Tag Archives: gender

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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New data on ACA enrollment shows problems in many states

The Department of Health and Human Services released updated data today on enrollment on the Exchanges including, for the first time, greater breakdowns on enrollment by several key categories: age, gender, and the metal level of purchase. The result of this long awaited and much requested data is, at first glance, very much a mixed picture. Some of the overall statistics do not look as problematic as some — including me — had feared they might be. But it looks as if there is a very serious potential for large adverse selection problems brewing in a number of states,  most notably West Virginia, Mississippi, Maryland and Washington State.


The good news for the ACA from the data

There are three major pieces of good news for those who support the goals of the ACA.

1. The overall gender distribution of enrollees, 54% female, 46% male does not appear on preliminary inspection to be sounding “red alert.” To be sure, the problem may be a little greater than would otherwise be suggested by the aggregated numbers if the middle age group is more heavily female and the oldest group of enrollees more heavily male that the aggregated numbers suggest.  And Mississippi is troubling with 61% female enrollment (and for other reasons, see below). But, overall, and if they hold up, these do not appear to be the the kind of numbers that would be way beyond what insurers likely expected or that, standing by themselves, would be devastating to an insurer on an Exchange.

2. Several states have total enrollments and the age distributions that should reduce the possibility of a serious death spiral getting started. New York and California are the two big states doing better than most.  Connecticut is doing very well also.

3. The metal tier distribution is 80% for Bronze and Silver policies and only 20% in Gold and Platinum.  That’s comforting for adverse selection. A higher proportion of enrollment in the more generous plans would have been a warning sign that enrollment was coming disproportionately from the sick.  There’s a footnote on this point later on — we are not out of the woods — but this is definitely better news for the ACA than a distribution of, say, only 50% Bronze and Silver purchases.

The bad news

Just because the ACA is doing better than some had forecast on an overall basis does not mean there will not be very serious problems in some states.  Given that the statute is presently unamendable as a practical matter, problems in just a few states can hurt a lot of people.  The data released by HHS today shows that there are a number of states in serious trouble.

The table below shows current enrollment in states that appear at first glance to be in significant trouble. (There may be states that are as bad as those shown in the table below; I kind of eyeballed the data, which was not provided in a nice electronic format, to select what appeared to be a problem).  I also show the projected number of purchasers, the percentage of current enrollees as a fraction of purchasers, the percentage of “young invincibles” as a fraction of the enrolled population and the percentage of the expensive 45-64 year old age group.


I also construct a “back-of-the-envelope”/quick and dirty “Maelstrom Index” that roughly measures the problems confronting the individual Exchanges in the state.  The maelstrom index is calibrated to run from 0 to 1 with a 0 score meaning the state is in excellent shape and a 1 meaning there is an extremely high risk of an adverse selection death spiral materializing.  It is not a probability measure.  The formula for the maelstrom index is shown at the end of this post.


As one can see, there are a number of states that have serious potential problems. West Virginia is problematic with 66% of its enrollees ages 45 to 64 and only 17% ages 18-34. Almost all experts would concede that this poses serious risk of adverse selection. And the overall fraction of enrollment relative to projections, just 20%, suggests that West Virginia’s insurance pool may be disproportionately populated by the sick. Mississippi is likewise a problem with enrollment only 14% of that projected, 58% in the age 45-64 bracket and, as mentioned above, 61% female enrollment. I have to believe that insurers writing in Mississippi are deeply concerned about these numbers.

Also  troubling are the numbers in Texas, Washington State, and Ohio simply because, as an absolute number, there is such a large absolute difference between the number of people projected to purchase and actual enrollment. I’ll speak more about all of these numbers and try to update the chart in the days ahead.

The unknown

There’s one key piece of data not found in the HHS release today. The number of “enrollees” who have actually purchased policies.  If this conversion rate is, as I fear, hardly 100%, the numbers presented today overstate the extent of purchases in the Exchanges and understate the dangers of adverse selection breaking out in many states.

The Maelstrom Index Formula

Max[0, (5*(1.4 – enrollmentPercentage – youngInvinciblePercentage))/7]

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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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