Tag Archives: adverse selection

Prices rising, choice declining for 2016 Obamacare

Data released yesterday at healthcare.gov shows the beginnings of an adverse selection death spiral that threatens the stability of the system of insurance created by the Affordable Care Act.  The data shows that, on plans using the “federally facilitated marketplace” created under the ACA, PPO plans that continued from 2015 to 2016 increased gross premiums an average of 16% and Gold and Platinum plans increased 15% and 21% respectively.  HMO plans, by contrast, increased a lesser 8% and Bronze and Silver Plans increased a lesser 12% and 9% respectively.  We should thus expect to see in 2016 relatively fewer people purchasing plans that give them a greater choice in physicians or that provide greater protection against medical expenses.

The tables below summarize the big picture.  The first table shows the mean change in gross premiums between 2015 and 2016 for plans that persisted over that timespan when grouped by metal level.  As one can see the more generous Gold and Platinum plans increased at rates considerably higher than the less generous Catastrophic, Bronze and Silver plans.

MetalLevel percent change
1 Bronze 12.1
2 Catastrophic 8.1
3 Gold 15.2
4 Silver 9.4
5 Platinum 20.9
mean change in premiums between 2015 and 2016 for 6,699 persistent plans

The second table shows the mean change in premiums between 2015 and 2016 for plans that persisted over that timespan when grouped by plan type.  As one can see the PPO plan, which offers the greatest choice of doctor, increased at a higher rate than other types of plans.  EPOs, which are similar to HMOs but restrict visits to specialists less, increased in gross premiums at a rate far higher than HMOs.

PlanType percent change
1 POS 12.3
2 HMO 8.3
3 EPO 12.2
4 PPO 16.5
mean change in premiums between 2015 and 2016 for 6,699 persistent plans

The third table combines the first two and shows, for each combination of metal level and plan type, the mean percentage increase in gross premiums between 2015 and 2016.

1 Catastrophic 1.9 5.8 6.9 14.8
2 Bronze 11.2 10.9 12.0 16.2
3 Silver 5.8 8.8 12.5 14.5
4 Gold 9.4 16.6 17.1 19.7
5 Platinum 12.2 25.6 7.5 25.9
mean change in premiums between 2015 and 2016 for 6,699 persistent plans

Premium increases are only part of the story, however.  Some types of plans are not available at any price any longer.  The table below shows the percentage of rating areas in 2015 and 2016 containing each type of plan.  Notice that the percent of rating areas containing any PPO has dropped significantly between 2015 and 2016; HMOs and POS plans have dropped as well, though EPO plans have become more prevalent.

PlanType AVG2015 AVG2016
1 HMO 92.6 88.6
2 EPO 78.3 82.5
3 POS 83.7 75.4
4 PPO 92.5 76.7
percent of rating areas having at least one of these plan types

We can also consider the prevalence of competition. The table below shows the percentage of rating areas in 2015 and 2016 containing at least two of each type of plan. Notice that with PPOs, the percentage of rating areas with competition has declined, although it has increased somewhat for HMOs, EPOs and POS plans.

PlanType AVG2015 AVG2016
1 HMO 71.3 72.5
2 EPO 66.5 74.0
3 POS 48.2 50.6
4 PPO 76.0 61.0
percent of rating areas having at least two of these plan types

The same analysis can be done on the metal levels of the plans available.  The table immediately below shows for 2015 and 2016  the percentage of rating areas in which there is at least one plan of the specified metal level.  Platinum plans have declined sharply in prevalence since 2015.  Now only just over half of the rating areas have even a single platinum plan available even if one were willing and able to pay the higher premiums.

MetalLevel AVG2015 AVG2016
1 Catastrophic 74.3 72.2
2 Bronze 91.8 88.1
3 Silver 91.1 89.7
4 Gold 90.9 88.5
5 Platinum 92.7 53.2
percent of rating areas having at least one of these metal levels

When it comes to competition, the picture is even worse for platinum plans.  In only about a third of the rating areas can one choose between platinum plans.

MetalLevel AVG2015 AVG2016
1 Catastrophic 33.5 30.3
2 Bronze 82.5 82.4
3 Silver 85.7 84.6
4 Gold 73.0 73.4
5 Platinum 44.9 34.6
percent of rating areas having at least two of these metal levels

Finally, since it seems to be the PPO plans whose prevalence is declining most, we can show the extent of that prevalence according to the metal level of the plan. The table below shows that the Platinum PPOs, the plan probably most helpful to the chronically ill that the ACA was supposed to help greatly, is diminish significantly in prevalence but that Gold and Silver PPOs are diminishing as well

PlanType MetalLevel AVG2015 AVG2016
1 PPO Catastrophic 85.8 71.1
2 PPO Bronze 94.9 81.6
3 PPO Silver 94.9 81.6
4 PPO Gold 94.9 81.6
5 PPO Platinum 89.5 53.5
percent of rating areas having at least one of these Platinum plan types


The data shows that platinum plans and PPO plans are shrinking in prevalence and that the gross premiums for such plans are going up. One might say that this development is not so awful since it leaves in place a market for more basic plans: HMO plans for example or silver and gold plans.  Perhaps the government should not be subsidizing individual’s choice of doctors or fostering plans, such as platinum plans, that fail to deter excess medical consumption.  Such is not, however, the promise of the ACA or, I suspect, the desires of many of its proponents.

Moreover, we are in a dynamic situation.  Think about next year when the insurer subsidies are supposed to disappear and when the chronically ill people who were in platinum and/or PPO plans migrate into the next best thing, a gold plan or, if one is available, a POS or EPO plan.  Suddenly those plans become vulnerable to adverse selection pressures.  And for 2017 we might thus expect to see yet further shrinkage of PPO and platinum plans and greater pressures on everything but the basic Bronze and Silver HMO plans.  When that happens, the adverse selection death spiral will not only start biting wealthier purchases or those with chronic conditions, but mainstream America. Private health insurance is fragile. It generally does not well withstand the sort of underwriting regulation imposed by the ACA.  The conceit of the ACA proponents was that they had engineered a system — the “three legged stool” so strong that it could resist the almost invariable pressures of adverse selection.  If I am right, and regardless what one thinks about the motives of those proponents, we are beginning to see that the engineering was just not good enough.

Caveats and further research

The computations shown above are based on the number of plans and not weighted by the number of enrollees.  This is largely of necessity since the federal government has not been releasing enrollment figure by plan in a clear way (although it may be possible to tease the figures out of rate review submissions filed and collated on healthcare.gov).  Although enrollment weighting will likely decrease the average mean premium (less expensive policies tend to be purchased more), it is not clear that enrollment weighting will have much effect on relative premium increases.

The figures are also not computed yet on a state-by-state basis, something that I hope to present in a later post.  They also contain only data for states whose plans are described in material available at healthcare.gov.  Data for states such as California and New York, which have their own exchanges, is not included here and might alter the numbers somewhat.

Finally, I present gross premiums here; as I have discussed at length elsewhere, net premium increases may well be higher, particularly where the purchaser wishes to retain a gold or platinum plan or a PPO plan whose premiums are rising even faster than those of the silver plans and the second lowest silver plan. The situation is worst where, due to some willingness on the part of a new entrant to take risk,  the second lowest silver plan drops in price, thereby decreasing subsidy levels, but other silver, gold and platinum plans increase in price.


