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We examine HMO participation and enrollment in the Medicare risk market for the years 1990 to 1995. We develop a profit-maximization model of HMO behavior, which explicitly considers potential linkages between an HMO's production decision in the commercial enrollee market and its participation and production decisions in the Medicare risk market. Our results suggest that the payment rate is a primary determinant of HMO participation, while the price of a supplemental Medicare insurance policy positively affects HMO Medicare enrollment. We also find empirical support for the existence of complementarities in the joint production of an HMO's commercial and Medicare products. (JEL I1, L1)


Medicare is the federal entitlement program that provides comprehensive health insurance coverage to individuals age 65 and older and to certain disabled people. In 1996, total Medicare expenditures reached $197 billion (U.S. Department of Health and Human Services [1998]). With the passage of the Balanced Budget Act of 1997, reforms are being implemented to address the program's financial condition and to expand beneficiary coverage options with the creation of Medicare Part C, otherwise known as Medicare + Choice.

Under Medicare + Choice, several types of coordinated care plans are eligible to contract with the Health Care Financing Administration (HCFA) to provide coverage to Medicare beneficiaries. [1] This expands and modifies the Medicare health maintenance organization (HMO) risk-contracting program formally begun in 1985. Under this program, an HMO entering into a risk contract receives a fixed monthly payment equal to 95% of an actuarial measure of the average cost of providing care to a beneficiary in the traditional Medicare program adjusted for geographic and demographic differences. This is called the Adjusted Average Per Capita Cost (AAPCC). In return, the HMO is responsible for providing all covered services and takes full financial responsibility for the actual costs generated. [2]

In addition to expanding the types of organizations eligible to enter contracts, Medicare + Choice also differs from the preceding program with respect to the payment methodology. Though organizations participating in Medicare + Choice still receive a fixed monthly payment to provide coverage for Medicare beneficiaries and bear the financial risk associated with the costs of providing care, a different methodology has been adopted for calculating this payment. Under Medicare + Choice, an organization's payment is based on the largest of three rates, which include a minimum payment amount (which for 1998 is $367 per month), a blended rate comprised of an area-specific rate and an input-price adjusted national rate, and a payment rate equal to the 1997 AAPCC rate adjusted by an annual, minimum percentage increase (Health Care Financing Administration [1998]).

There has been considerable growth in recent years in both the number of HMOs offering Medicare products and HMO Medicare beneficiary enrollment. HMO participation in the Medicare risk market for the years 1990 to 1995 is summarized in Table I. [3] During this period, the number of HMOs participating in Medicare risk contracting nearly doubled, from 66 to 114. As HCFA makes the transition into Medicare + Choice, effective implementation depends on participation by coordinated care organizations, enrollment by beneficiaries, and a payment methodology that yields savings to Medicare that would not be realized under the traditional program.

The purpose of this article is to directly examine two of these implementation issues: the decision by organizations to participate in the Medicare market and the factors that influence beneficiary enrollment in these organizations. Given the infancy of the Medicare + Choice program, we focus our analysis on HMO participation and enrollment decision-making as a way to identify insights that may apply more broadly to contracting organizations under this new program.

Two studies have examined HMO entry into the Medicare market. Adamache and Rossiter [1986] examine the determinants of HMO participation in the National Medicare Competition demonstration, modeling this decision as a function of an HMO's organizational, market, and performance characteristics, and then estimating a binary probit model. [4] Their results suggest that the AAPCC rate, federal qualification by an HMO, and prior experience with Medicare beneficiaries positively affect an HMO's probability of participation. Porell and Wallack [1990] model the problem similarly, using a different market definition and data set. The authors' findings confirm previous results, with additional results suggesting that stronger utilization controls and favorable financial performance by an HMO also increase the probability of entry into the Medicare market. However, both of these studies fail to directly address HMO production in the commercial enrollee market and how this may affect a firm's decision regarding Medicare , given the potential for important cost or demand linkages between these products. Furthermore, they also fail to consider the impact of what has become an important part of conventional Medicare--the price of supplemental Medicare insurance.

In this article, we develop a model of HMO behavior that explicitly considers the linkage between an HMO's production in the commercial enrollee (private) market and its decision to participate and produce in the Medicare market. We estimate the model using data from 1990 to 1995, which reflects a time period of significant growth and change in the HMO industry. The remainder of this article is divided into the following sections: Section II presents the theoretical model; a discussion of the data and measures is contained in Section III; Section IV outlines the econometric estimation strategy; Section V reports the results and provides a discussion of the findings; and Section VI identifies potential policy implications and contains concluding remarks.


In this section, we develop a profit-maximization model of HMO behavior. The primary objective for doing so is to examine how the Medicare price (the AAPCC payment rate), the price of substitutes for an HMO Medicare product (specifically the price of a supplemental Medicare insurance policy), and a firm's production in its private market influence its decision-making with respect to the Medicare market.

