Product Bundles under Three-Part Tariffs 1

Transcription

1 Product Bundles under Three-Part Tarffs 1 Png Xao Tat Chan Chakravarth Narasmhan 2 November, Ths s a very prelmnary draft. Please do not ce whout permsson from the authors. 2 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. Chan and Narasmhan would lke to acknowledge the fundng support from BCTIM. 1

2 Product Bundles under Three-Part Tarffs Abstract Product bundlng and non-lnear prcng are popular marketng strateges n ndustres such as wreless and nternet. Whle each has been extensvely studed separately n the economcs and marketng lerature there are no theoretcal or emprcal studes that consder both smultaneously. When consumers are exposed to dfferent product bundles that n turn contan several two or three part tarffs s mportant to understand the drvers of consumer choces. The consumer references for multple products whn bundles may be correlated; understandng such a preference structure could potentally lead frms to choose the optmal tarffs to offer and decde whether they should bundle dfferent servces or offer each servce plan at a separate prce. Further, consumers face both out of pocket and psychologcal costs for swchng between plans or droppng out of the market. Consumers may not be able to evaluate ther level of consumpton for the servces offered and wll only learn ths over tme. These behavors are potental factors whch determne how consumers choose or swch among product bundles. To explore these ssues we develop a structural model to study consumers' product bundle choce and usage decsons, and estmate the model usng a dataset from a wreless servce provder. We fnd swchng costs and consumer learnng play an mportant role n explanng the swchng patterns observed n the data. Based on the estmaton results, we conduct polcy experments to examne the focal frm's optmal prcng decsons. Results show that both whle bundlng ncreases frms prof through extractng consumer surplus, three-part tarff strateges help to ncrease frms prof but may also ncrease consumer surplus hence create a wnwn suaton. Furthermore, when consumer preferences for multple products and servces are posvely correlated, the optmal prcng scheme s a combnaton of two-part and three-part tarff servce plans. A counter-factual prcng experment 2

3 shows that, when consumer preferences are negatvely correlated, the optmal prcng scheme wll be a combnaton of two three-part tarff servce plans. 3

4 1. Introducton Three-part tarff s a non-lnear prcng mechansm popular n ndustres such as wreless, nternet and rental markets. The prcng structure under a threepart tarff scheme ncludes a fxed access fee, an amount of free usage (allowance), and a margnal prce per un for any addonal usage above the free amount. Jensen (2006) fnds that mplementaton of a smple two-part tarffs may not be an equlbrum strategy n a duopoly and analytcally demonstrates a three-part tarff as an equlbrum nonlnear prcng strategy n a dfferentated product duopoly case. Grubb (2005) shows that three-part tarff s optmal n markets where margnal costs are low and consumers are over-confdent n ther predcton of future usage. A few other emprcal studes also examne consumer's choce and usage decsons under three-part tarffs (see Iyengar 2005 and Lambrecht, Sem and Skera 2005). All of the above studes only consder a sngle product. However, bundlng s also a popular marketng practce n many ndustres, some examples nclude hamburgers sold wh french fres and a soft drnk, checkng, cred cards and nvestment servces bundled together, hardware bundled wh software and perpherals n the computer ndustry. Pror research has addressed the use of bundlng as a mechansm for seconddegree prce dscrmnaton by a monopolst to extract consumer surplus (Adams and Yellen (1976), Schmalensee (1984), McAfee, McMllan, and Whnston (1989), Salnger (1995), Armstrong (1999), Bakos and Brynjolfsson (1999), Crawford (2005), Chu, Lesle and Sorensen (2006) etc.). 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 (Schmalensee (1984), McAfee, McMllan, and Whnston (1989), and Wlson (1993) etc.) fnd that the negatve correlaton s not a necessary condon. They argue that bundlng leads to hgher frm profs than unbundlng even when demand are separable, or when preferences across products are nonnegatve or ndependent. Whle these studes clearly show that bundlng n a monopoly market s lkely to ncrease frm prof, they fal to reach consensus on whether bundlng ncreases consumer surplus and or socal welfare. Adams and Yellen (1976) fnd 4

5 that bundlng decreases socal welfare by causng dstrbutve 3 and allocatve neffcency relatve to unbundlng. Bakos and Brynjolfsson (1999) fnd that bundlng wll always reduce consumers surplus n a market wh ndependent lnear demand for multple products. Crawford (2005) tests emprcally the dscrmnatory hypothess of bundlng n the cable televson ndustry under two-part tarffs, and fnds that bundlng can lead to sx percent ncrease n frms profs and more than fve percent reducton n consumer surplus. Resnger (2004), however, fnds that bundlng may ncrease consumer surplus under a duopoly market, where consumers preferences are negatvely correlated. Schmalensee (1982) and Salnger (1995) conclude that welfare mpacts of bundlng can go eher drecton subject to dfferent condons. In ths paper we study the mpacts on both frm prof and consumer surplus under product bundlng and three-part tarffs. A recent bundlng practce n the wreless ndustry s to combne voce calls and SMS text messages 4, both offered by the same frm, nto a servce plan. Under such servce plan, consumers pay an access fee of A per month that entals them to free usage of up to, F 1 and F 2 of voce calls (n mnutes) and text messages (n number of messages) respectvely. Above these amounts consumers wll have to pay margnal prces of p 1 and p 2 for voce calls (per mnute) and text messages (per message) respectvely. Fgure 1 descrbes the total payment for a user under such a prcng scheme. We use a unque panel dataset provded by a wreless company n a Chnese cy. The purpose of ths paper s to explore consumers choces among several servce plans and how the structure of the consumer preferences for multple servces would mply the optmal prcng mechansm under product bundlng. More mportantly, we study the mpacts of ths prcng scheme on dfferent consumer segments n terms of consumer choces and usage patterns as well as consumer surplus and frm revenue. Hence, our research leads to a better understandng of the manageral and polcy mplcatons of the prcng scheme when the market conssts of heterogeneous consumers. 3 strbutve neffcency s caused by oversupply of both commodes, undersupply of both commodes, or oversupply of one and undersupply of the other. 4 SMS s a feature that allows users to receve and transm short text message usng ther wreless phones (see 5

