Estimating workers’ marginal valuation of employer health benefits: Would insured workers prefer more health insurance or higher wages?

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Journal of Health Economics 27 (2008) 89–105

Estimating workers’ marginal valuation of employer health benefits: Would insured workers prefer more health insurance or higher wages? Anne Beeson Royalty Indiana University–Purdue University at Indianapolis, Department of Economics, IUPUI, 425 University Blvd., Indianapolis, IN 46202, United States Received 3 July 2003; received in revised form 7 December 2005; accepted 24 October 2006 Available online 19 June 2007

Abstract In recent years the cost of health insurance has been increasing much faster than wages. In the face of these rising costs, many employers will have to make difficult decisions about whether to cut back health benefits or to compensate workers with lower wages or lower wage growth. In this paper, we ask the question, “Which do workers value more—one additional dollar’s worth of health benefits or one more dollar in their pockets? ” Using a new approach to obtaining estimates of insured workers’ marginal valuation of health benefits this paper estimates how much, on average, employees value the marginal dollar paid by employers for their workers’ health insurance. We find that insured workers value the marginal health premium dollar at significantly less than the marginal wage dollar. However, workers value insurance generosity very highly. The marginal dollar spent on health insurance that adds an additional dollar’s worth of observable dimensions of plan generosity, such as lower deductibles or coverage of additional services, is valued at significantly more than one dollar. © 2007 Elsevier B.V. All rights reserved. JEL classification: I1; I11; J32 Keywords: Health insurance; Employer-provided health insurance; Compensating differentials; Hedonic model

Dramatic changes in the U.S. health insurance market over the last two decades have had an enormous impact on our system of employer-provided health insurance. Employers have confronted soaring health insurance costs, a significant increase in the variety of health plans available, and substantial changes to public insurance programs. Of all of these changes, the increases in

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the cost of health insurance are certainly at or near the top of the list of health insurance worries. The New York Times (August 19, 2004) cites the “relentless rise in the cost of employee health insurance” and quotes experts who blame health insurance cost growth for the lack of job growth (Porter, 2004). In an Issue Brief, the Center for Studying Health System Change highlights employers’ pessimism about acceptable responses to the upward trend in insurance costs: “most employers see no viable alternatives on the horizon” (Regopoulos et al., 2004). Employers and policymakers face some difficult tradeoffs as they seek the optimal response with respect to health insurance offerings in this new health insurance environment, especially given the expectation of continued cost growth substantially greater than inflation. In the face of these rising costs, many employers will have to make difficult decisions about whether to cut back health benefits or to compensate workers with lower wages or lower wage growth. Policymakers may consider options such as mandated employer-provided coverage or minimum coverage levels for those offered insurance. As employers and policymakers confront these difficult choices, they need estimates of how much workers value an additional dollar in health benefits as compared to an additional dollar in wages. Which do workers value more—one additional dollar’s worth of health benefits or one additional dollar in their pockets? Using a new approach to obtaining estimates of insured workers’ marginal valuation of health benefits, this paper estimates how much, on average, employees value the dollars employers pay for their workers’ health insurance. However, health insurance premiums vary for a number of reasons, not all of which may be expected to generate value to a worker. Premiums reflect not only the generosity of the coverage but also factors such as administrative costs, competition, and risk selection. There is no reason to expect that workers value premium dollars spent on these other items. In the second part of the paper, we distinguish between worker valuation of premium dollars that reflect insurance generosity and premium dollars that reflect these other factors. We find that insured workers value the marginal health premium dollar at significantly less than the marginal wage dollar. However, workers value insurance generosity very highly. The marginal dollar spent on health insurance that adds an additional dollar’s worth of observable dimensions of plan generosity, such as lower deductibles or coverage of additional services, is valued at significantly more than one dollar. 1. Conceptual framework Before presenting an intuitive explanation of how we estimate the value to workers of additional dollars spent on health insurance, it is useful to discuss why that valuation is not necessarily simply equal to one. Although a tradeoff equal to unity may be a natural focal point, there are many reasons why the tradeoff between wage dollars and health benefit dollars may not be one-for-one. The tax advantaged status of fringe benefits relative to wages suggests that each dollar of health benefits may be worth more than a dollar in wages to employees since the health benefits dollars are not taxed. On the other hand, economists would generally expect wage dollars to be valued more highly by employees than dollars paid in in-kind benefits since workers’ preferences for those in-kind benefits are likely to vary. Although worker preferences affect health plan offerings, a firm offers some limited number of health plans and cannot expect to satisfy exactly the preferences of all employees (Moran et al., 2001; Bundorf, 2002). Yet, health insurance also differs from many other in-kind benefits because the same insurance can usually be purchased at much lower cost through an employer group than individually. This would push valuations of benefits relative to wages higher. It is also not obvious that employers will not offer health benefits if workers value dollars spent on health insurance less than wage dollars. It is possible that health insurance