Programming for this work was done in R using data from data.healthcare.gov and is available on request from the author. Packages used include data.table, tidyR, htmlTable and dplyr. There is a lot more work to be done mining these databases.

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Insurer losses in Exchanges of 10% not unlikely

Experts who have taken a look at the Affordable Care Act have separately considered the effects of three possible sources of unexpected losses by insurers selling policies in the individual Exchanges: purchasers being older than originally projected, more purchasers being women than originally projected, and purchasers having poorer health than originally projected.  And, at least with respect to the potential for age-based problems, the prestigious Kaiser Family Foundation has given supporters of the ACA considerable comfort by saying, worst case, older purchasers might result in only a 2.5% increase in insurer costs.  But no one to my knowledge — until now — has carefully considered the combined effects of these three sources of potential cost increases and, most likely, pressure for future premium increases.

I have now made an effort to consider the effects of these three sources of insurer losses acting together. Based on that effort, which represents the culmination of work over the past month, I believe it quite possible that insurer losses could amount to 10%, approximately 4% due to purchasers being older than expected, 1% due to greater purchases by women, particularly those in their 20s and 30s, and another 5% due to purchasers having poorer health than expected.

There are four major caveats that should be emphasized up front.  (1) These figures are estimates with large error bars; and anyone pretending to great exactitude in this field, particularly as much of the best data is not yet available, is, I suspect, likely pursuing more of a political agenda than a scholarly one. Losses could be close to zero; losses could be in the 15% range. Still, as I am going to show, significant losses are a serious possibility. (2) These losses are computed without consideration of “risk corridors” under section 1342 of the Affordable Care Act. That provision basically calls on taxpayers to pay insurers losing money on the Exchanges a significant subsidy. After consideration of Risk Corridors, average net insurer losses could range anywhere from close to zero to around 6%-7%. (3) These are national figures.  There are states such as West Virginia in which the age distribution is considerably worse right now than it is nationally.  One should not expect any of the rates of insurer losses (or profits) to be uniform across states or, indeed, across insurers. The figures developed here are an attempt at a  rough average. (4) The figures are based on the last full release of data by HHS on enrollment in the Exchanges; if matters change and, for example, the proportion of younger enrollees grows or the proportion of men grows, the loss rates I project here are likely to decline.

The graphic below summarizes my conclusions.  It shows insurer losses (or gains) as a function of a “health age differential” under two scenarios. By health age differential I mean the difference in ages between someone who has the expected health expenses of the actual enrollee and the chronological age of the enrollee.  Thus, if an enrollee was actually 53 but had the health expenses of an average 57 year old, their health age differential would be 4.  If they had the health expenses of a 50 year old, their health age differential would be negative 3. The yellow line shows insurer losses as a function of the health age differential assuming that the joint distribution of gender and age stays the way it was when HHS last released data.  The blue line shows insurer losses as a function of the health age differential assuming that the joint distribution of gender and age ends up the way it was originally projected to be.  As enrollment under the ACA increases and the proportion of younger enrollees increases, one might expect the ultimate relationship to head from the yellow line down to the blue line.  My assertion that losses could well be 10% is based on the assumption that the joint distribution of gender and age stays the way it is now but that the health of enrollees is equivalent, on average, to those 2 years older than their chronological age.  An assumption that enrollees could have health equivalent, on average, to those 4 years older than their chronological age, yields insurer losses of greater than 15% assuming the current joint distribution stays in place and about 10% assuming the original distribution ends up being correct.

The key graphic for this entry

The graphic above is useful because it gives what hitherto had been missing in discussions of problems in the individual Exchanges: some sense of the relative magnitude of problems created by age-based adverse selection (older people enrolling disproportionately) and health-based adverse selection (sicker people enrolling disproportionately). Roughly speaking, the degree of price increases induced by the current age and gender imbalances is roughly equivalent to what would occur if the health of the enrollees was, on average, equivalent to those of persons 2.5 years old than they actually are.

So what does it all mean?

At some point,  a journalist is likely to ask me what this all means?  Is there going to be a death spiral?  I would say we are right on the cusp.  Losses of 10% by insurers relative to expectations, coupled with whatever increase results from medical inflation, isn’t so enormous that I could say, yes, for sure we are heading into a death spiral. But neither is it such a small number that the risk can be ignored.  Moreover, as noted above, the 10% figure is a national average and we need to reduce it because of risk corridors.  In some states, however, where the age and gender figures may be worse or the health of enrollees is particularly problematic or where insurers just bid too low and the winner’s curse overtakes them, I still believe there is a substantial risk of a serious problem. In other states, where age and gender figures are better or insurers more accurately forecast the health of their enrollees, the risk of a death spiral is minimal. And, of course, the more people that actually end up purchasing policies in the Exchanges over the next few months, regardless of whether they come from the ranks of the previously uninsured or those who find that they can not keep their current policies, the more stable the system of insurance created by the ACA is likely to be.

So, after a lot of research, I feel more confident than ever in giving a lawyer’s answer —  it all depends — and a cliche — we’re not out of the woods yet.

Computation details

The results obtained here are based on essentially the same data as user by the Kaiser Family Foundation, which includes data on the relation between age and premium under typical plans, data from the Society of Actuaries (SOA), also used by Kaiser, on the relation between gender, age and expected medical expenses, and my own prior work attempting, based on data from the Department of Health and Human Services released earlier this month, to derive a joint distribution of enrollment in the individual Exchanges based on age and gender.  And, although the math can get a little complicated, the basic idea behind the computations is not all that difficult. It is essentially the computation of some complicated weighted averages.  Each combination of gender and age has some expected level of insurance cost (computed by the Society of Actuaries based on commercial insurance data) and some expected premium (computed by Kaiser based on a study of the ACA). Thus, if we know the joint distribution of gender and age, we can weight each of those costs and each of those premiums properly.

There are three areas of the computation that prove most challenging.  First, because HHS has not released all of the needed data, one must develop a plausible method of moving from the marginal distributions that were provided by HHS on enrollment by age and enrollment by gender into a joint distribution by gender and age. Second, one must calibrate the SOA cost data and the Kaiser premium data, which are expressed in somewhat different units,  such that, if the joint distribution of gender and age was as was originally expected an insurer would just break even.  And, third, one must develop a reasonable method of modeling insured populations that are drawn disproportionately from persons who have higher medical expenses. I believe I have now come up with reasonable solutions to all three issues.

Solution #1

The solution to the first issue, moving from a marginal distribution to a joint distribution, was detailed in my prior blog entry. In short, one finds a large sample of possible joint distributions that match the marginal distributions and scores them according to how well they match the property that people who are subsidized more likely to enroll.  One takes an average of a set of solutions that score best. There is an element of judgment in this process on the degree to which individuals respond to subsidization incentives and, all I can say, is that I believe my methodology is reasonable, avoiding the pitfall of thinking that subsidization is irrelevant or of thinking that it is the only factor that matters in determining enrollment rates. I present again what I believe to be the most likely joint distribution of enrollment by gender and age.

