adverse selection and the capped premium ... - Wiley Online Library

©The Journal of Risk and Insurance, 2002, Vol. 69, No. 2, 209-224

ADVERSE SELECTION AND THE CAPPED PREMIUM SUBSIDY IN THE FEDERAL EMPLOYEES HEALTH BENEFITS PROGRAM Bradley M. Gray Thomas M. Selden

ABSTRACT This article examines the relationship between adverse selection and the capped premium subsidy in the Federal Employees Health Benefit Program (FEHBP). Understanding this relationship is important, not only because the FEHBP is the largest employer-sponsored health program in the United States, but also because it has been proposed as a market-based model for the reform of both Medicare and the market for nongroup private coverage. We present a theoretical model of the FEHBP that we then test using enrollee data. In particular, we exploit the natural experiment that arises from variation in the premium subsidy cap across Metropolitan Statistical Areas (MSAs). Although the nominal subsidy cap is constant across MSAs, its real value varies greatly across MSAs with different price levels. The empirical analysis herein supports the contention that the premium subsidy in the FEHBP helps reduce adverse selection.

INTRODUCTION Economists frequently point to the benefits of undistorted consumer choice in promoting efficient resource allocation. Applying this logic to public and private health insurance systems, Enthoven (1978, 1988a,b) and others have stressed the advantages of offering consumers an open enrollment choice among competing private health plans, with sponsor contributions being held constant across all offerings. A potential disadvantage of this approach is that group premiums can be distorted by the enrollment decisions of other group members. This can lead to adverse selection, whereby low-risk consumers select suboptimal plans to avoid cross-subsidizing high-risk consumers. The result can be losses in terms of both efficiency (as low-risk enrollees Bradley Gray works for the Institute for Government and Public Affairs and School of Public Health/Division of Health Policy and Administration, University of Illinois at Chicago. Thomas Selden works for the Center for Cost and Financing Studies, Agency for Healthcare Research and Quality. This research was funded in part by the Robert Wood Johnson Foundation through its Changes in Health Care Financing and Organization Initiative Grant 030898. We are indebted to Kenneth Thorpe for the data we used in this article and for helpful comments on earlier drafts. The views expressed in this article are those of the authors, and no official endorsement by the Department of Health and Human Services or the Agency for Healthcare Research and Quality is intended or should be inferred. 209

210 THE JOURNAL OF RISK AND INSURANCE

receive less coverage than they would prefer) and equity (as high-risk enrollees face higher premiums for their coverage). In the extreme case, generous plans can experience premium spirals so that consumers of all risk levels would be forced into less generous plans. The question, therefore, is how to obtain the benefits of competition while avoiding the costs of adverse selection. From his earliest writings on this subject, Enthoven has stressed the importance of combining defined sponsor contributions with risk adjustment to help reduce incentives for adverse selection.1 However, in the market for employment-related group coverage few employers follow this prescription (Glazer and McGuire, 2001; Keenan et al., 2001). One reason may be that risk adjustment can be costly to administer. However, more widespread use is made of lower-cost strategies that may offer at least some of the benefits of risk adjustment. Examples include restricting the range of plan designs that are offered, providing reinsurance for high-cost enrollees, and the subject of this paper, premium subsidies.2 As shown in Selden (1999), if the sponsor contributes a fixed percentage of each plan’s premium, the largest premium subsidies would be paid for plans with the most expensive enrollees, thereby providing a de facto form of risk adjustment.3 The downside to premium subsidies is that they may weaken enrollee incentives to shop among competing plans (Hunt et al., 1997; Cutler and Reber, 1998). However, a capped premium subsidy may reduce adverse selection while at least partially preserving incentives for efficient plan choice (Selden, 1999). Empirical support is growing for the hypothesis that premium subsidies help control adverse selection.4 This article examines the leading example of an open enrollment system with a capped premium subsidy—the Federal Employees Health Benefits Program (FEHBP). Previous research has shown that while risk-based segmentation exists in the FEHBP, the market has largely remained stable over time (Price and Mays, 1985a,b; Merlis, 1999). Understanding the role of the capped subsidy in helping to control adverse selection in this program is of substantial public policy interest, not only because the FEHBP is the largest employer-sponsored health program in the United States, but also because the FEHBP has been proposed as a marketbased model for the reform of Medicare.5 It has also been proposed that the FEHBP be expanded to provide coverage to low-income individuals or small employers (see, for instance, Butler, 1996; Cutler, 1996). Analysis of the FEHBP may also provide insights 1 2

