Contracting with Limited Commitment: Evidence from Employment-Based Health Insurance Contracts

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1 Deartment of Economics, yracuse niversity orking Paer eries Contracting with imited Commitment: Evidence from Emloyment-Based ealth Insurance Contracts Keith Crocker John Moran orking Paer htt:// The Economics Deartment 0 Eggers all yracuse niversity yracuse, NY Telehone: All rights reserved.

2 Contracting with imited Commitment: Evidence from Emloyment - Based ealth Insurance Contracts * by Keith J. Crocker niversity of Michigan Business chool and John R. Moran Deartment of Economics yracuse niversity July 2002 Abstract hen an individual's health status is observable, but evolving over time, the key to maintaining a successful health insurance arrangement is to have the healthier members of the grou cross-subsidize those who exerience adverse health outcomes. e argue that imediments to worker mobility may serve to mitigate the attrition of healthy individuals from emloyer-sonsored insurance ools, thereby creating a de-facto commitment mechanism that allows for more comlete insurance of health risks than would be ossible in the absence of such frictions. sing data on health insurance contracts obtained from the 987 National Medical Exenditure urvey, we find that the quantity of insurance rovided, as measured by lifetime limits on benefits and annual sto-loss amounts, is ositively related to the degree of worker commitment. These results illustrate the imortance of commitment in the design of long-term contracts, and rovide an additional rationale for the ractice of bundling health insurance with emloyment. * Crocker: niversity of Michigan Business chool, 70 Taan treet, Ann Arbor, MI kcrocker@umich.edu. Moran: Center for Policy Research, yracuse niversity, 426 Eggers all, yracuse, NY jmoran@maxwell.syr.edu. The authors gratefully acknowledge suort from the National cience Foundation under grant number BR and the Management cience Grou of the Veteran s Administration for their sonsorshi of the 3 th Annual ealth Economics Conference. ecial thanks go to Dan Black, Richard Butler, Michael Chernew, Neil Doherty, Paul Gertler, Jon Gruber, Richard irth, Jeff Kubik, Mark Roberts and owell Taylor for roviding helful comments. A ortion of this research was conducted while the second author was a Fellow in the Robert ood Johnson Foundation s cholars in ealth Policy Research Program.

3 "haneen and Tom ahl were aying $47 a month for health insurance when Mrs. ahl was diagnosed with breast cancer in 996. Their remiums began rising steadily, and by August 2000, the ahls were told that their new rate would be $,88 a month. Mrs. ahl, whose cancer is in remission, tried to find out why. nsatisfied with answers they got on the hone, the coule visited the offices of the insurer. There an executive exlained why her remium was soaring: 'because of your dread disease.' It's called re-underwriting. A key challenge in individual health insurance is keeing the healthier eole enrolled. Their remiums are needed to subsidize those who get sick. The roblem, under the traditional aroach, is that the healthiest tend to dro out as rising medical costs gradually drive u remiums. Advocates of re-underwriting argue that because it gives smaller rate increases to the healthy, it kees more of them enrolled and aying remiums.". Introduction The recent debate over the use of annual re-underwriting in the context of individual health insurance olicies highlights the difficulties that insurers face when attemting to craft a stable insurance ool. In a setting where an individual's health status is observable, but evolving over time, the key to maintaining a successful insurance arrangement is to have healthier members of the grou commit to cross subsidize members who exerience adverse health outcomes. In the absence of a recommitment mechanism, however, those who turn out to be healthier than average may find it advantageous to leave the risk ool, and to urchase alternative coverage at a remium that more accurately reflects their own, observable, health status. 2 This erodes the actuarial integrity of the ool and, consequently, the ability of insurers to offer insurance against both the financial losses associated with a articular illness eisode, and the classification risk that results when insurance remiums are adjusted to reflect changes in one's health status over time. This aer examines a theoretical model of insurance contract design in which imediments to worker mobility may serve to mitigate the attrition of healthy individuals from emloyer-sonsored all treet Journal, "ealth Insurer's Premium Practices Add to Profit urge, Roil Customers," Aril 9, 2002,.. 2 This rocess is emirically documented in a convincing study by Altman, Cutler and Zeckhauser 998 which examines the changing enrollments for individuals insured through the Grou Insurance Commission of Massachusetts.