Plausible age/gender distribution of ACA enrollees
Plausible age/gender distribution of ACA enrollees

Solution #2

The solution to the second problem is obtained using calculus and numeric integration. One computes the expected costs and expected premiums given the original joint distribution of enrollees, which is taken to be a product distribution of which one distribution is a “Bernoulli Distribution” in which the probability of being a male or female is equal and the other is a “Mixture Distribution” in which the weights are those shown below (and taken from the  Kaiser Family Foundation web site) and the components are discrete uniform distributions over the associated age ranges.

Original estimate of age distribution of enrollees
Original estimate of age distribution of enrollees

The Society of Actuary data on the relationship between age, gender and medical costs is shown here.

Society of Actuaries data on gender, age and commercial insured expense
Society of Actuaries data on gender, age and commercial insured expense

The premiums under the ACA are shown here.

ACA Premiums
ACA Premiums

These two plots combined can give us a subsidization rate plot by gender and age.  It is shown below along with an associated plot showing the distribution of enrollees by age as was originally assumed and as appears to be the case.

Subsidization rates by gender and age along with anticipated and current age distribution of enrollees
Subsidization rates by gender and age along with anticipated and current age distribution of enrollees

Solution #3

To model adverse selection based on expensive medical conditions, I simply added a health age differential to the insureds.  That is, in computing expected medical costs, I assumed that people were their actual age plus or minus some factor.  (Ages after this addition were constrained to lie between 0 and 64). The graphic above showed insurer losses as a function of this “health age differential” under two scenarios.

Technical Note

A Mathematica notebook containing the computations used in this blog entry is available . here on Dropbox. I’m also adding a PDF version  of the notebook here. I want to thank Sjoerd C. de Vries for coming up with an elegant method within Mathematica of describing the joint distribution used in the computations of various integrals.  I am responsible for any mistakes in implementation of this method and my use of Mr. de Vries idea implies nothing about whether he agrees, disagrees or does not care about any of the analyses or opinions in this post.

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The distribution of individual market enrollees by age and gender combined

Earlier this month, the Department of Health and Human Services released more detailed information than it had before on the age distribution and gender distribution of enrollees in the individual markets serviced by the various Exchanges. What it did not do, however, and what needs to be done in order to better predict the likelihood of significant insurer losses in the Exchanges and, thus, greater pressure on premiums is to release data on the combined age and gender distribution of the enrollees. We don’t know, for example, how many woman aged 35-44 are enrolled in the Exchanges. This finer look at the data is important because, as discussed in a previous post, it is the combination of age and gender that bears a stronger statistical relationship to expected medical expenses.  And, while the ACA incompletely compensates for age in its premium rating scheme through dampened age rating, it does not compensate at all for gender.

With the help of Mathematica, I have combined some algebra and some numeric methods to try and reverse engineer out combined distributions of age and enrollment that meet various constraints. I believe I have succeeded in finding a plausible combined distribution that can be used in developing plausible models of the likely extent of adverse selection in the individual health insurance markets under the ACA. I present the result in the table below and the chart below. I then have a “how it was done” technical appendix.   My work involves creation of a high dimensional polytope that satisfies the existing data and then a search for points on that polytope that appear most plausible. I have also posted a Mathematica notebook on Dropbox that shows the computation.

Plausible age/gender distribution of ACA enrollees
Plausible age/gender distribution of ACA enrollees

The pie chart above first groups the enrollees by gender. The inner ring shows males and the outer ring shows females. It then groups the enrollees by age bracket. As one can see, women outnumber men significantly in the 18-45 group, are about equal among minors and those between age 45 to 55, and are outnumbered by men in the 55-65 age group.

The graphic below shows the same data, but now age is the first grouping mechanism.


I also attempted to find the combined distribution that would satisfy the observed marginal distributions of age and gender but that would greatly reduce adverse selection. The graphic below thus presents pretty much of a  “best case” for the combined age-gender distribution in the Exchanges. Notice that now it is only in the 18-35 year old age brackets that there are substantial variations in the rates of male and female enrollment. I very much doubt that the actual statistics are as promising for ACA success as depicted in the graphic below, but I present them here to show the sensitivity of my methodology to various assumptions.


Distribution of enrollees by age and gender that would substantially reduce adverse selection
Distribution of enrollees by age and gender that would substantially reduce adverse selection

The next step

The next step in this process is to try to compute the difference between premiums and expenses based on these  combined age-gender distributions.  I will then compare it to the difference between premiums and expenses based on an age-gender distribution that might have been expected by those who earlier modeled the effects of the ACA.  The result should provide some insight into the magnitude of combined age-based and gender-based adverse selection.  It should be similar in spirit to the work I showed earlier on this blog here. I hope to have that analysis posted later this week or, I suppose more realistically given my ever pressing day job, early next week.

How it was done

I have essentially 12 variables we are trying to compute: the number of enrollees in the combination of two genders and six age brackets. I know 9 facts about the distribution based on data released by HHS. I know the total number of males and females and I know the total number of persons in each age bracket.  And I have 12 constraints on the values: they must all be positive. Using Mathematica’s “Reduce” command, I can use linear algebra to find the polytope that satisfies these equations and inequalities. I get an ugly expression, but it is one Mathematica can work with.

I can then sample 12-dimensions points on the polytope using Mathematica’s “FindInstance” command. I found 2400 points. Each of these points represents an allocation of enrollees among age and gender that satisfies the known constraints. I can then score each point based on its “distance” from my intuition about the strength of adverse selection. That intuition is expressed by “guesstimating” likely ratios between males and females for each of the six age groups.  I use a “p-Norm”  and Mathematica’s “Norm” command to measure the distance between the six male/female ratios generated by each of the 2400 points and my intuition.  I then take the 10 best 12-dimension points and thus obtain a 10x2x6 array. I take the average value of each of the 12 values over all 10 sample points.  It is that average that I show in the first two graphics above.

I then permitted the strength of adverse selection to vary by exponentiating the ratios in my intuition. By setting the exponent to zero, I basically try to minimize gender-based adverse selection and keep the gender ratios as close to each other as possible. The results of this effort are shown in the final graphic.


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Small business, the ACA and a second potential debacle

Small_Businesses_and_Obamacare___National_Review_OnlineThe following are excerpts of an article written by me and published in the National Review Online.  It’s available here. I recommend starting here, seeing if you are interested, and then clicking over to the National Review to read the entire article.

We could be about to see the same clumsy reconciliations of egalitarianism and freedom [that we see in the individual market provisions of the Affordable Care Act] ensnare the nation’s 6 million or so small businesses, the 40 million–plus people they employ, and the millions more spouses and children who depend on those employees. If only because the number of people involved is so much larger, the consequences and the stresses created could be even more serious than those we have seen playing out over the past few months in the individual market. The major points of tension here are (1) the prohibitions in section 1201 of the ACA on experience rating and medical underwriting in policies sold to small employers; (2) the requirement, also in section 1201, that, if a small business purchases group health insurance from a state-regulated insurer, it must provide the same sort of generous protections (including “essential health benefits”) as do individual policies; and (3) the effective tax that section 1421 of the ACA (section 45R of the Internal Revenue Code) places on wage increases and hiring by some small businesses that choose to offer health insurance.

What [various provisions of the ACA mean] is that there are an awful lot of employers who, if they want to provide health insurance to their employees and dependents, will now be able to purchase those policies at prices that do not take into account their abnormally high projected medical expenses.