3 4

5

See also Van de Ven and Van Vliet (1992), Neudeck and Podczeck (1996), Selden (1999), Cutler and Zeckhauser (1998), Van de Ven and Ellis (2000), and Encinosa and Selden (2000). For more on employer strategies to control adverse selection, see Crocker and Moran (1998), Levy (1998), Encinosa and Selden (2000), Feldman, Dowd, and Maciejewski (2001), and Glazer and McGuire (2001). See also Monheit, Nichols, and Selden (1996), Cutler and Reber (1998), and Cutler and Zeckhauser (1998). Evidence regarding fixed versus subsidized contribution strategies in group coverage includes Buchmueller and Feldstein (1997), Cutler and Reber (1998), and Cutler and Zeckhauser (1998). For evidence on the magnitude of cross-subsidies within the market for employment-related coverage and the role of the tax subsidy, see Monheit, Nichols, and Selden (1996). See, for instance, Butler and Moffit (1995), Cain (1999), Feldman, Dowd, and Coulam (1999), and Wilensky and Newhouse (1999).

FEDERAL EMPLOYEES HEALTH BENEFITS PROGRAM 211

into the role of tax-related premium subsidies in helping to reduce adverse selection throughout the market for employment-related health insurance. The article begins by presenting a theoretical analysis that builds on the Rothschild and Stiglitz (R-S, 1976) model of adverse selection. The R-S model is modified to incorporate key features of the FEHBP, including both a capped subsidy and a national plan, the premium of which is exogenous to a particular market. Next, we use 1996 FEHBP enrollee data to test hypotheses derived from the theoretical model herein. The article focuses on the natural experiment that arises from variation in the subsidy cap across Metropolitan Statistical Areas (MSAs). Although the nominal subsidy cap is fixed across MSAs, its real impact can vary greatly across MSAs with different price levels. As a result of this variation across MSAs, FEHBP participants in different MSAs face very different effective subsidies—ranging from caps so low that the FEHBP is effectively a defined contribution scheme, to caps so high that the subsidy is nearly open ended. To the extent that adverse selection occurs in the FEHBP, one would expect higher-risk individuals to be enrolled, on average, in higher-premium plans. Furthermore, one would expect this relationship to be weakest (strongest) in markets where the subsidy cap is highest (lowest), thereby providing what amounts to a differences-in-differences estimation strategy across enrollees and across MSAs.

THEORY In the FEHBP, workers are offered a choice from a wide selection of (a) national plans, whose premiums are fixed across MSAs, and (b) qualifying local plans, whose premiums more closely reflect conditions in each MSA. The FEHBP is an open enrollment system in that insurers are prevented from charging individually risk-rated premiums. The federal government contributes a fixed 75 percent of premiums up to a capped amount that is set below the national plan premiums.6 One potential effect of open enrollment is adverse selection. In a separating, adverse selection equilibrium, low-risk consumers select less than optimal levels of coverage to avoid cross-subsidizing high-risk consumers, thereby leaving high-risk consumers by themselves in generous but high-premium plans. This can result in premium spirals that eliminate more generous plans as viable alternatives. Even those who are currently in good health can be harmed by adverse selection to the extent that they (a) receive less than optimal levels of coverage and (b) face the prospect of premium increases should they become higher risk in the uncertain future. Building on the R-S model of adverse selection, assume two risk types (high, H, and low, L), with insurers being unable to set premiums based on risk type. Assume that individuals obtain utility (U) from a single good (W ). They receive fixed total compensation of W E units of this good, but they risk losing an amount d with respective probabilities pH and pL (with pH > pL ). The proportion of high-risk individuals in the market is ∈ (0;1).7 Health insurance is represented by the contract ˛ = (˛1 ; ˛2 ), where ˛1 is the premium paid to the insurer if no loss occurs and ˛2 is the amount the 6 7