We employ the following set of assumptions. First, we consider the populations demanding each of these products to be separate, since only Medicare beneficiaries are eligible to enroll in a Medicare product, while most private enrollees are labor force participants and their families. Second, we assume that the products are distinguishable from one another by the fact that coverage under the traditional Medicare program and, therefore, HMO Medicare products, is typically broader than that required for private products produced by federally qualified HMOs (Zarabozo and LeMasurier [1996]). Third, we assume that all HMOs produce a positive quantity of the private product. Finally, we allow for the possibility of demand complementarities for a firm's private and Medicare products.

Private Demand

Let an HMO face a separate demand function for each of its products and let its demand function for the private product be specified as the following:

(1) [Q.sub.p] = [[theta].sub.0] - [[theta].sub.1][P.sub.p] + [[theta].sub.2][X.sub.p] + [[theta].sub.3][Q.sub.m], [[theta].sub.i] [geq] 0 [for all]i,

where the private quantity ([Q.sub.p]) depends on the price charged for the private product ([P.sub.p]), a set of exogenous factors that shift demand for the private product ([X.sub.p]), and the firm's Medicare enrollment ([Q.sub.m]). [5] This last factor captures potential complementarities in demand between the Medicare and private products.

Medicare Demand

We specify the "potential" market demand for an HMO's Medicare product to be some function of the demographic composition of the Medicare population, a set of exogenous factors that shift HMO Medicare market demand, and private enrollment. Individual firm demand is some proportion of this "potential" or residual market demand ([Q.sub.mR]), such that:

(2) [Q.sub.m] [leq] [Q.sub.mR].

We specify individual firm demand as the following:

(3) [Q.sub.m] = [m.sub.1]z + [m.sub.2][X.sub.m] + [m.sub.3][Q.sub.p],

where z represents the quality level of the Medicare product chosen by the firm, [X.sub.m] is a vector of exogenous factors that shift HMO Medicare market demand (such as the price of supplemental Medicare insurance), and [Q.sub.p] is a firm's private enrollment. [6] Including [Q.sub.p] here captures potential demand complementarities. One example is reputation, whereby an HMO with a large private enrollment may provide a signal to Medicare beneficiaries that the firm is established and reputable, which in turn may lead to an increase in the demand for the firm's Medicare product. Finally, we assume that [Q.sub.m] is not directly under the control of the firm, but rather is influenced by the quality of the product (z), which is set by the firm.

Medicare Price

In contrast to the private market, the Medicare price is set administratively by HCFA, rather than being determined as a function of quantity. Under federal guidelines, the price of the Medicare product ([P.sub.m]) is set equal to 95% of the AAPCC, which is an actuarial measure of the average cost of providing care to a beneficiary enrolled in the traditional Medicare program, adjusted for age, sex, geographic, Medicaid eligibility, and institutional status differences.


The firm faces the following cost function associated with its production of the private and Medicare products:

(4) C = [C.sub.1][Q.sub.m] + [C.sub.2][Q.sub.p] + [C.sub.3][Q.sub.p][Q.sub.m] + [C.sub.4][[Q.sup.2].sub.m] + [C.sub.5][[Q.sup.2].sub.p] + [C.sub.6]z[Q.sub.m] + [C.sub.7]z + [C.sub.8][z.sup.2].

Total cost is a function of the private and Medicare quantities and the quality level chosen by the firm. The third cost parameter, [C.sub.3], captures those costs associated with the joint production of the private and Medicare products. These complementarities may reflect a combination of economies of scope or scale, occurring as the result of shared inputs (e.g., administrative services, same provider panel, etc.) in the joint production.

The last two terms in the cost function specification capture the fixed cost associated with production of a Medicare product, where this cost is strictly increasing with the level of quality chosen by the firm. HMOs may incur fixed costs for such things as new equipment purchases, facility renovation for easier accessibility by the elderly, development of geriatric programs, marketing, or administrative services related to the contract application and regulatory compliance.

Entry Decision

Based on the above assumptions, the decision for an HMO to enter the Medicare market is a function of the variable profit and fixed cost associated with production of a Medicare product. Entry by the firm will occur when, for a given level of quality, the following condition holds:

(5) ([P.sub.m] - [C.sub.1] - [C.sub.3][Q.sub.p] - 2[C.sub.4][Q.sub.m] - [C.sub.6]z) X [Q.sub.m] - ([C.sub.7]z + [C.sub.8][z.sup.2]) [geq] 0.

Using this condition, we can assess how changes in the price, costs, or private enrollment affect a firm's probability of entry into this market. For example, if the Medicare price increases, this increases a firm's variable profit, and will increase its likelihood of participation. Second, if variable or fixed costs increase, this will decrease the probability of entry by the firm, ceteris paribus. Finally, the probability of participation depends on the presence of complementarities, which captures the explicit linkage between the private and Medicare markets. Given the entry decision specification, if there are demand or cost complementarities, then an increase in a firm's private enrollment ([Q.sub.p]), will serve to increase its probability of participation in the Medicare market.

