Category Archives: Risk adjustment

Bad news for Obamacare: Insurers lost a lot of money in 2014

In testimony before Congress last June,  I think I may have shocked some Representatives by estimating that insurers selling policies on the individual exchanges as part of the Affordable Care Act would be sufficiently unprofitable that they would get only 37% of what they would have received under the Risk Corridors program had the federal government not required that the budget for that program be balanced.  It turns out, however, that my gloomy estimate was, in fact, wrong — but only because it was far too cheery.  In fact, according to data released yesterday, insurers will receive only 12.5% of what they thought at one time they would receive.  There is a $2.5 billion shortfall between the money taken in under that program from profitable insurers and the money now owed to those who lost money, at least as the government measures it.

The shortfall spells trouble for Obamacare in a number of ways.  And it is difficult to overestimate how troubling this development should be for supporters of that program.

Some Exchange insurers are likely in serious trouble

First, it likely means that some of the smaller insurers who, at least  before passage of section 227 of the Cromnibus bill last December,  had anticipated receiving full payment for the money the government owes under the Risk Corridors program, are going to find themselves with a serious cash flow problem. Some may even find  themselves with solvency problems given the improbability that the full amount of the Risk Corridor obligation will ever be paid.  Companies that had booked Risk Corridor payments as receivables valued at 100% of the face amount, may have to start writing off at least part of them off as uncollectable.  Thus, when CMS says that the government’s inability to pay 87.5% of what it owes may create “some isolated solvency and liquidity challenges,” that is likely an understatement. Fortunately, as the Wall Street Journal reports, some insurers apparently saw the handwriting on the wall and accounted for the Cromnibus limitation properly so as not to deceive shareholders or state regulators.

Bad news for Exchange premiums

Second, it augurs severe pressure on insurance pricing in the healthcare exchanges.  The reason that there is a $2.5 billion shortfall is that a lot of insurers lost a lot of money selling policies on the Exchanges during 2014.  Insurers, like other businesses, have this habit of trying to make up for past losses by charging more in the future.  So we will see later this month some of the effect when the Obama administration releases data on premiums for 2016, but the massive losses in 2014 shown by the Risk Corridors results is likely to add to pricing pressures.

The Obama plan to rescue insurers has failed

Third, it shows that broken promises have consequences.  Let’s go through some history here.  Remember the infamous promise, “if you like your healthcare plan, you can keep it.  Period.”?  That was, of course, not exactly true in light of what the statute actually said.  And, when Americans saw their policies cancelled as a result, the Obama administration decided it would delay and relax enforcement of the various provisions of the ACA that would have killed enough many non-Exchange insurance plans.

But this refusal to salvage the political rhetoric by sacrificing the language of the statute got many insurers angry. The insurershad priced their policies on the assumption that of course the Obama promise was the usual political moonshine and that those healthy insureds previously owning now non-compliant policies would migrate their way over to Exchange policies and stabilize that market.  In true Cat in the Hat Comes Back style, the Obama administration “solved” that problem, as I explained twice (here and  here) in December of 2013, by fiddling with the accounting rules in the Risk Corridors program by making it more difficult for insurers to be deemed to have made sufficient money to owe the government and making it easier for insurers to be deemed to have lost money and thus be owed money by the government.  (Although its pronouncements were a bit cryptic, as I noted last April, the CBO may have estimated that the cost of this gimmick was as much as $8 billion).  Now, however, with the Cromnibus bill prohibiting the Obama administration from dipping into unspecified accounts to pay for Risk Corridors,  which I guess is what they planned since no money was ever appropriated for the program, that last bit of  multi-billion tinkering has backfired.   Insurers will not be paid for Risk Corridors for a long time if ever and, thus, they have indeed suffered a significant loss of a chain of make-it-up-as-you-go-along policies designed to salvage the ACA.

Don’t trust government accounting

Fourth, the Risk Corridors deficit exposes as pure bunkum the statements of many in Washington in the post ACA era — and continuing even today — about the state of the insurance market and the Risk Corridors program. Recall that at one point not too long ago the CBO was asserting that the Risk Corridors would actually make the government $8 billion.  This was done, perhaps not coincidentally, after an effort by Senator Marco Rubio gained prominence to defund Risk Corridors as an insurance industry bailout.  Devoted readers may also recall that I found the CBO’s estimate “baffling,” a bit of cynicism whose sagacity may have improved with age.  And even today with the announcement,  officials at CMS repeated the technically correct and yet practically dubious notion that, yes, there were shortfalls today, but Risk Corridor payments made by insurers in 2015 and 2016 might be enough not just to overcome the 2014 deficit now valued at $2.5 billion but also to make whole insurers who lost money in 2015 and 2016.

And the plea to undo Cromnibus

It is no wonder that former CMS head administrator Marilynn Tavener, now speaking for the America’s Health Insurance Plans, is now saying it is “essential that Congress and CMS act to ensure the program works as designed and consumers are protected.” By “as designed, Ms. Tavenner means  before Cromnibus when Congress, in a spasm of fiscal responsibility, required that Risk Corridors, for which no money was ever appropriated, actually pay for itself just like the Risk Adjustment program.  Translation of Ms. Tavenner: find someone else’s money somewhere to bail out insurers who lost money in the Exchanges.

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Continuing Resolution jeopardizes Risk Corridors

Amidst all the passion yesterday at the roasting yesterday by the House Oversight Committee of Glib MIT Professor Jonathan Gruber and Marilyn Tavenner, Administrator for the Center of Medicare and Medicaid Services, many have missed what may be the most important development of the day: Congress is closer to stopping the Obama administration from funding the Risk Corridors programs that insulates insurance carriers selling policies on the Exchanges from much of the financial risk.  Chapter G of the Continuing Resolution currently in the works  (the “Consolidated and Further Continuing Appropriations Act, 2015”) appears to block the Obama administration’s apparent plan of using a “slush fund” — the “CMS Program Management Account” — to pay insurers when obligations under the program exceed receipts. Many, including the non-partisan Congressional Research Service and Senator Jeff Sessions, believe that the earlier contemplated use of this account to pay for Risk Corridors was unlawful under the Antideficiency Act and Article I, section 9, clause 7 of the United States Constitution (“No Money shall be drawn from the Treasury, but in Consequence of Appropriations made by Law”).

Page 75 of Division G of the summary of the Appropriations Act of 2015
Page 75 of Division G of the summary of the Appropriations Act of 2015

The inability of the Obama administration to finance the Risk Corridors program is a direct threat to the operation of the Affordable Care Act.  Insurers who priced policies based on the assumption that, if they went too low in their premiums, they would be protected against substantial financial risk by Risk Corridor payments from the federal government, will now be facing — to their surprise — an environment in which at least some of the Risk Corridor payments will not be forthcoming. Insurers contemplating entry  or continued participation into the insurance markets created by Obamacare will now hesitate for at least 2016 — either that or they will price their policies higher to protect against the now assumed risk of loss. The effect for 2015 policies is unclear. In light of the forthcoming Supreme Court decision in King v. Burwell, insurers negotiated for a provision in their contract that gives them the ability to terminate their participate in the program if either cost sharing reduction payments or premium tax credits are not available to purchasers. They are not known, however, to have negotiated for a similar provision with respect to Risk Corridor underfunding and thus might be held by a court to have assumed that risk.

§_261Discharge_by_Supervening_Impracticability_-_WestlawNext
Section 261 of the Restatement of Contracts 2d

 

How severe the effect of this Risk Corridor limitation will be depends on how CMS uses whatever authority remains to make at least partial payments to insurers and, of course, the amount by which obligations under the program exceed receipts.  Suppose, for example, that obligations to losing insurers under the Risk Corridors program are three times receipts from winning insurers.  This means  that losing insurers would receive only 33 cents on the dollar, at least until any future surplus from the program could make them whole.  Such a result would likely infuriate insurers and induce them to seek further regulatory concessions from the Obama administration as a price of continued participation in the ACA exchanges. If as the Obama administration predicted, Risk Corridors will break even or even run a surplus, the limitation in Division G will have no effect at all.

In any event, the Continuing Resolution in which all this is contained is not yet law.  And there are apparently many points of contention — some possibly even more important than Risk Corridors — up for debate.  Who knows what weapons insurance lobbyists will bring to bear in the mean time to rid Division G of this critical limitation?  If, however, Division G’s limitation on Risk Corridor payments survives, expect further trouble in the market for individual and small business insurance created by the Affordable Care Act.

Addendum

It didn’t take long for my prognostication in the last paragraph to bear out.  Insurers are already in an uproar.  As reported in The Hill just now:

“American budgets are already strained by healthcare costs, and this change will lead to higher premiums for consumers and make it more difficult to achieve affordability,” said Clare Krusing, a spokesperson for the America’s Health Insurance Plans.

We shall see what happens.

And a thanks to Professor Josh Blackman of South Texas College of Law for bringing this development to my attention.

 

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CBO implies Obama regulation shoveled $8 billion to insurers

The Congressional Budget Office issued a report this week revising its February projections of the cost of the Affordable Care Act.  Although there is much to discuss regarding the report, I want to focus here on its troubling discussion of “Risk Corridors.”  That’s the part of the law under which the federal government reimburses insurers selling policies on the new Exchanges for sizable fractions of their losses. It also taxes insurers if they happen to make money selling policies on the new Exchanges. Between February and April, the CBO estimated cost of Risk Corridors jumped $8 billion.  In February, Risk Corridors were predicted to make the government a net of $8 billion over the three years of the program. Now, Risk Corridors are expected to net the government nothing. The CBO claims that this jump was caused by regulations issued by the Obama administration in March that drove up the cost of the program.

There’s a second explanation, however, for the $8 billion change between February and April that’s possibly more troubling. This past February I wrote a blog entry with a lot of math explaining that the CBO prior analysis of the Risk Corridors provision was baffling and rested on extremely dubious and factually unsupported assumptions about the profitability of insurers selling on the Exchanges.  That error, if it was one, was particularly salient because it ended up forestalling growing efforts within Congress to repeal Risk Corridors as an unwarranted “bailout” of the insurance industry.  Could it be that with the repeal threat gone, CBO is now using the “noise” created by an Obamacare regulation as cover for rectifying the unduly optimistic assumptions it made back in February regarding Risk Corridors? That would be very troubling, because while math errors merely challenge the CBO’s competence, the alternative behavior about which I am speculating here goes to something more important: the CBO’s integrity.

The CBO explanation means the Obama administration shoveled $8 billion to insurers through a regulatory “tweak”

The official explanation from the CBO on its change of $8 billion in the cost of Risk Corridors is as follows:

“In March 2014, the Department of Health and Human Services issued a final regulation stating that its implementation of the risk corridor program will result in equal payments to and from the government, and thus will have no net budgetary effect.  CBO believes that the Administration has sufficient flexibility to ensure that payments to insurers will approximately equal payments from insurers to the federal government and thus that the program will have no net budgetary effect over the three years of its operation. (Previously, CBO had estimated that the risk corridor program would yield net budgetary savings of $8 billion).”