See Thorpe, Florence, and Gray (1999) for a description of the FEHBP rules for participating plans. Throughout the article we abstract from the possibility that changes in the FEHBP subsidy structure might influence the supply of labor to the government (or the mix of risk types the government employs).


individual receives if the loss does occur.8 Premiums are subsidized at the ad valorem linear rate s = 0:75, with the subsidy capped at C. Out-of-pocket cost to the consumer is therefore max [(1 − s)˛1 ; ˛1 − C]. One can think of the FEHBP as being funded by a lump-sum reduction in cash wages (T) on all employees in all FEHBP markets.9 Selden (1999) introduces a premium subsidy of this form into the R-S model, showing that a capped subsidy can increase expected utility for both risk types. Capped subsidies act as a form of risk adjustment even though payments are not directly linked to differences in risk. Indeed, an appropriately chosen capped subsidy can attain the second-best (informationally constrained) Pareto optimum.10 The FEHBP adds another key element to this subsidy scheme, in that employees are also given the opportunity to enroll in national plans whose premiums are essentially exogenous to N any individual FEHBP market. Let ˛N = (˛N 1 ; ˛2 ) be a national plan that provides full N coverage while costing the employee ˛1 − C in out-of-pocket premiums. Depending in part on this out-of-pocket premium, consumers may find the national plan to be more or less attractive than the local plans with their locally based premiums.11 A Graphical Analysis of Market Equilibrium Figure 1 presents the incentives facing consumers of each risk type.12 The figure graphs consumption in the absence and presence of a loss, W1 and W2 , respectively. In the absence of subsidies, employees of both types would receive their full compensation in cash wages (W E (0;0)). Unsubsidized, actuarially fair insurance contracts for highand low-risk workers are arrayed along the thin lines running from this “endowment point” to the full-coverage insurance plans at FH(0;0) and FL (0;0), respectively. Introducing the FEHBP capped subsidy scheme (s;C) results in the boldface employee budget constraints in Figure 1. Cash wages decline to W E (s;C), while the subsidized full-coverage plans for the high- and low-risk employees shift to FH(s;C) and FL (s;C), respectively.13 Intuitively, the subsidy s causes the budget loci to become steeper, because employees can now purchase more coverage (a larger increase in W2 ) for a smaller out-of-pocket expenditure (a smaller decrease in W1 ). However, for plans with

8

Equivalently, one could specify the contract as ˛˜ = (˜˛1 ; ˛˜ 2 ), where ˛˜ 1 = ˛1 is the premium paid to the insurer in either state of nature and ˛˜ 2 = ˛2 + ˛1 is paid to the individual if the loss does occur (so that the net amount received in the event of a loss is still ˛2 ). 9 The incidence of FEHBP contributions across employees need not be uniform. Rather, the main point for this analysis is that individual employees cannot increase or decrease their cash wages by their health plan choices. 10 The capped linear subsidy essentially works in much the same way as the lump-sum tax/transfer system proposed by Crocker and Snow (1985a). For the definition of second-best informationally constrained efficiency, see Crocker and Snow (1985b). 11 The analysis throughout focuses on separating equilibria for simplicity. For more on pooling equilibrium, doubleton equilibrium, and disequilibrium in the presence of subsidies, see Selden (1999). 12 For an introduction to graphical analyses of the R-S model, see Rothschild and Stiglitz (1976). For more on the graphical portrayal of subsidized R-S equilibria, see Selden (1999). 13 In any given MSA the cash wage endowment W E (s;C) might shift by more or less than the amount the federal government pays for coverage in that MSA (no binding MSA-level resource constraint exists in the FEHBP system).


FIGURE 1 Effect of FEHBP Subsidy on Consumer Incentives

premiums above the subsidy cap C, high risks once again face the full (unsubsidized) marginal cost of coverage.14 Figure 1 also depicts two alternative scenarios for the national plan. In the first case, the national plan, depicted by N, has a (subsidized) out-of-pocket premium that is cheaper than the local full-coverage plan would have if it were selected by high-risk employees. In the second case, the national plan N is more expensive. These two cases yield different equilibria, as shown in Figures 2a and 2b. Figure 2a depicts separating equilibria in the presence and absence of the FEHBP system, focusing on the case in which the national plan is more expensive than the high-risk, full-coverage local plan. A separating equilibrium occurs when low-risk employees self-select into plans that are less generous than they would otherwise prefer to avoid cross-subsidizing high-risk employees. In the absence of the FEHBP system, high-risk employees select full coverage at W0H and receive expected utility V0H. Low-risk employees select W0L , which is the most generous actuarially fair plan lying on or below the high-risk indifference curve passing through V0L . Introducing 14

The subsidy cap is assumed to exceed the premium of the less expensive plans (as in the FEHBP).