A large number of these employers are likely to do so; even now 35 percent of employers with 50 or fewer employees provide some form of health insurance. Many small employers with lower-than-average projected health costs will strive to avoid being lumped in with their colleagues or competitors with higher costs. Instead, they will, if financially possible, “self-insure”: The section 1201 requirement of uniform premiums does not apply to arrangements whereby the employer (or union) itself nominally provides the medical benefits but throws off much of the financial risk onto reinsurers and many of the headaches of running a health plan onto “third-party administrators.” This option becomes even more attractive if employers can get away with the now-bandied-about “dumping strategy” of offering to pay their sickest employees enough so that they can purchase platinum health insurance in the individual exchanges and have money left over. Still other small employers may simply decide not to insure at all — reserving perhaps the delicious option of entering the exchange if some crucial employee or his dependents develop expensive medical conditions.

This self-segregation of small employers based on the projected health-care expenses of their employees will pressure small-group health insurers to raise prices. …

Of course, the curious thing about the looming debacle in the small-group market is that its possible contraction might be the one thing that could rescue the individual market from the probable death spiral. Right now, the individual markets are in danger as a result of lower-than-predicted enrollment and disproportionate enrollment of those over age 50. If small employers actually stop offering coverage — either because the costs of ACA-compliant policies prove too high or because of a death spiral in the SHOP exchanges (or both), they may end up just sending people to the individual exchanges. That won’t do much for President Obama’s promise that people could keep their health plans, and it won’t constitute a “silver lining” for people who want to reduce government’s role in health insurance, but it will do what many conservatives have wanted to do for years: undo the ideology that has previously tied the labor and health-insurance markets together.

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The Kaiser analysis of ACA enrollment has problems

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.

Comparison of baseline scenario v. worst case using better assumptions
Comparison of baseline scenario v. worst case using better assumptions

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.

Various scenarios showing changes in insurer profits due to different enrollment response functions
Various scenarios showing changes in insurer profits due to different enrollment response functions

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.

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Gender could be as big a problem as age for the Affordable Care Act

Concerns about whether insurance sold on  the individual Exchanges under the Affordable Care Act will succumb to an adverse selection death spiral have focused mainly on the shortage of younger enrollees into the system. This shortage is potentially a problem because, due to section 1201 of the ACA, premiums for younger enrollees must be at least one third of that for older enrollees even though actuarial science tells us that younger enrollee expenses are perhaps just one fifth of those for older enrollees. Younger enrollees are needed in large numbers to subsidize the premiums of the older enrollees. But at least premiums under the ACA respond at least somewhat to age.

The lesser studied potential source of  adverse selection problems, however, is the fact that medical expenses of women for many ages are essentially double those of men and yet the ACA forbids rating based on gender.  In a rational world, one would therefore expect women of most of the ages eligible for coverage in the individual Exchanges to enroll in plans on the Exchange at a higher rate than men. But, since the women have higher than average expenses than men, premiums based on the average expenses of men and women will prove too low, creating pressure on insurers to raise prices. And, of course, there could also be some disproportionate enrollment by older men who have higher medical expenses than women of equal age. While I welcome contrary arguments in what I regard as a fairly new area of study involving the ACA, gender-based adverse selection would certainly appear to be  a real problem created by the structure of that law.  To me, it looks to be potentially as large a problem as age-based adverse selection. It is certainly one that needs continuing and careful evaluation.


I see only three limited factors that reduce what would otherwise appear to be a significant additional source for significant adverse selection. As set forth below, however, I do not believe that any of these factors are likely to materially reduce the problem.

1. Ignorance

The first is ignorance. Adverse selection emerges only if individuals can accurately foretell their future medical expenses with some accuracy. To the extent, therefore, that men and women are ignorant of the effect of gender on their projected medical expenses, adverse selection is potentially diminished. I say “potentially,” however, because of a subtlety: people don’t have to know why their expenses are what they are in order for adverse selection to emerge; they only have to be somewhat accurate in their guess. Thus, even if men and women don’t make the cognitive leap from seeing lower (or higher) medical expenses to issues of gender, but they still on balance get it right, adverse selection can exist. Thus, I end up doubting that ignorance of the correlation between gender and medical expense is going to retard adverse selection problems very much.

2. Correlation between gender and expense is lower for those 50-65.

The second factor that might reduce adverse selection based on gender is, curiously enough, adverse selection based on age. The difference between male and female medical expenses diminishes as one exits the middle 40s and heads into the 60s. Indeed, somewhere in the late 50s, the rates cross and men have slightly higher average medical expenses than women. Therefore, to the extent that it is the 50-65 set that is disproportionately purchasing coverage in the individual Exchanges, the potential for gender-based adverse selection is diminished — but only somewhat .  I say “but only somewhat” because if males over the age of about 55 or 58 enroll at higher rates than women of similar ages there will actually be adverse selection pressures due to the higher medical expenses of men that age. On the other hand, to the extents efforts are made to reduce age-based adverse selection by promoting coverage to the younger (potentially child-bearing) set, the potential for most forms of gender-based adverse selection increases.

3. Gender-correlated risk aversion

The third factor that could in theory reduce adverse selection problems is if men are more risk averse than women with respect to medical expenses and therefore purchase health insurance at equivalent rates even though their risk is objectively lower. Men could conceivably be somewhat more risk averse due to prevailing gender roles in the economy: on average it is possible that health problems among men may affect the family’s income more than health problems among women.  Although as an academic I feel I would be remiss in failing to at least mention this possibility, in the end I doubt it amounts to very much. The roles of men and women in the family economy are complex and variegated. And the sources of risk aversion with respect to health are likewise multifold, having a lot to due with individual psychology, family history and family structure. And, of course, it could be that middle aged men are less risk averse than women, in which case the effects of adverse selection are worse.

The data

How do we know about the effects of gender? The graphics below show two studies on the topic. The first is from the Society of Actuaries and was relied on by the Kaiser Family Foundation in its recent study of the effect of age rating. Look at the solid blue (male) and pink (female) lines. (Cute, Kaiser). One can see that until age 18, the costs for men and women in the commercial market has been about the same. By the time we get to, say, age 32, the cost for women is about 2.5 times that for men. The gap then shrinks so that by the time we get to age 58 or so, men’s costs actually start to somewhat exceed women’s.

Society of Actuaries report on gender and healthcare expenses
Society of Actuaries report on gender and healthcare expenses

A study by the respected Milliman actuarial firm, although differing in detail, shows roughly the same pattern. At age 30 or so, female expenses (blue) and about double those of males (green). The gap shrinks until about age 55, at which point male expenses exceed female expenses.  (I’m not sure why Milliman shows female expenses being so much higher than male expenses for the age bracket marked “to 25” unless by “to 25” they mean ages 18-25.)


Is Gender-Based Adverse Selection Actually Happening?

As to whether the theoretical possibility of gender-based adverse selection is actually materializing, there is yet strikingly little evidence. I have scoured the Internet and found almost nothing on the gender of enrollees. In some sense this is not surprising since, unlike age, on which we have a trickle of data from CMS, which somehow is just unable to compile and release more complete information, gender is completely irrelevant to premium rates. On the other hand, as shown below, the federal application asks about gender, as do a few other state applications such as California, Kentucky and Washington State. So, in theory we should be able to get the information at some point.  In the meantime, if anyone has information on this issue, I would love to see it. What we really need is a breakdown of enrollees based on both age and gender because the ratio’s role varies depending on whether enrollees below age 55 or so are involved or whether enrollees above age 55 are involved.

