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Health plan choice: price elasticities in a managed competition setting.

I. Introduction

Using a unique panel dataset of the health plan choices and personal characteristics of employees at a single firm, this paper provides estimates of price elasticities for health insurance plans in a managed competition setting. Estimates of price elasticities in such a health insurance market are important because price competition is a crucial component of the managed competition approach to health care reform. The theory of managed competition suggests that health insurance plans should be structured to avoid competition on non-price attributes such as the coverage of particular services; that extensive information should be provided about all plans; and that plans should be priced such that consumers, as opposed to their employers, pay for their health insurance at the margin. These changes in the health insurance market are meant to provide incentives for health care consumers to choose their health insurance plans on the basis of price and quality (Enthoven 1978).

Price competition as envisioned in the managed competition framework depends on a restructuring of health insurance. Benefits are standardized across plans in order to eliminate the product differentiation that can make consumers insensitive to price. The elimination of these product differentiation barriers to choosing initially, or switching to, a health plan that provides equal quality services at lower cost is meant to encourage insurers to attract subscribers by controlling costs rather than by offering different services.

More important, perhaps, the managed competition model also suggests changes in how the costs of health insurance are divided between employer and employee. Employer provision of health insurance to employees as a fringe benefit has, in the past, often meant that employees choose their health plan and firms pay the bill. In this setting workers have no incentive to consider price in making their health plan choice since the firm will pay the full cost of whichever plan is chosen. The restructuring of benefits offerings so that employees pay the additional cost of a higher price plan is meant to provide individuals with incentives to take price into account in choosing a health plan. This restructuring would create, or perhaps resurrect, the price variation across health plans that has been eliminated or reduced by the custom of fully employer-paid premiums.

Barriers to switching health plans other than product differentiation may also exist, however, and these barriers may also be an important cause of low price elasticities among health plans. High transition costs, or switching costs, between health plans could seriously reduce the price elasticity between health plans and therefore the amount of price competition yielded by reform. These switching costs may be directly related to switching health plans or may be due to the fact that by switching health plans, one may have to switch doctors, which may itself be costly. Switching doctors may be costly because of the accumulated knowledge of a patient's health condition that develops over time and because of the trust developed in a longstanding doctor-patient relationship. Switching health plans may involve paperwork or administrative hassles; it may also be quite time-consuming to research alternative plans or difficult to evaluate their quality.

A 1985 study by Neipp and Zeckhauser finds considerable persistence in individuals' choice of health insurance plans. They find that at both of two Boston-area firms where employees were offered a choice among a number of plans, only 3 percent of employees switched health plans between 1984 and 1985. In light of that finding, it is important to ask whether such persistence will undermine the price competition that lies at the heart of the managed competition approach to reforming the health insurance market. Furthermore, it would be useful to know more about who does switch insurance plans. Neipp and Zeckhauser theorize that the persistence in plan choice that they find is due to transition costs. Clearly, individuals with lower transition costs are more likely to switch insurance plans than individuals with high transition costs. Because insurers will respond to likely "converts," we must consider that, if transition costs are empirically important, insurance companies will respond most to those with low transition costs since it is they who are most likely to switch plans. Such incentives for insurers may well compound incentives for risk selection or "creaming" when capitation payments are not risk-adjusted. If these "likely converts" are the least sick, the youngest, or the most educated, the managed competition incentives for change by insurance providers may not work to the advantage of those who need the health care system the most. If, on the other hand, it can be shown that transition costs are not a substantial deterrent to switching health plans, we might expect the incentives posited by this theory to be much more effective.

The dataset used in this paper consists of health plan choices and demographic data from 1993-95 on Stanford University employees. Administrative data are supplemented with data from a survey conducted by the authors. Prices vary in these data both in the cross-section and over time. With only minor exceptions, the health plan choices and fee structure at Stanford conform to the major innovations suggested in the managed competition model. It is important to know the extent of price responsiveness by employees in a managed competition market and the extent to which transition costs, many of which may be intrinsic to the problem since they involve doctor-patient relationships, continue to depress this price elasticity. Low price elasticities may inhibit the efficiency gains due to increased price competition envisioned by policy-makers.

We find that employees are sensitive to price. Our estimates imply that insurers face an elastic demand for health plans that would appear to have the potential to promote price competition. We find that fixed effects procedures that eliminate individual-specific unobservables that may cause omitted variable bias produce significantly larger (in absolute value) price elasticities than methods that ignore this potential bias. We also find notable differences in price elasticities across groups with older and less healthy enrollees being less sensitive to price. This finding has implications for the extent of adverse selection in the market.

In the next section, we review the literature on health plan choice, concentrating on the estimates of price elasticities. In the following section (Section III), we describe the data to be used in this paper and the setting from which these data were derived. In Section IV we estimate multinomial logit and nested multinomial logit models of health plan choice. From these models, we derive price elasticities. In Section V we estimate price elasticities by demographic group. In this section we ask whether the transition costs incurred in switching health plans are significantly higher (and therefore price elasticities are significantly lower) by health status, education level, or age, assuming that these variables can capture differences in transition costs across individuals. In Section VI we discuss health plan choice and tax policy. This study is also the first to use panel data methods to eliminate fixed individual effects that may bias coefficient estimates. A fixed effect logit model that accounts for individual heterogeneity in health plan choice is presented and its results discussed in Section VII. Conclusions are presented in Section VIII.

II. Literature Review

This study will estimate price elasticities of health plan choice using unique panel data on insurance plan choices made in a setting that closely resembles the structure of the managed competition model of the health insurance market. We seek to establish whether employees are responsive to health insurance premiums in this setting and the degree to which insurers face elastic demand for health plans. Previous work that estimates health insurance price elasticities suffers from a number of problems, most of which stem from the lack of adequate data. This study remedies those problems by using a new source of data, some of which was specifically collected to answer the questions posed, and also extends the literature methodologically by estimating fixed effect logit models of health plan choice. In order to understand the need for a new study of health plan price elasticities, let us turn to a discussion of the range of estimated elasticities in the existing literature and also the shortcomings of some of that work.

The most complete study using a nationally representative cross-section dataset is that by Short and Taylor (1989). They use data from the National Medical Care Expenditure Survey (NMCES) collected in 1977. Short and Taylor estimate two separate logit models, one of the choice between two fee-for-service plans and one of the choice between a fee-for-service plan and an HMO. They find a price elasticity of the probability of enrolling in the "high option" fee-for-service (FFS) relative to the "low option" FFS plan of -0.14.(1) They estimate a price elasticity of only -0.05 for the probability of enrolling in an HMO relative to a FFS plan. Although this study and dataset offer certain obvious advantages, most notably independent price variation in health plans across consumers, the dataset and methodology also suffer from some problems that may affect the results. For example, their strategy of defining the rejected alternative in bivariate logit models as the plan with the next lowest premium compared to the chosen alternative fails to take account of the full choice set available to the individual and the consistency of results relies heavily on the independence of irrelevant alternatives assumption also embodied in the logit specification itself. Also, only about 3.5 percent of households in the NMCES sample had any choice among employer-provided health plans in 1977, raising questions about the representativeness of the sample from which estimates were derived.

Feldman, Finch, Dowd, and Cassou (1989) use a sample of 17 firms in the Minneapolis-St. Paul area in 1984 to estimate a model of health plan choice. In their estimations, Feldman et. al. distinguish between two different types of HMO's: independent practice associations (IPA's) and prepaid group practices (PGP's). Independent practice associations generally provide a greater choice of physicians than PGP's since IPA's contract with a network of independent providers while the physician services of a PGP are provided by a particular group practice. Feldman et. al. estimate a nested multinominal logit model, testing the usual assumption of independence of irrelevant alternatives (IIA) that requires that all alternatives are equally similar or dissimilar in unobservable dimensions. They find that the distinguishing feature between nests or the feature that makes some plans more similar than others is the greater choice of physicians offered by FFS plans and IPA plans in contrast to PPG plans.

The Feldman et. al study provides a range of estimated price elasticities since, in the nested multinominal logit model, the own price elasticity depends on both the market share of that alternative and the share of that alternative within its own nest. For example, for a health plan with 50% of the overall market the estimated price elasticities range from -0.53 to -0.15 depending on the share of that plan in its own nest.(2) For plans with very small enrollments, elasticities are even larger in absolute value and for very large plans the elasticity is close to zero. Though the multi-firm sample used in this study has the advantage of price variation in plans across firms, it has the disadvantage of necessitating the use of a conditional logit model without identifiable types of alternative plans and where plans are identified only by the plan attributes included in the equation. In this type of model it is crucial to have data on all relevant characteristics of each health plan, since no plan-specific intercept can be included. In this model, omission (due to lack of data) of relevant features of the alternative plans that may be important in explaining the choices of individuals may leave important dimensions of plan quality unobserved. If these attributes are correlated with price or other observable plan characteristics, coefficient estimates may be biased. For example, Feldman et. al do not include (presumably due to lack of data) interactions of income with plan attributes such as quality. If income is correlated with premium, price elasticity estimates may be biased. For example, if high income employees have larger employer subsidies to health insurance, their out-of-pocket premium may be lower and the omission of interactions of income and desirable plan attributes could cause estimated elasticities to be overestimated (in absolute value).

