantage of our data s that the market s more tractable to model. We develop and estmate a dynamc model of plan choce and voce usage that makes use of detaled cellular phone data. Gven our parameter estmates, counterfactual smulatons predct that the net effect of bll-shock regulaton and assocated endogenous prces changes mplemented n 2002 would have been an overall annual reducton n consumer welfare of $33 per consumer. En route to makng our predcton about bll-shock regulaton s effect on consumer welfare we make two addonal contrbutons. Frst, we provde new evdence on how consumers make consumpton choces under margnal-prce uncertanty and estmate a tractable model ncorporatng such realstc behavor. In partcular, we fnd evdence consstent wh the student consumers n our sample beng nattentve to ther remanng mnute balance. Gven such nattenton, we assume that consumers optmally respond to exogenously arsng callng opportunes by choosng a callng threshold and makng only those calls more valuable than the threshold. Unlke standard models, ths approach allows for consumers to endogenously adjust ther callng behavor n response to bll-shock alerts n our counterfactual smulatons. (Attentve consumers would never fnd new nformaton n a bll-shock alert.) Second, we relax the standard ratonal expectatons assumpton and nfer consumers belefs about ther future callng opportunes from plan choces. In the context of our model, systematc dfferences at the populaton level between these belefs and actual usage dentfy choce patterns consstent wh consumer bases such as overconfdence. Identfyng consumer bases s mportant for our endogenous-prce counterfactual smulatons because frm prcng decsons are strongly nfluenced by overconfdence and other bases (Grubb 2009). Our prmary data were obtaned from a major US unversy that acted as a reseller for a natonal cellular phone carrer, and covers all student accounts managed by the unversy from 2002 to We begn by documentng fve stylzed facts n our data that shape our modelng approach. Frst, a sharp ncrease n callng when free off-peak callng begns shows that consumers usage choces are prce sensve. Second, absence of bunchng at tarff knk ponts and other evdence show that consumers are uncertan about the ex post margnal prce when makng callng choces. Thrd, novel evdence from call-level data suggests consumers n our sample are nattentve to ther remanng balance of mnutes. Fourth, consumers are uncertan about ther own average taste for usage when frst choosng a callng plan, whch leads to frequent ex post plan choce mstakes. However, consumers learn about ther own tastes over tme and swch plans n response. Ffth (absent an aggregate shock) some consumers n our sample must make ex ante mstakes. Moreover, evdence suggests these are predctable gven nformaton held by a frm. 2

4 The frst three stylzed facts suggest that the arrval of a bll-shock alert wll be nformatve and cause a consumer to reduce callng. The second stylzed fact, margnal-prce uncertanty, naturally arses whenever consumers make a seres of small purchase choces that are aggregated and blled under a multpart tarff, as n cellular phone servce, electrcy, and health care. Addressng such margnal-prce uncertanty represents a challenge for the lerature whch has typcally sde-stepped the ssue by assumng that consumers can perfectly predct ther future usage (Cardon and Hendel 2001, Ress and Whe 2005, Lambrecht, Sem and Skera 2007), or that consumers beleve they can perfectly predct ther usage up to an mplementaton error whch they gnore (Iyengar, Ansar and Gupta 2007). (Notable exceptons are Yao, Mela, Chang and Chen (2012) and Jang (2012).) By recognzng that consumers are nattentve, our modelng approach ncorporates margnal-prce uncertanty realstcally and tractably and allows consumers to endogenously respond to bll-shock alerts. Our consumers behave optmally gven ther nattenton, by choosng a callng threshold each month (related to expected margnal prce) and acceptng only calls valued above the threshold. Ths approach has been proposed n earler work (Saez 2002, Borensten 2009), but has not been mplemented n a structural model. 4 An advantage of our structural approach s that we can estmate the consumer belefs requred to calculate callng thresholds. To account for the last two stylzed facts concernng plan choce, we model consumer belefs and learnng. We call a consumer s average taste for callng hs true type. A consumer s plan choces are determned not by hs true type but by hs belefs about hs true type. We assume that each consumer s pror conssts of a pont estmate of her own true type and a level of uncertanty about ths pont estmate. We assume that consumers are Bayesan learners, followng Erdem and Keane (1996), Ackerberg (2003), Crawford and Shum (2005), and Goettler and Clay (2011) and therefore learn ther true types n the long run. At the same tme, to account for ex ante plan choce mstakes n the short run, we allow consumers nal belefs to be based. Our data are nformatve both about consumers actual average tastes for cellular phone usage and about ther pror belefs about ther own tastes. Consumers usage choces dentfy the dstrbuton of consumers true types, whle consumers nal plan choces and subsequent swchng decsons dentfy belefs. 5 The jont dstrbuton of belefs and true types determnes whether belefs are based n the sample populaton. For nstance, suppose that we consder the subset 4 In the context of electrcy demand, Borensten (2009) ndependently proposes that consumers choose behavoral rules, such as settng the thermostat, smlar to our callng threshold. Borensten (2009) uses the behavoral rule assumpton to motvate usng expected margnal prce rather than realzed margnal prce n reduced form estmates of electrcy prce elastces. Saez (2002) also suggests a very smlar model for labor choce by ncome tax flers. 5 Importantly, the dstrbuton of tastes s dentfed from usage after prce sensvy and belefs are dentfed and can be used to map observed usage nto underlyng tastes. See Secton 5. 3

