The Driven Snow

December 30, 2010

New York City received a lot of snowfall several days ago, greatly disrupting transportation within, into, and out of the city.  Having lived through several blizzards and Nor’easters, and even one epic blackout, I’m generally pleased and impressed by how effectively the city is able to cope with nature’s inconveniences.  Emergency personnel seem to clear streets and manage dangerous intersections pretty promptly, and ‘ordinary’ New Yorkers tend to show their better natures by helping taxis un-stick themselves from snow drifts, among other small acts of generosity.

The general consensus about this week’s blizzard, however, is that the city’s response was woefully inadequate.  Streets were too slow to be cleared, if they were cleared at all.  Subway and bus lines were disrupted to an unacceptable degree.  Critical services, such as emergency medical care, were strained beyond their contingency plans.  It certainly did not help that the ‘snowpocalypse’ arrived right after Christmas, when it’s difficult to accomplish anything on even a perfect day.  But, even so, there seem to have been some failures in judgment and execution that are worth reviewing and learning from. One ought to ask questions like: How could we have made a better decision with the information we had available?  Should we have had additional information and, if so, can we reliably obtain it in the future?  Did we experience poor execution because of known weaknesses (e.g., we have had to cut staff) or unknown weaknesses (e.g., hypothetically, we discover in hindsight that our weather forecasting models are really accurate and precise at estimating snowfall between 1″ and 3″, but not between 6″ and 18″, which obscured our understanding of the likely severity)?

I tend to think that firing visible (and potentially otherwise-highly-competent) people is the obvious political answer but not obviously the best answer.  It is also easy to take the position that “they should have done something” and propose a set of measures that perhaps could have mitigated the current problem but would not necessarily make good standing policy; the common and not-unfair criticism in finance is that regulators are always preventing the last crisis (or generals fighting the last war, or politicians winning the last election, etc.)

A more interesting set of questions, in my view, concerns how we prepare for and respond to ‘tail risks’ in a world of constraints.  In this instance, I’ll focus on tail risks whose nature and magnitude can be predicted with some reasonable confidence – e.g., we know that in a given winter, there’s about an x-y% of getting more than 12″ of snowfall in a single day.  One question to ask in such cases is whether these phenomena are analogous to insurance problems.

Insurance emerges in response to phenomena of reasonably predictable frequency and severity.  One can self-insure against such phenomena (i.e., do nothing, or perhaps set aside some ‘reserves’ via savings) or one can pay a premium to the expected cost of the occurrence in order to reduce volatility (assuming the insurance is well priced, although I don’t think that assumption matters for what follows).  If I told you that your flat-screen television, which just cost you $1000, has an 0.1% chance of having a fatal flaw that will render it inoperable and worthless (and happens not to be covered by a manufacturer’s warranty or retailer’s return policy… bear with me here) you might consider that your expected cost from the design flaw is $1 (for this simple example, the probability of incurring the loss multiplied by the severity of the loss given that it has occurred).  If someone offered a warranty against this flaw for any price less than $1, you’d be a fool not to take it.  More likely, it would perhaps cost you $3 for such a warranty, so that the insurance company would expect to earn a profit over a large enough sample of identical and independent risks.  Depending on your tolerance for volatility, among other considerations, you may be willing to ‘lose’ $3 in the 99.9% of scenarios where the flaw does not materialize in order to be protected from losing the full $1000 in that unfortunate tail event.  There is clearly some price at which the divergence between the expected cost to the insured, and the actual price of the insurance, becomes too great to justify buying the insurance.  You wouldn’t be able to judge the wisdom of an insurance purchase on the basis of the outcome; it does not become a good decision to have spent $100 on it just because your television breaks.

When one criticizes the city for not having had enough personnel or machinery to plow the streets promptly, was this an example of a self-insurance bet that didn’t work out?  Clearly it costs something to have those resources on a permanent basis.  It may also be that, in most scenarios, those incremental resources don’t add sufficient value relative to other competing demands for dollars across the city (or, for a purist, relative to however one conceives of the ‘cost of capital’ for the city).  Let’s call the cost of those resources our insurance premium; we could debate how to calculate that cost but we’ll save that for another time.

Certainly our ‘insurance resources’ would have mitigated some of the downside of the snowpocalypse scenario.  There are local examples where it’s easy to quantify the economic impact of the blizzard (e.g., the person who couldn’t get to work) but it’s difficult to imagine that one would have even the right order of magnitude on an attempt to aggregate these and their interactions into some sense of the impact on the city (though some brave souls in need of a citation will try).  It’s even harder to attempt a serious analysis of the marginal impact of, say, plowing the streets 10% more efficiently, or whatever would have been the operational consequences of having our insurance resources at the ready.  A lot of good this conceptual framework is, then.

