No more than 1% of those with household incomes between 139% and 400% and eligible to select a plan on the individual Exchanges have thus far done so. This is the information about those with middle incomes and lower-middle incomes one can derive from statistics released this week by Health and Human Services. The rate of plan selection among those with incomes over 400% of the federal poverty level is at least 3 times higher than that of persons with middle and lower-middle incomes. It could well be 4 times greater.

No matter how you fine tune the computations, I believe it is fair to say that the middle class is finding the carrots too small and the sticks too small. Some of this may be due to difficulties with the enrollment process rather than the underlying architecture of incentives under the ACA, but either way, most of those eligible to do so, are, at least for now, rejecting the benefit theoretically available to them on the individual Exchanges under the Affordable Care Act.

## Visualization

Here are two figures showing the results of my calculations in more detail.

### Rates of Take Up

The first graph shows the absolute rates of take up (selection of a plan) among with lower-middle and middle incomes (the lower surface) and the wealthier (the higher surface). The x-axis of the graph shows the assumption one makes about those reasonable eligible to purchase policies. When x is low, one assumes the income distribution of the eligible pool most closely resembles that of persons currently without health insurance. When x is high, one assumes the income distribution of the eligible pool most closely resembles that of persons currently with health insurance form their employer. The y-axis of the graph shows the assumption one makes about the number of persons current with health insurance from their employer who might reasonably be considered eligible to purchase insurance on a health insurance Exchange. A low value of y means that very few of these people should be considered eligible. A high value of y means that 10% of these people should be considered eligible. The z-axis (vertical) shows the fraction of people eligible to do so who have to date selected a policy on an Exchange.

As one can see the values are always less than 1% for the lower-middle and middle incomes. The values for the wealthier depends on the assumptions made but for all values are below 6% and is frequently below 4%. And these are values for selection of a plan, not for actual purchase of a policy. Those numbers are likely to be even smaller due to many people leaving items in their “shopping cart” without paying at the check out counter.

### Take Up Ratios

The second graphic shows the ratio between the take up rates among the wealthier and the take up rates among the lower-middle and middle income group. The x and y axes are the same as before. A value of 3.4 on the z-axis means that the take up rate among the wealthy is 3.4 times what it is among the lower-middle and middle income groups. As one can again see the ratio is above 3 for almost all assumptions one could make and is frequently above 4.

## Show me the calculation

How do I get to these figures? Algebra. Some of it is very nasty algebra, but I have the world’s best computer algebra system, Mathematica, at my disposal to make the problem much easier. Rather than include the somewhat complex computations directly in this blog post, I’m going to include a PDF file showing the computations and a CDF file (a Mathematica file format). You can read the CDF file either with Mathematica itself or with the free CDF Player available here. The data, by the way comes from a combination of this tidbit of information found on page 7 of the report released by HHS on December 11, 2013, and data from the Urban Institute and Kaiser Foundation.

## Sources

Distribution of the Nonelderly Uninsured by Federal Poverty Level (FPL)

Distribution of the Nonelderly with Employer Coverage by Federal Poverty Level (FPL)