5 of consumers that all share a partcular pror belef about ther own types. Absent an aggregate shock, ratonal expectatons mples that ths belef concdes wh the dstrbuton of true types whn ths subset of the populaton. We relax ths assumpton, separately dentfy both belefs and the dstrbuton of true types condonal on belefs, and then compare the two dstrbutons. We label dfferences between these dstrbutons as bases. 6 Moreover, we allow consumers uncertanty about ther future tastes to be mscalbrated. We fnd that students n our sample systematcally choose overly rsky plans (those plans that yeld hgh average blls and a chance of a very large bll gven underlyng uncertanty about usage). Whle ths could be due to rsk-lovng preferences, we assume that consumers are rsk neutral, and hence nfer that they underestmate the rsk they face. In partcular, we nfer that consumers are overconfdent because they underestmate the nose n ther own forecasts about ther future tastes for callng (by 62% at our estmates). 7 In our model, we attrbute ths equally to consumers underestmaton of the nose n ther own forecasts of ther average tastes and to consumers underestmaton of the monthly volatly n ther tastes. Holdng observed prces constant, our smulaton suggests that overconfdence reduces annual consumer welfare by $76 per student. Apart from underestmatng varance n tastes, consumers could also systematcally msestmate ther average tastes. In part to ensure we do not msattrbute mean bas to overconfdence, we estmate a flexble dstrbuton of nal belefs whch captures two potental mean bases. We are able to separately dentfy these mean bases from overconfdence due to the rch choce set of plans n our data that mportantly nclude both three-part tarffs and a two-part tarff. Holdng observed prces constant, these bases reduce annual consumer welfare by an addonal $15 per student, for a total annual cost of all bases of $91 per student. Turnng back to bll-shock regulaton, we conduct a counterfactual smulaton where we allow frms to adjust prces n response to bll-shock alerts. To do so, we add addonal supply sde structure to our model and calbrate frms margnal cost as well as an addonal parameter governng market power, 1/λ, whch s the log-error weght that we normalze to one n our estmaton. The 6 As cleverly shown by Goettler and Clay (2011), an alternate nterpretaton s that unmeasurable pror belefs were unbased at some prevous tme, but are now measurably and systematcally dfferent from realy at the populaton level (although consstent wh ratonal expectatons) due to the arrval of a correlated shock or sgnal at the populaton level. The dstncton does not matter for optmal frm prcng, consumer welfare, polcy counterfactual smulatons, or other ssues of nterest as long as we assume that the frms learn the correlated shock but that consumers do not try and nfer from the frms prces. 7 Accordng to a prcng manager at a top US cellular phone servce provder, people absolutely thnk they know how much they wll use and s pretty surprsng how wrong they are 4

6 calbraton fs predcted prces, condonal on our demand estmates, to observed market prces. 8 We predct that frms would respond to bll-shock regulaton by reducng overage rates, reducng ncluded mnute allowances, and rasng fxed fees. In response, 2% of consumers termnate servce and more than 25% swch to more expensve plans. As a result, frms mantan annual profs close to unregulated levels (rsng by just $7 per person 9 ). However, annual total welfare and consumer surplus both fall, by $26 per person and $33 per person, respectvely. Note that bll-shock alerts are only relevant f frms offer three-part tarffs, whch Grubb (2009) shows are talored to explo overconfdence. Thus, absent consumer bases, we fnd that frms offer two-part tarffs rather than three-part tarffs, so that bll-shock regulaton has no effect. These results should be treated wh cauton when extrapolatng to the polcy beng mplemented today. Frst, the current polcy may have large effects on text messagng and data plans or roamng, all of whch are absent from our study. Second, our sample conssts entrely of unversy students who may not be wholly representatve. 10 Thrd, our supply model makes many smplfyng assumptons, whch are all caveats to the analyss. Secton 2 dscusses related lerature. Secton 3 descrbes our data and documents fve stylzed facts that shape our modelng approach. Sectons 4 and 5 descrbe our model and dentfcaton n a smplfed settng that does not dstngush between n-network and out-of-network callng and assumes a lnear demand curve for calls. (Appendx 12 descrbes how the complete model makes the dstncton between n-network and out-of-network callng and mplements a pecewse-lnear demand curve.) Sectons 6-9 dscuss estmaton, present results and conclude. Addonal detals about the data, model, and estmaton are n the Onlne Appendx. 8 We use EconOne data on the prces of all cellular-phone plans offered durng n the vcny of the unversy that provded our prmary data. 9 Annual profs fall by $165 per consumer for any sngle frm that ndependently chooses to offer bll-shock alerts. Ths s (n part) because overconfdent consumers underestmate the lkelhood of recevng a bll-shock alert and so undervalue the servce. Thus the premum consumers are wllng to pay for bll-shock alerts s not large enough to offset reduced overage revenue. 10 In defense of the sample, two possble concerns are 1) students may not be payng ther own blls, and 2) students may be more overconfdent or make more mstakes than the general populaton. Wh respect to pont 1), we note that students were sent ndvdual blls to ther campus resdence; the students phone blls were not bundled wh tuon. It s therefore lkely that many students pay ther own blls and are resdual clamants on an allowance or graduate student stpend. As we show n Secton 3.2 Fgure 2, students respond strongly to margnal prces. In response to pont 2), note that a prcng manager from one of the top US cellular phone servce provders made the unsolced comment that the emprcal patterns of usage, overages, and ex post mstakes documented n Grubb (2009) usng the same data were hghly consstent wh ther own nternal analyss of much larger and representatve customer samples. 5