So, if the CBO is to be believed, the change isn’t due to any earlier error, but due to an administration regulation promulgated by the Obama administration that has resulted in a net of $8 billion more going to insurers.  That’s a big change for several reasons. First, it means that the regulatory changes instituted by the Obama administration cost the federal government $8 billion.  All of that money went to the insurance industry.  And so, in March of 2014, without much fanfare, the Obama administration would in effect have written a check to the insurance industry for $8 billion.  That payment would only have been motivated by one thing: a desire to keep insurers pacified and in the Exchanges after having deprived them of perhaps their most healthy potential insureds by a prior administrative ruling  — in violation of the ACA — that insurers could keep selling non-compliant policies.  The $8 billion would thus have been “damages” paid by the taxpayer in order to permit the President to honor his campaign promise that if you liked your insurance plan you could keep it.

In short, if you believe the CBO, a regulation for which statutory support will be extremely hard to find, resulted in the government shoveling $8 billion to insurers, basically to pacify them for the losses they suffered as a result of further regulatory changes of dubious legality.  The Obama administration can not afford to have its signature program enter a death spiral as a result of regulatory actions that, while mollifying those who otherwise would have lost their health insurance coverage, caused insurers to lose more money in the Exchanges. And, again, the Obama administration did so in a clever way that made it difficult for anyone to have legal standing to challenge them.  So far as I can discern, no insurer will be worse off as a result of the March 2014 regulatory changes. The real victims are taxpayers with diffuse interests and, of course, the Rule of Law.  

The CBO math is still baffling

A second reason the change by the CBO is big comes from a look at the math.  As I said in my February 2014 post calling the CBO February report “baffling,” consider the implications of asserting that the insurers would make so much money on the Exchanges that they would, on net owe the federal government $8 billion. If you do the math, it means that the CBO assumed that, over the course of three years, insurers would be earning about 8 cents on every dollar they earned via policies sold on the Exchanges.   I just ran the numbers again and came up with a very similar conclusion: the earlier estimate could only be true if insurers were supposed to make a hefty 8% or greater return on premiums. That estimate of 8 cents on the dollar was really peculiar at the time because enrollment — let alone actually paying customers — was running seriously behind projections and the number of “young invincibles” was particularly low.  Low overall insurance purchases and particularly low rates of purchases by the people who were most needed in the Exchanges caused many people to believe back in February that insurers would hardly make hefty profits and pay money to the government under Risk Corridors.  Instead, they thought insurers would fare poorly and probably have to be subsidized (or “bailed out”) by the government.

The effect of the February CBO pronouncement was to dampen enthusiasm for a bill proposed by Senator Marco Rubio that would have repealed the Risk Corridors provision as a bailout to the insurance industry.  If, after all, the federal government was, on balance, making money on Risk Corridors, it was hard to see it as a “bailout” to the insurance industry. Whether intended or not, the political effect of the February CBO announcement was to pull the rug out from one justification for repeal of Risk Corridors.

But is it even plausible to believe that the regulatory change made by the Obama administration in March without the approval of Congress could cause such a large change in the Risk Corridors program? I have done the math again and the answer is no.  I do not see how it is possible to get $8 billion out of the regulatory tweak that was made. Again, the calculations are baffling.

Here’s how we know.  The $8 billion the CBO thought back in February the government would make off of Risk Corridors represents about 4% of the premiums insurers on the Exchanges would take in during that time period. One can use that and other information from the CBO to reverse out a distribution for  “allowable costs” (basically claims expenses) We can thus make a respectable estimate of how many insurers would make money on the Exchanges, how many would lose, and how much these insurers would gain and lose. I describe the gory process in my post from February.  Call this distribution the CBO Insurer Profitability Distribution.  Then assume the government tweaks, as it did, two regulatory parameters used in the computation of Risk Corridor payments, changing something called a profit margin floor from 0.03 to 0.05 and changing an “administrative cost cap” from 0.2 to 0.22. If one then takes the CBO Insurer Profitability Distribution and computes how much the government would now make on Risk Corridors does one emerge with the CBO’s new prediction that Risk Corridors will produce no net revenue? No! One gets that the Risk Corridors program now generates about 2.8% of premiums for the government. In other words, the reduction in Risk Corridor revenue resulting from the administrative tweak is only 1/3 of what the government claims.

The easier way to reach the CBO’s April’s conclusion is to assume that the gain of $8 billion resulted from two phenomena: (1) the regulatory tweak mentioned by the CBO and discussed above, but (2) a recognition that the CBO Insurer Probability Distribution the CBO had used in February was, as I have said, wrong.  If, for example, one assumes that insurer claims were about 6% higher than the CBO estimated in February, the regulatory tweaks combined with higher insurer claims expenses indeed generate an $8 billion shift in the amount of revenue the government would make on Risk Corridors.

For those interested in the details, I link here to a Mathematica notebook showing the computations; I try to avoid black boxes.

Conclusion

So, what are we to make of this apparent discrepancy between the CBO’s explanation of its change in estimates and the actual effects of the regulatory changes it asserts to be the cause ?  It could, I suppose, be my mistake.  I have been careful and consider myself pretty knowledgable in this area, but I will hardly claim to be mathematically infallible. The problem is that the for ordinary Americans (like me), the CBO is a black box. It is not subject to the Freedom of Information Act and it does not publish enough of its methodology for even experts in the field to figure out what it is doing.  That, I would submit, is a real problem for the democratic process, where the fate of legislation depends essentially on trust rather than the Reagan doctrine of “trust but verify” (doveryai no proveryai, in the original Russian).

It could also, however, be a coverup for a mistake (or worse) back in February. There is, after all, an alternative explanation of the change in estimate. It was unrealistic all along for the CBO to think that insurers in the Exchange were going to make money on balance. That’s what I suggested in my February 2014 post.  So, rather than admit that the it had been guilty of unwarranted optimism, the CBO simply used a new distribution of likely claims expenses, came up with a different answer, and used the March 2014 regulatory changes as a smokescreen.

I will confess, however, that I am very uncomfortable with conspiracy theories or with theories that are premised on people acting in bad faith.  Nonetheless, I would not find it impossible to believe that a culture could emerge in a politically sensitive agency that was reluctant to expose forcefully the consequences of government programs that proved far more expensive and far less successful than forecast originally.  It would be a culture in which good news, or optimistic speculation, was uncritically embraced. What I challenge the CBO to do, therefore, not only with the Risk Corridors analysis, which is but the tip of a very big iceberg, but with the entirety of its ACA analysis, is to open it up for scrutiny.  When government policy is essentially set on the basis of models that are not subject to peer review or public scrutiny, there is a great chance for error and, frankly, for manipulation. Government by black box breeds suspicion.

Postscript: Is the tweak legal?

I have said before and I say again that the regulatory tweak that the CBO now says will cost the federal government $8 billion is extremely dubious.  It’s an extremely sneaky way of sending money to the insurance industry, resting, as it does, on arcane manipulations of mathematical formulae. And I have serious doubts that the changes are authorized by Congress.The submission of the original regulations in March, 2013 says that essentially all commenters agreed that a 3% margin for profit was appropriate.  No commenters indicated at that time that insurers were entitled to a higher imputed rate of return on capital.  No one said anything about 5%. Back in March of 2013, HHS thought 3% was the right number. There has been no fundamental change in the capital markets since that time.  The only thing that has changed is that the Obama administration has made the pool of insureds making purchases in the Exchanges less healthy on average. The regulatory “tweak” moving the profit margin from 3% to 5% is thus not consistent with the original goal of Congress for the Risk Corridors program, but is simply a way of compensating insurers for another regulatory change.

The change in the administrative cost cap from 20% to 22% that will likewise result in higher payments to insurers is likewise dubious.  The reason 20% was suggested in the original July 2011 proposal and chosen in the March 2013 regulations was to maintain parity with regulations governing the “Medical Loss Ratio” codified at 42 U.S.C. § 300gg-18 as part of the ACA. The idea, which was apparently supported by commenters on the original rules, was that if insurers — even small group and individual insurers — could not claim more than 20% administrative costs without owing rebates pursuant to section 10101(f) of the ACA then they should not be able to claim more than 20% administrative costs under the Risk Corridors provision.  Makes sense!  But, again, nothing has changed.  There is no indication that anything President Obama did that raised the administrative costs of running a health insurance plan on the Exchanges.  There is no indication that any factor in the real world (such as the cost of computers or paper) increased the administrative costs of running a health insurance plan on the Exchanges.  The limits for the Medical Loss Ratio computation have not changed.  There is no better reason now then there was a year ago to let the cap on administrative costs be higher for Risk Corridors than it is for Medical Loss Ratio.  And, yet, it is now 22% instead of 20%.  The only reason it has changed is to provide a vehicle for shoveling money to insurers.

Again, unless one thinks that the goal of keeping insurers in the Exchange is so overwhelming as to permit the Executive Branch to do anything, it is difficult to see a conventional, lawful justification for the regulatory change that results, according to the CBO, in $8 billion of compensation to the insurance industry. And I say that believing fully well that many of the Obama administration’s other regulatory changes — also of dubious legality — such as expanding the hardship exemption and permitting insurers to sell policies off the Exchanges that contain prohibited provisions have significantly hurt insurers selling policies on the Exchanges. Two wrongs do not make a right.

Technical Appendix

The following graphic shows the relationship between the Risk Corridor Ratio and the net receipts of the government for each premium dollar. As one can see, the higher the Risk Corridors Ratio, the less money the government receives or, in some instances, the more money the government pays out.

RiskCorridorsRatioToHHSNetReceipts

The following graphic compares the relationship between claims costs (“allowable costs”) incurred by an insurer as a percentage of premiums and the Risk Corridors Ratio. It does so for two sets of regulatory parameters.  It first uses the regulatory parameters that were in place prior to March of 2014 (3% profit margin and 20% administrative cost cap).  It next using the new regulatory parameters (5% profit margin and 22% administrative cost cap). As one can see, the regulatory changes increased the Risk Corridors Ratio for all levels of allowed costs and thus decreased the amount the government would receive from insurers (or increased the amount the government would pay to insurers).

AllowableCostsToRiskCorridorsRatio

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CBO projection of $8 billion from Risk Corridors is baffling

The Congressional Budget Office just issued a report that assumes the Affordable Care Act system of individual policies sold in Exchanges without medical underwriting can remain relatively stable. Tightly bound up with that assumption is its prediction about a controversial ACA program known as “Risk Corridors” that requires profitable insurers to pay the federal government up to 80% of profits they make on policies sold on the Exchanges but that also requires the federal government to pay insurers up to 80% of the losses they suffer from policies sold on the Exchanges.  The CBO now believes it has enough information to predict that Risk Corridors will actually make money — $ 8 billion over three years — for the government at the expense of insurers.

