Stop reporting enrollment and start reporting policies in force

In theory, open enrollment ends tonight. No longer can individuals without any excuse whatsoever wait to purchase health insurance policies on the Exchanges that will be in effect during 2014.   I very much expect we will hear numbers over the next few days such as 6.5 million or 7 million bandied about as “enrollment figures.” Many supporters of the ideas behind the original ACA who have managed to tolerate its metamorphosis over the past year will herald those numbers as signs of success.  And, indeed, those numbers are considerably better than many had feared.  I, for one, am prepared to confess that I may have been too pessimistic in the past about first year enrollment in the ACA. My pessimism is all the more glaring because the enrollment numbers are apparently coming notwithstanding the Obama administration’s decision to tie its hands behind its back by creating a new opportunity to evade the individual mandate via an undocumented “hardship exemption” and to delay making a  purchase decision based on “honor system” claims of difficulties in accessing or state enrollment systems.

That said, however, these enrollment figures are essentially irrelevant.  Those who persist in touting them as signs of success reveal themselves more as Obamacare fanboys than as credible advocates or serous scholars.  The aggregate enrollment figures are irrelevant for two reasons and of lesser value for another. In short, my predictions may have been on the low side, but the numbers that will be coming out tonight absolutely do not vindicate those who assured us that Obamacare would end up being just fine. Reciprocal honesty would be nice.

Nothing economically or legally in the ACA turns on “enrollment”

1. “Enrollment” is, as many have noted, simply checking boxes on a web site.  It is not the same thing as actually having a policy in force, of being covered by an insurer who will pay medical bills in the event the “insured” becomes sick. In terms of the real health of Americans, access to expensive medical care, enrollment numbers are as meaningful to the success of the ACA as knowing the number of individuals outfitting their fantasy Corvette Stingray on Chevrolet’s“build your own” web site is to the success of GM. The former is a leading indicator of interest in plans on the Exchanges just as the latter is a possible leading indicator for purchasing a snazzy car. But that, really, is all.  Responsible journalists and bloggers should stop bleating “enrollment” merely because it is the only number the Executive branch dispenses.

Friends of the Obama administration gain credibility and actually help their President by insisting that the Obama administration release the number of policies in force  This is so because there are only two and a half conclusions that can be drawn from silence: either the Obama administration has the number and is refusing to provide it or it just doesn’t have the number.  Not releasing a number or decent approximation is contrary to the transparency values that the Obama administration espouses.  My FOIA request on the topic is, like many others, I suspect, unanswered. Not having the number is perhaps even worse.  I have read much of the ACA and its regulations and I can not think of a single economic or legal matter that turns on the number of people who have “enrolled” in plans on the Exchange.  Insurers get paid, tax credits are advanced, and a whole host of other important financial and legal consequences depend instead  on the number of people who, for any given month, actually have coverage, have a policy in force.  I say “two and a half” conclusions because there is a variant of not having the information that is sometimes advanced — not having precise enough information to release.  But this is about as flimsy as it gets.  Governments release approximate numbers all the time.  I believe Americans are sophisticated to understand the word “about” and the concept of a “good faith estimate.” Any lack of precision down to a single individual does not excuse a failure to release relevant information. I am confident that the public would be well served by having a policies in force number that was accurate even to just two or three significant digits.

The difference between enrollment and purchase is not trivial. Suppose the fall off between enrollment and purchase is, as some have suggested, 20%.  And suppose further, as again some have said, that 3% of  the remaining policyholders don’t pay each month.  The graph below shows the fraction of policyholders persisting over 12 months.  The blue line shows the time series and the yellow dotted line shows the average level of policies in force. As one can see, by the end of 9 months, only 65% of the initial level of policies remain in force. The annual average is about 70% of the starting amount. Moreover, the healthy are the most likely to stop paying; those who are sick are most likely to persist in their policies. Thus, if 6.5 million enrollees start out, only 4.2 million will be left with policies at the end of 9 months and the average number of purchasers over the year will be 4.6 million.


Even if just 10% decline to pay their first month’s bill, only 70% of the policies remain in force at 9 months (see figure below on left); the annual average is about 79%. At 20% initial decay and 5% monthly decay thereafter, only about 55% remain after nine months; the annual average is 65% (see figure below on right).  And some, of course, have suggested the fall off between enrollment and retention of a policy is actually worse.