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provides incentives that induce some behavior by the employee that is valuable to the employer, such as lowering turnover. Alternatively, it could be that, offering health insurance acts as a screening mechanism, detering less desirable workers and attracting more desirable ones to the employer. Also, IRS non-discrimination regulations limit the extent to which employers can offer benefits only to certain workers, creating a situation where even workers recognized not to value health insurance highly may be offered insurance if the net gain to the firm of offering insurance to all workers is positive (Carrington et al., 2002). Whether workers value the dollars their employers spend on health insurance at more or less than one wage dollar is then an empirical question and it is that value of health benefit dollars that we seek to estimate in this paper. The estimates are generated from a linear logit or aggregated discrete choice model. The underlying individual model will be described in greater detail below but the intuition of the estimation can be described with a simple example. Many employers offer employees a menu of health plans. Different choices may entail a different employee contribution. The employee contribution required for a particular choice can be thought of as the wage that an employee must forego to purchase that option from the menu of health plans. Different choices often also carry different employer contributions. The employer contribution for a particular choice can be thought of as the health insurance fringe benefit dollars associated with that choice. The observed choice between offered health plan options conveys information about how much in wages workers are willing to give up to obtain additional firm dollars in the form of health benefits. That is the valuation of employer health insurance contributions that we want to estimate. This idea and the approach to estimation using plan share data are illustrated with an example. Consider two firms each of which offers two health plans to its workers. The employer and employee contribution for each plan and the share of employees choosing each plan is described in the following table.1 Total premium ($)

Employee out-of-pocket premium ($)

Share of covered workers enrolling

Firm A Plan A1 Plan A2

1000 1500

100 200

0.55 0.45

Firm B Plan B1 Plan B2

1200 1700

150 350

0.80 0.20

Workers at Firm A can choose to pay $100 more out of pocket for Plan A2 and obtain an additional $500 in health insurance. Workers at Firm B, on the other hand, would have to contribute $200 more for Plan B2 in order to obtain an additional $500 of total premium. The marginal cost of an additional $500 in insurance is higher at Firm B than at Firm A. By comparing the relative share of workers willing to pay $100 more for the more expensive plan at Firm A to the relative share willing to pay $200 more at Firm B, we can estimate workers’ willingness to pay for that marginal $500 in insurance. We do this using a grouped logit model and data on the share of workers choosing each plan offered by firms offering two or more plans. This method uses the within-firm variation in total premiums and out-of-pocket premiums by taking the differences in these plan characteristics and relating those differences to the relative share of workers choosing 1

I am grateful to an anonymous referee for suggesting this type of example and explanation.

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the two plans.2 The grouped logit model, as well as the underlying individual-level discrete choice model is described in more detail below. The approach described so far and the first model estimated below values the dollars spent for a plan without considering what those dollars are paying for. The estimated willingness-to-pay will reflect some average over worker valuations of all the various factors that determine total premium. This is appropriate if what one wants to know is whether the average worker would prefer to have an additional dollar in wages or an additional dollar in health insurance, given all the factors that contribute to differences across plans in total premiums, including the pricing of risk, and the load, as well as the specific coverage being provided by employer plans. One might also want to know how workers value different components of the plan premium. More generous plans will have higher premiums, other things equal, but there are also factors which influence premium but which may not be valuable to workers. As Chernew et al. (2004) put it in their discussion of price elasticity of health insurance, the interpretation of estimated elasticities depends on whether the price variation that generates the estimates stems from “factors that generate value to consumers.” For example, health plan premiums do not simply measure an actuarially fair rate for an individual enrollee. The premium for a plan reflects the risk pool of people who choose that plan. In firms that offer more than one plan, risk selection may induce differences in plan premiums across plans if, for example, one plan attracts a relatively greater share of sicker or high risk workers. The increase in premiums due to serving a high-risk pool does not generate additional value to an individual worker. Or, in other words, the differences in premiums due to differences in the risk of the covered population do not make the plan more “generous” to an individual worker. Other reasons that premiums may differ across plans but which may not be associated with differences in “generosity” (which we will define more precisely below) are administrative costs and competition. We can extend this framework to explore how much workers value what we label “generosity” by using information on the characteristics of each health plan. In a first stage regression, we estimate an hedonic premium model, letting the total premium of the plan depend on plan characteristics, including features such as cost sharing and covered services in order to estimate the implicit price of each plan characteristic. We estimate the hedonic premium model only for firms that offer exactly one plan so that the hedonic prices we estimate do not reflect the potentially strong risk selection effects on premiums that we expect for plans in firms offering two or more plans. We then use the estimates obtained from one-plan firms, to predict the total premium in firms offering two or more plans based on the characteristics of each offered plan. In the second stage, instead of simply using total premium in the choice equation as we did in the first set of models, we divide total premium into two parts – predicted total premium and the premium residual – and include both variables in the choice equation. We think of predicted total premium as capturing plan generosity and the residual as including factors such as risk selection effects and administrative costs. With this model, we can test whether workers value dollars that make plans more generous (using predicted premium) and how that valuation compares to premium increases which, by this definition, do not increase generosity (using premium residuals). 2 This method does not use variation in levels of benefits across firms. So, for example, we do not compare the $1000 premium and $100 contribution of plan A1 in the above example to the $1200 premium and $150 contribution of plan B1. Instead we compare the $500 marginal benefit and $100 price of that marginal benefit in Firm A to the $500 marginal benefit and $200 price of that marginal benefit in Firm B. Not using the variation in benefit levels across firms solves the problem of firm-level or individual-level fixed effects that are correlated with premiums or employees prices which could cause biased estimates.

