Mathematical analysis and healthcare

One of the first skills mathematics students develop when learning to solve difficult problems is analysis - the resolution of complex objects into simple elements. Problems often seem insurmountable when viewed as an indivisible whole. Mathematicians learn to tease out less formidable subproblems; unravelling string by string often suffices to overcome amazingly complex questions. (Of course, questions are often left for the mathematicians of later generations or centuries to solve.)

Let's analyse the current healthcare problem. First we must define the problem. The usual assertion is that health care costs are rising so quickly that neither businesses nor individuals can sustain the cost. Economic disaster will ensue unless costs are reined in. As costs rise, fewer people purchase insurance, pushing their healthcare costs onto the remaining insurance customers, driving prices yet higher in an unfortunate feedback mechanism. Republicans address these issues by identifying and attempting to rein in cost drivers such as rapacious malpractice lawyers, restriction of interstate competition in insurance markets, tax policy distortion of market incentives, and of course the shifting of Medicare and Medicaid patients' costs onto the backs and wallets of the insurance buying public. I'll give the Republicans a B for their analysis. The Democrats are unwilling to break the problem into its constituent parts because their answer to all healthcare problems is the same: surrender all healthcare decisions to the government. Mathematicians don't inflate grades as much as Humanities faculty do, so I'll award the Democrats an F, but will allow them to attempt to redo the assignment.

Why do the Republicans only earn a B? Their analysis misses part of the solution (admittedly a politically tricky part). To see this, we begin by enumerating several basic healthcare costs:

• Insurance costs.
  
• Drugs.
  
• Physician fees.
  
• Hospital costs.

In this post, I restrict attention to the first two costs - currently the object of the greatest demagoguery - insurance and drugs. How can we separate insurance costs from all other healthcare costs? First let's imagine that we are an insurance company pricing a policy for a 40 year old male. As a first pass, we should compute the average cost of healthcare for 40 year old males. Next we add a risk premium. This is the payment the company receives for shouldering the risk that the policy holder incurs medical costs which significantly exceed the average. Then the company adds charges for administrative costs. The sum of the average cost, the risk premium, and the administrative costs gives the total cost of the policy.

When computing the cost of insurance, we can compute in two ways. For the overall system, the cost is total policy cost minus total company payouts to healthcare providers. For the individual, the insurance cost is his policy cost minus total company payouts to healthcare providers for his healthcare. When politicians complain about the rising cost of insurance, are they complaining about administrative costs, risk premiums, or the average payout? The first two costs are a small percentage of the total healthcare cost; hence complaint about insurance cost is really a mislabelled concern about the average payout to healthcare providers. Is it proper to attribute the rapid rise in this cost to our insurance system? More precisely, does the insurance system contribute to inflation of the average healthcare cost?

There are obvious defects in our system which lead to increased consumption of healthcare. When rational people purchase their own insurance, their goal is to guard against the possibility that they incur financially devastating costs. It is irrational (ignoring tax incentives) to insure for any predictable or expected cost. If all 55 year olds are advised to have a colonoscopy, then 55 years olds should not purchase insurance that pays for colonoscopies. Insuring a predictable expense can only increase its cost. Moreover, if you happen to decide to avoid the procedure, you pay for it anyway. Therefore, self purchased insurance should only cover extreme events and should have high deductibles. When employers provide health insurance as a benefit, they are effectively purchasing both a coupon for predictable healthcare expenses plus insurance for extreme events. The coupon encourages the buffet effect - consume until you get your coupon's worth. This effect is targeted in Republican plans to alter the preferential tax treatment of employer sponsored insurance plans.

The fact that people are priced out of the insurance market implies this analysis is still missing something: rationing. Opponents of government controlled healthcare object that all government healthcare schemes require government rationing of healthcare. Left unsaid is the fact that all healthcare insurance necessarily implies some rationing. The fundamental difference is between concentration of rationing power in a single, too powerful, remote government body and rationing decisions spread out over a multitude of actors from private insurers to employers to individual policy holders, each making their individual judgments of priorities and tradeoffs. If people significantly above the poverty line are priced out of the insurance market, perhaps we should ask whether the average cost of healthcare is too narrowly defined. Consider, for example, the cost of drugs. Suppose you had the following options: (i) go without drug insurance because you could not afford to pay the high average cost for your age group or (ii) buying affordable drug insurance with the restriction that the policy paid only for drugs approved before 2001 (unless more recent therapies are cheaper). Which would you choose?