7 2 Related Lerature Complementary work by Jang (2012) also evaluates the recent bll-shock agreement va counterfactual smulaton, predctng a $163 mllon welfare mprovement. In contrast to our own approach, Jang (2012) mposes ratonal expectatons rather than estmatng consumer belefs and has crosssectonal data so cannot address learnng. (A strength of Jang s (2012) data s that they are natonally representatve and cover all frms.) In our settng, consumers usage choces are complcated by the fact that margnal prces ncrease wh usage. The standard approach to ths problem assumes that consumers can forecast ther usage perfectly, and so respond to the ex post margnal prce (Cardon and Hendel 2001, Ress and Whe 2005, Lambrecht et al. 2007). A recent alternatve relaxes perfect foresght but assumes consumers attentvely track ther usage from call to call (Yao et al. 2012). We show n Secton 3.2 that neher perfect foresght nor attentve behavor f our data. Whle all models are smplfcatons, these approaches mplcly assume no scope for bll-shock regulaton so seem napproprate for our purposes. We assume consumers do not have perfect foresght and are nattentve, so make only those calls more valuable than a chosen threshold. A fnal alternatve assumes that consumers choose a target quanty that s mplemented wh an exogenous error (Iyengar et al. 2007, Jang 2012). For comparson, our model of consumer choce can be renterpreted as choce of a target quanty mplemented wh an endogenous error. A draw-back of assumng that mplementaton errors are exogenous s that the resultng model does not predct how the errors wll be affected by bll-shock alerts. Hence, Jang s (2012) bll-shock counterfactual s mplemented by removng mplementaton error. In contrast, a strength of our approach s that consumers endogenously change callng behavor n response to nformaton n bll-shock alerts. Our model allows for overconfdence (overestmaton of forecast precson). A sgnfcant body of expermental evdence shows that ndvduals are overconfdent about the precson of ther own predctons when makng dffcult forecasts (e.g. Lchtensten, Fschhoff and Phllps (1982)). In other words, ndvduals tend to set overly narrow confdence ntervals relatve to ther own confdence levels. A typcal psychology study mght pose the followng queston to a group of subjects: What s the shortest dstance between England and Australa? Subjects would then be asked to gve a set of confdence ntervals centered on the medan. A typcal fndng s that the true answer les outsde a subject s 98% confdence nterval about 30% to 40% of the tme. A small number of emprcal papers relax ratonal expectatons for consumer belefs and estmate mean bases (Crawford and Shum 2005, Goettler and Clay 2011). Most smlar to our work s Goettler and Clay (2011), whch estmates mean bases as well as underconfdence. Goettler and 6

8 Clay (2011) dentfy underconfdence by a restrcton that lnks to one of two estmated mean bases. In contrast, the rch tarff choce-set n our settng enables us to dentfy overconfdence separately from mean bases. An alternatve approach taken by Hoffman and Burks (2013) and others s to use survey data on belefs. To dentfy belefs from plan choces, we assume consumers are rsk neutral. 11 In contrast, related work on health nsurance markets often does the reverse and mposes ratonal expectatons to dentfy rsk preferences from plan choces (Cardon and Hendel 2001, Handel Forthcomng, Enav, Fnkelsten, Pascu and Cullen Forthcomng). Followng a thrd approach, Ascarza, Lambrecht and Vlcassm (2012) mpose ratonal expectatons and rsk neutraly but estmate preferences for cellular phone usage that depend drectly on whether contracts are two or three-part tarffs. Our results are consstent wh a related sequence of papers about Kentucky s 1986 local telephone tarff experment (Mravete 2002, Mravete 2003, Mravete 2005, Narayanan, Chntagunta and Mravete 2007, Mravete and Palacos-Huerta Forthcomng). Frst, although the standard model of consumer choce does well at explanng behavor n the Kentucky experment, our estmate that consumers underestmate ther average taste for callng s consstent wh evdence n Mravete (2003) whch documents that on average all consumers who chose a small metered plan would have saved money on a larger flat rate plan. 12 Second, as n the Kentucky experment we fnd that most consumers (65 percent) nally choose the tarff that turns out to be optmal ex post. Moreover, consumers swch plans and most swches appear to be n the rght drecton to lower blls (Secton 3.2). (Ths s n contrast to Ater and Landsman s (2013) fndng that checkng account customers who have pad overage fees swch towards checkng plans that rase, rather than lower, ther blls.) Fnally, our counterfactual smulatons wh endogenous prces relate to the leratures on monopoly sequental-screenng (surveyed by Rochet and Stole ((2003), Secton 8), competve statc-screenng (surveyed by Stole (2007)), and optmal contractng wh non-standard consumers (for whch Spegler (2011) provdes a good gude, and of partcular relevance are DellaVgna and Malmender (2004), Elaz and Spegler (2006), Elaz and Spegler (2008), Grubb ((2009), (2012)), 11 We cannot separately dentfy consumers belefs about the varance of ther future tastes from ther rsk preferences over the resultng varaton n ther blls. When we observe consumers choose overly rsky plans we nfer that they underestmate the rsk by underestmatng the varance of ther future tastes. In other words we nfer that they are overconfdent. If we dd not assume rsk neutraly, however, we could not dstngush ths explanaton from the alternatve that consumers are rsk lovng. If consumers are rsk averse then stronger overconfdence s requred to explan rsky plan choces and our estmates of overconfdence are lower bounds on bas. See also footnote Interestngly, n Mravete (2003) the bas that can be nferred from elced expectatons dffers from that nferred from choces. Consumers were not offered three-part tarffs n the Kentucky experment so ther choces do not shed lght on overconfdence. 7