FIGURE 2a Separating Equilibrium (Impact of Capped Subsidy With Expensive National Plan)

FIGURE 2b Separating Equilibrium (Impact of Capped Subsidy With Inexpensive National Plan)


the FEHBP incentives (in boldface) causes high-risk employees to select full coverage (in a local plan) at W H(s;C;N). As a result of the subsidy, high-risk employees are better off. This in turn frees low-risk employees to select more generous coverage at W L (s;C;N). As depicted, both types of employees benefit from the introduction of the FEHBP subsidy. Indeed, low-risk employees can benefit even though they pay more in foregone wages than they receive in premium subsidies. This reduction in adverse selection forms the central hypothesis for empirical analysis: If the FEHBP subsidy is helping to reduce adverse selection, then one would expect the premium gradient L across risk types (˛H 1 =˛1 in the model) to be inversely related to the subsidy cap. Figure 2b portrays a separating equilibrium in the case where the national plan is cheaper than the local full-coverage option for high-risk employees. The availability of an inexpensive national plan essentially acts as an additional form of subsidy. Even though the direct beneficiaries are the high-risk employees who enroll, the availability of this plan can also confer benefits on low-risk employees by expanding their available choice of plans. The Effect of Changing the FEHBP Subsidy Cap and National Plan Premium In any given year, all enrollees in all MSAs face the same nominal premium subsidy cap and the same nominal national plan premiums. The real values of the subsidy cap and national premiums vary across MSAs inversely with local price levels, but this source of variation affects the real subsidy cap and the real national plan premium simultaneously. Figures 3a and 3b examine the effect of a simultaneous decrease in (a) the subsidy cap from C to C and (b) the national plan premium from N to N .15 Figure 3a depicts the case in which the national plan premium is relatively expensive, so that it is the decline in the subsidy cap that influences the market outcome. The result is increased adverse selection. In Figure 3b, the national plan is less expensive than the local full-coverage alternative. In this case, the reduction in the national plan premium governs market outcomes. This has the opposite effect of reducing adverse selection. Thus, whereas lowering the premium subsidy cap by itself would unambiguously increase adverse selection, this effect may be weakened or even reversed in markets where the national plan is relatively inexpensive. One can test for this relationship in the empirical work herein. To the extent that the national plan effect weakens or offsets the subsidy cap effect, one would expect to find the strongest subsidy cap effects in markets where the national plan is relatively expensive.

EMPIRICAL STRATEGY The FEHBP data for analysis contain cross-sectional observations on individuals who enrolled in single (nonfamily) plans during 1996. Although the FEHBP data provide no indication of enrollee health status or prior claims, the sample does contain data on enrollee age and the premium for the plan the enrollee selected.16 Let PREMij be the real premium of the ith enrollee in the jth MSA, and let AGEij be the enrollee’s age 15

Unsubsidized employee budget constraints have been removed from Figures 3a and 3b for greater clarity. 16 Using data from the Medical Expenditure Panel Survey (MEPS, described in Cohen, et al., 1996), average expenditures paid by private insurance in 1996 for individuals ages 25–34 with private insurance at any point during the year were $943;versus $2448 for similar individuals ages 55–64 (authors’ calculations).