6 We are not aware of any theoretcal or emprcal studes of three-part tarffs n a world where frms sell 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 and polcymakers to understand the mpacts of bundlng on frm profs and consumer surplus under such prcng schemes. Unfortunately, many results from prevous lerature cannot be appled to ths suaton. For nstance, the majory of prevous lerature on product bundlng assumes dscrete demand, where consumers can only choose zero or one un of each product. Ths assumpton substantally smplfes the bundlng models but at the cost of precludng the study of three-part tarffs where consumers may choose multple uns of products (Mchell and ogelsang (1991)). In ths research we provde an emprcal examnaton of bundlng under a three-part prcng scheme allowng for contnuous demand. There are a few emprcal studes of the mpacts of three-part prcng when the seller sells a sngle product. For nstance, Iyengar (2005) shows that the access fee affects consumer churn more than the margnal prce. Lambrecht, Sem and Skera (2005) fnd that demand uncertanty drves consumers' choce among threepart tarffs. They also fnd that access fee has a larger mpact on choce of a plan than the margnal prce or the free allowance. When the frm n our data sells multple servces consumers servce plan choces wll depend on the expected usages of the multple servces whch may be correlated. Takng account of ths correlaton s mportant for a frm's prcng decsons. Should the frm offer a bundle of servces, or sell them separately, or both? What s the optmal prcng scheme for such servce bundles? How wll varyng the free allowances and margnal prces for each servce whn a bundle affect consumers plan choce and usage decsons? How wll the above factors affect consumers welfare and frm s profs? To answer the above research questons we develop a structural demand model to explan consumers plan choce and usage decson of servce bundles. An mportant feature n our data s that a new servce plan was ntroduced n the mddle of the sample perod attractng a number of new consumers. The new servce plan and the exstng servce plan offer dentcal servces but use dfferent prcng 6

7 schemes. In order to explan the observed dynamc patterns of consumer swchng patterns (.e., drop out from the servce provder altogether, jon n as new users, or swch between servce plans), we nclude three mportant components n our model: Frst, 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.). Although there s no explc swchng fee charged by the frm, mplc swchng cost does exst. Iyengar (2005) fnds that consumers may not choose the best servce plan or swch to the best plan due to nerta. Eplng (2002) 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 ncur search and transacton costs (e.g. the tme and effort to arrange for the swchng). Moshkn and Shachar (2002) fnd that swchng cost can account for stckness n plan choce. For frms the exstence of swchng cost has mplcatons for customer relatonshp 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. Second, we assume that consumers are uncertan about ther preferences for voce call and text message. To allow for consumers to learn about ther preference weghts for these, we propose a learnng model. Many prevous emprcal studes have examned consumer learnng (see Erdem and Keane (1996), Ackerberg (2002), Crawford and Shum (2002), Coscell and Shum (2004) and Narayanan, Chntagunta and Mravete (2005)). We 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. We beleve that s mportant to ncorporate both swchng costs and consumer learnng n explanng these dfferental swchng behavors. 7

8 Thrd, we explcly account for the tme lag between plan choce decson and usage decson. At the tme of choosng a servce plan consumers form expectatons about ther usage level based on pror belefs. However, durng learnng consumers belefs about ther preferences for voce call and text message could be dfferent from the true preferences. Moreover ther actual usages can be hgher or lower than what ther true preferences would mply due to exogenous shocks. It s mportant to understand how usage uncertanty wll affect consumers servce plan servces (for examples see Tran, Ben-Akva and Atherton 1989 and Lambrecht, Sem and Skera 2005.) To conclude, our research objectves are the followng: 1. To examne the underlyng consumer preference structure for product bundles under the three-part tarff prcng scheme. 2. To model the mpact of swchng costs and consumer learnng on the choce of servce plans and swchng behavors. 3. To provde manageral and welfare mplcatons for the frm s product bundlng and prcng schemes under dfferent consumer preference structures. From our estmaton we fnd that consumer preferences for voce calls and text messages are posvely correlated. Compared to a base model, by ncorporatng both swchng costs and consumer learnng our model can better explan the observed swchng patterns after the new servce plan was ntroduced n our data. Based on the model estmates, we conduct polcy experments to understand how dfferent prcng schemes wll affect consumers' servce plan choces, usage decsons and ther surplus, as well as the consumer surplus and frm prof. We fnd better prcng schemes whch wll sgnfcantly mprove the frm s expected revenue, compare wh the current prcng scheme, but wll lower the expected consumer surplus. Compared wh two-part tarffs, three-part tarffs when optmal prces are set mprove the frm revenue as well as the consumer surplus. Comparng wh the unbundlng cases, we fnd that the frm expected revenue wll be hgher but consumer surplus wll be lower, a result consstent wh most prevous lerature on the use of product bundlng n extractng consumer surplus. Interestngly, we fnd 8