The study of health plan choice by Barringer and Mitchell (1994) uses individual firm data on the health plan choices of its employees. The advantage of this dataset is that every employee faces the same set of choices and we know precisely what those choices are. Like the other studies, Barringer and Mitchell find a negative and significant effect of premium on plan choice but the range of own price elasticities implied by their estimates for the traditional FFS plan is a very small -0.01 to -0.02.(3) The disadvantage of this dataset is that price variation occurs only within plans, across locations, by exempt or non-exempt employee, and by coverage level. Also the within plan variation in prices used to identify price effects may also pick up the effect of other plan attributes since no plan-specific intercepts are included in the model. Neither Barringer and Mitchell nor Short and Taylor test the IIA assumption imposed by the logit specification, a specification rejected by the Feldman, Finch, Dowd, and Cassou (1989) study.

More recently, Cutler and Reber (1996) estimate the effect of price on health plan choice among Harvard University employees after the Harvard employer contribution formula was altered in accordance with managed competition goals. Benefits were also fairly standardized across plans in the Harvard setting. Cutler and Reber obtain elasticity estimates for out-of-pocket premiums ranging from -0.30 to -0.60. The specification they use to derive these estimates introduces some measurement error, however, since by estimating a binary choice model rather than a model of all offered choices, they must group all HMO's together despite differences in premiums, observed plan attributes, or quality.

Other older studies using different methodologies or different types of data have also estimated price elasticities.(4) See for example, Marquis and Phelps (1987), Welch (1986), Merrill, Jackson, and Reuter (1985), Holmer (1984), and McGuire (1981). These studies, while not exactly comparable to those previously discussed have obtained price elasticity estimates in the same range as the above-cited studies. In particular, the Merrill, Jackson, and Reuter study offers some evidence that the standardization of benefits increases the price sensitivity of health insurance consumers as we expect that it should.(5)

Ideally, in order to establish the effect of managed competition reforms instituted at Stanford, we would compare the price elasticity of Stanford employees before and after the reforms. Only very aggregated historical data is available, however, so such comparisons must be made cautiously. A second possible approach would be to establish a range of price elasticities from nonmanaged competition settings based on previous work and then compare those estimates to the estimates of this paper. Unfortunately, the range of estimates from the previous literature is so wide that this approach is difficult to implement. Most previous price elasticity estimates fall between 0 and -0.20. Some others fall into the -0.20 to -0.60 range. And the Feldman el. al study itself estimates a range from almost zero to about -0.75 depending on the market share of the plan and the share of the plan in its own nest. It is possible to understand to some extent why estimates from one study are higher or lower than the estimates of another, but the wide range of estimates from nonmanaged competition settings in combination with the shortcomings of each of the prior studies suggest that there is no definitively established range of price elasticities in the literature. In all cases, consumers appear at least somewhat sensitive to price, although the lowest estimates would indicate a fairly small effect of price on health plan choice. Nevertheless, the significant effects of premium on health plan choice, despite possibly large transition costs in changing health plans, do indicate that price competition has some hope of success since most of these estimates were obtained from data on choices where standardized benefits were not the norm and where employees often did not pay for their health insurance at the margin. The importance of establishing the price responsiveness of employees under managed competition and the difficulties encountered in other studies due to inadequate data or econometric methods strongly support the need for new work in this area. The current study provides elasticity estimates based on uniquely useful data using a variety of flexible econometric methods.

III. Data

The current study provides estimates of the price elasticity of health plan choice in a setting where benefits are standardized and the employee pays for his or her own plan at the margin. The data are current and, though firm-specific, pertain to an area of the country that has been on the forefront of the managed care movement in health care. Another advantage of this dataset is that for many of the variables a panel is available. Health plan choices, for example, are known for 1993, 1994, and 1995. A supplementary survey of employees in one year also provides data typically unavailable in firm-level studies, such as an indicator of a chronic health condition.

The data used in this paper come from two sources. The first source is the Stanford University benefits office. The benefits data are a panel over three years (1993-95) of data on Stanford University employees and include information on the employees' choice of health plan in each year, the level of coverage (individual, family, employee and spouse, or employee and child(ren)), the cost of each plan to the employee and whether the employee pays premiums with pretax dollars, the age and sex of the employee, the job code, average salary by job code, date of hire, and whether the employee is exempt staff, nonexempt staff, faculty, or a union employee.(6) Due to changes in the plan offerings between 1993 and 1994 most analysis is carried out using the 1994 and 1995 data. The sample includes observations on 6,768 employees in 1993, 6,953 employees in 1994, and 6,512 employees in 1995.(7) 5,616 people appear in the sample in all three years. We refer to the 1994 and 1995 data provided by the University benefits office as the full sample. Means of the data are in Table 1.

The second data source is a survey of a random subset of Stanford employees conducted in 1994 by the authors. The survey collected information on income, education, length of residence in the Bay area, alternative health plan choices available to the spouse, qualitative information on health condition, as well as a variety of subjective measures of what was important to the person in choosing a health plan. Means of some of these variables are presented in Table 2. These supplementary data can be matched to the benefits dataset. We refer to the matched dataset, which includes [TABULAR DATA FOR TABLE 1 OMITTED] a greater number of variables but fewer observations than the full sample, as the survey sample.

Survey data were obtained in the following way. A random subset of 2,447 Stanford employees was chosen for the survey mailing. Because we expected a lower response rate from union employees due to possible language problems (the survey was available only in English) and higher turnover among this group, an additional random subset of 250 union employees were also mailed surveys. People who had not responded within five weeks were sent postcard reminders. People who had not responded within two more weeks were phoned. The final overall response rate was 51 percent for a total of 1,377 responses.(8)

Differential response rates across groups were found in some cases although the differences were generally small and therefore are not expected to exercise any influence on the results. For example, respondents were older on average than nonrespondents. However, because this difference was less than one year it is expected to have little effect on the results. The most serious example of differential response was, as we expected, between union employees and all other employee groups. Staff members, both exempt and nonexempt responded at the highest rate (approximately 58 percent). Faculty responded at a lower rate of 46 percent, leaving them slightly underrepresented in our sample. In contrast, only approximately one-third of union workers responded to the survey. Fortuitously, when the 30 percent of union workers who responded to our supplementary union sample are added to the sample, union workers are almost exactly represented in the sample proportionately to their representation [TABULAR DATA FOR TABLE 2 OMITTED] in the total population. When the supplementary sample is included, union members comprise 9.66 percent of the sample while they represented 10 percent of Stanford employees in 1994.(9) To examine the effect of nonresponse, we first compared the distribution of health plans of respondents to the distribution of health plans of non-respondents. There was no significant difference in the distribution of health plans for respondents as compared to nonrespondents. To investigate possible effects of nonresponse on our price elasticity estimates, we tested for differences in elasticities between the survey sample and the entire population using the full sample and a dummy variable for responding to the survey interacted with premium. The interaction effect is insignificant, leading us to believe that the survey sample adequately represents the full Stanford population.

The price structure of benefits at Stanford and current tax law produces cross-sectional price variation in several dimensions. First, as described in more detail in the next section and in Appendix A, different marginal tax rates produce different net premiums since health insurance premiums may be paid with pretax dollars. Second, the employer contribution to the total premium and thus the employee-paid portion of the premium varies with union/nonunion and full-time/part-time status. Third, in specifications that do not control for family status, premiums will also vary in this dimension. The premium is defined for each individual by the level of family or individual coverage actually chosen. Relative plan premiums do differ for families and individuals. Substantial relative price changes also occurred between 1994 and 1995 providing price variation across time. Prices vary in these data along more dimensions than has been the case in previous work. Because prices vary in several dimensions, we are also able to examine the robustness of our estimates to using only some of these sources of price variation. With our panel data, we are also able to estimate fixed effects models that purge the estimates of any bias due to individual fixed effects using only the variation in relative premiums over time to identify the price effects.

Over the years, the structure of employee benefits at Stanford has been adapted more and more to conform to the managed competition model of Enthoven (1978). For example, since January 1, 1992, all employees except union members choosing single coverage have paid for their own insurance at the margin.(10) The University determines its contribution to health insurance premiums as a percentage of the cost of the lowest cost plan.(11) This amount is called the University's defined contribution and varies by union/nonunion and full-time/part-time status. An employee must pay the full difference in cost between the defined contribution and the premium of the chosen plan. Standardization of benefits by the offered health plans also started in 1992. For example, all four major health plans offer the same or virtually the same hospital and physician visit coverage, emergency out-of-area coverage, prescription drug coverage, and mental health coverage. Copayments of $10/visit are also standard across plans for most services.(12) According to the published plan descriptions, actual coverage differences varied in very few dimensions.(13)

Additionally, since January 1, 1994, no traditional fee-for-service health plan was offered to Stanford employees.(14) For 1994 and 1995 employees were offered the choice of one health maintenance/point-of-service combination plan (POS), two network model health maintenance organizations (NET-1 and NET-2), and one prepaid group practice type HMO (PGP-HMO). The POS plan was new in 1994. The PGP-HMO and NET-1 plans had both been available for more than ten years in 1994. NET-2 had been available for six years. Stanford's point-of-service plan is a health plan that may be thought of as a compromise between an HMO and a traditional fee-for-service plan. The first "tier" of coverage is similar to HMO coverage, limiting the number of physicians available and charging only a small copayment for office visits or hospital stays. Specialists are available within this tier only with referral from a primary care doctor. Under the POS plan, if patients want to visit a doctor within the prescribed network without such a referral, they may do so but they will be reimbursed only after a deductible is met ($750/family) and then only at a rate of 80 percent for most services. This is labeled "tier 2" service. If patients choose to refer themselves to a doctor outside of this prescribed network (tier 3), the deductible is higher ($1,500/family) and the reimbursement rate lower (60 percent). The network HMO's are distinguished from the PGP-HMO primarily by the degree of choice of primary providers that is available. The network HMO's contract with independent group practices in the area while the PGP-HMO is its own group practice and enrollees must see its doctors. The two network HMO's offered by Stanford contract with many of the same local practices, also overlapping considerably with the network available in the first tier of the point-of-service plan. Medical groups available under the three plans are not identical, however, and may have an effect on plan choice.