FIGURE 3a Impact of Lower Subsidy Cap and Lower National Plan Premium (Expensive National Plan)

FIGURE 3b Impact of Lower Subsidy Cap and Lower National Plan Premium (Inexpensive National Plan)


in years. If PCAPj is the maximum (real) premium subsidized at the margin in that MSA (i.e., the premium associated with the cap on the subsidy), then ln(PREMij ) = ˇPCAP ln(PCAPj ) + ˇAGE ln(AGEij ) + ˇAGE∗PCAP ln(AGEij ) ln(PCAPj ) + fj + "ij ;

(1)

where the fj are MSA-level fixed effects that help control for unobserved MSA characteristics that are constant across enrollees.17 In the presence of adverse selection, one would expect to find @PREM=@AGE > 0, so that risk levels are correlated with premiums.18 More important, if the premium subsidy is helping to reduce adverse selection, then raising the cap should tend to dampen the risk-premium relationship: @2 PREM=@AGE @PCAP < 0. Price Indexes A key element of this empirical strategy is to estimate Equation (1) in real terms to exploit the natural experiment of sorts that occurs across MSAs with different price levels. This approach relies on MSA-leve price indexes to convert nominal dollar amounts to real values. The preferred measure herein is the Centers for Medicare and Medicaid Services (CMS) Geographic Practice Cost Index (GPCI). The GPCI has the advantage of focusing on a constant basket of physician practice inputs. In addition, these results are compared with those obtained using three other price indexes: (a) the CMS Hospital Wage Index (HWI), (b) the all goods and services price index constructed by the American Chamber of Commerce Research Association (ACCRA), and (c) the ACCRA price index for health care.19 While any individual MSA-level price index is likely to have important flaws, it is reassuring that the results in this article are relatively unaffected by choice of index. Separating the Impacts of Subsidy Caps and National Premiums As discussed in the “Theory” section, a potential obstacle to estimating Equation (1) is that the real FEHBP subsidy cap is perfectly collinear by construction with real national plan premiums (since the cap and the national plan premiums are constant across MSAs in nominal terms). This precludes entering the national plan premiums as explanatory variables along with the real subsidy cap, yet the theoretical model suggests that simultaneous changes in the national plan premium can diminish the effect of the subsidy cap. Fortunately, the theoretical model also suggests that the influence of the national plan is likely to be greatest in markets where the national plan is relatively inexpensive (i.e., where the local price index is high). For this reason, Equation (1) is estimated first using all MSAs and then using only the subset of 17

The inclusion of MSA-level fixed effects absorbs the MSA-level direct effect of the subsidy cap, but the interacted effect of the subsidy cap remains (see below). MSA fixed effects also absorb the linear impact of MSA market characteristics such as income and wealth levels, government regulation, and market structure. 18 It is perhaps useful to note that the FEHBP prohibits insurers from charging different workers different premiums for the same coverage. This is why we interpret @PREM=@AGE > 0 as evidence of sorting across plans rather than risk-rating of premiums across enrollees in a given plan. 19 The ACCRA indexes were obtained from the U.S. Bureau of the Census (1998, Table B-6).


TABLE 1 Sample Means and Standard Deviationsa Variable

Mean

PREM

2,107.65

393.36

PCAP

2,175.27

302.07

SALARY

Standard Deviation

42,284.22

17,313.98

MALE

43.86

49.62

AGE

43.47

10.62

N a

436840

All means and standard deviations are for variables in levels rather than natural logarithms.

MSAs with relatively low local price levels.20 The latter sample, while smaller, should in principle yield purer estimates of the subsidy cap effect in the event that the two effects are offsetting one another in the full-sample results.

DATA This analysis focuses on health insurance plans serving the under-65 (nonannuitant) and nonunionized segment of the FEHBP. We concentrate on the market for individual coverage because the relationship between policyholder age and expected claims is likely to be stronger for individual policies than for family policies. Data on health insurance premiums by enrollee are obtained directly from the Office of Personnel Management, the federal agency that administers benefits for federal employees. Plans are linked to markets (MSAs) using plan service area information in Francis (1996).21 Table 1 presents the means and standard deviations for all variables used. Of particular interest is the large variation in PCAP observed in these data. The standard deviation of PCAP is 20 percent of the mean, with minimum and maximum values of $1;249 and $3,166, respectively. The extent of this variation aids identification of the key parameters in the model and enables extrapolation of the results to either a pure defined contribution plan or an open-ended subsidy. As a final note, in addition to the enrollee’s age (AGE) and the AGE*PCAP interaction, the estimated models also include MALE (coded 1 for males and 0 for females) and the enrollee’s salary

20

Enrollment data from 1996 confirm that national plan enrollment is positively related to the local price level. In the quartile of MSAs with the highest hospital wages, the percentage of enrollees selecting national plans was 73 percent, versus national plan enrollment rates of 68, 57, and 44 percent in the second, third, and fourth quartiles, respectively. Although national plans play an important role in the market equilibrium of even the MSAs with the lowest price levels, one would expect differences of this magnitude to be reflected in the estimates herein if changes in national plan premiums were in fact influencing these results. 21 In some cases, MSA links in Francis (1996) were supplemented by contacting the health plan directly (Thorpe, Florence, and Gray, 1999).


