Adverse Selection, Welfare and the Optimal Pricing of Employer- Sponsored Health Plans

Transcription

1 Adverse Selecton Welfare and the Optmal Prcng of Employer- Sponsored Health Plans Carolne Carln Unversy of Mnnesota Robert Town Unversy of Mnnesota and NBER Aprl 009 Revson n Process Comments Welcome Abstract We assess the welfare mpact of adverse selecton n health nsurance choces usng detaled panel data on health plan choces and complete health care utlzaton. Our estmates suggest that adverse selecton plays an mportant role n explanng cost dfferentals across plans and much of the selecton occurs along dffcult to contract upon dmensons. The dstortonary consequences of the asymmetrc nformaton are modest because ndvduals are very premum nelastc n our data. Our fndngs show that the presence of sgnfcant adverse selecton need not cause meanngful welfare loss. We have receved helpful comments from semnar partcpants at Internatonal Health Economcs Assocaton Conference n Copenhagen Cornell Unversy Northwestern Unversy and the Unversy of Mnnesota. We thank Bryan Down Roger Feldman Thomas Holmes Sam Kortum and Dean Lllard for ther comments. Support provded by AHRQ Dssertaton Grant HS0557.

2 . Introducton It s wdely assumed among economsts that adverse selecton dstorts health nsurance market outcomes. Ths dstorton can emerge along two related dmensons. Frst selecton may affect the avalably and structure of nsurance contracts offered to consumers (Rothschld and Stglz 976). Second snce the health plan s average and margnal costs are dfferent functons of the denty of s enrollees for a gven set of health nsurance plans admnstrators and/or the market equlbrum wll have dffculty settng premums optmally (Akerlof 970; Newhouse 996; Cutler and Reber 998). The mportance of adverse selecton lkely becomes more acute n the presence of sgnfcant heterogeney n health plan qualy and cost. Dependng on the premum settng strateges employed by the sponsors of the nsurance small nal health plan cost dfferentals can be magnfed by adverse selecton nto neffcently large premum dfferentals. Furthermore the cost advantage or dsadvantage of a health plan may dffer by ndvdual health status. Some plans may spend more treatng the healther enrollees whle other plans may provde care to the relatvely sck at lower cost. The presence of health plan heterogeney thus complcates the welfare assessment of adverse selecton. In ths paper we assess the welfare mpact of adverse selecton n the health nsurance choces of employees workng for a large organzaton. The focus here s on the role selecton plays n dstortng premums -- a welfare consequence of asymmetrc nformaton dentfed by Akerlof (970). If enrollees dffer n ther health status and ther preferences across health plans the average and margnal cost curves (as functons of premums) dverge n the presence of selecton. Optmal sortng of enrollees nto plans requres premums to be set equal to the cost of the margnal enrollee. However n a competve equlbrum and n many employer-sponsored settngs premums wll equal (or be a functon of) the average cost of the plan and not the cost of margnal enrollee. Ths dstorton mples that that the plans attractng hgher-cost enrollees wll

3 be prced too hgh. Welfare loss s a consequence of enrollees falng to enroll n the hgh-cost plan due to premum dstorton when they value that plan more than ther margnal cost. We possess detaled nformaton on both the actual health nsurance choces and the complete health care utlzaton experence of a large number of ndvduals over multple years. Our data also allow us to formulate rch measures of the employee s health status that are based upon actual medcal care utlzaton and prevous dagnoses. These data provde suffcent detal to cleanly model heterogeney n ndvdual and health plan expendures a necessy n assessng the welfare mplcatons of adverse selecton. Furthermore the health status nformaton that s avalable usng the clams data allows us to decompose adverse selecton nto easly observable (to the nsurer) demographc varables and more dffcult to observe health status dmensons. It s well known that dentfyng adverse selecton separately from moral hazard can be dffcult (Chappor and Salane 000). Because we use clams nformaton from the prevous year to construct ndvdual-specfc health status measures n conuncton wh plan fxed effects exogenous premum varaton enable us to solate the role of adverse selecton n explanng cost dfferentals across health plans. Modelng Health Plan Choce To examne the role of adverse selecton we construct a model of health nsurance choce n whch ndvduals assess the qualy of the health plan ther estmated health status premums and expected level of expenses when selectng a plan. Here we explo the detaled data and formulate measures of the health status and expected out-of-pocket expendures that reflect actual enrollee medcal care utlzaton across dfferent plans. We estmate utly parameters usng an autoregressve multnomal prob choce model (Geweke Keane and Runkle 997). The prob model allows for flexbly n the correlaton Under dfferent premum settng mechansms the low-cost plan s premum could be set too hgh relatve to the optmum. If ths s the case the logc of the subsequence sentence holds substutng low-cost for hgh-cost.

4 structure of the choce-specfc errors. Our mplementaton also allows the unobserved chocespecfc error term to be autocorrelated and the autocorrelaton parameter can vary across health plans. Indvduals tend to reman n the same health plan for multple years suggestng that ncorporatng unobserved autocorrelated heterogeney nto the model may be mportant. Statstcal nference s generated usng Bayesan methods (Gelfand and Smh 990) as classcal approaches to estmatng the model are too computatonally ntensve to mplement and convergence usng classcal methods s often problematc. Ths model removes many of the unappealng mplcatons (and potental bases) of the lerature s workhorse emprcal model the d multnomal (or nested) log. The estmates from the choce model ndcate that adverse selecton manfests along both the relatvely easy-to-observe demographc varables and the much more dffcult to-observe health status dmenson. That s nformaton that ndvduals use to make health plan choce s prvate unlkely to be contractble and correlated wh ther expected cost. Furthermore our estmates also suggest that the use of the multnomal log choce models leads to erroneous conclusons over several mportant dmensons of health plan choce. We also fnd that unobserved heterogeney n plan preference s extremely persstent and falure to account for ths nerta leads to based estmates of premum elastces and other mportant factors that nfluence health plan choce. Modelng Health Plan Expendure As a precursor to the choce model we use the detaled clams data nformaton to estmate the parameters of a set of health expendure equatons allowng for ndvdual- and plan-specfc heterogeney. In keepng wh the spr of the choce model estmaton nference s done whn a Bayesan framework. The model allows for ndvdual-specfc random effects and allows nonlnear plan-specfc relatonshps between costs and health status. The estmates 3

