Wednesday, March 17, 2010

GOP's Pete Sessions leads party in rate of uninsured constituents

Dallas Morning News article "GOP's Pete Sessions leads party in rate of uninsured constituents" (March 17th, 2010) reports on Republican Pete Sessions of Texas's 32nd Congressional District, near Dallas, and his opposition to the Obama medicare reform. Specifically, it takes issue with his opposition by noting that a number of his constituents have not purchased health care.

Rep. Pete Sessions' Dallas-area district has the highest rate of residents lacking health insurance of any Republican-controlled district in the country, according to census data. No other red districts are even in the top 10 of that unlucky club.

The median family income in the 32nd Congressional District of Texas is approximately the same as the median family income in the United States. The article ignores the possibility that a number of individuals in this district, which is not poor, find insurance a bad gamble.

Individuals purchase insurance because they would rather smooth their potential outcomes. One of the central reasons for this is that they gain less from gaining $100 than losing $100, and have diminishing marginal returns to income. Therefore, they trade the not-valued personal highs with the high-valued personal lows and gain. This is depicted graphically below (click to enlarge). The two red dots are an individual's possible uninsured wealth. For simplicity, let us say they have a 50-50 chance at both wealth levels. The happiness an individual gets out of these wealth levels is depicted as UWealth1 and UWealth2. However, they are able to smooth out their consumption and swap their bundled high and low to an insurance company in return for a single, constant wealth level (depicted as a green dot here), which is midway in-between the two wealth levels, given their 50-50 chance. The straight red line, along with proper weighting of chances, represents all possible fair bets. The green dot also denotes, due to the 50-50 chance, the expected utility, weighting UWealth1 and UWealth2 equally. The purple dot denotes an individual's utility if insured. We can see that the individual is better off with insurance (much of this graphics can be summarized by Jensen's inequality, and how it does not hold given subtraction of a constant).

However, insurance is not quite a fair bet, at the very least due to information asymmetries, overhead, and moral hazard. Note that Corrections refers to a "fair bet" as one whose expected gain or loss in monetary (not utility) terms is zero. It is reasonable to see why some people would not want to take an unfair bet, if they did not have particularly concave utility functions, as depicted below (click to enlarge). Now, our utility if we are insured is lower than our expected utility if we are not insured. This is because even our concave utility function could not overcome the unfair pricing we faced. Note that our bets are no longer constrained to be on the red line. The bet depicted indicates the insurance company essentially weighed the low-wealth state as higher than it actually was (this may not be the case for this pricing to occur, but it helps give intuition).

It is not unreasonable to see this as a possibility for the not-poor residents of the Dallas area. To conclude that the residents of Texas's 32nd Congressional District would be better off being forced to buy subsidized insurance is an empirical question, not one solved simply by noting that they do not currently have insurance.

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