We model flexible spending accounts (FSAs) as a special type of insurance policy. We prove the following results given losses drawn from a continuous distribution: (1) the optimal election amount, [F.sup.*], is increasing in the consumer's level of risk aversion; (2) [F.sup.*] is increasing in the level of the maximum loss; If utility is decreasing in absolute risk aversion (DARA), then [F.sup.*] is (3) decreasing in income and (4) increasing in the marginal tax rate.
Flexible spending accounts (FSAs) for health care expenses offer an attractive way to avoid taxes. A recent survey of 681 major U.S. firms suggests that 79 percent of these employers offered such accounts in 1995 (up from 51 percent in 1990) and that a rapidly growing share of employees are taking advantage of these offerings (Hewitt Associates, 1996). The advantage to the employee can be significant, although a financial risk exists. The advantage is that qualified expenses escape both state and federal income taxation and all payroll taxes; the risk is that unused funds are forfeited to the employee's firm at the end of a calendar year. Employers also avoid payroll taxes on employee elections.
Though the actual reduction in tax revenues due to FSA usage is unknown, the potential effect on federal revenues is quite large. As an example, consider that estimated out-of-pocket medical expenses for 1997 were nearly $190 billion (U.S. Bureau of the Census, 2000, Table 161). If only 15 percent of those expenses were paid for with FSA monies and the average individual faced a 15 percent federal income tax rate plus a 15 percent payroll levy (employer and employee portions), the reduction in federal tax revenue would be more than $8.5 billion.
Recent work by Cardon and Showalter (2001) explores a model of FSA participation and usage. The most general model consists of two time periods: In period 1, a risk-averse individual chooses how much income to allocate to the FSA (the "election" amount). The amount in the FSA is tax-exempt and is used to pay for health expenditures up to the election amount. Health status in period 2 is subject to un- certainty, and thus the choice is made in an expected utility framework. In period 2, health status is revealed and the individual chooses between consumption and health care expenditures. Health expenditures beyond the election amount reduce consumption of the numeraire good. If health expenditures are less than the election amount, the difference is lost (the "use-it-or-lose-it" provision of FSAs). This model is difficult to analyze due to its generality and leads to ambiguous comparative statics results. In another, more tractable framework, instead of facing a continuum of choices for health expenditures, th e individual faces a loss in the second period of a fixed amount with probability p. This model yields sharper comparative static results.
This article builds on this framework in two dimensions. First, we model losses as draws from a continuous distribution. Second, we show how distributional changes and differences in the level of risk aversion will affect the election amount. We discuss implications and possible extensions in the conclusion.
An individual with initial pretax income I > 0 faces a loss x [member of] [0, L] where the maximum loss L < I. The continuous, nondegenerate probability density function' for the loss is g(x) with a distribution function represented by G(x). The individual has preferences defined over consumption C, represented by a smooth, concave utility function U(C) with U' > 0 and U" < 0. The individual is eligible to participate in an FSA program that allows the loss (or a portion of the loss) to be paid out of pretax dollars. The FSA election amount F must be chosen prior to the realization of the loss. Losses in excess of F are not covered and unused funds are forfeited. (2)
One can consider FSAs in a traditional insurance framework. …