Considerable attention in the U.S. has been focused on the development of high deductible insurance plans, largely with the expectation that consumers facing the full price of medical care will make more efficient consumption choices. While moving to higher deductibles should reduce spending below the deductible, economic theory does not provide strong rationale for spending above the deductible to be any different in a high deductible plan than in an otherwise similar health plan with a lower deductible. Proponents, however, argue that there might be savings and some data provides at least indirect support. For example, the Rand Health Insurance Experiment suggests sizable savings associated with increasing deductibles and, since most of the spending in any population is centered in people with high levels of spending, this would seem to imply savings at the high end of the distribution. Understanding whether or not high deductible health plans can affect high-spending patients is important for assessing their likely impacts on spending. To investigate, we reexamine data from the Rand Health Insurance Experiment. In parts of the HIE, some families were randomized to health plans with no deductible, and others were randomized to plans with deductibles of either $1,000 or a percentage (5, 10, or 15%) of their total family income, whichever was smaller. We examine spending patterns in these two groups, focusing on spending patterns at and above the deductible. We make the assumption that there is a relationship between the amount a family would spend if they were in a 0 deductible plan and the amount they would spend in a plan with a higher deductible, which can be expressed as an invertible function of the deductible (and other characteristics). We then use the fact that we observe the distribution of spending in a population with 0 deductible, and a matched (randomized) population with non-zero but known deductibles, to estimate the parameters of this function. Specifically, for any hypothesized set of function parameters, we can apply the inverse of the function to the observed spending by families in the deductible arm of the HIE and estimate what their spending would have been had this population been in a 0 deductible plan. The distribution of predicted spending can be compared to the true observed distribution of spending for persons randomized to the 0 deductible plan, and the difference between the two distributions can be summarized by Kolmagorov-Smirnov or similar statistics. This process can be performed iteratively over the space of possible function parameters to minimize the measures of deviation between the predicted and actual distributions, producing estimates of the optimal function relating spending in 0 deductible plans to spending in plans with higher deductibles. We find strong evidence for reduced spending in higher-deductible plans below the deductible, as might be expected. However, we find no evidence for reductions in spending above the deductible. This is consistent with the view that the potential for high deductible health plans to significantly reduce spending at high points in the spending distribution is limited. We discuss the implications of this finding for predictions about savings from high deductible plans. We can also extend the model to allow for "acceleration" of spending as individuals approach the deductible, for faster spending below the deductible among those who might reasonably anticipate reaching the deductible, and for variations in spending patterns for families with different demographic characteristics. We are currently exploring these extensions
