Creaming, skimping and dumping: provider competition on the intensive and extensive margins

1. Creaming, skimping and dumping: provider competition on the intensive and extensive margins Randall P. Ellis Journal of health economics September 1997 Yan Cheng, December 2001

2. Introduction • Reimbursement incentives influence both the intensity of services and who is treated when patients differ in severity of illness. • The social optimum is compared to the private Cournot-Nash solution for three provider strategies: • Creaming: the over-provision of services to low cost patients. • Skimping: the under-provision of services to high cost patients. • Dumping: the explicit avoidance of high cost patients.

3. Analytical model • The model is a three stage, complete information, noncooperative game in which two health care providers compete to attract patients. • First stage: the payer chooses the provider reimbursement system. • Second stage: two identical competing providers each announce a schedule of services for patients of each severity level. • Third stage: patients select a particular provider after observing each provider’s services and dumping threshold.

4. Analytical model-patients • Patients are assumed: • to be fully insured • Uniformly distributed over two dimensions of square: s (severity of illness) and t (distance measured in travel time) • Bj: Patient benefits of treatment • B() strictly concave and Bx>0, Bs>0 • Xj(s): the level of services provide by provider j to patients according to location. • : travel cost/unit of travel time • A patient of type s locate at t=N1 from provider 1 will be distance 1-N1 from provider 2.

5. Analytical model-patients • A patient at location N1<1/2 will be indifferent between treatment and no treatment if: • Esq. (2) & (3) define two different demand curves, which depend upon the level of patient severity • Monopoly: • For low severity patients, each provider can act as monopolist in choosing the level of treatment. • Duopoly: • For high severity patients, both providers interact and will need to act strategically. •  can be interpreted directly as a measure of responsiveness of demand to the difference between total benefits offered by the two providers.

6. Analytical model-payment system • Assume: • linear functions of the per patient cost of treatment. • No fixed costs or economies of scale across severity level. • Profit from a single patient from provider j=1,2 • j is per patient profits • R=lump sum reimbursement amount • r=marginal reimbursement amount • per patient cost to provider j of level of health services at severity s. • R=0, r=1 correspond to cost-based reimbursement • R>0, r=0 correspond to a fully prospective system • R>0, 0<r<1 represent a mixed payment system

7. Analytical model-provider • Objectives: • Providers care about profit j , and patient benefit Bj, but not travel cost. • provider j’s utility function: •  and (1-) are the weights attached to patient benefits and profits

8. Analytical model-provider dumping • Dumping: Providers avoid treating high cost cases altogether. • Assume: • Each of the two providers can take two types of actions for patients of each severity level: Eq. (7) or dump ( zero utility from patients) • Dumping is motivated by overall hospital profitability. • Provider 1 dump patients of severity above where satisfies: • is the minimum profit that provider 1 requires to operate

9. Analytical model-provider dumping • Dumping also affects total provider utility. • Provider 1’s objective is to choose and to maximize Eq. (9) subject Eq. (8)

10. Result-first best social optimum • First-best social objective function: • B( ), benefits people receive across severity levels • C(X(s)), treatment costs • , travel costs • Solution to this problem (no dumping) and • The first-best is generally not feasible, since fully insured patients will be willing to travel for treatment as long as total benefits of treatment are greater than travel costs

11. Result-second best social optimum • The number of patient seeking treatment is demand-determined rather than chosen by social planner. • Solution for this problem is:

12. Result-Cournot Nash solution • The problem can be set up as a Lagrange multiplier problem: • The problem is set up so that  will be positive • By solving Eq. (14) • V1() will be nonnegative at the maximum • Result 1: is negative, unprofitable patiens will be dumped.A provider must be making a loss on the marginal. • Result 2: pure profit max (=0) providers are only skimp

13. Provider choice of the X(s) schedule • The optimal choice of X(s) is given as: • Eq.(16) depends on N() which in turn depends on s • Three types of solutions to (16) • Low level of s, each provider can act as monopolist • High level of s, two providers will compete as Cournot competitors, use Eq. (5) • Middle level of s, out put should be chosen such that Eq. (4) is satisfied with N1=1/2

14. Example --Cost-based reimbursement • Provider profits are zero regardless of the level of services provided. • Creaming happens to attract all types of patients.

15. Example --Fully prospective payment • Assume that profitability constraint is binding • Assume that profitability constraint is binding, so that dumping occurs. • Three types of solutions derived above can occur. • Get profits on low severity types of patients. Providers try to ‘cream’ by over-providing to them. • Severity levels of patients located at midpoint of the distance, two providers are competing to attract these patients. • For high severity types, provider will provides fewer services, or dump them.

16. Mix payment system • Giving a lump-sum subsidy to each of the two providers. • Provider will provide some patients previously dumped. • Patients won’t get all cost reimburse, creaming decreased. • The best choice.