To examine how these factors affect a firm's probability of entry, we construct a binary dependent variable, OFFER, defined as

OFFER { = 1 if [Q.sub.m] [greater than] 0

= 0 if [Q.sub.m] = 0

and designate the model as the following:

(6) Prob(OFFER = 1)

= [[beta].sub.1] + [[beta].sub.2][P.sub.m] + [X.sub.m][[beta].sub.3]

+ [X.sub.p][[beta].sub.4] + (COST)[[beta].sub.5],

where the decision to offer a Medicare product is a function of a constant, the Medicare price, Medicare demand shifters, private demand shifters, and factors that shift an HMO's costs (COST). This equation is a reduced form specification derived from the entry condition.

Profit-Maximization Problem

We assume that HMOs seek to maximize profits. [7] The firm's problem is then:

(7) Max [pi] = [P.sub.p][Q.sub.p] + [P.sub.m][Q.sub.m] - [C.sub.1][Q.sub.m] [Q.sub.p], z - [C.sub.2][Q.sub.p] - [C.sub.3][Q.sup.p][Q.sub.m]

- [C.sub.4][[Q.sup.2].sub.m] - [C.sub.5][[Q.sup.2].sub.p] - [C.sub.6]z[Q.sub.m]

- [C.sub.7]z - [C.sub.8][z.sup.2]

subject to:

(1) [Q.sub.m] [geq] 0

(2) [Q.sub.p] - [Q.sub.m] [geq] 0

(3) [Q.sub.mR] - [Q.sub.m] [geq] 0,

where an HMO chooses its private quantity and level of quality to maximize profit subject to the three constraints. Constraint (1) reflects an HMO's choice to participate in the Medicare market. Constraint (2), also known as the "50/50 rule," reflects federal guidelines that require HMOs not to have more than 50% of their total enrollment from Medicare enrollees. Constraint (3) requires that no individual firm's demand for its Medicare product exceed its residual market demand. [8]

Four possible cases of HMO behavior exist under various combinations of slack and binding constraints. Case I includes all HMOs that have chosen to operate in the private market only. HMOs that fall into Case H participate in both the private and Medicare markets, and are constrained by the 50/50 rule. Case III includes HMOs that participate in both markets and are constrained by demand in the Medicare market. This suggests that an individual firm's demand equals its residual market demand, and, therefore, no further increases in quality can increase firm demand. Finally, Case IV includes those HMOs that operate in both markets and are constrained neither by the 50/50 rule nor by demand. Cases I, III, and IV appear to be the most empirically plausible. Descriptive statistics from the data reveal that less than 2% of all operational HMOs are constrained by the 50/50 rule and therefore fall into Case II.

To examine the determinants of an HMO's private and Medicare enrollment, we use the first-order conditions of the profit-maximization problem to specify the enrollment equations below. Specifically, we solve for [Q.sub.p] and [Q.sub.m] individually from the first-order conditions and impose an assumption of linearity. These single-equation, implicit solutions are expressed as the following:

(8) [Q.sub.m] = [[alpha].sub.1] + [[alpha].sub.2][P.sub.m] + [X.sub.m][[alpha].sub.3]

+(COST)[[alpha].sub.4] + [[alpha].sub.5][Q.sub.p];

(9) [Q.sub.p] = [[omega].sub.1] + [[omega].sub.2][P.sub.m] + [X.sub.p][[omega].sub.3]

+(COST)[[omega].sub.4] + [[omega].sub.5][Q.sub.m].

An HMO's Medicare quantity is a function of the Medicare price, Medicare demand shifters, factors that shift cost, and the firm's private enrollment. A firm's private quantity is a function of the Medicare price, private demand shifters, factors that shift cost, and its Medicare enrollment, as shown in equation (9).

We can distinguish between Case III (demand constrained) and Case IV (unconstrained) using the parameter on the Medicare price ([[alpha].sub.2]) in equation (8). If the firm is demand constrained in the Medicare market, an increase in the Medicare price ([P.sub.m]) will elicit no supply response. Therefore, finding no effect of a change in price on Medicare enrollment suggests that the firm is demand constrained, while a positive effect suggests that the firm is unconstrained by demand. The presence of demand complementarities suggests a positive effect of private quantity on Medicare quantity, since that will shift the demand constraint and, similarly, a positive effect of Medicare quantity and price on a firm's private quantity. Thus, finding positive parameter estimates on [Q.sub.p] ([[alpha].sub.5]) in the Medicare regression and on [Q.sub.m] ([[omega].sub.5]) and [P.sub.m] ([[omega].sub.2]) in the private quantity regression provide support for the presence of complementarities. These predictions are su mmarized in Table II. [9]



We used the InterStudy HMO Census to identify the population of HMOs in the United States from 1990 to 1995. The InterStudy Census describes the organizational structure of HMOs in terms of model type, profit status, headquarters location, and federal qualification. In addition, the Census indicates changes in ownership (e.g., organizational name changes, mergers) and plan terminations.