9 that under our computed optmal three-part tarff schemes the frm should offer one plan whout any free usages, whch s vrtually two-part tarff. The purpose of offerng a three-part tarff plan s to attract low preferences consumers, who wll not jon n whout such a plan. Those wh hgh preferences for voce calls and text messages wll choose the two-part tarff plan. The above results are based on the estmaton result of posve correlaton between consumer preferences for voce call and text message. To check how robust our experment results are we further conduct a counter-factual polcy experment, where we assume that the consumer preferences are negatvely correlated. In ths case we fnd that under the optmal prcng scheme the frm wll offer one servce plan wh free voce call usage, targetng consumers wh a hgh preference for voce calls, and another plan wh free text message usage, targetng consumers wh a hgh preference for text messages. Ths mples that optmal prces may be dfferent under dfferent consumer preference correlatons; hence, demonstrates the mportance of usng structural modelng approach n our paper to nfer the consumer preference structure. The rest of the paper s organzed as follows. Secton 2 dscusses the bundlng and prcng practces n the wreless servce ndustry and the data. Secton 3 presents our structural demand model. Secton 4 wll frst dscuss the model estmaton and then present estmaton results. Secton 5 presents the polcy experments results, and fnally Secton 6 concludes. 2. ata Servce bundlng s a common practce n the wreless ndustry. A wreless servce plan n general ncludes local call, long dstance call that covers both domestc and nternatonal, SMS message, GPRS 5, and other features such as call wang, caller I, three-way callng, call forwardng, and colorng rng back tones. Some sub-bundles may exst n each of these servce components. For example, a 5 GPRS (General Packet Rado Servce) s an emergng technology standard for hgh speed data transmsson over GSM networks. ( 9

10 voce call s a bundle of on-net and off-net calls. 6 SMS messages are also bundles of on-net and off-net SMS messages. To smplfy the analyss, we only focus on the two most popular servces, local voce calls and SMS text messages, n ths study. As we dscussed above, wreless servces are generally sold under a threepart tarff nonlnear prcng scheme. Ths prcng scheme can be very complex that nvolves varous amounts of free usages and margnal prces for numerous servce components. A wreless servce plan typcally requres consumers to pay a monthly access fee wh fxed quantes of free usages (allowances) for voce calls and text messages, followed by a posve margnal prce once the usage s above the usage amount. Fgure 1 llustrates the total payment scheme for a bundle of two servces (voce calls and text messages, denoted as 1 and 2 correspondngly) under a three-part tarff. A subscrber frst has to pay an amount of A each month n order to be able to use the servces. Then she wll be able to enjoy free usages F 1 and F 2 for the two servces. Above these amounts she wll have to pay a per un prce p 1 and p 2, respectvely. As shown n the dagram the total cost the subscrber has to pay s hghly non-lnear dependng on her usage decson for each of the servces. We collect a dataset wh a sample of 2,357 consumers from a wreless servce provder n a Chnese cy. The dataset conssts of ndvdual-level monthly servce plan choces and usage levels for local voce calls and SMS text messages from a cellular servce provder, wh a sample perod from July 2003 to September 2005, altogether 25 months. Numerous servce plans wh dfferent prcng schemes are offered by the servce provder. In ths study we only focus on the two most popular wreless servce plans: voce centrc and data centrc plans. Table 1 provdes some prcng detals of the two plans. The voce centrc plan charges dfferent access fees to users based on the avalably of roamng 7 ( 15 whout and 6 An on-net local call s a call that orgnates and termnates n the same network, and an off-net call s a call that orgnates and termnates n dfferent 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. 7 Roamng allows users to use wreless phones n an area outsde the coverage area. There s usually an addonal charge for roamng. When the servce provder's network has ncomplete coverage, roamng arses. ( 10

11 30 wh roamng 8, where Chnese dollar 1 s approxmately equal to $0.125 n US dollar), whle the data centrc plan allows roamng for every user at a sngle access fee ( 20). The voce centrc plan allows a hgher voce call allowance but no text message allowance, whle the data centrc plan allows 300 free text messages a month. Above the free usage lms, margnal prces for both servces are smlar under the two plans, except that the data centrc plan charges a lower prce for offnet outgong calls. Off-net ncomng and outgong margnal prces are hgher than on-net prces for both voce calls and text messages because the servce provder s charged an access fee or termnaton fee by local land-lne phone frms or other servce provders. Snce we only have data on the total mnutes of voce calls and number of text messages, we use the weghted average 9 of on- and off-net prces as the margnal prces for voce calls and text messages. Two major wreless servce provders co-exst n our cy. The servce provder n our data (Frm A) s the market leader wh more than 60 percent of market share durng the sample perod (see Fgure 2). Another major cellular competor (Frm B) has a market share between 20 and 30 percent. The thrd company (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 By subscrbng to ths servce, consumers can carry ther phones lke a cell phone, and the ncomng calls are free. Ths new servce proved to be very successful, wh the frm s wreless market share n the wreless ndustry ncreasng to about 12 percent at the end of the sample perod. Because of the new competon, the market share of our servce provder (Frm A) started to declne n As a response, the frm ntroduced n August 2004 a new data centrc plan targetng consumers wh hgher demand for text messages. That proved to be a powerful competve strategy. Its market share started to rebound snce August As shown n Fgure 3, the new plan gans new users quckly after s ntroducton. By the end of the sample perod the number of s users has 8 If a consumer on the voce centrc plan uses roamng servce n a partcular month, he or she wll pay 30 as monthly access fee; f not, he or she wll only pay 15 as monthly access fee. 9 Ths s computed by assumng balanced callng patterns, whch mples that when a consumer makes a telephone call, the recever of the call can be any other consumer wh equal probably ndependent of hs(her) current subscrbed network. 11