This CBO prediction of $8 billion in federal revenue, which has gained much publicity,  pulls the rug out from critics of the ACA such as Senator Marco Rubio who have introduced legislation that would repeal Risk Corridors as an insurance industry “bailout.” Such a blunting of Senator Rubio’s proposed repeal legislation is crucial in the ongoing battle over the ACA because repeal of Risk Corridors could  result in insurers (who just might not believe the CBO’s numbers) exiting the Exchanges for fear of having no government protection against losses resulting from unfavorable experiences in the new market the government has created. On the other hand, if the CBO is just getting its number wrong, Rubio’s case for repeal of Risk Corridors remains as strong (or problematic) as it ever was. The CBO projection is also important because Risk Corridors nets the government money if and only if the ACA works, insurers are able to make some profits, and a death spiral never takes hold. And this, as readers of this blog are aware, is a prediction about which many have serious doubts. 

Here’s the short version of the rest of this post.

I’ve done the math and I don’t see how the CBO is getting this $8 billion number unless it is assuming either very high enrollment in policies covered by Risk Corridors or very high rates of return made by insurers.  Or it made a mistake. I don’t think the CBO’s own numbers support very high enrollment in policies covered by Risk Corridors and I don’t believe either an emerging reality or the CBO’s own rhetoric justify assuming very high rates of return.  So I think the CBO ought to take a second look at its prediction. People should not yet make policy decisions based on the CBO estimate.

Reader, you now have a choice. I’m afraid that the next several paragraphs of this post become very technical. It’s kind of forensic mathematics in which one attempts to use statistics and numerical methods to deduce the circumstances under which something said could be true.  If that sounds dreadful, scary or tedious, I would not protest too loudly were you to skip ahead to the section titled “How could I be wrong?”  Before you leave, however, realize that what I am attempting to accomplish in the part you skip is a form of proof by contradiction. I prove that if what the CBO was saying were true, then insurers would have to be making 8% profit.  But nobody, including the CBO thinks they will make 8% profit, so the $8 billion number can’t be right.

On the other hand, dear reader, if you liked the Numb3rs television show (including my minor contributions thereto) or math or detective work or just care a lot about the Affordable Care Act, the rest of this post is for you.  What I am about to discuss is not only exciting math, but also the soul of the Affordable Care Act — whether the individual Exchanges without medical underwriting can remain relatively stable.

Forensic mathematics in action

Conceptually, here’s the calculation one needs to do.  What we want to figure out is the distribution of insurer profits (measured as a ratio of expenses divided by premium revenues)  upon which the CBO must be relying. I assume the CBO is using a  member from the “Normal” or “Lognormal” family of distributions because those are typical models of financial returns and there is little reason to think that the distributions of insurer profits (expenses minus revenues) will materially depart from those assumptions.  To continue reading this post, you don’t have to know exactly what those distributions are except that they look for our purposes like the “bell curves” you have seen for many years.  I’ve placed a graphic below showing some normal (blue) and lognormal (red) distributions. Although it should not matter all that much, I’m going to use a lognormal distribution from here on in because the ratio of insurer expenses to premiums should never be negative and the lognormal distribution, unlike its normal cousin, never takes on negative values.

Examples of probability density functions for normal and lognormal distributions
Examples of probability density functions for normal and lognormal distributions

The problem is that there are an infinite number of lognormal distributions from which to choose.  How do we know which distribution the CBO is emulating in its computations?  How do we know just how positive the CBO assumes the individual Exchange market is going to be on average or how dispersed insurer profits are going to be? As it turns out, the complexity of the lognormal distribution can be characterized with just two “parameters” often labeled μ (mu, the mean of the distribution) and σ (sigma, the standard deviation of the distribution).  Once we have those two parameters (just two numbers), we can deduce everything we need about the entire distribution.

Now, to solve for two parameters, we often need two relationships. And, thoughtfully, the CBO has given us just enough information.  It has told us how much money in total it intends to raise from Risk Corridors ($8 billion) and the ratio (2:1) between money it collects from profitable insurers and the money it pays out to unprofitable insurers. These two facts help constrain the set of permissible combinations of Risk Corridor populations (the number of people purchasing policies in plans subject to the Risk Corridor program) and insurer profitability distributions. What I want to show is that it takes an extremely high Risk Corridor population in order to get rates of return that are not way larger than most people — including the CBO — think likely to occur.

I first want to calculate the amount of money insurers would pay to HHS under the Risk Corridors program if the total amount of premiums collected were $1. Some of the payments — those by highly profitable insurers  —  will be positive.  Those by highly unprofitable insurers will be negative. To do this I take the “expectation” of what I will call the “payment function” over a lognormal distribution characterized by having a mean of  μ and a standard deviation of  σ.  By payment function, I mean the relationship shown below and created by section 1342 of the ACA, 42 U.S.C. § 18062. This provision creates a formula for how much insurers pay the Secretary of HHS or the Secretary of HHS pays insurers depending on a proxy measure of the insurer’s profitability. The idea is to calculate a ratio of “allowable costs” (roughly expenses) to a “target amount” (roughly premiums).  If the ratio is significantly less than 1 (and outside a neutral “corridor”), the insurer makes money and pays the government a cut. If the result is significantly greater than 1 (and outside the neutral “corridor”), the insurer loses money and receives a “bailout”/”subsidy” from the government.  The program has been referred to with some justification as a kind of “derivative” of insurer profitability, the ultimate “Synthetic CDO.

The graphic below shows the relationship contained in the Risk Corridors provision of the ACA.  The blue line shows the net insurer payment (which could be negative) to the government as a function of this proxy measure of the insurer’s profitability. Ratios in the green zone represent profits for the insurer; ratios in the red zone represent losses. Results are stated as a fraction of  “the target amount,” which, as mentioned above, is, roughly speaking, premium revenue.

How much the insurer pays (positive) or receives (negative) under Risk Corridors as a function of  measurement of profitability
How much the insurer pays (positive) or receives (negative) under Risk Corridors as a function of a ratio-based measurement of profitability

When we do this computation, we get a ghastly (but closed form!) mathematical expression of which I set out just a part in small print below. (It won’t be on the exam). I’ll call this value the totalPaymentFactor. Just keep that variable in the back of your mind.

Excerpt of the formula for insurer total payout
Excerpt of the formula for insurer total payout

I next want to calculate the amount of payments profitable insurers will make to HHS. To do this, we truncate the lognormal distribution to include only situations where the ratio between premiums and expenses is greater than 1. Again, we get a pretty ghastly mathematical expression, a small excerpt of which is shown below. I will call it the expectedPositivePaymentFactor.

Formula for expected negative insurer payments under risk corridors over a truncated lognormal distribution
Formula for expected negative insurer payments under risk corridors over a truncated lognormal distribution

Finally, I want to calculate the amount of payments unprofitable insurers will receive from HHS. To do this, we truncate the lognormal distribution to include only situations where the ratio between premiums and expenses is less than 1. Again, we get a pretty ghastly mathematical expression, which, for those of you who can not get enough, I excerpt below. I will call it the expectedNegativePaymentFactor.

Formula for expected positive insurer payments under risk corridors over a truncated lognormal distribution
Formula for expected positive insurer payments under risk corridors over a truncated lognormal distribution

The CBO has told us in its recent report that the government will collect twice as much from profitable insurers (expectedPositivePaymentFactor) as it pays out to unprofitable ones (expectednegativePaymentFactor).  We can use numeric methods to find the set of μ, σ combinations for which that relationship exists.  The thick black line in the graphic below shows those combinations.

 

Black line shows combination of mu and sigma that result in the correct ratio of positive and negative insurer payouts under Risk Corridors
Black line shows combination of mu and sigma that result in the correct ratio of positive and negative insurer payouts under Risk Corridors

To determine which point on the black line above, which combination of the parameters μ, σ , is the actual distribution, we need to use our information about the totalPaymentFactor.  The idea is to realize that the totalPaymentFactor must be equal to the quotient of the CBO’s estimated $8 billion and the total premium collected by Risk Corridor plans over the next three years.  But we know that the total premium collected should be equal to the mean premium charged by the Exchanges multiplied by the number of people in Risk Corridor plans. Some math, discussed in the technical notes, suggests that the mean premium under the ACA is about $3,962. And the CBO accounts for 8 million people being in Risk Corridor plans in 2014, 15 million being in Risk Corridor plans in 2015 and 25 million being in Risk Corridor plans in 2016. This means that the total premiums collected by insurers under Risk Corridor plans over the next 3 years should be about $190.2 billion. And this in turn means that the totalPaymentFactor must be 0.042.

Ready?

It turns out that of all the infinite number of lognormal distributions there is only one that satisfies the requirements that (a) the government will collect twice as much from profitable insurers (expectedPositivePaymentFactor) as it pays out to unprofitable ones (expectednegativePaymentFactor) and (b) for which the totalPaymentFactor takes on a value of 0.042. It is a distribution in which the mean value is 0.923 and the standard deviation is 0.113.  I plot the distribution below. A dotted line marks the break even point for insurers.  Points to the left of the break even line correspond with profitable insurers; points to the right correspond with unprofitable insurers.

Lognormal distribution of insurer profitability consistent with CBO data
Lognormal distribution of insurer profitability consistent with CBO data

Here are some factoids about the uncovered distribution.  The  average insurer will have expenses that are 92.3% of premiums and the median insurer will have expenses that are only 91.6% of profits. In other words, they will be making 7.7 cent and  8.4 cents respectively on every dollar of premium they take in.  For reasons discussed below, this is a difficult figure to accept. It is particularly difficult in light of the pessimistic news that is emerging about things such as the age distribution of enrollees , reports from Deutsche Bank that one of the largest insurers in the Exchanges, Humana, expects to receive (not pay!) a lot of money under the Risk Corridors program, the hardly exuberant forecasts of other publicly traded insurers about the ACA, and the recent general downgrading of the insurance sector by Moody’s partly because of the ACA.

Implicit in my finding about the most likely distribution of profitability is an assertion by the CBO that 76% of insurers will be profitable under the ACA while 24% will be unprofitable. About 17% will be sufficiently unprofitable that they will receive subsidies (a/k/a bailouts) from the federal government and 9% will be sufficiently unprofitable that their marginal losses will be covered at 80%. Only 15% of insurers will be “inside” the risk corridor and neither pay nor receive under the program.

How could I be wrong?

I feel  confident that I’ve done the ” gory math part” of this blog post correctly. Mathematica, which is the software I’ve used to do the integral calculus and the numeric components involved just does not make mistakes.  I also feel pretty confident that I understand how the Risk Corridors program works under section 1342 of the ACA.  That’s kind of my day job. And so, readers who skipped down to this part, I do believe that if the CBO were right about the $8 billion, that could only happen if insurers were, on average, earning an implausible 8% in the Exchanges.

If I’m wrong, then, it is because, except for the little issue I will mention at the end, I have made bad assumptions about the total premiums insurers expect to collect over the next three years in policies covered by Risk Corridors. That error could come from two sources. I could have the mean premium per policy wrong or I could have the relevant enrollment wrong. Let’s look at each of these.

Could I be wrong about the mean premium?

I computed the mean premium in the computation above by using data collected by the Kaiser Family Foundation on the ratio of premiums by age under most insurance plans and the typical Silver plan premium for a 21 year old (non-smoker). I then used the original forecast about the age distribution of insureds to compute an expected premium.  I got $3,962.  And this number seems very much in line with earlier HHS estimates, which were that mean premiums would be $3,936. So, I think I have the mean premium correct.

