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

Transcription

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. [email protected]. Unversy of Toronto, Rotman School of Management. [email protected].

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

21 pror to makng these choces consumers observe a standard normal sgnal s N (0, 1) that s jontly normal wh the taste nnovaton ε, wh correlatons ρ s,pk = Corr(s, ε pk ) and ρ s,op = Corr(s, ε op ). For techncal convenence, we restrct ρ s,op = ρ ε ρ s,pk. 34 Condonal on the sgnal s, the taste nnovaton ε follows a jont normal dstrbuton wh mean and varance gven by Bayes rule n Appendx Pror Belefs and Learnng Estmaton of consumer belefs and learnng s focused on a sngle dmenson of usage: total peakcallng. We make ths restrcton because plans 1-3 always offer free off-peak callng and hence the choce data are not rch enough to allow us to dentfy belefs about off-peak callng. For smplcy, we assume that whle consumers are learnng about ther peak type µ pk over tme, there s no learnng about off-peak demand because consumers know ther off-peak types µ op. 35 µ pk Consumers learn about ther own peak-type µ pk s normally dstrbuted wh mean µ pk,t pror belefs are µ pk specfc trple { µ pk 1, µpk over tme. At date t, consumer beleves that and varance σ2 t : µ pk I,t N( µ pk,t, σ2 t ). At date 1, N( µ pk 1, σ2 1 ). Therefore, each new customer s characterzed by the ndvdual customer s true type µ and pror belef., µ op }. Together wh the populaton parameter σ 2 1, ths trple specfes each The populaton s descrbed by the jont dstrbuton of { µ pk 1, µpk, µ op }, whch we assume s a trvarate normal dstrbuton: As descrbed above, the margnal true type dstrbuton s (µ pk, µ op ) N (µ 0, Σ µ ). The margnal dstrbuton of nal pont estmates s µ pk 1 N( µpk 0, ( σpk µ ) 2 ). Fnally, correlatons between pont estmates and true types are ρ µ,pk = Corr( µ pk 1, µpk ) and ρ µ,op = Corr( µ pk 1, µop ). q pk At the end of each bllng perod, peak usage q pk /ˆq(vpk j ). When qpk = θ pk s realzed and consumers can nfer θ pk = = 0, we assume that consumers can observe the latent taste shock θpk. The latent shock provdes an unbased normal sgnal about µ pk and consumers update belefs accordng to Bayes rule (see Appendx 11.3). 36 Over tme consumers learn ther own types: µ pk,t 34 The sgnal s correlaton wh off peak tastes, ρ s,op, s not well dentfed because has ltle effect on plan choce due to unlmed off-peak callng on most plans. We restrct ρ s,op = ρ ε ρ s,pk because mples that E [s ε ] s ndependent of ε op. 35 Ths assumpton does not effect our endogenous-prce counterfactual smulatons because we assume free off-peak callng. 36 In fact, gven our assumpton that consumers know µ op, consumers can also nfer ε op from off peak usage whch s nformatve about µ pk because s correlated wh ε pk. We assume consumers only update belefs usng θpk and not ε op for two reasons. Frst, consumers are unlkely to pay attenton to off-peak usage when they are on a contract wh free off-peak calls. Second, we only assume consumers know µ op for smplcy as we cannot dentfy off-peak belefs. In realy, consumers are unlkely to know µ op so cannot actually nfer ε op. 20

22 converges to µ pk and σ 2 t converges to zero. ( µ pk Followng a month wh surprsngly hgh usage, a consumer ncreases hs estmate of hs type,t+1 > µpk ) and, hence, hs future demand. In the standard model, the only behavor change that mght result s a swch to a larger plan. In our model, a consumer mght also swch to a larger plan but, condonal on not swchng, would cut back on usage by choosng a hgher callng threshold (v pk,t+1 > vpk,t ) and beng more selectve about calls. 4.5 Bas Our model allows for based consumer belefs n two ways. Frst, we relax ratonal expectatons restrctons typcally placed on the jont dstrbuton of pont estmates µ pk 1 and true types µpk. Second, we allow consumers to msperceve the varance of the sgnal s and peak taste nnovaton ε pk. Ths flexbly n the model allows for overconfdence and two mean bases descrbed below. Overconfdence Overconfdence causes consumers to choose overly rsky plans and underestmate the lkelhood of payng overage charges. In our model, consumers are overconfdent n two respects. Frst, consumers are overconfdent because the precson of ther belefs about ther own types s mscalbrated. Let σ t denote the populaton standard devaton of true peak types condonal on a tme t pont estmate: σ t = SD[µ pk µ pk ].37 In our notaton, σ t s a consumer s uncertanty about her peak type n perod t. Let σ 1 = δσ 1. In the absence of an aggregate shock, ratonal expectatons mples that δ = 1 so that consumer uncertanty s correctly calbrated n perod 1: σ 1 = σ 1. We do not mpose ths assumpton. If δ < 1, then consumers exhb overconfdence: they overestmate the precson of ther nal pont estmates µ pk 1. Second, consumers are overconfdent because they underestmate the volatly n ther own tastes. 38 In partcular, we assume that consumers underestmate the uncondonal standard devatons of the sgnal s and peak taste nnovaton ε pk by a factor δ. As a result, whle consumers correctly understand the condonal mean E[ε pk s ] = ρ s,pk σ pk ε s, they underestmate the condonal standard devaton σ pk ε s = SD[εpk s ] by a factor δ, percevng to be σ pk ε s = δσpk ε s. (Belefs about ε op condonal on s are descrbed n Appendx 11.3.) If δ = 1, then consumers perceptons 37 In perod 1, σ 1 = σ pk µ 1 ρ2 µ,pk. For later perods see Appendx In an earler verson of the paper we dstngushed ths second form of overconfdence as volatly bas and estmated two dstnct δ parameters. Whle conceptually the two parameters were separately dentfed by the rate of plan swchng, n practce we found that the separaton of the two was very sensve to functonal form assumptons. Thus we now estmate only a sngle overconfdence parameter δ. Note that, as a result, overconfdence does not dsrupt learnng: consumers approprately weght ther prors and new nformaton when followng Bayes rule. 21

23 match realy. If δ < 1, however, then consumers are overconfdent and overestmate the precson of ther forecasts of peak taste nnovatons ε pk.39 Consumers plan choces and threshold choces depend on belefs about the dstrbuton of tastes θ. If δ < 1 then consumers are overconfdent and overestmate the precson of ther forecasts about both ther types µ pk and ther taste nnovatons ε pk. For both reasons, overconfdent consumers overestmate the precson of ther forecasts about peak tastes θ pk. When choosng a plan and a usage threshold at the begnnng of perod t, consumers beleve: 40 θpk I N ( ) µ pk θ, σ 2 θt. In our notaton, µ pk θ = µpk + ρ s,pkσ pk ε s (6) s a consumer s pont estmate of her peak taste, σ θt measures the objectve uncertanty surroundng, σ θt SD[θ pk but an overconfdent consumer s uncertanty s lower: σ θt = δσ θt. µ pk θ ] = σ 2 t + (1 ρ2 s,pk )(σpk ε ) 2, (7) Mean Bases There are two mean bases n our model. Both arse because we relax typcal restrctons on the populaton dstrbuton of true types µ pk µpk µ pk 1 N µpk 0 µ pk 0, and nal pont estmates µ pk 1 : (σ pk µ ) 2 ρ µ,pk σ pk µ σ pk µ ρ µ,pk σ pk µ σ pk µ ( σ pk µ ) 2. Frst, absent an aggregate shock, ratonal expectatons mples that an average ndvdual s nal pont estmate s an unbased estmate of her true type: µ pk 0 = µpk 0. We relax ths assumpton and defne b 1 µ pk 0 µpk 0. If b 1 0, then there s aggregate mean bas and consumers wll predctably choose plans whch are too small (b 1 < 0) or too large (b 1 > 0). Second, absent an aggregate shock, ratonal expectatons mples that every ndvdual (and not just the average ndvdual) has an unbased estmate of her true type. Lettng b 2 1 Cov(µpk, µ pk 1 ) V ar( µ pk 1 ) pk σµ = 1 ρ µ,pk σ pk µ, (8) 39 For tractably, we assume that consumers learn about means but not varances, so ths bas s persstent. 40 Off-peak belefs are gven n Appendx