5 from the expendure equatons enable us to decompose cost heterogeney across plans nto dfferences that are a consequence of selecton and dfferences that are related to plan desgn. Desgn-based dfferences n plan costs may be a consequence of payng hgher prces to provders (Cutler McClellan and Newhouse 000) and/or dfferences n the ably to control utlzaton n the presence of potental moral hazard. In order to understand the role of moral hazard n the cost dfferentals across plans we de-lnk health care utlzaton from provder rembursement levels by measurng health care resource consumpton usng Medcare s Resource-Based Relatve Value Scale (RBRVS). For the purposes of Medcare rembursements the RBRVS maps the thousands of possble procedures and treatment codes n the clams data nto a sngle comparable resource utlzaton measure. Controllng for demographcs and health status we model dfferences n resource use across the plans. Results suggest that plan cost dfferentals are drven by dfferences n both provder prces and resource use. Our estmates from the expendure analyss suggest that adverse selecton plays an mportant role n explanng average cost dfferentals across plans. That s the magnude of health status selecton can adversely affect welfare. In addon the estmates from the expendure model ndcate that there s sgnfcant varaton n health plan costs and that these dfferences vary by the health status of an enrollee. Some plans provde health care coverage for enrollees at a lower cost than the other plans but the rankng of plans dffers by the health status of enrollees. We further decompose plan cost dfferentals nto a utlzaton provder prce dfferentals. The results ndcate that the lowest cost plan uses fewer resources (condonal on observables) and pays s provders less than the more expensve plans. Modelng Welfare Implcatons Whle there s substantal overlap n provder panels between the plans some group practces are excluded from the HMO and the Pont-of-Servce plans. 4

6 To explore the welfare mpact of selecton we perform several premum experments va smulaton. In these smulatons we adust premums accordng to commonly-used rsk adustment rules and we also calculate an optmal premum structure. Whle there s sgnfcant adverse selecton n our data the dstortonary consequences of the asymmetrc nformaton are modest. The welfare gan from usng optmal premum structures or the more easly computed rsk adusted premums lead to very small gans n welfare. The reason adverse selecton does not greatly affect welfare n our context s because plan choces are relatvely nsensve to changes n premums. Large changes n premums margnally affect the average health status of a gven plan s populaton. The remander of the paper has the followng structure. We provde an overvew of the relevant lerature n Secton. The data on whch the analyss rests s descrbed n Secton 3 and the model s lad out n Secton 4 wh detals of the Bayesan estmaton strategy provded n Appendces. The results of the model estmaton are presented n Secton 5 and the results of the employer prcng polcy experments shown n Secton 6. Secton 7 concludes.. Background Theoretcal concerns over adverse selecton n health nsurance markets date back at least to Rothschld and Stglz (976) where they show that non-contractble heterogeney n health rsk can lead to a suboptmal set of contracts beng offered. Newhouse (996) furthers ths dea argung that there s an mportant trade-off between competon and adverse selecton n healthcare and health nsurance markets. Newhouse notes that the ntroducton of competve forces nto health nsurance markets nduces premum reductons but also gves nsurers greater ncentve to attract favorable rsks. The premum reducton effect of competon ncreases welfare but the accompanyng rse n adverse selecton decreases welfare. Cutler and Reber (998) and Enav Fnkelsten and Cullen (008) hghlght how the use of market-lke ncentves 5

7 n health nsurance choce n the presence of adverse selecton and health plan cost heterogeney can lead to neffcent premum settng. 3 Snce s well known that adverse selecton can have deleterous mpacts on health nsurance outcomes s not surprsng that a large lerature has arsen examnng the prevalence of selecton-drven cost dfferentals by health plan. 4 The typcal research n ths lne of analyss studes dfferental demographc or cost experence between some form of managed care and a less restrctve health nsurance product (e.g. a preferred provder organzaton or fee-for-servce plan). 5 Whle there are a number of studes that fnd no selecton the typcal study fnds that the more restrctve the provder network or the more managed the care the more favorable s the health plan rsk selecton. Scker enrollees have a greater wllngness to pay for broad provder access and less nsurer nvolvement n ther care. In ths lerature the strategy of nferrng adverse selecton through use of explc rsk measures embedded whn choce models s atypcal however several papers of note use ths approach. Strombom Buchmueller and Feldsten (00) acqure data on hospalzatons and cancer dagnoses around the tme of plan enrollment and nclude ths nformaton as regressors n a choce model. Others use chronc llness ndcators or pad clams nformaton by partcpant (Parente Feldman and Chrstanson 004; Atherly Dowd and Feldman 004; Harrs Schultz and Feldman 00; Cardon and Hendel 00; Royalty and Solomon 999). 6 But n general 3 See also Pauly and Herrng (000). 4 Cutler and Zeckhauser (00) provde an excellent revew of ths research. More recent examples of adverse selecton n health plans studes are: Atherly Dowd Feldman (004) Barrett and Conlon (003) Tcherns et al. (003) Gray and Selden (00) Rphahn Wambach and Mllon (00) Feldman and Dowd (000) and Altman Cutler and Zeckhauser (003). 5 There s a modest but mportant body of work that examnes adverse selecton n the non-health nsurance context. An ncomplete lst of papers n ths lerature nclude Cawley and Phlpson (999) Chappor and Salane (000) Fnkelsten and Poterba (004) and Enov Fnkelsten and Schrmpf (007). 6 Parente Feldman and Chrstanson (004) use data from a smlar settng to ours supplemented wh an employee survey to examne the profle of those who enroll n a Consumer Drected Health Plan (CDHP). Usng a MNL approach they fnd the CDHP plan enrolled wealther employees and the CDHP was not more attractve to the young and healthy. 6

