Category Archives: Mathematics

Prices rising, choice declining for 2016 Obamacare

Data released yesterday at 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  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  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 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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Obama administration increases insurer subsidies

The Obama administration announced earlier today that it would increase the  rate of subsidy provided insurers under the transitional reinsurance program established by the Affordable Care Act.  This program, in effect for the policies sold in 2014, 2015, and 2016 on one of the individual insurance exchanges fostered by the ACA,  provides free specific stop loss reinsurance to insurers, something insurers would otherwise have to pay a lot of money to obtain.  The Center for Medicare and Medicaid Services  (CMS) announced today that instead of taxpayers giving insurers  80% of the losses on any individual for their claims between $45,000 and $250,000, it would now pay a full 100% of these losses.

The higher rate of reinsurance should not be interpreted as a sign that claims were lower than insurers expected — something that would run contrary to many of the recent insurer rate hike filings or the losses reported by many insurers.  It is not a sign of the success of Obamacare; rather it is an artifact of its problems.  If, for example, there were 14% fewer people enrolled in Obamacare than at the time the reinsurance rates were initially determined (7 million vs. 6 million), reinsurance payments could be, as here, yet more generous to insurers even if claims were 10% higher than originally projected.

There are several implications of today’s announcement.  First, it means that, on a percentage basis, the ACA is subsidizing exchange insurers for 2014 even more than regulations enacted under it had heretofore prescribed.  Since this same money paid to insurers could instead have been used to provide greater subsidies to poorer and middle class individuals trying to purchase health insurance, the candy distributed today to insurers is a bit troubling. Second, because CMS says it will actually have money left over from 2014 even after the increase in reinsurance rates,  and because enrollment in Obamacare remains considerably lower than was estimated at the time of its enactment, there is an increased likelihood of reinsurance payments to insurers being higher than originally authorized in 2015.

We can get some sense of the magnitude of the changes announced today.  To do so, I use data embedded in the Actuarial Value Calculator, a document produced by CMS for the purposes of figuring out whether various insurance plans met the standards for bronze, silver, gold and platinum policies.  For an average silver policy, for example, the reinsurance that would have been provided prior to today would have been expected to save insurers about 11% in expenses, and, quite likely, premiums.  With the new reinsurance parameters, the transitional reinsurance program will save insurers selling the same silver policies about 14%.

We can do the same exercise for platinum, gold and bronze policies.  The results are not much different.  The table below shows the results.

Metal Level Original subsidy New subsidy
Bronze 11% 13%
Silver 11% 14%
Gold 11% 13%
Platinum 10% 12%

Two foootnotes

1. This is actually the second time CMS has made the transitional reinsurance program for 2014 more generous.  Originally, the reinsurance would “attach” at $60,000.  If an individual’s claims were below that amount, no reinsurance would kick in. Leter, CMS changed the attachment point to $45,000.

2.  How could I do this computation so swiftly?  I’ve been preparing for testimony before the House Ways and Means Committee on, among other things, the effect of the transitional reinsurance program on insurer rate changes and I’ve been working on a talk on a similar topic for the R in Insurance Conference later this month.  So, all I had to do was plug the new parameters into my model, and out came the results. Be prepared.

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Why net premium increases will often be even larger than you think

I’ve written before that net premium increases for many individuals purchasing policies under the ACA will be higher than gross premium increases.  I’ve gotten some emails expressing puzzlement over this conclusion.  So, in this post I want to explain in some detail why this is the case.

An example

Consider five Silver policies on an Exchange. In 2015, here is a table showing their gross premiums

1. $4,161.55

2. $3,881.27

3. $4,338.10

4. $4019.11

5. $3550.64

So, the second lowest silver policy is Policy 2, which has a premium of $3,881.27. Suppose our individual can contribute $1,000 per year based on their income.  If they had purchased policy 2 their tax credit would have been $2,881.27 and their net premium would have been $1,000.  If our individual purchases policy 4, however, which has a gross premium of $4,019.11, their tax credit is still $2,881.27, so they will end up having a net premium of $1,137.84

Now, suppose the gross premium increases average about 6.33% but are distributed as follows among our 5 insurers.

1. 11.38%

2. -2.57%

3. 7.26%

4. 10.28%

5. 5.29%

The new gross premiums for 2016 are thus as follows:

1. $4,634.99

2. $3,781.70

3. $4,652.87

4. $4,432.30

5. $3,738.41

The new second lowest premium is Policy 2, which has a gross premium of $3,781.70.  Suppose now our individual has essentially the same income such that the amount they are deemed to be able to contribute is still $1,000.  This means the 2016 tax credit is $2,781.70. What if our individual wants to keep his health plan and stick with Policy 4. Maybe our individual likes the practitioners in the Policy 4 network.   The new difference between the new gross premium for Policy 4 ($4,432.30) and the tax credit of $2,781.70 is $1,650.60.

Thus, although the gross premium for the policy has gone up 10.28% (bad enough) the net premium has gone up 45.06%.

So, did I concoct some bizarre set of numbers so that the ACA would look bad?  I did not. The result you are seeing is baked into the ACA.

An experiment

Let’s run the following experiment.  Suppose premiums are normally distributed around $4,000 with a standard deviation of $500.  And suppose the gross premium increase is uncorrelated with premiums and is normally distributed around 5% with a standard deviation of 5%.  Assume there are five policies at issue. We can then calculate for each of the five policies,  the gross premium increase and the net premium increase in the same way we did in the example above. We run this experiment 100 times.

The graphic below shows the results. The horizontal x-axis shows the size of the gross premium increase (in fractions, not percent).  And the vertical y-axis shows the size of the net premium increase. The dotted line shows scenarios in which the gross premium increase is the same as the net premium increase.  What we can see is that for the larger gross premium increases, the net premium increases tends to be larger than the gross premium increases and for the smaller gross premium increases (or for gross premium decreases), the net premium increase tends to be smaller than the gross premium increase. Thus, about half the population will experience net premium increases larger — and sometimes way larger —  than they might think from reading the news.



Is this result an artifact of, say, having our policyholder being deemed by the government to be able to contribute $1,000 based on their income?  Not really.  The graphic below runs the same experiment but this time assumes our individual is poorer and is thus deemed able to contribute only $500.


What we can see from the graphic is that the result is even more dramatic.  The poor will see drastic divergences between gross premium increases and net premium increases. Many, for example who have gross premium increases of say just 5% experience net premium increases of over 30%.

And what of the less subsidized purchasers, those who, for example, are deemed able to contribute $3,000 towards a policy?  The graphic below shows the result.


Now we can see that the gross premium increases and net premium increases are clustered pretty tightly together.  Indeed, for the wealthier purchasers, net premium increases more often than not are smaller than gross premium increases.  However, since most purchasers of Exchange policies tend to be those receiving large subsidies, the graphic above is not representative of the situation for most purchasers.