9 and Herweg and Merendorff (2013).) 3 Background: Data and Evdence for Stylzed Facts 3.1 Data Our prmary data are a panel of ndvdual monthly bllng records for all student enrollees n cellular-phone plans offered by a natonal cellular carrer n conjuncton wh a major unversy from February 2002 to June Durng ths perod, cellular phones were a relatvely new product n the US, havng 49% penetraton n 2002 compared to 98% n Ths data set ncludes both monthly bll summares and detaled call-level nformaton for each subscrber.we also acqured EconOne data on the prces and characterstcs of all cellular-phone plans offered at the same dates n the vcny of the unversy. The prce menu offered to students dffered from that offered by the frm drectly to the publc: unversy plans ncluded a two-part tarff, a lmed three-month contractual commment, dfferent monthly promotons of bonus mnutes, and a $5 per month surcharge on top of frm charges to cover the unversy s admnstratve costs. The bulk of our work makes use of the monthly bllng data. For most analyss, we restrct attenton to the perod August 2002 to July 2004 and exclude ndvduals who began subscrbng before August We focus on customer choce between four popular local plans that account for 89% of blls n our data. We group the remanng prce plans wh the outsde opton. Ths leaves 1357 subscrbers used n our reduced form analyss (from whch we often exclude pro-rated blls). We estmate our structural model usng 1261 subscrbers and 15,065 subscrber-month observatons, as we exclude an addonal 7% of ndvduals due to a varety of data problems. 14 Fgure 1 shows the four popular plans, whch we label as plans 0 through 3. Plan 0 s a two-part tarff that charges $14.99 per month and 11 cents per mnute. Plans 1-3 are three-part tarffs that charge monthly fees (M j ) of 34.99, 44.99, and respectvely, nclude an allowance (Q j ) of 280 to 1060 free peak-mnutes, and charge an overage rate (p j ) of 35 to 45 cents per addonal peak mnute. Shares of plans 0-3 are 46, 27, 15, and 2 percent of blls, respectvely. Plan prces are shown for Sprng 2003 n Fgure 1 and are descrbed for all dates n Appendx 10 Table Ths feature makes our data deal for studyng consumer belefs about new products. Penetraton rates are calculated as estmated total connectons (CTIA - The Wreless Assocaton 2011b) dvded by total populaton (U.S. Census Bureau 2011). 14 The excluded ndvduals nclude those wh substantally negatve blls, ndcatng eher bllng errors or ex post renegotated refunds that are outsde our model. Also excluded are ndvduals who have nfeasble choces recorded (plans outsde the choce set or negatve n-network callng) and 8 ndvduals for whom we could not fnd startng ponts (nal parameter values from whch to begn maxmzng the lkelhood) wh posve lkelhood. 8

10 All four plans nclude surcharges of 66 to 99 cents per mnute for roamng outsde a subscrber s tr-state area and 20 cents per mnute for long dstance. Plans 1-3 always offer free off-peak callng but plan 0 does so only pror to fall Plan 0 ncludes free n-network callng, whle plans 1-3 do not wh the excepton of plan 2 n Once a customer chooses a plan, the plan terms reman fxed for that customer, regardless of any future promotons or dscounts, untl they swch plans or termnate servce. However, the terms of any gven plan, such as the ncluded allowances and overage rates for plans 1-3, vary accordng to the date a customer chooses the plan. We say that one plan s larger than another f concdes wh the lower envelope of the tarff menu at a hgher nterval of usage. Plans are numbered n order of sze, smallest to largest. Systematc consumer mstakes n choce of plan sze dentfy mean bases. We say that one plan s rsker than another f yelds a hgher expected bll for suffcently hgh usage uncertanty. Loosely speakng, ths orders plans by ther degree of convexy. We also say that one plan s rsker than another f gves a hgher rsk of a very large bll. Loosely speakng, ths orders plans by ther average steepness. Gven the plans n our data, both notons of plan rsk lead to the same orderng: Plan 0 s the safest plan, plan 1 s the rskest, and plans 1-3 are numbered n order of decreasng rsk. Consumer overconfdence s dentfed by the systematc choce of overly rsky plans Plan 1 Plan 2 Plan 0 Total bll ($) Plan 3 Plan M j Q j p j Plan 0 $ $0.11 Plan 1 $ $0.45 Plan 2 $ $0.40 Plan 3 $ $ Bllable mnutes Fgure 1: Popular Plan Prces, Sprng Wh a rcher choce set we could separately dentfy a rsk lovng preference (from the choce of overly steep plans) from overconfdence (from the choce of overly convex plans). For example, overconfdence alone should not affect preferences over two-part tarffs wh dfferent overage rates; In contrast, for two dfferent two-part tarffs wh the same expected cost, rsk averse consumers should prefer the plan wh a lower overage rate because that plan wll result n a lower ex-ante varance n cost. In our data, however, the steepest plans are the most convex so we cannot separately dentfy rsk preferences from uncertanty. We therefore dentfy overconfdence by assumng rsk neutraly. 9

