Consumer Choice of Service Plan: Switching Cost and Usage Uncertainty

Transcription

1 Consumer Choce of Servce Plan: Swchng Cost and Usage Uncertanty Png Xao Tat Chan Chakravarth Narasmhan 1 May, Png Xao s a doctoral student n Marketng, Tat Chan s an Assstant Professor of Marketng, and Chakravarth Narasmhan s the Phlp L. Seman Professor of Marketng, all at Washngton Unversy n St. Lous. We are grateful to Matthew Gentzkow, Ana Lambrecht and semnar partcpants at the 4 th QME Conference for many helpful comments. Chan and Narasmhan acknowledge the generous fnancal support from The Boeng Center on Technology, Informaton and Manufacturng. An early verson of ths paper was crculated under the tle Servce Bundles under Three-Part Tarffs. Correspondng author: Chakravarth Narasmhan: narasmhan@wustl.edu. Ph. (314)

2 Consumer Choce of Servce Plan: Swchng Cost and Usage Uncertanty Abstract A strategy used by frms n ndustres such as wreless s to bundle several servces nto a servce plan and admnster a nonlnear prce wh dfferent margnal prces for dfferent usage levels. Usually frms offer more than one servce plan. Whle product bundlng and nonlnear prcng have been extensvely studed separately n the economcs and marketng lerature there are no theoretcal or emprcal studes that consder them smultaneously. Consumers may be uncertan about ther tastes for dfferent servces, ther preferences may be correlated, and they may face psychologcal and out of pocket costs to swch among plans. A frm needs to take these nto account n desgnng s prcng strategy. To explore these ssues we develop a structural model of consumers' choce of plans and usage decsons, and estmate the model usng a dataset from a wreless servce provder. We fnd that consumers derve utly from both voce call and text message and gnorng the fact that consumers smultaneously determne consumpton levels of multple servces may lead to based estmaton results. Moreover, we fnd a somewhat counterntuve result that consumer preferences for voce call and text message are posvely correlated. We show that ncorporatng swchng costs, consumer uncertanty and learnng are mportant n explanng the swchng patterns observed n the data. We also conduct several what-f scenaros to llustrate how the servce penetraton process may be dfferent under varous behavoral assumptons. Keywords: Nonlnear Prcng, Wreless Servce, Three-Part Tarffs, Swchng Cost, Learnng, screte/contnuous Model

3 1. INTROUCTION A servce plan n ndustres such as wreless typcally conssts of two mportant components: () s a bundle of multple servces and, () the margnal prce for usage often vares wh the level of usage,.e. the prcng scheme s nonlnear. The prcng structure under a commonly used three-part tarff wh bundlng ncludes an access fee, free usages (allowances) for multple servces, and a margnal prce for addonal usage above the free usage for each servce. For example, under a servce plan of two servces 1 and, a consumer pays an access fee of A per month that entals hm to free usages F 1 and F. Beyond these free usages he wll have to pay margnal prces of p 1 and p. If the consumer s usage of servce 1 ( q ) s larger than F1 but hs usage of servce s less than F, he has to 1 pay an amount of A+p 1 (q 1 -F 1 ). If the consumer s usages of both servce 1 and ( q 1 and q, respectvely) are both hgher than free usage level, he has to pay for an amount of A+p1(q 1 -F 1 )+p (q -F ). Snce the access fee A nvolves the usage of both servces the consumer has to consder hs expected usage of the two servces when he makes servce plan choce decson. Pror research has examned how a monopolst could use bundlng as a second-degree prce dscrmnaton devce to extract greater consumer surplus. Adams and Yellen (1976) show that bundlng can ncrease a monopolst s prof when consumer preferences for the two products are negatvely correlated and margnal costs are not too hgh. Subsequent studes (for example, see Schmalensee (1984) and McAfee, McMllan, and Whnston (1989) etc.) fnd that the negatve correlaton s not a necessary condon. Crawford (005) tests the prce dscrmnaton hypothess usng data from the cable televson ndustry, and fnds that bundlng can lead to sx percent ncrease n frms profs and more than fve percent reducton n consumer surplus. Common practce of three-part tarff prcng n ndustres has also generated many studes of ths practce. Jensen (006) fnds that n a dfferentated product duopoly two-part tarff may not be an equlbrum strategy and shows that three-part tarff s an equlbrum prcng strategy. Grubb (006) shows that when consumers 3

4 are over-confdent n predctng ther future usage, three-part tarff s an equlbrum. A few emprcal studes have nvestgated the mpacts of three-part tarff when frms offer a sngle product or servce. For nstance, Iyengar (005) shows that the access fee affects consumer churn more than the margnal prce. Lambrecht, Sem and Skera (006) fnd that demand uncertanty drves consumers' choce among three-part tarffs. They also fnd that access fee has a larger mpact on choce of a plan than the margnal prce and free usage. We are not aware of any theoretcal or emprcal studes of three-part tarffs n a world where frms offer bundles of products or servces. Snce bundlng and three-part tarff prcng have become more and more popular n many ndustres s mportant for frms to understand the mpact on consumer choce when these strateges are combned. Unfortunately, many results from prevous lerature cannot be appled to ths suaton. For nstance, maory of the pror lerature on product bundlng assumes dscrete demand, where consumers can only choose eher zero or one un of each product. Ths assumpton comes at a cost of precludng the study of three-part tarffs that apples only when consumers choose multple uns of products or servces (Mchell and ogelsang (1991)). Smlarly, prevous research on three-part tarffs only focuses on sngle product or servce case. When frms offer multple plans (e.g., voce call and SMS text message n our data) consumers choce of a plan then would depend on ther expected level of usages of these servces. Takng account of the potental correlaton n preferences among the servces and hence the mpact of changng the prcng structure of one servce on the other s mportant for a frm's prcng strategy to effectvely dscrmnate among consumers. To summarze, we study consumer choces under bundlng and three part tarffs. Towards ths obectve, we develop a structural demand model to explan consumers choce of a bundle and usage decsons of the bundled servces. The model explcly allows for contnuous demand for each of the servces and correlaton n preferences between the servces. Hence, ths paper makes a contrbuton n fllng out the gap n the consumer choce lerature by consderng the smultaneous mpacts of bundlng and three-part tarffs, a combnaton that s a popular strategy n many ndustres. 4