12 almost caught up wh the voce centrc plan, the most popular plan of the frm whch also grows steadly durng our sample perod. 10 Ths mples that, for the data centrc plan, to attract new users and grow market share s at least as mportant as to nduce swchng between servce plans among the exstng users. Therefore, unlke most of the prevous studes (e.g., Lambrecht, Sem and Skera (2005) do not consder jon-ns durng the sample perod, and Narayanan, Chntagunta and Mravete (2005) only consder swchers between plans), s mportant for us to model why new users jon n (whose usage before jon-n s unobserved from data) and why exstng users drop out from (whose usage after drop-out s unobserved from data) the servce plans. To understand the usage behavor dfference among users, we break down the whole user sample nto () those who stay on the voce centrc plan and never swch, () those who jon n the new data centrc plan and then stay, () those who swch from the voce centrc plan to data centrc plan, (v) those who jon n the data centrc plan and then swch to the voce centrc plan, and (v) those who drop out from the frm s plans. Table 2 reports some summary statstcs of the usages for both voce calls and text messages. Whle the average usage of voce calls s not sgnfcantly dfferent across groups of users, the average usage of text messages for those who stay on the voce centrc plan s sgnfcantly lower than other groups. The usages of swchers from the data centrc to the voce centrc plan and dropouts are also lower than those who stay wh or swch from voce centrc to data centrc plan. Nevertheless, we note that usages are endogenous whch depend on free usages and margnal prces under dfferent plans. Usage dfferences may reflect eher dfferent nherent consumer preferences or dfferent prcng schemes. To nvestgate whether or not consumers adjust ther usage patterns and whether or not they gan from swchng, we look at those swchers observed from data. We compute the consumer costs under the voce centrc and data centrc plans, respectvely, based on dfferent usage patterns. Frst, there are 131 users n our data swchng from the voce centrc plan to the data centrc plan. Based on the 10 Because of the growng acceptance of cellphone 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. 12

13 observed usage patterns after they swch 11, 78 percent gan from swchng wh an average savng of 16.2, and 22 percent are worse off from swchng wh an average loss of 3.8. The average cost savng s 11.7 among all users. However, based on the usage pattern before they swch, 12 only 60 percent gan from swchng wh an average savng of 10.5, and 40 percent lose from swchng wh an average loss of The average cost savng s Fgure 4 llustrates the average gan and loss based on the two usage patterns. There are smlar gan and loss patterns among those users who swch from the data centrc to the voce centrc plan. Ths mples that consumers are on average makng correct swchng decsons. Moreover, consumers wll change ther usage patterns once they swch to another plan wh dfferent prces. We are concerned wh two ssues related to the swchng pattern here. Frst, agan look at Fgure 3. The market share of the new data centrc plan grows gradually n the 12 months after was ntroduced. Ths suggests that takes tme for users to realze the true benefs of jonng n or swchng to the new plan. As wll be dscussed n the next secton, we propose a consumer learnng model to explan ths dynamc pattern of swchng. Second, though we fnd that most swchers seem to make correct swchng decsons, there are users who choose to stay wh eher voce centrc or data centrc plan but could have been better off f they swch. For example, among the 965 users who choose to stay wh the voce centrc plan, 25 percent of them would be benefed had they swched to the data centrc plan, wh an average savng of Moreover, there are some swchers from the voce centrc plan to the data centrc plan ncurrng losses but choosng to stay wh the new plan. Why don t these consumers swch to a dfferent servce 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 12 months of the ntroducton of the new plan. As we have dscussed n the Introducton, we wll ratonalze ths phenomenon by explcly allowng for consumer swchng costs (both from 11 Ths provdes an approxmate upper bound on the savngs of swchng to the data centrc plan. 12 Ths can be vewed as a lower bound on the savngs of swchng to the data centrc plan. 13 Smlarly, among those 728 users who jon n and stay wh the data centrc plan untl the end of sample perod, about 15 percent of them would be better off had they swched to the voce centrc plan, wh a savng of

14 swchng between servce plans provded by the same frm, or jonng n or droppng out from the frm) n our model. We randomly select 564 consumers from the above 2,357 consumers n our model estmaton. Ths selected sample conssts of 6,774 monthly observatons, wh 55 percent stay wh the voce centrc plan, and 45 percent wh the data centrc plan, at the end of the sample perod. We compare the usage and swchng patterns of ths sub-sample and fnd them very smlar to that of the whole sample. 3. The Model In ths secton we wll frst dscuss the drect utly functon of usng voce calls and text messages usages. Then we wll explan how we model the consumer preference heterogeney. Wh these the optmal condons for usages, condonal on servce plan choces wll be derved. Based on these optmal usage condons we can further derve the ndrect utly functons for choosng servce plans when consumers can only form expectatons about ther usages n any perod, and hence the choce probably of each servce plan. We wll also explan n detal how swchng costs and consumer learnng are ncorporated n our model. 3.1 The Utly Functon We model consumers' decsons regardng the wreless servce n an ntegrated framework: consumers frst choose the servce plan ncludng an outsde opton 14 and then, condonal on the servce plan choce, make the usage decsons. 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 examples see Hanemann (1984) and ubn and McFadden (1984) 15.) wh the dfference that we also account for the tme lag between the plan choce and usage decsons (e.g., see Iyengar (2004) and Narayanan, Chntagunta and Mravete (2005)), where n each stage consumers nformaton sets may be dfferent. 14 The outsde opton ncludes the choce of not havng any wreless servces and the choce of other competng wreless servce provders. We cannot dfferentate them from our data. 15 Also for recent emprcal works see Hendel (1999), Km, Allenby and Ross (2002), ube (2004) and Chan (2005). 14