We matched the InterStudy data with information obtained from forms that HMOs file with state regulators. The state filings include financial information, enrollment figures, and utilization statistics. We obtained these from Health Care Investment Analysts (HCIA), who code the data and sell them in machine-readable format. We matched 2,564 (80.2%) of the 3,197 HMOs identified in the InterStudy Census with HMOs in the HCIA data. Matches did not occur for a variety of reasons: financial forms were not available from some states (e.g., Hawaii); some national firms filed the same statement in all states in which they operated; and some forms were missing for unknown reasons. We were more likely to have data for independent practice association (IPA) HMOs than non-IPA HMOs; for federally qualified HMOs; and for firms affiliated with a national HMO. We were less likely to have data for HMOs affiliated with a non-HMO based national firm (e.g., insurer) and for firms associated with Blue Cross Blue Shield. Fifty-tw o observations for which private enrollment was identified as being zero were excluded from the final empirical analysis.

County-level data from the Area Resource File were used to construct demographic and economic market measures. The Health Care Financing Administration was the source for data on the AAPCC, and data on supplemental Medicare insurance policy premiums were obtained from a report issued by the Families USA Foundation and supplemented through direct correspondence with the American Association of Retired Persons.

Unit of Analysis

The unit of analysis for this study is an individual state-licensed HMO subsidiary. Since HMOs frequently operate in multiple geographic markets, HMO market measures were developed through a process consisting of several steps. In the first step, the counties in which the HMO operates were obtained from InterStudy Censuses (1990 to 1995). Second, in a recent InterStudy survey, HMOs were asked to list enrollment by Metropolitan Statistical Area (MSA). We were able to allocate enrollments to MSAs and use county population weights to allocate enrollment within MSAs that span over more than one county. Residual enrollment not included in these MSAs was allocated over the counties served by the HMO that are not in MSA counties where the HMO allocated enrollment. In the third step, market characteristics (e.g., input prices) were created for each HMO, using a weighted average of the county-level variables over all counties where the HMO operates. Weights were calculated as the HMO's estimated enrollment in a count y divided by its total enrollment over all counties it serves. For example, if an HMO operates in two counties with enrollments of 10,000 and 30,000, and the average nurse wage rate is $12 and $16 respectively, then the nurse wage rate for the HMO market is [[(1/4).sup.*]12 + [(3/4).sup.*]16] = $15 (Wholey et al. [1995]).


As stated in the theoretical section, firms choose the quantity of the private product and level of quality for the Medicare product in order to maximize profits. While we do not have any empirical measures for quality, a firm's quantity of Medicare enrollees is a function of quality, and is observable. The product that an HMO produces is defined as a member month of health care coverage, with the private and Medicare quantities denoted as [Q.sub.p] and [Q.sub.m], respectively. We use the AAPCC county base rate for the aged as our measure of the Medicare price ([P.sub.m]).

Factors Affecting Medicare Demand ([X.sub.m]). We control for differences in the demographic composition of markets by including the proportion of the population 65 to 74 years of age and the proportion 75 years of age and older. Approximately 70% of beneficiaries purchase supplemental Medicare (Medigap) insurance to cover services not included in the traditional Medicare benefits package, as well as out-of-pocket costs, such as co-insurance and deductibles (Zarabozo and LeMasurier [1995]). An HMO Medicare product frequently includes a set of benefits that are comparable to a combination of traditional Medicare and a supplemental Medicare policy. In markets where Medigap premiums are high, an HMO Medicare product may be perceived as an attractive substitute. In 1992, supplemental Medicare insurers were required by federal law to limit their selection of policies to ten standardized packages (National Association of Insurance Commissioners [1996]). We use annual premiums for AARP/Prudential supplemental Medica re insurance (Package A) to proxy for the price of a supplemental Medicare policy (Dallek [1996]; Smolka [1996]). [10] To deal with missing premium data, we construct an indicator variable that takes on a value of one if the premium data is missing and sets the Medigap premium to zero. [11]

Factors Affecting Private Demand ([X.sub.p]). To capture the effect of income on private demand, we use the percentage of families below the poverty level. If the freedom to choose one's physician in the fee-for-service sector is a normal good, then there should be a positive relationship between poverty and demand for an HMO's private product. Second, we include the annual rate of change in the population under 65 years of age to proxy for the migration of younger persons into market areas served by HMOs. Third, we include the proportion of the population 25 years of age and older that has obtained at least a four-year college degree. Fourth, we include the proportion of active physicians in the market who are pediatricians, which should proxy for the prevalence of pediatric services provided in a market. Here, we assume that pediatricians' services are an input to the production of coverage for the private population only. [12] Finally, we include a set of indicator variables pertaining to the state regulat ory environment for HMOs. These measures cover such issues as whether subscribers have a policy-making role, whether employers are required to offer an HMO option for their employees' health coverage, whether HMO rates must have state approval, and whether HMOs are required to have an open enrollment period. [13]

Factors Affecting HMO Cost Structure (COST). While we do not observe empirical measures to differentiate among the cost parameters, we do employ a set of measures to capture various input prices. Nurse and administrative wage rates from the fee-for-service sector will be used to measure labor costs, based on the assumption that these measures are highly correlated with an HMO's corresponding labor costs. Hospital inpatient price per diem and the price of an office visit of intermediate complexity are both measures from the fee-for-service sector that should also be highly correlated with input prices faced by HMOs. To control for differences in health status across markets, we use an average infant mortality measure. We expect that in markets where the population is less healthy, there will be higher utilization of services, resulting in higher costs to an HMO. Finally, federal qualification may be considered to lower an HMO's fixed cost of offering a Medicare product, since those HMOs that are federally qual ified have already incurred some of the administrative costs associated with entering a risk contract.