5 We use a panel dataset provded by a wreless company n a Chnese cy. Consumers are not allowed to choose voce call and text message servces separately; nstead, they have to choose from a menu of multple servce plans offered by the company. A unque feature n our data s that a new servce plan was ntroduced n the mddle of the sample perod. The new servce plan and an exstng servce plan offered dentcal servces but were under dfferent prcng schemes. urng the observatonal perod, many oned n as new subscrbers, some swched between the two servce plans, and some swched out of the servces provded by the company. In order to understand these observed dynamc swchng patterns, we ncorporate three mportant components n our model: Frst, consstent wh prevous research, we explcly account for the tme lag between servce plan choce decson and usage decson. At the tme of choosng a servce plan consumers form expectatons about ther usage levels of voce call and text message n the comng month. However, the actual usage can be dfferent from these expectatons. It s mportant to understand how the usage uncertanty affects a consumer s choce of servce plan (for example see Tran, Ben- Akva and Atherton 1989, Narayanan, Chntagunta and Mravete 006 and Lambrecht, Sem and Skera 006). Second, we model the swchng cost consumers ncur when they swch. It s wdely recognzed n the lerature that consumer swchng cost s one of frms' mportant strategc elements to retan consumers (Porter 1980, 1985; Klemperer 1995, Leberman and Montegomery 1988, Kolter 1997 etc.). Moshkn and Shachar (00) emprcally fnd that swchng cost can account for stckness n plan choce. Although there s no out of pocket swchng cost charged by the frm n our data, mplc swchng cost may exst. For example, Iyengar (005) fnds that consumers may not choose the best servce plan or swch to the best plan due to nerta. Eplng (00) shows that nherent swchng cost s an mportant factor n subscrbers swchng decson to another servce provder. In terms of swchng among dfferent servce plans offered by the same frm, consumers may ncur search and transacton costs (e.g. the tme and effort to arrange for the swchng). For frms the exstence of swchng cost has mplcatons for customer relatonshp 5

6 management. For example, one way to ncrease swchng cost s through loyalty programs (Kotler 1997). Regulators often make nference about market power based on the exstence of sgnfcant swchng costs. Thrd, our model allows for the fact that consumers may be uncertan about ther true preferences for voce call and text message. A learnng model s embedded n our choce model where consumers wll gradually learn about ther preferences. Many prevous emprcal studes have examned consumer learnng (for examples see Erdem and Keane (1996), Ackerberg (00), Crawford and Shum (00), Coscell and Shum (004), and Narayanan, Chntagunta and Mravete (006)). Ignorng such consumer learnng we fnd that our choce model cannot explan the penetraton process n our data after the new servce plan was ntroduced. We also fnd from our data that some consumers stay on the same plan for the entre perod even when they would have been better off swchng to the new plan, whle others swch. Hence, we beleve that s mportant to ncorporate both swchng costs and consumer learnng n explanng these dfferental swchng behavors. Thus, whle others have studed learnng and swchng cost on s own, we consder them smultaneously n consumers choces. To conclude, our research obectves are the followng: What are the preferences of voce call and text message, and what s the correlaton between the two? Answers to these questons have mportant mplcatons for the frm n s segmentaton and prcng strategy. How do access fee, free usage and margnal prce under servce bundlng affect consumers choce of servce plan and usage decsons? Answer to ths queston has mplcatons for a frm s desgn of the prcng and bundlng strateges. How do swchng costs and consumer learnng mpact the decsons of swchng among servces plans? Answers to these questons help to understand the maor factors drvng the penetraton process when a new product s ntroduced. 6

7 From our estmaton we fnd a somewhat surprsng result that preferences for voce calls and text messages are posvely correlated,.e., consumers who make more calls are also more lkely to send out more text messages. The mplcaton for customer segmentaton s that a frm s more lkely to fnd customers wh hgh or low preferences for both of the servces. Results show that access fee affects the choce probables and frm revenue more than margnal prces and free usage. Moreover, change n margnal prce or free usage of one servce wll mpact the aggregate usage level of another servce, demonstratng a complementary relatonshp between servces that are bundled together n a servce plan. We also fnd that both voce call and text message have mportant weghts n the consumer utly functon; hence, gnorng eher of them (e.g., by focusng only on voce calls) may lead to based results n the choce model; swchng costs are mportant n explanng why some consumers choose not swch to the new servce plan though they would be benefed had they swched; consumer learnng explans the gradual growth n market share of the new servce plan. An out-of-sample valdaton exercse confrms that our proposed model outperforms competng models n terms of predctably. We further conduct some what-fs experments to llustrate how the product penetraton process wll change under dfferent assumptons of swchng costs and consumer uncertanty about ther preferences. These results help managers understand the underlyng factors whch determne the dynamc patterns of consumer servce plan choces. The rest of the paper s organzed as follows. In secton we dscuss the bundlng and prcng practces n the wreless servce ndustry and the data. Secton 3 presents our structural demand model. In secton 4 we frst dscuss the detals of the model estmaton and then the dentfcaton ssues. In secton 5 we present the estmaton results and dscuss other expermental outcomes. Secton 6 presents our concluson and dscussons on future research. 7