8 there s ltle attempt n the lerature to adust choce for dfferences n health status wh the excepton of dfferences nherent n employee age and gender. Cardon and Hendel (00) use data from the 987 Natonal Medcal Expendure Survey aggregatng many dfferent heath plans nto three choce categores to quantfy the nfluence of nformaton asymmetres on health plan selecton. Ther work s noteworthy for the ntegraton of ndvdual expected health care expendures nto the choce equaton n an nternally consstent manner. Cardon and Hendel model nformatonal asymmetres as a correlaton between errors n the expendure and choce equatons. In ther vew the observable factors of age gender race and geographc regon that are correlated wh both health care expendures and plan choce are observable by health plans and hence contractble. The cross-equaton correlaton coeffcents are small and not sgnfcantly dfferent from zero and therefore they conclude that there s no adverse selecton n health nsurance choce. In spe of the potental mportance of adverse selecton n health nsurance market outcomes very few estmates exst of the mpact of adverse selecton on welfare. Cutler and Reber (998) provde the frst econometrcally sophstcated estmates. Cutler and Reber study the health plan choces of Harvard employees after the mplementaton of a fxed employer premum contrbuton polcy. They show that under such a premum settng strategy the premum dfferentals between plans s lkely to be too hgh and result n welfare loss. Specfcally they note that the optmal premum dfferences between plans should be based solely upon the cost dfferental of treatng the margnal enrollee. However n most settngs the premum dfferentals wll reflect the average plan-specfc cost dfferental as well as the average health status of the enrollees. If scker enrollees prefer plans that offer a broader choce of provders and choce s more costly to offer the premum dfferentals wll be too hgh relatve to the optmum. Cutler and Reber estmate the parameters and utly functons usng multnomal 7

9 log methods and estmates of costs usng other data sources to conclude that adverse selecton resulted n a welfare loss of 4% of gross premums. However s uncommon for employers to rsk adust premums (Kennen et al. 00). Thus ther fndngs ntroduce a puzzle that our paper addresses. If the welfare loss from adverse selecton n health nsurance s so large why do not more employers rsk-adust ther premums? Two recent papers have estmated the welfare loss from adverse selecton n employersponsored health nsurance. Enav Fnkelsten and Cullen (008) note that the demand and cost curves can be separately dentfed from premum varaton alone. Ths observaton along wh lneary and premum exogeney assumptons makes estmatng welfare loss a smple OLS problem. Usng cross-sectonal data from a large employer and focusng on two plans they fnd evdence of modest welfare loss from adverse selecton of $9.55 per employee per year. Bundorf Levn and Mohoney (008) use data from a sngle health nsurance broker to analyze the welfare gans from ndvdually rsk-adustng the out-of-pocket premum to enrollees. The underlyng dea s that rsk-adustng the out-of-pocket premum better sorts enrollees to plans thereby ncreasng net surplus. Ths paper seeks to advance the welfare analyss of adverse selecton on two fronts. Frst we have detaled medcal care clams nformaton for our enrollees. Other analyses wh the excepton of Enav Fnkelsten and Cullen (008) rely on aggregate costs or estmated costs or use other sources to mpute costs. Our detaled data enable us to formulate ndvdual measures of health status. Second we construct a flexble two-part model of total and out-of-pocket costs that s consstent wh the censored and skewed structure of our data and allows us to calculate cost counterfactuals under dfferent plan enrollment scenaros. Thrd we use a rch choce model that explcly accounts for persstence n ndvdual heterogeney n the context of the panel structure of the data. Our estmates suggest that cross-sectonal estmates of health plan demand 8

10 can lead to based nference. Fourth we decompose health plan cost dfferentals nto the components attrbutable to adverse selecton enrollee utlzaton dfferences and the dfferences n prces pad to provders. There s a lerature on modelng health plan choces for Medcare and employer-based plans that s also relevant to our work. The am of much of ths lerature s to estmate premum elastces or adverse selecton. An ncomplete lst of the papers n ths lerature ncludes Feldman et al. (989) Dowd and Feldman ( ) Cutler and Reber (998) Royalty and Solomon (999) Buchmueller (000) Scanlon et al. (00) Strombom Buchmueller and Feldsten (00) Dowd and Feldman (003) and Atherly Dowd and Feldman (004). None of these papers nclude drect measures of out-of-pocket expendures and they all rely on the restrctve d log famly of choce models to estmate the parameters of nterest. 7 These papers estmate premum elastces for health nsurance that range from the moderately elastc to the very nelastc. 3. Data and Instutonal Settng The data used here are detaled employee health care clams and health plan enrollment hstory for a very large self-nsured employer. Lnked but de-dentfed enrollment hstory s avalable for and clams hstory s avalable for wh sx months of clams run-out pad n 005. As the employer s self-nsured all covered medcal care rendered to an employee wll have an assocated clam ncluded n our data. A clam contans all nformaton needed to process an nsurance payment and thus ncludes valuable nformaton such as prmary and secondary dagnoss codes procedure codes and dentfcaton of provder. The clam also contans nformaton on the amount pad by the organzaton and by the enrollee. For each 7 The only papers that we are aware of that nclude measures of the expected mean of out-of-pocket medcal expendures n a utly maxmzng model of health plan choce are Cardon and Hendel (00) and Marqus and Holmer (999). 9

