Individual Insurance Decisions under HR 3560 and HR 3962

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In an effort to induce a larger number of individuals in the United States to purchase health insurance and thereby reduce problems of adverse selection that would otherwise interfere with simultaneous efforts to limit medical underwriting and abolish pre-existing condition exclusions, legislation under debate in the United States Congress imposes penalties on most households that do not have and that do not purchase health insurance. This Demonstration examines the expected position of households under the two leading bills based on the household's decision whether to purchase insurance or whether to pay a penalty instead.


The Demonstration has four banks of parameters, each of which may be selected by the user. The "medical expenses" bank lets you select a lognormal distribution of the medical expenses a household faces during a year. A loglog plot displays the distribution you have selected. The "insurance contract" bank lets you select the premium, deductible, coinsurance, and out-of-pocket limit for a health insurance policy. A plot shows the payment resulting from each level of medical expense. The "penalties" bank lets you select the penalty that will be assessed against households who fail to have or purchase health insurance the government deems acceptable. This bank lets you select the penalty directly or lets the computer calculate the penalty based on your choice of which reform legislation passes and various factors relevant to that computation under each piece of reform legislation. The bank includes information on the size of the directly set or calculated penalty. The "advanced" bank lets sophisticated users select a risk aversion level for the household. A plot shows the "spectral risk function" corresponding to the selected risk aversion parameter. Tooltips provide further information on each of the controls.

The Demonstration outputs a table showing the expected position of the insured if it purchases the insurance contract and the expected position of the insured if it fails to purchase the insurance contract and instead pays a penalty. These expected positions are weighted using the risk aversion parameter so that worse outcomes are weighted more heavily. The decision that results in the smallest loss to the insured is highlighted in orange.


Contributed by: Seth J. Chandler (March 2011)
Open content licensed under CC BY-NC-SA



This Demonstration does not attempt to incorporate moral hazard, the proclivity of insurance to induce more of the behavior insured against, in this case using covered medical services. It omits this complication (a) because modern health insurance contracts through use of deductibles, coinsurance, and various exclusions such as medical necessity reduce moral hazard and (b) because one would then have to ascribe monetary value to the possible diminution in health status resulting from reduced medical services.

Using "spectral methods" to address risk aversion is discussed in a variety of sources. See, for example, the Wikipedia page for Spectral Risk Measure, or C. Acerbi, "Risk Aversion and Coherent Measures: A Spectral Representation Theorem,", 2001, or K. Dowd, J. Cotter, and G. Sorwar, "Spectral Risk Measures: Properties and Limitations," Journal of Financial Services Research, 34(1), 2008 pp. 61–75.

Snapshot 1: the same settings as in the "thumbnail", but showing the "medical expense" control bank

Snapshot 2: the same settings as in the "thumbnail", but showing the "insurance contract" control bank

Snapshot 3: the same settings as in the "thumbnail", but showing the "advanced" control bank; in this instance, risk aversion is set to zero

Snapshot 4: using the simple "direct" interface under which the penalty is set explicitly by the user

Snapshot 5: using the "computed" interface and setting the bill to HR 3590 to expose the parameters that determine the applicable penalty

Snapshot 6: using the "computed" interface and setting the bill to HR 3962 to expose the parameters that determine the applicable penalty

Snapshot 7: setting the year to 2018 and an inflation setting of 4% under HR3590

Snapshot 8: setting the mean medical expenses to $2,000 and the standard deviation to $4,000

Snapshot 9: setting the penalty directly to $500 and using low (0.5) risk aversion

Snapshot 10: setting the penalty directly to $500 and using high (3.0) risk aversion

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