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Table 1 Descriptive statistics Mean number of health plans per firm—2.7

premiuma

Mean total Mean employee-paid portion of premiuma Median difference between highest and lowest total premiuma Median difference between highest and lowest employee-paid portion of premiuma a

Single coverage

Family coverage

151.68 27.53

397.97 128.94

39.00

102.00

14.46

62.27

Premiums are monthly, in 1993 dollars.

2. Data The data are from the Robert Wood Johnson Employer Health Insurance Survey (RWJ-EHIS) of 1993. These are firm-level data and include detailed information on each health insurance plan offered by the firm, including the share of families and individuals enrolled in each plan and the employee and employer share of the premium for each plan. Following Berkson (1953) and Theil (1969), the individual logit model described in the following section can be aggregated and these share data can be used to estimate the model. This aggregation and the resulting econometric model is also described in the following section. The RWJ-EHIS surveyed approximately 2000 private employers and from 46 to 262 public employers in each of 10 states.3 We use only data on firms that offer two or more plans in order to analyze worker choices among plans.4 The data include information on 10,723 plans in 3849 firms that offer two more plans.5 Employers were asked about the total premium for each health plan for families and for singles and also the employer-paid portion of the premium for both groups. Firms were also asked to identify the share of enrollees by plan and the percentage of enrollees for each plan who were families, allowing identification of the share of family enrollment in each plan and the share of single enrollment in each plan. Employers were also asked about provisions of each plan such as deductible, copay, and whether various services were covered. We eliminate plans with missing values for total or employee share of premium and plans with no share of the firm’s market. After these selection criteria were imposed, we were left with 6827 single coverage observations in 2532 firms and 6810 family coverage observations in 2512 firms. Some key descriptive statistics are summarized in Table 1. Means of the variables used in the hedonic premium regression are included in the Appendix A. 3 The 10 states in which firms were surveyed are Colorado, Florida, Minnesota, New Mexico, New York, North Dakota, Oklahoma, Oregon, Vermont and Washington. Approximately 500 firms in four size categories (2–4, 5–9, 10–24, ≥25 employees) were sampled in each state. In a few cases, firms in particular geographic areas or SIC codes were oversampled to improve precision. 4 We use only the choices workers make between plans for those offered a choice of plans and those workers who enroll in an own employer plan. We do not have information about outside options available to workers, such as plans offered to a working spouse, so we cannot characterize the choice set beyond the sets of plans that the employer offers. 5 In total, the data include 22,465 health insurance plans in 22,890 firms. Of those, 7299 firms do not offer a plan and 11,742 firms offer exactly one plan. The 10,249 one-plan firms with no missing values for the included plan characteristics are used to estimate the hedonic premium model.

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3. A discrete choice model of health plan choice using premium data The individual-level theoretical model underlying the aggregate plan-level econometric model used here is a discrete choice model of the employee’s choice among health benefit packages. In the traditional health plan choice model where plans and plan characteristics differ across workers, we would let a worker’s choice depend on the premium paid by the worker and plan characteristics such as the deductible or whether or not certain services are covered (see, for example, Feldman et al., 1989; Scanlon et al., 1997; Atherly et al., 2004; Abraham et al., 2005). In such a model, the ratio of the coefficient of each plan characteristic to the coefficient on worker-paid premium represents the employee’s willingness to pay for that plan characteristic or the employee’s marginal valuation of that plan characteristic relative to dollars. The goal of this paper is not to estimate the value to employees of particular health insurance coverage provisions. The goal is to estimate employee preferences for an additional dollar in health insurance benefits as compared with a dollar in wages. To accomplish this, instead of characterizing each plan by its out-of-pocket premium and its coverage provisions, we characterize each plan by its out-of-pocket premium and its total premium. This is possible because employees often pay only a portion of their health plan premiums, giving us separate measures of worker cost (pj ) and total benefits (TPj ). Suppose firm g offers its employees Jg possible health insurance packages. Each package is described by a total premium TPj (including both employer- and employee-paid portions) and a price paid by the employee, pj . Health plan j is then defined as fj = (TPj , pj ) and the set of choices available to individual i at firm g is defined as Fig = (f1 , . . . , fJg ). Using a logit specification to estimate the effect of total premium and employee out-of-pocket premium on which plan a worker chooses implies that the probability of a worker at firm g choosing plan j is: eγp pj +γT TPj Πj = Jg γ p +γ TP . (1) p K T K k=1 e The ratio of the estimates of γ T and γ p provides an estimate of workers’ marginal valuation of health insurance benefit dollars relative to wage dollars. In other words, TPj is dollars spent on insurance benefits but the valuation of those dollars by the worker is incorporated in ␥T , which will depend on the value to the worker of the package of services that TPj buys.6 ␥p represents the effect on the employee’s utility of an increase in the wages foregone or cost of the plan. Therefore, estimates of ␥T /␥p obtained from this model produce an estimator of the worker’s marginal valuation of health benefits relative to wages.7 The parameters of interest are identified because both employee and employer contributions to health insurance premiums can differ across the plans offered to the employee. Some employers subsidize different alternatives by different amounts. For example, an employer may subsidize a 6 Using TP directly in this equation is somewhat analogous to an indirect utility function. We simply include the dollars j that it takes to purchase the bundle of characteristics that defines plan j in the estimation equation to obtain an estimate of the worker’s valuation of total fringe benefit dollars relative to wage dollars. As Small and Rosen (1981) point out, the discrete choice model is traditionally set up as what they call a conditional indirect utility function because utility depends both on the price of an alternative and its characteristics. This formulation pushes that notion further. The employee’s utility derives from the attributes that TP will buy but in this case we want to value the dollars spent on health benefits. Note also that plan characteristics are not included in Eq. (1) since we want to value the total dollars spent on health insurance benefits, not total dollars given coverage levels. 7 It is important to emphasize that this valuation is that of a marginal dollar for an insured worker. It is does not represent the value of having coverage relative to not having coverage or the value of insuring uninsured workers.