4 insurance ools, thereby creating a de-facto commitment mechanism that allows for more comlete insurance of health risks than would be ossible in the absence of such frictions. e characterize otimal health insurance contracts in an environment where a worker's evolving health status is ublicly observable, and in which emloyees vary in the transactions costs that they must incur when switching to an alternative emloyer. sing data on emloyment-based health insurance lans, we find that the structure of insurance contracts observed in ractice is consistent with the redictions of the model, roviding emirical documentation for the imortance of recommitment in the design of health insurance contracts. Traditional analyses of contracting in insurance markets have tended to emhasize the role of informational asymmetries, which engender roblems of adverse selection Rothschild and tiglitz, 976; Crocker and now, 986 or moral hazard havell, 979. A recent article by Cardon and endel 200, however, finds no evidence of adverse selection in health insurance markets, and suggests instead that the lack of commitment in long-term contracts examined by Cochrane 995 may be a more relevant source of market failure in health insurance settings. Accordingly, we consider a full information model in which insureds are initially identical, but who anticiate receiving a ublic signal that will rovide information about their exected future health care costs. As a consequence, the risk-averse urchasers of health insurance face two otential sources of uncertainty: the financial loss associated with adverse health outcomes, and the classification risk that results when their future insurance remiums reflect the ublicly available information on each individual s likely health-related exenses. In such a setting, an otimal insurance contract would entail full comensation for all the losses suffered from illness as well as a constant, ex ante actuarially fair, remium charged to all individuals indeendently of the state or their observed health status. hile such a ackage rovides full insurance against both tyes of uncertainty, the cross-subsidy from low- to high-risk individuals in the future, which is inherent in the non-exerience-rated remiums required to cover the classification risk, gives those with lower exected health care costs the incentive to exit the insurance ool, and to urchase indeendent coverage at a rice that more accurately reflects their own, observable, exected health care costs. As 2

5 others have noted Cochrane, 995; Pauly et al., 995, it is this inability of insureds to recommit to remain in the ool in light of favorable information on health status that rovides an imediment to the insurability of classification risk. 3 Paradoxically, the ability to insure against such risks is enhanced if there exist obstacles to the mobility of insureds that mitigate the erosion of the insurance ool caused by the dearture of lower-risk individuals. In an environment where emloyer-sonsored health insurance is the norm, one of the largest imediments to insured mobility is the cost of switching jobs. To the extent that health insurance is bundled with emloyment, any frictions associated with emloyee mobility across occuations or emloyers necessarily translate into a de-facto commitment to one s emloyer, which results in a more stable and, hence insurable, risk ool. Thus, the existence of frictions that imede worker mobility between alternative emloyments may have heretofore unareciated beneficent effects through its imact on the insurability of health risks. The validity of this aroach, of course, deends crucially on the requirement that insureds switch jobs in order to obtain alternative insurance coverage. This would aear to be a reasonable roosition in ractice since the vast majority of insured individuals receive their health coverage through emloyersonsored lans. The difficulties associated with the offering of rivate health insurance are well known, and include the traditional roblem of adverse selection with non-grou insurance Pauly, 986, as well as the high fixed costs generally encountered in the administration of individual olicies Diamond, 992. As a result, the terms associated with indeendently urchased health insurance, to the extent that it is available, are less than attractive when comared to the emloyer-sonsored alternative Gruber and Madrian, To mitigate this roblem, Cochrane 995 rooses the use of secially designated accounts into which consumers who find out that they are healthier than average ay an amount equal to the resulting exected decline in their future health care exenditures, while those receiving adverse health news receive a lum sum subsidy from the fund equivalent to the resent value of their increased health care costs. As long as theses severance ayments are enforceable, the result is that all consumers ay the same resent value of remiums and, at each oint in time after the lum sum ayments have been imlemented, face a remium equal to their exected actuarial cost. 3

6 The role of recommitment in the design of efficient multi-eriod contracts has received increasing attention in the literature. 4 The most germane for this study is a recent aer by endel and izzeri forthcoming who, in the context of life insurance, examine the use of front loaded remiums as a mechanism through which insureds can commit credibly to remain in the insurance ool. Theirs is a model of symmetric information in which the urchasers of insurance may face classification risk based on their evolving actuarial status, and in which those who turn out to have a lower risk of mortality may, in the absence of recommitment, exit the life insurance ool. hile the reayment of remiums may be an effective tool to lock-in customers in life insurance, Cutler and Zeckhauser 2000 note that it is less likely to rovide a solution to the commitment roblem in health insurance settings due to the greater comlexity of that market. 5 Thus, health insurers must use other commitment devices such as emloyer sonsorshi of health lans - to craft stable insurance ools. The aer roceeds as follows. In the next section, we examine a model of emloyer-sonsored health insurance in which the ublicly observed health status of emloyees changes over time. nder the assumtion that the insured workers incur a financial cost when switching jobs to obtain alternative insurance coverage, we characterize the structure of efficient emloyer-sonsored insurance contracts. Our model offers several redictions concerning the relationshi between these switching costs, which we term job attachment, and the amount of insurance coverage available through emloyment-based grous. e find that when emloyers offer the same contract to all of their workers, the otimal contract exhibits a coverage limitation that is inversely roortional to the amount of job attachment resent in the 4 endel and izzeri forthcoming and Chiaori 2000 rovide nice overviews of recent develoments in the emirical contracting literature. 5 In theory, health insurance could be sold for the long term on a level remium basis. In ractice, matters will be more comlex. Much health insurance is now bundled with the rovision of care. If an individual left a geograhic region, he might have to change rovider, and no new rovider/insurer would want to take him at his old level rate. Portability is but one roblem. Once individuals urchase lifetime medical insurance, why should an insurer strive for efficiency when eole are stuck in his lan? This roblem is exacerbated since the insurer must agree to ay for or rovide a changing level of services. ealth insurance olicies otimally change from year to year, as medical technology imroves and knowledge about otimal treatments exands. Finally, with future medical costs so unredictable, insurers cannot take on the risk, which would aly to all olicies, that costs will escalate beyond exectation. ith life insurance, by contrast, ortability, changing service mix, and varying costs are not roblems. Cutler and Zeckhauser, 2000,