8 . ATA In the context of the Chnese provder, a wreless servce plan offers local, long dstance ncludng nternatonal calls, text, GPRS, and other features such as call wang, caller I, three-way callng, call forwardng, and colorng rng back tones. Some sub-bundles also exst n each of these servce components. For example, a voce call ( voce hereon) s a bundle of on-net and off-net calls. 3 Text messages ( text hereon) are also bundles of on-net and off-net text messages. To smplfy the analyss, we only focus on the two most popular servces, local calls and text messages, n ths study. Consumers are requred to pay a monthly access fee wh fxed quantes of free usages (allowances) for voce and text, followed by a posve margnal prce once the usage exceeds the free allowance. Our dataset contans a sample of,357 consumers from a Chnese cy. The dataset conssts of monthly servce plan choces and usage levels for local voce and text from July 003 to September 005. Numerous servce plans wh dfferent prcng schemes are offered by the frm. In ths study we focus on the two most popular wreless servce plans: the voce centrc and data centrc plan. Table 1 provdes detals of the two plans. The voce centrc plan charges dfferent access fees to users based on the avalably of roamng 4 (f a consumer on the plan uses roamng servce n a partcular month, he wll pay 30 5 as monthly access fee, otherwse he pays only 15 as monthly access fee), whle the data centrc plan allows roamng at a sngle access fee ( 0). The voce centrc plan allows a hgher free voce usage but no free text usage, whle the data centrc plan allows 300 free text a month. Beyond the allowances, margnal prces for both servces are smlar, except that the data centrc plan charges a lower prce for off-net outgong calls. GPRS (General Packet Rado Servce) s an emergng technology standard for hgh speed data transmsson over GSM networks. ( 3 An on-net local call s a call that orgnates and termnates n the network provded by the same company, and an off-net call s a call that orgnates and termnates n networks provded by dfferent frms. Snce costs may be dfferent between on- and off-net calls, a servce provder wh a larger network of subscrbers usually has a competve advantage n the market. 4 We do not observe the margnal prce charged for roamng n our data (prces may vary a lot dependng where to call); hence, we only model the usage decsons of local phone calls n ths paper. We use the average access fees of roamng and non-roamng weghted by ther relatve market share as the access fee of the voce centrc plan. 5 Chnese dollar 1 s approxmately equal to $0.15 n US dollar. 8

9 Off-net ncomng and outgong margnal prces are hgher than on-net prces for both voce and text because the frm s charged an access fee or termnaton fee by local land-lne phone frms or other wreless frms. Snce we only have data on the total mnutes of voce and number of text, we use the weghted average 6 of on- and off-net prces as the margnal prces for voce and text. Two maor wreless servce provders co-exst n our cy. The focal frm n our data (Frm A) s the market leader wh greater than 60% share durng the sample perod (see Fgure 1). The other frm (Frm B) has a market share between 0 and 30 percent. The thrd frm (Frm C) s the land-lne provder n the cy. Tradonally ths land-lne provder s not a competor n the wreless market; however, ntroduced a wreless fxed lne servce n March 004. By subscrbng to ths servce, consumers can carry ther phones lke a cell phone. Ths new servce proved to be very successful, wh the frm s share of the wreless market ncreasng to about 1 percent by the end of the sample perod. In response to ths new threat, frm A ntroduced n August 004 a new data centrc plan targetng consumers wh hgh demand for text. Ths soon became a popular plan and frm A s market share has rebound snce then. As shown n Fgure, the new plan ganed new users quckly after s ntroducton. By the end of the sample perod the number of users n ths plan almost equaled the exstng voce centrc plan. 7 To explan the growth of the data-centrc plan we need to model the choces of not only the exstng users but also new consumers. Therefore, unlke most of the prevous studes (e.g., Lambrecht, Sem and Skera (006) do not consder new consumers durng the sample perod, and Narayanan, Chntagunta and Mravete (006) only consder swchers between plans), s mportant for us to model the on-n decsons of those users who orgnally chose the outsde opton. 8 6 We assume a balanced callng pattern,.e., when a consumer makes a telephone call, the recever of the call can be any other consumer wh probably ndependent of hs current subscrbed network. 7 Because of the growng acceptance of cell phone, total market demand n the cy grew over tme durng the sample perod. As a result, number of users for both plans and for the three frms n the cy also grew overtme. 8 The outsde opton ncludes the choce of not usng any wreless servces and the choce of usng other servces from competng frms. Snce we do not observe these outsde choces from data, they are not separately dentfed n our model. More detals wll be provded n the model secton. 9

10 To understand the dfference n usage among consumers, we break down the sample nto () those who stay on the voce centrc plan and do not swch, () those who on the new data centrc plan and then stay, () those who swch from the voce centrc plan to data centrc plan, (v) those who on the data centrc plan and then swch to the voce centrc plan, and (v) those who drop out. Table reports some summary statstcs of the usage patterns for both voce and text for the whole sample as well as for these fve segments. Whle the average voce usage s not sgnfcantly dfferent across groups of users the average text usage for those who stay on the voce centrc plan s sgnfcantly lower than the other groups. The level of voce usage of swchers from data centrc to voce centrc plan and drop-outs are also lower than those who stay wh or swch from voce centrc to data centrc plan. Nevertheless, we note that usage levels are endogenous dependng on the amount of free usages and margnal prces. Usage dfferences may reflect the dfference n eher nherent consumer preferences or prces or both. To nvestgate whether consumers change ther usage patterns and whether they gan from swchng, we examne the swchers. We compute the expendure under the voce centrc and data centrc plans based on the observed quanty. There are 131 users that swch from the voce to the data centrc plan. Based on the level of usage after they swch, 78 percent gan from swchng wh an average savng of 16., and percent are worse off from swchng wh an average loss of 3.8. The average cost savng s 11.7 among all users. Ths provdes an approxmate upper bound on the savngs of swchng from voce centrc to data centrc plan. Based on the level of usage before they swch, 60 percent of swchers gan wh an average savng of 10.5, and 40 percent lose from swchng wh an average loss of The average cost savng s Ths can be vewed as a lower bound on the savngs of swchng to the data centrc plan. Fgure 3 llustrates the patterns of average gan and loss of swchers from the voce centrc to the data centrc plan. Smlar patterns of gan and loss are found among those swchng from the data to the voce centrc plan. The results mply that consumers are on average makng optmal decsons. Moreover, consumers wll 10