The structural difference in how care is delivered is the primary difference between Stanford health plans other than price and any unobservable quality differences. The PGP-HMO offers local clinics, all under its own name, to provide patient care. It has offered the lowest premium for all types of coverage in all three years under consideration. Its total premiums are 11-15 percent lower than the average total premiums of the other three plans. For family coverage, the average employee-paid portion of the premium is 35-45 percent lower than the other plans. The network HMO's offer the HMO low copayment, no deductible payment structure but allows the choice of physicians from a wide range of well-established local clinics and private practices. The POS plan offers what is basically a network HMO as its first "tier" with added flexibility to leave the prescribed network of physicians by exercising the "tier two" and "tier three" benefits. The POS plan was roughly equivalent in price to the two network HMO's in 1994 and was more expensive than one and less expensive than the other in 1995. (Average premiums are documented in Table 3.)

Investigation of means and frequencies do reveal some interesting patterns in these data. The full sample indicates that the mean total monthly premium (employer- and employee-paid portions) [TABULAR DATA FOR TABLE 3 OMITTED] declined 6.3 percent from $285 in 1994 to $270 in 1995.(15) The average employee-paid portion of the premium declined from $76 to $68. The reduction in average premiums resulted from decreases in premium price for each plan, although the size of the decrease varied substantially across plans. As can be seen from the fourth column of Table 3, the average employee-paid monthly premium for single coverage for the PGP plan decreased from $18.44 in 1994 to $3.40 in 1995, a decrease of over 80 percent. The plan with the smallest decrease, labeled Network HMO-2 in the Table, decreased its premium for single coverage only 9 percent.

Table 3 shows the distribution of employees among health plans for 1994-95 for employees who chose Stanford coverage. The point-of-service plan enrolled approximately 46 percent of covered employees, the PGP plan about 19 percent, and the two network HMO's together about 35 percent. Table 4 breaks down the distribution of health plan choices for 1994 and 1995 by whether or not the employee was a "new hire" in that year. In both years, proportionately more newly hired employees chose the (newer) point-of-service plan and proportionately few newly hired employees chose either of the network HMO plans.(16) This gives some evidence of possible transition costs in switching health plans since longer tenure employees are overrepresented in the health plans that existed prior to 1994.
Table 4

Health Plan Distribution for "Nonnew" Employees Compared to New


                        "Nonnew" Employees         New Hires
                        Frequency   Percent   Frequency   Percent

Point of service plan     3,052      45.09        119      61.66
Prepaid group plan        1,269      18.75         30      15.54
Network HMO-1             1,593      23.54         30      15.54
Network HMO-2               790      11.67         12       6.22
Catastrophic plan            64       0.95          2       1.04


Point of service plan     2,637      46.06        425      53.93
Prepaid group plan        1,062      18.55        174      22.08
Network HMO-1             1,396      24.38        114      14.47
Network HMO-2               578      10.10         59       7.49
Catastrophic plan            52       0.91         16       2.03

We also see descriptive evidence of some price sensitivity in looking at these tables. As was pointed out above, the employee-paid premium of NET-2 decreased much less than the employee-paid premiums of the other plans between 1994 and 1995. NET-2 also lost 1.8 percentage points of market share, a statistically significant loss. This represents a loss of 20 percent of enrollees relative to a decrease in the total population of 6.5 percent. Confirming this price sensitivity, Table 5 shows the percentage of employees who switched health plans in 1994 and 1995. Between 1993 and 1994, over 30 percent of Stanford employees switched health plans. This was the year that the point-of-service plan was introduced and the traditional fee-for-service (FFS) plan was discontinued and the year that the Benefits Office emphasized the need to choose (actively, not by default) a health plan. The introduction of the new, flexible, and, relative to the old FFS plan, low cost POS plan is probably responsible for the exceptionally large number of switchers between 1993 and 1994. The number of switchers dropped dramatically between 1994 and 1995 to just less then 6 percent. Nonetheless this represents a large number of "switchers" relative to the 3 percent found in a more traditional health care market in Boston in 1984 (Neipp and Zeckhauser 1985). These descriptive data appear to indicate both price sensitivity and the existence of transition costs. The empirical analysis below investigates these issues more fully.
Table 5

Health Plan Switchers(a)

Alternative definitions                1993-94     1994-95

Any switch(b)                            34.1%       5.8%
Switch into or out of the PPG plan        4.3%       1.5%

a. 1993 fee for service (FFS) plan was discontinued in 1994. With
respect to the definition of "switching" plans, then FFS plan is
designated as equivalent to the new 1994 POS plan, the plan deemed
most similar to the unavailable plan.

b. A switcher is anyone included in both the (t - 1) year sample and
the t year sample who is not enrolled in the same plan in both years
or who chooses no Stanford coverage in only one year.

Before turning to the econometric model, a brief summary of the data gathered in the supplementary survey is useful. Table 1 shows that the mean age, tenure and premiums paid are quite similar for the survey sample and the full sample. Table 2 gives means of some of the other important survey variables. The sample is highly educated, as would be expected in a university community, and also has a high level of income. The survey provides some important information unavailable in firm administration data.

This dataset is unique among data of this sort in having information on health status. Twenty-three percent of respondents report that someone covered by their health plan has a chronic medical condition. Chi-squared tests reject the hypothesis that those with and without chronic conditions are equally distributed across health plans, indicating a possible adverse selection problem. Those with a covered person with a chronic condition are more likely to choose the point-of-service plan, the plan with greatest physician choice. This finding conforms to subjective information on what was most important to respondents in choosing their health plan. Workers who insured a person with a chronic condition were significantly more likely than others to cite ability to choose specialists and desire to maintain an existing doctor-patient relationship as "very important" in their choice of health plan. These respondents were significantly less likely to report cost as "very important" to their choice and were not significantly different from the rest of the sample in their value of convenience of doctors' offices, quality of doctors, waiting times, or administrative hassles. The importance of a chronic medical condition in health plan choice as well as possible differences in price elasticities by health status are explored in more detail below.

IV. Logit Models of Plan Choice

A four-alternative model of health plan choice can be represented in the following discrete choice framework:

(1) [y.sub.i1] = [Z.sub.i1][Gamma] + [X.sub.i][[Beta].sub.1] + [[Epsilon].sub.i1]

[y.sub.i2] = [Z.sub.i2][Gamma] + [X.sub.i][[Beta].sub.2] + [[Epsilon].sub.i2]

[y.sub.i3] = [Z.sub.i3][Gamma] + [X.sub.i][[Beta].sub.3] + [[Epsilon].sub.i3]

[y.sub.i4] = [Z.sub.i4][Gamma] + [X.sub.i][[Beta].sub.4] + [[Epsilon].sub.i4]

where [y.sub.ij] is the value of plan j to individual i; [Z.sub.ij] is a vector of variables such as premium that vary across plans (j) and individuals (i); [X.sub.i] is a vector of individual characteristics of individual i such as age that do not vary across plans; and [[Epsilon].sub.ij] is the unobservable error associated with the value of plan j for individual i. An individual i will choose plan j if [y.sub.ij] = max{[y.sub.i1], [y.sub.i2], [y.sub.i3], [y.sub.i4]}. If the errors, [[Epsilon].sub.ij], are independent and identically distributed with a type I extreme-value distribution, we can estimate [Gamma], [[Beta].sub.1], [[Beta].sub.2], [[Beta].sub.3], and [[Beta].sub.4] with the standard conditional multinomial logit (MNL) model. One premium effect, [Gamma], is estimated across plans, while the [Beta] coefficient on individual characteristics differ across plans. Deviations from the standard conditional MNL model are discussed in more detail below.

The measurement of price elasticities of health plan choice requires some explanation. The price elasticity to be measured differs from conventional price elasticities due to the discrete nature of the choice. Employees cannot choose among continuous quantities of health insurance but instead choose among some finite set of possible alternative health plans. The elasticity that we can measure, as is the case in any discrete choice setting is, therefore, the percentage change in the probability of choosing a particular alternative that is associated with a percentage change in price.

Health insurance plan choice is unique even among discrete choice consumer problems, however, in that the price paid by the employee is often not the price received by the insurer. The price of interest is the health insurance premium.(17) However, employers traditionally have paid some or all of an employee's health insurance premium. Studies of health plan choice, including this one, use the price to the employee (the employee-paid portion of the premium) as the relevant price in the discrete choice equations modeling health plan choice. This is certainly the appropriate price variable for this purpose since it is employee choice behavior that we observe and that we want to measure. A question arises, however, about the appropriate price to use when we move to calculating a price elasticity for each health plan. Elasticities are, by definition, defined in terms of a percentage change in price. Using total employee price instead of employee price as the base price produces a much larger price elasticity since the employee-paid premium is often such a small portion of the total premium.