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more expensive plan more heavily but also require a larger employee contribution for that plan. The estimates obtained from the discrete choice model will reflect the extent to which a worker is willing to pay for the extra health insurance dollars contributed by the firm.8 This logit model can be aggregated to the firm-plan level in order to use the firm-level health plan share data available in the RWJ-EHIS survey. It should be noted that the conceptual issues outlined above and the advantages of this approach relative to others are general to the discrete choice model and not specific to the logit model. The logit model is used, however, in the empirical work presented here because the available data are aggregated, necessitating grouped data methods, of which the logit model is the most convenient. Also it should be noted that alternative distributions are not less restrictive than logit unless the independence assumption is relaxed. The linear logit model estimated here is based on the fact that the probabilities represented by Eq. (1) can be combined and written as: ln

Πjg = γp (pjg − pJg ) + γT (TPjg − TPJg ). ΠJg

(2)

Following Berkson (1953) and Theil (1969), we form groups of individuals – in this case workers at the same firm – facing the same (pj –pJ ) and (TPj –TPJ ) and estimate j and J based on the observed proportion of individuals in that group choosing each alternative. Because the probabilities must sum to one, if there are Jg plans offered at firm g, there are only (Jg − 1) unique pieces of information, and firm g contributes (Jg − 1) observations to the regression (see Ben-Akiva et al., 1985 for a clear exposition of this and other mechanics of estimating this type of model). For the problem at hand, each firm g will be a group facing the same prices and total premiums. The unit of observation is then the group of employees at each firm.9 Let Njg be the proportion of enrolled workers at firm g choosing plan j. The model to be estimated is simply a linear regression: ln

Njg = γp (pjg − pJg ) + γT (TPjg − TPJg ) + θjg NJg

(3)

The model can be estimated as an OLS regression where the error θ comes from having to estimate the probability of the choice of plan j for each group. The estimated parameters will be consistent as each group size gets large. There are a number of advantages to this approach relative to possible alternatives. One alternative approach is a compensating differentials model for job attributes and the supply and demand for those job attributes (Rosen, 1974). In the compensating differentials approach, employer-paid health benefits are regarded as one in a set of job attributes that may also include other fringe benefits, risk of injury or death, pleasantness or unpleasantness of working conditions, and any other aspects of a job that workers value. In a compensating differentials model or hedonic wage regression, the worker’s wage is regressed on job attributes such as health insurance and human 8 In the data, we observe a variety of contribution policies. For example, although it is most common for the most expensive plan to be subsidized at least as much or more than other plans, in 9.5% (16.4%) of the firms, a single coverage (family coverage) plan with the highest total premium was subsidized at 95% or less than some other offered plan. 9 Groups must be homogeneous in the explanatory variables of the model. For some plans, firms report that the price to the employee varies with the employee’s age, income, wage/salary status or health habits. However, only one composite price is recorded in the data. In order to maintain a larger sample size, the main models include observations from these firms. We also report sensitivity checks describing the results when we eliminate plans where employee price varies across employees.

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capital characteristics expected to affect productivity. The coefficient on each job attribute is its “implicit price” or the price at which is traded off in the “market” for job attributes. Several difficulties arise in estimating the hedonic model but the most immediate problem is that health benefits are probably correlated with productivity variables such as ability that are unobservable but positively associated with wages. An hedonic wage equation with fringe benefits on the right-hand-side is therefore expected to produce upwardly biased estimates of the coefficient on fringe benefits. Researchers have always assumed this problem to be at the root of the frequent wrong-signed estimates obtained in studies of the wage-fringe tradeoff (Hwang et al., 1992). It has proven quite difficult in practice to solve the omitted variable bias problem encountered in the hedonic model.10 In the estimation of compensating wage differentials, this problem arises from individual-level unobservable omitted variables such as unobservable productivity. In these models, cross-section comparisons across individuals will inevitably pick up these individual-level unobservables and correlation of such unobservable fixed effects with included variables will cause biased estimates. In the discrete choice model used here, however, each alternative is evaluated relative to the others and therefore purely individual-level (additive) unobservable fixed effects play no role. They are differenced out by the very nature of the discrete choice problem. Suppose fixed unobservable characteristics of the individual or firm, μi or φg , affect the value of each alternative plan available to an employee. For example μi might be large if individual i values being covered by any type of health insurance more than the average worker. Or φg might be negative due to a firm effect if a small business with unhealthy workers can negotiate only below-average quality for each plan at a given price. Note first that the potential individualspecific unobservables in the discrete fringe benefit choice problem are different from those in the traditional hedonic wage equation and are expected to be much less troublesome in general. Second, if the individual- and firm-specific fixed effects enter linearly, they will present no problem at all since, in the comparison of one alternative with another, they affect both alternatives equally. Neither pure individual effects nor pure firm effects affect the choice probabilities; we see this clearly by allowing explicitly for μi and φg , and writing the probability of a worker at firm g choosing plan j in terms of differences across alternatives: eγp pj +γT TPj +μi +φg e(γp pj +γT TPj +μi φg )−(γp pm +γT TPm +μi +φg ) Πgj = Jg γ p +γ TP +μ +φ = Jg γ p +γTP +μ +φ )−(γ p +γTP +μ +φ ) . (4) p K i g p k i g p m m i g T K k k=1 e k=1 e By moving to the discrete choice setting and using data on multiple alternatives available to the worker rather than just the chosen alternative as in the hedonic model, we easily circumvent the major problem that that literature has had in obtaining unbiased estimates of the compensating differential for employer-provided health insurance. The problem of individual-level unobservables that plagues attempts to estimate compensating differentials for fringe benefits stands in contrast to the problem that more commonly troubles discrete choice consumer demand studies. Consumer demand studies must often confront the problem of choice-level unobservables such as product quality (Berry, 1994). Unobservable product quality that is correlated with price will produce upwardly biased price coefficient estimates in discrete choice models of product choice. This is not a problem in the model presented here because, since we want to value the dollars spent on benefits, we are using the total plan premium, 10