7 firm. In addition, if emloyers are able to offer multile contracts that induce self-selection by insureds, the contracts exhibit more comlete coverage of medical exenditures, albeit at remiums that artially reflect the health status of lan articiants. ection three resents emirical tests of the model s redictions using data on health insurance contracts obtained from the 987 National Medical Exenditure urvey matched to roxies for job attachment from the 977 Dictionary of Occuational Titles. Consistent with the redictions of our model, we find that the contracts associated with firms who offer a single health insurance olicy exhibit coverage limitations that are decreasing in job attachment while firms offering multile olicies have higher levels of coverage which are less sensitive to job attachment. A final section contains concluding remarks. 2. Theoretical Framework e consider an environment in which a continuum of individuals face the financial risk associated with becoming ill at some future date. All of the agents are assumed to be identical initially and have the same robability,, of sickness. Each agent also anticiates receiving ublicly observable information about her own health status rior to the state in which illness may occur. Accordingly, an individual realizes that with robability λ -λ she will turn out to be a high low risk with the robability of suffering illness, where > > > 0 and λ λ +. Individual consumers have an income Y and, in the event of sickness, suffer the financial loss. For the uroses of this model, we assume that workers obtain a health benefits ackage at the time they become emloyed, but rior to receiving the information on their health status. This ackage may consist of either a single insurance contract or a menu of otential insurance choices. Prior to becoming ill, however, workers obtain information on their health status, which may affect their incentives to remain in one of the lans offered by their emloyer, or to select alternative otions in cases where multi-lan benefit ackages are offered. This sequence of events is illustrated with a timeline in Figure. 5

8 Each individual is assumed to be risk averse and to ossess the von Neumann-Morgenstern utility function j, where j is the agent s wealth in the sick j = and not-sick j = N states. An insurance contract c {Z, R} consists of a remium, Z, aid by the insured individual rior to the state in which illness may occur, and a reimbursement, R, received by the insured in the event of illness. The exected utility of an agent who urchases the insurance contract c, and who has the robability of illness, is written as v c; +, N where Y Z + R, and Y Z. ince ublic information regarding each agent s tye will N be available rior to the eriod in which illness may occur, the information structure of the model ermits individuals to be treated differently deending on their ublicly-known tyes. etting c i = {Z i, R i } denote the contract associated with an individual whose observed health status indicates her to be a tye i {, }, a health insurance benefits ackage C { c c } obtaining health status information of V, results in an exected utility to an agent rior to C λv c ; + λ v c ;. 2 ince we assume that insurance firms are risk-neutral, we may write the rofit associated with the offering of ackage C as Π C λπ c ; + λ π c ; 3 i i i i i where the rofit earned on an individual of tye i is π c ; Z R. A. ot Markets and Efficient Benefit Packages Before roceeding, we consider two benchmark cases. The first is the equilibrium that would occur in the sot market were insurance not bundled with emloyment, and workers were to urchase actuarially fair insurance after their health status had been observed. It is straightforward to demonstrate that the equilibrium is characterized by a solution to the roblem of selecting C to maximize the exected utility of insureds 2 subject to the zero rofit constraint Z = R for each i {, }. hile the i i i 6

9 resulting contract rovides full insurance against the financial loss generated by an illness, so R i = for each i, the insured is comletely exosed to the classification risk associated with alternative health outcomes through the exerience-rated future remiums, Z i. The sot market contracts are deicted in Figure 2, where the insured receives ˆ c ˆ c if she is viewed to be high low risk. As an alternative to the sot market, insureds could ot for a contract negotiated rior to receiving knowledge of their health status. uch a full commitment insurance ackage is characterized by a solution to the roblem which maximizes insured utility 2 subject to C 0, Figure 2 and results in full coverage of all illness-related exenses R R Π which is deicted as C* in = as well as a constant, ex ante actuarially fair, remium which does not deend on revealed health status Z = Z. Although the full commitment ackage comletely insulates insureds from both the financial risk of illness and the classification risk associated with observable changes in health status, the remium structure entails a cross-subsidy in which low-risk high-risk individuals ay a remium which is above below their ublicly-known actuarially fair rate. ince the courts will not generally enforce long-term contracts against insurance urchasers, the low-risk -tye insureds may successfully renege on their romise to ay the ooling remium unless other mechanisms to enforce comliance can be imlemented. 6 B. Partial Commitment Through Emloyment Bundling hen health insurance is rovided only as art of an emloyment ackage, frictions associated with movement to alternative emloyers may serve to imede the ability of those individuals who find that they are low-risk from leaving the insurance ool. To investigate the extent to which such mobility frictions can serve as such a recommitment device, we assume that the low-risk workers can obtain full, and actuarially fair, health insurance after their health status is revealed, but in so doing must incur a 6 ee Estein 997 for a discussion of the legal roblems associated with enforcing long-term insurance contracts. A concise summary of the roblem can be found in Cochrane 995, who notes that,... courts often reinterret insurance contracts ex ost, judge the merits of each clause searately rather than how the clauses fit together to form a reasonable contract, and will not enforce severance ayments or bond forfeitures against consumers. 7