Did I rig the result by assuming that the income-based contribution stayed the same.  No.  Here’s a graphic showing gross versus net premiums first, under the assumption that income-based contributions remain the same and second, under the assumption that income-based contributions wander, sometimes going up, sometimes going down.



What you can see is there is not much difference between the yellow points — income based contribution remains the same — and the blue points — income based contribution wanders.

And, although I won’t lengthen this post with yet more graphics, the basic result generalizes to situations in which there are more than 5 Silver policies.  The pattern is the same.


It really is true. Net premium increases will often be larger than gross premium increases, particularly for the poor. The sticker shock some received on seeing the gross premium increase figures recently released at will, in many instances, be little compared to the knockout blow that will occur when people start computing their new net premiums.

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Many will experience premium hikes even larger than requested rate increases

Yesterday, the federal government released its list of proposed gross premium increases for health insurers selling policies on the Exchanges. To many, particularly supporters of the ACA, the results released at were jaw dropping. The median increase requested in New Mexico was 59%. In Pennsylvania, Highmark Health Insurance, the state’s “Blue Cross” insurer requested rate increases on many of its plans over 35%.  In Illinois, Coventry Health Care, an Aetna subsidiary, requested rate increases of over 30% on several of its plans. In Oregon, PacificSource, the state’s third largest health insurer, sought increases of 29% and higher on several of its plans. In short, in many states, very large increases in gross premiums were requested by a diverse set of major and minor players.

Pundits, including me, have pointed out that one should not leap from a view of these numbers to the conclusion that policyholders in the Exchange markets should invariably expect double digit increases.  The only companies in the data released yesterday are those requesting more than a 10% increase.  As Larry Levitt, a top executive at the influential Kaiser Family Foundation, said, “Trying to gauge the average premium hike from just the biggest increases is like measuring the average height of the public by looking at N.B.A. players.”

In fact, however, the math of Obamacare means that many purchasing policies on the Exchange will actually experience larger net premium increases than even the huge ones proposed by many insurers. This is so because of the way the Affordable Care Act computes the net premium paid by policyholders.

Let me take a quick example to illustrate the reason net premiums are going to go up even more than the numbers from suggest.  Take an individual who has an individual policy for which the gross annual premium is $4000.  And suppose that the premium increase for that plan, as is proposed in many places, 25% up to $5,000.   But suppose that the second lowest priced plan in the state, which was also charging $4,000 goes up only 5% to $4,200.  What happens to net premiums.?  Let’s make our individual a typical Exchange purchaser with an income equal to 250% of the federal poverty level.  In 2015, that individual would be paying about $2,334 in net premiums.  In 2016, because net premiums are pegged to the price of the second lowest silver plan, that individual would be paying about $3134 in net premiums.

In short, the policyholder experiences an increase not of 25% — bad enough — but of 34%, even worse. If the policyholder wants to keep its plan, and perhaps the network of medical practitioners that have developed an understanding of the policyholder’s medical conditions, it is going to require the policyholder to pay 34% more.  To be sure there are complications that might tweak that number a bit, but the basic math is right.

It will be even worse for some.  We know that in some states, a few plans are proposing reductions in their gross premiums.  In our prior example, if the second lowest plan went down by 2%, the net premium of the plan the individual actually purchases will go up to $3414 per month, an increase of 46%.

Or, keep the assumption that the second lowest silver plan goes up by 5%, but have the purchaser have a income not of 250% of FPL but of 175% of FPL.  Policies are supposed to be affordable for them too. Formerly they would have paid $1021 per year in net premiums.  Now, they will pay $,1821 per year in net premiums, an increase of 78%. It turns out that keeping your healthcare plan is going to be an extremely expensive proposition.

So, yes, in some sense the gross premium increases released yesterday by the federal government are unrepresentatively large.  But in terms of what people actually pay, they are, in many instances, unrepresentatively small.  Of course, many people will be unwilling to pay increases of 34% or 46%  or 78%.  But to avoid those increases, they will increasingly need to flock to the second lowest silver plan.  Doing otherwise will prove ever more expensive. And so, the promise of “choice” in healthcare plans contained in the ACA may be fulfilled significantly less than its proponents anticipated when the bill was passed.  The architecture of Obamacare may induce yet more purchasers to converge on Silver HMO plans.

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Government data shows potentially scary ACA premium increases for 2016

Under the implementation of the Affordable Care Act promulgated by the Obama administration, the federal government publishes a list each June 1 of health insurers seeking to increase their premiums by over 10% from one year to the next.  Today, the Obama administration released their data for 2016. There are a lot of insurance plans and a lot of very high requested increases on the list.

My examination of the data this afternoon shows 661 insurance plans in which a rate increase of over 10% is being requested.  And the increases requested by these insurers is often way over 10%.  The median increase requested by insurers on the list it varies from a low of 12% in New Jersey to 59% in New Mexico.  Median means half the numbers are below the median and half are above the median.  Thus a median increase of 32% in Pennsylvania means that half the insurers there on the list are asking for more than a 32% increase in premiums.

An aggregation of the data is also revealing. If one looks at the median increase in each state, the “median of the median” is 19%. Half of the states are seeing median increases of less than 19% and half are seeing median increases of more than 19%.

Most of the analyses of this data thus far have looked at particular states and found them troubling.  Taken as a whole, however, the widespread significant increases should be disturbing to those who were confident that the Affordable Care Act would continue to result in low premiums.

Moreover, the median figures cited above are by no means the maximum increases requested by insurers. Let us start with some heavily populated states and take a look at some representative high increase requests.  In Texas, Time Insurance is requesting a 65% increase. In Florida, Time Insurance is asking for 63% on one of its products; the better known UnitedHealthcare is asking for 31%.  In Illinois, Blue Cross is asking for a 38% increase on one of its plans; Coventry, also a good sized player, is asking for 34% on another.  In Pennsylvania, a Geisinger plan is asking for 58%; Geisinger is a significant player in that state.  The list goes on and on.

The table

The table below shows the data I was able to mine from on the rate increases.