24 can be shown that: [ µ pk 1 E µ pk ] µ pk 1 = b 1 + b 2 ( µ pk 1 µpk 0 ). Thus, nal pont estmates µ pk 1 are unbased f b 1 = b 2 = 0. We relax the restrcton b 2 = 0 (equvalently V ar( µ pk 1 ) = Cov(µpk, µ pk 1 )). Instead, we make the weaker restrcton mposed by Goettler and Clay (2011) that b 2 [0, 1 ρ 2 µ,pk ]. If b 2 > 0, then there s condonal mean bas and consumers overreact to ther own prvate nformaton, formng ndvdual pont estmates, µ pk 1, that dffer too much from the populaton average, µ pk 0. Condonal mean bas leads consumers to predctably choose plans that are too extreme. Nevertheless, as cleverly shown by Goettler and Clay (2011), the restrcton b 2 [0, 1 ρ2 µ,pk ] mples that both aggregate and condonal mean bases are consstent wh ratonal expectatons f there s an unobserved aggregate shock to mean tastes (µ pk 0 ).41 Connecton to Goettler & Clay (2011) The jont dstrbuton of true types (µ pk ) and pont estmates ( µ pk 1 ) s a prmve of our model. In contrast, Goettler and Clay (2011) derve ths jont dstrbuton from a common pror, an unobserved aggregate mean shock, and prvate sgnals. In our notaton, ths dervaton endogenously mposes the restrcton b 2 [0, 1 ρ2 µ,pk ]. By mposng ths restrcton exogenously, we therefore ensure that both aggregate and condonal mean bases are consstent wh ratonal expectatons gven an unobserved aggregate mean shock. 42 Moreover allows as specal cases both ratonal expectatons whout aggregate shocks (b 1 = b 2 = 0) and ratonal expectatons wh an aggregate shock drawn from a flat pror (Narayanan et al. s (2007) assumpton b 1 = 0 and b 2 = 1 ρ2 µ,pk ). 5 Identfcaton Parameters can be categorzed nto four groups: (1) the prce sensvy parameter β, (2) parameters governng belefs ( µ pk 0, ( σpk µ ) 2, δ, and ρ s,pk ), (3) the true dstrbuton of tastes (µ 0, ρ µ,pk, ρ µ,op, Σ µ, and Σ ε ), and (4) parameters related to swchng and qutng (P C and O). In Secton 5.1, we 41 The upper bound b 2 ρ 2 µ,pk does not affect our estmates but the lower bound b 2 0 resolves an dentfcaton problem. Absent the restrcton, σ pk µ and ρ µ,pk are not separately dentfed because there are two local maxma n the lkelhood functon wh smlar lkelhoods, one wh small σ pk µ and large ρ µ,pk (b 2 < 0) and another wh large σ pk µ and small ρ µ,pk (b 2 > 0). We prefer the maxma selected by the Goettler and Clay (2011) restrcton because s mean bases are consstent wh ratonal expectatons gven an aggregate shock and the alternatve provdes poor out-of-sample fs when we use a holdout sample. 42 Note that overconfdence about type µ pk cannot be ratonalzed by Goettler and Clay s (2011) model of an unobserved aggregate mean shock. Ther model also mposes the restrcton (whch we do not make) that σ 2 1 = Cov(µ pk, µ pk 1 )(1 ρ2 µ,pk)/ρ2 µ,pk. Ths corresponds to underconfdence about type µpk by a factor δ µ = (1 b 2) 1/

25 show that the prce sensvy parameter β s dentfed from plan 0 usage ndependently of other parameters. In Secton 5.2, we show that belefs about tastes θ are dentfed from plan choces condonal on β. We then argue that the dstrbuton of θ s dentfed from usage once β and belefs about θ can be used to map observed usage nto underlyng tastes. The dstrbuton of θ and belefs about θ jontly determne parameters governng bas such δ (overconfdence). Fnally, the rate of swchng and the rate of qutng dentfy, respectvely, the plan choce probably P C and the outsde opton O. 43 Below we expand on the dentfcaton of prce sensvy and belefs. 5.1 Prce Sensvy Parameter If consumers chosen thresholds (vj ) were known, the prce sensvy parameter β could be nferred from margnal prce varaton and the nduced varaton n ˆq(v k j ).44 Unfortunately, we requre β to calculate vj. We crcumvent ths problem by relyng on a source of margnal prce varaton for whch v j s known. Pror to fall 2003, vk j durng off-peak hours for plan 0 subscrbers. s 11 cents durng peak hours and 0 cents We break out the share of callng demand for weekday outgong-calls to landlnes mmedately before and after 9pm to help dentfy the prce sensvy parameter. The shock r 9pm = (r pk,9, r op,9 ) [0, 1] 2 captures the share of peak and off-peak callng demand that s whn 60 mnutes of 9pm on a weekday and s for an outgong call to a landlne. The dstrbuton of r k,9 for k {pk, op} s a censored normal, r k,9 = α k,9 + e k,9 r k,9 = 0 f r k,9 0 r k,9 f 0 < r k,9 < 1 1 f r k,9 1, where α k,9 s unobserved heterogeney and e k,9 s a mean-zero shock normally dstrbuted wh varance (σe k,9 ) 2 ndependent across, t, and k. We assume that α pk,9 s normally dstrbuted n the populaton wh mean µ pk,9 α and varance (σ pk,9 α ) The correlaton between usage and qutng also helps dentfy the outsde opton. The outsde opton wll be chosen predomnantly by those wh low usage who have a low value for cellular servce. Therefore f there s ltle correlaton between usage and qutng, suggests that most quters are swchng carrers rather than choosng the outsde opton. Ths n turn mples a low value for the outsde opton. 44 For nstance, there s one clean experment n the data n whch exstng plan 1 subscrbers were automatcally upgraded from 280 free mnutes to 380 free mnutes and ncreased ther usage n response by an average of 53 mnutes. (The 95% confdence nterval on ths ncrease s mnutes.) However, whout knowng how consumer thresholds were affected by the prce change, ths does not dentfy β. 24

26 Our dentfyng assumpton 45 for the prce sensvy parameter s that consumer s expected outgong callng demand to landlnes on weekdays s the same between 8:00pm and 9:00pm as s between 9:00pm and 10:00pm: [ E r pk,9 ] [ E θ pk ] [ = E r op,9 ] E [θ op ]. (9) In other words, we assume that the ncrease n observed callng to landlnes on weekdays mmedately after off-peak begns at 9pm s a prce effect rather than a dscontnuous ncrease n demand at 9pm. 46 As a result, equaton (9) mplcly defnes α op,9 Gven plan 0 prcng pror to fall 2003, θ op = q op as a functon of α pk,9 and θ pk and other parameters. = q pk / (1 0.11β). Moreover, the pre and post 9pm callng shares are always observed because callng thresholds are constant whn peak and whn off-peak hours: r op,9 = q op,9 /q op and r pk,9 solved for β as a functon of moments of the data: 5.2 Belefs β = [ E [ E q 9,pk q 9,op ] /q pk ] /q op = q pk,9 [ E q pk E [q op ] ] /q pk. Thus equaton (9) can be. (10) Next, consder dentfcaton of consumers pror belefs from plan choces. Choce data are que nformatve about belefs about peak usage, as llustrated by Fgure 7, but relatvely unnformatve about belefs about off-peak usage. Hence we assume consumers know ther own off-peak taste dstrbuton (ncludng µ op and σ op ε ). Pror to fall 2003, when off-peak callng s free on all plans, an ndvdual consumer s nal plan choce depends only on β (whch s already dentfed) and her belefs about θ pk 1, whch are descrbed by mean µ pk θ1 and varance σ2 θ1, as defned n equatons (6)-(7). Thus nal plan choce shares pror to fall of 2003 are suffcent to dentfy σ θ1 and the populaton dstrbuton of µ pk θ1. Inal choce shares n post fall 2003 data also ad dentfcaton, but requre a more complcated 45 Importantly, our model also assumes that peak and off-peak calls are not substutes. In realy consumers do delay calls from peak hours to off-peak. Thus the prce response measured at 9pm may overestmate consumers overall sensvy to the prce of peak callng (holdng off-peak prces fxed). Note, however, that other moments n the data lead to a more conservatve estmate of β than would be mpled from the 9pm usage jump alone. Substutng expectatons n equaton (10) wh ther emprcal analogs from the 6841 observatons where plan 0 s chosen (and both q pk > 0 and q op > 0), we compute β = 7.0. In comparson, our estmate of 2.7 s much lower. Moreover, unreported robustness checks show that our prmary results are robust to alternatve values of β. 46 We focus on calls to landlnes because the other party to the call pays nothng both before and after 9pm. The assumpton would be unreasonable for calls to or from cellular numbers snce such callng opportunes ncrease at 9pm when the calls become cheaper for the other party and the other party s more lkely to call or answer. 25