15 We assume that consumers utly s derved from both usng voce calls and text messages. Consumer, =1,, N, chooses a servce plan from the avalable wreless servce plan optons at tmet. Consumer has four optons: stays n the same plan as tme t 1, swches to another servce plan whn the same servce provder, drops out of the exstng servce plans (.e., choose the outsde opton), and sgns n for one of the servce plans as a new user. If she chooses an nsde servce plan from our servce provder, ndexed by j = 1,..., J, at tme t, she wll then choose the number of voce call mnutes x, the number of text messages x, and quanty of the outsde good x 0 other than the wreless servces. To consume a wreless servce bundle{ x, x }, the consumer pays an access fee A j, enjoys a free usage for voce calls F j and for text messages F j, and then pays a margnal prce for voce calls p j f x > Fj, and for text messages j p f x > F. For model estmaton we normalze the prce of the outsde good to 1. We j allow for the case that the consumpton of eher voce calls or text messages may be zero n some perods, that s, corner solutons for usages may exst. We assume that the consumer utly s addvely separable n usng voce calls and text messages. 16 The proposed utly structure, f consumer chooses an nsde servce plan j, follows the followng specfcaton: 0 (,, ) U x x x j ( x ) ( x ) 2 2 = δ + x + θ β x β + θ β x β + ε j jt () where U j s the consumer s drect utly functon, and δ j s a plan-specfc preference ntercept representng benefs other than voce calls and text messages offered by the plan that are not modeled here. For smplcy we assume the 16 We note that such addve separably assumpton may restrct the substuton pattern among the two servce usages. A more flexble specfcaton wll be to allow an nteractng term between the voce call and text message usages n the utly functon. However, snce there s no prce varaton for each servce plan durng our sample perod, such an nteracton s dffcult to be dentfed from our data. Furthermore, as wll be dscussed below, we allow the consumer preferences for voce calls and text messages to be correlated. Therefore our model s able to generate a flexble substuton pattern among the two servce plans at the aggregate level. (1) 15

16 ntercept s homogeneous to all consumers. The margnal utly derved from the outsde good 0 x s normalzed to 1. The sub-utly functon θ β x β ( x ) 2 2 s derved from voce call consumpton and θ β x β ( x ) 2 2 from text message consumpton. Note that ths addve separably structure mples neher complementary nor substutably between usng voce calls and text messages, and the utles from usng voce calls and text message are ndependent of the utly from consumng the outsde good. Parameters to be estmated nclude δ, θ, j θ, β and β, where the last two parameters are restrcted to be posve. The last component n (1) ε jt s the ndvdual-, plan- and perod-specfc..d. random shock that wll affect consumers servce plan choces but unobserved to 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 consumers' preference parameter for usng voce calls and text messages, θ L {, θ θ } =, has two components. Frst there s an ndvdualspecfc and tme-nvarant preference component θ L, and then an ndvdual- and L tme-specfc..d. unobserved preference shock ξ. That s, { } L L L θ = θ + ξ, L=, (2) 2 θ θ σ Let θ. We assume that θ (, θ normal ) Σ σ θ, and Σ. θ θ = 2 σ σ Ths set-up mples that the consumer preferences for usng voce calls and text messages may be correlated. We also assume the tme-varyng unobserved preference shocks ξ 0 ξ.. d. normal (, ) Σξ, where ξ 0 σ Σ ξ = σ Ths allows for the correlaton n tme-varyng preference shocks for usng voce 2 ξ ξ σ σ ξ 2 ξ. 17 Ths quadratc utly specfcaton s consstent wh prevous lerature such as Wlson (1992), Mravete (2002), Mravete and Roller (2003), Jensen(2004), Iyengar (2004) and Economdes, Sem and ard (2005). 16

17 calls and text messages. The tme-varyng and ndvdual-specfc preference shocks ε jt n (1) are assumed to be..d. wh double exponental dstrbuton. Fnally, as we wll show below, β and β n (1) drectly correlate wh usage responsveness to changes n margnal prces p j and p j, respectvely. Because there s no prce varaton whn each servce plan n our data, consumer heterogeney of usage responsveness s hard to be dentfed. We mpose the homogeney assumpton that β 3.3 Usage ecsons = β and β = β for all consumers. We start wh the consumer usage decsons for both voce calls and text messages, condonal on choosng a servce plan j. We assume that at ths stage the consumer preferences for voce calls and text messages, θ and θ, are realzed, as opposed to the servce plan choce stage when consumers can only form expectatons, whch we wll explan n later secton. However, the consumer cannot separate θ from ξ. That s, she only knows her preferences n perod t but does not know for sure how much wll reman unchanged and how much may fluctuate over tme. We assume that the consumer chooses usages that wll maxmze her utly subject to a budget constrant. The drect utly maxmzaton problem s specfed as ( ) 0 max U,, 0 j x x x d = j { x, x, x } ( ) { } ( ) { } st x p x F x F p x F x F A Y j j j + j j j + j () where U s consumer 's drect utly n (1) condonal on choosng plan j, d s j (3) the dscrete servce plan choce at tme t, and x 0,, x x are the endogenous usage decsons for the outsde good, voce calls, and text messages, respectvely. F j and F j are the correspondng free usages for local voce calls and text messages, and A j s the access fee, p j and p j are margnal prces for voce calls and text messages, and Y s the ncome of the consumer. Fnally {} n the second lne n (3) s an ndcator functon whch s equal to one f the logcal expresson nsde s true, 17

