Tax Sharing in Insurance Markets: A Useful Parameterization

ABSTRACT We use a principal-agent framework to evaluate the economic impacts of imposing a tax on insurance payment in presence of moral hazard using a Gamma conditional distribution of losses. Our results show that any tax paid by the insured would lower his effort to prevent loss, hence increasing insurance payments and decreasing profits. This result is reinforced as the insured becomes more risk averse unless the distribution of losses is uniform. We find that any decrease in the insurer's tax share would generate an overall decrease in welfare unless the insured characteristics prevent him from reacting to the policy. INTRODUCTION During the past few years, much attention has been placed on possible revenue sources to pay for health care. The recent political interest has been to tax insurance companies: the Baucus plan levies a nondeductible excise tax of 40 percent on insurance companies. In many insurance markets, the insurance provider determines the premium based on a coverage amount chosen by the insured. As a result, a tax on the premium amount corresponds to a proportional tax on the coverage amount. For example, in the long-term care insurance market, the future insured is prompted to choose a monthly benefit during the contract negotiation. In this article, we analyze the economic impacts of imposing a tax on payments out to the insured. The question then is: should the insurance provider pay the full amount of the tax as is proposed or should the insured bear a portion of it? And in case the insured bears a portion of it, should this portion be attributed uniformly across contract types? To answer these questions, we generalize the analysis to a case where the tax could be shared between the insurer and the insured. Unfortunately, the presence of asymmetric information in insurance markets complicates the analysis (Chiappori and Salanie, 1997, 2000; Dionne, Doherty, and Fombaron, 2000, Forthcoming; Villeneuve, 2000; Abbring, Chiappori, and Pinquet, 2003, to name a few). The lack of care enforcement on the part of the insurer, that is, moral hazard, complicates the welfare outcome of any policy aiming at redistributing health care coverage (see, e.g., Dionne et al., 1997; Doherty and Smetters, 2005, for empirical evidence of moral hazard in insurance markets; see Ketsche, 2004, for an empirical analysis of the impact of a subsidy on welfare). Indeed, the more health insurance an individual acquires, the lower his risk. This improves the social welfare of those with greater coverage. But as his coverage increases, the insured subsequently invests less in self-protection and consequently increases his use of health care services. This increased demand causes increases use of services, which results in higher prices, thus having the opposing effect on social welfare. Because risk-averse consumers would not purchase this additional care if they had to pay the full cost, the value of the extra service to consumers falls short of the social cost of producing that care. Therefore, although risk sharing increases social well-being, the change in moral hazard induces welfare loss. Early theoretical studies on moral hazard in insurance markets (Arrow, 1963; Pauly, 1968; Shavell, 1979) proposed solutions to the moral hazard issue. The solutions included (1) an incomplete coverage against loss, which gives the individual an incentive to prevent loss by exposing him to some financial risk (see Wang, Chung, and Tzeng, 2008; Chiappori et al., 1997; Koc, 2011, for empirical evidence of this solution in the market for automobile insurance and for physician services insurance, respectively) and (2) the observation of care, to link it to the premium or coverage in the event of a claim. The impossibility to fully observe care, however, has led to an increasing literature on the design of optimal contracts (Lewis and Sappington, 1995; Winter, 1992, 2000; Gollier, 2000; Doherty and Smetters, 2005). …