27 argument nvolvng belefs about off-peak tastes. σ ~ θ Plan 0 Plan 1 Plan 2 Plan µ~ θ1 Hstogram and fted Densy µ~ θ1 Fgure 7: Top panel: Plan choce as a functon of nal belefs { µ θ1, σ θ1 } mpled by the model evaluated at October-November 2002 prces gven β = 2. Bottom panel: Hstogram and fted normal dstrbuton over µ θ1 mpled by the assumpton σ θ1 = 80 and October-November 2002 new subscrber plan choce shares of 69%, 10%, 19%, and 2% for plans 0 to 3 respectvely. Inal plan choces place bounds on each ndvdual s pror belefs about the mean ( µ pk θ1 ) and varance ( σ 2 pk θ1 ) of ther frst taste shock, θ 1. Based on October-November 2002 prcng data (gnorng free n-network callng), Fgure 7 (top panel) shows plan-choce as a functon of pror belefs { µ pk θ1, σ2 θ1 } gven β = 2. Consumers jonng n October-November 2002 choose the plan correspondng to the shaded regon whn whch ther belefs le. Fgure 7 shows that plan 0 s chosen both by ndvduals wh low expectatons of usage (low µ pk θ1 ), as has the lowest fxed fee, and by ndvduals wh hgh uncertanty about usage (hgh σ θ1 ), as never charges more than 11 cents per mnute and s therefore a safe opton. Plan 1 s only chosen f σ θ1 s smaller than 107, an upper bound for σ θ1 mpled by plan 1 s observed posve share. 26

28 If we were to fx σ θ1 at any level below 107, ndvdual s plan choce bounds µ pk θ1 to an nterval. For example, the bounds are gven for σ θ1 = 80 by the vertcal lnes n Fgure 7. Combnng plan share data from customers who jon n October-November 2002 wh these bounds generates a hstogram over µ pk θ1 wh four bns, one for each of the four prcng plans. Snce we assume that µpk θ1 s normally dstrbuted, ths hstogram would then (over) dentfy the dstrbuton. The resultng hstogram and fted normal dstrbuton are both shown n the lower panel of Fgure 7 for the case σ θ1 = 80 and β = 2. The model dentfes σ θ1 as the value between 0 and 107 that generates the best f between the hstogram and the fted normal dstrbuton. Choosng a larger value for σ θ1 mples a hgher mean and a lower varance for the dstrbuton of µ pk θ1.47 Gven β = 2, the overall best f s at σ θ1 = 77. The precedng dentfcaton argument clearly bounds σ θ1 107 (gven β = 2) but then reles heavly on the functonal form assumpton that µ pk θ1 s normally dstrbuted for pont dentfcaton. Nevertheless, there s addonal nformaton n the data whch reduces relance on the functonal form assumpton: As prces change over tme, the bounds depcted n Fgure 7 change, so that plan share data from later dates provde addonal restrctons on σ θ1 and the dstrbuton of µ pk θ1. The exercse descrbed above dentfes consumer belefs about θ pk, ncludng uncertanty about nal tastes ( σ θ1 ) and the populaton mean (E[ µ pk θ1 ]) and varance (V ar[ µpk θ1 ]) of nal pont estmates of θ pk 1. In other words, we have dentfed the dstrbuton of the populaton over the space of Fgure 7 (and equvalently Fgure 9 n Appendx 11). As callng thresholds are a functon of belefs, we have thus also dentfed the dstrbuton of peak callng thresholds v pk j n the populaton. Next, gven β, the correlaton between plan choce and usage dentfes the correlaton between v pk j and usage. Ths gves us enough nformaton to nfer the dstrbuton of tastes θpk dstrbuton of usage q pk. Gven belefs about θ pk from the and s true dstrbuton, we can dentfy the populaton mean ( µ pk 0 ) and varance (( σ pk µ ) 2 ) of µ pk 1 as well as overconfdence (δ). Notce that (followng equatons (6)-(7)) µ pk 0 s equal to E[ µ pk θ1 ], ( σpk µ ) 2 s equal to V ar[ µ pk ] (ρ s,pk σ pk ε ) 2, and δ s equal to σ θ1 /σ θ1, where σ θ1 = (σ pk µ ) 2 (1 ρ 2 µ,pk ) + (1 ρ2 s,pk )(σpk ε ) 2. (11) Thus, for dentfcaton of µ pk 0, σpk µ, and δ, remans to show that σ pk ε, σ pk µ, ρ µ,pk, and ρ s,pk are dentfed. Now that we have enough nformaton to nfer the dstrbuton of θ from observed 47 Ths s because hgher uncertanty (hgher σ θ1 ) leads ndvduals who choose plans 1-3 to nsure themselves by choosng plans wh more ncluded mnutes. They are wllng to choose plan 2 over plan 1 and plan 3 over plan 2 at lower values of µ pk θ1. However, they are only wllng to choose plan 1 over plan 0 at hgher values of µpk θ1. 27

29 usage, the frst two parameters are straght forward. The whn and between ndvdual varances of θ pk correspond to (σ pk ε ) 2 and (σ pk µ ) 2, respectvely. Next, ρ µ,pk s dentfed from the correlaton between nal plan choces and long-run usage. We cover ρ s,pk next. The sgnal nformatveness, measured by correlaton ρ s,pk, s dentfed by the fracton of swches whch are nconsstent wh learnng based only on past usage. Whout a sgnal n the model (ρ s,pk = 0), any nal plan choce could be ratonalzed by an approprate pror belef µ pk 1. However, the model requres prvate sgnals (ρ s,pk > 0) to ratonalze swches that appear to be n the wrong drecton gven past usage. For example, suppose a customer wh hgh average usage chooses a small plan and subsequently experences a strng of overage charges. A low pror belef ( µ pk 1 small) could ratonalze the nal choce of a small plan. However, gven the assumpton of Bayesan learnng, no pror can smultaneously ratonalze the nal choce and a subsequent swch to an even smaller plan unless consumer belefs are nformed by more than past usage. 48 Gven ρ s,pk, the populaton mean and varance of nal pont estmates µ pk 1 and overconfdence are all dentfed. 6 Estmaton Procedure Ths secton brefly summarzes how the lkelhood s constructed and gves some detals of the estmaton procedure. A complete specfcaton of the lkelhood functon and estmaton procedure s provded n Appendx 13. An observaton n our lkelhood s a vector consstng of a consumer s plan choce and usage n each relevant category (peak, off-peak, 8-9pm, 9-10pm, n-network, and out-of-network) for a gven month. The lkelhood of an ndvdual s sequence of plan and usage choces has three groups of unobservables that must be ntegrated out: ndvdual specfc unobserved heterogeney, ncludng µ pk, µ op, and µ pk 1, prvate sgnals s, and..d. dosyncratc taste shocks ncludng ε and η. As the lkelhood functon does not have a closed-form expresson, we turn to Maxmum Smulated Lkelhood (Goureroux and Monfort 1993). To form the lkelhood, we ntegrate out some unobservables usng Monte Carlo smulaton, usng 400 shuffled draws from a Sobol quas random number generator. In partcular, we smulate out ndvdual specfc effects, prvate sgnals, and taste shocks ε k when usage n category k {pk, op} s zero. Gven a vector of draws, an ndvdual s lkelhood can be computed n closed-form usng the denses of the remanng structural errors, ncludng ε and η. To ensure that our lkelhood functon s smooth n the parameters, we draw s (and ε k when θ k s censored) by mportance samplng, as explaned n Appendx Occasonally we observe that a student does not swch plans when her current choce s domnated by a new plan offerng. Neher learnng nor prvate sgnals can explan ths - the parameter P C wll ratonalze ths behavor. 28