If regulations were simplified so that insurance companies could offer more differentiation of coverage than now allowed, it would have dramatic impact on our healthcare system. Currently, the latest advances in drugs, imaging technology, etc., propel healthcare costs ever higher. If we had a multitiered system, the rich would bear a greater part of the burden of funding the development of new technologies (and the occasional horrific errors such as thalidomide), while the rest of us could pay for well vetted albeit older techniques and technologies. The left abhors any such differential outcome, but it is clear that under government run healthcare, technical advance would stagnate anyway, consigning the entire population to older treatment regimens. Under a multitiered system, we provide a mechanism for the wealthy to fund advances while the rest of us merely wait a bit longer to reap the benefits. We then may choose what we value most: whether to use our funds to buy a bigger house or better car, private schooling for our children, or advance from, say, a 2001 level healthcare plan to a 2005 level healthcare plan. The actual details of how such a differentiated healthcare system would function would presumably be much more complicated than my toy model offered here, but with regulations relaxed to allow such differentiation, individuals and insurers would determine the optimal way for such a system to evolve.

Math and Gender Bias

Christina Sommers's Forbes article, Gender Bias Bunk, brings back memories of the time my department chairman called me into his office to ask me, "Why does the dean say you are crazy?" I had not been prowling through the sewer systems nor consulting with imaginary secret agents, but I did know how I had led the dean to doubt my sanity.

The previous week, the Mathematics Department faculty had attended a meeting organized by the Women's Studies Program. The topic of the meeting was how to introduce women's studies material into the mathematics curriculum. The idea was ludicrous to the Math faculty, and certainly none of us was inclined to honor the request. More interesting than the formal meeting was the mingling and discussion that preceded it. The director of Women's Studies approached a group of mathematicians and asked us whether we thought women were inherently less able to do mathematics than men, and if so, what should be done about it. I responded that there were many excellent female mathematicians and that the rate at which women entered mathematics continued to accelerate. It seemed likely (as has subsequently been borne out) that the number of women in mathematics would continue to grow.

The director appeared to be disturbed by my answer, and she followed up with a hypothetical: "Suppose it were true that women were inherently less able to do mathematics than men. What should we do?" "Nothing," I replied. "No," she said. "If men were inherently better at mathematics than women, then society must devalue mathematics." We were dumbfounded.

Later that week, I sent the dean an old Commentary article on the negative impact of the women's studies program on the intellectual climate at Kenyon College. I was a recently hired assistant professor, and that was my first dealing with the dean. (I had been hired during the tenure of the prior dean). The next day he told my chairman I was crazy. In retrospect, if not crazy, perhaps I was a bit foolish, but as I noted in a previous post, personal politics does not seem to affect hiring and tenure in Mathematics.

So, how can you distinguish between a liberal dean and a conservative mathematician in academe? The liberal dean thinks it is crazy to read Commentary. The conservative professor thinks it is crazy to think you should - or can - remove mathematics from our modern mathematically sophisticated world in order to rectify perceived biological inequities.

True Religion and Bosonic Politics

It's time to complete my field guide to mathematical liberals. The remaining commonly encountered species is the true believer. This species contains two subspecies, the believer and the bosonic believer (terminology explained below). Neither of these is endemic to academe; so, at best this post offers a new metaphor. For the believer, politics replaces religion, both in fervor of belief and unquestioning acceptance of precepts. Arguing with the faithful is never fruitful. My early introduction in graduate school to these acolytes included such revealing declarations as "I may not know the facts and figures as well as you do, but I know you are wrong. I don't know why, but you are wrong." It's hard to argue with that.

The bosonic believers are also beyond argument, but for a different reason. Their axiom system differs from that of the fiscal conservative. There can be no intelligent argument between two sides if they do not share the same fundamental axioms. This is a statement of logical rather than of social necessity. This is also the reason why 90% of arguments about social issues have no content. You cannot argue a point with someone if you differ on first principles.

So, what is the fundamental difference in axioms? My bosonic believers are sufficiently well versed in economic and political reality to concede that statist economic policies lower the average standard of living, yet still they advocate such policy. I have been told by a fellow professor that he "would prefer that everyone had less than that some had significantly more than others." Thus we are wrong to think these bosonic believers simply value the prosperity of the hive over the freedom of the individual. What they desire is a society that truly resembles a hive. Recall that in statistical mechanics, bosons refer to species of matter which can have unlimited numbers of indistinguishable particles in the same state. Substitute citizen for particle and this is the description of the ideal society for a bosonic believer. It is useless for the individualist to remind him: bosonic particles tend to cluster at the lowest possible energy level.

College Brands : Walmart vs Tiffany

John Steele Gordon, in A Crack in the College Cartel?, complains about the rising cost of college tuition. His analysis omits a few simple observations. Average tuition numbers should be read with care. He observes that average tuition today is $37,005, almost three times higher than the $12,500 that inflation might predict based on his college costs in the 60s. (My tuition costs were an order of magnitude lower than his, and I graduated decades later; it pays to shop around.) To put this average tuition int0 perspective, let's use Stanford for an example. Stanford tuition (I am using College Board numbers) is $37,380. Its average financial aid package is $40,204. Over half its freshmen receive financial aid. Hence the average tuition cost is arguably about $17,280. This is nearly 40% higher than what Gordon paid, but not the 200% increase that he asserts.