Could I be wrong about the number of people in Risk Corridor plans?

I computed the number of people enrolled in policies covered by Risk Corridors by looking at the CBO’s own figures.  I’m not vouching that the CBO is right in its projections, but this is not the day to argue that point.  The CBO now says (Table B-3, p. 109) that individual enrollment in the Exchanges will be 6 million, 13 million and 22 million respectively over the next three years.   And it says that employment-based coverage purchased through Exchanges (which I assume are SHOP Exchanges) will be 2 million, 2 million and 3 million respectively.  So , by addition, that’s where the figures I used of 8 million,  15 million and 25 million come from.  I’m not aware of anyone else who would purchase a policy subject to Risk Corridors. Again, bottom line, I don’t think I’m doing anything wrong here.

The little issue at the end: Could ACA definitions be responsible for the incongruity?

The only other conceivable explanation of the divergence between the CBO figures and my analysis is that I am failing to take a subtlety of Risk Corridors into account.  Remember, careful readers, that sentence earlier up that started out: “The idea is to calculate a ratio of “allowable costs” (roughly expenses) to a “target amount” (roughly premiums).” I stuck in the “roughlies” because the “allowable costs” are not exactly expenses and the “target amount” is not exactly premiums. When you look at the statute and the regulations, you can see that both of these terms are tweaked: basically you subtract administrative costs from both values.  And you subtract reinsurance payments from expenses — but that makes sense because the insurer reduced premiums in anticipation of those reinsurance payments.

So, in the end, I don’t see why these subtleties should affect my analysis in any significant way. But I am not infallible. And I do pledge that if someone points out an error to me, I will dutifully assess it and report it.

Sensitivity Analysis

Out of an abundance of caution, however, I have rerun the numbers on the assumption that premium revenue from policies subject to Risk Corridors is 50% greater than my original estimate either because of an underestimate of per policy costs or a failure to understand that there is some additional group within Risk Corridors protection.  When I do that, though, I find that the ratio of expenses to premiums is 0.943, meaning that insurers are still earning a pretty substantial 5.6%.  Although that is more believable than the earlier figure of 7.7%, it is still pretty high. 

Conclusion

To be honest, it makes me very nervous to say that the CBO did its math wrong or, worse, to accuse it of bad faith.  These are intelligent, educated professionals and they have access to a lot more data and a lot more personnel than I do.  Here at acadeathspiral  it’s just me and my little computer along with some very powerful software.  On the other hand, it’s not as if the CBO hasn’t been wrong before. It assumed earlier that the government would reduce its deficit $70 billion over 10 years as a result of Title VIII of the ACA (the so-called CLASS Act on long term care insurance) when many independent sources believed — rightly as it turned out — that the now-repealed CLASS Act was obviously structured in a way that could never fly.  The CBO assumed in July 2012 that 9 million people would enroll in the Exchanges in 2014, a number that is now down to 6 million. And, while there are explanations for each of these changes, the bottom line is that CBO is fallible too.

So, if I might, I would strongly urge the CBO to double check its numbers and provide more information on the data it relied upon and the methodology it employed in getting to its results.  I’d ask Congress, which has ongoing oversight of the ACA, to insist that the Congressional Budget Office, which is exempt from Freedom of Information Act requests from ordinary citizens, provide further detail.  American healthcare is indeed too important to have policy decisions made on the basis of what could be some sort of mathematical error.

Really Technical Notes

  1. I’m using a reparameterized version of the lognormal distribution that permits direct inspection of its mean and standard deviation rather than the conventional one, which in my opinion is less informative.   The explanation for doing so and the formula for reparameterization is here.
  2. To compute the average premium, I took the premium ratios used by the Kaiser Family Foundation, calibrated it so that a 21 year old was paying the national average payment for a silver plan purchased by a 21 year old. I then computed the expected premium over the distribution of purchase ages originally assumed by those modeling the ACA.
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Could the “low” ACA premiums just be “the winner’s curse” in action?

Those optimistic about the success of the Affordable Care Act have been noting over the past several months that the premiums offered by insurers have been lower than those earlier forecast.  But if one looks carefully at the original rhetoric, the comparison tends to be between some of the lowest premiums offered within a jurisdiction and those originally forecast.  And this metric, according to ACA proponents, is appropriate because they expect consumers to focus purchases on the lowest cost policies.

But what if the lowest premiums are lower than expected not because the mix of purchasers is thought to be fine or because of cost cutting measures enabled by the ACA, but simply because all this metric exposes is the work of the insurers who priced their policies below actual risk?  The “winner’s curse” is the term economists and game theorists give to situations in which, in an atmosphere of uncertainty, people bid on an item in an auction environment. What will often happen is that the “winning” bidder will tend to be one that loses money.

It is quite possible that all we are seeing with “low” ACA pricing, as measured by ACA proponents, is “the winner’s curse” in action.  We may well be looking at insurers who (a) got it wrong or (b) thought the government would most greatly subsidize their losses or (c) for strategic reasons, decided to  sell a “loss leader” in the first year or so of the ACA in order to lock consumers into their networks and their doctors with the idea that they could substantially raise premiums in the future. If this hypothesis is correct, individual policies under the Exchange are a lot less stable than many ACA proponents are asserting.

To summarize the results of the computations shown below, if the mean premium charged by insurers selling a type of policy (Silver HMO Plans, for example ) in a given geographic region (Harris County, Texas, for example) reflects the true risk posed by ACA policy purchasers, about 20% of the low bidders — the ones that I suspect will get a disproportionate share of the business — stand to lose at least 20% on their policies before the Risk Corridor program bails them out.

The big story as the ACA unfolds may be that some insurers — the ones who ended up with the business — simply made an error of exuberance in a new market and priced their policies too low. While these insurers will, thanks to a federal subsidization program for losing insurers called Risk Corridors, not entirely lose their shirts in the first year of the program as a result, they do stand to lose a lot of money that they will likely want to make up in any subsequent years of the Affordable Care Act.

New data analysis finds significant dispersion in plan premiums

This post will contribute some new data analysis that suggests the likelihood of the winner’s curse materializing as well as the magnitude of such a curse. Basically, I have sucked into my computer official government data on the 78,000 plans sold on the federal marketplace and done a lot of number crunching.  The data shows a significant dispersion of prices offered by insurers for plans in the same geographic area,  of the same metal tier and offering the same form of coverage (PPO, POS, HMO, or EPO) .  While this dispersion does not prove that the low prices are outliers reflecting either miscalculation by some insurers or only-temporary use of low prices, it does  suggest a significant possibility that such is the case.

Let’s take an example. Here are the prices offered where I live, Harris County, Texas — mostly Houston — for an HMO Silver Policy to a couple with two kids. The couple has an average age of 50 years old.  We’ll call this hypothetical family “The Chandlers,” as a matter of convenience. The graphic shows the dispersion of premiums normalized so that the lowest price for a given policy is given a value of 1.

Dispersion plot for Harris County, Texas, Silver HMO policies sold to Couple, aged, 50 with two children
Dispersion plot for Harris County, Texas, Silver HMO policies sold to Couple, aged, 50 with two children

As one can see, for the Harris County, Texas policies shown here, although there are three policies that have premiums fairly close to the minimum, there are, however, two policies that have premiums  more than 30% more than the minimum. If the mean premium estimated by insurers is “correct,” the insurer selling a Silver HMO policy at the lowest price will lose about 17%. The implication, if the Harris County plan is representative and if the mean premium is closer to the true risk than the low premium, is that the insurers most likely to win business due to low prices are likely to lose a considerable amount of money.

There are several potential rejoinders to the suggested implication of the graphic.  Let me address each of them in turn.

Might Harris County, Texas be unusual?

One response is that the example for Harris County, Texas Chandlers is unrepresentative. Houston, for example, has some very fancy hospitals and some not so fancy hospitals; so maybe premium dispersion for Harris County simply reflects whether one has access to the fancier hospitals (and the doctors who have admitting privileges to them).  I have considered this possibility and find that, actually, the example I provide is pretty representative. Here, for example, are 20 randomly selected examples. For each plan, I show the amount the low bidder would lose if the average premium is “correct,” the dispersion of premiums, and the plan and purchaser randomly chosen. Of the ones in which there are any significant number of policies available, most of the premiums show a dispersion pattern qualitatively similar to that in Harris County for The Chandlers. Indeed, some of the random examples show dispersion considerably greater than that for the Harris County silver HMO policies. Except where there is little competition for plans and the low bidder is thus selling at the average price, the result presented above does not look like a fluke.

Dispersion Plot and potential losses of low bidder for 20 random plans and purchasers
Dispersion Plot and potential losses of low bidder for 20 random plans and purchasers

I can double check this result by computing for 5,000 random combinations of plans and purchasers the losses of the low bidder if the true risk was equal to the mean premium charged for policies and purchasers of that type. The graphic below shows the “survival function” (or “exceedance curve”) for the resulting distribution of these losses.  The value on the y-axis is the probability that the losses will exceed the value on the x-axis. The results shown below confirm that the situation for Harris County Silver HMO plans sold to The Chandlers is not all that unusual.  As one can see, losses of more than 10% take place more than 30% of the time and losses of more than 20% take place about 17% of the time. A rather scary picture.

Exceedance curve of the distribution of losses of low bidders for random plan-purchaser combinations on the assumption that the mean premium represents the true risk
Exceedance curve of the distribution of losses of low bidders for random plan-purchaser combinations on the assumption that the mean premium represents the true risk

In fact, however, the situation may be even worse than depicted in the graphic above. Sometimes the losses computed by this method are low because the low bidder is also the only bidder.  If we consider situations in which there is more than one bidder, here is the resulting survival function (exceedance curve) of the distribution. As one can see in the graphic below, the distribution of risks is shifted slightly to the right.  Now 40% of the low bidders stand to lose at least 10% and about 21% stand to lose at least 20%.

Exceedance curve of the distribution of losses of low bidders for random plan-purchaser combinations where at least two premiums exist on the assumption that the mean premium represents the true risk
Exceedance curve of the distribution of losses of low bidders for random plan-purchaser combinations where at least two premiums exist on the assumption that the mean premium represents the true risk

Maybe the higher priced policies are better?

Another potential explanation for price dispersion is that, even if the policies are priced differently, that does not mean that the cheapest policies are selling for too low a price.  All Silver HMO policies sold in Harris County, Texas to The Chandlers may not be the same.  Some may have different deductibles or different networks.

The first response to this rejoinder is that the actuarial value of the policy — the relationship between expected payments by the insurer and premiums — should be about the same for each metal tier of policies. Silver policies should all have actuarial values, for example, of 70%.  So it should not be the case that one silver policy has cost sharing different than the cost sharing of another silver policy in a way that would affect the premium charged for the policy. Moreover, the calculations underlying this post keep HMOs, PPOs, POS plans and EPOs apart; so it should not be the case that observed premiums differ because, perhaps, the cheaper plans are HMOs whereas the more expensive ones are PPOs.