11 enrollee we aggregate all ther health care clams throughout the year to formulate a precse measure of both the total clams pad for the enrollees care and the share of these expendures ncurred by the enrollee as out-of-pocket costs for covered medcal care. The employer offers health nsurance coverage for ndvduals spouses/domestc partners and famles. Informaton about the spouse/domestc partner employment-based benefs choces are not avalable -- we do not know what the exact choce set s n ths case as the partner may have nsurance benefs at another frm. For ths reason our analyss focuses solely on ndvduals contnuously enrolled n sngle coverage over the three years. Whle sngle coverage does not equate to sngle maral status the approxmaton lkely ntroduces ltle error. In addon employees outsde the metropolan servce area were elmnated from the analyss sample because they have a dfferent health nsurance choce set. Ths leaves 3578 employees for the estmaton. 8 Employee demographcs nformaton s gathered from several sources. Age and gender are taken drectly from the encrypted plan enrollment fles. Employee earnngs was mputed from a separate accountng fle provded drectly from the employer based on brth date gender home zp code work locaton and ob classfcaton. Ths demographc nformaton s merged wh health plan enrollment fles along wh health status and expendure data culled from the clams fles. Plan characterstcs (provder panel structure out-of-pocket lmaton employee contrbuton levels) are drawn from the employer s open enrollment materals. The employer offered a total of four plans n 00 through 005. The employer contracts wh the plans to access ther provder network and specfes the benef desgn. The plans charge the employer a fee for accessng ther network and processng the clams whle the employer pays the medcal care clam net of enrollee out-of-pocket payments. The plans nclude one 8 The relatve plan shares of the entre sample before mposng our ncluson restrctons closely match the relatve shares of our analyss sample suggestng that our ncluson crera s not nducng a sample selecton bas. 0

12 closed-panel health mantenance organzaton (HMO) two pont-of-servce (POS) plans and a Consumer-Drven Health Plan (CDHP). The HMO s a restrcted provder network plan n whch enrollees ncur modest co-pays for any whn-network utlzaton however the plan does not cover any out-of-network medcal care. The organzaton offered two POS plans wh dfferng provder networks both across and whn the plans. One of the POS plans (POS ) has three ters each wh dfferent premum levels; the ters correspondng to successvely broader provder networks. Ter ncludes all the provders n Ter as well as offerng enrollees access to addonal potentally hgher cost provders. Lkewse Ter 3 ncludes all the provders n Ter n addon to other hgher-cost provders. 9 The other POS plan (POS ) has only one opton. The POS plans charge hgher copays than the HMO but allow out-of-network care (wh a hgher co-pay). Out-of-pocket payments dffer somewhat across the non-cdhp plans. The HMO offce vs co-pay n 003 was $5 and ncreased to $0 n The correspondng rates for the POS plans were $0 n 003 and $0 n 004 whle the offce vs copayments for the POS plan were $5 n 003 $5 n 004 and $30 n 005. There was no co-pay for HMO enrollees for outpatent surgery or npatent care whle the POS plans had outpatent surgery and npatent stay co-pays of $75 and $00 over the entre sample perod respectvely. All of these plans had the same prescrpton drug benefs ($0 co-pay n 003 and $5 co-pay n ) and the same out-of-pocket lms of $500. The CDHP s a recently developed health nsurance product that combnes a catastrophc ndemny plan matched wh an employer-funded medcal spendng account. In the CDHP a sngle enrollee s gven an account of $750 (003 and 004) or $600 (005) to draw upon for medcal care. Once the account s exhausted the enrollee pays the balance of the $500 9 Whle the Ters were advertsed as dfferng n the prces pad to provders as we dscuss n Secton 5 we found ltle cost dfferental between the ters n POS.

13 deductble out of pocket. After the enrollee utlzes more than $500 of medcal care there s no addonal copayment for n-network health care. In sum there are a total of sx health plan choces avalable to the employee: HMO POS /ter POS / ter POS / ter 3 POS CDHP. Table presents the annualzed premums and enrollment shares for the plans n our data. The out-of-pocket premums vary across plans and tme. The organzaton spends consderable resources attemptng to nform employees of ther health plan optons thus enrollees are well nformed of the premums and benef dfferences across the plans when makng ther plan selectons. Durng the open enrollment perod brochures and emals are dstrbuted to all employees detalng the premums and changes n premums from the prevous year as well as the plan benef structures and provder panels. In addon the detaled plan nformaton s avalable on the organzaton s human resources web se. The temporal varaton n out-of-pocket premums s drven by two types of changes n the employer s premum-settng strategy. Frst the employer used a defned contrbuton strategy and the formula used to construct the premums changed over tme. For the employee share for sngle coverage was set to zero for the base plan. Employee share for other plans was smply the excess of other plan total premum over base plan total premum. For the employee share was set at 0% of the base plan premum. Employee share for other plans was 0% of ths base amount plus the excess of other plan total premum over base plan total premum. These changes were drven by the organzaton s drve to push more of the cost of health care onto employees. The second change was that the employer moved from a strategy of no rsk-adustment n 00 to one of rsk-adustment lght by the end of our data. Importantly we have dscussed the premum settng strategy wh the human resource personnel and they assured us that the changes n the relatve premums do not reflect specfc changes n the plan