11 3.2 Evdence for Stylzed Facts Three stylzed facts relevant to modelng usage choces Three features of the data are mportant to accurately model usage choces by customers of cellular phone servce. Frst, consumers usage choces are prce sensve. Second, consumers usage choces are made whle consumers are uncertan about the ex post margnal prce. Thrd, consumers are nattentve to the remanng balance of ncluded mnutes durng the course of a bllng cycle. These three stylzed facts motvate our assumpton that, rather than choosng a precse quanty, consumers choose callng thresholds and proceed to make all calls valued above the threshold. Consumer prce sensvy s clearly llustrated by a sharp ncrease n callng volume on weekday evenngs exactly when the off-peak perod for free nght and weekend callng begns (Fgure 2). Ths s not smply a 9pm effect, as the ncrease occurs only on weekdays, and at 8pm for plans wh early nghts-and-weekends. 16 Two peces of evdence demonstrate consumer uncertanty about ex post margnal prce. Frst, gven clear sensvy to margnal prce, f consumers could antcpate whether they would be under ther allowance (zero margnal prce ex post) or over ther allowance (35 to 45 cents per mnute margnal prce ex post) we would expect to see substantal bunchng of consumers consumng ther entre allowance but no more or less. Fgure 3 shows there s no bunchng, whch s consstent wh smlar fndngs n the contexts of electrcy consumpton (Borensten 2009) and labor supply (Saez 2010). Second, consumers who antcpate beng strctly under ther allowance (zero margnal prce ex post) should exhb no prce response at the commencement of off-peak hours. However, Fgure 4 shows that the sharp ncrease n callng at 9pm shown n Fgure 2 perssts even n months for whch the peak allowance s under-utlzed. 17 These are natural consequences of usage choces made under uncertanty about ex post margnal prce. Hence the standard model (Cardon and Hendel 2001, Ress and Whe 2005), whch assumes perfect consumer foresght, fs our data poorly. Now we turn to evdence that consumers are nattentve. Fgure 4 shows a sharp ncrease n weekday outgong calls to landlnes at 9pm durng months for whch fnal usage s 65 percent or less of the ncluded mnute allowance. As already noted, the fact that a prce response s observed 16 For plans wh free weeknght callng startng at 8pm, there s stll a secondary ncrease n usage at 9pm (Fgure 2 panel C). Restrctng attenton to outgong calls made to landlnes (recpents for whom the cost of recevng calls was zero) almost elmnates ths secondary peak (Fgure 2 panel D). Ths suggests that the secondary peak s prmarly due to calls to and from cellular numbers wh 9pm nghts (the most common tme for free evenng callng to begn) rather than a 9pm effect. 17 Ths s true even for outgong calls to landlnes for whch the jump n callng at 9pm cannot be due to call recpents tryng to avod callng charges. 10

12 A: Weekday (Peak 6am 9pm) B: Weekend (Peak 6am 9pm) Mean Mnutes of Usage am 9am 12pm 3pm 6pm 9pm 12am 3am 6am Mean Mnutes of Usage am 9am 12pm 3pm 6pm 9pm 12am 3am 6am C: Weekday (Peak 7am 8pm) D: Weekday Outgong Landlne (Peak 7am 8pm) Mean Mnutes of Usage am 9am 12pm 3pm 6pm 9pm 12am 3am 6am Mean Mnutes of Usage am 9am 12pm 3pm 6pm 9pm 12am 3am 6am Fgure 2: Daly usage patterns for subscrbers wh free nghts and weekends. Top row: weekday (Panel A) and weekend (Panel B) usage patterns for subscrbers wh 6am-9pm peak hours. Bottom row: weekday usage patterns for subscrbers wh 7am-8pm peak hours. Panel C shows all weekday callng, whle Panel D s restrcted to outgong calls to landlnes. when the ex post margnal prce s zero before and after 9pm s explaned by ex ante uncertanty. At the tme consumers make ther callng choces they place posve probably on an overage and respond to a posve expected margnal prce before 9pm. Evdence for nattenton comes from comparng Panels A and B n Fgure 4. Panel A shows usage patterns durng the frst three weeks of the month and Panel B shows usage patterns durng the last week of the month. If consumers are attentve, some of ther ex ante uncertanty about usage should be resolved by the fnal week of the month and should be becomng ncreasngly clear that there wll be no overage n the current month. Thus, f consumers were attentve, we would expect the prce response to be dmnshed n Panel B relatve to Panel A. In fact, usage patterns are remarkably smlar n the two panels, consstent wh consumer nattenton. 18 Appendx 10 provdes addonal evdence of nattenton. In that analyss we note that an attentve consumer should cut back usage at the end of the month followng hgh usage at the 18 The fndng s perhaps not surprsng because servce was resold by a unversy and, as a result, consumers could not contact the carrer to check mnute balances. 11

13 Densy Plan 0: flat rate Peak mnutes used Densy Plan 1: ncluded mnutes Peak mnutes used Densy Plan 2: ncluded mnutes Peak mnutes used Densy Plan 3: ncluded mnutes Peak mnutes used Fgure 3: Usage denses for popular plans are constructed wh 9,080, 5,026, 2,351, and 259 blls for plans 0-3 respectvely. The sample for plans 1-3 s selected to only nclude blls for whch n-network calls were costly and for whch ncluded peak mnutes were whn a narrow range, as ndcated above each plot. Vertcal lnes bound the range of ncluded free mnutes for each plan. A: Frst Three Weeks B: Fnal Week usage relatve to the mean am 9am 12pm 3pm 6pm 9pm 12am 3am 6am usage relatve to the mean am 9am 12pm 3pm 6pm 9pm 12am 3am 6am Fgure 4: Weekday usage patterns of outgong calls to landlnes for plan 1-3 subscrbers durng months n whch total usage was at most 65 percent of the ncluded allowance. Usage patterns are shown for the frst three weeks of the month (Panel A) and the last week of the month (Panel B). begnnng of the month to adjust for the ncreased chance of payng overage fees (and vce versa). We look for such attentve behavor n a regresson framework but fnd no evdence for. In contrast to our fndngs, Yao et al. (2012) reject our statc callng threshold model n favor 12