Of course, cost sharing is not the only way in which policies within a given location, of the same metal tier and sold to the same purchaser could vary.  One policy might offer richer benefits than another.  It could have a richer network with more doctors available or more prestigious and expensive hospitals inside the network. Could that be responsible for a substantial part of the premium dispersion we see?  It’s impossible to tell for sure — the data published by HHS does not attempt to quantify the richness of the network being offered.  I do find it difficult to believe, however, that such differences are responsible for the entirety of differences in excess of 20% between the low bidder and the mean bid, or, for that matter, differences in excess of 40% that sometimes occur between the low bidder and the higher bidders.

Maybe the average premium is meaningless; the low bidder got it right

Of all the potential rejoinders I have considered, the one now forthcoming is the one that is most troubling. There is nothing the data standing by itself can tell us whether most of the insurers have it right and the low insurers are about to lose their shirts or whether the low insurers have been more insightful or have managed to keep costs down such that they will break even (or even make money) selling their policies at low premiums.  And, yet, I am doubtful. One can view the mean or median of the premiums as an “ensemble model” of the true cost of providing care under the Affordable Care Act. And there is research (examples here, here and here) suggesting that ensemble models predict better in many open-textured situations than individual models.  So, while it’s possible, I suppose, that in every jurisdiction the low bidder is predicting more accurately than the group of insurance companies as a whole, such a result would be surprising.  A far simpler explanation is that the low bidder — the one who is likely to win business from price sensitive insureds — is succumbing to “the winner’s curse.”

Maybe the disaggregation of plans is misleading

This is a very technical objection, but consider carefully what I have done.  I have looked at all policies of a given metal tier and a given plan type in a given geographic location sold to a certain family type such as “all silver policies in Harris County, Texas, sold to The Chandlers.”  But, really, plans are sold not to just to The Chandlers but to all family types. So, it could conceivably be that while the plans sold to the family type I am looking at are highly dispersed, the average premiums over all family types (weighted by prevalence of the family type) are far less dispersed.  This strikes me as unlikely — why would an insurer be overcharging one family type relative to another — but you can not rule it out a priori.  Maybe — just maybe — the dispersion we are observing is not real; it is just an artifact of my disaggregation of the data.

I would, of course, love to aggregate the data and see if the high degree of dispersion persists. The difficulty with this cure comes with the problem of weighting the data.  We don’t know the distribution of policies sold among family types.  We don’t know, for example, whether The Chandlers constitute 2% of policies sold or 5% of policies sold. So, I can’t  perform a perfect aggregation of the data. One way to get a feel for the objection, however, is to simply take an unweighted average of the premiums for all the family types identified in the database and aggregate it that way.  This is far from perfect, and we could spend a lot of time refining it, but it should provide a clue as to whether the disaggregation of plans is significantly responsible for the high degree of observed dispersion.

The graphic below shows the exceedance curve for losses of the low bidder assuming the mean premium is the true risk based on an unweighted average of family types purchasing the policies.  One can see that 20% of the low bidders will lose at least 20% if it turns out that the mean premium charged for similar policies reflected the true risk. Upwards of 35% will lose more than 10%. A quick comparison of this curve with those above shows that it is essentially the same.  There is nothing that I can see suggesting that the fundamental result shown in this blog entry — high dispersion of premiums among what should be similar policies and the potential for significant losses by low bidders — is an artifact of the methodology I have employed.

Exceedance curve for losses of low bidder assuming mean premium is true risk for aggregated purchaser types
Exceedance curve for losses of low bidder assuming mean premium is true risk for aggregated purchaser types

Conclusion

In the end, even the extensive data that the government is put out is insufficient to determine definitively whether the lower priced insurers in the individual Exchanges are about to lose money. There are more optimistic interpretations of the observed premium dispersions: maybe it is the low bidders who are “getting it right” or maybe the low bidders have just found ways to keep costs down through better negotiating or cheaper care networks. But if these optimistic explanations prove insufficient, what this post shows is that while some insurers will likely do just fine there are a substantial minority of insurers who are about to get bitten by the “winner’s curse” and get a large volume of purchasers for whom the premiums charged will be insufficient to defray the expenses incurred.

 Technical Notes

The data used here was taken directly from the United States Department of Health and Human Services. It was analyzed using Mathematica software, which was also used to produce the graphics shown here.

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The Kaiser analysis of ACA enrollment has problems

On December 17, 2013, the Kaiser Family Foundation published an influential study that comforted many supporters of the Affordable Care Act who had been made nervous by early reports that the proportion of younger persons enrolling in Exchanges was significantly less than expected.  If true, such a disproportion could have created major stress on future premiums in the Exchanges because the private Exchange system under the ACA depends — or so it was thought — on younger persons subsidizing older persons. The Kaiser study asserted, however, that even if one cut the number of younger persons by 50%, insurer expenses would exceed insurer premiums by “only” 2.4%.  This finding under what it thought was a “worst case scenario” underpinned Kaiser’s conclusion that a “premium death spiral was highly unlikely.”

This post evaluates the Kaiser analysis. I do so in part because it disagreed a bit with my own prior findings, in part because it has gotten a lot of press, and because I have had a great deal of respect for Kaiser’s analyses in general.  I conclude that this Kaiser analysis rests, however, on an implausible assumption about the behavior of insurance purchasers and lacks much of a theoretical foundation. Once one eliminates this implausible assumption and employs a better theory of insurance purchasing, the threat of a death spiral becomes larger.

The reason for all this is a little complicated but try to bear with me and I will do my best to explain the problem.  Essentially, what Kaiser did was to run its simulation simply by lopping off people under the age of 34 and assuming that, for some reason, the disinclination of people to purchase health insurance on an Exchange would magically stop at age 34.  Thus, if an enrollment of, say, 2 million had been projected to come 800,000 from people age 18-34, 600,000 from middle aged people and 600,000 from the oldest group of enrollees, the “worst case” scenario Kaiser created (Scenario 2) would reduce enrollment to 1.6 million by having 400,000 come from people age 18-34, 600,000 from middle aged people, and 600,000 from the oldest group of enrollees. Thus, the youngest group would now constitute 25% of enrollees rather than 40%, and the other groups would constitute 37.5% of enrollees rather than 30%.

Although there is often nothing automatically wrong with this sort of “back of the envelope computation” — I have done many of them myself —  sometimes they give answers that are wrong in a meaningful way. And sometimes “meaningful” means a difference of just a few percentage points. Thus,  although the difference between 0.045 and 0.024 is not large on an absolute scale, this is one of these instances in which there could be a big difference between predicting premium increases augmented by 2.4% due to this particular form of adverse selection and predicting a premium increases augmented by 4.5% due to this particular form of adverse selection.   The first might be too small to lead to a quick adverse selection death spiral; the second, particularly if it combined with other factors increasing premiums, might be enough to start a problem. Death spirals are  a non-linear phenomenon a little like the “butterfly effect” in which small changes at one point in time can cascade into very large changes later on. What I feel comfortable saying is that the additional risk of a death spiral created by disproportionate enrollment of the an older demographic is greater than Kaiser asserts.

By simply lopping off the number of people under 35 who would enroll, the Kaiser model lacked a good theoretical foundation.  The model Kaiser should have run — “Scenario 3” —  is one in which the rate of enrollment is a sensible function of the degree of age-related subsidy (or anti-subsidy). Their two other scenarios could then be seen as special cases of that concept. Had they run such a “Scenario 3”, as I will show in a few paragraphs, the result is somewhat different.

Let me give you the idea behind what I think is a better model. I’m going to present the issue without the complications created by the messiness of data in this field.  We need, at the outset to know at least two things: (1)  the number of people of each age who might reasonably purchase health insurance if the subsidy were large enough (the age distribution of the purchasing pool); and (2) the subsidy (or negative subsidy) each person receives for purchasing health insurance as a function of age. By subsidy, I mean the ratio between the expected profit the insurer makes on the person divided by the expected expenses under the policy, all multiplied by negative one. The bigger the subsidy, the more money the insurer loses and the more likely the person is to purchase insurance.

Suppose, then, that the probability that a person will purchase health insurance is an “enrollment response function” of this subsidy. For any such enrollment response function, we can calculate at least three items: (1) the total number of people who will purchase insurance; (2) the age distribution of purchasers (including the “young invincible percentage” of purchasers between ages 18 and 35); and (3) — this is the biggie — the aggregate return on expenses made by the insurer.  Thus, some enrollment response function might result in 6.6 million adults purchasing insurance of whom 40% were “young invincibles” that generated a 1% profit for the insurer on adults while another enrollment response function might result in 2.9 million adults purchasing insurance of whom 20% were “young invincibles” that generated a 3% loss for the insurer on adults.

What we can then do is to create a family of possible enrollment response functions drawn from a reasonable functional form and find the member of that family that generates values matching the “baseline assumptions” made by both Kaiser and, apparently, by HHS about total enrollment and about the “young invincible percentage.” We can then calculate the aggregate return of the insurer on adults and call this the baseline return. What we can then do is assume different total enrollments and different young invincible percentages, find the member of the enrollment response function family that corresponds to that assumption, and then calculate the new revised return on adults. The difference between the baseline return and the new revised return on adults can be thought of as the loss resulting from this form of adverse selection. There are a lot of simplifications made in this analysis, but it is better, I believe, than either the back of the envelope computation by Kaiser that has gotten so much press and, frankly, the back of the envelope computation I did earlier on this blog.

Here’s a summary of the results.  When I (1) use the Kaiser/HHS age binning of the uninsured and indulge the simplifying assumption that the age distribution is uniform within each bin; (2) use Kaiser’s own estimate of the subsidy received by each age, (3) assume 7 million total purchasers ; and (4) assume 40% young invincibles with uniform age distribution within age bins, I find that the baseline return on adults is 1.0%. When I modify assumption (3) to have 3 million total purchasers and, as Kaiser did in Scenario 2, modify assumption (4) to have 20% young invincibles, the baseline return on adults is -3.5%.  Thus, a better computation of Kaiser’s worst case scenario is not a reduction in insurer profits of 2.4%, but rather a reduction of 4.5%.  

The graphics here compare enrollment rates, the age distribution of enrollees and various statistics for the baseline scenario and the scenario in which there are 3 million total purchasers and approximately 20% young invincibles.

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

We can use this methodology to run a variety of scenarios. I present them in the table below. A Mathematica notebook available here shows the computations underlying this blog entry in more detail. I am also making available a CDF version of the notebook and a PDF version of the notebook.

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

Please note that the computations engaged in here essentially ignore those under the age of 18.  This is unfortunate, but I do not have the data on the expected premiums and expenses of  children. It does not look as if Kaiser had that data either. Since children are expected to comprise only a small fraction of insured persons in the individual Exchanges, however, this omission probably does not change the results in a major way.