30 Computatonal dffcultes n the estmaton arse prmarly from three sources: Frst, s the hgh dmensonal unobserved heterogeney, whch requres many evaluatons of the lkelhood functon. Second s the computaton of v pk j, whch requres a nonlnear equaton solver to solve equaton (4) numercally. We must do ths for each smulaton draw, at each tme perod, for every ndvdual, at every choce that s not the outsde good or the two-part tarff, plan 0. Thrd, s that when we draw s, the mportance samplng method we employ requres that the drawn s ratonalzes observed choces. Ths means that for every choce we must compute the bounds on the set of s s where the utly for the chosen plan domnates other plans offered by the unversy. 49 consumer chooses plan 0, typcally the sgnal s wll be bounded above. For example, f 7 Results 7.1 Parameter Estmates We estmate 28 model parameters n total. The estmates and standard errors for the 21 parameters dscussed n the man text are shown n Table n-network callng are presented n Table 13 of Appendx 12. Estmates of the seven parameters related to Turnng to Table 2, the callng prce coeffcent β s 2.7, whch ndcates that a prce ncrease from 0 cents to 11 cents per mnute decreases usage by 30%. The next 9 parameters characterze the jont normal dstrbuton of consumers nal pont estmates, µ pk 1, and true types, µpk and µ op. The average consumer s pont estmate, µ pk 0, s estmated to be 216 mnutes, whle the average consumers true peak type, µ pk 0, s 272 mnutes. (Accountng for censorng of the latent shock, the average consumer beleves the mean of θ pk s 217 mnutes and the true mean s 294 mnutes.) The average off-peak type, µ op 0, s larger than the peak value at 419 mnutes. (The model predcts an even larger gap between peak and off-peak usage due to consumer prce sensvy.) The populaton standard devatons of µ pk 1, µpk and µ op ( σ pk µ, σ pk µ and σ op µ ) are 210, 148, and 421 mnutes respectvely. The estmates of ρ µ,pk and ρ µ,op ndcate that nal belefs about peak type, µ pk 1, are weakly posvely correlated wh the true types µpk and µ op. The correlaton between the peak and off peak type µ k s If a student qus, then ther subsequent plan choce s unobserved and s can le anywhere on the real lne. 50 We compute standard errors usng the subsamplng method of Pols and Romano (1994). We frst draw 200 datasets, each consstng of a 10% subsample of ndvduals chosen randomly whout replacement. We estmate our model on each dataset, and compute the standard error as the standard devaton of the estmates across datasets, multpled by a scalng factor. 29

31 Table 2: Parameter Estmates Coeff. Descrpton Est. Std. Err Coeff. Descrpton Est. Std. Err β Prce Sensvy (0.437) σ op ε µ pk 0 E[µ pk 1 ] (19.933) ρ ε Corr(ε pk µ pk 0 E[µ pk µ op 0 E[µ op σ pk µ SD[µ pk ] (22.904) µ pk,9 α σ pk µ SD[µ pk ] (9.201) σ pk,9 α σ op µ SD[µ op ] (39.078) σ pk,9 e Corr(µ pk 1, µpk ) (0.064) σ op,9 e Corr(µ pk 1, µop ρ µ,pk ρ µ,op ρ µ σ pk ε SD[ε op ] (9.451) ) (0.021), εop ] (11.129) ρ s,pk Corr(s, ε pk ) 0.41 (0.025) ] (31.066) δ Overconfdence (0.021) Corr(µ pk SD[ε pk Log-lkelhood E[α pk,9 ] (0.002) SD[α pk,9 SD[e pk,9 ] (0.003) ] (0.003) SD[e op,9 ] (0.004) ) (0.012) Plan Consderaton (0.003), µ op ) (0.051) Outsde Good Utly (0.992) ] (10.082) The last row of column 1 and the frst three rows of column 2 descrbe the dstrbuton of the sgnal s and the error term ε. The standard devatons of the error terms, σ pk ε and σ op ε, are 248 and 325 mnutes for peak and off-peak usage, respectvely, and ther correlaton, ρ ε, s Notce that the varance of the peak usage error s hgher than the varance of µ pk, ndcatng that more of the varaton n peak usage can be attrbuted to monthly volatly than the consumer-level fxed effect. The correlaton between the sgnal and the peak error, ρ s,pk, s 0.41, ndcatng that a substantal porton of the upcomng month s taste shock s predctable by the consumer. Contnung down column 2, our estmate of δ s 0.38, whch s consstent wh strong consumer overconfdence. The next four parameters of column 2 descrbe consumers tastes for 8:00 pm to 10:00 pm usage. The low value of µ pk,9 α ndcates that outgong 8:00 to 9:00 pm landlne usage s small as a fracton of total peak usage, whch s consstent wh the data. Parameter σ pk,9 α captures ndvdual specfc heterogeney n the fracton of peak callng fallng between 8:00 pm and 9:00 pm, whle σ pk,9 e and σ op,9 e capture dosyncratc volatly. 51 Shown next s the plan consderaton parameter, P C, whch we estmate to be 0.06, ndcatng that consumers seldom look at prces. Below that s the outsde good utly, O, estmated to be 51 Recall that we do not need to estmate a mean or ndvdual specfc varance for off peak 9:00 pm to 10:00 pm usage because we restrct average peak and off-peak tastes for 8:00 pm to 10:00 pm usage to be equal n equaton (9). 30

32 1.16 (although ths estmate s mprecse). Compared to average utles of about 90, ths low estmate of the outsde good utly mples that consumers prefer nsde goods to the outsde good by a large margn and ratonalzes the low qu rate observed n the data. We report the f of our estmated model to the data n Appendx 13 (Table 14 and Fgure 12). Our model does a good job of ftng plan choce shares and the rate of plan swchng. The model generally matches observed usage moments but has some dffculty ftng the exact shape of the usage densy, whch s hghest near zero and smoothly drops as usage ncreases. Our censored normal specfcaton produces a hump near zero that s not replcated n the data. A more flexble usage specfcaton, such as a mxture of normals, mght f the observed usage dstrbuton better. 7.2 Bases and Learnng Returnng to consumer belefs, we dsplay estmates of bas parameters n Table 3, ncludng those that are functons of our estmated parameters. Our estmate of δ, 0.38, s consstent wh strong overconfdence. Whn our model, ths mples that consumers underestmate the nose n ther own forecasts about ther future tastes for callng by 62%. In partcular, the standard devaton of pk consumers nal uncertanty about θ 1, δσ θ1, s 103 mnutes, 62% less than the correctly calbrated σ θ1 = 269 mnutes. Ths leads consumers to systematcally choose overly rsky plans such as plan 1. (Note that f consumers are rsk averse rather than rsk neutral then ths estmate s a lower bound on the magnude of overconfdence.) Table 3: Consumer Bases Bas Parameter Unbased Estmate Std. Err. Fndng Choose overly Overconfdence δ δ = δ < 1 rsky plans Aggregate Mean Bas b 1 b 1 = b 1 < 0 small plans Condonal Mean Bas b 2 b 2 = b 2 > 0 extreme plans Our model attrbutes overconfdence equally to two factors. Frst, the standard devaton of consumers nal uncertanty about ther type, δσ 1, s 56 mnutes, 62% less than the correctly calbrated σ 1 = 146 mnutes. Second, consumers perceve the standard devaton of monthly volatly n peak usage to be δσ pk ε σ pk ε = 248 mnutes. = 95 mnutes, whch s 62% less than the correctly calbrated Next, b 1 s 55, consstent wh negatve aggregate mean bas. Whn our model ths mples that the average consumer underestmates her peak type µ pk by 55 mnutes and wll systematcally 31

