بیمه سلامتی، طرح درمان، و هیئت با پزشک نوع دوستانه

We study delegating a consumer's treatment plan decisions to an altruistic physician. The physician's degree of altruism is his private information. The consumer's illness severity will be learned by the physician, and also will become his private information. Treatments are discrete choices, and can be combined to form treatment plans. We distinguish between two commitment regimes. In the first, the physician can commit to treatment decisions at the time a payment contract is accepted. In the second, the physician cannot commit to treatment decisions at that time, and will wait until he learns about the patient's illness to do so. In the commitment game, the first best is implemented by a single payment contract to all types of altruistic physician. In the noncommitment game, the first best is not achieved. All but the most altruistic physician earn positive profits, and treatment decisions are distorted from the first best.

Physicians have different practice styles. Patients with similar medical conditions often get treated differently. Practice-style variations are present across specialties such as obstetrics (Epstein and Nicholson (2009)), cardiology (Molitor (2012)), and primary care (Grytten and Sørensen (2003)). Practice variations can be very costly if physicians deviate from using cost-effective treatments. In fact, Phelps and Parente (1990) estimated an annual welfare loss valued at US $33 billions due to hospitalization rate variations. Current theory explains practice variation by information diffusion and physician learning (Phelps (1992), Phelps and Mooney (1993)). Under this hypothesis, practice variation should be smaller within markets than between markets, and should diminish over time. However, Epstein and Nicholson (2009) find the opposite: for risk-adjusted cesarean-section rates, within-market variation is twice that of between-market variation; almost 30% of the variation is due to time-invariant, physician-specific factors other than experience, gender, race, and where a physician received residency training. This time-invariant, physician-specific factor likely reflects physicians’ intrinsic preferences about the appropriate treatments for their patients. In this paper, we model practice styles by physicians’ heterogenous preferences towards their patients. Physicians are partially altruistic, their utilities being weighted sums of profits and patients’ utilities. Physicians have multiple treatment options, and patients’ illness severities differ. Physicians’ tasks are to match patients with different severities to different treatment plans. However, physicians possess private information about patient's illness severity, and their treatment decisions are noncontractible. We study the following questions. What is the efficient treatment plan when there are multiple treatment options? Under what conditions can payment contracts implement the efficient treatment plan? If the efficient treatment plan is not implemented, what are the distortions? Finally, how are insurance premiums affected? Since Arrow (1963) observed the importance of altruistic physicians in the health market, the altruistic-physician assumption has been widely adopted.2 While most papers in the literature have assumed that the degree of altruism is given and known, we go beyond the fixed-altruism assumption and allow the physician to be of many different types, this being his private information.3 An altruistic physician may trade off his own profit against the consumer's utility. This formal construct does permit an ultra altruistic physician to run a financial loss to subsidize treatments. This, however, is unrealistic. Being an economic agent, a physician must face some financial constraints, so we assume that a physician must on average earn a minimum profit. We do allow a physician to sustain some financial loss sometimes, but he must expect to earn a minimum profit on average. We normalize this minimum expected profit to zero.4 The physician practice-style issue rests on an environment in which many treatment options for an illness are available. We model multiple treatment options in the simplest way. A less costly treatment succeeds in eliminating a patient's illness disutility with a lower probability. A second treatment is more costly, but succeeds with a higher probability. In contrast to papers in the literature, we let physicians combine treatments. For example, a high-cost treatment may be used after a low-cost treatment fails to eradicate the illness. The physician decides on sequences of treatments, which we call treatment plans or protocols. Our main findings are the following. First, the first-best treatment plan prescribes a conservative approach under a cost-convexity assumption, which says that the higher the success probability, the higher is the cost per unit success probability. If the severity is low, then no treatment is used; if it is of medium value, a low-cost treatment will be used; if it is high, then the low-cost treatment will be used, followed by the high-cost treatment if necessary. In other words, the consumer should never take the high-cost treatment before trying the low-cost treatment. Second, the first best can be implemented by a single contract when the physician can commit to treatment plans before learning about patients’ severities. This result is surprising both because in principal-agent models, information asymmetry often generates information rent and distortions, and because the first best is implemented without the use of any contract menu. Third, the first best is infeasible when the physician cannot commit to treatment plans; the physician earns excess profits, and treatment decisions are distorted from the first best. To explain our results, we should first describe the extensive-form game. In Stage 1, an insurer offers an insurance contract to the consumer, and a payment contract to the physician, which consists of a capitation payment and the physician's share of treatment cost. In Stage 