A humbling thought

The more I engage in this analysis, the more I realize how difficult it is.  There are data issues and, more fundamentally, behavioral issues that we do not yet have a good handle on.  Neither my model nor Kaiser’s model can really explain, for example, why, as has recently been noted, enrollment rates are so much higher in states that support the ACA by having their own Exchange and with Medicaid expansion than in states that more greatly oppose the ACA.  As I have suggested before, there is a social aspect and political aspect to the ACA that is difficult for simple models to capture.  Moreover, as I noted above, this is an area where getting a number “close to right” may not be good enough.  Premium increases of, say, 9% might not trigger a death spiral; premium increases of 10% might be enough.  And neither my nor anyone else’s social science, I dare say, is precise enough to distinguish between 9% and 10% with much confidence.

So, longer though it makes sentences, and less dramatic as it makes analyses and headlines, the humbling truth is that we can and probably should engage in informed rough estimates as to the future course of the Affordable Care Act, but it is hard to do much more as to many of its features. I wish everyone engaged in this discussion would periodically concede that point.

Other Problems with Kaiser

There are  other issues with the Kaiser analysis. Let me list some of them here.

Even accepting Kaiser’s analysis premium hikes would likely be more than 2%

Kaiser’s discussion of insurer responses to losing money is inconsistent. Look, for example, at this sentence in the report: “[i]f this more extreme assumption of low enrollment among young adults holds, overall costs in individual market plans would be about 2.4% higher than premium revenues.”  Kaiser further reports “Insurers typically set their premiums to achieve a 3-4% profit margin, so a shortfall due to skewed enrollment by age could reduce the profit margin of insurers substantially in 2014.” I don’t have a quarrel with this sentence.  But then look at what the Kaiser report says. “But, even in the worst case, insurers would still be expected to earn profits, and would then likely raise premiums in 2015 to make up the shortfall,” No! According to Kaiser’s own work, “even in the worst case,” insurer costs would be 2.4% greater than premium revenues.  Since there is little float in health insurance and investment return rates are low these days, insurers would likely not earn profits.  Then it gets worse. “However, a one to two percent premium increase would be well below the level that would trigger a “death spiral.” Perhaps so, but if insurers need to earn 3-4% to keep their shareholders happy and they are losing 1-2%, a more logical response would not be a 1-2% increase in premiums but a 4-6% increase. And, as Kaiser points out, larger premium increases could trigger a premium death spiral in part because death spirals are like avalanches: they start out small, only a little snow moves, but once the process starts it can become very difficult to abort.

Logical Fallacies

The first paragraph of Kaiser’s report asserts:  “Enrollment of young adults is important, but not as important as conventional wisdom suggests since premiums are still permitted to vary substantially by age. Because of this, a premium “death spiral” is highly unlikely.” Even if the first sentence of this quote were correct — a point on which this entry has cast serious doubt — the second sentence does not follow.  To use a sports analogy, it would be like saying that,  the role of a baseball “closer” is important but not as important as conventional wisdom suggests. Therefore the Houston Astros, who lack a good closer, are highly unlikely to lose.  No!  There are multiple factors that could cause an adverse selection death spiral.  Just because one of them is not as strong as others make out, that does not mean that a death spiral is unlikely. That’s either sloppy writing or just a pure error in logic.

Other Factors

And, in fact, if we start to look at some of those other factors, the threat is very real.  As discussed here in more depth, I would not be surprised if adverse selection based on completely unrated gender places as much pressure on premiums as adverse selection based on imperfectly rated age. And, as I have discussed in an earlier blog entry, the transitional reinsurance that somewhat insulates insurers from the effects of adverse selection will be reduced in 2015. This will place additional pressure on premiums.

And, on the other hand, the individual mandate, assuming it is enforced, will triple in 2015 and risk adjustment measures in 42 U.S.C. § 18063, will likely provide greater protection for insurers.  These two factors are likely to dampen adverse selection pressures.

Notes on Methodology

There are a number of simplifying assumptions made in my analysis.  Some of them are based on data limitations. Here are a few of what I believe are the critical assumptions.

1. Functional form: I experimented with two functional forms, one based on the cumulative distribution function of the logistic distribution and the other based on the cumulative distribution function of the normal distribution.  These are both pretty conventional assumptions and make sure that the enrollment rate stays bounded between 0 and 1. The results did not vary greatly depending on which family of functions the enrollment response functions were drawn from.

2. Uniform distribution of ages within each age bin of potential purchasers. I believe this is the same assumption made by Kaiser and it results from the absence of any more granular data on the age distribution of the uninsured that I was able to find.

3. The enrollment rate depends on the subsidy rate standing alone and not other possibilities such as subsidy rate and age. The data on enrollment rates is very sparse and so it is difficult to use very complex functions.  Perhaps a more complex analysis would assert that enrollment depends on both subsidy rate and age, since age may be a bit of a proxy for the variability of health expenses and thus of risk.

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Coverage on January 1, 2014 matters

Contrary to the views of some, the number of people who have insurance coverage through the Exchanges as of January 1, 2014, matters to everyone.  It matters because the pool that exists on that date will determine, at least for a while, whether the premiums charged by insurers in the Exchange are likely to be stable and the extent of the federal government’s multiple obligations to subsidize plans purchased on the various Exchanges. It is not as if insurers get a claims paying holiday simply because more and healthier people may enroll later in the year. It also matters because a major point of the Affordable Care Act was to increase in an efficient and relatively painless way the net number of people who have insurance or social protection against significant illness.  If the numbers in the Exchanges and in the expanded Medicaid program do not way more than offset the number of persons who lose their insurance as a result of the ACA, or if the cost of extending health protection in this fashion proves too high, the ACA will not have accomplished its goals.

Given the chaos that has erupted as procrastination strains Exchange infrastructure and deadlines are repeatedly extended, it is difficult to tell right now whether the ACA is performing as hoped. A few things are clear, however. The first thing is that the Obama administration is not releasing the sort of information from which an objective assessment could be made.  Platitudes such as “Millions of Americans, despite the problems with the website, are now poised to be covered by quality affordable health insurance come New Year’s Day,” from President Obama at his last press conference are just not a substitute for knowing how many people have enrolled in the plans in the various Exchanges, and more importantly, have paid for coverage. What are their ages? How about some real numbers as a Holiday present?

Second, the Obama administration is acting as if a large number of enrollees in the aggregate is the measure of success. This is simply not true. Putting aside the problem of it being paying customers rather than mere enrollment that ultimately matters, meeting or exceeding projections in some states does not compensate for deficiencies in many other states.  Because the pools are state-based, Texas insurers and insureds are not helped if enrollment in New York or Connecticut exchanges ultimately equals or exceeds targets. The insurance market in Texas and many other states will still be unstable with some insurers likely pressing for significant premium increases, contemplating withdrawal from the Exchanges, and demanding larger subsidies from the federal government via Risk Corridors and other programs.

Third, even those who have been on the more pessimistic side of matters, must acknowledge that there has indeed been a surge in many state Exchanges and in many states covered by the federal Exchange. On December 11, I wrote: “With a decent last minute kick, it is not unimaginable that California could make 1/3 of its total by the December 23, 2013 deadline and get closer to its ultimate goal by the end of March.” With enrollments at 17,000 per day, California may in fact be there. Colorado, which previously had dismal enrollment numbers, reports 33,356 enrolled as of Monday, which puts it at of the 136,000 projected enrollment for 2014 and 52% of the way towards the Obama administration’s projections for this time of the open enrollment season. (33356/(0.47 x 136000)). Other states such as New York and Connecticut, which previously were doing better than most, have also reported a high pace of enrollment.

Whether that surge has been as large in many other states remains to be seen. Proponents of the ACA like to cherry pick their states with at least as much zest as opponents do. Perhaps both sides share the belief that insurance enrollment is at least much a social phenomenon as a purely economic one. Numbers for large states (with large numbers of uninsureds) such as Texas, Florida, Georgia, Indiana,  Illinois, North Carolina and Florida have yet to report any numbers that I have seen.   And, as mentioned above, even if California and New York and some other states have enrollment sufficient to forestall premium instability and possible entrance into an adverse selection death spiral, that will not greatly help states in which enrollment ends up being less than half of that projected.

Finally, we need to look beyond the last minute holiday rush for health coverage and see what happens between now and March 31, 2014. The carrot of the ACA has basically been eaten for 2014.  If you wanted health care coverage and could afford the prices on the Exchange it made little sense to wait until after the December deadline to acquire it.  This is all the more true given that the President has permitted people to game the system by simply enrolling in a plan now and deciding until January 10, 2014, whether to pay.

Now, however, the first surge is likely over.  Will there be the needed second surge? All that really remains is the stick: the individual mandate tax penalty.  Many people, including me, believe that even before the events of last week, it was too small in 2014 to achieve its goal of inducing enrollment by those in good or average health.  The number of people for whom insurance would not be a good deal at, say, $2,000 a year net but for whom it would be a good deal at (effectively) $1,705 per year ($2,000 – the $295 per person tax penalty) is not likely to be enormous. This is so because ACA premiums often depart greatly from actuarial risk by their prohibition on medical underwriting, accurate age rating, gender rating and their — shall we say — loose enforcement of tobacco rating.

Moreover, with the administration exempting last week upwards of half a million people from the individual mandate, the number of people who need fear the stick got even smaller.  So, yes there are mega-procrastinators or people who have been stymied by the dysfunctionality of various Exchange website in obtaining coverage. There are former skeptics who see their neighbors helped by health insurance coverage under the ACA and who now enroll just as there may be some turned off by whatever problems emerge in administration of the plans.  On balance, I would not be surprised to see modest increases in enrollment between now and the middle of March.  I remain highly skeptical, however, that there will be a second surge equivalent to what has occurred this past week.  As they say, however, only time will tell.

Personal Note

I am enjoying a family vacation in the Colorado mountains this winter holiday.  It’s snowing outside my window as I write this and the beauty of a quiet snowfall can eclipse what may seem so important at other times. So please continue to read ACA Death Spiral periodically, but don’t expect a huge amount of activity for about the next week.  I’m confident we’ll be back exploring issues in the new year.

 

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Phantom costs: The lawless proposal to buy off the insurance industry via a “fix” to Risk Corridors

In my last blog post, I began to explain the proposed “fix” to the Risk Corridors program that the Obama administration seeks to achieve through modifications of its regulations. This is the provision of the Affordable Care Act under which the federal government reimburses large proportions of money lost by insurers over the next three years selling insurance to individuals in the Exchanges or to small employers.  Originally thought by many to be budget neutral, if, as appears increasingly possible, insurers on average lose significant money in the Exchanges, Risk Corridors could cost the federal government hundreds of millions of dollars or more.

I also suggested in that prior blog post that the “fix” raised serious concerns about the rule of law and separation of powers.  In this post, I want to follow up and explain further the accounting trickery and word play in which the administration is engaged and why it is not authorized by any law passed by Congress. Basically, the proposed changes in the regulations amount to an illegal pay off to the insurance industry so that they do not exit the Exchanges after having had the rug pulled out from under them by another decision not to enforce the law as written.