18 and zero otherwse. The consumer wll be charged by the margnal prces only f her usage exceeds the number of free mnutes or the number of free text messages n the plan. If she chooses the voce-centrc plan n our data, there s no free usage for text messages n the servce plan, therefore F = 0. Solve for (3) we have the followng Kuhn-Tucker condons for optmal usage of voce calls ( x messages ( x ) 18 : * j * ) and text * 1 1 * x ( θ pj j j ) θ F + p x = 0 β β * 1 1 * x ( θ pj θ Fj pj x ) + = 0 β β Condons (4) allow for the exstence of corner solutons,.e., * (4) * x = 0 or x = 0. Ths s the case when eher θ or θ are negatve. Moreover, when L L 1 L 0 < θ < Fj + p L j, L= or (hence the ndcator functons n (4) are equal to β zero), then x L* L L L 1 L = θ ; otherwse f θ Fj + p L j (hence the ndcator functons β n (4) are equal to one), x L* L 1 L θ p L j =. β 3.4 Servce Plan Choces Based on the drect utly functon n (1) and the objectve functon n (3), we can plug n the Kuhn-Tucker condons n (4) to derve an ndrect utly functon of choosng servce plan j as the follows: 18 Followng conventon we assume the there always exsts an nteror soluton for the outsde good 0* consumpton,.e., x > 0. 18

19 ( ;, ;, ; ) 2 ( ) { } ( ) 2 θ β θ β Y A 0 { 0} A F F p p Y j, j j j j j = δ j + j + θ > + θ > θ pj + ( pj ) + pj Fj θ > Fj + p j 2 β β θ pj + ( pj ) + pj Fj θ > Fj + p j 2 β β + ε (5) jt Interpretatons of equaton (5) are as follows: If both θ < 0 and θ < 0, the ndrect utly functon wll be 1 0 < θ Fj + p j and β ( ) ( ) j, = δ j + Y A j + ε jt ; f both 1 0 < θ Fj + p j, we wll have β 2 2 θ β θ β j, = δ j + Y A j εjt ; fnally f both θ 2 2 and θ 1 > F + p, we wll have β j j ( θ ) ( θ ) 2 β j, = δ j+ j + θ j + ( j ) + jfj Y A p p p 2 2 β 2 β θ pj ( p j ) pj Fj εjt β 1 > F + p β j j The ndrect utly functon of choosng servce plan j depends on the consumer preferences for usng both voce calls and text messages. If consumer chooses the outsde opton, we assume an ndrect utly functon as follows: = δ + Y + ε (6) 0, 0 0t In the estmaton model δ 0 s normalzed to 0 for model dentfcaton. We assume that ε 0t s ndependently and dentcally dstrbuted wh double exponental dstrbuton. 19

20 The consumer makes the servce plan choce at the begnnng of perod t. As L opposed to the usage decsons n (4), she does not exactly know the value of θ, where L= or (see equaton (2)), whch conssts of a tme-varyng dosyncratc demand shock ξ L whose value the consumer only knows the dstrbuton, and a tme-nvarant preference type θ L that she can only learn gradually over tme (we wll further dscuss n the learnng model later). The consumer has to form an expectaton for j, based on her past usage hstory or nformaton set Ω,.e., E [ Ω ]. The consumer wll choose the opton wh the hghest expected j, 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 or non-swchng patterns observed among consumers, we allow for the exstence of swchng costs and consumer learnng of ther own preference types n our model. Frst, we assume that consumer ncurs swchng cost, 1 SC by the same frm, whch s dstrbuted as, when she swches to a dfferent servce plan provded ( 1, 2 1 ) normal SC σ sc. If the consumer decdes to drop out or jon n from the outsde opton, ncurs another swchng cost, 2 SC. For dentfcaton ssue we restrct ths cost to be homogeneous across consumers. As dscussed before, swchng between servce plans whn a frm may ncur a dfferent cost, eher physcally or psychologcally, compared to swchng between frms. 19 We gnore n our model that some consumers may not be aware of the exstence of the new servce plan,.e., the new plan s not n ther consderaton set. 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. 20

21 Suppose the consumer s a user of the voce centrc plan (plan 1) n perod t- 1. In perod t, she wll agan choose the same plan, nstead of the data-centrc plan (plan 2) or the outsde opton, f the followng s true: 1 2 { } E[ Ω ] max E[ Ω ] SC, SC, 1, 2, 0, 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 2t 0t ( d = ) Pr = Pr ( ε 1t, ε2t, ε0t) : E1, + ε 1t max( E 2, SC+ ε2t, 0 SC + ε0t) (7) _ exp E1, = 2 1 exp( 0 SC ) + exp E1, + exp E 2, SC where d s the dscrete servce plan choce of consumer n perod t, _ E j, s the determnstc part n E [ j, Ω ] whout the dosyncratc component ε jt, and 0 s smlarly defned. Smlarly, the consumer wll swch to servce plan 2 f the followng condon s true: And she wll choose to drop out f { } E[ Ω ] SC max E[ Ω ], SC 1 2 2, 1, 0, { } SC max E[ Ω ], E[ Ω ] SC 2 1 0, 1, 2, wh choce probables smlar to equaton (7). If the consumer s not a user of our servce provder n perod t-1, by jonng eher plan 1 or 2 she wll ncur swchng cost SC 2. Hence, she wll only choose servce plans 1 or 2 f eher or { } E [ Ω ] SC max E [ Ω ] SC, 2 2 1, 2, 0, { } E [ Ω ] SC max E [ Ω ] SC, 2 2 2, 1, 0, 21