14 characterstcs but changes n the premum-settng strategy of the organzaton. Thus to the best of our understandng tme varyng dfferences n premums are exogenous. The most popular plan s the HMO and s also the cheapest plan. Another noteworthy pattern n Table s that whle the premums of the plans shfted consderably the shares dd not. Ths pattern suggests that controllng for autocorrelaton n enrollee preferences s lkely to be mportant. Measurng Health Status An mportant feature of ths study s that we are able to use past clams nformaton to formulate health status measures that are ncorporated nto the choce model. In order to do ths we need to map the thousands of ICD-9CM codes (and mllons of potental combnatons of codes) nto a parsmonous representaton of future health status. To do ths we rely on commercal algorhms that are desgned to forecast future morbdy for the purposes of rsk adustment ncorporated n the evaluaton of provder performance forecastng healthcare utlzaton and settng payment rates. The health status ndcators are constructed for ndvdual enrollees through the use of the Johns Hopkns Unversy ACG Case-Mx System (v. 6) developed by the Health Servces Research and Development Center. The ACG Case-Mx System uses a combnaton of clncal assessments and groupng of dagnoses and procedures along wh extensve regresson ftng to take the thousands of ICD-9CM codes that are embedded n the clams to construct smple measures of health status. The predctve modelng feature of the ACG software produces a concurrent weght (CW) that s a summary measure of the current ndvdual health status and resource utlzaton. The CW s constructed so that the natonal average s.0 wh hgher values denotng poorer health and lkely hgher expendures. A potental concern wh our measure of health status s that s based on the prevous year s 3

15 health care utlzaton whch n turn s potentally a functon of the characterstcs of the plan. That s our measure of health status may ncorporate aspects of moral hazard. The nfluence of moral hazard wll be mgated by the fact that the CW s based on dagnoss code hstory rather than clams dollars pad. Thus moral hazard can only nfluence the CW through dfferences n accessng care. To nvestgate ths possbly we regress the logarhm of CW on plan and ndvdual fxed effects. Snce we are controllng for tme-nvarant ndvdual dfferences n CW f the plan coeffcents are nsgnfcant strongly suggests (but s not dsposve) that our measure of health status does not nclude a moral hazard component. The plan fxed effects are all ndvdually nsgnfcant and the ont test of ther sgnfcance does not reect the hypothess that they are equal to zero suggestng that n fact CW vares only wh the health status of the ndvdual. These fndngs do not mply that moral hazard s not present but only that s nfluence on our measure of health status s at best modest. Table provdes summary statstcs of our estmaton sample. The organzaton has a hgh percentage of female employees and the average health status of the employees s poorer than the natonal average as measured by the CW. Interestngly there are mportant dfferences n the mean demographc and health status measures across the plans however the health status measures dsplay much greater across-plan varance than the demographc varables. Ths suggests that relyng solely on demographc varables to measure rsk varaton may underestmate the true magnude of adverse selecton. The smple summary statstcs n Table show that health plans dffer n both demographcs and n measured health status and ths s prma face evdence of adverse selecton. The HMO attracts a younger more male lower-pad and healther populaton than the other plans. The plan that garners the least favorable selecton s the POS plan the mean age and CW s sgnfcantly hgher than the HMO. The CDHP enrolls an older populaton wh a 4

16 hgher salary and a hgher CW than the HMO but a lower CW than the other plans. From these summary statstcs s dffcult to decompose the dmensons of the selecton nto the parts that can be easly contracted upon (age and gender) and those dmensons that are more dffcult to contract upon the non-age and non-gender components of health status. One of our goals s to understand the welfare loss from adverse selecton. For these reasons we estmate structural parameters from a model of health plan choce. 4. Emprcal Approach To measure the welfare consequences of adverse selecton we frst must accomplsh two tasks: ) estmate the expected total health clams and patent out-of-pocket expendures that ndvduals would ncur f they were to enroll n any of the avalable plans; and ) estmate the parameters of an ndrect utly functon. Medcal Care Cost Model To predct total health care expendures and patent out-of-pocket (OOP) expenses we face three mportant modelng challenges. Frst we need to account for unobserved ndvdual heterogeney. Second much of the data s censored at zero. Thrd OOP and total clams expendure are determned ontly wh plan-specfc rules placng nonlnear restrctons on the OOP realzatons. To mplement a framework that accounts for these features of the data we use a two-part three-equaton censored regresson model buldng upon the work of Cowles Carln and Connet (996). The frst equaton n the model s an ndcator of whether the patent receves care. The thresholds are stochastc and are a functon of observables a tme-nvarant unobservable ndvdual effect and an d error. Condonal on the threshold beng breached the other two equatons of the model predct total clams expendure denoted Clm and total outof-pocket expendure OOP. 5

17 More specfcally the varable T s a zero-one ndcator of non-zero clams and s a functon of the latent varable T n the followng way: T 0 = f T f T 0 > 0 Posve values of clams and out-of-pocket expendures are observed only when ths threshold s met. Lettng the astersk denote latent values the process gudng the realzed data for Clm and OOP s gven by 0 f T 0 Clm = Clm f T > 0 and lettng I denote the set of plan s enrollees: OOP 0 = OOP OOPLm t f OOP f 0 < OOP f OOP 0 or T < OOPLm OOPLm 0 ( t) I and T where ( t) I and T t t > 0 > 0 Each plan places explc lms on the total OOP expendures ncurred by an enrollee n a year and ths nstutonal feature s modeled by cappng out-of-pocket expendures by OOPLm t. We allow for ndvdual-specfc unobserved tme-nvarant shocks that dffer across equatons. The system of latent varables s smply: T = z b th th β + + ξ th Clm = z c c β + b + ξ c OOP = z o o β + b + ξ o where b = b th b c o [ b ] are the tme-nvarant ndvdual-specfc ntercepts. In the language of frequentst econometrcs the b s are random effects. The d error vector s assumed to be th c o normally dstrbuted: = [ ξ ξ ξ ] (0 ) ξ N Γ for ( t) I. Note that the covarance matrx 6