In sum, the Obama administration is proposing without any statutory authorization to let insurers increase the amount they get from the federal government under the Risk Corridors provision of the Affordable Care Act by treating as a “cost” money that the insurers have not spent and that can not be fairly said to be a cost of doing business.  The Obama administration makes this use of phantom costs appear more palatable by terming it “profit” and likening it to an opportunity cost of capital. But the increased “profits” the Obama administration now seek to permit insurers to subtract as a cost has completely detached itself from anything to do with real opportunity costs of running a business. The Obama administration would have been equally dishonest had they permitted insurers to place triple their rent on their Risk Corridor accounts and term the extra 200% a cost of business that entitled them to yet more money from the government. The proposed regulations should be seen as unlawful as an attempt by the Executive branch to change hard percentages used in the statute such as  80% into 95% simply because the Executive thought it better balanced the interests at stake.

Background

The fundamental problem stems from the divergence between what the President repeatedly told Americans during his presidency — if you like your health care plan, you can keep it — and what the Affordable Care Act (a/k/a Obamacare) really said, particularly as it ended up being implemented by the President’s own executive agencies (here and here). The insurance industry acted as if the rule of law mattered, not the campaign rhetoric or people’s perceptions of it, and set its prices in the healthcare Exchanges in accord with the law and the administration’s own forecasts of its effects on competing policies otherwise available to healthy people.  So, when the President announced on November 14, 2013, that his administration would conform the law to his rhetoric and public expectations (by declining under certain circumstances to execute sections 2701-2709 of the Public Health Service Act as modified by the Affordable Care Act), the insurance industry had a fit. It appropriately warned the President that, by reviving competitive sources of health insurance for some of their healthiest potential insureds, he was destabilizing the insurance markets. And, since the keystone of the President’s signature piece of legislation, the Affordable Care Act, depends on happy private, profitable insurers, this was a warning the President and his executive agencies had to heed.  Instead of backing down on the November 14, 2013 announcement, the President doubled down on regulatory change. This past week the Department of Health and Human Services proposed in the Federal Register how current Risk Corridor regulations might be amended to give insurers relief.

A Quick Look at the Statute

For ready reference, here’s an excerpt of the key part of the Risk Corridors statute in question.  You can try to read it now or refer to it periodically as you progress through the remainder of this blog entry.

(b) PAYMENT METHODOLOGY.—
(1) PAYMENTS OUT.—The Secretary shall provide under the
program established under subsection (a) that if—
(A) a participating plan’s allowable costs for any plan
year are more than 103 percent but not more than 108
percent of the target amount, the Secretary shall pay to
the plan an amount equal to 50 percent of the target
amount in excess of 103 percent of the target amount;
and
(B) a participating plan’s allowable costs for any plan
year are more than 108 percent of the target amount,
the Secretary shall pay to the plan an amount equal to
the sum of 2.5 percent of the target amount plus 80 percent
of allowable costs in excess of 108 percent of the target
amount.

The Federal Register Proposal

The fundamental idea in the new Risk Corridors proposal is to put the insurers back in the same position they would have been in had the non-enforcement announcement (“the transitional policy”) not been made.One can see this point made repeatedly in the Federal Register proposal:

Therefore, for the 2014 benefit year, we are considering whether we should make an adjustment to the risk corridors formula that would help to further mitigate any unexpected losses for issuers of plans subject to risk corridors that are attributable to the effects of the transition policy. (78 FR 72349)

We are considering calculating the State-specific percentage adjustment to the risk corridors profit margin floor and allowable administrative costs ceiling in a manner that would help to offset the effects of the transitional policy upon the model plan’s claims costs. (78 FR 72350)

Although the adjustment that we are considering would affect each issuer differently, depending on its particular claims experience and administrative cost rate, we believe that, on average, the adjustment would suitably offset the losses that a standard issuer might experience as a result of the transitional policy. (78 FR 72350)

Two clearly illegal ways to “fix” the problem

The problem the administering agency (Health and Human Services) faces, however, is how. How does HHS “suitably offset the losses that a standard issuer might experience as a result of the transitional policy?” One simple way might have been to adjust the reimbursement percentages contained in the statute, changing them from 50% and 80% for different levels of losses to higher levels. The problem is that the statute (42 U.S.C. § 18062) specifically sets forth the 50% and 80% reimbursement percentages and it would challenge even the most fertile imaginations to contend that it was within the province of an administrative agency to interpret those, as, say, 70% and 95%. And in the current gridlock — and with proposals to repeal Risk Corridors circulating —  getting such a proposal through Congress would seem impossible.

Alternatively, the administration might have made the insurers whole by adding state-by-state constant terms to the formula for reimbursement that roughly approximated the amount a typical insurer might lose in that state. Again, though, that would just constitute a statutorily unauthorized give away of federal taxpayer to the insurance industry.  Congress did not authorize payments so that insurers could maintain the same profits they would have earned in an alternative regulatory environment; instead Congress attempted to compress the profits and losses of insurers based on the regulatory environment that they in fact were in.

The “fix” suggested by the Federal Register proposal: what’s the difference?

What I now want to persuade you of, however, is that, after one strips away the confusing accounting, the Federal Register proposal, in its essence, amount to the same thing as these clearly unauthorized alternatives.  They are, in effect, a coverup for a giveaway of government money. The are very much the assumption of legislative powers by the executive branch of government.

The conceptual problem

One can almost see the problem without doing the math. The very objective set forth repeatedly in the Federal Register proposal — of putting the insurer back into some alternative financial condition, almost as if the government had taken their property or committed a tort by changing the rules — is nowhere to be found in the Risk Corridors statute. Section 1342 speaks of real premiums earned and real costs incurred and looks at their ratio in order to determine federal aid to insurers writing in the Exchanges. That perspective is echoed in the initial regulations published in the Federal Register months before the “transitional policy” brouhaha broke out. The definitions of critical terms adopted in those regulations speak of costs “incurred” or the “sum of incurred claims” or “premiums earned.” (See note below on definitions). Moreover, the definitions are nationwide. There is no sense that the values in the regulations (such as limits on the amount of administrative costs that can be claimed by an insurer) need to be adjusted on a state-by-state basis. And that refusal to adjust the regulations based on different economics in different states exists under the current regulations even if insurers in different jurisdictions have different financial experiences under the Affordable Care Act or face different state regulatory environments.

So, with those darned percentages statutorily nailed down, how does one achieve the objective in the Federal Register proposal of giving insurers their anticipated profits back? The answer is that the Federal Register proposal attempts to add a phantom cost that will vary state-by-state in precisely the amount needed to do the job.  Of course, writing “state-specific phantom cost” into the regulations would alert everyone that the plan was just to shovel money to insurers to keep them happy regardless of what was in the law. So, instead, the idea was to seize upon a word already in the regulations — “profit” — and alter its definition beyond recognition. Expanded “profit” could then do the same job as “state specific phantom cost.”

The math

Here are the specifics. The statute makes the amount the insurer receives in Risk Corridor payments (or pays) depend on a ratio.  A higher ratio often results in more payments and never results in smaller payments from HHS. The numerator of the ratio is something called “allowed costs,” so the higher the allowed costs, the better HHS treats the insurer under Risk Corridors.  The denominator of the ratio is something called “the target amount.” Because higher ratios are good for the insurer, the smaller the “target amount” the better HHS treats the insures under Risk Corridors. (Remember, dividing by a smaller number yields a higher result.) And “target amount” is defined as total premiums less administrative costs.  So, the more an insurer can stuff into administrative costs, the smaller the denominator, the higher the ratio, and the better the insurer fares under Risk Corridors. Indeed, much of the regulatory effort has been appropriately devoted to deterring insurers from exploiting the formula by stuffing overhead they incur servicing non-ACA policies into “administrative costs” that increase their Risk Corridor payments. (Good idea!)

Back in March of 2013, in trying to figure out how to operationalize the ideas contained in the Risk Corridors statute, HHS decided to recognize that the insurer risks its capital in order to operate an insurance company. HHS recognized that it is therefore appropriate to treat some of that opportunity cost as a true cost. (I have no particular problem with the concept). Perhaps unfortunately, but as a convenient shorthand, HHS called this opportunity cost “profit.” Be clear, however, the term “profit” as used in the regulations had little to do with how much money the insurer actually made; it was just an easy term to reflect the fact that when insurers use money to establish offices and buy computers they forgo interest and dividends  that they might otherwise have earned.

But how much of this opportunity cost called “profit” should an insurer be entitled to use to reduce its Risk Corridor denominator?  After receiving comments that were apparently almost uniform on the subject — the one dissent advocated a lower number — HHS decided to use 3% of after-tax premiums. It called this number, “the profit margin floor.”

Several things are significant about the decision to use 3% of premiums.  First, the profit margin floor is 3%, not 6% or 9% or some higher number yet. No one apparently thought the number should be higher. Second, the number is uniform across states. This is entirely sensible because, to the extent that an allowance for capital costs is appropriate at all, capital costs of an insurer are incurred in a national market. Insurers in California do not have opportunity costs of capital that differ very much from insurers in Texas. And, third, the number is a coefficient of net premiums rather than assets probably because use of premiums provides a sensible surrogate for the amount of capital risked by running an Exchange insurance operation instead of running one’s entire insurance business.

What the new Federal Register proposal does is to increase the profit margin floor and to do it in a state-specific way. By increasing the profit margin floor, one can decrease the target ratio denominator and increase the Risk Corridors ratio, which in turn can increase the payment made by HHS to the insurer.  Mathematically, increasing the profit margin floor is little different than permitting the insurer to count triple-rent on its offices rather than real rent or to just pad its electric bills by, say, a million dollars. All are additions of non-existent “phantom costs” that act to decrease a denominator and, derivatively, increase a ratio upon which reimbursement depends.

Moreover, the amount by which the profit margin floor will need to be increased is not a trivial amount.  As shown in the Risk Corridors Calculator, “profit margins” may need to be tripled or more to bring an insurer back to the same position they were in originally.  I would not be surprised to see the profit margin floor in some states in which adverse selection proves particularly problematic to be upwards of 12%.  I am not aware of many insurers making 12% of their premiums in profits, which is precisely why, before they saw the need to repair the damage done by the President’s change of mind, HHS was using 3% as the appropriate figure with only lower numbers being suggested.

Why the proposed fix is unlawful

Any thought that the proposed increase in profit margin floor might have something to do with economic reality, with changes in the cost of capital, is belied by the way HHS explains the change and by the state-by-state approach it now proposes to take.  The HHS explanation is that, because different states are implementing “the transitional plan” differently, the need to adjust Risk Corridors to bring insurers back to their former position differs as well.

We believe that the State-wide effect on this risk pool will increase with the increase in the percentage enrollment in transitional plans in the State, and so we are considering having the State-specific percentage adjustment to the risk corridors formula also vary with the percentage enrollment in these transitional plans in the State. (78 FR 72350)

Of course, in some sense, this is true. But this simply highlights the point that the adjustments to profit margin floor have nothing to do with real costs, the concept the statute cares about.

Not enough? Take a look at the explanation for why HHS did not adjust profit margin floors it on an insurer-by-insurer basis.  It has nothing to do with different costs of capital that different insurers might face, but again, the state-by-state approach is used because it is a simpler way of approximating and offsetting the loss insurers would face in each state as a result of differential effects of the transition policy.