HMO Characteristics Affecting Both Demand and Costs. An HMO's age may be an indicator of the acceptance of the HMO concept in a market. Also, over time, HMOs may gain experience and organizational knowledge in the provision of care, leading to more efficient production. Ownership (for-profit or non-profit status) may also affect both demand and cost. Debate continues regarding the role of for-profit organizations in health care, with some considering profit-seeking behavior as inappropriate for this industry (Hansmann [1987]). With regard to costs, it is plausible that the profit motivation may lead managers of for-profit institutions to place greater emphasis on cost minimization in production. However, an alternative demand-side argument suggests that individuals frequently associate not-for-profit HMOs with higher quality of care, and thus may be more likely to enroll in a not-for-profit, than in a for-profit HMO (Wholey et al. [1995]).

Additionally, HMO model type may suggest different production technologies, leading to differing abilities to contain costs. The relationship between model type and an HMO's physician panel may also influence demand. A set of dummy variables are included to control for HMO model type (staff, group, network, and mixed, with IPA as the excluded variable) (Wholey et al. [1996]). We also include indicator variables for whether a firm is affiliated with a national HMO, a national insurer that is not an HMO, or Blue Cross Blue Shield. Affiliations with these institutions may affect a firm's access to capital and organizing expertise, which may, in turn, affect its production decision. Finally, we include a set of dummy variables for each year in our sample (1990 as the excluded variable) to capture time trends.


We estimate a two-part econometric model for this analysis. In the first part, we focus on an HMO's participation decision in the Medicare risk market. As discussed in Section II, the decision to offer a Medicare product is modeled as the following:

(10) Prob(OFFER = 1) = [[beta].sub.1] + [[beta].sub.2][P.sub.m] + [X.sub.m][[beta].sub.3] + [X.sub.p][[beta].sub.4] + (COST)[[beta].sub.5] + [[epsilon].sub.1].

We estimate the participation regression as a population averaged panel data model using a generalized estimating equations framework. Additionally, we use a Huber/ White/ sandwich estimator of variance that allows for generalization within HMO group correlation and heteroskedasticity across HMOs. [14]

The second part of the model focuses on the factors that determine HMO enrollment in both the Medicare and private products.

Following the theoretical model, the enrollment equations to be estimated are specified as:

(11) [Q.sub.m] = [[alpha].sub.1] + [[alpha].sub.2][P.sub.m] + [X.sub.m][[alpha].sub.3] + (COST)[[alpha].sub.4] + [[alpha].sub.5][Q.sub.p] + [[epsilon].sub.2]

(12) [Q.sub.p] = [[omega].sub.1] + [[omega].sub.2][P.sub.m] + [X.sub.p][[omega].sub.3] + (COST)[[omega].sub.4] + [[omega].sub.5][Q.sub.m] + [[omega].sub.6](OFFER) + [[epsilon].sub.3].

Equation (11) is estimated only for firms that participate in the Medicare market (N = 490), while equation (12) is estimated for all firms in the sample. [15]

Two estimation issues include the simultaneity of [Q.sub.p] and [Q.sub.m], and the presence of unobserved HMO-specific effects. Instrumental variables estimation is used to deal with the simultaneity of our enrollment measures. To instrument for an HMO's private enrollment, we use our private demand shifters. The rate of change in the population under 65 years of age reflects the potential growth of the market for an HMO's commercial product and should be exogenous with respect to a firm's Medicare enrollment. Second, we use the percentage of poor families, asserting that this measure reflects the income of the non-Medicare beneficiary population. The ratio of pediatricians to active medical doctors is also used, since this measure should reflect the potential market demand for pediatric services, which should be used predominantly by an HMO's commercial enrollees. Finally, indicator variables capturing an HMO's regulatory environment as well as the proportion of the population who have four or more years of college are also used as private enrollment instruments.

To instrument for an HMO's Medicare quantity, we use the supplemental Medicare insurance premium and our two demographic measures which capture the proportion of the population ages 65 to 74 and the proportion 75 years and older. [16] These factors should all serve to influence HMO Medicare enrollment but not to directly affect an HMO's private enrollment. We again use the Huber/ White/sandwich estimator of variance to obtain consistent estimates of our standard errors.