This distinction is important for at least two reasons. First, comparisons across studies must be made on the basis of the same calculation of the price elasticity.(18) Second, policy conclusions must be made on the basis of the price elasticity appropriate to the particular question under consideration. Although the behavior we observe and the price sensitivity we measure will be based on employee-paid premiums, the "insurer-perspective" elasticity may, in many cases, be the policy-relevant measure of interest. For example, in investigating the potential heightened competitive pressures on insurers due to managed competition reforms, we want to know the effect on market share (or the probability of an employee choosing a particular health plan) of an insurer raising its total price by some percentage. Although the difference is trivial in some sense because it is due only to the price base used to calculate the percentage change, the larger measured elasticity based on the total premium should give a more accurate picture of the price competition faced by insurers.

Multinomial logit models of health plan choice yield some interesting results. Table 6 presents results from the survey sample and Table 7 presents results from the full sample. Results from alternative specifications and for all variables are included in Appendix B. These tables present the derivative of the probability of the choice of each health plan with respect to each continuous explanatory variable and the difference in the predicted probabilities evaluated at one and zero for each dummy variable. Standard errors are also reported.(19) Table 8 presents the own price elasticity and its standard error for each health plan for the basic model specifications. The left-most panel of both Tables 6 and 7 presents the derivatives for the point-of-service plan. Successive columns present the results for the PGP HMO, the network HMO-1 and the network HMO-2.(20)

Explanatory variables included in the survey sample logits are taxable family income (in 10,000's), whether the individual insures anyone with a chronic medical condition, sex, the individual's education level, age, the number of years the person has lived in the Bay area, years of job tenure at Stanford, and dummy variables for [TABULAR DATA FOR TABLE 6 OMITTED] [TABULAR DATA FOR TABLE 7 OMITTED] [TABULAR DATA FOR TABLE 8 OMITTED] whether the person was exempt staff, nonexempt staff, or faculty.(21) Models were also estimated that included a dummy variable for whether the person was married or had children. The results with the family dummy included are reported in Appendix B. Premium price was controlled for in two different ways. A net premium variable was constructed to take into account the fact that many Stanford University employees pay the employee portion of their health insurance premium with pretax dollars.(22) based on the categorical income data reported in the survey, a marginal tax rate was estimated for each individual in the survey sample.(23) For those employees who pay premiums with pretax dollars, a net premium variable was constructed based on the assigned marginal tax rate. Estimations were also conducted using the full employee-paid portion of the premium, or gross premium, as the price variable for each individual. The results of the models with gross premium are included in Appendix B. We emphasize the results using net premium since that is the actual price to the employee given the tax structure and the price we expect the employee to base choices on, We make comparisons to the gross premium results in order to shed light on tax effects and because only gross premium is available in the full sample data.(24)

Explanatory variables in the full sample logits include age, years of job tenure, a mean salary of employees in the individual's job code, a dummy variable for sex, and dummy variables for whether the person was exempt staff, nonexempt staff, or faculty.(25) The premium variable for these estimations is the gross employee-paid portion of the premium. For both the results of Tables 6, 7 and 8, data from 1994 and 1995 are pooled.(26) Data for 1993 are not included because the plan offerings changed between 1993 and 1994. We discuss below estimations that take into account the panel structure of these data.

Interest in the effect of having a chronic medical condition on health plan choice centers on the problem of adverse selection. Do some plans serve a less healthy population than others? Do HMO's achieve cost savings relative to other types of plans by attracting a healthier population? These important questions are difficult to answer given standard datasets. The supplemental survey of this study asked respondents whether anyone covered by their health plan suffers from a chronic medical condition. Covering a person with a chronic health condition is found to have a negative and significant effect on the choice of the PGP HMO, reducing the probability of a person's choosing this plan by approximately 4 percentage points (Table 6). This variable has a corresponding positive (although statistically insignificant or, in some cases, marginally significant) effect on the probability of enrolling in the point-of-service plan, the plan with the greatest choice of physician and options for leaving the prescribed network of doctors. On the basis of this evidence, it appears that some selection in favor of the PGP HMO is occurring. This could possibly explain at least some part of the large rate decrease offered by this plan for 1995. We also find a positive and significant effect of age on the probability of enrolling in the point-of-service plan. An increase of ten years of age increases the probability of enrolling in this plan by 5 percentage points (Table 6). A positive effect of age on the probability of the POS plan is also found in the more limited specification estimated on the full sample (Table 7). The PGP-HMO and NET-2 see smaller but usually significant decreases in the probability of enrollment with an increase in a person's age. Because older people have, on average, higher medical costs this too is an indication of some adverse selection in this market.

Income and education also have a positive and significant effect on the probability of enrolling in the point-of-service plan. An increase in income of $10,000 increases the probability of enrolling in this most liberal plan a modest 1-2 percentage points (Table 6). In the full sample results (Table 7) the job salary variable has an even larger effect on the POS plan. Income has a negative and significant effect on the probability of choosing the PGP HMO. This is not surprising since this plan is the lowest priced plan. An increase in education or being faculty or staff rather than a union employee also increases the probability of choosing the POS plan and decreases the probability of choosing the PGP HMO.

Before moving to the estimated price elasticities note that the estimates obtained using the larger set of variables available in the survey sample (Table 6) produce larger price effects (in absolute value) as well as different estimates in some other dimensions as compared to those estimates from either the survey or full sample but using the fewer number of variables from the full sample dataset (Table 7). We believe these differences are caused by omitted variable bias in the estimates obtained using only the administrative data available in the full sample. The administrative data includes no information on health, length of residence in the Bay Area, education, or family income. The omission of any of these variables could be a source of bias. A comparison of the results of Tables 6 and 7 emphasizes the importance of data such as that that we collected in our survey when estimating health plan choice.

The logit results indicate that people are responsive to price in choosing a health plan, although the size of this price effect is sensitive to whether or not we control for having a family (defined as being married or having one or more children) as can be seen in Table 8 and in Table B 1. Rows 1 and 2 of Table 8 present price elasticities by plan estimated on the survey sample and measuring premium as the net premium adjusted for pretax payment. The results in Row 2 are based on a specification that includes the family dummy variable that is omitted in the model used to obtain the results in Row 1. "Employee-perspective" elasticities from models without the family dummy range from -0.449 to -0.760.(27) Differences between these estimates and those using the gross premium (Row 3 and Row 6 of Table 8) are discussed in Section VI below. Estimated elasticities are somewhat smaller when we control for family status.(28) Whether models ought to control for family status is arguable.(29) It is certainly reasonable to think that the family dummy is to a large extent picking up a nonlinear price effect since families are overrepresented in the least expensive plan and underrepresented in the more expensive point-of-service plan and because the price of family coverage is substantially more than individual coverage. For this reason, we emphasize the model without the family dummy as the preferred specification. On the other hand, if workers with families have preferences for a particular plan that differ from the preferences of single employees in unobservable ways that are unrelated to price, then the specification with the family dummy variable should be preferred. Because it seems unlikely that employees buying coverage for two or more people would prefer the more restrictive (in terms of available in-plan doctors, location, and coverage of outside-the-plan physician services) PGP-HMO more than employees covering only themselves for reasons other than price, we prefer the model that does not control for family status.(30)

The larger "insurer-perspective" elasticities for the two models are also presented in Rows 4 and 5 of Table 8. The size of these elasticities, ranging from -2.15 to -3.5 depending on the plan in the preferred model and from - 1.02 to - 1.69 in the model with the family dummy, points to substantial effects in response to a price change from the insurer's perspective. Estimated ("employee-perspective") price elasticities from previous studies using data from more traditional settings ranged from almost 0 to -0.75 but most were in the lowest 20 percent of that range. Our results, with "employee-perspective" elasticities averaging -0.55 in the preferred specification, provide at least some evidence that managed competition produces more price sensitive health insurance consumers. At the very least, we conclude that in this setting, employees are sensitive to price and the price effects are strong enough to be felt by insurers.

We provide further evidence that managed competition reforms have had the intended effect by estimating group logits on aggregate historical health plan data at Stanford. We have eight years of data on two of the current health plans including their market share and employee premium for individuals and families. Group logits using the historical data from a period where employees did not pay for their choices at the margin and where benefits were not standardized, show no significant effect of premium on health plan choice.(31) Although, we use these results cautiously due to the highly aggregated nature of the data, the omission of explanatory variables other than price and coverage level, and the small sample size, we interpret the results using the historical data as consistent with our conclusion that managed competition seems to have increased the effect of price on health plan choice.

We have tested the robustness of these results in a number of ways. Including different sets of explanatory variables, such as quadratics in age and income, the log of income, and many other variables, had no substantial effect on the estimates. A 1994 year dummy interacted with premium was insignificant as was an interaction with whether the employee had been enrolled in the fee-for-service plan that was discontinued in 1994.

We have also explored alternative econometric models. The simple multinomial logit model embeds the independence of irrelevant alternatives (IIA) assumption. The IIA assumption requires that the error associated with each alternative be independent and implies that each alternative is equally substitutable in unobservable dimensions. The only previous study of health plan choice to test this assumption rejected it (Feldman et. al 1989). To test this assumption, we have also estimated full information maximum likelihood nested multinomial logit (NMNL) models of health plan choice. The nested logit model allows some choices to be more similar than others by putting them in the same "nest." Within a "nest" the IIA assumption still holds but the choices within a nest are allowed to be more similar to each other than to the choices outside that nest. For example, nests might be characterized as in Feldman et. al (1989) by the degree of choice of physicians allowed by the plans or the ability to go for care outside a PPO's prescribed network of physicians.