State Number of plans reporting Median Rate Increase (Conditional on Rate Increase > 10%) Rank
Alabama 14 24 13
Alaska 13 24 14
Arizona 24 20 17
Arkansas 3 21 16
California 0 N/A
Colorado 0 N/A
Delaware 26 16 28
District of Columbia 8 14 38
Florida 13 18 25
Georgia 27 16 29
Hawaii 6 18 22
Idaho 57 19 20
Illinois 16 15 31
Iowa 30 25 11
Kansas 15 35 3
Kentucky 0 N/A
Louisiana 15 18 26
Maine 0 N/A
Maryland 8 30 6
Massachusetts 0 N/A
Michigan 12 15 33
Minnesota 0 N/A
Mississippi 6 26 10
Missouri 13 16 30
Montana 12 34 4
Nebraska 12 15 32
Nevada 25 14 36
New Hampshire 11 44 2
New Jersey 7 12 40
New Mexico 3 59 1
New York 0 N/A
North Carolina 17 26 8
North Dakota 3 18 23
Ohio 15 14 34
Oklahoma 8 28 7
Oregon 23 20 18
Pennsylvania 51 32 5
Rhode Island 0 N/A
South Carolina 10 24 12
South Dakota 18 17 27
Tennessee 12 14 35
Texas 22 26 9
Utah 31 19 21
Vermont 0 N/A
Virginia 19 14 37
Washington 24 13 39
West Virginia 14 19 19
Wisconsin 12 18 24
Wyoming 6 23 15


All of that said, the figures should not be misinterpreted.  The following caveats must be considered.

1. The data only lists those insurers that requested an increase of more than 10%.  There are many plans that requested increases less than that amount.  So it is incorrect to say that the average or median increase in insurance prices is going to be 19%. If a lot of big insurers are requesting increases less than 10%, the average increase will be less than 19%.  On the other hand, if the big insurers are over 19% and it is mostly small insurers that are submitting rate increase requests of under 10%, then the 19% figure is too low.

2. The data is not weighted by the number of policies sold by an insurer.  With all respect to small insurers (and small states), in the grand scheme of things it does not matter much if a small insurer in a small state is raising its rates 40%.  Of course it will affect the people involved, but it is not a good bellwether of the performance of the ACA.  On the other hand, if a big insurer in a big state, like Scott & White in Texas, is requesting increases (as is the case) of 32%, that is a very big deal. Until we have an estimate of the number of policies sold by each insurer, a secret that seems to be more tightly guarded than many diplomatic communications, it is hard to know perfectly what the numbers in the list actually mean.

3. The data for some important states is missing.  We have no data for New York and California, for example, and no data from about seven other states. Does that mean that there are no insurers there requesting more than a 10% increase, that the data is just delayed, or is there another explanation?  Until this mystery is resolved, it’s hard to know fully what the numbers published today imply.

4. Ask does not equal get. All we have right now are the rate increases requested by insurers.  There now follows a review process in which the reasonableness of the rate increases are examined.  If the federal government or, in some instances, the states find the rate increases unreasonable, then they do not go into effect.  Of course, insurers who see their rate increases denied, may decline to sell the policies, which results in less competition and leaves many insureds without any continuity in coverage. Yes, it is possible that some insurers are bluffing and requesting pie in the sky.  The risk in calling that bluff by denying or modifying a rate increase is that the insurer may pull out.

5. I basically did this analysis by hand because CMS has not released the data in a form (such as Excel, CSV, JSON or others) that would facilitate machine analysis.  I tried to do the work carefully, but I am an imperfect human.  I am doubtful, however, that any errors materially affect the conclusions here.



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Yes, you can pick your health plan or your doctor for now, but prepare to start paying a lot more for the privilege

Much has been written about the general issues associated with higher premiums for plans purchased on the various Exchanges under the Affordable Care Act. The fear is that higher premiums will price individuals out of the market — at least lower risk individuals — and result in a spiral of premium increases. Supporters of the ACA counter, however, that increases in gross premiums — the amount insurers say they charge — does not matter much because the amount most individuals pay under the Affordable Care Act does not depend on gross premiums so much as it depends on one’s income. Recent studies, after all, suggest that about 87% of purchasers receive tax credits to purchase plans that depend solely on their income.

The truth, however, about the effect of premium increases under Obamacare is more complex. Basically, increases in gross premiums for basic silver plans can have a non-linear and frightening effect on increases in the net premiums Americans pay to persist in plans that are more generous either because they afford greater choice in selecting one’s doctors or because they require less cost sharing by insureds. The remainder of this blog post explains why.

Let’s start with a simple example drawn from real life to illustrate the general idea. Data taken directly from shows that in my home city of Houston (Harris County, Texas), the gross premium for the second lowest silver plan (an HMO plan) is about $250 per month for a 40 year old individual. If that person’s net income is $25,000, under 26 U.S.C. § 36B their net premium can be computed as  $143 per month for that second lowest silver plan; the remainder is supposed to be paid via a $107 tax credit from the federal government. (Mathematica notebook containing the analysis available on request)  Suppose, however, the individual does not want an HMO plan but wants a PPO plan so they can have greater choice of doctors. The cheapest one in Harris County has a gross premium of $338 per month or about 35% more. But, because the tax credit stays constant at $107, the net premium is $231. This means that the right to select one’s own doctor costs our hypothetical individual 57% more in the amount they actually pay.

The situation is similar if one is willing to accept an HMO plan but one wants the plan to pay a higher percentage of expected medical expenses. The second least expensive gold plan in Harris County is $297 per month or 18% more than the second lowest silver plan. Again, however, because the tax credit remains the same, there’s a problem: the actuarial value of the gold plan is actually just 14% higher than its silver counterpart, but because of the way subsidies are calculated, the cost is 33% higher. Only two types of people would likely be willing to incur this “double payment” to get a better plan: people who are unhealthy for whom a small improvement in a plan might mean a great deal or people who are just extremely risk averse.

The situation persists for the few platinum purchasers. If one goes from the second lowest silver plan all the way to the second least expensive platinum plan, it turns out that the net premium increases a whopping 138%. And this is true even though the while the gross premium goes up by 79% to $448 per month and the actuarial value of the policy goes up only about 29% and the gross premium goes up “only” by 79%. One can imagine that the only people of this income level willing to incur this high a premium increase in exchange for only somewhat better coverage would be those who expected to use the coverage extensively — exactly the people that force insurers to increase future prices.

Some of the same mathematical logic that drives the disproportionate increases in net premiums in a single year applies in a similar way to premium changes over time. Let us consider our same individual and project forward to 2016. Imagine that they purchased that PPO silver plan in 2015 and wish to continue in it. To do the computations, we’ll have to make a few assumptions: (1) that the federal government’s expected contribution from income increases for 2016 at the same rate it increased for 2015 and that the federal poverty levels for 2016 likewise increase at the same rate that they did in 2015. Suppose further that the gross premium for the second lowest silver plan and the gross premium for the increases by 4% but the gross premium for the gold HMO plan or the silver PPO plan increase by 8%. If our individual’s income again increases by 10%, the net price of the more generous policy jumps by 13.5%. The effect is non-linear.