18 Γ s plan-specfc as we expect dfferent correlatons between the threshold clams and OOP expense across the plans. In order to flexbly model health plan costs the vector of explanatory varables z ncludes the demographc and health status varables and nteractons of those varables. Specfcally z ncludes age age squared female ndcator age nteracted wh female CW (health status) and female status nteracted wh age and CW. We estmate plan-specfc parameters for all of the explanatory varables. In ths way we allow for the possbly that some plans may be more effcent at treatng enrollees wh relatvely good health status whle others may be more effcent n provdng care for scker enrollees. Bayesan nference s used to formulate our estmates of the parameters of nterest. The am n Bayesan estmaton s to construct the posteror dstrbuton of the parameters gven assumptons on the pror dstrbuton of the parameters and the data. We smulate the posteror dstrbuton of the parameters usng Monte Carlo Markov Chan (MCMC) methods. Specfcally we use the Gbbs sampler (Gelfand and Smh 990) and data augmentaton technques (Tanner and Wong 987). Chb (99) frst proposed a Bayesan approach for estmatng the tob model. The detals of the estmaton algorhm are descrbed n Appendx A. Our estmates wll be unbased as long as resdual unobserved health status s uncorrelated wh plan choce. We beleve ths s a reasonable assumpton n ths applcaton as we nclude n the set of regressors a health status measure based on very detaled nformaton on pror dagnoses and procedures. Wh some notable exceptons the health status measure s based on much of the same nformaton the enrollee has access to when selectng a health plan. 0 The most mportant knds of nformaton the enrollee possess that we cannot ncorporate nto the 0 There s a sense n whch we have better health status nformaton than the enrollee as we are runnng ther clams hstores through a sophstcated algorhm constructed for the purposed of predctng future health care expendures. 7

19 analyss are: known genetc predsposons for whch the dsease s not manfest materny plans (a relatvely uncommon outcome n our data as we focus on sngle coverage enrollees) the presence of symptoms for whch the enrollee does not seek care and perhaps most mportantly llness severy whn a dagnoss that s not captured by dagnoss and procedure codes and s known and acted upon by the patent. Wh the excepton of genetc predsposons these effects are generally tme varyng and thus would cause concern f plan swchng were common n the data. Only 7% of employees n the data change plans n any gven year. Whle we beleve that that the nstutonal settng and the qualy of our data make unlkely that condonal on our measure of health status enrollees are cognzant of health status nformaton that affects ther choce of plan s clearly stll a possbly. However we perform two drect and two ndrect tests for the presence of unobservable health status nformaton that s correlated wh plan choce. In the frst drect test we estmate health care costs condonal on the costs beng greater than zero usng both ndvdual fxed and random effects. We compare the parameter estmates between the random effects and fxed effects models usng a standard Hausman-Wu test. If ndvduals use tme-nvarant nformaton about ther health status to nform ther plan choce then we should expect the coeffcents estmates between the random effects and fxed effects models to dffer. The Hausman-Wu test fals to reect the hypothess at the 0% level that the coeffcents are dfferent between the models. That s there s ltle evdence that our estmates from the cost equaton wll be based due to enrollees usng tme nvarant nformaton n selectng a plan. In addon others have argued (and tested) that the type of rsk adustment we employ corrects for unobserved selecton bas n an envronment where unobservable health status s more lkely to bas the results (Shea et al. 007). Petz and Peterson (007) fnd that other measures of self-reported health status beyond the dagnostc nformaton n clams do not help predct mortaly. Less than 0% of the enrollee/year observatons have zero reported health care clams. 8

20 The second drect test combnes the expendure and choce models ncludng the error terms from the choce utly equatons as a covarate n the expendure equatons (Deb Munkn and Trved 006). The parameters on the utly errors are not statstcally dfferent from zero mplyng that plan choce s not correlated wh unobserved health status nformaton. (We choose to retan separate expendure and choce models to allow the ncluson of an estmate of the varance of out-of-pocket expendures as a covarate n the choce model to explore rsk averson.) The ndrect tests examne the role of health shocks on plan choce. To mplement the ndrect tests we frst construct a predctve cost resdual -- the dfference between actual and our cost model s predcted expendures. In the frst test we nclude the year t cost resdual nteracted wh the plan ndcator varables n the plan choce model. If ndvduals antcpate future health status and they use that to nform ther choce of plan then the parameters on the contemporaneous resdual/plan dummy nteracton should be dfferent than zero. For all parameters at least 0% of the estmated posteror dstrbuton cross zero ndcatng that the resdual/plan dummy nteractons do not sgnfcantly explan plan choce. In the related second ndrect test we use a prob framework to model an ndcator for whether the ndvdual swch plans between year t and t-. Ths ndcator s regressed on the expendure resdual n year t nteracted wh an ndcator for the plan they enrolled n the prevous year and s square controllng for demographc varables CW t- nteracted wh plan ndcators and year ndcators. If ndvduals posses more nformaton about ther future health expendures than s captured by our measures of health status and use to nform plan selecton then the resdual should predct swchng behavor. The coeffcent estmates on the resdual nteracted wh the ncumbent plan ndcators are all dfferent from zero at tradonal levels of 9

21 confdence. 3 In sum these tests suggest that enrollees do not possess nformaton that s not emboded n the CW and other demographc varables when selectng a health plan. Once the cost model s estmated we construct estmates of the expected Clm and OOP expenses for each ndvdual (n logarhm scale) across all plans ncludng the plan actually selected by the ndvdual. The mean s an argument n the utly functon. Because the Gbbs Sampler method results n a sample from the posteror dstrbuton of the parameters ncludng the latent expendure varables we can use ths sample to calculate the sample mean and varance for each ndvdual n each plan. Health Plan Choce Model We model health plan choce usng a multnomal prob wh autocorrelated errors (AR- MNP). In our model the unobservable components of plan utly are allowed to be freely correlated across plans and autocorrelated over tme. Most analyses of health plan choce rely upon the d log model or the heteroskedastc but ndependent nested log model. Our results suggest that these assumptons may lead to based nference. As we noted above only 7% of the enrollees swch plans n any gven year suggestng that plan preferences are lkely to be correlated over tme; our framework explcly accounts for ths autocorrelaton. We are unaware of any analyss of health plan choce that allows for both full freedom n cross-plan correlaton and correlaton of unobserved preferences across tme. In selectng ther health plan we assume enrollees observe ther health status and formulate consstent estmates of both the mean and varance of ther out-of-pocket expendures across all plans. Gven these estmates they select the plan that maxmzes ther utly. Let be the ndrect utly of the th person ( K N ) = for the th plan ( K J ) U t = at tme t 3 The largest t-statstc (n magnude) s.4 for the resdual nteracted wh the POS plan. The ont test of all of the plan nteractons s also nsgnfcant. 0