But we could, for example, ask ourselves what we would need to believe about their marginal impact in order to think the insurance premium was worth paying.  We should have a pretty good basis for predicting the likelihood of one, two, three, etc. blizzards in any given calendar year.  (Assume for now a binary world of blizzards and not-blizzards; it’s conceptually easy to introduce gradations of storm severity.)  We should also have a good estimate of the cost of our insurance premium: some number of fully-loaded workers, some number of machines and their maintenance, some number of managers and technicians, etc.  If hypothetically we estimate our insurance premium cost is $5 million annually, and the risk of a blizzard is 0.5% annually, we should feel pretty comfortable with that cost if we think we’d save the city from about $1 billion or more in damages in the event of a blizzard.

Imagine if instead of hiring $5 million worth of insurance resources, the city bought an insurance policy that paid out $1 billion to NYC in any year where there was a blizzard.  That type of risk could probably be priced pretty efficiently by a major insurance company and its reinsurers; say, a Berkshire Hathaway.  The cost of that insurance relative to the cost of our insurance resources seems like a meaningful indicator about the efficiency of retaining those resources.

Ah, but the “damage” to NYC isn’t borne entirely by the city treasury; non-salaried laborers and retail establishments, to name a few examples, suffer directly as well.  Let’s say there are 8.5 million people in NYC.  What if the city bought an insurance policy that paid about $117 to every man, woman, and child in NYC (about $1 billion in total) in any year where there was a blizzard – call it compensation for lost wages, or for strain from shoveling, or from general inconvenience.  What if we levied a $0.59 blizzard preparedness tax on every man, woman, and child in NYC to finance the purchase of that insurance policy (assuming it cost the same $5 million as our insurance resources)?  Obviously all these numbers are made up, but perhaps there are some levels where we’d frankly rather have a cash rebate than incrementally quicker-plowed streets?

In any event, I hope that some lessons are learned from this blizzard and that the response is not a reflexive addition of capacity to clear the last snowstorm.


Creation Myths

December 30, 2010

Like many an amateur’s foray into the Collective Discourse, this blog begins with some navel-gazing about writing.

My Virtuous Self (the one who eschews carbs and studies Mandarin in his spare time) has long argued that I’d be happier if I devoted more time to writing.  Being a clever homonculus, he has anticipated a variety of my objections.  If I publish in the blogo-forest and nobody reads it, I suppose I’m still enriched by the exercise.  The entire Twitterverse (excepting the brilliant Andy Borowitz) consists of billions of characters unconstrained by the criterion of materiality to human progress.  And, most damningly, if I can find the time to peruse a Gossip Girl recap, surely I can commit some thoughts to virtual paper on a semi-regular basis?  So, the experiment begins.

Perhaps my greatest fear in beginning this exercise is that it will reveal an inconvenient truth that I’ve begun to suspect: namely, that my writing is a lot crappier than it was in college.  Yes, eye of the beholder and all that; but should I not have at least some concern that years of exposure to dry business prose, on the one hand, and the (shallow?) concision encouraged by our text-message culture, on the other, have conspired to ruin my capacity for coherent and engaging exposition?  (Perhaps this is the Y-chromosome talking: if I don’t go the doctor, I can’t be sick, right?)

Ah, but the beauty of submitting to diagnosis in the public sphere is that shame is a powerful prescription.  One of my favorite courses was a writing tutorial called “Daily Themes,” which featured (wait for it…) daily prompts that pushed us to explore specific elements of style and technique.  (One favorite: write the same paragraph twice, one version using Germanic words, the other Latinate.)  The class was always over-subscribed and preference was given to those majoring in English or some other humanities discipline.  (Imagine: an English professor implying my degree was useless!).  The rest of us had to submit a writing sample to weed out the most hopeless cases (consolation prize: you could always join the school newspaper for the thrill of daily deadlines and withering criticism!).  I obsessed about finding the right vignette to show my exceptional emotional range and (in terms I didn’t have at the time) deep grasp of sensory-affective detail, finally finding a sure-fire winner…

As we settled in for the lecture after which our fates would be announced, the professor used the exercise to share some general wisdom even for those of us who were about to be rejected.  One of the few grave offenses in writing, she warned, was to be trite.  “If you could only imagine how many privileged undergraduates write stories about experiencing a moment of shared humanity with a homeless person!”


I was wait-listed for the course, but apparently the prospect of, yes, daily homework that could not be procrastinated was too much to bear for some, and my persistence in attending class paid off.  I look back with pride on what I went on to produce that semester and continue to challenge myself to be richer, finer, sharper.

I’m honored to have your company.