(thereby helping to identify the health risk effect of aging separately from the effect of age-related salary differences).22

RESULTS Table 2 presents results for Equation (1) under a range of alternative specifications.23 In addition to the full-sample fixed-effects model using the GPCI in column 1, column 2 presents estimates from the subsample of MSAs with low price levels. Columns 3-5 present full-sample results for the full model constructed using three alternative price indexes. In all cases, the fixed-effects results show that within-MSA differences in enrollee age are significantly correlated with differences in the premiums that enrollees select— evidence consistent with the presence of risk-based selection across plans.24 Moreover, the interaction of AGE with PCAP yields a negative cross-partial derivative—a result consistent with the hypothesis that the FEHBP subsidy is helping to reduce adverse selection. To put these results into context, one can simulate the age-premium gradient under alternative assumptions regarding the subsidy cap. Figure 4 graphs simulated agepremium gradients (normalized to percentages centered around 100) for (a) a defined contribution plan (with no marginal subsidy), (b) an open-ended (uncapped) subsidy, and (c) the FEHBP average subsidy cap in 1996.25 Even under the extreme case of a defined contribution, the age-premium gradient is not large, only changing approximately 9 percent between ages 25 and 64. This is perhaps not surprising, since age is only a very imperfect measure of health risk. Essentially, there is an error in variables problem in these data relative to the ideal of measuring health risks that enrollees observe when they are choosing among plans. For this reason, it is likely that the observed age-premium gradient is flatter than the true risk-premium gradient.26 Thus, perhaps the most salient finding is not the magnitude of the observed gradient, but rather the fact that it largely disappears as the subsidy cap is increased. 22

We also estimated models with MALE*PCAP and AGE*MALE*PCAP, thereby exploiting the different age-expenditure profiles of men and women. These models yield very similar results for AGE. However, the results for sex are rarely statistically or economically significant. Results are presented in Appendix A (available from the authors upon request). 23 All estimates in this article were constructed using the AREG procedure in Stata 6.0. Standard error estimates were corrected for heteroskedasticity across MSAs using the HuberWhite method. Partial derivative estimates were corrected using estimated smearing factors. In all cases the smearing factors were less than 1.01, so substantial prediction bias due to heteroskedasticity is not likely (see Mullahy, 1998). 24 Nonlinear Wald tests for the marginal effects were constructed using the delta method. 25 Figure 4 is constructed using (smearing-corrected) predicted premiums obtained from Equation (1) holding MALE and SALARY at their sample means and allowing AGE to vary from 25 to 64. We approximate a defined contribution plan (open-ended subsidy) by setting the PCAP at the bottom (top) 1 percent of the real premium distribution. 26 Indeed, age explains only 1 percent of the total variation in expenditures paid by private insurance across individuals ages 25 to 64 with private coverage at any point during 1996 in the MEPS data (authors’ calculations). This is less than one-tenth of the explainable expenditure variation that might serve as a basis for selection (Newhouse, 1996), suggesting that the results herein may substantially understate the true extent of risk segmentation.