22 ( t =... T ). Indvduals choose plan f and only f U t U kt k. It s well known that U t s not dentfable because level and scale are rrelevant to the maxmzaton problem. The J th plan s used to normalze the level of utly so that W t = U U. The CDHP s used as the t Jt baselne choce because of s dstnct plan desgn. We normalze for scale by settng the varance of the unobserved preferences for the HMO to. It s assumed that W t s lnearly related to the characterstcs of the ndvduals and the choces ( x t ) so W β t = x t + ε t where t ε s the unobservable component of utly. Stackng the choces nto matrx form we have the relatonshp W to be normally dstrbuted: ε N( 0Σ ) = β + ε. The errors are assumed X. In a slght modfcaton of Geweke Keane and Runkle (997) the stckness of plan choce across tme s captured va an AR() relatonshp n the error terms. Specfcally ε = ρ t ε t + η wh η d N ( 0Τ). The varance matrx Τ s a dagonal matrx whose dagonal elements τ are plan-specfc varances. The AR() coeffcent ρ t s a plan-specfc parameter based on the plan ndvdual s n at tme t when the tme t plan electon s made. Gven the apparent persstence n plan market shares we antcpate the estmated values of ρ closer to one than to zero. 4 There are a number of dsadvantages to estmatng the parameters of an autoregressve multnomal prob model usng a classcal maxmum lkelhood approach. It s computatonal challengng to calculate the lkelhood functon the thousands of tmes necessary to fnd the maxmum and convergence s often elusve. However the parameters can be readly estmated usng Bayesan methods. As n the cost model we specfy a dffuse pror dstrbuton for the 4 It s an open queston whether ε captures pure exogenous preference dfferences for plans or f captures swchng costs that accrue as patents develop relatonshps wh provders. That s s an open queston whether the errors capture state dependences (e.g swchng costs) or correlated heterogeney. In the results secton we provde some evdence that suggests that correlated errors do not capture swchng costs.

23 parameters and smulate the posteror dstrbuton usng MCMC methods. Specfcally we use the Gbbs sampler and smulate the latent varables usng data augmentaton technques. Appendx B descrbes the lkelhood functon and the Gbbs algorhm n detal. The xt vector ncludes the followng plan nvarant varables: age female ndcator age nteracted wh female and CW (the measure of health status n the year the enrollment electon s made). The parameters on these varables can vary by plan. The x t vector also ncludes the followng varables that vary across plan and tme: natural log of net salary log( salary premum t ) and the expected value of the natural log of out-of-pocket (OOP) expendure the varance of the natural log of the OOP expendure and the offce vs copayment level for the plan. 5 Our model mposes fewer restrctons than tradonally used multnomal estmaton approaches. In so far as the mpled elastcy estmates from our model dffer from the MNL s nstructve to decompose the source of those dfferences nto the mportance of capturng heteroskedastcy and modelng persstence n health plan preferences. Specfcally we wsh to decompose dfferences nto the mportance of accountng for seral correlaton and cross-plan correlaton n the resduals. For comparson purposes we use frequentst methods to estmate a cross-sectonal multnomal log model and a cross-sectonal nested-log model 6. We use a Bayesan approach to estmate a cross-sectonal multnomal prob and an autoregressve MNP model wh a dagonal covarance matrx. The later model s the same as our base model except the off-dagonals of the varance-covarance matrx are constraned to zero. 5 We have estmated models wh dfferent specfcaton over the functonal form of premums and salares. Specfcally we have ncluded out-of-pocket premums and salares as separate polynomal arguments n the utly functon. When the Markov chan converged the results from these specfcatons are very close to our base estmates. However n several of the alternatve specfcatons the chans dd not converge. 6 All cross-sectonal models are based on data wh one year drawn randomly from the panel for each ndvdual to elmnate temporal correlaton. The cross-sectonal multnomal prob had very poor convergence perhaps due to ths restrcted sample sze.

24 5. Results Cost Model For the cost model the Monte Carlo chans converge well after the nal burn-n of 500 eratons. 7 Gven the space constrants the cost model contans too many parameters to report here. However the posteror dstrbutons for the parameters look sensble. Costs are ncreasng n age female and CW. We decded to combne all the POS ters nto one plan as there s no meanngful cost dfference across the ters. The model fs the data well and closely replcates the realzed dstrbuton of costs prmarly because the panel data allows the estmaton of ndvdual-specfc ntercepts. The R s 0.56 for clams and 0.68 for out-of-pocket expenses. In Fgure we present the actual and fted dstrbutons of total expendures and out-of-pocket costs. The model under-predcts the number of zeros but otherwse does capture the skewness of both the total cost and OOP dstrbutons. The results of the cost model mply that there are sgnfcant cost dfferentals across the plans. Ths s not surprsng as the plans have dfferent provder networks rangng from the restrctve HMO network to the open access CDHP plan. The plans also mpose dfferent out-ofpocket payment structures that also can affect margnal utlzaton. For example the HMO generally has constant co-payments for a doctor vs whle the CDHP wll have very low effectve out-of-pocket expendures for both low and hgh utlzaton and hgh out-of-pocket n the doughnut hole. To get a sense of the mean cost dfferentals we perform the followng experments. We take the entre sample populaton and estmate ther mean expendures (the total of expendures pad out-of-pocket and by the plan) as f they were all to enroll n each plan. We also take the 7 Detals on the convergence of the MCMC chans and estmated parameters are avalable from the correspondng author. 3