22 s true, respectvely. Based on that choce probables of jonng can be derved smlarly as equaton (7). We wll dscuss how we compute _ E j, n detal later. Consstent wh most prevous lerature on learnng, we allow that consumers may not know ther own tme-nvarant preference types {, } θ θ hence have to form expectatons based on past experences. Ths type of consumer learnng s mportant 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 own usages x and these usages are posve, the optmal condons of usages mply that x. Suppose 1 θ = θ + ξ = x + b p θ > F + p β j j j 1 θ = θ + ξ = x + b p θ > F + p β j j j (8) L where b = 1 L, L= or. Though there s a one-to-one mappng between usage β x and the tme-varyng preference θ L (we assume that b L s known to the L consumer) so that she can use the observed usages to nfer preferences, she cannot L separate θ and ξ from the sum θ L. We assume that the consumer knows that L ( ξ, ξ ) are dstrbuted as N (0, Σ ξ ). Regardng θ L, we assume that n the frst perod t=1 all consumers have the same pror belefs dstrbuted as θ θ 0 ~ N, Σ θ 0 θ θ 0, where θ 0 represents the pror preference means, and θ 0 2 σ 0 0 Σ θ 0 = 2 0 σ 0 s the pror varance-covarance matrx whch measures the consumer uncertanty. 20 At the end of every perod, after observng ther usages, consumers update the belefs of ther preference types usng the Bayesan rule 20 For the smplcy of model estmaton we assume that consumers beleve that ther preferences for voce calls and text messages are ndependent. It s generalzable to the case when preferences n pror belefs are not ndependent. 22

23 (egroot (1970)): Assumng after t perods the consumer s belef of her preference type for usng servce L s N ([ θ, θ, ]', Σ θ, (, + 1, + 1 θ, t+ 1) ) t 21, then her belef at tme t +1 are dstrbuted as [ ]', N θ θ where [ θ θ ]' and Σ are gven by 1 1 (( ) ( ) t ) θ, t+ 1 ξ θ, Σ, + 1, + 1 θ, + 1 θ, x + b p j 1 θ, =Σ, 1 ( ) (, ) θ t+ Σ + Σ ξ t θ, 1 x b p θ + j θ +,. (9) Σ = Σ + Σ 1 Zero usages, though nfrequent, do exst for eher voce calls or text messages n the data. When the consumer experences, say, x = 0, she can only nfer that 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., 2 (,, N θ, σ θ + ξ 0) (10) 2 where θ, and σ, are the mean and varance n pror belefs for θ at tme t, respectvely. In model estmaton we smulate ths condonal dstrbuton to obtan 2 the estmates for θ, + 1 and σ, + 1. t 4 Estmaton Results 4.1 Some etals for the Estmaton Model The optmal condons for voce call and text message usages n equaton (4) mply a Tob-type regresson: If the observed usages L L L L L L we can derve that θ ξ x pj { x Fj } L L x, L= or, s posve, 1 + = +. If x L 0 L =, we can nfer that β L θ + ξ 0. Condonal on ( θ, θ ), we can wre down the probably functon of the observed usages ( x, x ) as Pr( x, x θ, θ ), followng our assumpton that the dosyncratc preference shocks ( ξ, ξ ) are dstrbuted as N (0, Σ ξ ). Note L that θ here s the true preference of consumer and not the pror belef because the 21 Here the subscrpt t denotes consumers belefs of own preference types after perod t. 23

24 true value has been realzed n the usage decson stage. In the model estmaton, we smulate the uncondonal probably functon of usages by usng a frequency smulator for θ : Let s represents a smulaton. We draw, for each consumer, θ θ s, θ from the assumed populaton dstrbuton N (, θ ) Σ θ for ns tmes and s, θ fxed these smulated draws over tme for each consumer. The smulated lkelhood of the observed usages for consumer from perods t=1,, T s evaluated as the follows: 1 Pr (, ;...;, ) [Pr(,, )... Pr(,, )] ns s x1 x1 xt xt = x1 x 1 θ, s θ, s xt xt θ, s θ, s ns s= 1 Now 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 j,, whch s the determnstc part n E [ j, Ω ] whout the dosyncratc component jt ε (also see equaton (5)). As opposed to evaluatng the probably functon for usages Pr( x, x ;...; x, x ), E j, s a functon of the consumer s belefs of 1 1 T T _ 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 j, can be wrten as the 24

25 _ E j, = δ + Y A j j ( ) 2 { } ( ) 2 % θ + ξ β % θ + ξ β,, % θ + ξ > 0 +, {% θ + ξ > 0, } ( % θ + ξ, t ) p + j ( pj ) + p F % F p j j θ + ξ > +, t j j df( % θ, % θ ) df( ξ, ξ ),, 2 β β ( % θ + ξ, t ) p + j ( pj ) + p F % 1 θ + ξ j j > F + p, t j j 2 β β The above expresson, unfortunately, does not have a closed-form expresson. To compute ths functon we agan use the smulaton method by drawng (% θ,, % θ, ) from the pror belef dstrbuton N ([,, ]', θ, t) θ θ Σ, and ( ξ, ξ ) from the assumed dstrbuton N(0, Σ ) to form the smulated ξ _ s j, E n the above expresson. We then plug the smulated E _ s j,, for every servce plan j, every consumer, and every perod t, nto the multnomal log functon analogous to equaton (7) to become our servce plan probably functon, Pr s ( d j) =. We jontly estmate the lkelhoods of both usage and servce plan choce decsons. Let Θ be the vector of parameters ncludng the utly functon coeffcents, swchng costs and means and varances n pror belefs. Our estmator ˆΘ satsfes the followng condon: N s s x 1 x1 xt xt ( d j ) Θ= ˆ arg max {Pr (, ;...;, Θ) Pr = Θ} Θ = 1 t= 1 2 σ 0 0 Σ θ 0 =. Parameters θ 2 0 and θ 0 are known to be dffcult to be 0 σ T (11) Some more detals for the model specfcaton here: we assume that at tme θ θ 0 t=1 all consumers have the same pror belefs as ~ N, 0, where Σ θ θ θ 0 0 dentfed from data (for example see Chan and Hamlton (2006)); hence, we restrct them to be equal to θ and θ, the populaton mean preferences for usng voce 25

