Academic journal article Journal of Risk and Insurance

Flexible Spending Accounts and Adverse Selection

Academic journal article Journal of Risk and Insurance

Flexible Spending Accounts and Adverse Selection

Article excerpt


I model the interaction of flexible spending accounts (FSAs) and conventional insurance in a simple discrete loss setting with asymmetric information. I show that FSA availability can break a separating equilibrium, even when one would otherwise exist, because high-risk types might prefer the lower-coverage contract supplemented with FSA funds. In this case there may exist a Pareto-inferior separating equilibrium. It is also shown that FSA availability alters the optimal pooling contract. Employers can reduce coverage levels, raising expected utility for low-risk types, and can compensate high-risk types by offering supplemental FSA coverage. Thus, it is possible that FSAs strengthen pooling contracts.


Flexible spending accounts (FSAs) for health care expenses offer an attractive way to avoid taxes. According to the Kaiser Family Foundation's Employer Health Benefits 2007 Annual Survey, 22 percent of all firms offering health insurance benefits offered FSAs as an option to their employees, but 73 percent of large firms (200 or more workers) offered FSAs. The advantage to the employee can be significant, although there is a financial risk. The advantage is that qualified expenses escape both state and federal income taxation and also all payroll taxes; the risk is that unused funds are forfeited to the employee's firm. Employers also avoid payroll taxes on employee elections.

FSA participation decisions are made concurrently with insurance plan choices each year during the firm's open enrollment period. Therefore, these decisions are made jointly and with the same information. Because FSAs reduce out-of-pocket costs, their availability should have predictable effects on insurance choices. Yet there is little theoretical or empirical work on the interaction of FSAs and insurance. Cardon and Showalter (2001) look at FSA usage patterns conditional on insurance choices, whereas Hamilton and Marton (2008) use panel data to examine the joint insurance/FSA choice.

I build on a simple insurance model used in Cardon and Showalter (2003). In that article individuals choose FSA participation levels in order to cover their out-of-pocket expenditures, taking the level of insurance coverage as given. It is shown that FSAs can be considered as a type of insurance, with FSA election amounts increasing in the level of risk, in risk aversion, and in the marginal tax rate, but decreasing in income level if risk aversion is decreasing in absolute risk aversion.

This article extends these results by allowing for endogenous insurance choice. I show that supplemental FSA coverage has the potential to break an existing separating equilibrium. In this case, there may exist a Pareto-inferior separating equilibrium. It is possible that FSA coverage can change the optimal pooling contract. Specifically, an employer can make both high (H) and low (L) risk types better off by reducing coverage, which L types prefer, and allowing H types to supplement partial insurance using FSA. Such a change may help to stabilize and strengthen risk pooling arrangements by making it less likely that L types will exit the pool.


An individual with initial, pretax income I > 0 and tax rate t faces a loss X < I(1 - t) that occurs with probability p. The individual has preferences defined over consumption C, represented by a smooth, concave utility function U(C) with U' > 0 and U" < 0. I assume that the individual is offered employment-based insurance contract with total premium [pi]q, where [pi] is the premium per unit of coverage and q is the amount of coverage. Consumption is equal to [C.sub.2] = (I - [pi]q)(1 - t) - X + q if the loss occurs and [C.sub.1] = (I - [pi]q)(1 - t) if no loss. The individual's problem is to choose q to maximize expected utility

EU(q) = pU([C.sub.2]) + (1 - p)U([C.sub.1]). (1)

Full insurance is when consumption is constant across states, or when [C. …

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