25 enrollees of each plan and estmate the costs of the enrollng that populaton n the other plans. Ths latter exercse provdes a sense of the dfferental selecton nto each plan. Table 3 presents the results of ths exercse. The results n Table 3 show that adverse selecton s present n our data and economcally mportant. The realzed HMO costs are predcted to be % lower than f they had to treat the entre enrollment. In contrast the percapa costs for the POS are 8% hgher the POS plan s 43% hgher and the CDHP plan s 3% hgher than f they enrolled the entre populaton. The large cost dfferentals across the plans mply that the welfare loss from premum dstortons are potentally large. It s mportant to note that these cost fgures are total cost dfferentals and do not breakout the adverse selecton nto easly observable and hence contractble and non-contractble components. Not surprsngly the HMO s the cheapest plan and the CDHP plan s the most expensve. Usng the estmated per-capa cost of the entre sample as the comparson the HMO has 9% 6% and 4% lower cost than the POS POS and the CDHP plan respectvely. The large dfferences n plan costs mply there s potental for large welfare loss from adverse selecton nduced by premum dstorton. The results presented n Table 3 also suggest that the relatve costs of the plans dffer by health status. For example the cost dfferental between the HMO and the POS plans depends upon comparson populatons. The cost of the POS plan s 38% hgher than the HMO for those who enrolled n the HMO but s 9% hgher for those who enrolled n the POS plan. Fgure hghlghts ths phenomenon. It graphs the estmated logarhm of costs (plan payment plus out-of-pocket expense) for a 47-year old woman as a functon of the logarhm of the CW for each plan. Interestngly the CDHP plan s the second lowest cost plan for the very healthy but s the most expensve plan for the sck. Below we attempt to decompose the source of the cost dfferences across plan nto utlzaton and provder prce dfferences. 4

26 Fgure 3 graphs the expected logarhm of out-of-pocket expendures for a 47-year old woman as a functon of the logarhm of the CW for each plan. Ths fgure gves a sense of the varaton across plans and CW n OOP that s used to dentfy the parameters on the expected logarhm of OOP n the choce model. Not surprsngly OOP s monotoncally ncreasng n the CW for each plan; however there are nterestng patterns across the plans n both the level and the slope of OOP as a functon of CW. The HMO plan desgn has the lowest co-payments (for whn-network utlzaton) as reflected n Fgure 3 where the HMO has the lowest OOP for all CW levels. Conversely the CDHP plan has the hghest expected OOP expendures for all but the lowest CW levels. For low CW values the POS plan has lower OOP than POS but the margnal effect of CW s hgher for POS than POS so that by for those wh CW greater than (Log(CW) = 0) the OOP for POS and are vrtually dentcal. Analyss of the Source of Costs Dfferences Across Plans The large cost dfferentals across plans for treatng a patent wh smlar health status characterstcs rase an obvous queston: Are these costs dfferences drven by dfferences n health care utlzaton or dfferences n the prces pad to provders? The plans dffer n ther benef structure wh the HMO beng the lowest cost opton (wh modest co-pays for most nnetwork provders) the POS plans havng somewhat larger co-pays and the CDHP plan havng a large deductble (wh a health spendng account attached to ). These dfferental benefs across plans may lead to dfferental demand for medcal care (e.g. moral hazard) by enrollees. However the members of the provder panels dffer sgnfcantly across the plans. The HMO s culture reputedly emphaszes a more conservatve practce style suggestng that utlzaton (and hence cost) dfferences across the plans could also be a consequence of dfferent provder behavor. 5

27 To better understand the source of the cost dfferences across plans we construct a measure of healthcare resource usng Medcare s Resource-Based Relatve Value Uns (RBRVUs). The RBRVU scale was developed for physcan rembursements under Medcare but s wdely used to pay for physcan servces n prvate health plans. The RBRVU assgns resource value uns (RVUs) to the thousands of procedure codes where the RVUs measure the resources used to provde the care. The nal resource measurement for each procedure code was performed by a team at Harvard Unversy (Hsao Dunn and Verrll 993). All codes are re-evaluated at least once every fve years by the Amercan Medcal Assocaton. We apply the RBRVU scale to the clams from all of our plans. Dfferences n RVU across the plans reflect dfferences n resource use and not the prces pad to provders. To examne the role of dfferental utlzaton we estmate the mpact of plan enrollment on enrollee RVUs controllng for age gender ncome and mportantly the concurrent weght. Lke the dstrbuton of medcal care clams the dstrbuton of RVUs s censored at zero and rght skewed. Thus we use the same two-part censored regresson model to estmate the mpact of plan enrollment on RVUs as we dd to estmate the relatonshp between plan enrollment demographcs measured health status and medcal care costs. Agan nference s generated usng Bayesan methods. Specfcally the posteror dstrbuton of the parameters s estmated usng MCMC wh Gbbs samplng and data augmentaton. Table 4 presents the descrptve statstcs of the estmated posteror dstrbuton of the parameters. There s vrtually no dfference between the plans on the probably of posve resource use. However condonal on resource use beng posve the HMO has meanngfully lower utlzaton than the POS and CDHP plans. The expected dfference n utlzaton between the HMO and the other plans s approxmately 5%. As mentoned above the costs of the HMO are 9% 6% and 4% lower than PPO PPO and the CDHP respectvely. These results 6