Built into this tuition and financial aid system is the usual liberal redistribution of wealth. The high tuition/high financial aid model allows colleges to force the upper middle class and wealthy to subsidize everyone else's tuition.

Gordon further compares colleges to a cartel. I cannot speak to the lower tier colleges, but it is clear that prestige colleges think that high tuition helps maintain their brand mystique. I once heard a top university administrator assert that it was essential that he maintain his school's brand, and "that brand is Tiffany, not Walmart." High prices are part of luxury branding.

I am more of a Walmart shopper myself. This year the average tuition and fees at U.T. Austin are $8500-$10,000. Don't complain about prices if you feel compelled to shop at Tiffanys.

Hayek, Health Care, and Reconciliation

Democrats often cite Hayek's implicit approval of state assisted health insurance (The Road To Serfdom, chapter 9) when supporting the current Democratic efforts to drastically remake the U.S. health industry. This legislative sausage, however, is better treated as an illustration of one of Hayek's arguments for the incompatibility of socialism and democracy. The illustration does not require you to accept the assertion that this legislation is, in fact, creeping socialism.

In The Road To Serfdom (Chapter 5), Hayek argues that while it is possible for a democratic people to agree to empower the state to manage a sector of the economy in order to achieve a desired social goal, the execution of such a program "requires more agreement than in fact exists." Too many choices between competing priorities and too many value judgments must be determined for any majority to agree to the entire plan. Hayek argues that success can only be achieved by taking the plan outside the democratic process, placing ever more power in the hands of unelected and unaccountable individuals, paving the way for the eventual loss of democracy.

The broad goals behind the attempt to reconstruct our entire health care system, especially universal coverage, garner broad support. A vast array of choices including: who pays, how to ration care, and ultimately whom the state will allow to die must be included in such a vast state mandated plan. None of the proffered plans have been able to win majority support of the voters for all these myriad elements. The Democratic leadership, however, has invented a new technique for bypassing Hayek's problem: drafting 1000+ page bills and forcing votes on them without allowing the congress an opportunity to read the bills. Even these corruptions of our democratic process have foundered on the rules of the senate. In order to push such a plan through, the Democratic leadership talks of further subverting the rules of the senate using the reconciliation process.

The Democrats forget that each corruption of the democratic process introduced for what they deem a current good can be used later, perhaps to achieve an end they abhor.

Evil Spirits, Markov Processes, and The New York Times

Last week we classified the commonly encountered liberal mathematicians into four species: the spherical horse, the happily ignorant, the NYT victim, and the true believer. Having dealt with spherical horses, we turn now to the happily ignorant and the victims of the New York Times.

The happily ignorant are an innocuous group consisting of those mathematicians who devote so much of their mental energies to mathematics that the little residual brain power remaining for their political discussions leaves them sounding like children in elementary school. No one on the left or right pays them much heed; so, we need not concern ourselves with them further.

The victims of the New York Times (and NPR - thank goodness the Valentine's Day fund raiser is finally over) constitute the largest subgroup of liberal mathematicians. Their primary sources of information are the NYT and NPR. These scholars, often extremely intellectually aggressive within their own disciplines, passively accept the most vacuous political analysis that the Times can offer. Reflecting their information sources, their understanding of the economics of any policy question is extremely primitive. Because they all have the same news source, a circuit around the faculty lounge yields the same regurgitation of Krugman "analysis" from multiple mouths. Left wing politics ensues.

I would like to see an assault on the NYT's dominant position on the academic's breakfast table - an assault that moves beyond moaning about the obvious liberal bias of the paper. I began reading the Wall Street Journal in my teen years, hoping that regular reading of the Journal would make me a savvy investor. When I began grad school, the NYT was everywhere, and I started reading it regularly too. By the time I graduated, however, I had largely abandoned the Times. When comparing the Times to the Journal, I was deeply impressed by the Journal's far better track record in predicting the future consequences of current actions. I assume this is due to their conservative outlook and their focus on economic analysis. For years they railed about the ticking time bomb that was Fannie Mae and the devastating impact its implosion would have on the economy. They were painfully correct. When Chavez first campaigned in Venezuela, they predicted his eventual assault on democracy. Correct again. On a smaller time scale, the rapid run up in credit card interest rates following the recent congressional imposition of new restrictions on credit card issuers, followed very closely the scenario predicted by the Journal. By contrast, the Times's aneconomic analysis seems to leave them unable to link cause and effect. They often call to mind people in a preliterate, prescientific society who attribute their illnesses and mishaps to evil spirits because they don't understand the link between hygiene, contagion, and disease. Blithely reading the Times is what probabilists call a Markov process. Quoting Wikipedia: a Markov process "is a mathematical model for the random evolution of a memoryless system, that is, one for which the likelihood of a given future state, at any given moment, depends only on its present state, and not on any past states."