And what if we start talking not about individuals, but about families?  Consider, now, the family of four with two adults each age 40. We’ll give the family an income of $50,000 per year. Again, for concreteness, I’ll place them in Harris County, Texas. The gross premium for the second lowest silver plan (an HMO) is $748 per month. But with a tax credit of $456, the net premium for that policy is $292 per month. If the family wants to purchase a silver PPO, the cheapest one will feature a gross premium of $1013. Since the tax credit stays the same at $456 per month, this means the net premium is $557 per month, an increase of 91% just to get more choice in picking doctors. Or, if the family wants to purchase the second cheapest Gold HMO, that will cost $890 gross and $434 net. This is an increase of 49% just to get a plan with 14% richer expected benefits. Now, whom do you suppose might pay such a disproportionately higher amount?

The diversity of metal levels and of plan types has always been touted as a benefit of Obamacare. It is supposed to distinguish the ACA from  administratively simpler (“one size fits all”) regimes such as single payor plans. But the existence of premium subsidies pegged to the price of the second lowest silver plan means that the present diversity of plans may be a short run phenomenon or that the diversity may exist only on paper. There may technically still be gold plans or PPOs, but very few may be purchasing them. Assuming Obamacare lasts a few more years, we may effectively see the demise in the marketplace of Gold and Platinum plans and, even more likely, the demise of Gold and Platinum PPO plans. Choosing one’s doctor may, as a practical matter, become a sensible option only for the few wealthy purchasers that do not depend on subsidies.

Might this all be just sort of bug that would be easy to fix if only Congress were more cooperative? Actually, not. The high marginal costs of more generous policies is a fundamental feature of Obamacare’s architecture. It is one  that is simply becoming more apparent as the program matures. Once you tell people that government will essentially buy you an HMO silver plan if you contribute some amount based on your income – but will pay no more – the net costs of buying anything more generous than that inevitably look very high.

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Individual policies on the Exchanges: Cheap plans, prices down, Better plans, prices up

I’ve been doing a lot of research on the state of policies sold on the health insurance exchanges.  It’s not easy because the Obama administration, as even its friends acknowledge, has not been forthcoming with information.  It has, however, placed some useful information in the public domain: two large databases of the plans being sold on the “Federally Facilitated Marketplace.”  That’s the health insurance Exchange for states, like Texas and many others, that declined to establish their own exchanges.  With the help of the R computer language, I’ve been sorting through this database and have reached the following conclusions.

  1. The change in premiums between 2014 and 2015 depends significantly on the metal level of the plan and whether it is a PPO or HMO.
  2. Gross premiums for platinum plans are up significantly in price, 21%, whereas bronze plans and catastrophic plans are down over 11%. The high increase in gross premiums for platinum plans creates a serious potential for an adverse selection death spiral in that segment of the market.
  3. Net premiums will show larger percentage increases and decreases than gross premiums for many individuals. This is so because substantial parts of the premiums are paid via subsidies from the federal government.
  4. PPO plans are up substantially in price, 8%, whereas HMO plans are down substantially, -18.%.
  5. The combination of increases in the more generous platinum and PPO plans and decreases in the less generous bronze and HMO plans may start to divert Americans into healthcare plans that offer lower benefits and somewhat less choice, albeit at a lower price than was paid this past year.
  6. Among plans that persisted between 2014 and 2015, the premium variations are less extreme: persistent bronze plans increased in price by 9.5% whereas persistent platinum plans increased in price by 14%. The larger variation in gross premiums overall is thus likely due to the exit of carriers who priced at extremes and low pricing by new entrants for bronze plans but very high prices for the more generous plans.
  7. Cost sharing for the plans has increased somewhat, but many cost sharing arrangements have remained largely the same.
  8. Competition, as measured by the number of unique issuers offering plans in each county, has increased substantially since 2014, but a market in which three or more insurers are actively competing is still a rarity, particularly for the plans that give consumers a greater amount of choice in selecting their doctor.

You can read a copy of the full report, which contains 29 tables of information, here.


I’m also happy to provide the data and code on request. 

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Reinsurance reduction will add 7% to gross premiums for 2015

That’s in addition to whatever increases are caused by medical inflation and adverse selection


As we draw to what was originally to be the close of the 2014 regular open enrollment period for policies sold on Exchanges under the Affordable Care Act and as the evidence comes in on the actual numbers and demographics of purchasers, it’s time to start thinking about 2015. In this post, I’m not going to speculate today about the effects of the expanding the “hardship exemption” from the individual mandate on insurers’ experience in 2014, the effect of the “Honor System” in extending the time in which individuals can purchase coverage on the Exchange without medical underwriting, or on the effects of any of the other the myriad changes in the law that have been promulgated by the Executive Branch since Congress passed the ACA in 2010. Instead, I want to focus on the effect of statutory changes in the government-created reinsurance program on likely premiums in 2015.

First, a refresher. One of the ideas behind Obamacare was to lure people into the Exchanges with carrots and sticks.  The most frequently discussed carrots were advanced premium tax credits that reduced the effective price of insurance for many individuals and, for many of those receiving the premium tax credits, contracts with extra benefits (cost-sharing reductions) for which the purchasers do not have to pay. Not only, however, are Exchange policies subsidized by reducing the price to the consumer but also by reducing the cost the insurer faces in paying claims.  A key mechanism for this latter reduction for the first three years of the program is free “reinsurance” provided to all insurers for slices of their claims. Of course, the reinsurance isn’t really free; there’s a $63 per insured life tax levied on other health insurance policies in order to make policies on the Exchange more attractive, a transfer whose justice will not be considered today.

The reinsurance works in 2014 by having the government reimburse insurers for 80% of the amount of any insureds claim between $45,000 and $250,000. Thus, if an insured had claims of $105,000, the government rather than the insurer would pay for $48,000 of the claim while the insurer itself would pay for the remaining $57,000.  If an insured had claims of $30,000, the insurer would pay the whole bill.  And if an insured had claims of, say, $300,000, the government would cover more than half — $164,000 — while the insurer itself would pay the remaining $136,000.

Sample of the data embedded in the Excel spreadsheet for The Actuarial Value Calculator
Sample of the data embedded in the Excel spreadsheet for The Actuarial Value Calculator

One can use information contained in the government’s own “Actuarial Value Calculator” to estimate the effect of this reinsurance on Exchange premiums.  (I’ve placed a graphic above this paragraph showing some of the information in the Calculator.)  Based on my computations using Mathematica and done in connection with a recent academic conference, the reinsurance should lower the price of an Bronze policy by about $450 (11%), a Silver policy by $531 (11%), a Gold policy by $545 (11%) and a Platinum policy by $616 (10%).

