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Tuesday, December 28, 2010

Overproduction of Ph.Ds

The Economist has another article on the overproduction of Ph.Ds. There is no question that many students who enroll in graduate school would be better served pursuing other career paths. The Economist, however, minimizes and dismisses the passion that leads so many mathematicians and other scientists to gamble years of their lives on the wager that they will be the successful researchers who ultimately capture a tenured position. Most mathematicians I have known love mathematics. The Economist says that
"Academics tend to regard asking whether a Ph.D. is worthwhile as analogous to wondering whether there is too much art or culture in the world." This assertion does not ring true to me. To most passionate mathematicians, their love of mathematics is more important than any abstract notion of whether or not there is too much mathematics in the world. In order for an outsider to understand the mindset, imagine the budding mathematician as a close relative of the aspiring musician, athlete, writer, or actor. Each of these knows that only a small fraction of their number will become famous artists or athletes, etc.; yet their love of their craft (or their thirst for fame) drives them to risk years of their lives in pursuit of their dreams. Graduate students in the sciences face far better odds of success than the aspiring actresses and writers who bus tables while waiting for their big break. Moreover, their education buys graduate students an excellent insurance policy. Should they fail to secure a tenured position, many employers are happy to hire these highly educated, driven, and tenacious workers .

In my pretenure days I viewed the academic job market as a meat market. Departments blithely terminated the appointments of anyone whose research did not sufficiently advance the departments' reputations. Criteria for 'sufficiently' were strongly influenced by a department's view of how readily they could hire a better researcher on the open market. My comrades in graduate school all knew the cut throat market we faced, and we each believed (or hoped, depending on personality) that we would be the ones to succeed. Fewer than a quarter of us ended up as research mathematicians. Those who changed career paths included some who seemed to be extremely intellectually gifted, but their personalities or intellectual strengths were not compatible with a career as a mathematician.

As in athletics, the excess of strivers over available positions works to ensure the high quality of the resulting research community. I do not understand how economists and numerous conservative bloggers can understand the virtues of competition (and creative destruction) in business but yet be so appalled by its manifestations in science. I suspect, however, that one constributor to their cloudy vision is that they do not appreciate the sheer joy of doing mathematics and science. It is difficult to monetize joy, especially as this particular joy requires hours of effort incompatible with holding a more remunerative but nonscientific 8AM-6PM job. Conservatives and libertarians object to the intrusion of government into our lives, in part because most big government programs require the noxious implicit assumption that we all (should?) have the same values and priorities as our federal overseers. It ill behooves these same conservatives and libertarians to be distressed by individuals who are willing to make economic sacrifices in order to pursue goals more prized by them than by the staff of the Economist. Let's leave the worship of uniformity in the hands of statists where it belongs.

Sunday, December 12, 2010

Unbundling Health Insurance

Last month I read Mark Pauly's Health Reform without Side Effects, a short book analyzing our health care system. As a recipient of generous employer provided health insurance for most of my adult life, I found Pauly's discussion of the inefficiencies of the individual insurance market the most illuminating section of the book. The treatment of coverage for high risk individuals was also careful, but it led me to realize that health insurance policies contain a hidden component which I have not yet seen analyzed and did not include in my prior post on health insurance. In addition to claims administration, benefit coupons, and insurance against catastrophic illness, insurers are required to include, as part of their insurance plans, an option for the insured to purchase insurance at a later date at a (strike) price that does not take into account the individual's health history subsequent to acquisition of the option. It would be interesting to see how this option would be priced if it were unbundled from the rest of the health care plan.

If I buy healthcare insurance while I am in good health, and then have a heart attack, I feel betrayed if my insurance premiums rise precipitously the subsequent year. Thus I expect my yearly insurance premium to pay both for protection against any catastrophic illness in the policy year and for an option to purchase insurance in subsequent years at rates set for healthy adults of my age. If this option feature of insurance were made explicit, more carefully defined, and separated from the rest of the policy, people could decide exactly what such an option is worth. Insurers might then offer `points' on insurance like bankers do on mortgages. Paying a certain number of points in advance, one can lower the nominal interest rate on a mortgage. Insurers could sell points that allowed one to buy insurance at rates set for lower risk individuals. What purpose could such points serve since insurers would have no incentive to sell points at a lower cost than the difference between the premiums for the buyer's actual risk level and the desired lower risk level? Points introduce the possibility that an entity other than the insurer could sell the option contracts. Options would essentially become options to purchase points. Assuming competition kept point costs fairly uniform, sellers could offer `universal' options which could be exercised at many large insurers. An immediate benefit of such an unbundled system would be increased portability of insurance. If an employer's insurance plan provided an explicit option, then a high risk employee who wished to leave his job need not worry about a subsequent dramatic increase in insurance costs. He would simply exercise his option at his new place of employment (or in the less efficient individual insurance market).