Proposed methods rely on panel data (Brown, 1980; Duncan and Holmlund, 1983) or difficult-to-find instruments (Garen, 1988; Biddle and Zarkin, 1988) and, in any case, have been only partially successful in finding the theoretically predicted empirical results.

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TP, in the utility of each alternative rather than the observed attributes of each plan. Total plan premium reflects the market price of both observable and unobservable attributes of the plan. The estimated effect of total premium from the first set of models will provide an estimate of the value of the dollars spent on both observable and unobservable attributes of the health benefit. One central issue that remains is whether a worker’s choice among jobs and the implied matching of workers to firms induces a correlation between the explanatory variables and the error terms in the proposed model. As before, we must remember that workers are comparing amongst the alternatives in the choice set, so the issue is not whether, for example, TP1 is correlated with ε1 across firms but whether TP1 –TP2 is correlated with ε1 –ε2 . To decide whether this is a problem, let us consider the worker-firm matching process. Workers and firms may be matched based in some part on the fringe benefit package offered and demanded. If firm k is a “high fringe” firm, a worker with a high demand for fringes may be more likely to accept a job with firm k. However, if the firm heterogeneity in fringes across which workers choose jobs based on demand for fringes is fixed across all plans of the firm then those unobservable firm fixed effects will difference out. In other words, selection on levels of fringe benefits across firms (for example, φg in Eq. (4) or average TP for the firm), does not produce biased coefficient estimates in this model. Differencing across alternatives rids us of the first order part of the endogeneity problem that is due to job matching on benefit levels. The differencing of the discrete choice model will circumvent the job matching problem whenever the choice among jobs is made on the basis of something that is fixed across the menu of fringe benefit choices, such as job-level generosity of benefits which we think is the most likely way that benefits offerings affect workers’ job choices.11 A different type of selection may occur in firms that offer two or more health plans. Suppose a firm offers an HMO and a more generous PPO. If the PPO attracts a disproportionately high number of less healthy workers, then the price of the PPO will be higher not only because it is more generous but also because it attracts more costly enrollees. The model described thus far will provide an estimate of the average willingness-to-pay for the marginal dollar spent on health insurance, given factors such as risk selection which will affect total premiums but which may not actually make plans more valuable to an individual worker. Other such factors include the administrative costs and market power. These factors may affect premiums but may not make a plan more valuable to workers, in contrast to coverage provisions or other forms of generosity that are more costly and are also valuable to workers. In order to understand more about how much workers value the dollars employers commit to health insurance premiums, we next decompose total premiums into two parts, one measuring generosity and the other the residual factors that we cannot attribute to more generous coverage. To do this, we estimate an hedonic premium model of the form: TPg = β Xg + ug

(5)

where TPg is the total premium for the health plan offered at firm g and Xg are characteristics of that plan, including an HMO dummy, a PPO dummy, the deductible, the copay, a dummy for whether there is annual out-of-pocket limit, a dummy variable indicating whether the plan covers 11 The problem is not solved by this differencing if matching of workers to firms also occurs on the price differences of plans within firms or any factor that is not fixed across the menu of fringe benefit choices. We argue that this is second order relative to the selection on levels described above. That is, we do not think that workers make choices based on the difference in TP1 and TP2 or p1 and p2 at a particular firm or, in other words, selection across jobs on benefit price differences within firms is not nearly such a substantial problem as the aspect of selection due to firm heterogeneity in price levels that is differenced away in the discrete choice model.

