On December 17, 2013, the Kaiser Family Foundation published an influential study that comforted many supporters of the Affordable Care Act who had been made nervous by early reports that the proportion of younger persons enrolling in Exchanges was significantly less than expected. If true, such a disproportion could have created major stress on future premiums in the Exchanges because the private Exchange system under the ACA depends — or so it was thought — on younger persons subsidizing older persons. The Kaiser study asserted, however, that even if one cut the number of younger persons by 50%, insurer expenses would exceed insurer premiums by “only” 2.4%. This finding under what it thought was a “worst case scenario” underpinned Kaiser’s conclusion that a “premium death spiral was highly unlikely.”

This post evaluates the Kaiser analysis. I do so in part because it disagreed a bit with my own prior findings, in part because it has gotten a lot of press, and because I have had a great deal of respect for Kaiser’s analyses in general. I conclude that this Kaiser analysis rests, however, on an implausible assumption about the behavior of insurance purchasers and lacks much of a theoretical foundation. Once one eliminates this implausible assumption and employs a better theory of insurance purchasing, the threat of a death spiral becomes larger.

The reason for all this is a little complicated but try to bear with me and I will do my best to explain the problem. Essentially, what Kaiser did was to run its simulation simply by lopping off people under the age of 34 and assuming that, for some reason, the disinclination of people to purchase health insurance on an Exchange would magically stop at age 34. Thus, if an enrollment of, say, 2 million had been projected to come 800,000 from people age 18-34, 600,000 from middle aged people and 600,000 from the oldest group of enrollees, the “worst case” scenario Kaiser created (Scenario 2) would reduce enrollment to 1.6 million by having 400,000 come from people age 18-34, 600,000 from middle aged people, and 600,000 from the oldest group of enrollees. Thus, the youngest group would now constitute 25% of enrollees rather than 40%, and the other groups would constitute 37.5% of enrollees rather than 30%.

Although there is often nothing automatically wrong with this sort of “back of the envelope computation” — I have done many of them myself — sometimes they give answers that are wrong in a meaningful way. And sometimes “meaningful” means a difference of just a few percentage points. Thus, although the difference between 0.045 and 0.024 is not large on an absolute scale, this is one of these instances in which there could be a big difference between predicting premium increases augmented by 2.4% due to this particular form of adverse selection and predicting a premium increases augmented by 4.5% due to this particular form of adverse selection. The first might be too small to lead to a quick adverse selection death spiral; the second, particularly if it combined with other factors increasing premiums, might be enough to start a problem. Death spirals are a non-linear phenomenon a little like the “butterfly effect” in which small changes at one point in time can cascade into very large changes later on. What I feel comfortable saying is that the additional risk of a death spiral created by disproportionate enrollment of the an older demographic is greater than Kaiser asserts.

By simply lopping off the number of people under 35 who would enroll, the Kaiser model lacked a good theoretical foundation. The model Kaiser should have run — “Scenario 3″ — is one in which the rate of enrollment is a sensible function of the degree of age-related subsidy (or anti-subsidy). Their two other scenarios could then be seen as special cases of that concept. Had they run such a “Scenario 3″, as I will show in a few paragraphs, the result is somewhat different.

Let me give you the idea behind what I think is a better model. I’m going to present the issue without the complications created by the messiness of data in this field. We need, at the outset to know at least two things: (1) the number of people of each age who might reasonably purchase health insurance if the subsidy were large enough (the age distribution of the purchasing pool); and (2) the subsidy (or negative subsidy) each person receives for purchasing health insurance as a function of age. By subsidy, I mean the ratio between the expected profit the insurer makes on the person divided by the expected expenses under the policy, all multiplied by negative one. The bigger the subsidy, the more money the insurer loses and the more likely the person is to purchase insurance.

Suppose, then, that the probability that a person will purchase health insurance is an “enrollment response function” of this subsidy. For any such enrollment response function, we can calculate at least three items: (1) the total number of people who will purchase insurance; (2) the age distribution of purchasers (including the “young invincible percentage” of purchasers between ages 18 and 35); and (3) — this is the biggie — the aggregate return on expenses made by the insurer. Thus, some enrollment response function might result in 6.6 million adults purchasing insurance of whom 40% were “young invincibles” that generated a 1% profit for the insurer on adults while another enrollment response function might result in 2.9 million adults purchasing insurance of whom 20% were “young invincibles” that generated a 3% loss for the insurer on adults.

What we can then do is to create a family of possible enrollment response functions drawn from a reasonable functional form and find the member of that family that generates values matching the “baseline assumptions” made by both Kaiser and, apparently, by HHS about total enrollment and about the “young invincible percentage.” We can then calculate the aggregate return of the insurer on adults and call this the baseline return. What we can then do is assume different total enrollments and different young invincible percentages, find the member of the enrollment response function family that corresponds to that assumption, and then calculate the new revised return on adults. The difference between the baseline return and the new revised return on adults can be thought of as the loss resulting from this form of adverse selection. There are a lot of simplifications made in this analysis, but it is better, I believe, than either the back of the envelope computation by Kaiser that has gotten so much press and, frankly, the back of the envelope computation I did earlier on this blog.

Here’s a summary of the results. When I (1) use the Kaiser/HHS age binning of the uninsured and indulge the simplifying assumption that the age distribution is uniform within each bin; (2) use Kaiser’s own estimate of the subsidy received by each age, (3) assume 7 million total purchasers ; and (4) assume 40% young invincibles with uniform age distribution within age bins, I find that the baseline return on adults is 1.0%. When I modify assumption (3) to have 3 million total purchasers and, as Kaiser did in Scenario 2, modify assumption (4) to have 20% young invincibles, the baseline return on adults is -3.5%. **Thus, a better computation of Kaiser’s worst case scenario is not a reduction in insurer profits of 2.4%, but rather a reduction of 4.5%. **

The graphics here compare enrollment rates, the age distribution of enrollees and various statistics for the baseline scenario and the scenario in which there are 3 million total purchasers and approximately 20% young invincibles.