For the nested logits, assume that [Y.sub.ijk] = [Z.sub.Aijk][[Gamma].sub.A] + [Z.sub.Bik][[Gamma].sub.B] + [X.sub.i][[Beta].sub.j] + [[Epsilon].sub.ijk] where i indexes individuals, j indexes the [N.sub.k] plans in each nest k, k indexes the (1, ..., C) health plan nests, and Z is now partitioned into two sets of variables, one of which depends on both the plan and the nest (A) and one of which depends only on the nest (B). In this model the probability of choosing a particular plan j given its nest k and of a particular nest is represented as:

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

and [Mathematical Expression Omitted]. [I.sub.ik] is often labeled the "inclusive value" and represents the maximum expected utility to be derived by individual i from the alternatives in nest k. The parameter, [Sigma] (or 1 - estimated coefficient on the inclusive value) captures the extent to which the alternatives within a nest are similar. If [Sigma] = 0, then the model reduces to the simple MNL model. In our case that would mean that we need not model unobservable similarities between, say, the HMO's as compared to the POS plan.

We test two possible nesting structures for the health plan choices of Stanford employees. In the first, we defined the nest to be the HMO's without the POS option. Outside the nest is the POS plan and inside the nest are the PGP-HMO, NET-1, and NET-2. The first nesting structure is pictured in Figure 1.

The second nesting structure is defined on the basis of the network structure of these plans. Outside the nest is the PGP-HMO and inside the nest are the POS plan, NET-1, and NET-2. The second nesting structure is pictured in Figure 2.

NMNL estimations with both nesting structures were carried out using a sample of single employees and a sample of employees with a spouse or children. Using nesting structure 1 on the family data produces a coefficient on the inclusive value of 0.82 for families (s.e. = 1.20) and 0.86 for singles (s.e. = 0.43). The second nesting structure produces an estimated coefficient of 1.07 for families (s.e. = 0.79) and 2.64 for singles (s.e. = 0.95). In all cases, the hypothesis that the coefficient is 1 cannot be rejected at standard significance levels; therefore we do not reject the simpler MNL model.(32)

Because we might have expected there to be unobservables that are correlated across plans, this result may appear surprising. On the other hand, as discussed above, the health plans at Stanford have been carefully standardized and are certainly much more similar to each other than the alternative plans in the Feldman et. al data where the simple MNL was rejected in favor of a nested model. Standardization may be responsible for the fact that we cannot reject the simple logit specification with these data. Note, however, that the coefficients estimated to test for similarity across alternatives in the NMNL models and used to test the NMNL model against the MNL are estimated very imprecisely. This imprecision is largely responsible for our support of the simple MNL. Therefore, these results should be viewed cautiously.

Because the MNL cannot be rejected in favor of the NMNL, the nested logit results are not reported. It should be noted, however, that results reported above would not be substantially altered were we to use the NMNL estimates instead. In particular, price elasticities are generally in the same range as reported above.

V. Price Elasticities by Group

The conclusion that consumers may be more sensitive to price under managed competition would seem to imply that the costs of switching health plans are not so great as to undermine the other incentives restored by the reforms of managed competition. However, the results of this study do provide some caveats to this optimistic conclusion. The models of Tables 6 and 7 included the number of years as a Stanford employee (years of tenure) as an explanatory variable. After controlling for income and age, tenure is not expected to have an effect on health plan choice in the absence of costs of switching health plans. If there are costs to switching health plans, we would expect to find employees with long tenures overrepresented in those health plans that have been offered by Stanford for the longest period of time. In the presence of switching costs, these long-tenured employees would be less likely to have switched to a new plan while newer employees would have had no such deterrent to choosing one of the newer plans initially (and then sticking with that plan). The two oldest plans offered by Stanford are the PGP-HMO plan and the NET-1 plan. We do in fact see that years of tenure has a positive effect on the probability of choosing the older NET- 1 and, in some specifications, a positive effect on choosing the PGP HMO, Ten additional years of tenure is found to increase the probability of choosing NET-1 by 6 percentage points. In contrast, years of tenure decreases the probability of choosing the point-of-service, the plan most recently introduced. Thus there is some evidence of the existence of costs in switching health plans despite the above-average price elasticities estimated with these data.

Tables 9 and 10 also provide evidence of substantially different price elasticities across groups. These estimates were obtained with logit models that included a premium variable as well as interactions with premium. Separate models were estimated that included an interaction of premium with either age, education, tenure, or the indicator for a chronic medical condition. Table 9 reports results for the survey sample and also includes controls for income, medical condition, education, tenure, sex, age, length of residence in the Bay area and dummy variables for exempt staff, nonexempt staff, and faculty. The premium variable used in these models is the net premium adjusted for pretax payment of premiums. Table 10 reports similar results for the full sample. The premium variable is the gross employee-paid premium. Controls included are sex, age, years of tenure, salary (by job code), and whether the employee is exempt staff, nonexempt staff, or faculty.

The evidence of Tables 9 and 10 suggests that there are striking, although not always statistically significant, differences in the estimated price elasticities by group that go in the direction predicted if there are greater costs in switching health plans for those who are older, sicker, or who have worked at Stanford longer. For example, the estimated price elasticity for the POS plan is almost three times higher (in absolute value) for those without a chronic medical condition than for those with such a condition, although the difference in the probabilities is not statistically significant. The survey sample estimates evaluated at different ages indicate substantially greater (in absolute value) price elasticity for a 30-year-old worker as compared to a 50-year-old worker.(33) The differences in the elasticities at age 30, 40, and, 50 are significant at standard levels. The effect of age on the ("employee-perspective") price elasticity estimated with the full sample is smaller but still corresponds to a statistically significant decrease (in absolute value) with age. Age effects due to increasing transition costs with age might alternatively be interpreted as wealth effects since wealth is generally strongly correlated with age. The coefficient on the age-premium interaction does decrease by about 50 percent when an age-income-premium interaction is included as a wealth-premium proxy, indicating that at least some of the decreased price sensitivity with age may be attributed to a wealth effect. The survey sample results reported in Table 9 also indicate a significant decrease in price sensitivity with tenure at Stanford. When a tenure-squared interaction with premium is also included the magnitude of the decrease diminishes somewhat but a likelihood ratio test cannot reject the simpler specification with only the tenure-premium interaction.

A decrease in price sensitivity with increasing levels of education is also found. This is not the result expected if higher education is associated with lower transition costs. This education effect does not seem to be merely an income effect since an income-premium interaction was insignificant with a t-value of only 0.07. It also does not seem to be purely a wealth effect since the education-premium interaction remains significant and approximately the same size when age-premium and age-income-premium interactions are also included in the model. The decrease in price sensitivity with education also does not disappear when a premium interaction with the faculty indicator is also included. These results might be explained if time costs are an important component of switching costs and time costs rise with education. The results certainly provide no evidence that transition costs are higher for the less educated.
Table 9

Survey Sample: Multinomial Logit Price Elasticities by Group(a),
"Employee-perspective"(b) Own Price Elasticity (Standard Errors in

                                   Model 1: Without Family Dummy
                                          (Table 6 results)

                                 POS     PGP HMO    NET-1     NET-2

No interactions with premium   -0.449    -0.425    -0.555    -0.760
                               (0.118)   (0.112)   (0.146)   (0.200)
Chronic medical condition      -0.167    -0.171    -0.214    -0.299
                               (0.235)   (0.243)   (0.304)   (0.423)
No chronic medical condition   -0.537    -0.499    -0.654    -0.893
                               (0.136)   (0.125)   (0.166)   (0.226)
Age 30                         -0.943    -0.763    -0.101    -0.136
                               (0.229)   (0.181)   (0.240)   (0.325)
Age 40                         -0.588    -0.531    -0.693    -0.949
                               (0.134)   (0.120)   (0.156)   (0.215)
Age 50                         -0.283    -0.287    -0.372    -0.515
                               (0.127)   (0.129)   (0.168)   (0.231)
Education = 12                 -0.979    -0.736    -0.979    -1.483
                               (0.266)   (0.200)   (0.262)   (0.397)
Education = 16                 -0.528    -0.471    -0.616    -0.867
                               (0.128)   (0.115)   (0.149)   (0.210)
Education = 20                 -0.157    -0.165    -0.215    -0.279
                               (0.168)   (0.177)   (0.231)   (0.300)
Tenure = 1                     -0.699    -0.688    -0.973    -1.252
                               (0.165)   (0.161)   (0.228)   (0.293)
Tenure = 5                     -0.591    -0.570    -0.775     -1.028
                               (0.133)   (0.128)   (0.174)   (0.231)
Tenure = 10                    -0.446    -0.418    -0.540    -0.748
                               (0.120)   (0.113)   (0.145)   (0.200)
Tenure = 20                    -0.120    -1.059    -0.121    -0.186
                               (0.210)   (0.186)   (0.212)   (0.326)

                                    Model 2: With Family Dummy
                                        (Table B1 results)