By estimating this model as two separate parts, we have not considered the issue of selection, whereby HMOs choose whether or not to offer a Medicare product. In taking this approach, our inferences may be applicable to only those HMOs in the sample. Given the possibility of selection issues, we also adopt the conventional approach in the literature and estimate the Medicare enrollment regression with an inverse Mill's ratio measure (lambda), constructed using predicted values from the participation regression [17]


Definitions and descriptive statistics of the measures used in this analysis are provided in Tables III and IV. Missing values for 75 observations reduce the sample size to 2,437. Results from the participation regression, which are generally consistent with theoretical predictions, are shown in Table V. Most notably, we obtain a positive and significant coefficient on the AAPCC measure. In our sample, the average AAPCC payment rate is $349. Using our estimates, we find the average impact of a $35 increase in the AAPCC to increase the probability that an HMO offers a Medicare product by .028. [18] Additionally, the elasticity of the probability of entry with respect to the AAPCC payment rate evaluated at the mean is equal to 1.39, suggesting a large behavioral response by HMOs.

Finding this response suggests that the payment rate, which is set to reflect the predicted costs of providing coverage to beneficiaries, does a poor job of adjusting for differences in risk between beneficiaries in traditional Medicare and those who enroll in HMOs. Since the AAPCC rate is constructed to correspond to HMOs earning zero economic profits in the Medicare market, cross-sectional differences in its value should not be associated with differential entry. However, finding this effect indicates that areas with higher AAPCC rates are more profitable, and thus cost differences have not been accurately adjusted.

The proportions of the population 65 to 74 years of age and 75 years and older are also statistically significant, with positive and negative coefficient signs, respectively. This suggests that the demographic composition of the Medicare population affects an HMO's participation decision in a way that is consistent with favorable selection. [19] Finally, HMOs that have federal qualification, are affiliated with a national HMO organization, and are older are associated with an increased probability of Medicare market participation.

Results from estimation of the enrollment regressions are shown in Table VI. We find that the results for the Medicare enrollment regression do not change substantially when the selection correction is included, and that the estimate on the inverse Mill's ratio is statistically insignificant. In both the private and Medicare enrollment regressions the coefficients on the instrumented enrollment measures are positive and statistically significant, suggesting complementarities in the joint production of a firm's private and Medicare products. Though, given the particular model specification, we are unable to empirically distinguish between demand and cost complementarities. [20]

With respect to the AAPCC payment rate, we find that it has no significant effect on Medicare enrollment. Two possible interpretations suggest that either the coefficient estimate is so imprecisely estimated that we simply can't discern an effect or that the coefficient is truly zero, which is consistent with the demand constrained case. While we find no effect of the payment rate on Medicare enrollment, we find a positive and significant effect of the price of a supplemental Medicare insurance policy on Medicare enrollment. This result is consistent with the argument that as supplemental Medicare premiums increase, beneficiaries are likely to consider enrollment in an HMO as a substitute for the combination of traditional Medicare and a supplemental policy.

Relating our empirical results to theory, we refer back to the predictions outlined in Table II. First, we cautiously conclude that HMO behavior is consistent with the demand constrained case, given our insignificant effect of a change in the Medicare price on Medicare enrollment ([[alpha].sub.2] = 0). Second, we find support for the presence of complementarities in production. We find a positive and significant relationship between a firm's private and Medicare quantities in the enrollment regressions, which suggests either demand or cost complementarities ([[alpha].sub.5] [greater than] 0, [[omega].sub.5] [greater than] 0). Additionally, we find a positive effect of the Medicare price on private quantity; however, because of the imprecision with which the coefficient is estimated, it provides only marginal support.


Policy Implications

The Medicare + Choice payment methodology establishes three rates (a minimum payment, a blended rate, and a payment rate based on the 1997 AAPCC rate with a minimum percentage increase), from which contracting organizations receive the largest. Coordinated care organizations located in geographic markets with historically low AAPCC rates or, alternatively, those located in markets with historically high AAPCC rates, appear to be the most affected by this change.

Establishing the minimum payment level provides one method to induce entry by coordinated care organizations into the Medicare market. To assess the effect of implementing such a policy, we compute a set of predicted probabilities of entry into the Medicare market for a subset of HMOs that reflect the characteristics of the target group affected by the minimum payment policy. Specifically, our subset consists of HMOs that do not offer a Medicare product and that have AAPCC payments less than the Medicare + Choice minimum payment level. [21] Using our participation regression results, we compute a set of predicted probabilities of entry into the Medicare market for the minimum, median, and maximum payment rates associated with this group, with all other regressors held at the sample mean. These results are shown in Table VII. While the predicted probabilities for this set of HMOs are low, ranging from .0785 to .1373, increasing the payment rate from the minimum in the sample to the designated Medicare + Choic e minimum payment rate increases the predicted probability of entry by almost 75%.

Using the payment rate for the purpose of inducing entry raises two additional issues. First, adopting such a policy may lead to the payment of rents to incumbent HMOs who are already operating in markets for which the minimum payment rate applies. Second, there may be factors other than the payment rate that deter entry by firms. Such issues may include a scarcity of potential enrollees or lack of negotiating power with providers (Serrato et al. [1995]).