2, nature determines the physician's degree of altruism, which is privately known to the physician. In Stage 3, the physician and the consumer decide whether to accept the contract. The physician also decides on a practice style which is a rule for prescribing a treatment plan for any illness severity. In Stage 4, nature determines the patient's illness severity. The physician learns the illness severity and follows the treatment plan decided in Stage 3. The commitment power manifests in Stage 3. At that time, the physician has not learned the patient's illness information (he already has the private information about the degree of altruism), but he does anticipate learning that in Stage 4. What he does in Stage 3 is to formulate a rule for how the patient is to be treated: if the severity turns out to be such and such in Stage 4, then this or that treatment will be used. Stage 3 is also the contract acceptance stage, and the physician must simultaneously assess whether the capitation payment and cost share can generate a minimum expected profit. The first best can be implemented by a contract designed as if the physician were the least altruistic type. Suppose the least altruistic physician puts a 10% weight on consumer's utility. The insurer should offer a contract with a 10% cost share and a transfer equal to 10% of the expected first-best cost. The 10% altruistic physician will fully internalize the social costs and benefits when bearing 10% of the cost. A lump-sum transfer equal to 10% of the expected cost in the first best allows the least altruistic physician to break even. Why can this contract still implement the first best when the physician puts, say, a 50% weight on the consumer's utility? If the physician accepts the contract and implements the first best, he also breaks even. The doctor would have liked to offer more generous treatments because he was more altruistic. But if he had done so, he would not break even. The transfer is so low—only 10% of the expected first-best cost—that more generous treatment plans would put the 50% physician in the red. The nonnegative expected profit constraint is so binding that the 50% physician must follow the strategy of the least altruistic physician. It follows that the 50% altruistic physician implements the first best. Next, we study a game in which the physician does not have commitment power. The first two stages of the game remain the same. But now in Stage 3, the physician only decides on whether to accept the contract. He does anticipate learning the illness severity in Stage 4, but the treatment decision is postponed until then. The difference, therefore, is that any capitation payment specified in Stage 3 has been paid, and has no bearing on the physician's treatment decision in Stage 4. Now, the single contract in the game with commitment fails to implement the first best. The 50% altruistic physician will reject a 10% cost-share contract. In Stage 4, bearing only 10% of costs, the physician now cannot resist offering treatments that are more generous than the first best. It is time inconsistent for the 50% altruistic physician to stick to the first best. However, the low transfer in the 10% cost-share contract would not allow him to break even. Anticipating the deficit in the continuation, the 50% altruistic physician rejects the contract in Stage 3. If the insurer has to retain a physician with high degrees of altruism, contracts with higher cost shares must be offered. In fact, a menu of incentive-compatible payment contracts will be offered, and physicians may earn positive profits. Distortions from first-best treatment plans will result, and the insurance premium for the consumer will be higher. Our results confirm the efficiency loss due to practice-style variations. However, our analysis also indicates how this loss can be avoided. If treatment plans can be finalized when the financial constraint is relevant, efficiency can be attained. A sort of “bottomline medicine” principle is being advocated whereby resources, including lump-sum payment, and medical treatments should always be considered together. The policy implication is that the insurer should encourage doctors to formulate their treatment plans at the point of contract acceptance, and give doctors incentives to carry out the plan when seeing patients. For example, when offering the single contract, the insurer also suggests the efficient treatment plan as a medical guideline. In addition, the insurer announces that he will only renew contracts with physicians whose total treatment cost (say in a year) is below a threshold. In economic models, it has been shown time and again that commitment is powerful. Yet, it appears that here, a physician's commitment power is being exploited by the insurer. A physician earns a zero profit when he is able to commit to a treatment plan, but a positive profit otherwise. However, physicians in our model are altruistic and their preferences are not based on profits alone. In fact, a physician's total utility may be higher when he has commitment power and is very altruistic. Although we analyze games in which physicians may or may not commit to treatment plans, commitment itself is taken to be exogenous. In the literature, many researchers have posited that commitment requires a player of a game to take a costly action, but others have assumed that a player may be a commitment type that can stick to a strategy.5 We are agnostic about whether commitment must require a prior costly action or not. Our interest is to identify circumstances in which efficiency can be achieved. As it turns out, our researh points to the importance of medical practice style as a commitment that may be used for implementing efficienct treatments. As Arrow (1963) has pointed out, physician altruism seems so natural, and important in the health care market. The economic analysis following such a hypothesis has only been studied quite recently. A contribution here is that altruism interacts with profit motives. The implementation of the first best depends on