No interactions with premium   -0.214    -0.204    -0.263    -0.362
                               (0.128)   (0.122)   (0.157)   (0.216)
Chronic medical condition      -0.015    -0.016    -0.020    -0.027
                               (0.233)   (0.252)   (0.310)   (0.432)
No chronic medical condition   -0.281    -0.259    -0.339    -0.464
                               (0.147)   (0.135)   (0.178)   (0.243)
Age 30                         -0.611    -0.501    -0.654    -0.879
                               (0.239)   (0.193)   (0.253)   (0.341)
Age 40                         -0.332    -0.302    -0.391    -0.536
                               (0.145)   (0.131)   (0.169)   (0.233)
Age 50                         -0.093    -0.096    -0.123    -0.170
                               (0.134)   (0.137)   (0.176)   (0.244)
Education = 12                 -0.663    -0.509    -0.665    -1.012
                               (0.272)   (0.208)   (0.269)   (0.411)
Education = 16                 -0.281    -0.254    -0.328    -0.463
                               (0.138)   (0.124)   (0.160)   (0.227)
Education = 20                  0.034     0.036    -0.046     0.060
                               (0.175)   (0.184)   (0.238)   (0.310)
Tenure = 1                     -0.435    -0.430    -0.602    -0.776
                               (0.175)   (0.173)   (0.242)   (0.312)
Tenure = 5                     -0.342    -0.332    -0.447    -0.595
                               (0.144)   (0.139)   (0.187)   (0.249)
Tenure = 10                    -0.219    -0.207    -0.264    -0.368
                               (0.129)   (0.122)   (0.156)   (0.217)
Tenure = 20                     0.057     0.052     0.058     0.090
                               (0.213)   (0.192)   (0.216)   (0.333)

a. Based on separate models that include an interaction of premium
with either age, education, tenure or the indicator for a chronic
medical condition. Variables other than the interaction variable are
evaluated at the mean.

b. Uses net employee-paid premium as the base price.

The differences in price elasticities by age, years of tenure, and chronic medical condition are consistent with the hypothesis that there exist costs to switching health plans that increase with either length or intensity of the doctor-patient relationship.(34) Legislative forms of health care reform are not likely to influence this aspect of health care choice. Although the implementation of managed competition or other structural changes in health insurance may foster a market and thus increase the [TABULAR DATA FOR TABLE 10 OMITTED] price sensitivity of consumers, there is apt to remain some underlying persistence in choices by consumers in this market. Our evidence indicates that the degree of persistence is likely to vary across demographic groups and by health status. When prices are changing, this persistence is likely to exacerbate adverse selection problems since younger and healthier employees are more price sensitive. On the other hand, the lower price sensitivity of the more educated and perhaps the wealthier, may mitigate the selection problem somewhat since education and wealth are generally positively correlated with health status.

VI. Tax Policy and Price Elasticities

Another important aspect of the health care market is the tax treatment of benefits and premium payment. Since the income tax was instituted in 1913, employer contributions to health insurance have been excluded from taxable income. Beginning in 1978 employees were permitted to make their own contribution to health insurance premiums with pretax dollars if the employer set up what has come to be known as a "cafeteria plan."(35) The effects of preferential tax treatment on the health insurance market has not gone unnoticed by observers, and proposals for reform in this dimension have also been set out (Enthoven 1984, Taylor and Wilensky 1983). Tax preferences for employer-provided fringe benefits such as health insurance provide strong incentives for provision, and perhaps over-provision, of these benefits. Pretax payment of premiums by employees dampens the sensitivity of consumers to changes in premiums since the price paid in terms of consumer goods foregone is only premium(*) (1 - t) where t is the marginal tax rate. Theoretically, the current tax structure exacerbates the lack of sensitivity to price by consumers that managed competition and other reform proposals hope to correct.

Although these data do not provide an ideal way of investigating the effect of tax preferences on price elasticities, we do try to shed some light on the effect of preferential tax treatment of employee-paid health insurance premiums on the price sensitivity of consumers. First and most simply, using the price elasticities estimated above with net premiums as an explanatory variable, we contrast the size of the response of a 1 percent increase in the (post tax) premium in the scenario where employees pay with pretax dollars to the case where employees face the full marginal cost of that increase. Using the results of Table 8 Row 1, a 1 percent increase in the premium paid by employees will produce an estimated 0.45 percent decline in the probability of choosing the point-of-service plan. If the employee is in the 15 percent tax bracket, he or she will feel only 85 percent of this increase and the resulting decline in the probability of choosing this plan will be only -0.38 percent. If the employee is in the 28 percent or 38 percent bracket, the percentage decrease in the probability is only -0.32 percent and -0.28 percent, respectively.

When the gross employee portion of the premium is entered as the price variable in the logit model, we find an estimated price elasticity relative to the net premium elasticity in exactly the range that marginal tax rates would suggest. The results in Row 3 of Table 8 are comparable to those in Row I except that the gross employee portion of the premium is entered as an explanatory variable rather than the estimated net premium. The price elasticity estimated with gross premium is approximately 80 percent of the elasticity estimated with net premium as the explanatory variable. Employees look substantially less price elastic if we look at the gross rather than the net premium, as would be expected if they take into account the tax preference.

VII. Fixed Effect Logit Models

All of the above results were obtained from multinomial logit and nested multinomial logit models that assume that the errors in the equations of Equations 1 are uncorrelated with the explanatory variables. If there exist unobservable individual-specific tastes for health plans that are correlated with the explanatory variables, estimates obtained from models that ignore these individual-specific unobservables will be biased. For example, there are almost certainly dimensions of health status that are not captured by our chronic medical condition variable. Poor health may make an employee more likely to choose the more expensive plans that offer greater choice among physicians. Poor health may also be associated with part-time employment or lower income, both of which are associated with larger relative net premium differences. Omitting indicators for poor health could therefore produce upwardly biased price coefficients and price elasticities too small in absolute value. Under certain conditions, the panel structure of the data allows us to solve this problem and obtain unbiased estimates of the coefficients on the variables that change over time.

For example, suppose the set of Equations 1 should, in fact, be written:

(2) [y.sub.it1] = [[Alpha].sub.i1] + [Z.sub.it1][Gamma] + [] [[Beta].sub.1] + [[Epsilon].sub.it1]

[y.sub.it2] = [[Alpha].sub.i2] + [Z.sub.it2][Gamma] + [] [[Beta].sub.2] + [[Epsilon].sub.it2]

[y.sub.it3] = [[Alpha].sub.i3] + [Z.sub.it3][Gamma] + [] [[Beta].sub.3] + [[Epsilon].sub.it3]

[y.sub.it4] = [[Alpha].sub.i4] + [Z.sub.it4][Gamma] + [] [[Beta].sub.4] + [[Epsilon].sub.it4]

where y, Z, X and [Epsilon] are as above but are now subscripted by time period, t. In this specification [[Alpha].sub.ij] represents an unobservable individual-specific fixed effect for individual i that affects the value of alternative j. Unless the number of time periods grows infinitely large, it is impossible to treat the [Alpha]'s as estimable fixed effects. With short panels estimated [Alpha]'s will be inconsistent and, in nonlinear models, the inconsistency of the [Alpha]'s implies inconsistency in the estimates of the other parameters as well. This problem is solved if the fixed effect [Alpha]'s can be conditioned out.

In general it is difficult or impossible to condition out the fixed effects in nonlinear models. However, as Chamberlain (1980) shows, the logit model is an exception to this general rule. The particular structure of the logit model makes it possible to find a sufficient statistic for [Alpha]. After conditioning on this sufficient statistic the problem no longer depends on the unobserved [Alpha]'s and the transformed model still has a logit structure, making it tractable.

The basic intuition underlying the fixed effects (FE) logit model arises from the observation that the fixed [Alpha]'s determine the time-constant dimension of observed choices while the time variation in the X and Z variables determines the particular time sequence of choices and identifies [Beta] and [Gamma]. Following Boersch-Supan and Pollakowski (1990), define [] = j if [y.sub.itj] = max{[y.sub.it1], [y.sub.it2], [y.sub.it3], [y.sub.it4]}. Let [s.sub.ij] = [summation over t = 1, ..., T] [[Delta].sub.itj] where [[Delta].sub.itj] = 1 if [] = j, [[Delta].sub.itj] = 0 otherwise. Then [s.sub.ij] is a sufficient statistic for [[Alpha].sub.ij]. This is seen most readily by considering the case of an individual who makes the same choice in every period t = 1, ..., T. In this case, observing that [s.sub.ij] = T for choice j and that [s.sub.ik] = 0 for all other choices, implies that we can let [[Alpha].sub.ij] = [infinity] and [[Alpha].sub.ik] = [infinity] [for every] k [not equal to] j, thereby producing [P.sub.ij] = 1 and [P.sub.ik] = 0 [for every] k [not equal to] j where [P.sub.ik] equals the probability that individual i will choose alternative k. Therefore, when fixed effects are included, we can learn about [Gamma] and [Beta] only from individuals who change alternatives over time. Conditioning on [s.sub.i], the vector of ([s.sub.i1], ..., [s.sub.ij]) where J is the number of alternatives, we can write the probability of a particular sequence of choices in a multinomial logit structure that does not depend on [Alpha]. Using data only for the individuals who change choices over time, we can estimate a logit model of choices among sequences for a given [s.sub.i], where [Gamma] is identified by changes in Z over time. If there is sufficient variation in [] over time, we can also identify [Beta]. Boersch-Supan and Pollakowski (1990) give a detailed description of exactly how to implement such a model using standard logit estimation techniques but redefining the choices, choice sets, and explanatory variables appropriately.