10 switching cost, K, of moving to an alternative emloyer. Accordingly, the extent to which an insurance ackage can insure against classification risks is limited by the following feasibility constraint v c ; 4 O where O = Y K -, which guarantees that a low-risk individual refers their current insurance lan to the actuarially fair, full insurance outside otion. The existence of the worker attachment conferred by the switching cost K ermits some degree of commitment on the art of insureds to remain in the insurance ool even if they turn out to be healthier than average. e will examine the effect of this ability to recommit in two insurance settings, the first of which requires that insurers offer the same contract to all insureds indeendently of their revealed health status, while the second ermits insurers to design benefit ackages which induce the members of the ool to voluntarily select insurance contracts that result in exerience-rated remiums. 7 B. ingle-contract Benefit Packages One method of mitigating classification risk is by offering an insurance ackage that does not take into account each insured s evolving health status. et C P denote a ooling ackage in which c P = c c. The otimal ooling ackage consists of the contract c P { Z P R P }, that maximizes 2 subject to the zero rofit 3 and feasibility 4 constraints. The contract associated with the otimal ooling ackage is formally characterized by Theorem in the Aendix, and may be described with reference to Figure 3. For sufficiently low levels of worker commitment K, the indifference curve associated with the feasibility constraint, V =, lies everywhere below the ooling zero-rofit locus, R. In such a O setting, there is no ooling contract accetable to low- risk individuals, so that a ooling ackage cannot be imlemented. As K becomes larger, resulting in higher degrees of emloyee commitment, eventually a critical value K is reached at which the indifference curve associated with the feasibility constraint 7 hen workers are free to choose among lans, inducing self-selection is necessary even with observable tyes. 8

11 intersects the ooling zero rofit locus, resulting in a feasible ooling insurance ackage. Further increases in K cause the contract c P to migrate u the zero-rofit ooling locus, which is the situation deicted in Figure 3. As K continues to increase, eventually the critical value K 2 is reached that ermits the contract C* to be achieved. The imlication is that firms offering a single health insurance lan should have coverage limitations that are decreasing in the degree of worker commitment, K. B.2 Multi-Contract Benefit Packages In some cases, firms may offer multile choices to workers, who choose their referred coverage from amongst the various insurance otions. hile emloyer-sonsored insurance lans rarely engage in mandatory exerience rating of individual articiants in an insurance ool, 8 some benefit designs rovide the mechanism by which a form of voluntary exerience rating can be effected through the offering of insurance contracts that induce self-selection by the insureds. Formally, an insurance ackage {c, c } can discriminate based uon health status as long as vc ; v c ; 5 which requires that high-risk individuals refer the insurance contract c to c. 9 An otimal multicontract benefit ackage, which is formally characterized in Theorem 2 of the Aendix, is a solution to the roblem that selects { c c }, to maximize 2 subject to the zero rofit 3, feasibility 4 and selfselection 5 constraints. 0 8 But, as noted in the anecdote rovided in the introduction, some individual health insurance roviders have been forced to re-underwrite in order to kee the lower risk customers in the insurance ool. The roblem, of course, is that in the individual market there are not significant transactions costs incurred by low risk individuals who wish to exit the ool. 9 Formally, we must have v, c v, c as well. e ignore this constraint since it is never binding. 0 The zero rofit constraint 3 allows for the ossibility that either the insurer or the emloyer may wish to cross subsidize the remiums associated with the two contracts. For insurers, this would be ossible in cases where both contracts are issued by the same insurance comany. In 997, over half of all emloyers who offered multile olicies did so through a single insurer Marquis and ong, 999; Encinosa, 200. Alternatively, the emloyer could ay the actuarially fair remium for each contract and vary emloyee remium contributions to effect the desired level of cross subsidization. Of course, it may be that neither the insurer nor the emloyer wishes to imlement cross subsidized remiums, in which case equation 3 will still hold since, in the absence of cross subsidization, each contract will earn zero rofits individually. 9