Two other notes

1. Someone might, I suppose, think that since the role of gender reverses at about age 55, the effects of gender on adverse selection cancel each other out. This would be totally wrong.  If women have higher medical expenses than men up to about age 55 and if women therefore enroll at higher rates, that can cause adverse selection and premium pressures for enrollees of those ages. And if men have have higher medical expenses than women after about age 55 and if men therefore enroll at higher rates, that can cause adverse selection and premium pressures for enrollees of those ages. The effects are cumulative and not offsetting.

2. Does this mean I am opposed to unisex rating? No, not necessarily. First, women face higher medical expenses than men from about 20 to 50 significantly because of childbearing expenses. A family law expert on my faculty confirms what I suspected, which is that there is certainly no routine cause of action by the pregnant female against the prospective father for prenatal maternity expenses. We currently ascribe these expenses to the woman even though a male generally has contributed to those expenses through consensual sex. One could argue that unisex rating offsets this proxy for responsibility.

Second, if there are adverse selection problems caused by unisex rating, they can, in theory, be addressed by programs that that subsidize insurers for female enrollees. Impolitic as it might be to say so, one could treat being a fertile woman as a “risk factor” in the same way that section 1343 of the ACA currently treats medical conditions such as heart disease.  The cost of the subsidies resulting therefrom could be seen as compensating somewhat for the transaction costs of figuring out which childbearing expenses the male partner has contributed to as well as tracking down the male partner and trying to hold him financially responsible.

What I am concerned about, however, is ignoring the issues created by unisex rating. Since it is not currently corrected for by section 1343 of the ACA and corrected for only in a very indirect and partial way by sections 1341 and 1342 of the ACA, there is the potential for the absence of gender rating to destabilize and ultimately shrink the insurance markets in ways that do few people any good. Wishing that a problem would go away or hoping that people don’t see the opportunities to optimize their behavior is seldom a recipe for successful government programs.


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Just read Avik Roy this morning

Avik Roy has saved me a lot of time this morning with a brilliant post on the Forbes website. Read it.

Or at least read these excerpts.




Request for readers

1. The healthcare.gov web site does not even let one access Catastrophic plans if one is over the age of 30.  The shadow website, thehealthsherpa.com does not permit one to do so either probably because it was thought that the number of persons qualifying over 30 would be extremely small. When I just tried to chat with healthcare.gov and get the answer, I was told ” Sorry, Health Insurance Marketplace Live Chat isn’t available right now. We’re having technical problems.” I have thus not yet been able to figure out what the prices are for someone over 30 with one of the new “hardship” exemptions.  If anyone can figure out what prices over-age hardship exemption folks pay for a section 1302 Catastrophic Plan, please contact me.

2. How many people have purchased these Catastrophic plans anyway?  The federal government has not released metal tier distribution data, but the data from a few states suggests that it is an extremely low number.  Many under the age of 30 can stay on their parents plans and others find that it is not much better than a Bronze Plan or, under some circumstances, a worse deal.  I would bet that  the overall number of Catastrophic Plan enrollees thus far is less than 20,000. There is no subsidy for Catastrophic Plans. What would actually happen if people took advantage of the Secretary’s hardship exemption and instead of just pocketing the tax savings, these older insureds purchased these Catastrophic Plans.  Could be the over 50s could end up being a greater number than the under 30s. We will see if I ever get an answer to question 1 above, but I suspect the insurance industry did not price the policies on the assumption that older enrollees would predominate.



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Obama administration shocking decision to drop individual mandate — but only for some

I’m going to have to wait until tomorrow to say much more, but the Obama administration issued a shocking decision late today to exempt those who had individual policies cancelled this year from the individual mandate contained in the Affordable Care Act.  The Wall Street Journal apparently broke the story.  Here is the New York Times article.  Here is a Washington Post article from a strong Affordable Care Act supporter. Here is the Huffington Post article. Here’s Fox News. (CNN has yet to publish anything I can find on the subject) Not surprisingly, the insurance industry has already protested the apparent move. “This latest rule change could cause significant instability in the marketplace and lead to further confusion and disruption for consumers,” said Karen Ignagni, president of America’s Health Insurance Plans, the industry’s main trade group.

A copy of the decision, made thus far only in a letter from Secretary Kathleen Sebelius to six senators (all of whom are apparently facing tough re-election battles) is here.

Excerpt from Sebelius letter to senators
Excerpt from Sebelius letter to senators


The purported legal basis for the exemption comes in 26 U.S.C. 5000A(e)(5), which reads:

(e) Exemptions

No penalty shall be imposed under subsection (a) with respect to— …

(5) Any applicable individual who for any month is determined by the Secretary of Health and Human Services under section 1311 (d)(4)(H) to have suffered a hardship with respect to the capability to obtain coverage under a qualified health plan.

The Obama administration is now apparently interpreting having to comply with the mandate itself — but only after one’s individual insurance policy was cancelled — as the requisite hardship. A prior regulation issued on July 1, 2013, by HHS had taken a narrower view of what the requisite hardship was:

(g) Hardship—(1) General. The Exchange must grant a hardship exemption to an applicant eligible for an exemption for at least the month before, a month or months during which, and the month after, if the Exchange determines that—
(i) He or she experienced financial or domestic circumstances, including an unexpected natural or human-caused event, such that he or she had a significant, unexpected increase an essential expenses that prevented him or her from obtaining coverage under a qualified health plan;
(ii) The expense of purchasing a qualified health plan would have caused him or her to experience serious deprivation of food, shelter, clothing or other necessities; or
(iii) He or she has experienced other circumstances that prevented him or her from obtaining coverage under a qualified health plan.

I look forward to hearing from others, and in particular from people with a commitment to the rule of law who previously have supported the ideas behind the ACA, but it is not clear to me that any of the pre-existing bases contained in this regulation for claiming a hardship exemption would apply to having a predicted cancellation in one’s individual insurance policy. Maybe at this late hour there are arguments and other documents I am not considering. Surely, however, the existence of the ACA itself can not be the human-caused event creating the hardship. Moreover, I have trouble seeing how the cancellation of a plan makes it more difficult for these individuals — as opposed to others in similar circumstances — from obtaining coverage under a qualified health plan.  I can well imagine cynics saying that the only real hardship involved here is having believed President Obama when he said that if you liked your health plan you could keep it and thus not having saved up for the higher prices that often exist in policies with “Essential Health Benefits.” Of course, if , as the Obama administration has claimed, many of these cancelled policies were junk that the policyholder should be glad to be rid of, it becomes yet more challenging to see much of a hardship at all in being offered real insurance coverage with all of its greater benefits.

In any event, it does not take a fertile imagination to foresee legal challenges to this limited exemption from those not fortunate enough to have had health insurance in the past but who are not being given a similar exemption from the individual mandate. I can easily see challenges based on failures of administrative procedure and equal protection.