Individual predicted probabilities cannot be calculated with the estimates obtained from FE logit estimation since estimates of [[Alpha].sub.i] would be necessary to calculate [P.sub.i]. The parameters of variables that do not vary over time are also not identified in this model. Assuming the [[Alpha].sub.ij]'s are fixed over time, however, the FE logit model produces consistent estimates of [Gamma]. These estimates can then be used to calculate aggregate elasticities with respect to variables in Z.

Table 11 presents some descriptive statistics that illustrate the type of comparisons made more formally in the FE logit model. The first column reports all the possible sequences of plans that involve a switch between plans that could have occurred in 1994 and 1995. Column 2 reports the percentage of switchers who chose each sequence. Column 3 reports whether the premium of the plan chosen in 1994 increased or decreased in 1995 relative to the premium of the plan chosen in 1995. As is clear from the table, significantly more switches went in the direction of a relative decrease in premium.

Allowing for the possibility of fixed effects in our model as in Equation 2 by [TABULAR DATA FOR TABLE 11 OMITTED] estimating the FE logit does change the estimated own price elasticity. Note that the FE method will difference out any unobservables that are constant over time, thus mitigating the problems associated with using the full sample and its more limited set of control variables as compared to the survey sample. The price coefficient (and corresponding price elasticity) is the only parameter identified in the FE model since the other explanatory variables do not vary, or vary very little, over time. Using the full sample to maximize the available observations on employees who switched plans (N = 178), the FE model again produces a significant and negative premium effect (t-statistic = -3.38). The estimated premium effect translates into an "employee-perspective" price elasticity of -1.025 for the point-of-service plan, -0.966 for the PGP HMO, and - 1.318 and - 1.753 for Net- 1 and Net-2, respectively. These elasticities are higher in absolute value than the corresponding elasticity estimated from the full sample when fixed effects were ignored.(36) From the "insurer-perspective" this translates to a range of elasticities from -3.706 to -6.175. A Hausman specification test of the simple logit model that ignores possible fixed effects and other correlation across individuals over time versus the FE logit, based on the two estimated premium coefficients and their variances, rejects the simple logit at a significance level of 0.01.

Note that the price variation used to obtain these FE estimates is the price change from 1994 to 1995. The FE elasticities therefore might more generally be interpreted as year effects and could be attributed to unmeasured yearly changes other than price. However, the local setting provides a strong justification in this case for interpreting the year effect as a true price effect since so much is known about each plan over these two years. Because we know that there were no major changes in coverage and no major market shocks, we feel quite confident in ascribing the fixed effect shifts in plan choice to the price changes that occurred between 1994 and 1995.

The results from the fixed effect model strengthen the conclusions already put forward. The price elasticities estimated in the FE model are considerably larger in absolute value than estimates from previous studies and provide further evidence that substantial price competition exists in this market.

VIII. Conclusion

This study has used a unique dataset to explore the choice of health plans and premium sensitivity of workers in a setting where many of the structural changes proposed by the managed competition model of health care reform have already been implemented. We provide suggestive evidence that managed competition does increase the price responsiveness of health insurance consumers. All of our estimated price elasticities are higher on average than most of the others that have been calculated in the literature, and our preferred fixed effects estimates are substantially higher than previous estimates. The estimated elasticities are also large in absolute value. From the "insurer-perspective" (using the total premium rather than employee-paid premium as the base price for calculating percentage price increases), elasticities range from -1.0 to -1.8 in full sample simple logit estimations or from -3.7 to -6.2 in the preferred fixed effects model. The magnitude of these elasticities certainly suggests that insurers will experience price competition, competition that may have produced the premium decreases for all plans observed between 1994 and 1995 and for two of the plans between 1995 and 1996.

We also find evidence that price elasticities are lower in absolute value for older workers, employees with longer job tenure, and enrollees who insure a family member with a chronic medical condition. We interpret this as evidence of higher transition costs in switching health plans for those who are sick or who may have longer established doctor-patient relationships. This interpretation is not distinguishable, however, from the "creaming hypothesis" that has also been put forward in the literature. In fact, the existence of transition costs for these groups provide added incentives for creaming and lower price sensitivity for older or less healthy workers may exacerbate adverse selection in this market. We provide some evidence of favorable selection for the PGP-HMO. Such selection may well increase in a market where prices are changing and better risks are more price sensitive. These adverse effects may be mitigated somewhat by the apparent lesser price sensitivity of the more highly educated.

We also find that preferential tax treatment through pretax payment of health insurance premiums seems to reduce the price sensitivity of employees to increases in premiums. Tax reform is therefore another important area to focus on in the process of health care reform. By taxing premiums in excess of the lowest cost plan, price sensitivity may be increased even while maintaining the current tax incentives for health insurance purchase if desired.

Our results are subject to the caution that single firm data may not be representative of national health insurance experiences, and that a university community is unrepresentative in some very particular ways. Also, we are unable to address questions about the unmeasured quality of these plans and the effect price competition may have on this dimension of the health insurance market. However, California has long been considered a bellweather in the health care arena and its changes and reforms are being replicated in other states. We interpret out data, not as currently nationally representative, but as a window on what might become representative if managed competition reforms were more widely adopted.


Assigning a Marginal Income Tax Rate

A marginal tax rate was computed for each individual in the survey sample based on the person's reported income, person's reported marital status, and data published in the Internal Revenue Service publication Individual Income Tax Returns, 1991, the most recent version of this publication available.

The first step in assigning the marginal tax rate was the conversion of the categorical income data obtained by the survey to income estimates. Column 2 of Table A1 indicates the income level assigned to each bracket. For the majority of the brackets, the midpoint was used.

The second step used the actual tax parameters of the 1993 Federal Income Tax Rate Schedules. A person's standard deduction was determined by the following formula:

Standard Deduction = $3,700 + ($2,500 * Married)

where "Married" equals I if the survey respondent indicated that he or she was married, and equals 0 otherwise. Similarly, a person's income exemption was determined by the following formula:

Exemption = $2,350 + ($2,350 * Married) + ($2,350 * Number of Children)

where "Number of Children" is the number of children each respondent reported that could be covered under a Stanford health plan.

The next step of the assignment of a marginal tax rate used the data from Individual Income Tax Returns, 1991. This publication reports, by income level, the number of persons in the United States that take the standard deduction and the number that itemize their deductions. In addition, it reports the average amount of the itemized deduction by income level. The income brackets used by this publication did not correspond exactly to the income brackets on the survey, so this information had to be interpolated. Details of this interpolation will be provided upon request. These estimates are listed in Columns 3 and 4 of Table A1.

Since the data on average deductions is from 1991, and the income data is from 1993, the estimates in Column 4 were then adjusted to 1993 dollars using the Consumer Price Index. This amounted to inflating them by a factor of 1.061.

Total expected deductions were then calculated for each individual by the following formula:

Total Expected Deductions = Probability of Itemizing * Average Itemization

+ Probability of Standard Deduction * Standard Deduction

+ Exemption

where the relevant probabilities and the average itemization used were determined by the individual's income bracket, and the standard deduction and exemption used were determined as described above.

Each individual's estimated net income was then defined as the person's assigned income (Column 2 in Table A) minus total expected deductions.

The final step was to use this estimated net income for each individual and assign the appropriate marginal tax rate from the 1993 Federal Income Tax Rate Schedules, which again was dependent on whether or not the individual was married. The assigned marginal tax rates were then used to convert employee-paid premiums to net employee-paid premiums to reflect the pretax payment of premiums for employees who are eligible for and elect that option.




1. The high option plan was defined as the one with the higher premium.

2. Feldman and Dowd (1993) also provide a followup to this study based on aggregate data on employees of the state of Minnesota and the University of Minnesota. They use parameter estimates from the 1989 study to predict enrollment changes. The follow-up study finds that the relatively large (in absolute value) elasticities estimated in the original study describe the later data relatively well.

3. Revised estimates obtained from communication with the authors.

4. A more recent study by Buchmueller and Feldstein (1995) addresses related issues but does not actually estimate health plan choice. Buchmueller and Feldstein estimate the probability that an individual will switch health plans in response to price increases. They find price to be an important factor in the decision to switch health plans but their "switcher model" forces them to define premium changes relative to the plan they define to be the individual's "next best option." They find a $10 increase in an individual's previous year plan is associated with a 25 percent probability of switching plans. This is conceptually different from the price elasticities reported in this paper and should be interpreted as the effect of a change in each person's previous year plan premium on the sum of the joint probabilities of all possible combinations of previous and current year plans that involve a switch. Estimating a full model of plan choice allows the estimation of price effects and price elasticities for a particular plan given all other available plans and their premiums.

5. Merrill, Jackson, and Reuter estimate two logit models of plan choice, one on a dataset of state employees in Tallahassee, Florida and one on a dataset of state employees in Salt Lake City, Utah. In Salt Lake City, the choice was between an IPA-type HMO and a FFS plan and the benefits offered in the two plans were very similar. In Tallahassee, the choice was between a PGP-type HMO and a FFS plan and the benefits coverage between the two plans was substantially different. As we would expect, premium price matters much more in Salt Lake City than in Tallahassee though other predictors were much less significant in Salt Lake City where the choices were very similar.