12 An otimal insurance ackage with multile contracts is illustrated as {c, c } in Figure 4, where the efficient ooling contract, c P, has been included for comarison uroses. The locus AC* deicts the set of contracts sold to low-risk individuals which, when couled with a full-coverage R = contract that is equally valued by high-risk individuals so vc ; = v c ;, satisfies the aggregate zero rofit constraint 3 with equality. In the absence of the feasibility constraint imosed by the otential exit of low-risk individuals, the otimal contract would be the full commitment ackage C*. hen that feasibility constraint binds, however, the closest the insurer can get to the full-commitment contract is the multi-contract ackage deicted as {c, c } in the figure, which exoses the low-risk insureds to a financial loss in the event of illness, and the high-risk insureds to some classification risk. There are several asects of the otimal multi-contract ackage that are worthy of note. First, {c, c } reresents a Pareto imrovement over the ooling contract c P, since high risks are strictly better, and low risks no worse, off. 2 econd, the multi-contract ackage rovides some insurance against classification risk, although that rotection is not comlete due to the need to kee the low risks in the Note that these three conditions define a class of contractual airs which consist of a full-coverage contract for high risks, a artial coverage contract for low risks located on AC* which is equally valued by the high risks, and which together make zero rofit on average. One element of this class is the contract which awards the allocation A to low risks and ĉ to high risks. These contracts are located on the same high-risk indifference curve and corresond to the well-known Rothschild-tiglitz searating allocation, where each contract makes zero rofit. These are the contracts we would exect to observe when there is no mechanism for effecting cross subsidization within the ool, as would be the case, for examle, if c and c were issued by different insurers and emloyee remium contributions were not adjusted by the emloyer. hen cross subsidization is ossible, the low risk contract migrates toward c* along the AC* locus and the high risk contract on the same v indifference curve moves from ĉ toward c* as the magnitude of the cross subsidy increases. One such contract is that denoted as {c, c } in Figure 4, where rofit earned on low-risk individuals subsidizes losses incurred on the contract sold to higher risks. The limiting case occurs when both contracts coincide at the ooling allocation c*. As indicated in Theorem 2, the articiation constraint for low risks imlies that not all of the members of this class of contracts in articular, those in the vicinity of c* are feasible. 2 The reason, of course, is that the multi-contract ackage, which is a second-best contractual resonse to the feasibility constraint 4, entails distortions in two margins, exosing the insured to both financial risk and classification risk. In contrast, the single ooling contract loads all of the distortion into financial risk while eliminating comletely the insured s exosure to the risk of reclassification. As is often the case in second-best settings, the otimal resonse to the resence of a constraint involves small distortions in all of the choice variables, as oosed to a large distortion in only one. hile multi-contract benefit ackages are generically suerior, many firms may not have sufficient enrollment to suort more than a single lan. 0

13 insurance ool. 3 Third, the otimal ooling contract always rovides less coverage than do either of the P contracts offered under the multi-contract ackage R < R < = R. Finally, since c P and c both converge to C* as K increases and coincide with C* at K 2, the effect of increased worker commitment on coverage limitations is more ronounced in the otimal ooling ackage than in either of the contracts offered in the efficient multi-contract ackage. These results will be useful when we imlement our emirical tests because they eliminate the need to identify which tye of contract c or c is held by survey resondents in firms that offer multi-contract insurance ackages. e therefore have the following testable imlication of the theory. Theorem 3: Firms which offer a single insurance contract to their workforce should have lower levels of coverage that are more sensitive to worker commitment than firms which offer multicontract ackages. Thus, i R < R, and dr dk i dr dk >, for i {, }. Proof: Contained in the Aendix. The imortance of job attachment K > 0 is that it ermits a limited degree of cross subsidization from the low-risk to the high-risk customers to be imlemented, without inducing the former to leave the insurance ool. This allows the health benefits ackage to rovide some insurance against the classification risk faced by the insureds. In settings with no job attachment K = 0, there is no way of effecting such a subsidy, which is exactly the situation encountered in the individual heath insurance 3 Note that the cross-subsidization from low risks to high risks inherent in the otimal multi-contract ackage rovides another reason why emloyer-sonsored health insurance may be desirable. uch a subsidy would be quite difficult to effect were insurance rovided to workers in a cometitive market environment, since in such a setting insurers would always have the incentive to dro the unrofitable contract being sold to high risks, and cometitors could always offer a suerior contract for examle, ĉ, deicted in Figure 3 to low risks. By roviding insurance to workers, the emloyers can collect the efficient cross-subsidized remiums from the insureds and then urchase i insurance coverage from outside insurers at actuarially fair rates Ẑ for each tye. Alternatively, the insurers themselves could effect the desired level of cross subsidization in cases where both contracts are issued by the same insurance comany.