The Death Spiral

I and others will need to think hard about the issue of magnitude. Obama administration officials are reported as having stated at a briefing that all but 500,000 of those with canceled policies will be enrolling in policies under the Exchange. This claim, however, is impossible to reconcile with existing enrollment statistics and assertions that millions of individuals have had their individual policies cancelled.  It is difficult to see how this decision would not exacerbate at least somewhat the risk of an adverse selection death spiral overtaking the Exchanges in many states.  The tax created by the mandate has always been justified as necessary to induce people of low or moderate risk to join those of higher risk in purchasing policies on the Exchange. By now exempting perhaps millions of people from this requirement — and, in particular, people who are most likely to have satisfied medical underwriting in the recent past — the Obama administration decision will likely diminish enrollment, at least somewhat, in the insurance Exchanges and, correlatively increase price pressures and insurer losses during 2014. To the extent that insurers systematically lose money as a result of this apparent decision, the federal government will be spending millions more — perhaps hundreds of millions more — in payments under the Risk Corridors program.


There’s one more implication we need to think about.  Although experts vary greatly on the magnitude, clearly a number of small businesses are going to lose their health insurance policies this coming year for failure to conform to the new ACA requirements.  This is the “second wave” that is sometimes spoken about. Are the significant number of employees and dependents who are thus subject to a risk of loss of coverage likewise going to receive an exemption from the individual mandate?

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Shocking secrets of the actuarial value calculator revealed!

That might be how the National Enquirer would title this blog entry.  And, hey, if mimicking its headline usage attracts more readers than “Reconstructing mixture distributions  with a log normal component from compressed health insurance claims data,” why not just take a hint from a highly read journal?  But seriously, it’s time to continue delving into some of the math and science behind the issues with the Affordable Care Act. And, to do this, I’d like to take a glance at a valuable data source on modern American health care, the data embedded in the Actuarial Value Calculator created by our friends at the Center for Consumer Information and Insurance Oversight (CCIIO).

This will be the first in a series of posts taking another look at the Actuarial Value Calculator (AVC) and its implications on the future of the Affordable Care Act. (I looked at it briefly before in exploring the effects of reductions in the transitional reinsurance that will take effect in 2015).  I promise there are yet more important implications hidden in the data.  What I hope to show in my next post, for example, is how the data in the Actuarial Value Calculator exposes the fragility of the ACA to small variations in the composition of the risk pool.  If, for example, the pool of insureds purchasing Silver Plans has claims distributions similar to those that were anticipated to purchase Platinum Plans, the insurer might lose more than 30% before Risk Corridors were taken into account and something like 10% even after Risk Corridors were taken into account. And, yes, this takes account of transitional reinsurance. That’s potentially a major risk for the stability of the insurance markets.

What is the Actuarial Value Calculator?

The AVC is intended as a fairly elaborate Microsoft Excel spreadsheet that takes embedded data and macros (essentially programs) written in Visual Basic, and is intended to help insurers determine whether their proposed Exchange plans conform to the requirements for the various “metal tiers” created by the ACA. These metal tiers in turn attempt to quantify the ratio of the expected value of the benefits paid by the insurer to the expected value of claims covered by the policy and incurred by insureds. The programs, I will confess, are a bit inscrutable — and it would be quite an ambitious (and, I must confess, tempting) project to decrypt their underlying logic — but the data they contain is a more accessible goldmine. The AVC contains, for example, the approximate distribution of claims the government expects insurers writing plans in the various metal tiers to encounter.

There are serious limitations in the AVC, to be sure. The data exposed has been aggregated and compressed; rather than providing the amount of actual claims, the AVC has binned claims and then simply presented the average claim within each bin.  This space-saving compression is somewhat unfortunate, however, because real claims distributions are essentially continuous. Everyone with annual claims between $600 and $700 does not really have claims of $649. This distortion of the real claims distribution makes it more challenging to find analytic distributions (such as variations of log normal distributions or Weibull distributions) that can depend on the generosity of the plan and that can be extrapolated to consider implications of serious adverse selection. It’s going to take some high-powered math to unscramble the egg and create continuous distributions out of data that has had its “x-values” jiggled.  Moreover, there is no breakdown of claim distributions by age, gender, region or other factors that might be useful in trying to predict experience in the Exchanges.  (Can you say “FOIA Request”?)

This blog entry is going to make a first attempt, however, to see if there aren’t some good analytic approximations to the data that must have underlain the AVC. It undertakes this exercise in reverse engineering because once we have this data, we can make some reasonable extrapolations and examine the resilience — or fragility — of the system created by the Affordable Care Act. The math may be a little frightening to some, but either try to work with me and get it or just skip to the end where I try to include a plain English summary.

The Math Stuff

1. Reverse engineering approximate continuous approximations to the data underlying the Actuarial Value Calculator

Nothwithstanding the irritating compression of data used to produce the AVC, I can reconstruct a mixture distribution composed mostly of truncated exponential distributions that well approximates the data presented in the AVC.   I create one such mixture distribution for each metal tier. I use distributions from this family because they have been proven to be “maximum entropy distributions“, i.e. they contain the fewest assumptions about the actual shape of the data. The idea is to say that when the AVC says that there were 10,273 claims for silver-like policies between $800 and $900 and that they averaged $849.09, that average could well have been the result of an exponential distribution  that has been truncated to lie between $800 and $900.  With some heavy duty math, shown in the Mathematica notebook available here, we are able, however, to find the member of the truncated exponential family that would produce such an average. We can do this for each bin defined by the data, resorting to uniform distributions for lower values of claims.

The result of this process is a  messy mixture distribution, one for each metal tier. The number of components in the distribution is essentially the same as the number of bins in the AVC data. This will be our first approximation of “the true distribution” from which the claims data presented in the AVC calculator derives. The graphic below shows the cumulative density functions (CDF) for this first approximation. (A cumulative density function shows, for each value on the x-axis the probability that the value of a random draw from that distribution will be less than the value on the x-axis).   I present the data in semi-log form: claim size is scaled logarithmically for better visibility on the x-axis and percentage of claims less than or equal to the value on the x-axis is shown on the y-axis.

CDF of the four tiers derived from the first approximation of the data in the AVC
CDF of the four tiers derived from the first approximation of the data in the AVC

There are two features of the claims distributions that are shown by these graphics.  The first is that the distributions are not radically different.  The model suggests that the government did not expect massive adverse selection as a result of people who anticipated higher medical expenses to disproportionately select gold and platinum plans while people who anticipated lower medical expenses to disproportionately select bronze and silver plans. The second is that, when viewed on a semi-logarithmic scale, the distributions for values greater than 100 look somewhat symmetric about a vertical axis.  They look as if they derive from some mixture distribution composed of a part that produces a value close to zero and something kind of log normalish. If this were the case, it would be a comforting result, both because such mixture distributions would be easy to parameterize and extrapolate to lesser and greater forms of adverse selection and because such mixture distributions with a log normal component are often discussed in the literature on health insurance.

2. Constructing a single Mixture Distribution (or Spliced Distribution) using random draws from the first approximation

One way of finding parameterizable analytic approximations of “the true distribution” is to use our first approximation to produce thousands of random draws and then to use mathematical  (and Mathematica) algorithms to find the member of various analytic distribution families that best approximate the random draws. When we do this, we find that the claims data underlying each of the metal tiers is indeed decently approximated by a three-component mixture distribution in which one component essentially produces zeros and the second component is a uniform distribution on the interval 0.1 to 100 and the third component is a truncated log normal distribution starting at 100.  (This mixture distribution is also a “spliced distribution” because the domains of each component do not overlap). This three component distribution is much simpler than our first approximation, which contains many more components.

