# 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.

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.

### 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.

# 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.

### Caveats

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.

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.

# California provides a detailed look at enrollment in its Exchange

The State of California is doing neither the best nor the worst when it comes to enrolling people in individual healthcare plans on its Exchange (Covered California), but it is doing the best job I have seen in releasing detailed information.  In particular, it has released detailed information on the the age distribution of enrollees, “metal tiers” being selected by enrollees, subsidization rates, and the distribution of enrollees among insurance companies, and rates of enrollment among different language groups.  Let’s look at the data and see what can be learned. And, other states, would you please do what California is doing. You have the data. It’s not that hard to put out the numbers.

## Age Distribution

As shown in the paired bar graph below, the distribution of enrollees in individual Exchange plans by age in California is weighted far more heavily towards those in the older age brackets.  There is, in particular, a dearth of children relative to the large numbers in the population and a disproportionately high number of those in the 55-64 age bracket.

The graphic here is less “bullish” on the enrollment of younger enrollees than Covered California would like to make it appear.  This is because in various press releases, Covered California has been comparing the proportion of younger people enrolled against the proportion of younger people in the population and suggesting that they are similar.  But this is highly misleading because the relevant statistic is the proportion of younger people in the eligible population. The elderly are not eligible to purchase policies on the Exchange.  Thankfully, however, California has released the raw data that lets people do their own analyses. When the results are examined properly, in my opinion, the distribution of the young is more problematic.

## Metal Tier Distribution

As noted in an earlier blog entry, a high proportion of purchases of Gold and Platinum policies could be worrisome because those policies are likely to be disproportionately purchased by those in poorer health.  These policies generally have significantly less cost sharing than the Bronze and Silver policies. The chart below, taken from data provided by Covered California, shows that this concern has not materialized thus far in California.  “Sub.” in the graphic shows policies that are eligible for subsidy under 26 U.S.C. § 36B and possibly under 42 U.S.C. § 18071 whereas “Unsub.” shows policies that are not eligible for subsidy. Silver is by far and away the most popular plan selected. And, contrary to earlier information released by California, which initially got matters backwards, subsidized policies are significantly more prevalent than unsubsidized ones.

## Insurer Distribution

The pie chart below shows the distribution of enrollees by insurer.  As one can see, enrollment in California has been dominated by large insurers. The top 4 insurers have 96.2% of the market.  No small insurers have broken into the top 4. Moreover, some insurers are likely to have problems with the small absolute size of their pool if it does not increase significantly: Valley Health Plan has just 122 people enrolled to date in its health plans; Contra Costa Health Plan has just 178.

## Language Distribution

California has released information the primary language of enrollees. As shown in the paired bar graph below, the data demonstrates that English speaking individuals are enrolling at a rate significantly higher than those whose primary language is something else. People whose primary language is Spanish, for example, constitute 28.8% of the California population but only 4.6% of persons who have enrolled to date.

# California data shows disproportionate enrollment by those over 55

California has frequently been cited as an early Affordable Care Act success story with enrollment coming at least closer to projected numbers than in other states. Today’s release of information from Covered California, the state entity organizing enrollment there, shows a mixed picture about the likelihood that the ACA will become a stable source of non-discriminatory relatively inexpensive health insurance in the nation’s most populous state.

A highlight from the report is that 79,891 have at least gotten as far as selecting a plan since enrollment opened on October 1, 2013.  That’s better than any other state and better — at least as of the last report — of all the other states combined using the healthcare.gov portal. And, because, contrary to the wishes of California Insurance Commissioner Dave Jones, Covered California has decided not to permit those with recently enrolled in underwritten individual health insurance to “uncancel” policies that do not provide Essential Health Benefits, there is the potential to add more people to the Exchange pools than would otherwise be possible.  Additional good news: the pace of enrollment has picked up over the past two weeks. Still, to date, the 79,891 who have at least selected a plan are only 6% of the 1.3 million that the federal government projected California would enroll through 2014. And the web site in California appears to be working acceptably.

Perhaps the news on the number of enrollees is equivocal.  It’s better than other states, and it’s still early, but, relative to the projections on which the ACA was premised, it is not good at all.  There is also, however, what appears to me to be distinctly troubling news coming from California.  We have another report on the age distribution of enrollees: so far, it is disproportionately old. And this is true in the state in which enrollment has progressed the furthest and in the nation’s most populous state. So, the data is potentially significant not just as an augury of what may be seen in other states but because a disproportionately elderly population in the largest state is, in an of itself, a problem.

Although persons age 55 through 64 constitute about 18% of the California population aged 18 through 64, they constitute double that, 36%, of persons in that same age segment who have enrolled for a plan. Similarly, although persons age 45 through 64 constitute about 41% of the California population, they constitute 59% of those who have enrolled thus far. As discussed earlier on this blog and elsewhere, because premium ratios between old and young are capped at 3 to 1, whereas actual claim ratios are likely to be higher, disproportionate enrollment of the elderly can help drive an adverse selection death cycle.  This would be all the more true if the older people — it’s hard to call people age 55 “elderly”” —  that are enrolling are disproportionately unhealthy relative to their age-group peers. Claims, therefore, by Covered California Director Peter Lee that “enrollment in key demographics like the so-called young invincibles is very encouraging” rest on theories of economics and statistics that I do not understand.

### A Side Note on Market Concentration

By the way, who’s on the hook in the event the ultimate pool is distinctly more expensive than insurers anticipated?  It’s the usual suspects. The big “winners” in California thus far are the usual suspects: Anthem Blue Cross has 28.1%, Kaiser Permanente, a California fixture, has 26.8%, Blue Shield of California has 25.6% and Health Net (with headquarters in Southern California) has 15.7%. Together, these four have 96% of the market with a “Herfindahl Index” of a moderately concentrated 2410. Dreams, therefore, of new competitors entering the marketplace, thus far seem illusory.  But it is these “winners” that stand to lose the most money — and be the greatest recipient of federal redistributions under Transitional Reinsurance, Risk Corridors and Risk Adjustments — in the coming year if the trends hold up.