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In order to evaluate whether workers are over- or under-insured through the Disability Insurance (DI) program, we develop a framework that allows us to simulate the benefits as well as the costs associated with marginal changes in payment generosity from a representative cross-sectional sample of the population. Under the assumption that individuals are reasonably risk averse, we find that the typical worker would value increased benefits somewhat above the average costs of providing them. However, whether the benefit increases tend to lower or raise utility when we average across all individuals in our sample is sensitive to assumptions that affect the relative marginal utility of income to disabled individuals.

Disability status is increasingly used as a means for targeting resources in the United States. In 1999, 5.6 million disabled individuals and 1.6 million spouses and dependent children received a total of $42 billion in Disability Insurance (DI) benefits, representing over one-eighth of the Social Security budget for benefit payments. Given its importance and continuing growth, an evaluation of whether the DI program provides adequate insurance against the income losses associated with the onset of severe limitations is overdue. The empirical literature on DI has primarily focused on the impact of program parameters on the costs of the program, either in terms of caseload growth or reduced labor force attachment. This focus on the efficiency costs of DI provides an incomplete view of the social desirability of the program and of the adequacy of payment levels. The effectiveness of the program depends on how the costs relate to the social gains from redistributing toward individuals and states of the world with higher marginal utilities of income.1 What is striking is that there has not been any explicit valuation of the benefits associated with providing DI.2 In order to provide a more comprehensive view, our analysis accounts for both the benefits and costs associated with a marginal change in benefit generosity. Our goal is to determine whether, given the degree of moral hazard and screening stringency under the existing DI system,3 individuals are over- or under-insured, and which factors are important to drawing a conclusion. How an individual worker fares under this marginal reform depends on the expected change in lifetime utility. This expectation in turn depends on the impact on the path of family income and work effort both in the case where the worker becomes disabled and either successfully or unsuccessfully applies for DI and in the case where the worker never applies, and on the likelihood of each of these outcomes. Our approach is based on the intuition that if the population is in steady state, a representative cross-sectional sample of the population can be thought of as capturing the distribution of potential life-cycle paths for a representative individual or cohort. We can therefore use observed income and labor supply patterns to simulate the impact of increasing DI benefits for current recipients, potential new applicants, and workers in the sample. Combining data from the 1991 March Current Population Survey (CPS) with plausible assumptions about behavioral responses, we calculate the expected financial benefits accruing to and financial costs borne by each individual in the sample as a result of a 1% increase in DI payments. The ratio of the total costs associated with the reform to the increase in transfers to current recipients yields an estimate of the average implicit price of providing an additional dollar of income to recipients in the presence of moral hazard. This price exceeds one only to the extent that there are behavioral responses to the benefit increase that generate additional tax and transfer costs. We first use this average price to explore whether representative workers should find purchasing additional insurance through reduced take-home pay financially attractive.4 We then account for the underlying distribution of costs and benefits across workers, recognizing that the value of DI derives from its dual role as a program that redistributes resources across individuals as well as insures individuals against adverse events.5 To determine the lifetime incidence, we value the changes in income for each member of our sample assuming constant relative risk aversion.6 The sum of individual valuations describes whether or not individuals gain on average from the payment increase, where this average puts more weight on the low end of the income distribution due to diminishing marginal utility of income.7 Under our baseline assumptions, we estimate the total cost of providing an additional $1 of income to current DI recipients to be $1.50. While the load factor due to moral hazard is fairly high, we demonstrate that it is moderate enough that representative workers should be willing to “buy” additional insurance at this price. The reform, however, is not financed in proportion to expected benefits. The average implicit price of an additional dollar of insurance is actually much higher than $1.50 for more highly educated workers due to the redistributive nature of the program, so that representative workers from these groups would not find purchasing additional insurance attractive. Not surprisingly, when we average utility gains across workers, we predict that the reform leads to a net welfare loss for these groups regardless of the level of risk aversion. These qualitative results are