Note: it is possible that some of the losses due to non-payment will be offset by those purchasing policies via “special enrollment.”  These individuals, however, may be particularly high risk.

2. The state-by-state totals matter a lot; aggregate purchases matter little

Aggregate purchases or, worse yet, aggregate enrollment is largely irrelevant to the success of the ACA.  There are at least 51 markets for individual policies.  The fact that California may have exceeded expectations in terms of purchases does nothing to help Texas, Louisiana, Arizona and other states where enrollment has been low.  Insurers in states where enrollment is low or the demographics are particularly problematic — few young people, lots of middle age women — will not be compensated for their losses by the fact that enrollments are better in California, New York and Connecticut.  Even if it is the same parent company that makes money in one jurisdiction, that will not deter the subsidiaries in losing jurisdictions from either withdrawing or raising premiums. There will still be immense pressure on insurers in the less successful states to either drop out entirely — something the make-it-up-as-you-go-along implementation of Obamacare  fosters — or to raise prices substantially.

As I said in a story broadcast on National Public Radio and as the New York Times admits, we need to stop thinking about the ACA as a single narrative and start to think about it as multiple complex narratives.  Indeed, it’s probably more like 175 or more narratives (the number of issuers in all federal plans) because not only will the experience vary between states, they will also vary by insurer.  An insurer who charged a very low premium in a given state and attracted a good deal of business may react very differently next year in pricing policies than an insurer even in the same state who charged a high price and got less.

3. Experience matters most

But the life of the Affordable Care Act will not be enrollment or even purchases, it will be experience.  Did insurers set prices realistically or did they underestimate the medical problems and demand for services of enrollees?   Does the fact that many of the purchasers on the Exchange actually had policies already actually help insurers because many of those purchasers would have undergone at least some recent medical underwriting? Are the networks that have been created by insurers so narrow that they will lead to unsatisfactory medical care or will they in fact keep prices low? Will insurers regard uncertainty in the political environment  — like not knowing whether Obama will extend the inchoate hardship exemption into next year when, otherwise, the individual mandate/tax/penalty more than doubles — result in at least some insurers pulling out of the market? Will the diminishing reinsurance available to insurers writing in the Exchanges have the effect I predicted of increasing prices by about 7%?


Tonight, March 31, is a milestone for the ACA, but it is hardly the end of the challenge. We’ll see lots more important data start to dribble in over the next few months, including, critically, information on premiums insurers hope to charge in 2015. In the interim, though, could everyone please start to focus on statistics and data that matters rather than proxies such as “enrollment.”  Use of enrollment rather than policies in force may at one time have been a necessary evil. But persisting in doing so is a practice that is no longer useful other than as a vehicle for spreading political propaganda.

My suggestion, only slightly tongue in cheek, is that, just as the IRS imputes some awful income to you if you don’t file a tax return, journalists and bloggers start reporting appallingly low purchase numbers until the Obama administration releases the actual data. I’ll start:

“Tonight’s disclosure by the Obama administration that about 4.5 million individuals will have coverage via Exchanges under the Affordable Care Act during 2014 means that some big states such as New York and California have done reasonably well in making it likely that their insurance markets will be stable. It also means, however, that Exchanges could be under great stress in a number of states, most notably Texas.”




My rough estimate of the rate of decline in Obamacare enrollment appears to be vindicated by an article appearing here in Kaiser News titled  “Why Some Don’t Pay Their Obamacare Premium: It’s Not What You Think.”  Kaiser reports that Covered California, the Exchange for the nation’s largest state, has produced a report projecting a significant drop in the number of enrollees throughout the year:

According to the report between 53 and 58 percent of Covered California enrollees are expected to stay in a Covered California plan for 12 months. This analysis is consistent with a Kaiser Family Foundation study published earlier this year. It found that of people who enrolled in an individual insurance plan in 2010, years before the health law fully kicked in, only about 48 percent were still in the individual market two years later. (Kaiser Health News is an editorially independent program of the foundation.)