The parameters of the reinsurance policy will change in 2015.  HHS currently says that instead of “attaching” at $45,000, reinsurance will only kick in if an individual’s claims exceed $70,000. And instead of reimbursing the insurer 80% of the slice between the attachment point and the $250,000 limit, the government will now reimburse just 50% of the slice. The table below shows the results of this change in reinsurance on the expected value of the reinsurance policy. If one assumes that medical inflation will be 4%, the value of the reinsurance will range from $192 for Bronze policies to $243 for Platinum policies. These computations are all again done using Mathematica based on data provided by the government itself in its Actuarial Value Calculator.

Value of reinsurance subsidy in 2015 for varying rates of medical inflation
Value of reinsurance subsidy in 2015 for varying rates of medical inflation

Insurers will need to compensate for the diminished reinsurance by raising prices.  How much?  The table below shows the answer: somewhere between 7 and 8% depending on the type of policy being sold and the rate of medical inflation.

Increase in premiums for 2015 just to cover reduction in reinsurance subsidies
Increase in premiums for 2015 just to cover reduction in reinsurance subsidies

If one adds regular medical inflation to the increases induced by reduced subsidization, here’s a picture of what we get. To obtain a single result for each rate of medical inflation, I’m going to weight the metal tiers according to their rough proportions in the market as last measured.

Projected premium increases for 2015 with reinsurance subsidy reductions taken into account for varying rates of medical inflation
Projected premium increases for 2015 with reinsurance subsidy reductions taken into account for varying rates of medical inflation

The results of combining ordinary medical inflation with reinsurance reductions are a bit scary.  While most people seem to believe the ACA system can survive premium increases of 6% or 8%, what we see is that even if medical inflation is kept to 4%, the results of combining medical inflation with subsidy reduction is a 12% hike.  And, if insurers are nervous about pricing in 2015 due to higher than expected claims experience in the early parts of 2014 or the persistence of problematic demographics such that they expect ordinary claims inflation of 10%, then we start getting into premium increases of about 18%.

Is there a workaround?

It is fair to say that the Obama administration has not been reluctant to change implementation of the Affordable Care Act in response to changing circumstances.  And, I suspect that if the Obama administration starts getting hints that insurers selling on the Exchanges are either thinking of pulling out of the Exchanges or of raising premiums significantly, one of the ways it will respond is by altering the parameters of the reinsurance program.  The attachment point, limit and reimbursement rate are all matters as to which the Obama administration has regulatory flexibility.  Indeed, it changed the 2014 reinsurance parameters favorably for insurers late into the process. And, of course, by providing a lower attachment point, higher reimbursement rate and/or a higher limit, the government can increase the effective subsidy created by the free reinsurance and thereby reduce pressure on insurers to raise premiums.

If, for example, the Obama administration were to go to, say, a 65% reimbursement rate rather than a 50% rate for 2015 and were to go to a $60,000 attachment point rather than a $70,000 one, a 4% increase in medical inflation might result in a lesser 9% increase in premiums rather than 12%.  And even a 10% increase would result in a lesser 14% increase in premiums rather than an 18% one.

The problem with this “fix,” however is that it costs money.  And, by statute, the government is supposed to spend $4 billion less on the reinsurance program on claims for 2015 than it spent on claims for 2014.  That’s why HHS reduced the reinsurance parameters for 2015 in the first place.

I can foresee two ways around this limitation.  The first is for the Obama administration to engage in creative math and find a theory under which the projected cost of its reinsurance program aligns with statutory requirements.  While cynics may be fond of my projection of this response, there is a serious question as to the extent that principled actuaries in the Executive branch will permit this “methodology” to be used. The second possibility is for the Obama administration to stockpile funds from 2014  and use them to pay reinsurance in 2015.  Section 1341(b)(4)(A) of the ACA appears to make this possible.  This scheme only works, however, if the government actually has money left over from its 2014 reinsurance pool.  And, while lower than expected enrollments in the Exchanges increase the probability that there will be money remaining, that potential surplus could well be eaten away if claims for 2014 are higher than expected.

A result of improper conceptualization

Amidst all the technical detail, it’s worth thinking about how this could have happened. How could the architects of the ACA, who were acutely aware of the risks of an adverse selection death spiral, create a system in which there were built in pressures to increase premiums? I think the answer comes in examining the rhetoric of the reinsurance program.  It was not articulated as a subsidy but rather as a way of reducing the risk of entering the Exchanges. See here, here and here for examples.   If adverse selection or moral hazard drove claims costs up, the government would significantly insulate insurers from that risk by providing reinsurance. This, along with Risk Corridors in the first three years of the program, and Risk Adjustment thereafter, was supposed to provide insurers with comfort as they deliberated whether to enter an untested market for health insurance in which most of their conventional underwriting mechanisms were prohibited. And, indeed, the Transitional Reinsurance program does reduce risk. Based on my computations, it reduces the standard deviation of losses for Bronze policies from $16,403 to $11,430 and for Platinum policies from $17,215 to $11,598.

If one conceptualizes the transitional reinsurance program merely as a risk reduction policy, it makes sense to phase it out as insurer experience with the purchasing pools in the ACA.  Insurers gain confidence in how to price their policies.  But what appears to have been forgotten in that calculation is that these reinsurance subsidies also save insurers lots of money.  And insurers will need to respond to the phasing out of these substantial subsidies by raising premiums.  Whether that tunnel vision in conceptualization contributes to an implosion of the ACA, at least in some states, remains to be seen.


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Does competition in the Exchanges result in lower premiums?

One of the touted benefits of the Affordable Care Act was that, by fostering transparency, there would be greater competition in the health insurance market and that premiums would go down as a result.  We now have data to help see whether competition within the various Exchanges has succeeded in reducing prices. This post, based on a scholarly talk I recently gave at the University of San Diego’s Workshop on Computation, Mathematics and Law, will suggest that the effect, if there is one, is small and subtle.  It looks as if having just one seller of a product within a county may lead to somewhat higher prices, but the effect may not be robust. The methodology used here is a first cut. Whether other methodologies might tease out a larger relationship remains to be seen.

Note to ACA Death Spiral Fans: The USD conference mentioned above is one reason for the infrequent posts as of late.  It’s been a busy period. Sorry. There’s A LOT to write about.  Keeping track of Obamacare is at least a full time job.


The data for this project comes mostly from good old, which, if one forages around a bit, actually contains a user-friendly database exportable in various standard formats such as CSV and JSON describing all 78,392 plans currently being sold in 2,512 counties via the federal Exchange. Each plan is described by 128 fields, including the metal tier of the plan, the name of the issuer of the plan, the type of plan (PPO, HMO, POS, EPO), the monthly gross premiums of the standard plan for various family types, the deductibles and cost sharing arrangements of the standard plan, and the deductibles and cost sharing arrangements of the variants of the plan that feature cost sharing reductions as described in 42 U.S.C. § 18071. The remaining data comes from the United States census.