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Table 2 Linear logit model Coefficients and willingness-to-pay estimates (heteroskedasticity-corrected standard errors in parentheses)

Worker’s share of premium in $/100 Total premium in $/100 Estimated willingness-to-paya total premium N (for differenced data) a * ** ***

Total premium model family plans

Total premium model single plans

−0.122*** (0.025) 0.043** (0.019) 0.35** (0.16) 4298

−0.336*** (0.078) 0.067 (0.040) 0.20* (0.12) 4295

Coefficient on total premium/coefficient on worker-paid premium. Significant at 10%. Significant at 5%. Significant at 1%.

dental care, prenatal care, maternity care, mental health care, and alcohol abuse treatment, and a dummy variable indicating whether the plan can exclude workers based on health.12 We estimate the hedonic premium model only on the sample of plans in firms that offer exactly one plan so that the estimated hedonic prices do not pick up the effects of risk selection on premiums that are described above. The estimated coefficients represent the average market price of each plan characteristic. We then use the estimated coefficients to predict total premium for the plans offered at firms offering two or more plans. The predicted total premium is our measure of generosity. It captures dollars spent to “buy” observed plan characteristics such as lower deductibles or dental insurance. The generosity measure for a plan incorporates both the observed characteristics of the plan and the average (implicit) price of those characteristics in the market. The residual will then capture other determinants of the plan premium such as risk selection, administrative costs, and competition that are not included in the hedonic regression and which we do not attribute to a plan’s generosity. The residual will also include the effect on premium of any unmeasured plan characteristics, including attributes that may be valued to workers. The empirical work will allow us to compare how much the measured generosity is valued as compared to these residual factors.13 To analyze this question, we then estimate the grouped logit model including predicted premium rather than actual total premium and examine the effect of this measure of generosity on the choices of workers. Last, we include both predicted premium and the premium residual in the model, in order to look explicitly at the relative willingness-to-pay for each of these two components of total premiums. 4. Results The model described by Eq. (3) was estimated separately for single and family coverage. Coefficient estimates are reported in Table 2. Robust heteroskedastic-consistent standard errors are reported since the use of estimated plan shares from groups of different sizes is expected to 12

The RWJ data include some other plan characteristics that might also be valuable. The plan characteristics that we do not use either have a very high proportion of missing values or the proportion of plans offering the service was very close to 1. 13 Other researchers have used hedonic premium models to investigate other questions such as the effect of competition on premiums (Wholey et al., 1995) and the cost implications of particular coverage provisions (Jensen et al., 1990).

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introduce heteroskedasticity in the errors. The willingness-to-pay estimate is presented in row three. The standard errors on the willingness-to-pay estimates are bootstrapped. Note first that the coefficients on employee and total premium are significant with the expected signs. Higher total premiums have a positive effect on workers’ utility and higher employee-paid premiums decrease utility.14 The implied estimates of willingness to pay for health benefits are reported in row three of Table 2. The estimates, 0.35 for families and 0.20 for singles are small. Both are significantly different from zero but also significantly less than one. However, since the worker premium variable used in the estimations does not account for the tax preferenced status of employer-paid premiums, we might prefer to test, not whether the estimate is significantly different from one, but rather whether it is significantly different from 1/(1 − t), where t is the marginal tax rate. The Tax Policy Center of the Urban Institute and the Brookings Institution reports that a family with the median income in 1993 faced a marginal tax rate of approximately 30% which implies that we might instead test whether the estimates are less than (approximately) 1.4.15 The willingness-to-pay estimates reported in Table 2 are obviously also significantly different from 1.4. Although we have discussed reasons that employers might offer health benefits even when some workers value additional wage dollars more than additional dollars spent on health insurance, it still seems somewhat surprising to find that workers appear to value these health insurance benefits offered by employers at so much less than the equivalent amount in wages, especially once the tax advantage is taken into account. The next set of models explores this further by decomposing the total premium measure into two parts, one capturing the dollar value of the generosity of the plan and one measuring the difference between the actual premium and that generosity measure or, in other words, the residual. Table 3 presents results from two sets of models for both family coverage and single coverage. The results presented in columns 1 (family coverage) and 3 (single coverage) are from models analogous to those in Table 2 except that total premium is replaced with the predicted total premium based on the hedonic premium regression described above. The predicted premium variable represents observable generosity (measured in dollars). This model allows us to investigate how workers value health insurance generosity relative to wage dollars as distinct from the valuation of actual total premium dollars as above. In columns 2 and 4, we present estimates from models that include the total premium residual from the hedonic premium regression as well as the predicted total premium. These models allow us to compare explicitly the valuation of those aspects of premium that we label generosity (using the coefficient on predicted total premium) with those which cannot be attributed to generosity (using the coefficient on the residual). The results are strikingly different from the results of Table 2. We find a willingness-to-pay for plan generosity of 8.6 for families and 4.6 for singles. Both families and singles value health insurance dollars that buy more generous plans very highly. And, as we see from the small and insignificant estimates from the models that also include the residual premium measure, neither

14

The coefficients on the worker’s out-of-pocket price are similar in size to those reported from the preferred health plan choice models in Feldman et al. (1989). 15 The reported median income for four-person family in 1993 was $45,161. The marginal combined tax rate was 30.3%. The combined rate includes federal income and employee plus employer social security and medicare (FICA) tax rates (http://taxpolicycenter.org/taxfacts/tfdb/tftemplate.cfm, “Historical Combined Income and Employee Tax Rates for a Family of Four.”) The adjustment for tax-preferenced status can also be understood to mean that a worker would need to earn $1.40 (pre-tax) to spend $1 (post-tax) on a good which does not enjoy a similar tax preference.