CMS Geographic Practice Cost Index (GPCI) Models Constant MALE

Low-Price MSAs

CMS HWI

ACCRA General

∗∗∗

∗∗∗

∗∗∗

∗∗∗

7.1436

(0.0053)

(0.0053)

7.1033

7.1000∗∗∗ (0.0058) −0.0081∗∗∗ (0.0004)

−0.0073∗∗∗ (0.0004)

−0.0081∗∗∗ (0.0004)

∗∗∗

∗∗∗

−0.0825

∗∗∗

(0.0425) (0.0055)

0.7917

(0.1068)

0.0343∗∗∗ (0.0006) −0.0979

∗∗∗

(0.0138)

0.3415

(0.0382)

0.0341∗∗∗ (0.0005) −0.03914

∗∗∗

(0.0059)

ACCRA Health Care

(0.0058)

∗∗∗

0.0328∗∗∗ (0.0005)

(0.0301)

0.1951∗∗∗ (0.0328)

0.0365∗∗∗ (0.0006)

0.0365∗∗∗ (0.0005)

0.1407

−0.0128

∗∗∗

(0.0043)

−0.0198∗∗∗ (0.0043)

1.8611∗∗∗

2.1106∗∗∗

1.9594∗∗∗

2.0775∗∗∗

2.0658∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

−0.0005∗∗∗

2

−0.0021

2

0.528

R

7.1256

−0.0074∗∗∗ (0.0005)

ln(SALARY)

@ PREM=@AGE @PCAP

(0.0070)

∗∗∗

0.6730

@PREM=@AGE

7.2469

−0.0075∗∗∗ (0.0004)

ln(AGE) ln(AGE)*ln(PCAP)

Models Using Other Price Indexes

Full Sample

∗∗∗

F-test of Homogeneity

242.06

N

446,261

−0.0028 0.385 197.73

∗∗∗

244,371

−0.0010 0.600 227.71

∗∗∗

436,840

−0.0003 0.674 264.28

∗∗∗

374,712

0.658 280.46∗∗∗ 374,712

Notes: All variables in natural logarithms (except MALE). Huber-White robust standard errors are in parentheses. Nonlinear Wald hypothesis tests for whether derivatives are statistically significantly different from zero performed using the delta method. *** Indicates coefficient estimate significantly different from zero at 1 percent level.


TABLE 2 Cross-Sectional Regressions for Natural Logarithm of Premiums for Individual Enrollees, 1996


FIGURE 4 Simulated Impact of Premium Subsidy Cap in FEHBP Single Coverage Markets

CONCLUDING DISCUSSION The objectives of this article are twofold. First, a theoretical analysis introduces key elements of the FEHBP premium subsidy scheme into the R-S model of adverse selection. Second, enrollee-level data help examine how changes in the FEHBP subsidy cap affect the extent of adverse selection in that system. The empirical analysis exploits the substantial variation in the real subsidy cap across MSAs. In some MSAs, real caps are so low that the FEHBP subsidy comes close to approximating a defined contribution. In other MSAs, the real cap is so high that the subsidy is nearly open ended. It would clearly be preferable if the variation observed in the real subsidy cap had arisen from random assignment in a controlled experiment, rather than through differences in price levels across MSAs. However, no such experiment has been undertaken. Nevertheless, through the careful use of alternative price indexes and fixed-effects estimation strategies, one can derive valuable insights from the “naturally occurring” price-driven variation observed. The empirical findings are consistent with the theoretical prediction that the FEHBP subsidy is acting to dampen adverse selection. Perhaps because the only proxy for health risk is enrollee age, the magnitude of the adverse selection observed is relatively small. Certainly one finds less adverse selection using this approach than others have found using actuarial methods (Price and Mays, 1985a,b). Nevertheless, the most salient implication of the results herein is not how much adverse selection one finds, but rather the result that the FEHBP premium subsidy appears to be reducing the adverse selection observed. It is well known in the health economics literature that premium subsidies can weaken incentives for minimizing the cost of care (Feldstein, 1973). These results contribute to a growing body of evidence suggesting that premium subsi dies should be designed to strike a balance between preserving incentives to minimize cost versus


structuring incentives to reduce adverse selection. This finding is relevant not only for the design of employment-related open enrollment plan offerings, but also for proposals that would extend a government-sponsored choice of private health insurance to intrinsically more heterogeneous populations, such as Medicare beneficiaries or the uninsured. In the context of Medicare reform, Wilensky and Newhouse (1999) highlight the potential for defined contribution vouchers to result in adverse selection. Their solution is to adjust vouchers to reflect beneficiary health risk. The analysis in this article suggests that an alternative (or perhaps complementary) strategy may be to incorporate a more easily administered FEHBP-type capped premium subsidy.

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