14 of attentve dynamc behavor usng Chnese cellular phone data. 19 The dscrepancy between Yao et al. s (2012) fndng and our own may be due n part to the fact that, unlke consumers n our data, the Chnese consumers could check ther mnute balance. Moreover, the fnancal ncentves to pay attenton were lkely stronger for Chnese consumers than ther Amercan counterparts Two stylzed facts relevant to modelng plan choces Two mportant features of the data are mportant to accurately model plan choce by cellular customers. Frst, whle 30% of contract choces are suboptmal ex post, consumers learn about ther own usage levels over tme and swch plans n response. Second (n the absence of aggregate shocks or rsk-lovng preferences) the pattern of ex post mstakes mples that some consumers make ex ante mstakes and s consstent wh overconfdence. Among the 1357 customer n our data, 183 (14%) swch plans and 26 (2%) swch plans more than once, leadng to a total of 221 plan swches. 20 Of these swches, 85 (38%) are to plans that have eher dropped n prce or been newly ntroduced snce the customer chose ther exstng plan. These swches could be motvated by prce decreases rather than learnng. However, the remanng 136 (62%) swches are to plans that are weakly more expensve than when the customer chose hs or her exstng plan. These swches must be due to learnng or taste changes. Not only do consumers swch plans, but they swch towards plans whch save them money. To substantate ths clam, we make two calculatons for each swch from an exstng plan j to an alternate plan j that cannot be explaned by a prce cut for plan j. 21 Frst, we calculate how much the customer would have saved had they sgned up for the new plan j nally, holdng ther usage from the orgnal plan j fxed. Ths provdes a lower bound on the benefs of swchng to plan j because, by holdng usage on the orgnal plan j fxed, does not account for the addonal benef from optmzng callng choces for plan j. Second, we calculate how much money the customer would have lost had they remaned on exstng plan j rather than swchng to the new plan j, now holdng usage from plan j fxed. Ths provdes an upper bound to the benefs of swchng. It calculates the addonal costs that would have been ncurred on former plan j gven usage on the new plan j, whout accountng for the fact that some costs would be avoded by adjustng usage. 19 Yao et al. (2012) show that a scatter plot of cumulatve weekly usage whn a bllng cycle aganst s lag s concave. In contrast, the relatonshp s lnear n our data, whch s consstent wh our constant callng threshold. 20 The students n our sample could swch plans at any tme and cancel after only three months, whout any cost except hassle costs. 21 The swch cannot be explaned by a prce cut for plan j f plan j s weakly more expensve at the swchng date than at the date the exstng plan j was nally chosen. 13

15 We conclude that expected benefs from swchng are between $10.87 and $24.56 per month and 60 to 69 percent of swches save money (see Appendx 10). In unreported analyss, addonal evdence of learnng s that: (1) the lkelhood of swchng declnes wh tenure, and (2) the lkelhood of swchng to a larger plan ncreases after an overage. Narayanan et al. (2007) estmate that consumers n the Kentucky experment learn to swch up from overuse faster than they learn to swch down from underuse. In the context of retal bankng, Ater and Landsman s (2013) results suggest that the asymmetry could be large enough that bankng customers tendency too choose overly large plans grows overtme through swchng. For smplcy, we mplement symmetrc learnng n our structural model. The presence of ex post mstakes alone shows only that consumers face uncertanty ex ante at the tme of plan choce. The pattern of ex post mstakes reveals more, however. Assume that (1) consumers are rsk-neutral wh standard preferences, (2) there are no aggregate shocks correlated across consumers, and (3) there are no ex ante mstakes. Then the followng must hold: Alterng plan choces usng a rule that depends only on observables at the tme of nal plan choce (whle keepng observed usage constant) must weakly ncrease expected blls. Table 1 shows three volatons of ths predcton, n whch average blls are reduced by movng everyone from one plan to another safer plan. Thus (n the absence of an aggregate shock or rsk-lovng preferences) some consumers make ex ante mstakes. Table 1: Savngs Opportunes Opportuny (1) (2) (3) Enrollment Dates 10/02-8/03 9/03 onwards 10/02-8/03 Enrollment Change plan 1-3 plan 0 plan 1 plan 2 plan 1 plan 2 Affected Customers 246 (34%) 437 (56%) 96 (14%) Savngs Per Affected Bll $8.73 $2.68 $5.45 Savngs opportunes ndcate that consumers predctably choose overly rsky plans (overconfdence). Savngs estmates are a lower bound because we cannot always dstngush n and out-of-network calls. Turnng to Table 1, column (1) shows that, n the academc year when plan 0 offered free off-peak callng, sgnng the 246 students who selected plans 1-3 up for plan 0 would save an average of $8.73 per affected bll. In the followng year, the elmnaton of free off-peak callng on plan 0 made a poor choce. However, column (2) shows that an alternatve was to sgn up the 437 students who chose plan 1 onto plan 2, whch would have saved an average of at least $