6. Exempt staff are those staff exempt from overtime laws. Non-exempt staff are wage employees subject to overtime laws.

7. The sample excludes Stanford hospital employees and employees of the Stanford Linear Accelerator. Employees who were "out-of-area" in a particular year are excluded. Also, the 1993 sample excludes employees who were at Stanford in 1993 but left before 1994.

8. This response rate is very similar to the 47.8 percent response rate observed in the survey conducted by Feldman et. al. (1989).

9. There remains, of course, the problem of whether the one-third of union employees who did respond are representative of the total population of union members. We have only a few variables with which to compare observable characteristics of the two groups. Like employees as a whole, union respondents were somewhat older than nonrespondents. The distribution of health plans was not significantly different for respondents and nonrespondents.

10. Union employees have voted to maintain a different payment schedule that includes a full University contribution for single employees regardless of which plan is chosen.

11. The set of plans considered in determining the lowest cost plan excludes the catastrophic plan described below.

12. Since 1994, Stanford has also offered a "catastrophic" health plan with much higher deductibles and lower premiums. Most of this paper excludes this plan from consideration since it enrolled less than 1 percent of employees in both 1994 and 1995 and because attempts to include it as a fifth choice in the estimations were unsuccessful due to the small number of people choosing that option.

13. The point of service plan offers chiropractic services while the others do not. That plan also has no copayments for well-baby care. The two network HMO's plans offer "Health Improvement Plan" assessment exams for only a copayment while the others charge a larger fee. Infertility treatment coverage varies somewhat across plans but is available at some level in each plan. Otherwise, coverage is virtually identical across plans.

14. Due to changes in the benefits structure for the upcoming year, during the November 1993 open enrollment (when choices were being made for 1994) the Benefits Office conducted a major educational campaign about the choices available. Defaults to the previous year's choices were not allowed for 1994 as is usually the case since the available plans were being changed. The point-of-service plan is the most similar to the discontinued fee-for-service plan. The fee-for-service plan enrolled 20 percent of employees in 1993.

15. Benefits office staff who negotiated with insurers attribute the decrease to the pressure on all plans exerted by decreases in premiums by the lowest cost plan. This pressure results from the fact that the University defined contribution is based on the price of the lowest cost plan.

16. A chi-squared test rejects the null hypothesis that no differences in the distribution of health plan choices exists across new hires and employees with tenure greater than one year.

17. Copayments, coinsurance, deductibles, etc. are here defined to be characteristics of a plan, not dimensions of price. The price of the plan in this study as in almost all previous work is defined in terms of the plan's premium. Since copayments and deductibles are almost completely standard across plans in this case, price is adequately defined by premium.

18. Most of the literature on health plan choice (and all of the studies that we review most thoroughly above) reports what we label the "employee-perspective" elasticity; that is, the elasticity using the employee-paid premium as the price base. Some other studies (see, for example, Dowd and Feldman 1994/95) report what we label the "insurer-perspective" elasticity or the elasticity using the total premium (employer- and employee-paid portions) as the price base. Cutler and Reber (1996) report both.

19. Standard errors are calculated by first using the linearization employed in the TSP Statistical package for the nonlinear functions and then calculating variances based on these approximations.

20. The probability derivatives and differences in Tables 6 and 7 and the elasticities reported in Table 8 are evaluated at the sample means for each variable. Because the probabilities and elasticities are a nonlinear function of the estimates, these estimates evaluated at the sample means will be a consistent estimate for a person with mean characteristics but not of the mean effect in the population. However, we have also calculated the mean estimated derivatives and the estimated elasticity over all individuals in the sample which is a consistent estimate of the population mean. The estimates are very similar to those reported in Tables 6, 7 and 8. For example, the mean own price derivatives for the model without the family dummy are -0.0059, -0.0039, -0.0048, and -0.0025 for POS, PGP, Net-1, and Net-2, respectively. Previous work is divided in its use of elasticities evaluated at sample means or mean elasticities. ln any case, our results are similar using the two different methods.

21. To make the survey questionnaire easier and faster to answer and thereby to encourage survey participation, most questions requested only categorical responses. For example, possible answers to the question "What is the highest level of education that you completed?" were "did not complete high school," "graduated high school," "some college," "graduated college," "continued study beyond college degree," and "completed advanced degree." Categorical answers were also obtained for household income and number of years in the Bay area. Logit models have been estimated with dummy variables for each category. However, the results presented use continuous variables created by assigning the midpoint or model value for the category as the value of the variable. The results are qualitatively the same as using the dummy variable data. The results for the assigned continuous variables are presented because the nature of the four choice discrete choice model makes the presentation of results cumbersome even without having such a multitude of dummy variables in each specification.

22. Some employees such as employees on leave are not eligible for pretax payment of premiums. Also, different benefit structures exist for union and nonunion employees. Nonunion employees who are eligible for the program automatically pay premiums with pretax dollars while union employees must choose to pay in this way. This option is well-advertised to union employees and yet many still do not take advantage of it. Possible reasons cited by administrators for this choice include the reduction of social security eligible wages.

23. Details of the assignment of marginal tax rates are found in Appendix A.

24. Short and Taylor (1989) also use net premium. Feldman et. al use gross premium but few employees were offered tax advantages for employee contributions to health insurance in 1984 so gross premium is essentially equivalent to net premium. Cutler and Reber (1996) use net premium.

25. Job codes are reasonably disaggregated. There are 511 different job codes represented in the sample. The mean number of individuals per job code is approximately 13 and the maximum is 531.

26. The survey was conducted between the November 1993 and November 1994 open enrollment periods when health plan choices for 1994 and 1995 were made. In order to pool the data from 1994 and 1995 we assume that the relevant survey data was constant over this year. For some variables such as education, this seems a reasonable assumption. In the case of number of years in the Bay Area, we increment the variable by I in 1995. Because of the nature of a chronic medical condition, this is unlikely to be misspecified in the 1995 data for those people who answered "yes" to this question prior to this time. We will not pick up, however, people who developed a chronic condition between the survey and the next open enrollment.

27. The "employee-perspective" elasticity uses the employee-paid portion of the premium, while the "insurer-perspective" elasticity uses the total premium, as the base price in calculating the percentage change in price.

28. Likelihood ratio tests do not reject this model relative to a model that estimates singles and families separately. The price effect is also very similar to that reported here when the model is estimated separately for the two groups.

29. Some previous studies have controlled for family status while others have not.

30. Interestingly, the price effects are not significant, although they are of roughly the same magnitude, when the model is estimated on the sample of single employees only. This is particularly interesting since it is some single employees who do not pay for their own insurance at the margin. In this group, there is no price variation across plans for some single employees. The somewhat smaller and insignificant price effects may therefore reflect this payment structure. Employees with the "reformed" payment structure where more expensive plans are not subsidized by the University show greater price sensitivity, as expected. The presence of this group of single employees who do not pay for their choice at the margin could also be depressing the price elasticity in the model that controls for family status relative to the model that does not.

31. The premium coefficient has a t-statistic of only -0.105.

32. In two cases the point estimates of these coefficients are outside the (0,1) range that is consistent with a random utility model as presented in Equation I above. However, in no case can we reject the hypothesis that the coefficient is one.

33. A likelihood ratio test cannot reject that an additional interaction of age-squared with premium is equal to zero.

34. The hypothesis that these differences are due to differences in transition costs by group is indistinguishable from the "creaming hypothesis" that health plans will try to select the beneficiaries with the best health risks in their marketing campaigns. In fact, the two are likely to occur simultaneously since the existence of transition costs in these dimensions increases incentives for creaming.

35. The tax exclusion for employer-paid noncash fringe benefits was made explicit by Congress in 1954 in Section 106 of the Internal Revenue Code but a "de facto" exclusion existed prior to that time. The option of an employer setting up a "cafeteria plan" where employees could choose among a variety of non-taxable fringe benefits including the election of paying medical expenses or health insurance premiums with pretax dollars was established by Congress in Internal Revenue Code Section 125 in 1978. See Congressional Budget Office (1994) for more details.

36. Fixed effect estimates were also obtained limiting the sample to those employees who did not change from family to single or single to family coverage between years. The results were virtually identical.


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Anne Beeson Royalty is an assistant professor of economics at Stanford University. Neil Solomon participated in the survey research while he was a Robert Wood Johnson clinical scholar in the Department of Medicine at Stanford University. He is now a Utilization Specialist at Permanente Interregional Consultants, Kaiser Permanente. The authors thank Laurence Baker, Alain Enthove, Anjini Kochar, Tom MaCurdy, Julie Schaffner, Sara Singer, Joanne Spetz, workshop participants at Yale and the Public Policy Institute of California, and two anonymous referees for useful comments on previous drafts of the paper. They also gratefully acknowledge the cooperation of Jim Franklin, Karin Taber, and Elise Watzka of the Stanford Office of Total Compensation in providing data for this paper, the excellent research assistance of Marc Spear, and financial support from the Center for Economic Policy Research at Stanford and the Kaiser Family Foundation. The data for this article are available from Anne Beeson Royalty, Department of Economics, Stanford University, Stanford, CA 94305-6072, <> from May 1999 through April 2002.
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Title Annotation:includes appendix
Author:Royalty, Anne Beeson; Solomon, Neil
Publication:Journal of Human Resources
Date:Jan 1, 1999
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