A Theory of Crowdout and Group Insurance

care and health are in fact the very same. The design of the Oregon lottery measures the treatment effect for the average of the lottery- eligible adults. In contrast, this study focuses on the local treatment effect for the parents of the marginally eligible child. This study considers these marginal parents in all sampled states, so it may be con- sidered more general in some ways, as Koch 2013 fi nds a great deal of variation in treatment effects across states. My work also relates to Anderson, Dobkin, and Gross 2012, which uses regression discontinuity on a different threshold—the age 19 cutoff for public health insurance plans. Similarly, they estimated a large drop from public to no insurance, though they had limited data on medical spending and its sources. Their fi ndings on emergency and inpatient care are not a contradiction to my work; they focus on a separate population, using a different source of identifi cation. Moreover, their estimated dropoff in insur- ance is ostensibly forced as children age out of insurance, while the rise in uninsurance here is at least partly a matter of choice. A similar RD design was employed in two studies of the causal effects of Medi- care—Card, Dobkin, and Maestas 2009 and Card, Dobkin, and Maestas 2008. Like Anderson, Dobkin, and Gross 2012, a discontinuity in age, not income, was used to fi nd the causal impact of a separate public insurance program. Those studies focused on the impact of Medicare as it creates near- universal insurance for the newly elderly population. The predominant transition under study here, the switch from private to no insurance, is related to studying the universalization of insurance due to Medicare. This is, again, a test of the generalizability of the results for Medicare to the broader adult population. Use of age cutoffs raises a more general concern that the strategy used here avoids. When using an RD design in age, the empirical specifi cation compares the just- eligible to the about- to- be- eligible. Absent extreme discounting, the treatment effect calculated with that comparison may not be valid when individuals gain or lose eligibility with something less than exact predictability. Previous estimates, such as those found in Currie and Gruber 1996a, 1996b, found that increasing the number of eligible children would lead to increases in the quality and quantity of care. While seminal contributions to the literature, their data were limited either to survey questions of healthcare use “Did you go to the doctor in the previous year?” or focused measures of utilization on special groups the healthcare quantity and outcomes of pregnant women and their newborn children. Here, we can bridge those two works by utilizing data that is both focused on a variety of healthcare outcomes but also provides a representative sample of those on the margin of public policy.

II. A Theory of Crowdout and Group Insurance

Consider a household H with N = sizeH members. In the absence of public programs, full insurance has value π i to each member i ∈ H. The cost of insuring each member is p i . In a market unfettered by household- level constraints, a member of the household is insured if π i p i and not otherwise. However, such constraints do exist in the employer- provided group market. In par- ticular, insurance typically must be taken up by the parent before it can be acquired for the child. Thus, it may be the case that the parent would not take up employer- provided insurance him- or herself π parent p parent but would when that insurance is bundled with insurance for a dependent π parent + π dependent p parent + p dependent . Also, with group insurance, there is a disconnect between individual- level charac- teristics, such as health and expected medical costs, and the price of insurance. In a competitive market with symmetric information, we would expect π parent + π dependent p parent + p dependent to hold as a consequence of each component inequality π i p i via risk aversion. However, with group insurance, each component inequality may not hold. When a child becomes eligible for public health insurance, this provides a low- cost and lower- quality substitute for private insurance. 1 The theoretical model of Cutler and Gruber 1996, itself an extension of Peltzman 1973, describes why and when this would happen. The public insurance offer will diminish the consumer surplus from private health insurance, π dependent – p dependent , and potentially reverse the household- level insurance bundle choice. The effects measured here may not be due purely to changes in insurance. The switching of children from private to public insurance, and the dropping of insurance for the parent altogether, coincides with a pretax growth in income, p parent + p dependent , or whatever fraction of that is returned to the employee when insurance is not part of compensation. If healthcare both quantity and quality is more normal than other goods, this should bias the estimates up that is, make them less negative.

III. Data and RD Design