14 market and the reason that insured individuals end u exosed to classification risk. e now turn to an examination of the data. 3. Emirical Analysis In the revious section we demonstrated that with limited commitment efficient health insurance contracts cannot fully insure both the financial risk associated with adverse health outcomes and the classification risk arising from the ex ost categorization of agents into risk classes. here only a single insurance olicy is offered by firms, workers are fully rotected against classification risk, but remain uninsured against large losses due to the imosition of coverage limitations. Conversely, in firms offering multile searating contracts, workers benefit from more generous loss insurance, but at the cost of receiving only artial insurance against the rosect of health-related increases in remiums. In ractice, both distortions reresent a major source of uninsured risk for consumers. As discussed in Cochrane 995, the imosition of lifetime benefit cas and the lack of rotection against health-related increases in remiums revent agents from fully insuring themselves against the often catastrohic medical exenditures associated with chronic illnesses such as diabetes, cancer, or organ failure. From an emirical ersective, the main testable imlication of the model is the finding that the amount of insurance contained in emloyment-based health insurance contracts should be ositively related to agents ability to recommit to remain in a articular insurance ool. Because workers often must change jobs to obtain more favorable health insurance coverage, measures of the transactions costs associated with moving among emloyers can be used to roxy for insured commitment, thereby ermitting a direct test of the effect of recommitment on the design of contractual agreements. A. Data Our emirical analysis is conducted using detailed emloyment and health insurance data from two comonents of the 987 National Medical Exenditure urvey NME: The ousehold urvey and the ealth Insurance Plans urvey IP, matched to roxies for job attachment from the 977 Dictionary of Occuational Titles DOT. The DOT rovides information on the hysical demands, 2

15 environmental conditions, and educational and vocational rearation associated with each of 2,000 occuations. The NME ousehold urvey is a stratified random samle of the civilian non-institutionalized oulation of the nited tates containing rimarily individual-level data on the medical exenditures, demograhic characteristics, emloyment status, and health insurance coverage of some 35,000 individuals in 4,000 households. ousehold urvey resondents who reorted coverage from rivate insurance 6549 individuals were re-interviewed in the IP to obtain more detailed information on their tye and level of coverage, remiums, deductibles, maximum benefits and covered illnesses. The IP was designed to rovide a random samle of all rivate health insurance olicyholders in the civilian oulation of the nited tates at the end of 987. The data available in IP further sulements the ousehold urvey data by roviding detailed firm-level information on the characteristics of resondents emloyers as well as their emloyer-sonsored health insurance lans. The 987 NME is well suited for our uroses because it contains data from a eriod when managed care organizations were relatively minor layers in the health insurance market MOs comrise only about ercent of our estimation samles. This is imortant because we need easily quantifiable measures of the overall amount of insurance contained in each contract, something that is considerably harder to measure when insurers and health care roviders are vertically integrated. One disadvantage of the IP data is that it yields a fairly small samle when one restricts attention to workers who hold emloyment-based health insurance olices who also meet other necessary criteria and rovide comlete data on all relevant variables. These small samle sizes limit the statistical ower of our analysis, leading to less recision in our estimates that one would like. owever, to our knowledge, the NME/IP surveys are the only data sets available that would allow us to link measures of job attachment with detailed information on emloyment-based health insurance contracts. Given this limitation, our objective is to uncover consistent atterns in the data that are congruent with the redictions of our theoretical model. If the model s redictions are uheld across a variety of 3

16 secifications and deendent variables, this should bolster confidence that the effects we find are genuine, desite their being less recisely estimated than would be ossible with a larger samle. B. Measuring Commitment / Job Attachment To test the redictions of our model, we require an observable roxy for the degree of job attachment resent in firms. A number of imediments to job mobility have been identified in the literature, with articular attention being focused on human caital secialization, which refers to the subset of a worker s knowledge or skills which are differentially valued by a articular firm, or within a articular occuation or industry. In general, the more secialized one s skills become, the costlier it will be to change emloyers. In the case of firm-secific training, these costs reflect reductions in roductivity and earnings at rival firms. 4 Alternatively, when skills are occuation- or industry-secific, the transactions costs of changing emloyers may reflect either reduced roductivity if the switch entails leaving one s occuation or industry, or simly the increased costs of finding a job as emloyment becomes more secialized. In the latter case, the costs of moving among emloyers may be high even in the absence of firm-secific training. 5 To roxy for job attachment and by imlication, the degree of commitment to a articular emloyment-based insurance ool, we use a measure from the DOT of the training secificity required in various occuations. The variable, known as ecific Vocational Prearation VP is defined as, the amount of time required to learn the techniques, acquire information, and develo the facility needed for average erformance in a secific job-worker situation, and is based on the nine categories of vocational 4 Available evidence suggests that the returns to secialized training are substantial. Toel 99, for examle, finds that, 0 years of job seniority raises the wage of the tyical male worker in the nited tates by over 25 ercent relative to what he could obtain elsewhere. 5 To take one examle, consider an academic health economist and a retail sales worker, both living in yracuse, New York. Although neither erson has significant firm-secific human caital, the set of emloyment oortunities available in the yracuse area is quite limited for the health economist, but not for the retail worker. In order to find a comarable emloyment oortunity elsewhere, the health economist would almost certainly have to re-locate - a rocess that is both time-consuming and costly whereas the retail worker is likely to have many emloyment oortunities that would not require relocation. The difference between the two stems from the more secialized nature of emloyment for academic economists which, although not based on firm-secific human caital er se, is related to their having more secialized training overall. 4