We can see how good the second-stage distributions are by comparing their cumulative distributions (red) to histograms created from random data drawn from the actuarial value calculator (blue).  The graphic below show the fits to look excellent.

Note: I do not contend that a mixture distribution with a log normal distribution perfectly conforms to the data.  It is, however, pretty good for practical computation.

Actual v. Analytic distributions for various metal tiers
Actual v. Analytic distributions for various metal tiers


 3. Parameterizing health claim distributions based on the actuarial value

The final step here is to create a function that describes the distribution of health claims as a function of a number (v) greater than zero. The concept is that, when v assumes a value equal to the actuarial value of one of the metal tiers, the distribution that results mimics the distribution of AVC-anticipated claims for that tier.  By constructing such a function, instead of having just four distributions, I obtain an infinite number of possible distributions. These distributions collapse as special cases to the actual distribution of health care claims produced by the AVC. This process enables us to describe a health claim distribution and to extrapolate what can happen if the claims experience is either better (smaller) than that anticipated for bronze plans or worse (higher) than that anticipated for platinum plans. One can also use this process to compute statistics of the distribution as a function of v such as mean and standard deviation.

Here’s what I get.

Mixture distribution as a function of the actuarial value parameter v
Mixture distribution as a function of the actuarial value parameter v

Here is a animation showing, as a function of the actuarial value parameter v, the cumulative distribution function of this analytic approximation to the AVC distribution.  

Animated GIF showing Cumulative distribution of claims by "actuarial value
Cumulative distribution of claims by “actuarial value”


One can see the cumulative distribution function sweeping down and to the right as the actuarial value of the plan increases. This is as one would expect: people with higher claims distributions tend to separate themselves into more lavish plans.

Note: I permit the actuarial value of the plan to exceed 1. I do so recognizing full well that no plan would ever have such an actuarial value but allow myself to ignore this false constraint.  It is false because what one is really doing is showing a family of mixture distributions in which the parameter v can mathematically assume any positive value but calibrated such that (a)  at values of 0.6, 0.7, 0.8 and 0.9 they correspond respectively with the anticipated distribution of health care claims found in the AVC for bronze, silver, gold and platinum plans respectively and (b) they interpolate and extrapolate smoothly and, I think, sensibly from those values.

The animation below presents largely the same information but uses the probability density function (PDF) rather than the sigmoid cumulative distribution function. (If you don’t know the difference, you can read about it here.)  I do so via a log-log plot rather than a semi-log plot to enhance visualization.  Again, you can see that the right hand segment of the plot is rather symmetric when plotted using a logarithmic x-axis, which suggests that a log normal distribution is not a bad analytic candidate to emulate the true distribution.

Log Log plot of probability density function of claims for different actuarial values of plans


Some initial results

One useful computation we can do immediately with our parameterized mixture distribution is to see how the mean claim varies with this actuarial parameter v. The graphic below shows the result.  The blue line shows the mean claim as a function of “actuarial value” without consideration of any reinsurance under section 1341 (18 U.S.C. § 18061) of the ACA.  The red line shows the mean claim net of reinsurance (assuming 2014 rates of reinsurance) as a function of “actuarial value.” And the gold line shows the shows the mean claim net of reinsurance (assuming 2015 rates of reinsurance) as a function of “actuarial value.” One can see that the mean is sensitive to the actuarial value of the plan.  Small errors in assumptions about the pool can lead to significantly higher mean claims, even with reinsurance figured in.

Mean claims as a function of actuarial value parameter for various assumptions about reinsurance
Mean claims as a function of actuarial value parameter for various assumptions about reinsurance

I can also show how the claims experience of the insurer can vary as a result of differences between the anticipated actuarial value parameter v1 that might characterize the distribution of claims in the pool and the actual actuarial value parameter v2 that ends up best characterizing the distribution of claims in the pool.  This is done in the three dimensional graphic below. The x-axis shows the actuarial value anticipated to best characterize an insured pool. The y-axis shows the actuarial value that ends up best characterizing that pool.  The z-axis shows the ratio of mean actual claims to mean anticipated claims.  A value higher than 1 means that the insurer is going to lose money. Values higher than 2 mean that the insurer is going to lose a lot of money.  Contours on the graphic show combinations of anticipated and actual actuarial value parameters that yield ratios of 0.93, 1.0, 1.08, 1.5 and 2. This graphic does not take into account Risk Corridors under section 1342 of the ACA.

What one can see immediately is that there are a lot of combinations that cause the insurer to lose a lot of money.  There are also combinations that permit the insurer to profit greatly.

Ratio of mean actual claims to mean expected claims for different combinations of anticipated and actual actuarial value parameters
Ratio of mean actual claims to mean expected claims for different combinations of anticipated and actual actuarial value parameters

Plain English Summary

One can use data provided by the government inside its Actuarial Value Calculator to derive accurate analytic statistical distributions for claims expected to occur under the Affordable Care Act.  Not only can one derive such distributions for the pools anticipated to purchase policies in the various metal tiers (bronze, silver, gold, and platinum) but one can interpolate and extrapolate from that data to develop distributions for many plausible pools.  This ability to parameterize plausible claims distributions becomes useful in conducting a variety of experiments about the future of the Exchanges under the ACA and exploring their sensitivity to adverse selection problems.


You can read about the methodology used to create the calculator here.

You can get the actual spreadsheet here. You’ll need to “enable macros” in order to get the buttons to work.

The actuarial value calculator has a younger cousin, the Minimum Value Calculator.  If one looks at the data contained here, one can see the same pattern as one finds in the Actuarial Value Calculator.


Probably I should have made the title of this entry “Shocking sex secrets of the actuarial value calculator revealed!” and attracted yet more viewers.  I then could have noted that the actuarial value calculator ignores sex (gender) in showing claims data.  But that would have been going too far.

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Proposed cuts in transitional reinsurance could increase Exchange premiums 7-8% in 2015

Late last week, HHS released its 255-page HHS Notice of Benefit and Payment Parameters for 2015. Buried away in this technical documents are at least two interesting matters.

  1. HHS is planning to cut reinsurance payments to insurers participating in its Exchanges in a way that, in and of itself, could increase gross premiums 7-8% in 2015 and increase the risk of further adverse selection
  2. HHS has validated the claims of insurers that President Obama’s recent about-face on the ability of insurers to renew certain policies not providing Essential Health Benefits could destabilize the insurance market.  The Notice proposes changing the way insurers calculate their profits and losses so that the amount of payments made by government to insurers in the Exchange would increase. It claims, however, that it does not know how much this will cost.
The HHS Notice for 2015
The HHS Notice for 2015

Less reinsurance

Under the system in place for 2014, if insurers in an Exchange have to pay between $45,000 and $250,000 on one of their insureds, the government picks up 80% of that loss (assuming the $63 per insured life it taxes various other health insurance plans is sufficient to pay that amount). But in 2015, the money that goes into this transitional reinsurance pool (section 1341 of the ACA, 42 U.S.C. sec. 18061) declines by a third from $12 billion to $8 billion and the head tax correspondingly declines from $63 to $44. As a result, HHS proposes to now pick up only 50% of the tab for losses between $70,000 and $250,000. Thus, losses between $45,000 and the new $70,000 attachment point will now fall entirely on insurers without federal help and insurers will have to pay 30% more on losses between $70,000 and $250,000.