33 choose too small a plan. Fnally, the posve estmate of b 2 s consstent wh strong condonal mean bas. 52 Whn our model ths mples that consumers choose plans whch are too extreme and wll moderate ther plan choces over tme. Our model accounts for learnng, whch means that mean bases dsspate over tme. Our smulaton predcts that after one year, aggregate mean bas dmnshes 40% (b 1 ncreases from -55 to -33) and condonal mean bas dmnshes 33% (b 2 decreases from 0.86 to 0.58). 7.3 Fxed-Prce Counterfactual: Impact of Based Belefs Before proceedng to smulate endogenous prce changes n Secton 8, we brefly smulate the change n annual frm profs, consumer welfare, and total welfare that results from debasng consumers whle holdng observed prces fxed (Table 4). We construct these counterfactual smulatons at our data n the sense that we hold fxed the number of consumers, and when consumers enter and ex the data set. Annual surplus changes are measured n dollars per student averaged over the two year perod that they are observed. We assume margnal cost s $0.02 per mnute based on a calbraton descrbed n Secton 8. The frst three columns of Table 4 show the welfare effects when students face unversy prces, whle the last three columns show the welfare effects when consumers face publcly avalable prces. Table 4: Annual per-student change n surpluses from bas elmnaton (fxed prces) Unversy Plans Publc Plans Profs Cons. Welf. Total Welf. Profs Cons. Welf. Total Welf. Welfare at Estmates δ = No Bases Annual Changes n surpluses (profs, consumer welfare, and total welfare) are measured n dollars per student averaged over the 2 year sample perod. Changes are relatve to surpluses at estmates n row 1. The frst row of Table 4 shows profs, consumer surplus, and socal welfare at our estmated parameters. The second two rows of Table 4 show the mpact of removng bases: Row 2 shows the mpact of removng overconfdence and row 3 shows the mpact of removng all bases. In all cases, debasng consumers rases consumer surplus and lowers frm profs because debased consumers make better choces and pay fewer overage charges. Gven publc prces, consumer surplus ncreases by $76 when overconfdence s removed and by $91 when all bases are removed. Frm profs fall 52 In the context of grocery home delvery servce, Goettler and Clay (2011) also fnd b 1 < 0 and b 2 > 0. 32

34 by a smlar magnude and hence changes n total welfare are relatvely small Endogenous-Prce Counterfactual: Bll-Shock Regulaton 8.1 Endogenous Prce Calbraton To calculate endogenous equlbrum prces we ntroduce a smple supply model: We assume that there are three symmetrc frms, equlbrum s symmetrc statc Nash n prces, overage rates are at most ffty cents, and each frm offers a menu of three plans. 54 We assume that frms pay a monthly fxed cost F C of servng a customer account, a per-mnute margnal cost c to carry peak calls, and no cost for off-peak calls when capacy constrants are slack. To smulate equlbrum prces s mportant to accurately capture the degree of frm market power and frm costs n the ndustry. In our model, log-errors gve consumers dosyncratc frm preferences (whch mght result from dfferences n network coverage or phone avalably) that create market power. The degree of market power s governed by the log-error varance, whch s normalzed to one n our estmaton. Now, however, we adjust the model and weght the log error (η f ) n consumers utly functons by the factor 1/λ (revsng equatons (1) and (5)). We calbrate λ and frm margnal costs c usng supply-sde prce data: We select the values of λ and c that best ratonalze observed prces of the major frms condonal on our demand estmates. Our algorhm, whch s descrbed n Appendx 15, calbrates λ to be 0.03 and peak margnal cost c to be 2 cents per mnute. 55 Fnally, we assume that monthly fxed costs are F C = $15 per customer based on ndustry fnancal reports. 56 In an unreported specfcaton, we normalzed the outsde good utly to zero and estmated λ. The estmate of λ s 0.06 compared to our calbrated value of We use the value calbrated 53 As margnal costs are small, total welfare ncreases when callng ncreases and vce-versa. Holdng plan choces fxed, de-basng consumers reduces callng because consumers more fully apprecate the rsk of overages. Gven publc prces, however, total welfare ncreases when consumers are fully de-based because de-based consumers (who don t have access to unversy plan 0) swch to larger plans wh more ncluded mnutes. 54 Whout an upper bound on overage rates, the combnaton of based belefs and nattenton lead to mplausbly hgh overage-rate predctons. Frms are not actually symmetrc but we lack the data to dentfy frm dfferences. A new consumer chooses among three carrers and no-servce whereas an exstng consumer who consders swchng chooses among her current carrer, a randomly chosen outsde carrer, and no servce. 55 A margnal cost of 2 cents per mnute s reasonable, beng posve but small. Hausman (2000) estmates margnal cost to be 5 cents per mnute when takng nto account some costs of ncreasng network capacy. 56 T-moble and AT&T fnancal reports dsclose that n 2003 ther costs of acqurng a customer, or Cost Per Gross Add (CPGA) were $329 and $377 respectvely (T-Moble 2004, AT&T Wreless Servces, Inc. 2003). A substantal porton of these costs are handset subsdes. Averaged over a 24 month contract perod, these correspond to monthly fxed costs of $14 to $16 per month. 33

35 from observed prces because the estmated value s not well dentfed by our demand data and mples too ltle market power to explan observed prces. 57 Before proceedng, we make two addonal comments on our calbraton approach. Frst, one potental problem s that our demand estmates were made condonal on λ = 1, but dfferent values of λ mght produce dfferent demand estmates. Fortunately, our demand estmates are relatvely nsensve to λ, whch we dscuss n Appendx 15. Second, n prncple we could have estmated λ and the other parameters jontly by usng constraned maxmum lkelhood and constranng observed prces to be optmal at the estmated parameters. We avoded ths approach because we prefer only to mpose our supply-sde structural assumptons (that competon s symmetrc statc Nash n prces and that our student populaton s representatve) only when they are necessary n the endogenous-prce counterfactual smulatons Modelng bll-shock alerts In our bll-shock regulaton counterfactual, consumers are nformed when ther usage reaches Q j, ther allotment of free mnutes. (Alerts are not applcable to two-part tarffs wh constant margnal prces.) In response to ths new polcy, a consumer s usage rule changes: A consumer wll accept all calls valued above v pk j untl she exhausts her ncluded mnutes. After that pont, she only accepts calls valued above p j. Because the consumer adjusts her callng threshold upon makng Q j calls, the optmal nal threshold v pk j s lower than that characterzed by equaton (4). (The reducton n v pk j s never more than about $0.025.) The threshold falls slghtly because the consumer can afford to make more calls pror to an alert (usng up more ncluded mnutes n a low demand month) safe n the knowledge that a bll-shock alert wll protect her from a large bll n a hgh demand month. Appendx 11.2 descrbes expected utly and characterzes v pk j 8.3 Counterfactual Smulaton Results under bll-shock regulaton. Table 5 shows the results of our endogenous-prce counterfactual smulatons. Column 1 shows predcted plan prces and welfare outcomes under our estmated demand parameters. (These are the prces whch were calbrated to match publcly avalable callng plans, whch are reported n Table 7 n Appendx 10 for October 2003.) The model predcts that frms offer a menu of three-part 57 We observe neher frm market shares on campus nor the alternate frms chosen by students qutng unversy plans. Hence only the qutng rate s avalable to dentfy utly of the outsde good, average utly of unversy plans relatve to other frms, and λ. Outsde prce varaton s too lmed to separately dentfy λ from the outsde good utly. In our man specfcaton we assume λ = 1 and frm symmetry to dentfy the outsde good utly. 58 In realy, unversy plans are not symmetrc to other carrer offerngs and our populaton of students s lkely overweghted towards new and low-volume users relatve to the overall populaton. 34