After several years of seeing the Journal's forecasts frequently verified six months later, while the Times would simply change the subject from the failure of their analyses, I became unwilling to waste my precious time on the New York Times. Unlike Adam Sandler's character in 50 First Dates, I could not invest in a partner who greeted each new day apparently oblivious to everything learned in the previous 24 hours.

Of course all papers have their own weaknesses and ideological blind spots, the Journal included. So, it is useful to obtain your news from multiple sources. My conservative friends are amused by my regular daily attention to National Public Radio. Yes, NPR is strongly biased to the left, and Daniel Shore makes me nauseated whenever he blathers on. On the other hand, the primary way for any reasonable news source to mislead is not by telling bald lies, but by describing the mouse in the room in great detail while neglecting to mention the elephant looming over the mouse. (Reputedly, the NYT is no longer reasonable). With multiple sources, someone always mentions the elephant.

The conservative blogosphere should focus less on the bias of the Times and its ideological clones (which Taranto describes so well) and focus more on concrete examples of the greater clarity and predictive power associated with the conservative worldview.

The Spherical Horse

Conservatives spend hours and hours discussing how far left our media and our universities tilt. As a conservative scientist embedded in one of America's top liberal universities, I am far less interested in how far left the professoriate leans than why they are so liberal. If conservatives want to persuade liberals rather than to complain about them, it is important that we understand what makes them tick. The liberal dominance of academe, in particular, is important not only for the impact on college students, but also for the intellectual seal of approval it awards to a bankrupt ideology. In this and subsequent posts, I will offer my untutored field observations on the field markings of the liberals commonly found in my habitat.

First I should dispel one conservative myth. I have never seen any prejudice against hiring or promoting politically conservative mathematicians. (I have no personal insight into political bias in the hiring in departments in the humanities and social sciences.) Mathematics itself is fundamentally apolitical. This makes mathematicians a good group to examine when exploring faculty political leanings. I should also remark that my liberal colleagues are generally my liberal friends. They are good people with confused politics rather than the demons some of our more fiery conservative orators like to describe.

The four dominant species we encounter are: the spherical horse, the happily ignorant, the NYT victim, and the true believer. I will discuss these four overlapping types in the following weeks. Today I will restrict attention to the spherical horse. The description of this species is somewhat labored, but I am sure that I will find ample opportunity to refer to spherical horses in subsequent posts.

To explain the spherical horse I must first retell an old lame math joke:

A wealthy playboy is disappointed with his stable of racehorses. He hires an economist, a biologist, and a mathematician to advise him how to develop a winning racehorse. The economist devises a system of incentives to motivate the horses to produce optimal speed. After several horses die of starvation, the playboy fires the economist. He fires the biologist after being told that he will have an award winning racehorse in only 200 generations of careful breeding. Finally, the playboy asks the mathematician if he has solved the problem. The mathematician excitedly answers that after much deep thought he has worked out a beautiful solution: "First assume the horse is a sphere..."

This joke amuses mathematicians (and physicists and engineers) for several reasons. It underscores mathematicians' reputed willingness to focus on the mathematics of a problem to the exclusion of practical applications. It also casts light on the dirty secret of all mathematical modelling: a mathematically sophisticated model need not have any real world utility if the simplifying assumptions (always present) are insufficiently realistic. I will return to this latter aspect of modelling when I discuss global warming.

Mathematicians (and many other species of academics) are fond of abstraction, and many are willing to assess real world political, economic, and social issues in the context of oversimplified theories which, unfortunately, relegate such concepts as incentive, moral hazard, inefficiency of central planning, etc., to the same discard pile that holds the limbs of our playboy's racehorses. So, my most generous explanation for academe's attachment to left wing ideology is that professors are accustomed to thinking abstractly and are willing to ignore important detail in order to force the real world to fit into their abstract constructs. Some of my conservative colleagues assert that this explanation of left wing professors' willingness to embrace unworkable policy prescriptions is too generous; it is true that, in my experience, the riders of spherical horses are less numerous than the other species mentioned above. The notion is convenient, however, for providing some explanation for why so many smart people can have such poorly considered political positions. Besides, the spherical horse is an appealing metaphor that deserves wider circulation. Next week I will turn to the happily ignorant and the victims of the New York Times.