Rather than using the payment rate to induce entry, an alternative policy tool would be for the government to individually subsidize the sunk costs of entry for organizations operating in markets with little or no program participation. Without having estimated the parameters of the cost function, we are unable to directly calculate firms' sunk costs using the entry condition identified in Section II. However, using data from 1995, we calculate an approximation of the upper bound on sunk costs for entry into the Medicare market under three hypothesized profit rates. Since variable profits must exceed sunk costs for a firm to enter, an estimate of variable profits serves as an upper bound on sunk costs. We calculate variable profits as [P.sub.m] . [Q.sub.m]. [phi], where [phi] is equal to the profit per dollar of revenue. We simulate this for various values of [phi].

For this exercise, we subdivide the group of new entrants into three geographic regions (West, Central, and East), and select the firm with the largest Medicare enrollment in its first year of participation. Choosing the largest new entrant allows us to get an upper bound on the sunk costs in each of the regions, presuming that sunk costs are not decreasing in size. The estimated sunk costs of entry for each firm under values of [phi] equal to .05, .1, and .2 and a calculation of the sunk cost per member month are reported in Table VIII. With direct information on [phi] one could then compare the actual cost of using the payment rate per beneficiary as a method for inducing plan participation versus direct subsidization of sunk costs.

Introducing a payment rate based on the 1997 AAPCC rate with a specified annual increase (e.g., 2% above the 1997 AAPCC rate for 1998), which may or may not reflect actual cost growth, has led many HMOs to reconsider participation in Medicare + Choice. This change, as well as the implementation of new compliance regulations, has contributed to HMO exits from particular geographic service areas as well as the Medicare market altogether, affecting nearly 700,000 Medicare beneficiaries since 1998 (Pear [1999]. [22] These exits are consistent with the analytical framework presented here, if one assumes that the new administratively set price is closer to HMO marginal costs or, alternatively, if fixed costs are increasing given the new regulations.

A final policy implication stems from the complementarities result. Finding empirical support for the presence of demand and/or cost linkages across a firm's private and Medicare markets has important ramifications for policy design and evaluation. First, it suggests that federal policies for this program should take account of firms' private market activities when designing Medicare policy related to participation and enrollment. Second, with respect to policy evaluation, if there are linkages between these markets, then it becomes increasingly difficult to isolate the effect of a policy intervention on Medicare market activity (e.g., growth in HMO Medicare enrollment) from changes that result simply due to a firm's private market activities.

Concluding Remarks

In this article we have developed a model of HMO behavior to examine both participation in the Medicare market and HMO Medicare enrollment. Estimating a two-part model using data on HMOs in the United States over the time period of 1990 to 1995, we obtain results that are generally consistent with our theoretical predictions.

Three primary conclusions can be drawn from this research. First, we find evidence to support the assertion that changes in the payment rate may have direct implications for participation by firms in the Medicare market. While the specific payment methodology has been revised with the institution of Medicare + Choice, changes in payment structure continue to have a significant effect on participation by coordinated care plans. Second, while enrollment by Medicare beneficiaries is dependent on plan participation, it is also a function of the set of insurance alternatives available to beneficiaries, such as the combination of traditional Medicare and supplemental insurance policies. If Medicare + Choice is successful in terms of broadening the set of coverage choices available to beneficiaries, this may subsequently introduce additional issues for regulators with respect to competitive behavior by contracting plans. Third, we find empirical evidence in support of a linkage between a firm's private and Medicare products, giving rise to additional concerns regarding policy design and evaluation. While this study covers a time period prior to the implementation of Medicare + Choice, we believe that the analytical framework, and the general findings are still applicable in terms of helping policymakers to understand how the structure of payment rates and beneficiary options affect implementation strategies and the design of future Medicare policy.

Abraham: Doctoral Candidate, Carnegie Mellon University, Phone 1-412-268-8717, Fax 1-412-268-7036, E-mail

Arora: Associate Professor, Carnegie Mellon University, Phone 1-412-268-2191, Fax 1-412-268-7036, E-mail

Gaynor: E. J. Barone Professor of Economics and Health Policy, Carnegie Mellon University, Phone 1-412-268-7933, Fax 1-412-268-7036, E-mail

Wholey: Professor, University of Minnesota, Phone 1-612-626-4682, Fax 1-612-624-2196, E-mail

(*.) We wish to thank Jonathan Caulkins, John Engberg, William B. Vogt, Gloria Bazzoli, Willard Manning, George Jakubson, workshop participants at Carnegie Mellon University, and two anonymous referees for helpful comments and suggestions. The usual caveat applies.

(1.) Medicare + Choice also permits private, fee-for-service insurers and religious fraternal benefit society plans to contract with HCFA.

(2.) Additional regulations capped net revenues for risk-contracting HMOs. If an HMO exceeded the limit, then the firm would be required to take a lower payment rate or pass the savings onto the beneficiaries in the form of supplementary benefits or lower out-of-pocket costs. Premium rebates were prohibited. See Zarabozo and LeMasurier [1996] for discussion of program guidelines.

(3.) Table I was constructed using data from a national sample of HMOs in the United States. Therefore, the number of risk-contracting HMOs reported in Table I is smaller than the number reported by HCFA for this time period.

