Tax Deductions for Losses and Equilibrium in Competitive Insurance Markets
Li, Chu-Shiu, Liu, Chwen-Chi, Yang, Chen-Sheng, Atlantic Economic Journal
Insurance is a common mechanism for transferring the burden of possible personal economic loss. Although the insured may receive indemnity if a loss occurs, this is not the only way to be compensated. Many countries incorporate loss deduction policies in their tax systems to subsidize consumer losses. The uninsured portion of personal losses, such as estate damages or medical expenses, is tax-deductible. In this way, consumers enjoy a reduced burden of losses even without insurance. Kaplow (1992) argues that a tax system with no deductions for personal losses is Pareto-superior to one with tax deductions which acts as partial insurance. Since tax deductions cause individuals to be less protected against risk in the aggregate, it is more efficient for governments to encourage individuals to purchase private insurance or to directly provide compulsory insurance.
In this paper, we examine how tax deductions for losses incurred may be Pareto-improving if there are inefficiencies in insurance markets due to adverse selection. In our view, although loss deductions might have a negative effect in creating moral hazard or in insurance markets without informational problems, the conclusion may be different if a loss deduction policy is administered in the context of adverse selection by including individuals with different risk types.
The main result we obtain is that circumstances exist under which tax allowances Pareto-dominate the free market separating equilibrium along the lines of Rothschild and Stiglitz (1976), RS hereafter. In other words, a loss deduction policy might help correct market failure due to adverse selection. A tax allowance system supported by income taxes creates cross-subsidization in insurance contracts that could reach the separating equilibrium but which cannot be achieved in a free market.
By incorporating risk types into the RS model, our paper contributes three major findings that are contrary to existing arguments about loss deduction policies. First, we analyze the demand for insurance under tax allowances for high-risk individuals. Normally a loss deduction policy provides some protection for high-risk individuals at the cross-subsidized population price in terms of an income tax, whereas with no loss deduction policy in the RS model, these individuals must purchase insurance at the risk-type-specific actuarially fair price. It is natural to conclude that as the effective insurance premium increases under the loss deduction policy, high-risk individuals would purchase less coverage. This argument holds for individuals with constant absolute risk aversion. However, a person with decreasing absolute risk aversion might treat insurance as a Giffen good when the income effect is greater than the substitution effect. In this situation, an increase in the tax rate might encourage these individuals to purchase more insurance.
Second, we find that the demand for insurance under tax allowances, both for high- and low-risk individuals, is less than that without such allowances. Given that high-risk individuals purchase only partial insurance under a loss deduction policy, insurers have the difficulty of identifying the risk type of individuals under asymmetric information. Thus, insurers would offer insurance contracts corresponding to their actuarial risk with lower coverage to low-risk individuals. Low-risk individuals would purchase less coverage under a tax system with loss deductions than one without them under adverse selection and in equilibrium.
Third and most importantly, we provide a positive view of loss deduction policies by showing that they more easily reach a separating equilibrium than does the free market in the RS equilibrium concept. The rationale relies on the fact that income tax rates under a loss deduction policy help raise the pooling insurance rate. In addition, the value of marginal rate of substitution at the equilibrium point for the low-risk contract would increase. …