We can use this methodology to run a variety of scenarios. I present them in the table below. A Mathematica notebook available here shows the computations underlying this blog entry in more detail. I am also making available a CDF version of the notebook and a PDF version of the notebook.

Please note that the computations engaged in here essentially ignore those under the age of 18. This is unfortunate, but I do not have the data on the expected premiums and expenses of children. It does not look as if Kaiser had that data either. Since children are expected to comprise only a small fraction of insured persons in the individual Exchanges, however, this omission probably does not change the results in a major way.

### A humbling thought

The more I engage in this analysis, the more I realize how difficult it is. There are data issues and, more fundamentally, behavioral issues that we do not yet have a good handle on. Neither my model nor Kaiser’s model can really explain, for example, why, as has recently been noted, enrollment rates are so much higher in states that support the ACA by having their own Exchange and with Medicaid expansion than in states that more greatly oppose the ACA. As I have suggested before, there is a social aspect and political aspect to the ACA that is difficult for simple models to capture. Moreover, as I noted above, this is an area where getting a number “close to right” may not be good enough. Premium increases of, say, 9% might not trigger a death spiral; premium increases of 10% might be enough. And neither my nor anyone else’s social science, I dare say, is precise enough to distinguish between 9% and 10% with much confidence.

So, longer though it makes sentences, and less dramatic as it makes analyses and headlines, the humbling truth is that we can and probably should engage in informed rough estimates as to the future course of the Affordable Care Act, but it is hard to do much more as to many of its features. I wish everyone engaged in this discussion would periodically concede that point.

## Other Problems with Kaiser

There are other issues with the Kaiser analysis. Let me list some of them here.

### Even accepting Kaiser’s analysis premium hikes would likely be more than 2%

Kaiser’s discussion of insurer responses to losing money is inconsistent. Look, for example, at this sentence in the report: “[i]f this more extreme assumption of low enrollment among young adults holds, overall costs in individual market plans would be about 2.4% higher than premium revenues.” Kaiser further reports “Insurers typically set their premiums to achieve a 3-4% profit margin, so a shortfall due to skewed enrollment by age could reduce the profit margin of insurers substantially in 2014.” I don’t have a quarrel with this sentence. But then look at what the Kaiser report says. “But, even in the worst case, insurers would still be expected to earn profits, and would then likely raise premiums in 2015 to make up the shortfall,” No! According to Kaiser’s own work, “even in the worst case,” insurer costs would be 2.4% greater than premium revenues. Since there is little float in health insurance and investment return rates are low these days, insurers would likely not earn profits. Then it gets worse. “However, a one to two percent premium increase would be well below the level that would trigger a “death spiral.” Perhaps so, but if insurers need to earn 3-4% to keep their shareholders happy and they are losing 1-2%, a more logical response would not be a 1-2% increase in premiums but a 4-6% increase. And, as Kaiser points out, larger premium increases could trigger a premium death spiral in part because death spirals are like avalanches: they start out small, only a little snow moves, but once the process starts it can become very difficult to abort.

### Logical Fallacies

The first paragraph of Kaiser’s report asserts: “Enrollment of young adults is important, but not as important as conventional wisdom suggests since premiums are still permitted to vary substantially by age. Because of this, a premium “death spiral” is highly unlikely.” Even if the first sentence of this quote were correct — a point on which this entry has cast serious doubt — the second sentence does not follow. To use a sports analogy, it would be like saying that, the role of a baseball “closer” is important but not as important as conventional wisdom suggests. Therefore the Houston Astros, who lack a good closer, are highly unlikely to lose. No! There are multiple factors that could cause an adverse selection death spiral. Just because one of them is not as strong as others make out, that does not mean that a death spiral is unlikely. That’s either sloppy writing or just a pure error in logic.

### Other Factors

And, in fact, if we start to look at some of those other factors, the threat is very real. As discussed here in more depth, I would not be surprised if adverse selection based on completely unrated gender places as much pressure on premiums as adverse selection based on imperfectly rated age. And, as I have discussed in an earlier blog entry, the transitional reinsurance that somewhat insulates insurers from the effects of adverse selection will be reduced in 2015. This will place additional pressure on premiums.

And, on the other hand, the individual mandate, assuming it is enforced, will triple in 2015 and risk adjustment measures in 42 U.S.C. § 18063, will likely provide greater protection for insurers. These two factors are likely to dampen adverse selection pressures.

### Notes on Methodology

There are a number of simplifying assumptions made in my analysis. Some of them are based on data limitations. Here are a few of what I believe are the critical assumptions.

1. Functional form: I experimented with two functional forms, one based on the cumulative distribution function of the logistic distribution and the other based on the cumulative distribution function of the normal distribution. These are both pretty conventional assumptions and make sure that the enrollment rate stays bounded between 0 and 1. The results did not vary greatly depending on which family of functions the enrollment response functions were drawn from.

2. Uniform distribution of ages within each age bin of potential purchasers. I believe this is the same assumption made by Kaiser and it results from the absence of any more granular data on the age distribution of the uninsured that I was able to find.

3. The enrollment rate depends on the subsidy rate standing alone and not other possibilities such as subsidy rate and age. The data on enrollment rates is very sparse and so it is difficult to use very complex functions. Perhaps a more complex analysis would assert that enrollment depends on both subsidy rate and age, since age may be a bit of a proxy for the variability of health expenses and thus of risk.