17 rearation shown in Table. 6 Note that VP was not designed to measure the general educational requirements of jobs, because a searate variable General Educational Develoment is rovided for that urose. A roxy for worker-level job attachment was obtained by imuting an VP value to each worker in the ousehold urvey. Because the ousehold urvey occuation codes are based on the occuation codes used in the 980 Census, it was ossible to imute an VP value to each worker using the Commerce Deartment s tandard Occuational Classification OC codes as a crosswalk. 7 The DOT rovides a finer occuational classification than the Census, so there were often multile VP values associated with each Census occuation code. To imute a unique VP value to each Census occuation code, we took a simle average of the VP values associated with each Census occuation. A list of reresentative occuations for each VP quartile is rovided in Table 2. The VP variable, although erhas not familiar to many readers, offers several advantages over other ossible measures of job attachment. First, unlike job tenure or turnover, it is not a function of the quality of health insurance offered by the resondent s emloyer. econd, we are not using the actual amount of training received by a articular worker, which is also otentially endogenous, but rather the amount of training tyically required in the worker s occuation. These observations suggest that one can lausibly treat VP as exogenous when considering the amount of insurance offered by a articular firm. At the level of an individual worker, VP would aear to be a good roxy for job attachment. owever, because decisions regarding health insurance are made at the firm level, the best concetual 6 The comlete definition of VP is as follows: This [VP] reresents the amount of time required to learn the techniques, acquire information, and develo the facility needed for average erformance in a secific worker-job situation. The training may be acquired in a school, work, military, institutional, or vocational environment. It does not include orientation training required of even every fully qualified worker to become accustomed to the secial conditions of any new job. ecific vocational training includes training given in any of the following circumstances: a Vocational education such as high school commercial or sho training, technical school, art school, and that art of college training which is organized around a secific vocational objective; b Arentice training for arenticeable jobs only; c In-lant training given by an emloyer in the form of organized classroom study; d On-the-job training serving as learner or trainee on the job under the instruction of qualified worker; e Essential exerience in other jobs serving in less resonsible jobs which lead to the higher grade job or serving in other jobs that qualify. 7 The OC codes are the occuational analogue of the well-known tandard Industrial Classification IC codes. 5

18 measure for our uroses is one that measures job attachment at the firm level; that is, one measuring the average amount of job attachment in a articular firm. Given the need to obtain a firm-level measure, there were two ways in which we might have roceeded. One ossibility was to simly use the VP value assigned to each worker as a roxy for the average degree of emloyment secialization in that worker s firm. This aroach would have been desirable if we believed that within-firm human caital heterogeneity was not very large. An alternative aroach, and the one adoted in this aer, was to construct a measure of the average degree of secialization in various industries, and use this as a roxy for the tyical amount of secialization arising in articular firms within those industries. This latter aroach will be referable if, as aears likely, there is less skill heterogeneity across firms in narrowly defined industries than within firms. To construct a measure of job attachment at the firm level, we first comuted the average VP value in each worker s industry labeled 980 by averaging the VP values by industry for all emloyed ersons in the 980 Census PM 5 ercent samle. To control for income differences at the industry level, which may confound 980 if more secialized training is associated with higher earnings, we also comuted average income in each industry using the PM data. Because the industry codes in the NME ousehold urvey are at the three-digit level reresenting some 230 distinct industries, we believe that 980 is likely to rovide a good measure of the average amount of job attachment resent in individual firms. One roblem with this measure is that it is based on the distribution of occuations existing in 980. If between 980 and 987 the year of the NME survey there were imortant changes in the distribution of occuations within industries then 980 will be subject to measurement error. To avoid this roblem, we calculated a second job attachment variable, 987, using the 8,000 ersons in the NME ousehold urvey who reorted a Census occuation code. 8 This variable catures the within-industry distribution of occuations that existed at the time of the survey. 8 To reserve comarability, we also calculated a measure of average industry income using this grou of workers. 6

19 owever, unlike 980, which is based on millions of observations and therefore thousands of observations er industry, 987 is based on only 8,000 observations in total, so the number of observations er industry is quite small in some cases. As a result, 987 may also be subject to measurement error. ince these two otential sources of measurement error should be unrelated, we will use both measures of job attachment in our analysis and examine the robustness of our findings across the two variables. In addition, we will re-estimate each model using 980 as an instrument for 987. It is well known that the instrumental variables estimator remains consistent in the resence of a mis-measured exlanatory variable, even in cases where the instrument itself is measured with error, rovided there is not a common comonent to the measurement error across the two variables. C. Measures of Insurance e use two standard contract rovisions as measures of the amount of insurance available through each olicy. The first is the lifetime limit on benefits, which is ositively related to the amount of insurance coverage secified in a lan, and robably the best overall measure of the extent to which longterm, costly medical conditions are insured. The second is the annual sto-loss, defined as the threshold level of medical exenditures above which the olicyholder is no longer required to make co-ayments. In contrast to the lifetime benefit cas, the annual sto-losses are less closely tied to catastrohic medical exenditures, but are more likely to be reached, and could therefore be viewed as a more immediately relevant measure of the amount of insurance contained in a lan. e make use of these two contract rovisions, in lieu of others such as the annual deductible or the lan actuarial value because we believe they ma most directly to our theoretical model, which is fundamentally a model of insurance rovision. e emhasize the word insurance because many health insurance lans combine reaid medical care i.e., care for common, low cost afflictions with true insurance, by which we mean rotection against less common, but significantly more costly, medical conditions. In articular, because our aer deals with the role of recommitment in maintaining viable risk ools, we would exect our measure of job attachment to matter most for insuring losses that require 7