The idea here is to consider each county of the United States as a market for health insurance and to find, for each county, the number of issuers selling plans on the Exchange, a representative measure of the price being charged by each issuer, and, therefore, a representative measure of the price charged within each county.  If competition resulted in lower prices, one would expect to see — all other things being equal, which of course they are not — an inverse relationship between the number of issuers and the representative price charged within each county.  We can also see, however, whether any such correlation is either spurious as a result of factors that correlate with both the number of issuers and the premiums charged or whether a stronger correlation might appear if other factors were controlled for. Here, the one other factor I took account of was county population density, the idea being that insurers might be less eager to enter counties in which the population density was low and that prices might be higher in such areas due to transportation costs.

Visualizing the Results

The “Distribution Chart” below shows a typical result from this data exploration.  Here is the distribution of representative monthly premiums charged a couple in which the members are both 40 years old for a Silver PPO plan.  The plot is broken down by the number of issuers within the count.  If the insurer sells more than one Silver PPO plan within a county — which sometimes occurs — I take the median price for that insurer.  And to determine the county price, I take the median price for all of the issuers.

Distribution Chart (basic)
Distribution Chart (basic)

The Distribution Chart works by using a dot to represent each gross monthly premium broken down by number of issuers. It  applies different background colors that depend on the number of issuers within the county and shades each part of the background according to the density of premiums at that price level.  Darker shades represent higher density.

We can run the same analysis for different purchasers, different metal levels, different types of plans and using different measures to move from issuer prices within a county to a single representative issuer price and to move from representative issuer prices to a representative county price.  Here, for example, is the Distribution Chart for gold PPO plans purchased by couples age 40 with two children in which I use the minimum price offered by the issuer within each county and then use the 25th percentile price of those minimum prices to come up with a representative county price.

Distribution Chart for Gold PPOs (Coupled +2 children, Age 40), minimum by issuer, 25th quantile to derive county price
Distribution Chart for Gold PPOs (Coupled +2 children, Age 40), minimum by issuer, 25th quantile to derive county price

We can also aggregate matters. Here is the Distribution Chart for all Bronze plans of all types (HMO, PPO, POS, EPO) in which I take the median of multiple plans issued by a single issuer and then take the median value of all issuers to derive a county price. I do this for a single adult, age 30.

All bronze plans
All bronze plans

Here’s an analysis examining all types of Bronze plans but using a variant of the visualization.  The individual dots are suppressed and we now have little histograms for situations in which there is 1 issuer through 8 issuers.

Histogram density visualization of all bronze plans
Histogram density visualization of all bronze plans


Eyeball Analysis

When I eyeball this data and many more permutations that I have produced, I at least do not see any dramatic and widespread relationship between the number of issuers within a county and the representative gross premium being charged.  For some combination of parameters, one occasionally sees higher prices when there is only one issuer in the county, but generally the picture, at least the naked eye is quite blurry. The one thing I can say with some certainty is that the family-type of the purchaser — individual, couple, family with children — does not appear to affect matters. Premiums appear quite uniformly scaled across these groups.

What I do consistently is, as noted here and here, that there are many counties in which there is only one issuer of a particular level and type of plan. For Silver PPO plans, for example, in which one wants a medium level of cost sharing but wants at least some freedom in selecting a provider, of the 2,512 counties, 20% of the counties have no issuers with such a plan while another 36.6% have only one such issuer.  Only 13% of the counties have three or more issuers of these plans. The pie chart below shows the distribution of issuers.

Distribution of Silver PPO issuers
Distribution of Silver PPO issuers

Or, suppose one simply wants a bronze plan of any sort. What we see is that 16.2% of the counties apparently have no such plan, 27.9% have only one issuer and 31% have 2.  Thus, only about one third of the counties have 3 or more choices for a simple bronze plan.  The pie chart below shows the result.

Distribution of bronze issuers
Distribution of bronze issuers

Statistical Analysis

Sometimes the human eye and the human brain, magnificent as those organs are, do not see patterns that in fact emerge when studied through the lens of statistics or machine learning. Modern computers and statistical activities make it easy to go beyond eyeballing data. What I have done, therefore is to merge representative premium data with data on the population density of each county and see if any statistically significant relationship emerges between the number of issuers within each county and the county representative price.

I want to start with the simplest model: a linear relationship between the number of issuers and the county representative premium.  I will do the analysis at first for my baseline Silver PPO purchased by a couple age 40 where I use the median price of the issuer if they sell more than one Silver PPO within the county and the median price of issuers .  The graphic below shows the results.  There is a statistically significant relationship between the number of issuers and the premium.  For each additional issuer, the gross premium goes down by about $16.  The model overall, however, accounts for only 2.1% of the variation in representative county prices, meaning, roughly speaking, that 98% of the variation in premiums is correlated with factors other than the number of issuers.

Linear regression of county representative price on number of issuers
Linear regression of county representative price on number of issuers

The problem with leaping from this finding to an attempted vindication of claims about the virtues of the ACA is that the result, even weak as it is, depends a bit on specification of the model.  This gets a little technical, but unless one assumes a priori that there is some good reason to think that the relationship between number of issuers and price is in fact a linear one, restricting the regression to a simple linear model is potentially misleading.  Here, for example, I regress the same data on n (the number of issuers), n-squared and the log of n.  All of the coefficients in front of the various terms are still significant, but if one looks at the picture one gets a much more complex story.  It appears that having one issuer does lead to high prices and that having two issuers may minimize the number of prices. As one increases the number of prices beyond two prices go up again until we peak at four issuers.  This model explains almost 9% of the variance in pricing, which is considerably better than the simplest linear model but still not very good.  Clearly, pricing is determined by much more than the number of issuers within a county.

Pricing model based on linear, quadratic and logarithmic term
Pricing model based on linear, quadratic and logarithmic term

The observed pattern when this more complex regression model is used appears roughly to persist for all metal types of HMOs and PPOs except platinum PPOs where we see the price increase as the number of issuers within a county increases.  The family type of the purchaser appears not to affect the general shape of the relationship.  I am never able to explain more than about 12% of the variance in premium pricing when I use just the number of issuers within the county as my single explanatory variable.

I have some sense that the population density of a county might have an effect on pricing. Perhaps lower density counties are more expensive.  Or, it could be the case that higher density counties, which may have fancier equipment, are more expensive.  The regression below shows a simple linear regression using two variables: number of issuers within the county and population density of the county. As one can see, the results are little changed.  Both variables have effects that are statistically significant but small. As one goes from 1 to 2 issuers, the price drops by about $17 per month.  As one goes from a county in which the population density is 4.3 (which would put it in the 10th percentile) to a county in which the population density is 491 (which would put it in the 90th percentile), the price goes up by $7 per month. The model still does not explain much (adjusted R-squared <0.03).  Here are the results in more detail.