11 change ther usage patterns once they swch to another plan wh dfferent prces; hence, we observe the dfference between upper and lower bounds. We want to hghlght two ssues related to the swchng patterns. Frst lookng at Fgure we see that the market share of the new data centrc plan ncreases gradually n the 1 months after was ntroduced. Ths s consstent wh consumers learnng ther preferences gradually hence swchng over tme. To accommodate ths we propose a consumer learnng model that could explan ths dynamc pattern of swchng. Second, though we fnd that most swches seem to be optmal, there are stll a sgnfcant proporton of consumers that choose to stay wh eher voce centrc or data centrc plan but could have benefed f they had swched. For example, among the 965 consumers who choose to stay wh the voce centrc plan, 5 percent of them would have benefed had they swched to the data centrc plan, wh an average savng of Smlarly, among those 78 consumers who on and stay wh the data centrc plan untl the end of sample perod, about 15 percent of them would have been better off had they swched to the voce centrc plan, wh a savng of Moreover, there are some swchers ncurrng losses by swchng but choose to stay wh the new plan. Why don t these consumers swch back to the orgnal plan? A consumer learnng story may not be suffcent to explan the fact that so many users choose to stay wh the exstng plan after 1 months of the ntroducton of the new plan. An alternatve story that the frm may put n dfferent marketng efforts for the two servce plans durng the sample perod cannot explan why a sgnfcant proporton of consumers from both plans do not swch to another less costly plan. We hypothesze that consumers ncur swchng costs to swch among plans or to drop out to better account for ths behavor. We randomly select about 5% consumers from the,357 consumers for our model estmaton. Ths selected sample conssts of 6,774 monthly observatons wh a spl between the voce centrc and data centrc plans. We compare the usage and swchng patterns of ths selected sample and found them to be very smlar to that of the whole sample. 11

12 3. THE MOEL In ths secton we develop a structural model to explan consumers choce of servce plan and usage under three-part tarff prcng. Consumers maxmze expected utly and we specfy a drect utly functon over voce and text usage. Allowng for consumer preference heterogeney we derve consumer usage decsons condonal on the choce of a servce plan. Based on these we can derve the ndrect utly functon of servce plan choce and probably of choosng the dfferent servce plans when consumers form expectatons about ther usages. We explan n detal how swchng costs and consumer learnng are ncorporated n our model. Fnally we dscuss dentfcaton ssues n model estmaton. 3.1 The Utly Functon We model a consumer s decsons usng an ntegrated framework: consumer frst chooses from among many servce plans ncludng an outsde opton and then, condonal on the choce of a plan, makes the usage decsons for voce and text. Whle the servce plan choce s a dscrete decson, usage decsons are contnuous. Ths set-up s analogous to the dscrete/contnuous demand model (for example see Hanemann (1984) and ubn and McFadden (1984)). For recent emprcal work see Hendel (1999), Km, Allenby and Ross (00), ube (004) and Chan (005).) wh the dfference that we also account for the tme lag between the plan choce and usage decsons (e.g., see Iyengar (005) and Narayanan, Chntagunta and Mravete (006)), where n each stage consumers nformaton sets may be dfferent. We assume that consumers utly s derved from usng both voce and text. Consumer, =1,, N, chooses a servce plan from the avalable servce plan optons at tme t. The exstng consumer has three optons: stay n the same plan as tme t 1, swch to another servce plan from the same frm and drop out of the exstng servce plans (.e., choose the outsde opton). On the other hand the new consumer has two optons: stay out or sgn n for one of the servce plans as a new user. If she chooses a servce plan, ndexed by tme t, she wll then choose the number of voce mnutes = 1,..., J, from the focal frm at x, the number of text and quanty of the outsde good x 0 whch s the consumpton of products and x, 1

13 servces other than the wreless servces. To consume a wreless servce bundle {, } x x from servce plan, the consumer pays an access fee A, enoys a free usage for voce F and for text F, and then pays a margnal prce for voce p f x > F, and for text p f x > F. For model estmaton we normalze the prce of the outsde good to 1. We allow for the case that the consumpton of eher voce or text may be zero n some perods,.e., corner solutons for usages could exst. text. 9 We assume that a consumer s utly s addvely separable n voce and We defne the utly when consumer chooses a servce plan as: 0 (,, ) U x x x ( x ) ( x ) = δ + x + θ β x β + θ β x β + ε 0 t () where U s the consumer s drect utly functon, and δ s a plan-specfc preference ntercept representng benefs other than voce and text offered by the plan that are not n our data. For smplcy we assume that δ s homogeneous among consumers. The margnal utly derved from the outsde good x 0 s normalzed to 1. The frst square bracketed term s utly from voce and the second square bracketed term s utly from text. Note that ths addve separable structure mples that there s neher complementary nor substutably between voce and text at the ndvdual level, and the utles from usng voce and text are ndependent of the utly from consumng the outsde good. Parameters to be estmated n (1) ncludeδ, θ, θ, β and (1) β, where the last two parameters are restrcted to be posve. The last component n (1) ε t s the ndvdual-, plan- and 9 We note that such addve separably assumpton may restrct the substuton pattern among usages of the two servces. A more flexble specfcaton s to allow an nteracton term between the voce and text usages n the utly functon. However, snce there s no prce varaton n eher plan durng our sample perod, s not possble to dentfy ths from our data. Furthermore, as wll be dscussed below, we allow a consumer s preferences for voces and texts to be correlated. Therefore our model s able to generate a flexble substuton pattern between the two servce plans at the aggregate level. 13

14 perod-specfc..d. random shock that follows a double exponental dstrbuton whch affects the consumer s choce of servce plan but unobserved by researchers. The quadratc sub-utly functons wh posve β and β mply that consumers are rsk averse and there s a sataton pont n usage Preference Heterogeney We assume that a consumer's preference parameter for usng voce and text, { } θ L, L=,, has two components. Frst there s an ndvdual-specfc and tmenvarant preference componentθ, and then an ndvdual- and tme-specfc..d. unobserved preference shockξ. That s, { } L L L L L θ = θ + ξ, L=, () θ θ σ Let θ. We assume that θ (, θ normal ) Σ σ θ, and Σ. θ θ = σ σ Consumer preferences for voce and texts are correlated whenσ 0. We also ξ 0 assume the tme-varyng preference shocks ξ.. d. normal (, ) Σξ, ξ 0 where σ Σ ξ = σ ξ ξ σ σ ξ ξ preference shocks for usng voce and text.. Ths allows for the correlaton n tme-varyng Fnally, as we wll show below,1/ β and 1/ β are margnal prces effect on voce and text usage, respectvely. Because there s no prce varaton whn each servce plan n our data, consumer heterogeney of usage responsveness cannot be dentfed. We mpose the homogeney assumpton that β = β and β = β for all consumers. 3.3 Usage ecsons We start wh modelng a consumer s usage decsons for voce and text, condonal on choosng a servce plan. We assume that at ths stage the 10 Ths quadratc utly specfcaton s consstent wh prevous lerature such as Wlson (199), Mravete (00), Iyengar (005) and Economdes, Sem and ard (005) etc. 14