(4.) The National Medicare Competition demonstration occurred in 1982, and included 52 risk-contracting plans. See Langwell and Hadley [1982, 1986] for discussion.

(5.) This specification does not explicitly model strategic interaction by firms in the private market. Assume this represents a reduced form residual demand curve with [X.sub.p] capturing factors that shift rivals' demands as well as the firm's own demand.

(6.) This specification also does not explicitly model strategic interaction among firms in the Medicare market. It subsumes rivals' actions and should be considered a reduced form specification. We assume that HMOs only seek to enroll beneficiaries from the traditional Medicare population and not those beneficiaries who are already enrolled in other HMOs.

(7.) Profit-maximization is the appropriate assumption, even for non-profit HMOs, provided that the HMO seeks to maximize the income of a decisive set of agents, or that the residual claimants can agree on maximizing their joint gain (Pauly [1987]; Danzon [1982]). A separate model for non-profit HMOs is required only if something which affects demand (e.g., output) also appears in the HMO's objective function. Since this is uncertain, we do not believe there is a need for a special model of non-profit HMOs (Wholey et al. [1995]). In our data set, approximately 70% of HMOs have for-profit status.

(8.) First-order and second-order conditions of the profit-maximization problem are contained in an appendix available at [langle][rangle]

(9.) These predictions are derived from comparative statistics also contained in an appendix available at [langle][rangle].

(10.) Package A includes coverage for the Medicare Part A coinsurance amount for the 6lst-9Oth day of hospitalization; coverage for the Part A coinsurance amount for each of the 60 nonrenewable lifetime hospital inpatient reserve days; coverage for 100% of the Medicare Part A eligible hospital expenses; coverage for three pints of blood; and coverage for the coinsurance amount for Part B services after the $100 deductible has been met (National Association of Insurance Commissioners [1996]).

AARP/Prudential uses a community rating method to calculate premiums, which means that it does not charge differentiated prices based on age, health status, or geographic location within a state. We acknowledge that endogeneity issues may be present if HMOs in the market experience favorable selection, leading to a costlier traditional Medicare population on which supplemental Medicare insurance premiums are calculated.

(11.) See Greene [1993] for a discussion of this technique. Most of the missing premium data come from Massachusetts, Minnesota, and Wisconsin, which all received waivers for alternative simplification plans prior to 1990.

(12.) Note that while we considered including measures of HMO competition and market penetration for the private enrollee population, we chose not to because of endogeneity issues.

(13.) To deal with missing regulations data, we again adopt the indicator variable technique discussed in Greene [1993].

(14.) An additional discussion of econometric estimation methods is continued in an appendix available at [langle] than][rangle]. See also Liang and Zeger [1986].

(15.) We include both OFFER and the Medicare quantity in the private quantity equation because we consider the decision whether to offer and how much to offer to capture a joint outcome.

We also estimate the model using various transformations of the enrollment measures, including the natural log and the square-root of private and Medicare quantities. The results are qualitatively similar, and the linear model was chosen based on fit.

(16.) One issue regarding the use of the Medigap variable as an instrument is that it reflects general health care costs and health status of the population in a market. It is unclear if expenditure growth patterns for the Medicare and private populations are the same. In fact, for the time period of the study, Medicare expenditures were growing significantly faster than private personal health care expenditures (U.S. Department of Health and Human Services [1996]). Nor is it clear that health status for the under-65 and Medicare-eligible populations are highly correlated in a given market.

To examine the "quality" of our instruments, we separately ran regressions of our enrollment quantities on all predetermined variables in the system and then performed joint F-tests on the instruments. In both regressions, the instruments were jointly significant at the 1% level. See Staiger and Stock [1997].

(17.) We specify federal qualification of an HMO to affect the decision to offer a Medicare product, but not to affect enrollment. This specification enables identification to be based on something in addition to functional form assumptions.

(18.) The average predicted probability for our sample is .198. We find the effect of the AAPCG on an HMO's probability of entry to be smaller in magnitude as compared with the findings of Adamache and Rossiter [1986] and Porell and Wallack [1990].

(19.) We are cautious in this assertion since this result may be partially due to the fact that the AAPCC payment measure used in this analysis is not specifically adjusted to reflect the actual demographic composition of enrollees that an HMO would face.

(20.) The studies of Wholey et al. [1996] and Given [1996] find the presence of diseconomies of scope in the joint production of private and Medicare products. This suggests that our results may be due to demand complementarities.

(21.) We first deflated the 1998 minimum payment level of $367 to 1995 dollars before selecting our subset of HMOs. In 1995 dollars, this value equals $341.

(22.) The decision to exit a particular geographic service area (e.g., county) is a decision that is nested within the participation decision investigated here.


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AAPCC: Adjusted Average Per Capita Cost

HCFA: Health Care Financing Administration

HCIA: Health Care Investment Analysts

HMO: Health Maintenance Organization

IPA: Independent Practice Association

MSA: Metropolitan Statistical Area
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