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

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.

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.

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) –B j : Patient benefits of treatment –B() strictly concave and B x >0, B s >0 –X j (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=N 1 from provider 1 will be distance 1-N 1 from provider 2.

Analytical model-patients A patient at location N 1 <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.

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

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

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

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)

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

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:

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

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 N 1 =1/2

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

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.

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.