16 per affected bll. 22 These two savngs opportunes show consumers choosng plans that are overly rsky. We beleve rsk-lovng preferences are unreasonable n ths settng and therefore conclude that there are eher aggregate shocks or ex ante mstakes. Whle we cannot dstngush the two possbles, the observed choce of overly rsky plans s consstent wh overconfdence. 23 Dstngushng whether a consumer s unnformed about an aggregate shock or makes an ex ante mstake s less mportant than understandng predctably. 24 In our counter-factual smulatons we assume that frms antcpate consumers choce patterns based on ther knowledge of exstng subscrbers. In other words, f there s an aggregate shock we assume the frm observes and knows consumers do not. Equvalently, f there are ex ante mstakes we assume they are predcted by the frm. Column (3) of Table 1 suggests that ths s reasonable by replcatng the fndng from column (2) usng only data from the pror year. (The exercse s only suggestve due to the prce change between the two perods.) 4 Model At each date t, consumer frst receves a sgnal s about her perod t taste shock θ, next chooses a plan j from a frm f, and fnally chooses peak and off-peak quantes summarzed by the vector q = (q pk, qop ). (The text suppresses the dstncton between n-network and out-of-network callng, whch are covered n Appendx 12.) Total bllable mnutes for plan j are q bllable j = q pk + OP j q op, where OP j s an ndcator varable for whether plan j charges for off-peak usage. At the end of perod t, consumer s charged P j (q ) = M j + p j max{0, q bllable j Q j }, where prcng plan j has monthly fee M j, ncluded allowance Q j, and overage rate p j. (A gude to these and other model parameters s provded n Appendx 11.) We assume consumers are rsk neutral, consumers have quas-lnear utly, and peak and off- 22 Note that the frst savngs opportuny s robust to droppng the top 30 percent of customers wh the hghest average savngs, whle the second savngs opportuny s robust to droppng the top 2 percent of customers. 23 Aggregate and condonal mean bases could explan one or other savngs opportuny but only overconfdence can smultaneously explan both savngs opportunes. 24 See footnote 6. 15

17 peak calls are neher substutes nor complements. 25 Consumer s money-metrc utly n month t from choosng plan j and consumng q uns s u j = V k {pk,op} ( ) q, k θ k P j (q ) + η f, (1) where V ( ) q, k θ k = 1 ( β qk 1 1 ( q k 2 /θ) ) k (2) s the value from category k {pk, op} callng, whch depends on a par of non-negatve taste-shocks θ = (θ pk, θop ), and η f s a frm-specfc..d. log error. 26 (The value functon used for estmaton s slghtly rcher than that n equaton (2), leadng to pecewse-lnear rather than lnear demand, as elaborated n Appendx 12.) The margnal value of a dollar and the log-error varance are both normalzed to one. 27 The prce sensvy parameter, β, determnes how sensve callng choces are to the margnal prce of an addonal mnute of callng tme. Our choce of functonal form for V ( q k, θk ) mples that the taste shock θ k enters demand multplcatvely and can be nterpreted as the mnutes of category-k callng opportunes that arse, as dscussed below. 4.1 Quanty Choces Recognzng that consumers are uncertan about the ex post margnal prce when makng usage choces from three-part tarffs s a key feature of our model and where we take a new approach (also suggested ndependently by Borensten (2009)). We assume that at the start of bllng perod t, consumer s uncertan about her perod t taste shock θ. She frst receves a sgnal s that s nformatve about θ, next chooses a plan j, and fnally chooses a callng threshold vector v j = (vpk j, vop j ) based on chosen plan terms and her belefs about the dstrbuton of θ. Durng the course of the month, the consumer s nattentve and does not track usage but smply makes all category-k calls valued above v k j.28 Over the course of the month, for k {pk, op} ths cumulates 25 In realy, consumers lkely do delay calls untl off-peak perods. Our assumpton rulng out such substuton should not bas our fnal results. In partcular, as the margnal prce and margnal cost of off-peak callng s assumed to be zero n our counterfactual smulatons, whether peak calls are foregone entrely or shfted off-peak does not effect frm profs or peak-prcng. Moreover, n eher case, foregone peak calls carry a socal cost captured n our welfare estmates. 26 We model consumers choce between the four most popular prcng plans (plans 0-3), comparable plans from other carrers, and an outsde opton. The log error η f has a clear economc nterpretaton: ncludes all unmodeled carrer heterogeney ncludng network qualy and avalable phones. 27 We calbrate the log-error varance for our bll-shock counterfactual smulatons n Secton Leder and Sahn s (2012) callng choce experment fnds that a majory of lab subjects use threshold rules when choosng whch calls to make. 16

18 to the choce: q k = q(v k j, θ k ) = θ k ˆq(v k j), (3) where ˆq (v) = 1 βv and ˆq (0) = The nterpretaton s that θ k s the volume of category-k callng opportunes that arse and ˆq(v) Choose plan j Choose threshold v s the fracton of those callng opportunes gven Taste θ k worth more than v per and usage q k mnute. = θ k Tmng q (v k s ) gven pror θ summarzed ~F plan j and pror θ ~F realzed for k {pp, oo}. Belefs updated. n Fgure 5. Fgure 6 shows the callng threshold v pk j and resultng consumpton choce θpk ˆq(vpk j ) n relaton to a consumer s realzed nverse demand curve for callng mnutes, V q (q pk, θpk ). Learn sgnal s. Update belefs θ ~F Choose plan j gven pror θ ~F Choose threshold v gven plan j and pror θ ~F Taste θ k and usage q k = θ k q (v k ) realzed for k {pp, oo}. Belefs updated. Fgure 5: Model Tme Lne $ 1 β v * V q q, θ Calls worth more than v* q(v * ) q Fgure 6: Inverse Demand Curve and Callng Threshold Makng all peak calls valued above the constant threshold v j s the optmal strategy of an nattentve consumer who does not track usage whn the current bllng cycle and hence cannot update hs belefs about the lkelhood of an overage whn the current bllng cycle. (It s analogous to an electrcy consumer settng a thermostat rather than choosng a quanty of klowatt hours.) When margnal prce s constant, a consumer s optmal callng threshold s smply equal to the margnal prce. Thus for plan zero, whch charges 11 cents per mnute for all bllable calls, vj = (0.11, 0.11OP j). Further, v op j = 0 for plans 1-3 because they offer free off-peak callng. Condonal choosng one of plans 1-3, whch nclude free off-peak callng and an allowance of peak mnutes, consumer chooses her perod t peak-callng threshold v pk j to maxmze her expected 29 The fact that demand s multplcatve n θ k follows from the assumpton that V ( ) q, θ k can be expressed as V ( ( q, θ) k = θ k ˆV q/θ) k for some functon ˆV. In ths case, ˆV (x) = x(1 x/2)/β. The fact that ˆq(0) = 1 smply reflects the chosen normalzaton of θ k. 17