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Coefficients and willingness-to-pay estimates (heteroskedasticity-corrected standard errors in parentheses) Family plans Predicted total premium model Worker’s share of premium in $/100 Predicted total premiuma in $/100 Total premium residuala in $/100 Estimated willingness-to-payb predicted total premium Estimated willingness-to-payc premium residual N (for differenced data) a

−0.108*** (0.024) 0.930*** (0.088) – 8.59*** (2.26) – 4298

Single plans Predicted total premium model with residuals −0.114*** (0.025) 0.933*** (0.088) 0.011 (0.019) 8.18*** (2.14) 0.09 (0.18) 4298

Predicted from a hedonic premium regression on the sample of firms offering only one plan. Coefficient on predicted total premium/coefficient on worker-paid premium. c Coefficient on premium residual/coefficient on worker-paid premium. * Significant at 10%. ** Significant at 5%. *** Significant at 1%. b

Predicted total premium model −0.333*** (0.071) 1.538*** (0.201) – 4.62*** (1.35) – 4295

Predicted total premium model with residuals −0.344*** (0.078) 1.543*** (0.201) 0.016 (0.040) 4.48*** (1.40) 0.046 (0.13) 4295

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Table 3 Linear logit model with predicted premium

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families nor singles value plan premiums which are not associated with observable generosity.16 Although our measure of generosity can capture only observable features of plans, these estimates suggest that those observable features capture the plan characteristics that workers value. Any unobservable plan characteristics such as unobservable plan quality that are priced in total premium but which are not captured in predicted total premium (because they are unobserved or unmeasured in our data) is in the residual premium measure. Yet that residual premium has no effect on workers’ choices. The residual also includes administrative costs, competition, and the effects of risk selection as well as any other factors that are not priced explicitly in the hedonic premium model we have estimated. The insignificant effect of the residual premium, or equivalently the estimated willingness-to-pay for the residual of zero, illustrates that workers do not value factors that increase premiums but which do not contribute to the plan’s observed generosity. It should be noted here that these estimates are derived using data on the share of a firm’s covered workers enrolled in each plan. It is likely that the workers who choose not to enroll in an employer plan have a lower valuation of benefits than do the workers represented here. We do not think the bias and its effect on the interpretation of our results this might cause should be too severe for several reasons. First, although take-up rates for own employer insurance are around 80%, what Cooper and Schone (1997) label the “family take-up” rate is higher. Family take-up is the percentage of workers offered employer insurance of their own or through a family member who take up either their own or the family member’s employer coverage. They calculate the family take-up rate to be 89.1% in 1996. So the workers who decline all employer coverage and who may have, on average, lower valuations are a smaller proportion of the population than it might at first seem. Also, given the results reported above, we do not think that a small upward bias would change our interpretations. In the case of the valuation of the actual premiums, the results are already small. If they are upwardly biased at all, then the result is even more striking. On the other hand, the valuation of “generosity dollars” is very large—so large that we do not think the 10% or so of workers who decline all employer insurance would lower the estimates enough to change the qualitative results. The qualitative results are not sensitive to sample definition changes or alternative specifications of the hedonic model. Consider first changes to the specification of the hedonic premium model. In order to mitigate any effects of risk selection across firms (rather than only risk selection across plans within firms offering multiple plans), we also ran the hedonic premium model only on larger firms (25 or more and 50 or more workers), assuming that risk selection effects on premiums would be smaller at larger firms. The results were not sensitive to this change. We also considered the possibility that the plan type dummies could be picking up effects of competition or administrative costs if, for example, HMOs are associated with higher competition or plan type is correlated with administrative costs. Since we do not want predicted premium, our measure of generosity, to include these types of factors, we estimated the hedonic model without the plan type dummies. While the willingness-to-pay for family coverage generosity was approximately the same in this specification, the willingness-to-pay for single coverage generosity was approximately 20% higher than in the primary specification. This suggests that the plan type dummies may pick up some competition or administrative costs which are not valued by workers and highlights the fact

16 Since the coefficient estimates used to predict total premium and its residual were obtained from a hedonic model estimated on a different sample (the sample of one-plan firms), the predicted premium and the residual are not perfectly orthogonal, explaining why the coefficient on predicted total premium changes somewhat when the residual is added to the regression.