15 consumer s preferences for voce and text θ and θ n () are realzed. Ths s n contrast to the consumer s decson at the servce plan choce stage when consumers have expectatons about ther preferences. However, the consumer cannot nfer the tme-nvarant preference component θ from the tme-specfc preference shock ξ. That s, she only knows the sum of preferences n perod t and therefore does not know how ths changes over tme. We assume that the consumer maxmzes her utly subect to a budget constrant. The drect utly maxmzaton problem s specfed as ( ) 0 max U,, 0 x x x d = { x, x, x } ( ) { } ( ) { } st x p x F x F p x F x F A Y () where U s consumer 's drect utly n (1) condonal on choosng plan, d s (3) the dscrete servce plan choce at tme t, and x 0,, x x are the endogenous usage decsons for the outsde good, voce, and text, respectvely. F and F are the correspondng free usages for voce and text, and A s the access fee, p and p are margnal prces for voce and text, and Y represents the ncome of the consumer. Fnally {} n the second lne n (3) s an ndcator functon whch equals 1 f the logcal expresson nsde s true, and 0 otherwse. The consumer wll be charged the margnal prces only f her usage exceeds the number of free mnutes or the number of free text n the plan. If she chooses the voce centrc plan n our data, there s no free usage for text n the servce plan, therefore F = 0. Solvng the maxmzaton problem n (3) we have the followng optmal usage levels for voce ( x ) and text ( x ) 11 : * * 11 Followng conventon we assume there always exsts an nteror soluton for the outsde good 0* consumpton,.e., x > 0. 15

16 x L* L 1 L L L 1 L θ p f L θ > F + p L β β L L L L 1 L = F f F < θ F + p L β, (4) L L L θ f { 0 < θ F } L 0 f { θ 0 } for L={, }. The condon n (4) allows for the exstence of corner solutons,.e., L* L L x = 0. Moreover, when 0 < θ F, x L* = θ ; and when θ L 1 > F + p, L β L L L x L* L 1 L θ p L =. There s a stcky pont n (4) when β F 1 < θ F + β L L L L L p, under whch condon the usage amount wll be at the free usage level when θ L changes. 3.4 Servce Plan Choces Based on the drect utly functon n (1) and the obectve functon n (3), we can plug n the optmal usages n (4) to derve an ndrect utly functon of choosng servce plan as the follows: ( ;, ;, ; ) ( ) { } ( ) θ β θ β Y A 0 { 0} A F F p p Y, = δ + + θ > + θ > ( F ) β ( θ ) β 1 + θ β F F < θ F + p β ( F ) β ( θ ) β 1 + θ β F F < θ F + p β θ p + ( p ) + p F θ F p β > + β θ p + ( p ) + p F θ F p β > + β + ε (5) t 16

17 Interpretatons of equaton (5) are as follows: If both θ < 0 and θ < 0, the ndrect utly functon wll be, = δ + Y A + ε t ; f both 0 < θ F and ( ) ( ) θ β θ β 0 < θ F, we wll have, = δ + Y A εt ; f both F 1 < θ F + β p, F 1 < θ F + p, we wll have β ( F ) β ( F ) Y A F F β, = δ + + θ β + θ β + εt fnally f both θ 1 > F + p and θ β ( θ ) ( θ ) 1 > F + p, we wll have β β 1 1, = δ + + θ + ( ) + F Y A p p p β β 1 1 θ p ( p ) p F εt β The ndrect utly functon of choosng servce plan depends on the consumer preferences for usng both voce and text. If the consumer chooses the outsde opton, the ndrect utly functon s = Y + ε (6) 0, 0t We assume that ε 0t s ndependently and dentcally dstrbuted wh double exponental dstrbuton. The consumer makes the servce plan choce at the begnnng of each perod t. As opposed to the usage decsons n (4), she does not exactly know the value of L θ, where L= or (see equaton ()), whch conssts of the tme-varyng L dosyncratc demand shock ξ of whch the consumer only knows the dstrbuton, and the tme-nvarant usage preference θ L that she may only learn over tme (we wll further dscuss the learnng model later). The consumer has to form an expectaton for, condonal on her nformaton set Ω whch conssts of her. ; 17

18 past usage hstory,.e., E [, Ω ]. The consumer wll choose the opton wh the hghest expected ndrect utly. The new data centrc plan was ntroduced n the mddle of the sample perod. Before the new plan s avalable, consumers consderaton set conssts of the exstng voce centrc plan and the outsde opton. After the new plan s avalable, consumers' consderaton set now conssts of the voce centrc plan, the data centrc plan and the outsde opton Swchng Costs and Learnng To explan the dynamc swchng patterns observed among consumers, we allow for the exstence of swchng costs and consumer learnng of ther own preferences. Frst, we assume that consumer ncurs swchng cost,, when she swches to a dfferent servce plan provded by the same frm and by assumng that the swchng cost s dstrbuted as ( 1, 1 ) N SC σ sc 1 SC we allow ths cost to vary across consumers. To dentfy the parameters of the model, we do not allow ths swchng cost to be tme-varyng. However, one may nterpret the fluctuaton n swchng cost n each perod as part of the tme-specfc..d. shock ε t (see equaton (1) and (5)). If the consumer decdes to drop out as a user of the frm, or on n from outsde, another type of swchng cost would ncur whch may be dfferent from swchng between servce plans whn a frm. In our estmaton we fnd that allowng for heterogeney of ths cost leads to dffculty n dentfcaton, perhaps due to the lack of varaton n data among consumers whn these categores. Therefore we restrct ths cost to be homogeneous across consumers as SC. Suppose the consumer s a user of the voce centrc plan (plan 1) n perod t- 1. Based on the above dscusson, she wll agan choose the same plan n perod t, nstead of the data centrc plan (plan ) or the outsde opton, f the followng s true: 1 { } E[ Ω ] max E[ Ω ] SC, SC, 1,, 0, 1 We gnore n our model that some consumers may not be aware of the new servce plan. Though may take tme for consumers to learn the exstence of the servce plan, such a learnng process s dffcult to be dentfed from our data, especally that cannot be dstngushed from the process of consumers learnng own usage preferences, whch s modeled n the paper. 18