36 tarffs wh monthly fees of $42.88, $48.64, and $58.12, correspondng allowances of 216, 383, and 623 peak mnutes, and the maxmum overage rate of $0.50 per mnute. Table 5: Effect of Bll-Shock Regulaton & Removng Bases wh Endogenous Prces Est, Bll Shock Est (fxed prces) Est, Bll Shock δ = 1 No Bases (1) (2) (3) (4) (5) Plan 1 M Q p Share Plan 2 M Q p N/A N/A Share Plan 3 M Q p Share Outsde Good Share Usage Overage Revenue Annual Prof Annual Cons Welfare Annual Total Welfare Annual Prof Annual Cons Welfare Annual Total Welfare All welfare and prof numbers are expressed n dollars per customer per year. Because the counterfactuals n columns 4 and 5 produced two part tarffs, bll-shock regulaton has no addonal effect. We smulate 10,000 consumers for 12 months. Column 2 of Table 5 holds constant the predcted prces from column 1 but mposes bll-shock regulaton. Holdng prces constant, bll-shock alerts help all customers reduce overages and also gves 4% of customers the comfort to choose a smaller plan, as they know that the alerts wll protect them from overages. (In fact wh an overage rate of $0.50 per mnute and prce sensvy parameter β = 2.7, consumers stop almost all callng after recevng an alert and pay neglgble overage fees.) Avoded overage charges and smaller plan choces correspond both to reduced blls 35

37 and to reduced callng. Average annual welfare falls by $93 per student because margnal costs are only 2 cents and, hence, the reduced callng hurts consumers more than lowers frm costs. 59 Reduced blls drve annual frm profs down by $196 per student but reduced callng means average annual consumer surplus rses by only $103. Column 3 of Table 5 mposes bll-shock regulaton but allows frms to adjust prces. Frms adjust prces n several ways to mgate lost overage revenues. Frst, frms adjust prces by lowerng overage fees to $0.17 (plan 1) or $0.12 (pans 2-3), whch encourages consumers to make some calls even after recevng a bll-shock alert. Absent bll-shock alerts, nattentve consumers use callng thresholds between $0 and $0.15 per mnute (see Appendx 11.1). At the estmated prce sensvy parameter of β = 2.7, ths mples nattentve consumers make 60 to 100 percent of calls whether or not they have exhausted ther allowance of peak mnutes. Wh bll-shock alerts, however, an overage rate of $0.50 essentally stops consumers makng all calls after recevng an alert and generates neglgble overage fees. By reducng overage rates to $0.17 or $0.12, frms ensure that consumers contnue to make 54 or 68 percent of calls after recevng an alert. Thus lowerng overage rates prevents the complete collapse of overage revenue. Next, frms adjust prces by lowerng allowances of peak mnutes, whch helps offset reduced overage revenues n two ways. Frst overages are trggered at lower usage levels and second causes consumers to choose larger plans (the share of plan 3 ncreases from 14% to 40%), and hence rases average monthly fees. Fnally, frms ncrease the plan 3 monthly fee by $10 and make smaller changes to monthly fees of plans 1 and 2. The net effect s that annual overage fees per customer fall to $152 (rather than to $2 whout prce adjustment) and annual profs actually rse by $7 per person. 60 (Note that an addonal counterfactual smulaton predcts that a frm whch ntroduced bll-shock alerts unlaterally would lose $165 per customer annually, explanng why frms dd not offer bll-shock alerts pror to regulaton.) In response to bll-shock alerts and prce changes, 2% of consumers (largely plan 1 customers) swch to the outsde opton. Ths s not because plan 1 becomes a worse deal. In fact, the monthly fee on plan 1 s reduced suffcently that the average plan 1 consumer s better off by $13 per year by stayng on plan 1. Unfortunately, bas causes consumers to undervalue both bll-shock alerts 59 Holdng average total callng constant, bll-shock alerts reduce welfare by nducng consumers to call more n low demand months (by choosng a lower v pk j ) and to call less n hgh demand months (when recevng an alert). Ths reduces the average value of placed calls. In addon, average total callng s reduced because based consumers choose too low a callng threshold v pk j, but correct ther behavor followng a bll-shock alert. 60 The fact that regulaton lmng revenues from one set of fees may lead frms to rase other fees to compensate has been dubbed the waterbed effect. Genakos and Vallett (2011) document the waterbed effect followng Europe s ntroducton of caps on moble call termnaton charges. 36

38 and reduced overage rates. Overconfdence causes consumers to underestmate the chance of hgh usage and hence underestmate the lkelhood of payng a reduced overage rate or recevng a bllshock alert. As a result, the average plan 1 customer perceves hmself to be worse off by $137 per year by stayng on plan 1. Thus the outsde opton becomes a more competve alternatve and gans share. Gans n the outsde good share correspond to lost profs, lost socal surplus, and lost consumer surplus. Addonal losses to socal surplus occur because, whle those who mantan servce make almost the same number of calls on average (239 rather than 240 mnutes monthly) they make on average lower value calls than before. Ths s because those who reman on the same plans reduce callng n response to lower allowances and bll-shock alerts whle those who swch up to plan 3 ncrease callng n response to unambguously lower margnal prces. Those cuttng back forgo relatvely hgh value calls whle those callng more add relatvely low value calls and average value falls. Combnng the shft to the outsde good wh the shft to lower value calls, bll-shock regulaton lowers annual socal surplus by $26 per person. The fact that frm profs ncrease overall reflects the fact that profs per customer ncrease for those that mantan servce, n large part from ncreasng the average monthly fee pad. As a result, average annual consumer surplus falls by $33 per person. The $33 reducton n annual consumer surplus from bll-shock regulaton reported n Column 3 of Table 5 s an average effect. The left panel of Fgure 8 shows a hstogram consumer utly changes due to the regulaton. The dstrbuton s rght skewed meanng that there s a tal of ndvduals who benef substantally. Moreover, as we assume consumers are rsk neutral, the predcted change n consumer surplus depends on changes n average blls but not on changes n bll dsperson. The rght panel of Fgure 8 shows that bll-shock regulaton leads to an ncrease n small overages below $50 but a decrease n large overages above $50. Regulators may feel that reducng the ncdence of large overages justfes reduced market coverage, less effcent callng, and hgher frm margns. Turnng to columns 4 and 5 of Table 5, we nvestgate the consequences of debasng consumers. Column 4 shows the effect of elmnatng overconfdence. In column 4, the frm fnds optmal to offer only two two-part tarffs: a $0.13 per mnute plan and an unlmed talk plan for monthly fees of $42.32 and $70.63, respectvely. Column 5 shows the effect of elmnatng all bases (except myopc plan choce). In ths case, the menu looks smlar to column 4 but plan 1 s more smlar to the unlmed talk plan, havng a lower $0.07 rate per mnute and a hgher monthly fee of $ Comparng prcng n columns 4 and 5 to columns 1-3, notce that three-part tarffs dsappear when overconfdence s elmnated they are only offered to explo overconfdence. Prcng n column 4 can be understood as a response to condonal mean bas. Estmated condonal mean 37

39 Densy Densy Unregulated Bll Shock Reg Annual Utly Change from Bll Shock Monthly Overage Fee ($) Fgure 8: Left panel: Hstogram of changes n consumer utly due to bll-shock regulaton. Rght panel: Densy of overage fees wh and whout bll-shock regulaton (excludng atoms at zero). bas mples that those who choose plan 1 underestmate ther usage (so that an overage rate above margnal cost s optmal) but those who choose plan 2 overestmate ther usage (so that chargng an overage rate below margnal cost s optmal) (Grubb 2009). Prcng n column 5 s smlar to that n column 4 because de-based consumers stll make plan choces myopcally. In our model, myopa has a smlar effect to condonal mean bas. Ths s because myopc consumers who receve a large sgnal s 1 wll choose a large plan talored to hgh expected usage n the frst month. Over tme, however, nerta (P C = 0.06) wll keep them on the same large plan whle ther future sgnals and usage revert downwards toward the mean. Smlarly, those who receve small sgnals wll choose plans approprate for ther frst month s low usage but too small for ther long-run usage. As a result, prcng n column 5 shows qualatvely the same dstortons away from margnal cost as column 4 but the dstortons are smaller. Somewhat surprsngly, whle elmnatng all bases rases total welfare, elmnatng overconfdence alone lowers total welfare. It s straght forward to see why total welfare s hgher n column 5 than column 4. Ths s because margnal prces are closer to margnal cost n column 5 and so callng choces are more effcent. It s less clear why total welfare s lower n column 4 than column 1. The reason s that the margnal prces n column 4 ($0.13 and $0.00) are on average farther from margnal cost ($0.02) than are the callng thresholds (v pk j ) nduced by the prce menu n column 1. (Fgure 9 n Appendx 11.1 depcts the callng thresholds nduced by observed prces.) Because three-part tarff prcng s drven by overconfdence, elmnatng also elmnates three- 38