Linear regression using number of issuers in county and population density
Linear regression using number of issuers in county and population density

Again, I can use a more complex specification.  Below I show the results of using linear, quadratic and logarithmic terms for both number of issuers and population density.  What we see is a complex picture in which having just one issuer appears to persist in causing somewhat higher prices and in which population density plays a small role.  But we are still able to explain less than 10% in the variation of premiums.  Again, whatever is going on in premium pricing models, is a lot more complex.

Linear, quadratic and logarithmic terms for number of issuers and population density
Linear, quadratic and logarithmic terms for number of issuers and population density

A Foray into Machine Learning

I also attempted to see whether a computer could find a formula that predicted county representative gross premiums any better than my statistical models when given free rein to do so.  To do this, I loaded the data into a program called Eureqa from Nutonian .com, which basically uses “genetic programming” to find models that predict well. The basic idea is to treat mathematical formulae kind of like strands of genetic material and permit mathematical formulae that perform better to evolve via mutation and “sex” to produce what may be yet formulae.  Sometimes it produces amazing results and — well — sometimes it does not.  Either way, however, genetic programming and other methods of machine learning are a useful complement to traditional techniques. They help one  check whether the apparent incapacity of traditional methods such as regression are an artifact of limited specifications or the result of unavoidable noise in the data.

In this case, Eureka basically found little. It found some functional forms a human might not come up with such as the one below, which appeared to predict decently, but in fact did not do any better than the models I developed by hand.  The foray into machine learning suggests, then, that the limited ability of our our statistical models to predict well is not the result of a failure to specify the model correctly but rather the result of noise in the data and unobserved variables.

Formula discovered by genetic programming


Unfortunately, perhaps, the results shown here are not the sort one writes home about or that get on the front page of either scholarly publications or news reports.  They are kind of “meh” results. Maybe market concentration has an effect, but, at least as revealed by the data here it is small. So, why might this be?

1. Perhaps the number of insurers in the Exchange is not as relevant anymore as might be thought. Given the availability of individual policies off the Exchange in some states, the number of individual polices within the Exchange may not be as important.  I don’t have the data on off-Exchange policies and neither, so far as I know, does anyone else.

2. Maybe pricing is determined more by the identity of the insurer than the number of insurers.  Suppose, for example — and I do not say this is true — that Blue Cross made different assumptions about adverse selection and moral hazard with the purchasing population than did, say, United Healthcare. Markets that Blue Cross entered aggressively might thus have lower representative county prices than markets in which they did not.  Or suppose that Blue Cross was able to use market power and/or superior skill to create narrower networks that nonetheless satisfied regulators.  This might account for markets in which Blue Cross was present exhibiting lower prices.  Or suppose that Humana was more willing to take a loss the first year in order to supposedly lock in business than was Blue Cross.  This too might explain lower pricing.  This suggests another experiment in which one looks at pricing as a contest and seeing how each of the competitors fared against each other.

3. Maybe consumers are very sophisticated such that “Silver PPO plans” are  not comparable.  If consumers, for example, value the precise package of benefits and providers offered by, say, Blue Cross in a county as being quite different from the precise package of benefits and providers offered by, say, Humana, then we can’t just count issuers in determining the level of competition in a county.

4. Population density isn’t the right variable to include.  Maybe what we need is some measure of medical pricing by counties. Or maybe, as the Wall Street Journal suggested, we need to include some measure of income or income inequality.  Sadly, it may be that healthcare costs more in poorer counties, perhaps because the poor have more serious health problems.  At the moment I have not included those variables.  Future examinations of this area should probably do so insofar as the data permits.


Ordinarily, it would be my practice to make the Mathematica notebooks used to conduct this analysis fully available.  I very much believe in transparency.  Unfortunately, this analysis was conducted using features in a beta version of Mathematica 10 and I have signed a non-disclosure agreement with respect to that software.  While I received consent to show certain results from use of that software, I did not request or receive consent to show code.  Moreover, the code would not work on computers that do not have Mathematica 10.  I commit to releasing the code as soon as Mathematica 10 is out of beta.  I don’t think my NDA stops me from saying, however, that Mathematica 10 looks somewhere between absolutely spectacular and completely mind-blowing.



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The ACA’s transitional reinsurance tax: the numbers are funny again

Most sellers of health insurance in the United States outside of health insurance Exchanges will be forced to add $63 per member on to premiums for 2014 to cover a new tax imposed by the Affordable Care Act on the sale of such policies. That tax revenue coupled with $2 billion out of the federal treasury will go to subsidize individual policies sold on the federal Exchanges, probably lowering their gross premiums by about $525 per person.  If, however, enrollment in the federal Exchanges remains considerably lower than projected and enrollment in non-grandfathered, non-Exchange plans does not compensate for the reduction, the revenue collected from the tax is likely to be in excess of that which needs to be paid to support the statutory subsidies.  The $63 per member tax, which has precipitated considerable protest, thus might end up being overly high. And if the Executive branch can exercise its discretion to delay or waive taxes for one part of the ACA based on alleged new developments, why not for another?

The Center for Medicare & Medicaid Services (CMS)  has many options for addressing the surplus.  It might choose to to use the surplus tax revenue either to cut similar taxes in the subsequent years of the program or to rebate the excessive tax back to health plans and others who paid it. CMS might, I suppose, inflame people from both ends of the ideological spectrum by gifting insurers with more generous reinsurance this year.  Or CMS might simply squirrel the surplus away to provide reinsurance after the normal sunset of the program in 2016. I suspect, however, that  CMS is likely to use the surplus to increase the generosity of reinsurance provided in subsequent years of the program such as next year. Doing so could mask problems of adverse selection that could otherwise result in large premium increases. Such a choice would not  necessarily be a bad thing: it just highlights yet again the expense of the ACA, the fragility of attempts prior to its passage to model its effects, and the problems with thinking about its interlocking web of provisions in a linear, reductionist manner.

Here’s a more detailed explanation.

The Affordable Care Act subsidizes both insurance purchases made on the individual Exchanges and  individual policies still sold off the Exchange that conform with various ACA rules.  Doing so lowers the price of insurance and decreases the systematic risk associated with selling policies in a new regulatory environment in which the population of insureds may have different (and worse) health profiles than those previously composing the insurance pool.  A key way that the ACA does this is through a program of “transitional reinsurance” provided free of charge to insurers willing to write policies in the individual market — so long as those policies haven’t been exempted from the requirements of the ACA by being “grandfathered.” The program is “transitional” because it is supposed to end after three years. One way of thinking about all this is that free reinsurance lowers both the mean and the standard deviation of the net claims distribution faced by eligible insurers.