robust to a series of sensitivity tests that employ alternative assumptions in the calculations. The average implicit price of insurance is always such that typical workers should find purchasing additional insurance attractive, and more highly educated workers never gain on average from the marginal increase given they bear a disproportionate share of costs. For this group, the average implicit price is less than $1. However, despite the fact that the typical worker faces a subsidy, the expected utility gain when we average across workers turns negative for dropouts under our baseline assumptions and high levels of risk aversion. This counterintuitive finding arises since the utility calculation weighs low-income states and individuals more heavily as risk aversion increases, and worker-years with current income below the floor provided to DI recipients help to finance the benefit increase.8 In fact, a modification that accounts for additional economic risks associated with disability leads to the expected pattern. Average utility gains for this group increase with the level of risk aversion when high out-of-pocket health care expenditures are treated as one of the costs associated with disability, lowering the income position of DI recipiency relative to other low-income states. We take this sensitivity to small permutations in the effective replacement rate to imply that the level of generosity is not too far from the level that would adequately insure individuals with low levels of human capital, holding the other program parameters constant. The results, as a whole, suggest that to the extent that individuals are over-insured under the DI system, it is not due to moral hazard costs.9 Rather, what drives these findings is that DI only insures against one kind of income risk. Benefit increases are to some extent paid for by able-bodied workers with low incomes and high replacement rates and by disabled workers who do not qualify for DI. This redistribution across various low-income states of the world represents a hidden cost of any across the board benefit increase and is relevant to other categorical transfer programs. The remainder of the paper proceeds as follows. The next section provides background on the DI program. Section 3 develops the conceptual framework we use to evaluate the welfare impact of increasing DI benefit generosity. 4 and 5 present and discuss the baseline results and sensitivity tests, and Section 6 concludes.

We develop three basic insights into the desirability of increasing DI benefits from our baseline analysis. First, while the indirect costs of benefit increases appear substantial, the value attached to such increases for the typical worker is also substantial. Given our estimated average implicit price of $1.50, representative workers of all education levels should be willing to purchase an additional $1 of disability insurance under moderate levels of risk aversion. Second, while the moral hazard costs appear to be relatively low, the implicit price of additional insurance can be quite large for some subgroups of the population due to redistribution. The implicit price of an additional dollar varies from less than $1 for individuals with less than a high school degree to more than $7 for individuals with a college degree. While the importance of redistribution across broad education categories has not been previously quantified, this pattern in implicit prices is not surprising given differences in the incidence of disability and in replacement rates. Our final conclusion is the least acknowledged and perhaps most surprising. We find that an increase in benefits leads to transfers from lower income individuals and states of the world to individuals and states with more moderate income, such that these transfers lead to net welfare losses at high levels of risk aversion. From an individual insurance perspective, a marginal increase in DI benefits is less attractive because of this potential redistribution to bad states from worse states. From a social perspective, inequality aversion also plays a role. This highlights that DI treats disability as a more “deserving” cause of low income than other negative shocks that affect able-bodied individuals, and that the disabled are treated as more deserving than the non-disabled poor. The incompleteness of the safety net could lead to similar counterintuitive findings for analyses of the adequacy of other categorical social insurance programs as well. Although our initial finding is that individuals are, if anything, over-insured against the subset of career-ending disabilities covered by DI, it is important to remember that we are evaluating a marginal change in benefit generosity. These results are derived in the context of a program that provides generous benefits to low-income workers who qualify. Our estimates of willingness to pay make it clear that individuals would/should place a high value on the existence of the program. Thus, an analysis that began from a base of less generous replacement rates would be expected to reach different conclusions. The fact that we do indeed reach the opposite conclusion about the adequacy of the income security provided by DI under the alternative model that incorporates health insurance, which alters effective replacement rates, highlights this point. Though our tools do not allow us to say much about the optimal level of DI benefits, this sensitivity of our results may imply that the current level is in the neighborhood of what would be conditionally optimal.