40 part tarff prcng. Thus bll-shock regulaton has no effect whout overconfdence. Moreover, the fact that bll-shock regulaton s less mportant for unbased consumers does not depend entrely on the elmnaton of three-part tarffs. In a fnal counterfactual, we smulate the effect of bll-shock regulaton whle holdng observed publc prces constant. In ths smulaton, bll-shock regulaton benefs consumers wh estmated bases by $25 per year but benefs debased consumers by only $1 per year. Debased consumers are affected less by bll-shock alerts because (even holdng prces constant) they make better plan choces that lead to lower ncdence of overages. A weakness of the counterfactual smulaton s that at our estmates (column 1), the upper bound on overage rates of $0.50 s bndng. Whout ths restrcton, our predcted overage rates would be far too hgh. Comparson to columns 3 and 4 shows that hgh overage rates result from the combnaton of overconfdence and nattenton. The fact that we overpredct overage rates absent our restrcton suggests one of three thngs. (1) We may be mssng a countervalng force lmng overage rates such as lmed lably, rsk-averson, or regulatory threat. (2) Complete nattenton of all consumers may be too extreme an assumpton. (3) Our estmate of overconfdence may be too hgh. The forces n (1) we om for prmarly to avod addonal complexy. In unreported analyss we found that addng lmed lably at $100 per month to the supply model restrcts overage rates to smlar levels charged for roamng. A hard $100 monthly lm on lably s lkely too extreme. However, when overage fees enter hundreds of dollars customer servce costs and ex post renegotaton wll start to lm the true value recovered. Complete nattenton s the rght assumpton for our sample because our students could not check ther balances but had to mentally keep track of callng. In the general populaton balance enqures are feasble so s lkely some customers are attentve. Smlarly, could be that overconfdence s weaker among the general populaton than among students. Eher factor could explan lower overage rates. Emprcally, overage rates range from $0.35 to $0.50, whch s why we chose $0.50 as an upper bound n our smulatons. In unreported analyss we conducted addonal smulatons wh $0.35 and $0.75 lms on overage fees and found our results to be robust. For nstance, wh overage rate caps of $0.35 and $0.75, the model predcts that bll-shock regulaton wll reduce annual consumer surplus per person by $27 and $32 respectvely, compared to $33 wh the $0.50 overage rate cap. 9 Concluson We specfy and estmate a model of consumer cellular-phone plan and usage choces. We dentfy the dstrbuton of consumer tastes from observed usage and consumers belefs about ther future 39

41 usage from observed plan choces. Comparng the two we fnd that students usage and plan choces are consstent wh based usage forecasts. In partcular, students systematcally choose overly rsky, overly small, and overly extreme plans. These choces are consstent wh underestmatng nose n forecasts (overconfdence), overly low forecasts (negatve aggregate mean bas), and overly extreme forecasts (condonal mean bas). Note that whle we mantan the bas nterpretaton throughout the paper, there are other nterpretatons for some bases. For nstance, as shown by Goettler and Clay (2011), the mean bases n our model are consstent wh ratonal expectatons and an unobserved aggregate shock to average tastes. Fnally we reerate that our sample conssts of students who may not be wholly representatve. We conduct counterfactual smulatons n whch we (a) elmnate bases and (b) quantfy the welfare mpact of mplementng bll-shock regulaton n Our model predcts that elmnatng bases ncreases consumer welfare, by $91 annually per consumer holdng observed publc prces fxed, but only by $4 annually per consumer accountng for frms endogenous prcng response. If observed prces do not respond to bll-shock regulaton, then the average consumer wll benef by $25 annually. Ths fndng s reversed when frms optmally respond to bll-shock regulaton. Although consumers avod overage fees, frms rase average monthly fees and average consumer surplus falls by $33 annually. Ths loss s an average and many consumers benef from the polcy. Moreover the ncdence of overages over $50 falls substantally. Fnally, we fnd that bll-shock regulaton would have ltle to no effect f consumers were unbased. For a number of reasons, our predctons should be appled to the bll-shock agreement mplemented n 2013 wh cauton. For nstance, consumers today are more experenced and may be less based. Moreover, text messagng and data plans were beyond the scope of our study. Nevertheless, there are some robust predctons that can be appled wh more confdence: Endogenous prce changes should make frm profs robust to bll-shock regulaton, thereby undermnng the benefs to consumers. Our evaluaton of bll-shock regulaton could be nsghtful n other relevant contexts as well. For nstance, n 2009 US checkng overdraft fees totalled more than $38 bllon and have been the subject of new Federal Reserve Board regulaton (Martn 2010, Federal Reserve Board 2009). Convncng evdence of consumer nattenton (Stango and Znman 2009, Stango and Znman 2012) suggests that ths fee revenue would be dramatcally curtaled f the Fed mposed s own bll-shock regulaton by requrng deb card processng termnals to ask users $35 overdraft fee apples, contnue Yes/No? before chargng fees. Our counterfactual shows that n the cellular context consumers are nevertheless made worse off after accountng for all prce changes. 40

42 References Ackerberg, Danel A., Advertsng, Learnng, and Consumer Choce n Experence Good Markets: An Emprcal Examnaton, Internatonal Economc Revew, 2003, 44 (3), Altschul, Mchael F., Chrstopher Guttman-McCabe, and Bran M. Josef, Comments of CTIA - The Wreless Assocaton, January 10th d= Ascarza, Eva, Anja Lambrecht, and Naufel J. Vlcassm, When Talk s Free : The Effect of Tarff Structure on Usage under Two- and Three-Part Tarffs, SSRN elbrary, Ater, Ita and Vard Landsman, Do Customers Learn from Experence? Evdence from Retal Bankng, Management Scence, Artcles n Advance, pp. 1-17, AT&T Wreless Servces, Inc., Form 10-K, / /v96781e10vk.htm, accessed May 31, Berry, Steven, James Levnsohn, and Arel Pakes, Automoble Prces n Market Equlbrum, Econometrca, 1995, 63 (4), Borensten, Severn, To What Electrcy Prce Do Consumers Respond? Resdental Demand Elastcy Under Increasng-Block Prcng, Prelmnary Draft Aprl Cameron, A. Coln and Pravn K. Trved, Mcroeconometrcs: Methods and Applcatons, New York, NY: Cambrdge Unversy Press, Cardon, James H. and Igal Hendel, Asymmetrc Informaton n Health Insurance: Evdence from the Natonal Medcal Expendure Survey, The RAND Journal of Economcs, 2001, 32 (3), Chng, Andrew, Tüln Erdem, and Mchael P. Keane, The Prce Consderaton Model of Brand Choce, Journal of Appled Econometrcs, 2009, 24 (3), Crawford, Gregory S. and Matthew Shum, Uncertanty and Learnng n Pharmaceutcal Demand, Econometrca, 2005, 73 (4), CTIA - The Wreless Assocaton, CTIA-The Wreless Assocaton, Federal Communcatons Commsson and Consumers Unon Announce Free Alerts to Help Consumers Avod Unexpected Overage Charges, October Year-End 2010 Top-Lne Survey Results, Techncal Report CTIA_Survey_Year_End_2010_Graphcs.pdf. DeGroot, Morrs H., Optmal Statstcal Decsons, New York: McGraw-Hll, DellaVgna, Stefano and Ulrke Malmender, Contract Desgn and Self-Control: Theory and Evdence, The Quarterly Journal of Economcs, 2004, 119 (2),

