A Supplementary Appendix: Health Insurance and Consumer Choice

Typically, however, consumers do not bear the cost of their hospitalization directly, as either all or most of the cost is borne by an insurer. Similarly, consumers’ choices of both which hospital to patronize and what care to consume are determined substantially by their insurer through selective contracting and utilization review.1 This is especially true of HMO patients who often pay little or nothing when they consume care and whose utilization is often heavily managed by the HMO.2 Hence, we model the HMO’s choices. We posit a very simple model of HMO behavior. HMOs sell policies to consumers, consisting of a premium, M , and decision rules specifying the hospital to which a consumer will be sent and the quantity of care he will be provided, depending on his characteristics, Ri. We will denote the hospital-choice decision rule by a J-vector of indicator functions χ(Ri), where a 1 in the jth place indicates that a consumer with characteristics Ri is sent to hospital j. We will write the jth function in this vector for the ith consumer in the mnemonically convenient notation, χi→j . The decision rule for quantity of care consumed is q(Ri). We assume that Ri is unobservable ex ante, so that the consumer evaluates the desirability of the HMO by its premium and its average quality, v = ∫ Ri ∑J j=1 χj (Ri) v (q(Ri), Ri, Sj) dFRi , i.e., the average utility across consumers from consuming hospital care. Thus each HMO contract is characterized, for the consumers’ purposes, by a pair, (M, v̄). Different consumers choose different policies since their incomes differ. We are agnostic about the insurance market — by some means, (M, v̄) are chosen for each insurer and consumers are allocated among them.3 The HMO must choose rules to assign consumers to hospitals, χ(Ri) and rules to assign quanConsumers are also influenced by the advice of their doctors, who in turn are also often influenced by incentives from the insurer. We do not model the doctor-patient interaction here. HMOs seek to limit medical expenditures by selectively contracting with health care providers, and most also attempt to control care via financial incentives for doctors. We are assuming that the allocation is independent of consumer characteristics observable to the market participants but unobservable to the econometrician. We have not specified ex ante observable consumer characteristics in our model, however there certainly are such factors that affect M and v, e.g., age and sex. Therefore this analysis should be thought of as conditional on ex ante observables. When we discuss the solution below, it will also be conditional on ex ante observables. We are assuming, therefore, that HMOs can “price discriminate” among consumers with different observables and that they can offer them, either implicitly or explicitly, different decision rules in their benefits.