On the Value of a Checkup: Adverse Selection, Moral Hazard and the Value of Information

Abstract

INTRODUCTION The view that insurance deters people from taking medical checkups and diagnostic tests has had widespread currency during the debate over health care reform. If a test revealed favorable results (e.g., HIV negative or the absence of the genetic defect causing Huntington's disease), the insurer would probably lower the premium, but unfavorable test results would result in a prohibitive premium or uninsurability. This classification lottery clearly is unattractive to risk averse consumers and might dissuade them from taking the test despite any medical or public health benefits. This view has been aired in the scientific and popular press and has entered policy analysis in Washington (Tabarrok, 1994).(1) We will show that markets will provide optimal incentives for consumers to take diagnostic tests if there are initially informed and uninformed consumers and an option for treatment, and if information status and the test results are confidential. We will show that the social value of information revealed by diagnostic tests is also positive. Consumers must anticipate how their private knowledge will affect the choices they exercise from policy menus offered by insurers in a competitive market. We will show that the information revealed by the test has positive private value, thus encouraging consumers to be tested. This positive value arises jointly from the ability of consumers to hide information status and the value of the contingent option for treatment. Thus, competitive markets will encourage consumers to make socially optimal choices. Formally, our study addresses adverse selection, moral hazard and the value of information. We will show that the hidden nature of information status adds an important second dimension to the standard Rothchild-Stiglitz model. Self selection screening models traditionally start with an assumption that one agent is uninformed of the risk type of the others, and the uninformed party offers a menu designed to induce sorting. We start with both informed and uninformed consumers but the latter can choose whether to acquire information. Uninformed consumers must decide whether to take a test which will reveal their propensity for death or ailment. Insurers who are uninformed as to who takes the test or the results, offer a menu of life (or health) insurance policies(2) designed to induce self selection according to information status and test results. Moreover, insurers must anticipate that those taking the test may receive options for treatment which can be exercised after insurance is chosen, thus introducing an element of moral hazard. In choosing whether to take the test, consumers anticipate how information revealed will affect their choice from the insurer's menu and how they will exercise the treatment option. Thus, we model a game in which insurers cannot tell whether a consumer possesses hidden knowledge, and some consumers are initially uninformed but may choose to acquire hidden knowledge, thereby changing the nature of the informational asymmetry from one in which the uninformed cannot be contracted with separately ex ante to one like the Rothchild-Stiglitz model wherein all consumers possess hidden knowledge. We will show that taking the test is the dominant strategy for the uninformed for the preliminary information game and that the Nash equilibrium requires that all consumers become informed. This article is related to a previous literature on the social value of information, insurance classification, adverse selection, medical decision making, etc. We will mention only some of the closer fits. The social value of information has been addressed by Hirshleifer (1971) and Arrow (1978) who, extending the work of Dreze (1960), showed that improved public information may make everyone worse off (by eliminating opportunities to reallocate risk through trade). Milgrom and Stokey (1982) and Marshall (1974) show that if parties negotiate ex ante efficient contracts, subsequently generated information does not expand allocative opportunities and has no social value. …