19 Based on the double exponental dstrbuton assumpton for plan choce shocks (,, ) ε ε ε the choce probably for servce plan 1 n perod t s 1 t 0t ( d = ) Pr 1 1 = Pr ( ε 1, εt, ε0t) : E1, + ε 1 max( E, SC + εt, 0 SC + ε0t) _ exp E1, = (7) 1 exp( 0 SC ) + exp E1, + exp E, SC where d s the dscrete servce plan choce of consumer n perod t, _ E, s the determnstc part n E [, Ω ] whout the dosyncratc component t ε, and 0 s smlarly defned. Smlarly, the consumer wll swch to the data centrc plan f the followng condon s true: And she wll choose to drop out f { } E[ Ω ] SC max E[ Ω ], SC 1, 1, 0, { } SC max E[ Ω ], E[ Ω ] SC 1 0, 1,, wh choce probables smlar to equaton (7). If the consumer s not a user of the frm n perod t-1, by onng eher servce plan wll ncur a swchng cost SC. Hence, she wll only choose the voce centrc or the data centrc plan f eher or { } E [ Ω ] SC max E [ Ω ] SC, 1,, 0, { } E [ Ω ] SC max E [ Ω ] SC,, 1, 0, s true, respectvely. Based on that, the probably of onng eher plan can be derved smlarly as equaton (7). We wll dscuss how we compute later. _ E, n detal 19

20 Turnng to consumer learnng and consstent wh prevous lerature on learnng, we assume that consumers may not know ther own tme-nvarant preference types {, } θ θ hence form expectatons based on past experences. Ths type of learnng could be one source n explanng why n our data consumers only swched to the new data centrc plan several perods after the plan had been ntroduced (and some dd not swch at all) even when ther savngs are large had they swched earler. At the end of each perod, consumer observes her usages x and usages x. Suppose these usages are posve and not exactly equal to the free F and F, the optmal condons of usages mply that 1 1 θ = θ + ξ = x + p θ > F + p β β 1 1 θ = θ + ξ = x + p θ > F + p β β Though there s a one-to-one mappng between usage x L and the tme-varyng L preference θ (we assume that the prce sensvy coeffcent b L = (8) 1 L β s known to the consumer) so that she can use the observed usages to nfer preferences, she L cannot separate θ and L ξ from the sum the dstrbuton functon of (, ) ξ ξ, N ( 0, Σ ξ ) L θ. As pror knowledge, we assume that, s known by all consumers. L Regardng θ, we assume that n the frst perod t=1 consumers have the same pror belefs dstrbuted as θ θ 0 ~ N, Σ θ 0 θ θ 0, where θ 0 represents the θ 0 pror preference means, and σ 0 0 Σ θ 0 = 0 σ 0 matrx whch measures the consumer uncertanty. 13 s the pror varance-covarance At the end of every perod, after observng ther usages, consumers update the belefs of ther true preferences usng the Bayesan rule (egroot (1970)): Assumng after t perods the 13 For the smplcy of model estmaton we assume that consumers beleve that ther preferences for voces and texts are ndependent. It s generalzable to the case when preferences n pror belefs are not ndependent. 0

21 consumer s belef of her preference type for usng servce L s N ([,, ]', θ, t) θ θ Σ, where the subscrpt t denotes consumers belefs of own preference types after perod t. Suppose n perod t usages of both voce and text are above the free usage levels, then her belef at tme 1 t + are dstrbuted as N ([ θ, + 1 θ, + 1 ]', θ, t+ 1) Σ where [ θ, 1 θ ]' +, + 1 and, 1 Σ θ t + follow the specfcatons below: 1 x + p θ, 1 1 β 1 θ +, =Σ, 1 ( ) (, ) θ t+ Σ ξ + Σθ t θ 1, + 1 θ x, + p β. (9) 1 1 (( ) ( ) t ) Σ = Σ + Σ θ, t+ 1 ξ θ, 1 If usages are below free usages, the terms 1 p β and 1 p wll not be β n the above equaton. Zero usage, though nfrequent, does exst for eher voce or text n the data. In ths case the one-to-one relatonshp between usages and preferences does not exst. We assume that, for example, when consumer can only nfer that x = 0, the θ 0 at tme t. The updated belef for θ wll follow the pror belef dstrbuton at tme t condonal on the truncated usage,.e., (,, N θ, σ θ + ξ 0) (10) where θ, and σ, are the mean and varance n pror belefs for θ at tme t, respectvely. There s no closed-form expresson for these posteror belefs, so n model estmaton we smulate ths condonal dstrbuton to obtan the estmates for θ, + 1 and. We do smlar smulatons for θ + and σ + when x = σ, + 1, 1, 1 4 MOEL ESTIMATION 14 There s another complcaton n the updatng process when the consumer s usages are exactly equal to F or F, n whch case θ and θ are defned whn a range. Ths never happens n our data; hence, we can gnore such updatng process n our model estmaton. 1