But most of these people dropping ACA Exchange coverage won’t become uninsured, the report says.  Instead, they will go on to the state’s expanded Medicaid program or find better/cheaper coverage elsewhere. It’s not clear from the Kaiser article or the Covered California report whether they expect those moving out of the Exchanges to be healthier than average.  In any event, though, the report further establishes why touting “enrollment” is ridiculous.

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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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How Virginia insurers got the federal government to pay for bariatric surgery under Obamacare

I’ve been doing some research into the effects of market concentration on health insurance premium pricing on the health insurance Exchanges run by the federal government.  During the course of that research, I discovered what I first thought had to be a programming error on my part or a database error on the part of Silver and Gold plans that were costing individuals age 50 upwards of $2,000 per month.  Yes, per month!

It turns out, however, that these exorbitant prices are not errors. They represent a clever attempt by several insurers in Virginia — Optima Health, Coventry Health Care of Virginia, Inc., Innovation Health Insurance Company, and Aetna —  to get the federal government to pick up a substantial part of the tab for bariatric surgery. Here’s how it works.  The insurer offers the consumer a premium that is often $2,000 per month ($24,000 per year) more than it charges for other essentially identical plans. The bonus is that the insurer offers the consumer,  in addition to the usual benefits, bariatric surgery, which is otherwise subject to coverage restrictions in Virginia. Now, the only person who would rationally purchase such a policy is one who is pretty certain to undergo such surgery. And, as it happens, bariatric surgery (such as a gastric bypass) appears to cost between $20,000-$25,000. In effect, then, the insured prepays for the surgery via augmented premiums and perhaps piggybacks on the insurer’s bargaining power with surgeons to get a cheaper price.

So far, however, this does not seem like a compelling business model for insurance; at best it converts insurance into an elaborate financing scheme. But wait: if the insured has a relatively low income (and obesity correlates with poverty in modern America), under the cost sharing reductions provisions of the ACA (42 U.S.C. § 18071) the federal government now picks up much of the deductible and coinsurance that would otherwise be owed. Instead of there being, say, an $3,500 deductible and a $6,350 coinsurance limit, as there is under the Aetna Classic 3500 PD:MO policy offered in Virginia, if the person is poor enough (100-150% of federal poverty level), the deductible under the Aetna Classic 3500 PD: CSR 94% MO  is now $300 and the out-of-pocket limit is now $1,250. The federal government is thus likely to pay for $3,200 to $5,100 of the bariatric surgery that would otherwise come out of the patient’s pocket.

Is this legal under the ACA? I believe it may well be. I don’t see a violation of the “metal tiering” provisions of the ACA.  Under section 1302 of the ACA (42 U.S.C. § 18022), whether something qualifies as a Silver or Gold plan depends on the cost to the insurer of providing essential health benefits to a standard population, not on the cost to the insurer of providing its actual health benefits to the population it anticipates attracting.  That may not be a very good system, but is the one in the law; it is probably simpler than some alternatives. Moreover, section 1302(b)(5) of the ACA makes clear that a health plan may provide “benefits in excess of the essential health benefits described in [the ACA].” And, since some states apparent include bariatric surgery in their list of essential health benefits, it’s hard to say that Congress implicitly rejected paying for this procedure.

Footnote: I suppose there could be an issue as to whether this plan conforms to Virginia insurance regulations.  I’m not an expert on that, but my working assumption is that the Virginia regulatory apparatus has approved these plans.

Is what these insurers are doing appropriate?  That’s a tricky question. Basically what they are doing is the result of a decision by the Department of Health and Human Services relating to implementation of sections 1201 and 1302 of the ACA. HHS, instead of creating some uniform concept of Essential Health Benefits for those states that elected not to make their own decision, instead decided to try and mimic features of the “largest plan by enrollment in the largest product by enrollment in the State’s small group market.” 45 C.F.R. 156.100) That essentially made it a bit a matter of luck as to the circumstances under which bariatric surgery or other weight loss programs would be covered by plans permitted to be sold after 2013 on the individual market. It meant that in some states the risk of needing (or badly wanting) bariatric surgery would be spread among all those purchasing non-grandfathered plans after 2014 whereas in other states either the risk would not be transferred at all or would be transferred, as in Virginia, only at a high price. The map below created by the “Obesity Care Continuum” shows how the states differ.