26 2 calls and text messages, respectvely. We also mpose the restrcton that σ and σ are equal to the varances of preferences among the populaton. 2 0 A unque feature n our data s that many new consumers jon n (especally after the data centrc servce plan was ntroduced) and exstng consumers drop out n dfferent tme perods. Usages of these consumers before jon n or after drop out are not observed from data. In order to evaluate the probably of not jonng n the servce plans we have to make assumptons about ther belefs of own preferences. In the model estmaton, we assume that these consumers mantan the same pror belefs θ 0 N, Σ θ 0 θ 0 overtme untl they jon 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. An nterpretaton whch makes the assumpton of constant belefs before jon n or after drop out vald s that the outsde opton s not to use any cellular servces hence consumers do not know what ther usages would be had they subscrbed to the servce plans. The consumers outsde opton choce before jon n or after drop out s ncluded n the lkelhood functon n (11). Though ths assumpton may be restrctve, we are not able to nfer how belefs are updated durng these perods because of the lack of data. However, gnorng new jon-ns or drop-outs consumers may create bas n the model estmaton. Snce one of our research purposes s to evaluate how the servce provder may attract new customers or retan exstng customers through ntroducng new servce plans, we consder mportant to correctly nfer the relatve value of the outsde opton avalable to the potental consumers. Fnally, we estmate three models: Model 1 s a base model whch does not allow for swchng costs or consumer learnng. Model 2 s the model allowng for swchng costs but no consumer learnng. Model 3 s our proposed model whch 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 the components of swchng 0 26

27 costs and consumer learnng, helps to explan the observed patterns of servce plan swchng, jonng n and droppng out n our model. 4.2 Estmaton Results Estmaton results are reported n Table 3. All of the three models suggest that, whle the mean preference for usng voce calls (voce demand ntercept) s hgher than the mean preference for usng text messages (message demand ntercept), there s a larger heterogeney n text message preference (standard devaton of message demand ntercept). The demand slopes for usng both voce calls and text messages are sgnfcantly negatve, suggestng that consumers do respond to margnal prce changes n voce calls and messages. One of the unexpected results s that the voce call preference s posvely correlated wh messages preference (The estmated correlatons are 0.029, and n three models.), mplyng that consumers who have a hgh voce call preference are also lkely to have a hgh text message preference. Another unexpected result s that the voce call usage shock s also posvely correlated wh text message usage shock (parameter l 12 ). Ths estmate mples an estmated covarance of 0.374, and n three models (see footnote n the table), mplyng that consumers wh a hgh voce call usage shock n a perod are also lkely to have a hgh text message usage shock. Although these results are counter-ntuve, they are consstent wh our data. For example, we fnd that consumers who stay wh or swch to the data centrc plan have a hgher usage for both voce calls and text messages, compared to those consumers who stay wh or swch to the voce centrc plan (see Table 2). Snce the latter plan offers more free voce call mnutes, such voce call usage dfference should reflect dfferences n consumer voce call preferences nstead of prce dfferences. Such a fndng has an mportant mplcaton for the frm s prcng strategy for servce bundles, whch we wll further explore n the later secton. Models 2 and 3 show that on average consumers, when they swch servce plans whn the servce provder, ncur a mean swchng cost of and wh standard devatons and 0.98, respectvely, and 6.4 when they swch to and from the outsde opton. Ths s consstent wh our ntuon that the latter swchng should be more costly, eher physcally or psychologcally, than the 27

28 former. Furthermore, the small dfference n the swchng costs (from 10 to 40 cents) seems to mply that to most consumers the outsde opton s not to use any cellular servces at all, snce f s swchng between cellular companes consumers are requred to change phone numbers and vs or call both companes, hence the swchng cost should be much larger. Although overall the swchng costs are small (less than US $1), may not be unreasonable consderng that the purchasng power of the Chnese consumers n our cy s relatvely low (e.g., compared wh Amercans). Takng nto account of swchng costs mproves the model f a lot (as lkelhood value mproves from -19,019 n Model 1 to -12,980 n Model 2), suggestng that swchng cost s useful n explanng the choce patterns observed n the data. Allowng for consumer learnng n Model 3 the lkelhood further mproves to -12,954. Snce the numbers of parameters n Models 2 and 3 are dentcal, our learnng model domnates other models n terms of sample f. A further support for usng our proposed model s to compare the predcted swchng patterns from the models wh data. Accordng to the data there are 5.6% swchers who swch from voce-centrc plan to data-centrc plan. The predcted swchng proportons are 13.4%, 2.8%, 4.1% accordng to Models 1, 2 and 3, respectvely. Ths clearly shows that Model 3 has better explanatory power for the swchng pattern n data. Based on the results from our proposed Model 3, we compute some elastces correspondng to how plan choce probables, voce call and text message usages, as well as the frm revenue, change wh respect to changes n the prcng scheme ncludng access fee, voce call and text message margnal prces, and free usages for voce calls and text messages. 22 The results are reported n Table 4. Frst, when we compare the usage elastces for both voce call and text message under the current voce-centrc and data-centrc plan prcng schemes, an nterestng result s that the former s always more elastc than the latter. Ths mples that a one percent change n eher access fee, margnal prces, or free 22 We frst compute the elastces at the consumer-level, and then average all the ndvdual elastces. 28