20 large, foreseeable cross subsidies from other members of the insurance ool. This is most likely to occur in cases where a coworker develos a serious medical condition that is both chronic in nature and costly to treat, such as diabetes, cancer, or heart disease. For such conditions, we would exect that the overall amount of financial rotection conferred by the lan would be determined disroortionately by contract rovisions that aly to the right tail of the loss distribution. 9 D. Estimation amles To create our samles we alied a common set of restrictions to the 6549 IP resondents reorting emloyment-related health insurance coverage. ecifically, we droed any erson who was classified as unemloyed, or for whom a link to a current main job was unavailable. e also droed any erson who did not hold an emloyer- or union- sonsored lan, and anyone whose emloyer did not offer grou coverage, or who was emloyed by a sub-chater cororation. 20 e also deleted a small number of ersons who held olicies from more than one emloyer. These restrictions, couled with observations lost from missing or incomlete data, resulted in final samles of 2038 olicyholders for the lifetime benefit samle and 898 olicyholders for the annual sto-loss samle. To control for factors other than job attachment which might affect the level of coverage rovided under emloyment-based health insurance contracts, we include controls for tye of coverage single, two-arty, family, or other, self-insurance status of the emloyer fully self-insured, artially self- 9 In our samle, the average annual deductible is aroximately $50 in 987 dollars. Actuarial values measure the fraction of medical exenditures reimbursed by the lan for the average erson in the oulation. Thus, for a reresentative individual who will have low medical exenses, a generous lan is one that rovides a lot of firstdollar coverage, even if it omits coverage for catastrohic illnesses which, due to their low likelihood of occurrence, do not affect exected medical exenses very much. owever, from an insurance ersective, it is exactly these low robability, high exenditure conditions that risk averse individuals will most want to insure. This illustrates why the actuarial value is not a articularly good measure of insurance coverage, even thought it may accurately reflect lan generosity in a different sense. 20 ub-chater cororations have much higher lifetime limits than other tyes of firms an average of $,543,848 vs. $857,297 for the entire samle, erhas due to the large number of hysicians who incororate themselves in this way. Including cororations in our samle distorts our results unless their mean effect is controlled with an indicator variable. nfortunately, the NME variable for firm ownershi tye contains so many missing observations that our samles sizes are cut by roughly a third when we use this variable, reducing the recision of our estimates substantially. owever, the coefficient estimates on the variables of interest are little changed when we include cororations in our samle and control for their influence with a dummy variable. 8

21 insured, or commercial insurance, tye of insurance MO or indemnity, tye of emloyer for rofit, nonrofit, government, or other, region of the country northeast, midwest, south, or west, urban location MA or non-ma, firm size indicator variables for: < 0 emloyees, 0-25 emloyees, emloyees, emloyees, > 500 emloyees, emloyer unionization fully unionized, artially unionized, or non-union, and industry income. 2 e include a measure of average industry income in all of our regressions to ensure that is not simly icking u income differences across industries that are otentially correlated with insurance urchases. In the sto-loss samles, we also include controls for whether the sto-loss alies to all covered exenses or only the olicyholder s outof-ocket exenses, and whether the annual deductible is counted toward the sto-loss. ummary statistics for the lifetime benefit and annual sto-loss samles are dislayed in Tables 3 and 4, resectively. The mean lifetime benefit in 987 was aroximately $850,000, and there is substantial variation in these benefits; in our samle the range runs from a low of $0,000 to a high of $25,000,000. Although amounts below $50,000 may seem unusual, we have only included lifetime maximums that aly to coverage categories likely to yield high exenses, such as hosital room and board charges, inatient surgical benefits, and inatient hysician fees. e imosed this restriction to ensure that these lower limits were limits for the olicy as a whole and not for secialized tyes of care that sometimes have their own maximum benefits such as mental health or substance abuse treatment. Nonetheless, our results do not change if we eliminate maximum benefits below $50,000 or $00,000. The mean annual sto-loss is aroximately $2400 and there is considerable variation in this variable as well. ere we have less reason to worry that the reorted sto-losses do not aly to the olicy as whole because there is generally only one sto-loss reorted for each olicy. Again, our results do not change if we dro otential outliers, such as values below $500 or above $25, e control for lan- and firm-level variables, rather than erson-secific characteristics, because it is unlikely that the characteristics of a articular olicyholder would influence the attributes of a grou health insurance olicy. Recent work suggests that the set of insurance lans offered by emloyers, as well as the rovisions of the offered lans, are determined by the references of the workforce as a whole Moran, Chernew, and irth, 200; Bundorf,