Obesity treatment under state benchmark plans
Obesity treatment under state benchmark plans

And should bariatric surgery itself be covered?  It’s not an easy decision.  On the one hand, bariatric surgery frequently results in part from poor health choices made by the individual. Yes, there may be contributing factors such as access to healthy foods, genetics, access to safe methods of exercise, but, still, most people have a choice not to become obese.  And, if the condition is viewed as substantially the result of individual choice, the case for socializing and spreading the risk is weaker. On the other hand, there are plenty of risks that health insurance policies do pay for — both before and after the ACA — that likewise result substantially from personal choice.  They cover orthopedic surgery for (mostly wealthy) people who choose to ski. They cover smoking related conditions — albeit for an additional premiums which, if actually collected, would still probably be less than the actuarial risk of tobacco use. They cover treatment in at least some forms for the variety of conditions created by substance abuse (drugs, alcohol). They sometimes cover non-surgical costs to which obesity contributes even when those problems are partly the result of individual choices. And they covers the costs of treating sexually transmitted diseases even when those diseases might, in some instances, have been prevented by safer sexual practices. Untangling fault out of medical need is often a tricky proposition indeed.

So, perhaps these Virginia insurers are doing the public a service by evading/working around restrictions in the Obamacare package of essential benefits provided in some states that were unduly narrow.  Indeed, on this view, the problem is not that the federal government is subsidizing bariatric surgery, it is that individuals have to pay these enormous extra premiums for a risk that should be shared and that are shared in some states. It will be interesting to see what happens with these Virginia plans and whether what has started there extends to other states in which bariatric surgery is not presently considered an essential health benefit.

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Latest unlawful Obama administration “fix” may create standing for challenges

This past Thursday, the Obama administration issued its latest “fix” to the troubled roll out of the Affordable Care Act. The Center for Medicare & Medicaid Services issued a guidance that permits federal funds to go to insurers and insureds involved in sale of an individual health insurance outside of either a federally established or state-established Exchange. The premise of the guidance is that, in certain states such as Maryland, Massachusetts, Hawaii and Oregon, the complete dysfunctionality of the websites that were intended to determine eligibility for Obamacare subsidies may have led people to enroll in policies off the Exchanges; these purchasers, the guidance directs, should be treated the same as if the state Exchanges had made a timely determination and the individuals had enrolled in an Exchange policy. The guidance implements this concept by retroactively making such individuals eligible for premium tax credits the same as if they had purchased a policy on the Exchange and requires their insurers to readjudicate their claims both retroactively and for the remainder of the policy year as if they were eligible for the same cost sharing reductions that would have applied had they purchased a policy on the Exchange.

The Obama administration’s guidance calling for expenditures of taxpayer money plainly violates the Affordable Care Act. Unlike prior violations incurred in an effort to rescue the ACA from implementation and architectural infirmities, however, this one may actually hurt legal entities in a traceable and individualized fashion.  Some off-Exchange insurers may have standing to challenge the violation in court should they have the courage to pursue that option.

The illegality problem

Here’s why the Obama administration’s action is unlawful.

Premium Tax Credits

Under section 1401 of the ACA, which creates new section 36B of the Internal Revenue Code, the government may provide premium tax credits to the individual only for a “coverage month.”  The idea was that households with incomes less than 400% of the federal poverty level would ultimately see their federal income  taxes reduced to help compensate for the cost of purchasing health insurance.  But not any kind of health insurance purchase constitutes a “coverage month.”  Under section 36B(c)(2)(A), a coverage month is only one in which the taxpayer “is covered by a qualified health plan … that was enrolled in through an Exchange established by the State under section 1311 of the Patient Protection and Affordable Care Act.”  (emphasis mine) But the policies the Obama administration are now going to subsidize were not enrolled in through an Exchange established by a State (or the federal government); indeed, such is the entire “innovation” of this CMS guidance. And, thus, there is no statutory authorization for the federal government to be giving these taxpayers a credit.