19 utly condonal on her perod t nformaton I. Gven allowance Q j, overage rate p j, and multplcatve demand (equaton (3)), the optmal threshold (derved n Appendx 11.1) s unquely characterzed by equaton (4): [ ] ( ) E θ pk v pk j = p j Pr θ pk Q j /ˆq(v pk j ) I θ pk Q j /ˆq(v pk j ); I [ ]. (4) E θ pk I The threshold v pk j wll be between zero and the overage rate p j. 30 The callng threshold v pk j s ncreasng n the consumer s belef about the mean and varance of callng opportunes, as both ncrease the antcpated lkelhood of payng overage fees. (Fgure 9 n Appendx 11 plots v pk j as a functon of belefs.) q T Note that choosng threshold v pk j E[θ pk ]ˆq(vpk j ), whch s mplemented wh endogenous error (θpk s equvalent to choosng a target peak-callng quanty E[θ pk ])ˆq(vpk j ). Importantly, consumers are aware of ther nably to h the target precsely and take ths nto account when makng ther threshold/target choce. 4.2 Plan Choces We model consumers choce between the four most popular prcng plans (plans 0-3), comparable AT&T, Cngular, and Verzon plans (Sprnt offered no local plans), and an outsde opton whch ncorporates all other plans. We adopt Chng, Erdem and Keane s (2009) consderaton set model by assumng that consumers make an actve choce wh exogenous probably P C and keep ther current plan wh probably (1 P C ). 31 The plan consderaton probably P C, whch allows for nerta n plan choce, s dentfed by the rate at whch consumers swch plans. Customer s perceved expected utly from choosng plan j at date t s U j = E k {pk,op} V ( ) q(vj, k θ k ), θ k ( P j q(v j, θ ) ) I + η f, (5) and from choosng the outsde opton s U 0 = O + η 0. The parameter O wll be dentfed from the frequency at whch consumers leave the data set. Condonal on makng an actve choce, a 30 Equaton (4) may seem counter-ntuve, because the optmal v pk j s greater than the expected margnal prce, p j Pr(q(v pk j, θpk ) > Qj I). Ths s because the reducton n consumpton from rasng vpk j s proportonal to θpk. Rasng v pk j cuts back on calls valued at vpk j more heavly n hgh demand states when they cost pj and less heavly n low demand states when they cost Ths s equvalent to assumng swchng costs are zero wh probably P C and nfne otherwse. 18

20 consumer s consderaton set ncludes plans offered by her current provder, the outsde opton, and plans from a randomly selected alternatve frm. 32 Consumers myopcally 33 choose the plan (or outsde opton) from ther consderaton set that maxmzes expected utly n the current perod. 4.3 Dstrbuton of Tastes and Sgnals We assume that the non-negatve taste-shocks whch determne usage are latent taste shocks censored at zero: θ k 0 = θk θk < 0 θk 0, k {pk, op}. We assume that the latent shock θ k s normally dstrbuted and that consumers observe s value at then end of the bllng perod even when censored. Ths adds addonal unobserved heterogeney to the model but preserves tractable Bayesan updatng. Censorng makes zero usage a posve lkelhood event, whch s mportant snce occurs for 10% of plan 0 observatons. The latent taste shock satsfes θ = µ + ε, where µ = (µ pk, µ op ) s customer s true type and ε = (ε pk ) s a normally-dstrbuted meanzero shock wh varance-covarance matrx Σ ε = (σpk ε ) 2 ρ ε σ pk ε σ op ε ρ ε σ pk ε σ op ε (σ op ε ) 2, εop. Consumers true types, µ, are normally dstrbuted n the populaton wh mean µ 0 = (µ pk 0, µop 0 ) and varance-covarance matrx Σ µ = (σpk µ ) 2 ρ µ σ pk µ σ op µ ρ µ σ pk µ σ op µ (σ op µ ) 2 Consumers make plan and callng threshold choces before learnng the taste shock θ. However,. 32 We avod ncludng all plans n the consderaton set to reduce computatonal tme. 33 We assume learnng s ndependent of plan choce, so there s no value to expermentaton wh an alternatve plan. Nevertheless, myopc plan choce s not optmal for several reasons. Frst, when a consumer s currently subscrbed to a plan that s no longer offered (and s not domnated) there s opton value to not swchng, snce swchng plans wll elmnate that plan from future choce sets. Second, f P C < 1, a forward lookng consumer would tend to dscount her current perod log-error η f and sgnal s. Thrd, f P C < 1, a forward lookng consumer should antcpate that her current plan choce may persst n the future but her future callng threshold choces v pk j wll mprove as she learns about her type µ. Ths consderaton makes plans 1 and 2 margnally more attractve relatve to plans 0 and 3 but the effect s not large. We gnore these ssues for tractably. 19