22 4.1 Estmaton Procedure We frst dscuss the estmaton procedure for the usage decsons, condonal on servce plan choce. The optmal usages of voce and text n equaton (4) mply a Tob-type regresson: f the observed usages L L L L L L posve, we can derve that θ ξ x p { x F } L x, L= or, s 1 L + = + >. If x 0, we can L = β L L nfer that θ + ξ Condonal on the servce plan choce d, we can wre down the probably functon of the observed usages ( x, x ) as Pr( x, x d ) = Pr( x, x d, θ, θ ) df( θ, θ ), where F( ) s the ont dstrbuton functon of ( θ, θ ). Note that θ L here s the true preference of consumer and not the pror belef because the true value has been realzed n the usage decson stage. Snce L L L L θ = θ + ξ and θ s tme-nvarant for each L consumer, θ wll be correlated overtme. Further, we have to account for the correlaton between preferences for voce and text n θ and ξ. rect evaluaton of the lkelhood of the consumer s whole usage hstory of both voce and text wll be dffcult n model estmaton. Instead, we smulate the uncondonal probably functon of usages by usng a frequency smulator for θ : Let s represents a θ draw n the smulaton. We draw, for each consumer, θ θ, s, s from the assumed θ populaton dstrbuton N (, ) Σ θ θ for ns tmes and fxed these smulated draws over tme for each consumer. Because of our..d. assumpton for ξ, the lkelhood of the whole observed hstory of usages for consumer can be evaluated for each perod t, t=1,, T, as the follows: 15 Agan we gnore the case that the consumer s usages are exactly equal to not observe n our data. F or F, whch we do

23 ~ x 1 x 1 xt xt d 1 dt x 1 x 1 xt xt d 1 dt Pr (, ;...;,,..., ) Pr (, ;...;,,..., ) 1 = ns ns, s, s, s, s [Pr( x 1, x 1 d 1, θ, θ )... Pr( xt, xt dt, θ, θ )] s= 1 ~ where n the frst lne Pr represents the smulated verson of Pr, and x x d θ θ, s, s Pr(,,, ) n the second equaly s evaluated condonal on the smulated tme-nvarant preferences and the dstrbuton assumpton ξ normal(0, Σξ ). Let us turn to the lkelhood functon of servce plan choces n each perod. Equaton (7) provdes an example of the choce probably that a consumer chooses servce plan 1 at tme t. All other probably functons are smlarly defned. The dffculty n actual model estmaton comes from evaluatng _ E,, whch s the determnstc part n E [, Ω ] whout the dosyncratc component t ε (also see equaton (5)). As opposed to evaluatng the probably functon for usages above, _ E, s now a functon of the consumer s belefs of θ θ and not her true preferences. Let ( θ,, θ, ) be a par of random varables that represent the consumer s belefs of her true preference types at tme t, wh the dstrbuton ( ) functon F( θ,, θ, ) = N [ θ, θ, ]', Σθ, t, where [ θ, θ, ]' and Σ, are the updated θ t means and varances of her preferences, respectvely. follows: _ E, can be wrten as the _ E, = δ + Y A ( ) { } ( ) θ + ξ β θ + ξ β,, θ + ξ > 0 +, { θ + ξ > 0, } ( θ + ξ, ) p + ( p ) + p F F p θ + ξ > +, df( θ, θ ) df( ξ, ξ ),, β β ( θ + ξ, t ) p + ( p ) + p F 1 θ + ξ > F p, t β + β 3

24 The above expresson, unfortunately, does not have a closed-form expresson. To compute ths functon we agan have to rely on the smulaton method: we draw,, ( s s θ,, θ ), from the pror belef dstrbuton ( ), s, s N [ θ, θ, ]', Σ θ, t, and ( ξ, ξ ) from the assumed dstrbuton N(0, Σ ), where s n the superscrpt denotes a ξ,, smulated draw, for ns tmes. Each par of ( s s θ, θ ), s, s and ( ξ, ξ ) are plugged,, nto the above equaton, then we take the average to form the smulated plan n perod t condonal on past usages E _ s,. Let Pr ( d = x, t, x, t) be the probably functon of consumer choosng servce ( x,, x, ) before perod t (whch are t t used to form the pror belef dstrbuton N ([,, ]', θ, t) θ θ Σ ). We plug the smulated _ s, E nto the multnomal log functon analogous to equaton (7) for every servce plan to become the correspondng smulated probably functon ~ ( d x, t x, t) Pr, pror belef dstrbuton functon ( ~ d x, t x, t Pr, (, + 1, + 1 θ, t+ 1). Ths procedure s repeated for every perod: n perod t wh N ) ([ θ, θ, ]', Σθ, t ) the smulated servce plan probably s evaluated. Then the belefs wll be updated to [ ]', N θ θ Σ after usages { x, x } are revealed. We wll draw ( θ, θ ), + 1, + 1 based on ths updated dstrbuton to evaluate the smulated servce plan probably functon ( ~ d+ 1 x, t+ 1 x, t+ 1 Pr, ) for perod t+1. We ontly estmate the lkelhoods of both usage and servce plan choce decsons. Let Θ be the vector of parameters n the model. Our estmator maxmzes the followng ont lkelhood: ˆΘ 4

25 N = 1 {Pr ( x, x, d ;...; x, x, d Θ) T T T ~, s, s N ns Pr 1 ( d1 x, 1, x, 1; Θ) Pr( x 1, x 1 d 1, θ, θ ; Θ)... ~ 1 ns = s= 1, s, s Pr ( dt x, T, x, T ; Θ) Pr( xt, xt dt, θ, θ ; Θ) (11) A few more detals about the estmaton model as follows: For smplcy we assume that at tme t=1 all consumers have the same pror belefs θ θ 0 ~ N, Σ θ 0 θ θ 0, where σ 0 0 Σ θ 0 =. Snce these parameters relate 0 σ 0 to consumers belefs that are unobserved, they can only be nferred from the servce plan choces n partcular n the early perods before belefs are updated. Ther exact values are dffcult to dentfy from the data (for related dscusson see Chan and Hamlton (006)). Hence, we restrct them to be equal to θ and θ, the populaton mean preferences for usng voce and text, respectvely. We also mpose the restrcton that σ and σ are equal to the varances of preferences 0 0 among the populaton. Though our model wll be ms-specfed f such assumptons are nvald, we beleve that our estmaton results wll not be much affected snce wh consumer learnng the mpact of these pror belefs on the consumer choce quckly declnes. Chan and Hamlton (006) also use smlar assumptons and fnd that ther estmaton results are robust to dfferent assumptons of pror belefs. Snce under ths set-up the learnng model s restrctve and does not ncrease the number of parameters n the model, any mprovement n terms of f wll clearly ndcate the advantage n ncorporatng consumer learnng n explanng the consumers servce plan choces. A unque feature n our data s that many new consumers on (especally after the data centrc servce plan was ntroduced) and exstng consumers drop out n dfferent tme perods. Past hstores of these consumers before they on or usages after they drop out are not observed from data. In order to evaluate the probably of choosng the outsde opton we have to make assumptons about these customers belefs of own preferences. In the model estmaton, we assume that 5