This reduction in free reinsurance provided by the taxpayers will almost certainly result in increased premiums for insureds. My estimate is that the average premium hike induced by this reduction in reinsurance is likely to be about 7-8%.

Here’s how I did this computation. I took loss distributions contained in the government’s “Actuarial Value Calculator.” That’s the Excel spreadsheet the government (and insurers) use to figure out what metal tier, if any, their policy falls into. I then performed the following steps.  You can verify what I have done in the Computable Document Format (CDF) document I have placed on Dropbox. You can view the document using the free CDF player or using Mathematica

Step 1.  I determined the expected value of claims under those loss distributions with reinsurance parameters set at the 2014 rates.  I get four results, one for each metal tier: {3630.52, 4223.87, 4468.95, 5556.06}. I then do exactly the same computation but use the 2015 reinsurance parameters. I get four results, one for each metal tier: {3906.67, 4550.95, 4807.06, 5948.53}.

Step 2. I multiply each result by the actuarial value of the associated metal tier to approximate the size of the premium needed to support the expected level of the claims. I get {2178.31, 2956.71, 3575.16, 5000.46} for the 2014 reinsurance parameters and {2344., 3185.67, 3845.65, 5353.68} for the 2015 reinsurance parameters.

Step 3. I then simply compute the percent increase in the needed 2015 premiums over the needed 2014 premiums and get {0.0760631, 0.077436, 0.0756584, 0.0706371}

If losses are, as I suspect they will be, greater than those assumed in the actuarial value calculator — because the pool is going to be drawn for a variety of reasons from a riskier group than originally anticipated —  the diminution in reinsurance is yet more significant and, standing by itself, could add more than 7-8% to the gross premiums charged in the Exchanges.

Whether the increase in gross premiums is about 7-8% or whether it is higher, it creates a heightened risk for an adverse selection problem.  This is so because, although subsidies insulate many people in the Exchanges from increases in gross premiums — net premiums are pegged to income rather than gross premiums for them — it will affect the significant number (estimated by HHS to be about 18% (4/22)) who are expected to purchase policies inside the Exchanges without subsidies.  The higher premiums go, however, the more we would expect to see the healthy drop out and find substitutes for the non-underwritten policies sold in the Exchanges. (If premiums are low enough, adverse selection is not a problem: insurance is a good deal for everyone and healthy and sick purchase it alike. See, e.g., Medicare Part B, which is very heavily subsidized and does not suffer seriously from adverse selection.)

Note to experts. Some of you might think I erred in saying that the 2014 reinsurance attachment point is $45,000 and not $60,000. But the 2015 notice says on page 11 that it will retroactively reduce the attachment point to $45,000.

HHS Validates Insurer Fears About Obama Reversal and the Destabilization of Insurance Markets

Many individuals, including me, have claimed that President Obama’s recent decision to permit insurers to “uncancel” certain individual plans that do not contain Essential Health Benefits could destabilize insurance markets. The Notice of Benefit and Payment Parameters just released appears to validate that assertion. Stripped of bureaucratese, the HHS document basically says that insurers are right to be disconcerted by the President’s about face.

For those who enjoy bureaucratese, however, or who properly want to validate my own conclusions about the document, here’s what it actually says.

On November 14, 2013, the Federal government announced a policy under which it will not consider certain non-grandfathered health insurance coverage in the individual or small group market renewed between January 1, 2014, and October 1, 2014, under certain conditions to be out of compliance with specified 2014 market rules, and requested that States adopt a similar non-enforcement policy.

Issuers have set their 2014 premiums for individual and small group market plans by estimating the health risk of enrollees across all of their plans in the respective markets, in accordance with the single risk pool requirement at 45 CFR 156.80. These estimates assumed that individuals currently enrolled in the transitional plans described above would participate in the single risk pools applicable to all non-grandfathered individual and small group plans, respectively (or a merged risk pool, if required by the State). Individuals who elect to continue coverage in a transitional plan (forgoing premium tax credits and cost-sharing reductions that might be available through an Exchange plan, and the essential health benefits package offered by plans compliant with the 2014 market rules, and perhaps taking advantage of the underwritten premiums offered by the transitional plan) may have lower health risk, on average, than enrollees in individual and small group plans subject to the 2014 market rules.

If lower health risk individuals remain in a separate risk pool, the transitional policy could increase an issuer’s average expected claims cost for plans that comply with the 2014 market rules. Because issuers would have set premiums for QHPs in accordance with 45 CFR 156.80 based on a risk pool assumed to include the potentially lower health risk individuals that enroll in the transitional plans, an increase in expected claims costs could lead to unexpected losses.

So, the government wants help in figuring out what to do. One method it is contemplating involves technical adjustments to the Risk Corridors program in a way that would get insurers more money (pp. 101-105).  Although I will confess to considerable difficulty in understanding exactly what it is that HHS suggesting, the basic idea, as I understand it, would be to assume that those who, by virtue of the President’s about face, “uncancel” their policies would have had claims expenses equal to 80% of the average claims of the rest of the pool (page 103-04). HHS will then, on a state-by-state basis figure out what the position of the insurer would have been and try to adjust Risk Corridors such that the position of the insured after application of adjusted Risk Corridors is similar to that which it would have been in had these persons, who pay the same premium as the rest but who tend to have only 80% of the claims expenditures, enrolled in their plan.

It is not clear to me where the statutory authority to make this change comes from. Section 1342 of the ACA (42 U.S.C. 18062) does not define its key terms of “target amount” and “allowable costs” in a fashion that would appear to my eye to extend to hypothetical costs and hypothetical premiums. I will also confess to being unsure as to who would have standing to challenge this proposed give away of taxpayer money to the insurance industry.

What is clear to me, however, is the proposed reform, by necessity, will result in greater previously unbudgeted expenditures by the federal government. If we are really talking about making insurers whole and the people in question might have profited insurers something like $1,000 a person, the federal government appears to be suggesting a change in regulations that could cost it hundreds of millions of dollars.  The HHS Notice declines to put an exact figure on the cost of the change:

Because of the difficulty associated with predicting State enforcement of 2014 market rules and estimating the enrollment in transitional plans and in QHPs, we cannot estimate the magnitude of this impact on aggregate risk corridors payments and charges at this time.

HHS is probably correct in saying it is difficult to estimate the cost of the proposed changes to Risk Corridors.  I don’t think we have a good feel for how many people will return to the plans President Obama has carved out for special treatment.  It does look, however, as if a floor of a couple of hundred million dollars on the cost of the proposal would be quite reasonable. This, of course, could give some ammunition to those, such as Florida Senator Marco Rubio, who have called for repeal of the Risk Corridors provision as an insurance “bailout.” (For a discussion, look here, here and here)

Final Note

Yesterday, I said I hoped to provide a major post.  This actually is not the post I was speaking about. There’s still more news coming.  Maybe today or maybe while recovering from a turkey overdose tomorrow.

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