43 Deloney, Amala, Lnda Sherry, Susan Grant, Parul P. Desa, Chrs M. Rley, Matthew F. Wood, John D. Breyault, Jessca J. Gonzalez, and Benjamn Lennett, Comments of the Center for Meda Justce, Consumer Acton, Consumer Federaton of Amerca, Consumers Unon, Free Press, Meda Access Project, Natonal Consumers League, Natonal Hspanc Meda Coalon and New Amerca Foundaton Open Technology Inatve n response to notce of proposed rulemakng., January 10th Dutang, Chrstophe and Petr Savcky, randtoolbox: Generatng and Testng Random Numbers., R package verson Enav, Lran, Amy Fnkelsten, Iulana Pascu, and Mark Cullen, How General Are Rsk Preferences? Choces under Uncertanty n Dfferent Domans, Amercan Economc Revew, Forthcomng. Elaz, Kfr and Ran Spegler, Contractng wh Dversely Nave Agents, The Revew of Economc Studes, 2006, 73 (3), and, Consumer Optmsm and Prce Dscrmnaton, Theoretcal Economcs, 2008, 3 (4), Erdem, Tüln and Mchael P. Keane, Decson-Makng under Uncertanty: Capturng Dynamc Brand Choce Processes n Turbulent Consumer Goods Markets, Marketng Scence, 1996, 15 (1), Federal Reserve Board, Federal Reserve announces fnal rules prohbng nstutons from chargng fees for overdrafts on ATM and one-tme deb card transactons, Press Release November GAO, Telecommuncatons: FCC Needs to Improve Oversght of Wreless Phone Servce, Government Accountably Offce Report GAO-10-34, Genakos, Chrstos and Tommaso Vallett, Testng the Waterbed Effect n Moble Telephony, Journal of the European Economc Assocaton, 2011, 9 (6), Goettler, Ronald L. and Karen B. Clay, Tarff Choce wh Consumer Learnng and Swchng Costs, Journal of Marketng Research, 2011, 48 (4), and Ron Shachar, Spatal Competon n the Network Televson Industry, The RAND Journal of Economcs, 2001, 32 (4), Goureroux, Chrstan and Alan Monfort, Smulaton-based nference : A survey wh specal reference to panel data models, Journal of Econometrcs, 1993, 59 (1-2), Grubb, Mchael D., Sellng to Overconfdent Consumers, Amercan Economc Revew, 2009, 99 (5), , Consumer Inattenton and Bll-Shock Regulaton, MIT Sloan Research Paper No Avalable at SSRN: and Matthew Osborne, Cellular Servce Demand: Based Belefs, Learnng, and Bll Shock, MIT Sloan Research Paper No Avalable at SSRN: ssrn

44 Hajvasslou, Vassls A. and Paul A. Ruud, Classcal Estmaton Methods for LDV Models Usng Smulaton, n R.F. Engle and Danel L. McFadden, eds., Handbook of Econometrcs, Volume IV, Amsterdam: North-Holland, Handel, Benjamn, Adverse Selecton and Swchng Costs n Health Insurance Markets: When Nudgng Hurts, Amercan Economc Revew, Forthcomng. Hausman, Jerry, Effcency Effects on the U.S. Economy from Wreless Taxaton, Natonal Tax Journal, 2000, 53 (3), Herweg, Faban and Konrad Merendorff, Uncertan Demand, Consumer Loss Averson, and Flat- Rate Tarffs, Journal of the European Economc Assocaton, 2013, 11 (2), Hoffman, Mchell and Stephen Burks, Tranng Contracts, Worker Overconfdence, and the Provson of Frm-Sponsored General Tranng, Workng Paper. Horrgan, John and Ellen Satterwhe, Amercan s perspectves on early termnaton fees and bll shock, Federal Communcatons Commsson Consumer Survey DOC A1, http: //hraunfoss.fcc.gov/edocs_publc/attachmatch/doc a1.pdf. Iyengar, Raghuram, Asm Ansar, and Sunl Gupta, A Model of Consumer Learnng for Servce Qualy and Usage, Journal of Marketng Research, 2007, 44 (4), Jang, La, The Welfare Effects of Bll Shock Regulaton n Moble Telecommuncaton Markets, Workng Paper March Lambrecht, Anja, Katja Sem, and Bernd Skera, Does Uncertanty Matter? Consumer Behavor under Three-Part Tarffs, Marketng Scence, 2007, 26 (5), Leder, Stephen and Ozge Sahn, Contracts, Bases and Consumpton of Access Servces., CESfo Workng Paper No Avalable at Lchtensten, Sarah, Baruch Fschhoff, and Lawrence D. Phllps, Calbraton of Probables: The State of the Art to 1980, n Danel Kahneman, Paul Slovc, and Amos Tversky, eds., Judgment under uncertanty : heurstcs and bases, Cambrdge ; New York: Cambrdge Unversy Press, 1982, pp Martn, Andrew, Bank of Amerca to End Deb Overdraft Fees, The New York Tmes, March Mravete, Eugeno J., Estmatng Demand for Local Telephone Servce wh Asymmetrc Informaton and Optonal Callng Plans, The Revew of Economc Studes, 2002, 69 (4), , Choosng the wrong callng plan? Ignorance and learnng, Amercan Economc Revew, 2003, 93 (1), , The Welfare Performance of Sequental Prcng Mechansms, Internatonal Economc Revew, 2005, 46 (4),

45 and Ignaco Palacos-Huerta, Consumer Inerta, Choce Dependence, and Learnng from Experence n a Repeated Decson Problem, Revew of Economcs and Statstcs, Forthcomng. Narayanan, Srdhar, Pradeep K. Chntagunta, and Eugeno J. Mravete, The role of self selecton, usage uncertanty and learnng n the demand for local telephone servce, Quantatve Marketng and Economcs, 2007, 5 (1), Pols, Dmrs N. and Joseph P. Romano, Large Sample Confdence Regons Based on Subsamples under Mnmal Assumptons, Annals of Statstcs, 1994, 22 (4), Ress, Peter C. and Matthew W. Whe, Household Electrcy Demand, Revsed, The Revew of Economc Studes, 2005, 72 (3), Rochet, Jean-Charles and Lars A. Stole, Nonlnear Prcng wh Random Partcpaton, The Revew of Economc Studes, 2002, 69 (1), and Lars Stole, The Economcs of Multdmensonal Screenng, n M. Dewatrpont, Lars Peter Hansen, and Stephen J. Turnovsky, eds., Advances n economcs and econometrcs: theory and applcatons - eghth world Congress, Vol. 36 of Econometrc Socety Monographs, New York: Cambrdge Unversy Press, Roodman, Davd, How to do xtabond2: An ntroducton to dfference and system GMM n Stata, Stata Journal, 2009, 9 (1), Saez, Emmanuel, Do Taxpayers Bunch at Knk Ponts?, Workng Paper June 2002., Do Taxpayers Bunch at Knk Ponts?, Amercan Economc Journal: Economc Polcy, 2010, 2 (3), Spegler, Ran, Bounded Ratonaly and Industral Organzaton, Oxford Unversy Press, Stango, Vctor and Jonathan Znman, What do Consumers Really Pay on Ther Checkng and Cred Card Accounts? Explc, Implc, and Avodable Costs, Amercan Economc Revew Papers and Proceedngs, 2009, 99 (2). and, Lmed and Varyng Consumer Attenton: Evdence from Shocks to the Salence of Overdraft Fees, Workng Paper March Stole, Lars A., Prce Dscrmnaton and Competon, n Mark Armstrong and Robert K. Porter, eds., Handbook of Industral Organzaton, Vol. Volume 3, Elsever, 2007, chapter 34, pp T-Moble, T-Moble USA Reports Second Quarter 2004 Results, Press Release. Tran, Kenneth, Dscrete Choce Methods wh Smulaton, 2nd ed., Cambrdge Unversy Press, U.S. Census Bureau, Table 1. Prelmnary Annual Estmates of the Resdent Populaton for the Uned States, Regons, States, and Puerto Rco: Aprl 1, 2000 to July 1, 2010, Techncal Report NST- PEST February xls. 44

46 Yao, Song, Carl F. Mela, Jeongwen Chang, and Yuxn Chen, Determnng Consumers Dscount Rates wh Feld Studes, Journal of Marketng Research, 2012, 49 (6),