26 θ 0 these consumers mantan the same pror belefs N, Σ θ 0 as n perod 1 untl they on n. Then they wll update ther belefs usng the observed usages. After they drop out, we assume that they wll mantan ther updated belefs rght before they leave. Choces of the outsde opton before consumers on n or after drop out are ncluded n the lkelhood functon n (11). An nterpretaton whch ratonalzes ths assumpton of constant belefs s that by choosng the outsde opton consumers do not use any wreless servce hence they do not know what ther usages would be had they subscrbed to the servce plans. We note that ths assumpton may be restrctve; however, we are not able to nfer how belefs are updated snce usages of wreless servces durng these perods are unobserved. We estmate three types of model: Model 1 s a base model that does not allow for swchng costs or consumer learnng. Model allows swchng costs but no consumer learnng. Model 3 allows for both swchng costs and consumer learnng. Comparng these three models helps to shed lght on the robustness of our estmaton results. It s also useful n understandng how much better, by addng swchng costs and consumer learnng, helps explan the observed patterns of swchng. 4. Model Identfcaton Usng the data on voce and text usages helps us dentfy many of the parameters n the utly functon. In partcular, the average usages over tme across consumers dentfy the mean and varances preferences, θ 0 θ, θ, σ and σ, for voce and text. Moreover, the correlaton of observed usages of voce and text across consumers wll dentfy the covarance parameter, σ (see dscusson n Secton 3.). The fluctuaton of usages for same consumer n dfferent perods helps to dentfy the varances of tme-varyng usage shocks, σ ξ and σ ξ. The correlaton of the usage fluctuatons for voce and text wll dentfy the covarance parameterσ. ξ 6

27 Two parameters n the utly functon n (1) that are dffcult to estmate are the prce coeffcents b = 1/ β and b = 1/ β, snce there s no prce change for eher servce plan n the data. However, two features n the data help to dentfy these parameters. Frst, about 10 percent of consumers swched eher from voce centrc to data centrc plan or from data centrc to voce centrc plan. Gven that margnal prces are dfferent n the two servce plans, changes n usages among these swchers help to dentfy the prce coeffcents among the whole populaton, as these coeffcents are restrcted to be homogeneous n our model. Second, usages of choosers of both plans may be above the amount of free usages, at whch level margnal prces wll affect the usage decsons. For example, there s no free usage of text for the voce centrc plan whle that for the data centrc plan s 300; hence, the dfference n text usage between choosers of both plans wll, condonal on the preference parameters n the utly functon, dentfy the prce coeffcent b. Snce there are no addonal parameters n the learnng model, the dentfably of our proposed model (Model 3) s vrtually the same as the swchng cost only model (Model ). Condonal on the pror belefs of true preferences (whch s derved from the pror belef n perod 1 and observed past usages), f a consumer swches from one servce plan to the other later than another consumer, though the expected benef of swchng s the same, mples that her swchng cost of changng plans 1 SC s hgher. Fnally, snce we do not have the usage data of those consumers before they oned n as users of the frm, dentfcaton of the swchng cost SC would solely rely on the observatons of those consumers who drop out from the frm - condonal on the belefs, f some consumers choose to stay wh the frm though ther expected ndrect utly generated from eher of the servce plans s much lower than the outsde opton value, mples that SC s large. 5 RESULTS 5.1 Estmaton Results 7

28 We report the results from the estmaton n Table 3. All three models suggest that, whle θ hgher than θ, the mean preference for usng voce (voce demand ntercept), s, the mean preference for usng text (text demand ntercept), there s a larger heterogeney n text preference,.e., σ (standard devaton of text demand ntercept). The demand slopes for usng both voce and text, b = 1/ β and b = 1/ β, are sgnfcantly negatve, suggestng that consumers do respond to margnal prce changes n voce and text. To examne the mportance of ncorporatng preference for text n the utly functon, we smulate the utly 16 of usng both servces based on the estmates of Model 3. After that, we compute the preference weght of usng text, relatve to that of usng voce. Two suatons are evaluated: 1. every consumer uses the voce centrc plan; and. everyone uses the data centrc plan. The resultng preference weghts have a mean of 0.7 and 0.8 under above suatons, respectvely. That s, the utly of usng text messages accounts for at least 40 percent of the total utly. Furthermore, the utly of usng text servce s hgher than usng voce servce for about 10% of consumers. One nterestng result s that the correlaton between tme-nvarant voce and text preferences (correlaton between voce demand ntercept and text demand ntercept) s posve (the estmated correlatons are 0.09, and n three models), mplyng that consumers who have a hgher preference for voce are also lkely to have a hgher preference for text. Based on our draws of tme-nvarant preferences θ and θ, we dvde consumers nto four segments usng the medan creron: 1. hgh voce and hgh text preferences,. hgh voce but low text preferences, 3. low voce but hgh text preferences and, 4. low voce and low text preferences. The segment shares are 6.6%, 3.4%, 3.4%, 6.6%, respectvely. That s, the segments of hgh-hgh type (segment 1) and low-low (segment 4) type n both usages are larger than the hgh-low (segment ) or low-hgh (segment 3) types. We wll not be able to recover such consumer segmentaton pattern f we only model the demand for sngle servces. Another ntrgung result s that the 16 The utly s normalzed by the prce coeffcents, voce demand slope and text demand slope n Table 3. 8