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that what workers appear to value are those things that explicitly measure what services a plan covers and what the out-of-pocket cost for those services will be. Changing the sample definition also does not change the interpretation of our results, though we do find some sensitivity to the sample restrictions. When we further restrict the sample, we find that willingness-to-pay estimates are, in some cases, somewhat larger, especially for families. For example, when we limit the sample to firms in which the employee price for a plan does not vary by any employee characteristics and the firm offers 10 or fewer plans,17 we find a willingness-to-pay for family coverage of 0.51. The estimates remain significantly less than one for both family and single coverage. In all of the models used to check sensitivity of the estimates, the single estimates are smaller than the analogous estimate for families. The willingness-to-pay for predicted total premium are consistently substantially larger than the estimates for actual premium. The two are the closest when using the more restricted sample described above and, even in this case, the willingness-to-pay for predicted total premium is an order of magnitude greater than the willingness-to-pay for the actual premium. 5. Conclusions We use worker choices among alternative health plans to identify worker preferences for health benefits versus wage dollars. Results suggest that insured families value health insurance benefits substantially more than singles but that neither group is willing to trade off one dollar of wages for an additional dollar of health insurance, especially once the tax advantage of the health insurance spending is taken into account. Given the structure of premiums, including the pricing of risk, administrative costs, and differences in competition, insured workers would, on average, prefer one more dollar in their pockets than one additional dollar of health insurance benefits. In considering the implications of these results, it is critical, however, to keep in mind that these results do not speak to the value of providing access to group health insurance for those workers not offered employer health insurance. The results are specific to insured workers and the value of increasing health insurance benefits for those insured by employer plans. When we use predicted premium as a measure of health insurance generosity, we find dramatically different results. Workers value an additional dollar of health insurance generosity, as we define it, at significantly more than one dollar. They do value and are willing to pay for additional health insurance if the dollars are spent on increasing observable benefits. Workers do not value residual premium dollars which are not associated with generosity but which may incorporate factors such as administrative costs, competition effects, and the effects of risk selection. It is clear from this evidence that workers respond very differently to premium increases that increase generosity as compared to those that do not and suggests that premium increases that generate value to workers must be evaluated very differently from premium increases that do not. This finding has some important implications for policy analysis. For example, the results confirm the importance of the Chernew et al. (2004) observation that the interpretation of estimated elasticities depends on whether the premiums vary due to “factors that generate value to consumers” 17 The second restriction was meant to address the possibility that the entire plan choice set was not relevant to all firm employees. Specifically, the restriction was meant to eliminate situations where plans were offered in many geographic locations represented by the firm that would not be relevant choices for workers in other geographic areas, sometimes producing plan shares of essentially, though not exactly, equal to zero. This sample restriction combined with the restriction that the employee price not vary across employees produces a much smaller sample size of 2075 differenced observations for family coverage and 2140 for single coverage.

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or other factors that affect premiums. We must be clear both about whether the estimates were obtained using premium variation that reflects variation in generosity or other factors and whether the situation to which we want to apply the estimates reflects changes in premiums due to changes in generosity or not. Similarly, we must conduct analyses of the welfare implications of rising premiums with the source of those rising premiums in mind. The results also suggest some key points that employers and policymakers working on benefits design should keep in mind. The efficiency and implications of pricing strategies such as defined contributions or consumer-driven care options must be evaluated in light of this evidence that workers value an additional value of health insurance generosity very highly but residual dollars not at all. For example, the effects of making workers more price sensitive through pricing strategies such as defined contributions will depend on whether the premium differences workers face are due to differences in generosity across plans or not. Acknowledgements I am grateful to many colleagues who have discussed these ideas with me in various forms over several years including Kate Bundorf, Dan Hamermesh, John Pencavel, Julie Schaffner, two anonymous referees, and workshop participants at Brown, Yale, Duke, University of Maryland, BLS, West Virginia University, SMU, the New York Federal Reserve Board, IUPUI, UC Davis, UC San Diego, Northwestern and Hunter College. This material is based upon work supported by the National Science Foundation under Grant No. 0096094. Funding from the American Compensation Association Emerging Scholar Program is also gratefully acknowledged. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation (NSF) or the American Compensation Association. Appendix A See Tables A.1 and A.2. Table A.1 Means of variables used in hedonic total premium regression (standard deviations in parentheses) Total family premium Total single premium HMO dummy PPO dummy Annual deductible Copayment ($) for provider visit Maximum annual out-of-pocket dummy Covers out of plan use dummy (=1 if indemnity plan or if other plans are reported to cover out of plan use) Dental care dummy Plan can exclude employees for health reasons dummy Prenatal care dummy Maternity care dummy Prescription drug dummy Mental health dummy Alcohol treatment dummy

380.43 (140.36) 150.90 (67.17) 0.16 (0.37) 0.35 (0.48) 259.19 (334.25) 8.14 (5.23) 0.83 (0.37) 0.88 (0.33) 0.31 (0.46) 0.26 (0.44) 0.93 (0.26) 0.93 (0.25) 0.88 (0.32) 0.93 (0.25) 0.90 (0.30)

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Table A.2 Hedonic premium model (standard errors in parentheses)

HMO dummy PPO dummy Annual deductible Copayment ($) for provider visit Maximum annual out-of-pocket dummy Covers out of plan use dummy Dental care dummy Plan can exclude employees for health reasons dummy Prenatal care dummy Maternity care dummy Prescription drug dummy Mental health dummy Alcohol treatment dummy Constant * **

Total family premium

Total single premium

−20.968**

−16.144** (2.748) −7.889** (1.439) −0.004 (0.002) −0.456** (0.123) −1.956 (1.949) 8.670** (2.873) 9.214** (1.410) −5.505** (1.497) 8.398* (3.991) −7.200 (4.082) 3.296 (2.073) −0.253 (2.835) 1.912 (2.344) 147.720** (4.818)

(5.918) −8.838** (3.100) −0.022** (0.005) −0.978** (0.266) 1.904 (4.238) 18.893** (6.185) 23.819** (3.025) −20.204** (3.232) 30.591** (8.781) −8.162 (9.003) 18.125** (4.526) −4.253 (6.216) 16.314** (5.116) 332.928** (10.722)

Significant at 5%. Significant at 1%.

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