Cost Sharing Reductions

Under section 1402 of the ACA (codified at 42 U.S.C. § 18071), the Secretary requires insurers to offer contracts with reduced cost sharing (deductibles, copays, out-of-pocket limits etc.) to individuals who purchase “Silver” plans. Purchasers are broken down into categories such that purchasers who fall into progressively lower income categories receive progressively more generous reductions. The program effectively converts “Silver” policies into “Silver-Plus”, “Gold Plus” and “Platinum Plus” policies. The government subsidizes insurers issuing these policies so that the cost sharing reductions should not cost them anything (providing the math is done properly). What the Obama administration is proposing is to extend these cost sharing reductions to insurance purchased off the Exchanges, at least where an application had been made to an Exchange.

Again, the problem is that the statute does not authorize cost sharing reductions for all “qualified health plans” sold on or off an Exchange. Under section 1402(a), such payments are authorized only for an “eligible insured.”  And the definition of “eligible insured” is quite clear. Section 1402(b)(1) requires that an eligible insured “enroll in a qualified health plan in the silver level of coverage in the individual market offered through an Exchange …” (emphasis mine).  Again, that pesky “through an Exchange” language gets in the way of the administration’s goal.  The policies now being offered subsidization are precisely those not offered through an Exchange.” The payments to these insurers announced by the Obama administration are illegal. From a financial accountability standpoint, it is not much different than if the Obama administration just decided to give government money to those ineligible for Medicaid simply because it felt badly for some of them.

Why insurers may have standing to challenge the new regulations

The Obama administration has made a habit in its implementation of the Affordable Care Act to exploit the law of “standing.” This is the doctrine that usually denies individuals with generalized grievances about a law or its implementation from bringing suit. Standing usually requires, among other things, that the plaintiff in a legal action have suffered individualized injury from the statute. Thus, when the Obama administration simply declines to collect taxes (as with the refusal to enforce the employer mandate), it becomes challenging to find someone who can use the judicial system to overturn the action. A similar problem plagues efforts to challenge the Obama administration’s decision to permit insurers to continue to sell policies that do not conform to the requirements of the Affordable Care Act. It’s challenging to find an individual or business that is hurt in a particularized and traceable fashion.

With the latest lawless action, however, the Obama administration may have gone too far.  Insurers who sold off Exchange will be hurt by the cost sharing reductions.  The reason is “moral hazard.” The idea of moral hazard is that the more generous an insurance policy is the greater the frequency with which insureds encounter covered events. In the health insurance arena, people with lower co-pays and deductibles go to the doctor more.  Indeed, the major reason for co-pays and deductibles is precisely to induce insureds to be judicious in their use of expensive medical services.  Moral hazard is one of the major reasons that platinum policies cost more than bronze ones.

When cost sharing reductions imposed on off-Exchange insurers effectively convert their silver policies into silver-plus, gold-plus and platinum-plus policies, those insurers end up paying more in claims.  And, while insurers selling policies on the Exchanges could have taken the induced demand created by cost sharing reductions into account in pricing their policies, there may well be insurers who sold only off the Exchange who, of course, did not take this additional moral hazard into account. Those insurers never dreamed that the government would reduce the amount its insureds would owe in cost sharing. Such insurers should have a strong case for standing in bringing a declaratory judgments to challenge the new guidance or, perhaps, in refusing to honor the demand for cost sharing reductions. Such insurers will, of course, need to be willing to take the political heat that may come from taking on an Executive Branch that more than ever is regulating their products.

A practical problem with imposition of cost sharing reductions on off Exchange policies

There’s also a practical problem with retroactive imposition of cost sharing reductions on off-Exchange insurers.  The guidance issued last week does not seem to address it. There are a lot of ways of achieving cost sharing reductions.  Some insurers might choose to reduce a deductible for some benefits.  Other insurers might choose to reduce a different deductible.  Still others might choose to keep the deductible but reduce copays.  For this reason, insurers selling policies on the Exchanges needed to specify in advance how they were going to achieve cost sharing reductions for their policies. Hence the government’s “Actuarial Value Calculator.” But insurers selling policies off the Exchange may never have gone through such an exercise.  Since CMS is now going to tell these insurers to readjudicate claims once they find out the income level of their insureds, the insurers are somehow going to have to come up, retroactively, with a system of cost sharing reduction.  How the insurer chooses to do so will affect how much each insured gets rebated.