Under section 1341 of the ACA and the regulations CMS has developed to implement it, the transitional reinsurance program is ultimately supposed to break even. If tax revenues that fund it are less than the expenditures it requires, CMS has provided in 45 C.F.R. § 153.230(d) that reinsurance payments are cut in that year in order to prevent a deficit. If tax revenues that fund the transitional reinsurance program are greater than the expenditures it requires, CMS has stated in 45 C.F.R. § 153.235(b) that the surplus will be spent in subsequent years of the program on reinsurance benefits.  The program also works with a one year lag: money is collected and paid in each year is for claims made the preceding year.

The Center for Medicare and Medicaid Services has funded the transitional reinsurance program this year by levying (with the help of its IRS friends)  a $63 per insured life tax on most (but not all) health insurance policies sold in the United States this year. (The payments are deductible for for-profit enterprises). CMS says it is planning an exception to the tax for self-funded plans that are also self-administered, a rule that, as shown in the graphic below, CMS previously said (correctly) it lacked statutory authority to issue and that will significantly benefit labor unions. This tax revenue, coupled with a required $2 billion from the United States Treasury, is estimated to yield $12 billion to be paid in 2015 for claims arising in 2014.  CMS will use the the money to provide a form of stop-loss reinsurance that attaches at $45,000 of claims per member and that provides 80% reimbursement for claims up to $250,000. In earlier versions of the regulation, the attachment point was a less generous $60,000.

Comparison of regulations: March 11, 2013 v. October 30, 2013
Comparison of regulations: March 11, 2013 v. October 30, 2013

How would you spend $12 billion?  Well, using the “continuance tables” (statistical claims distributions) contained in CMS’s “Actuarial Value Calculator,” one can show that the expected payments under the reinsurance system created by CMS for 2014 will range from about $433 per member for a bronze plan up to about $597 for a platinum plan. The weighted average expected payment will be about  about $525. The enhanced size of this subsidy, rather than other miracles of Obamacare, may explain in part, by the way, why premiums on the Exchanges came in somewhat lower than some had projected. If CMS is planning on spending about $12 billion on transitional reinsurance and it spends $525 per insured person, simple division shows that it takes about 23 million people who might trigger the reinsurance obligation in order to exhaust the fund.

The problem, however, is that, given recent developments, there are unlikely to be 23 million persons in 2014  (a) who might trigger the reinsurance obligation (“reinsurance triggering”) and (b) who are insured by reinsurance-eligible insurers (“reinsurance eligible”). You could just take my word on this point and skip to the end of this entry or, better yet, follow the accounting done here.

An accounting

Let me concede, temporarily and for the sake of discussion, that there will be 6 million people on average in 2014 who are paying premiums based on policies purchased in the individual Exchanges.  That’s hard to believe given (a) that the number with a month to go is probably about 3.2 million (President Obama’s alleged 4 million enrollment reduced by 20% shrinkage for nonpayment); (b) that the number of insured in the Exchanges would have to be 7 million post March for there to have been 6 million on average during all of 2014; and (c) Vice President Joe Biden’s augury that 5 million would be a “heck of a start.”  I will grumpily concede it nonetheless.

How many off-Exchange purchasers should we then add?  Here the numbers are slippery too.  I am indebted, however, to some careful work by the Kaiser Family Foundation on this point.  You can read it here. The highest estimate I have seen for the number of nonelderely persons covered by  a plan purchased directly from an insurer at any one time in a calendar year is 19 million.  But many of these 19 million will (a) not have insurance the entire year; (b) will have insurance that is secondary to other insurance and thus unlikely to accumulate the $45,000 attachment point in claims; and (c) will be in grandfathered policies not eligible for reinsurance and persisting through 2014 only by dint of President Obama’s magic waiver of the terms of the ACA.  When one looks at the situation at any given point in time — which is the proper basis for figuring out an average — it looks as if there might be 13-14 million who have some form of individual health insurance and 10-11 million who have primary health insurance coverage of the sort that might trigger a reinsurance obligation.

So, should I add 11 million to the 6 million and say that there are 17 million insureds that might trigger a reinsurance obligation?  No! That would ignore two substitution effects.  We know from various studies that a lot (perhaps 65% – 89%) of the people purchasing policies on the Exchanges simply swapped non-Exchange policies that would not be eligible for the other big federal subsidy — premium tax credits — for Exchange policies.  So, even if we assume, contrary to the evidence, that only half of the Exchange purchasers came from the ranks of the uninsured, that means there are really only 3 million new purchasers of policies eligible for reinsurance. Moreover, the 10-11 million figure isn’t right anymore either.  For 2014, individual insurers have to choose. They can stop selling their policy altogether, they can expand benefits to conform with the tougher requirements of the ACA and obtain a right to reinsurance or, at least in some instances, they may be able to grandfather their policy and avoid many ACA mandates but forfeit a right to reinsurance. I have not seen any good statistics on how many of the 11 million will persist into 2014, but I would be surprised if more than 80% did.  So, rather than 11 million, it seems to be the better upper bound on the number of extant non-Exchange, reinsurance eligible policies is 9 million.

It thus seems to me as if the better upper bound on  the number of policies that might trigger a reinsurance obligation is 12 million: 3 million genuinely new policies plus 9 million sold outside the Exchange but eligible for reinsurance. This means, however, that if CMS’s estimates of claims under the ACA are correct, a reasonable upper bound on reinsurance payments under section 1341 of the ACA are likely to be at most $6.3 billion ($525 x 12 million) rather than $12 billion.

Given all this, there are two aspects of CMS’ s behavior that are a bit puzzling.  Why is CMS not adjusting the reinsurance benefit for this year say to provide 100% coverage rather than 80% coverage and/or removing the $250,000 cap on claims triggering reinsurance? Or, given the belief of the President that he has discretion to waive taxes in light of changed circumstances, why is CMS not waiving, say, half of the taxes that would otherwise be owed.  (Not that I think this is constitutional).

The answer to the puzzler, I suspect, is either a cognitive failure or a very clever strategy. It is possible that it has not dawned on CMS that changing enrollment patterns means that it will not be able to exhaust the $12 billion it expects to receive pursuant to section 1341. More likely, however, someone at CMS has done the math and has been delighted to discover a slush fund that it can use the money to provide extra generous reinsurance next year and thus keep the price of premiums down.  How will we know? If we see an announcement from CMS in the next few months changing the parameters for the 2015 reinsurance plan to be considerably more generous, believe that it is the result of collecting “too much” in taxes in 2014. In the meantime, however, we have another example of ACA “details” that don’t seem to stand up under close scrutiny.

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