Although the adjustment that we are considering would affect each issuer differently, depending on its particular claims experience and administrative cost rate, we believe that, on average, the adjustment would suitably offset the losses that a standard issuer might experience as a result of the transitional policy. (78 FR 72350)

The administrative law and separation of powers issue is whether the agency empowered with administering Risk Corridors can count as a cost not an expense the insurers actually incur as a result of being in an Exchange but the “regulatory taking” that will occur differentially in each state as a result of President Obama changing his mind. I suppose that, if there is someone with standing to challenge this give away of government money, it will ultimately be for the courts to decide this question.  (By the way, if anyone can suggest someone who might have standing, email me). And I suppose someone can argue that it actually fulfills some general intent of the ACA to keep insurers involved in the Exchanges and not have them flee when other regulations change.

Executive administrative agencies such as the Department of Health and Human Services have the authority under some circumstances to interpret statutes; courts will often then defer to their interpretations. But this fix is not a stretch; if it actually does what its drafters intend, it will be a redraft of the Affordable Care Act itself. I see no difference except opacity between what the Obama administration has done by seizing on a code word “profit” and expanding its definition beyond recognition and saying that when the statute says 80% of losses, surely that could be construed as 95%. Both are unlawful.

Two final notes

The allowable administrative cost cap percentage and the medical loss ratio

Careful readers of the Federal Register will note that there are two other matters it discusses.

The Federal Register proposal also discusses the need to adjust the “allowable administrative costs ceiling (from 20 percent of after-tax profits) in an amount sufficient to offset the effects of the transitional policy upon the claims costs of a model plan.” This provision is needed because otherwise, even if the profit margin floor were increased, insurers would bump up against the existing administrative cost ceiling of 20%.  So, to make sure that the phantom cost “profit margin floor” increase really works, the proposed regulations propose removing that constraint. And to make sure that evil insurers do not take advantage of the relaxed constraint to allocate more of their costs to Exchange plans, the regulations make clear that the insurer would had to have met the 20% standard before consideration of increased “profit” was made.

The Federal Register proposal also discusses a need to adjust the Medical Loss Ratio (MLR) percentages. This is the provision of the ACA that says that if insurers spend too much of their money on non-claims matters, they have to pay a rebate to their insureds.  The problem becomes that if insurers are permitted to treat more than 20% of their premiums as administrative costs for purposes of Risk Corridors they might want to treat more than 20% of their premiums as legitimate administrative costs for purposes of MLR rebates. It’s a little fuzzy, but it sounds as if HHS wants to tweak the MLR regulations so that the MLR provisions do not take away from insurers what they will be winning if the remainder of the Federal Register proposal goes into effect.

The typo in the statute

There’s a complication we have to work through. This whole area is complicated by the fact that there is a typographic error in section 1342.  Here again is the relevant part.

(b) PAYMENT METHODOLOGY.—
(1) PAYMENTS OUT.—The Secretary shall provide under the
program established under subsection (a) that if—
(A) a participating plan’s allowable costs for any plan
year are more than 103 percent but not more than 108
percent of the target amount, the Secretary shall pay to
the plan an amount equal to 50 percent of the target
amount in excess of 103 percent of the target amount;
and
(B) a participating plan’s allowable costs for any plan
year are more than 108 percent of the target amount,
the Secretary shall pay to the plan an amount equal to
the sum of 2.5 percent of the target amount plus 80 percent
of allowable costs in excess of 108 percent of the target
amount.

See in subparagraph (1)(A) where it says “the Secretary shall pay to the plan an amount equal to 50 percent of the target amount in excess of 103 percent of the target amount.” But if you think about it, this could never happen.  Taken literally, there could never be a payment under this provision. So long as the target amount is a positive number, which it always will be since premiums are positive, the target amount can NEVER be in excess of 103% of the target amount.  5 can never be in excess of 103% of 5 (5.15).  10 can never be in excess of 103% of 10 (10.30). Can’t happen.

Looking at the next subparagraph, (1)(B), resolves the mystery of subparagraph (1)(A). It speaks about paying “ 80 percent of allowable costs in excess of 108 percent of the target amount.” (emphasis mine). And this makes complete sense.  The more the insurer loses, the more the government reimburses the insurer.  That’s the whole point of the provision.  I therefore believe that  subparagraph (1)(A) should be interpreted to mean “the Secretary shall pay to the plan an amount equal to 50 percent of  allowable costs in excess of 103 percent of the target amount.”

So, I assume that courts will interpret the statute to read as Congress must have intended it and not as some sort of cute joke resting on a mathematical impossibility.  See United States v. Ron Pair Enterprises, 489 U.S. 235 (1989) (“The plain meaning of legislation should be conclusive, except in the ‘rare cases [in which] the literal application of a statute will produce a result demonstrably at odds with the intentions of its drafters.’ Griffin v. Oceanic Contractors, Inc., 458 U. S. 564, 571 (1982). In such cases, the intention of the drafters, rather than the strict language, controls. Ibid.” )

Note on Definitions

As set forth in the regulations, “Allowable costs mean, with respect to a QHP [Qualified Health Plan], an amount equal to the sum of incurred claims of the QHP issuer for the QHP.” The regulation sensibly uses the word “incurred.” This is so because costs are things the insurer has to pay out or has to accrue liabilities for, not things that, under some other set of circumstances they might otherwise have had to pay out.  If that were not the case, the administration could redefine costs to include anything at all, such as the costs the insurer would have faced if every one of their insureds had cancer.

The regulations tweak the definition of “administrative costs” by adding an extra adjective. They introduce the concept of “allowable administrative costs.”  The insurer is not permitted to reduce its “target amount” by claiming some enormous sum (such as private jets for the CEO) as non-claims costs, subtracting them from premiums and reporting low net premiums (target amount) in order to get paid more by the government under the Risk Corridors program. Instead, the regulations define “allowable administrative costs” as non-claims costs that are not more than 20% of premiums. That makes some sense because section 10101 of the ACA (42 U.S.C. § 300gg-18) often requires insurers whose administrative costs are more than 20% of premiums to pay a rebate to their insureds.

Premiums are also reasonably defined under the existing regulations. They sensibly say, “Premiums earned mean, with respect to a QHP, all monies paid by or for enrollees with respect to that plan as a condition of receiving coverage.” Thus, under the statute and existing regulations, premiums must refer to real premiums, not hypothetical premiums. Premiums are moneys the insurer receives, not money the insurer might have received under some other set of circumstances. Again, this just has to be the case; if it were not true, the administration could funnel virtually an infinite amount of money to the insurance industry by saying that premiums are funds the insurer would have received if no one signed up for their plan. 

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The Risk Corridor Calculator: How the government plans to use fictitious profits to shovel more money to insurers

Snapshot of the Risk Corridor Calculator
Snapshot of the Risk Corridor Calculator

This is a different kind of blog entry.  There isn’t going to be too much text here. Instead, I want to direct you to a spreadsheet I created (The Risk Corridors Calculator) available on Google Docs and the first (click here to watch it on YouTube) of two videos I’ll be making that explain

(1) how Risk Corridors work under the regulations originally proposed by the Department of Health and Human Services (HHS)

(2) how the insurance industry could lose money notwithstanding Risk Corridors as a result of President Obama changing his mind and conditionally permitting certain insurers for one year to “uncancel” certain  policies that the Affordable Care Act would otherwise have have prohibited starting in 2014; and

(3) how the proposed revisions to the Risk Corridor regulations will shovel money to many insurers and could put them back in the same position they would have been had President Obama not changed his mind.

[Note from 8:32 a.m. 12/6/2014: I discovered a small error in the Risk Corridors Calculator. It has been fixed.  It does not affect anything essential in this blog. Unfortunately, I will need to conform the video to the Calculator, which is likely not to happen until later today. So, if you watch the video today, it is conceptually fine, but just be aware that one of the formulas was off.]

In essence, however, the proposed HHS regulations impute fictitious “profits” to insurers that they then get to subtract from their net premiums.  As a result, it will look to the Risk Corridors program as if the insurer is losing more money in an Exchange plan and therefore entitled to greater government assistance.  (The government has now acknowledged that, although the Congressional Budget Office scored it as costing nothing, Risk Corridors need not be budget neutral.) Another way of thinking about the proposal is that it creates phantom costs that affect the apparent (though not the real) profitability of the insurer and then shovels money to insurers based in part on those phantom costs. It is little different than the government insisting that the insurer lost money due to claims that it actually did not pay and is therefore entitled — even under a formula that is formally unchanged — to greater payments from the government.  Viewed yet another way, it is almost as if the proposed regulations treat what President Obama did as a “tort,” and remedy the wrong by licensing the aggrieved insurers to use contorted accounting to place themselves back in the same position they would have been in had the President not, in effect, interfered with the prospective economic advantage they thought they had in the Exchanges.

Neither this blog entry nor the video will address whether the proposed regulations are permissible as a matter of administrative law or separation of powers. Nor will I explore today whether the regulatory changes can be seen as a necessarily evil. Exposing what is actually going on here, however, must create some serious concerns for all concerned about the rule of law. When section 1342 of the Affordable Care Act (42 U.S.C. § 18062) speaks of “allowable costs,” one would initially think it referred to costs actually incurred by the insurer as a result of running its program. Those costs might be paying claims, paying the electric bill, marketing costs and, perhaps, some reasonable allowance for profit — such as the 3% of after tax premiums actually placed in the original regulations.

But it is going to take some work to show that, by “allowable costs,” the statute meant costs that the insurer did not actually incur in running its program. The burden will be even higher due to the fact that the proposed regulations apparently contemplate varying this heightened profit allowance from state to state. This will be done not in response to different rates of return on capital in the different states, but only to take account of differential losses to insurers caused by different state responses to President Obama’s about-face on whether certain plans that violate ACA requirements could continue to be sold outside of the Exchanges.

In short, the increase in “profit” sure looks like a book-keeping entry whose sole purpose has nothing to do with anything in the statute but is instead designed to restore the insurer to the position it would have been in had federal policy not changed. It is as if the insurers are being given some sort of entitlement to the profits they would otherwise have made and the administration is looking for any term in the statute not glued down (such as an 80% reimbursement rate on certain losses) in order to accomplish this goal.

Fleshing out  more fully these matters of statutory interpretation, separation of powers, and administrative law will be left for later, however, along with a fuller explanation of what is going on inside the Risk Corridor Calculator that I created. For now, play with the spreadsheet and enjoy the video.

Resources

Society of Actuaries, Health Watch: Risk Corridors under the Affordable Care Act — A Bridge over Troubled Waters, but the Devil’s in the Details

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Shocking secrets of the actuarial value calculator revealed!

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

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

What is the Actuarial Value Calculator?

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

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

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

The Math Stuff

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

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

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

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

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

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

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

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

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

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

 

 3. Parameterizing health claim distributions based on the actuarial value

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

Here’s what I get.

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

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

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

 

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

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

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

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

 

Some initial results

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

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

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

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

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

Plain English Summary

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

Resources

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

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

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

Joke

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

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