Unbundling of options might lower their cost. If you wish to purchase an option today which cannot be exercised for ten years, then the seller of the option will factor in ten years of returns on investing the option premium when pricing the option. (Of course you must also consider your loss of use of the funds for ten years in valuing the purchase.) In buying insurance, we know we should rationally only purchase insurance for catastrophic events unless our insurance is subsidized. If you can afford to pay 2 years of the higher insurance premium charged to high risk individuals, perhaps you would only wish to purchase options which cannot be exercised until three years after the date of purchase, decreasing their cost further.

None of the potential savings consequent to the decoupling of options from insurance plans is large enough to offset the price inflation associated with third party payment of basic medical services, but the concept introduces numerous ways to decrease cost and increase flexibility.

Sunday, December 5, 2010

Leroux and Global Warming

For a change of pace I have added Marcel Leroux's Global Warming - Myth Or Reality? to my bedtime reading. I don't recall why I chose this particular climate book from the shelf, but it is published by Springer, a publishing house respected by most mathematicians. In general it is difficult for an outsider to establish the reliability of a putative expert in a distant field. In fields in which I have some expertise, I frequently see the media promote extremely marginal scientists as expert spokesmen. Given the extent to which climatology appears to foster charlatanism, I am wary of all authors in the field.

I was especially eager to read Leroux's treatment of climate modelling. I have already written on why mathematicians are wary of the computer simulations responsible for the alarmist gloom and doom scenarios which lead so many people to advocate wrecking the world economy, abandoning democracy if necessary, in order to limit CO_2 output. My post on this subject dealt only with those universal features of the simulations that one could address without delving into the details of the models. I hope Leroux will shed more light on the nuts and bolts of the models.

Leroux's treatment of models (Chapter 7 of his book) is tinged with an antipathy to models qua models, which I consider misplaced. My objections are simply to the abuse of models. Leroux does provide us with more information about the models and their defects, although I assume that details such as grid sizes change monthly or yearly. I will rephrase and repackage Leroux's more coherent criticisms into a more mathematical framework.

Computer simulations of climate phenomena require dividing the atmosphere into a collection of volumes known as cells and assigning numerical data to each cell representing 'average' climate data for that cell for some time interval. At the time Leroux was writing, typical cell size ranged from hundreds to tens of thousands of cubic kilometers. He does not mention the typical time interval involved. Obviously, the smaller the cell and time step, the more reasonable is approximation of the climate within by some average. Ever increasing computer power is the only inherent limit on the number and therefore the size of the cells. Ideally, we would like to start with some initial approximate climate state, and compute the approximate evolution of the system by numerically approximating the solutions to the complex nonlinear fluid dynamics and other equations governing the system. Any phenomena which take place at smaller time or space scales than the time intervals or cells of our simulation cannot be modelled. Of course one can model such phenomena with a simulation adapted to the given phenomenon. Thus one could not use a simulation designed to model a century of global climate evolution to model the path of a hurricane. Instead, one uses a model adapted to the time and space scale of the hurricane, and corrects the simulation with new information several times a day.

In addition to errors arising from cell size and absence of real world initial data, climate evolution includes too many interactions to include in a realistic deterministic model. For example, the quantity of the main greenhouse gas, water vapor, depends on temperature, pressure, particulate matter, surface water, plant respiration, etc. These do not all admit simple modelling with numerical partial differential equations. Those features which are too complex for current deterministic models are ignored (the most honest path) or added into simulations by ad hoc mechanisms. These latter admit fine tuning to reach any desired conclusion.

Another source of error in simulations is the fact that the earth is not a closed system. Time varying solar radiation is the fundamental driver of our climate, but I am unaware of the existence of climate models that include realistic simulations of the complex dynamics of the sun's nuclear reactions.

Leroux appears to be bothered by the deterministic attitude of the climate modellers, a concern which I do not share. It seems reasonable to me that the extremely complex large scale dynamics of our climate stem result from small scale fundamental physical and chemical processes. Nonetheless, it is clear that since current climate models that are adapted to short time predictions are only crudely accurate for a few days, long term predictions have no value.

The more of Leroux I read, the less reliable he appears. His logic is generally quite poor. He frequently points out some weakness in the arguments of proponents of anthropogenic global warming, and then immediately concludes that CO_2 does not cause global warming, when, in fact, he has only countered an argument in support not actually presented an argument against. He also has a worrisome single factor explanation for most features of our climate. All phenomena of interest can be explained (according to Leroux) by his contribution to climatology: mobile polar highs. I have checked out a few books on atmospheric physics to make myself somewhat better able to analyze his claims. From my currently inexpert position, many of his assertions seem to be the atmospheric equivalent to the assertion that water runs down a mountain into a valley because the mountain is higher than the valley, and not because the valley is lower than the mountain. Such a distinction makes no sense to me; so, I need to learn more. Fortunately climate books are much lighter reading than math books, and hence can be read before bed without stimulating the brain enough to interfere with sleep.