physicians caring about their patients, having to make a minimum expected profit, as well as being able to commit to treatment protocols. In the literature, the idea that economic agents have nonmonetary motives has been studied intensively. Here is sample of such recent papers: Akerlof and Kranton, 2005, Bénabou and Tirole, 2003, Besley and Ghatak, 2005, Delfgaauw and Dur, 2007, Delfgaauw and Dur, 2008, Francois, 2000, Makris, 2009 and Murdock, 2002, and Prendergast, 2007 and Prendergast, 2008. Our paper differs from these works in that the physician's degree of altruism is unknown (see also footnotes 2 and 3 above). Unknown altruism generally brings in a second dimension of asymmetric information. Our paper contributes methodologically to the multi-dimensional asymmetric information problem. A few papers in the literature use a limited liability constraint, which is identical to our minimum expected income constraint. Makris and Siciliani (2011) consider incentive schemes for altruistic providers who possess private information about production efficiency, but who must be able to break even. Makris (2009) uses a slightly different setup in which an agent must not be asked to use any of his own wealth. In these two papers, the degree of altruism is common knowledge. Choné and Ma (2011) also use a minimum income constraint. The requirement of minimum profit for altruistic agents appears to be both natural and necessary. Unknown altruism in the health market has been considered before by Jack (2005) and Choné and Ma (2011). Nevertheless, our paper differs in many ways. In Jack (2005) and Choné and Ma (2011), risk aversion and insurance are not considered. Jack's model considers noncontractible quality choices by a provider, and lets the physician suffer some financial losses. We do not consider quality, and impose a nonnegative expected profit constraint. Choné and Ma study a more general agency problem in which the physician's preferences may not be altruistic. In addition, in Choné and Ma, health care quantities are contractible, and the physician possesses private information about patient illness severity and his degree of physician agency before accepting a contract, so commitment is irrelevant. Moreover, in Jack (2005) and Choné and Ma (2011), there are no equilibria in which the first best is implemented. The literature on physician payment is large. An earlier survey is McGuire (2000), and a more recent one is Léger (2008). Despite the prevalence of multiple treatment options, most existing works either do not model treatment plans (Pauly, 1968), Zeckhauser, 1970 and Choné and Ma, 2011), or allow patients to take only one treatment (Ma and Riordan (2002)). Several more recent papers (Chernew et al., 2000, Malcomson, 2005 and Siciliani, 2006) allow the patient to choose one treatment out of many options. However, they do not allow the patient to take a treatment sequence. Different from all these works, our model has multiple treatment options and examines optimal treatment sequences. The rest of the paper is organized as follows. Section 2 presents the model and the first best. Section 3 studies the two delegation games. Section 4 discusses related issues and policy implications. Section 5 draws conclusions. Proofs are in the Appendix.

We study how an insurer can reduce the unnecessary cost due to practice-style variations by designing payment contracts for heterogenous physicians. Our model consists of two new elements. Treatments can be combined, and physicians are altruistic, with different degrees of altruism. We develop new principles from this setup. First, we show that the first-best treatment plan follows a conservative pattern. Second, we consider delegating treatment decisions to physicians, and show that the first best can be implemented only when a physician can commit to treatment plans at the time of contract acceptance. We offer various policy implications. Treatment plans involve a time dimension, and it is natural that commitment plays a role in the analysis. The physician committing to using particular plans may result in time-inconsistent decisions. But such commitment has social value; it reduces premium and inefficient search. The treatment technology is richer than the usual health care quantity approach. This lets us rule out some treatment combinations as inefficient. However, our main results for delegation under treatment plan commitment and noncommitment should hold without any modification if the physician is choosing a quantity of services. We acknowledge that our model abstracts from learning. Two issues naturally arise when learning is important. First, the likelihood of treatment success may itself be uncertain. A first treatment is often an experimentation for the physician to learn about treatment efficacy. The failure of a treatment may then update the likelihood that other treatments may be successful. Second, illness severity may be uncertain. A first treatment may reveal that the illness is more or less severe than initially thought. This new information will impact subsequent treatments. We have focused on payment contracts based only on the physician's reported type and on full insurance contracts for consumers. In general, the physician's cost shares can depend on the chosen treatments, and consumers may incur copayments. These more general contracts are unnecessary under treatment plan commitment. We already can implement the first best with the restricted contracts. More general contracts can potentially improve outcomes when treatment plan commitment is invalid. However, the trade-off between efficiency, risk sharing, and incentives is complicated. We have found the characterization under such general contracts intractable. Apparently, separate analyses of demand-side and supply-side incentives are common in the literature, and we have chosen to study supply-side incentives. It is clear, however, that adding demand-side incentives would not permit the implementation of the first best because full insurance of financial risks cannot be achieved.