The demand for readjudication gives insurers a second basis for standing.  Claims adjudication is not free.  The insurer is now going to have to go back through claims and resolve them for a second time.  Programming computers to adjust claims on a new basis is not costless. Figuring out whether a given service qualifies for cost sharing reductions is not costless. Cutting checks is not costless. And, having an actuary figure out what forms of cost-sharing reductions actually qualify as appropriate under the ACA is hardly costless either.  In short, the CMS guidance places new and completely unanticipated burdens on insurers who may have chosen to sell off Exchange precisely to avoid some of the regulatory burden that comes with on-Exchange sales.

The possible abortion problem

The “fix” concocted by the Obama administration may also end up violating restrictions in the ACA on federal funds being used to fund elective abortions. I will admit this is a bit speculative, but here’s the issue.  The general problem is that the ACA is an extremely integrated federal statute in which various provisions were enacted on the assumption that the conditions set forth in other provisions would hold.  Once the administration starts lawlessly changing certain parts of the ACA, other sections of the act begin to unravel. With abortion, the problem is that section 1303 of the ACA  (42 U.S.C. § 18023) prohibits federal tax dollars from being used to pay insurers via advances on premium tax credits  to fund elective abortions. Nor may federal funds be used to reduce the amount of “cost sharing” (deductibles, copays) that certain poorer ACA policy purchasers would otherwise pay for services other than elective abortions. There’s an elaborate mechanism specified by the statute involving segregated accounts and allocations that keeps government out of the elective abortion business, almost as if the insured purchased two policies — one for elective abortion and one for everything else — only the latter of which was subsidized by the government.   As a result, to the extent that various plans sold on the Exchanges provided for elective abortions — and apparently plans in at least nine states do so — they were structured to avoid receipt of such payments through segregated accounts.

Policies sold off Exchange never anticipated being the recipient of federal taxpayer money via premium tax credits and cost sharing reductions.  To the extent they provided for elective abortion coverage — and probably some of them did — there would have been no reason to structure them with segregated accounts to avoid receipt of federal funds for abortion.  Thus, when the Obama administration now proposes paying these off-Exchange policies federal tax dollars, the mechanisms for addressing abortion will not exist. I suspect that insurers who chose to sell off Exchange will not be excited by the administrative costs of now establishing segregated accounts. And, of course, if these off-Exchange insurers are not required by the Obama administration to prevent use of federal funds to pay for elective abortions, expect a firestorm of protest from those who believe that the federal government should not be subsidizing elective abortion.


One can be sympathetic to the plight of individuals in states such as Oregon, Maryland and others that wanted subsidized and community rated health insurance and, through no fault of their own, could not get it due to dreadful implementation of database systems that many states managed to accomplish with far fewer problems.  In a world of cooperation, it might have been possible for the Executive branch and Congress to work together to hold these individuals harmless for these failings while preserving political and legal accountability for government officials and contractors who collaborated in the various debacles. Instead, however, we have an illegitimate attempt to use the Executive pen to write around the problem and bail out those responsible for embarrassing state implementations of the ACA.

This fix is not only lawless, it is very sloppy.  It fails to prescribe a method by which the retroactive cost sharing reductions are to be done.  It imposes costs on insurers who may have traded the opportunities of selling on the Exchanges in favor of the comparative regulatory freedom that came with selling off the Exchanges. If the guidance is not clarified, it  may enable strategic behavior by those who purchased off the Exchange without suffering through a dysfunctional Exchange first; it may permit those people to apply for Exchange coverage now, reject it, but still obtain retroactive premium tax credits and cost sharing reductions for their off Exchange policies.  And the guidance as it stands fails to take into account sensitivities concerning elective abortion funding. And, of course, this spending of taxpayer money appears to be proposed via a “guidance” and not even a full fledged regulation promulgated with at least minimal process.

For proponents of the “flexibility” the Obama administration has shown in implementing the ACA in the face of a hostile Congress, however, the main sloppiness with the latest guidance is that it enables the judicial branch to rule on the pattern of unilateral Executive action that has characterized recent implementation of the ACA. Insurers off the Exchange will be hurt by the cost sharing reductions imposed by the guidance and by the administrative costs it creates. The question is, will any of them have the guts to sue.

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