Governments and Power Law Distributions

Popular Mechanics has a cover article on debunking Katrina myths, which includes under the heading of Government Subsidies Encourage Bad Planning the following information:

The National Flood Insurance Program (NFIP), administered by FEMA, was started in 1968 for homeowners who live in flood-prone areas considered too great a risk by private insurers. And for more than 30 years, the program was self-supporting. But studies by Conrad's NWF team revealed a disturbing fact: Just 1 to 2 percent of claims were from "repetitive-loss properties" - those suffering damage at least twice in a 10-year period. Yet, those 112,000 properties generated a remarkable 40 percent of the losses - $5.6 billion. One homeowner in Houston filed 16 claims in 18 years, receiving payments totaling $806,000 for a building valued at $114,000.

Just as significantly, the five Gulf Coast states accounted for half the total of repetitive-loss costs nationwide. Taxpayers across the country are paying for a minute number of people to rebuild time and time again in the path of hurricanes.

That is proving to be an expensive habit. Following Katrina, Rita and Wilma in 2005, claims could exceed $22 billion - more than the total amount paid in premiums in the program's 38-year history. In mid-November, the NFIP ran out of money; to pay claims, Congress will have to authorize FEMA to borrow more money.

Readers may recall the Malcolm Gladwell piece on power-law distributions I posted earlier, of which this is a classic example. There are actually two different hockey-stick distributions described here: flood claims by property and flood claims by storm.

It's worth noting that, like flood insurance, both of the programs Gladwell was talking about were government-run or imposed - the requirement that emergency rooms treat anyone, and state smog certification. The former is abused by the chronically homeless who rack of hundreds of thousands of dollars in emergency room costs a year, the latter by rolling smokestacks that emit hundreds of times as much crud as the average car, yet can manage to pass the occasional smog check. In all of these cases, systems that work pretty well most of the time fail miserably for extreme cases that weren't in their design plan. In other words, power-law distributions amply the failures of the one-size-fits-most solutions generated by democracy.

Perhaps such distributions are one of the mechanisms by which governments waste money. Bureaucrats design a program which is reasonable most of the time for most people, but fails to take into account the exceptions which break the bank. A private company would see their mistaken assumptions reflected in their bottom line, identify the problem, and change their tactic. But when our money is being spent, there is no bank to break, so we pay again and again for houses built on shifting sands.

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Didn't John Stossel do

Didn't John Stossel do something on the flood insurance for people who build houses in stupid places?

I've always wondered if a

I've always wondered if a similar analysis applies to the FDIC & FSLIC. Small scale bank failures, and even the "S&L crisis", can be born by averaging out the costs over everyone else. But a serious meltdown in the banking industry could not be covered and the government would face an economically crippling burden to raise taxes to cover all of the liability. That could be worse than simply letting people lose their bank deposits (and obviously the current system doesn't reward people for seeking more secure assets). I suppose a banking crisis is no longer a high risk in the way a natural disaster is, but even so a changed regulatory environment could encourage risky loans like the moral hazard that created the S&L crisis.

I don't think private

I don't think private corporations are any better at adjusting to the extreme events than governments are. In fact, I don't think humans do very well with estimating either the true frequency of such catastrophic but rare events, or the true cost of not being prepared for them when they do happen. By our nature, humans have a difficult time planning for the future (just ask any economist why people don't put more money into their savings, even when they know they should).

I do agree that the decentralized process of a democratic government (and, I claim, the decentralized process of a free market) often leads to solutions that work well for the average case - after all, for a politician (or businessman) it's usually a safe assumption that whatever distribution they are dealing with is typically strongly peaked, i.e., the average case is representative of the entire distribution. But, naturally, when the distribution is heavily skewed, i.e., when the average is not representative of the entire distribution, as is the case with a power-law distribution (I truly loathe the term "hockey-stick" to describe it; when people use that term, they're actually meaning a bimodal distribution, but a power law is quite different). For these, I suspect that people (politicians and businessmen) simply write-off the extremal events as being "outliers" or "exceptions" and cling to their previous assumptions.

Oops... forgot to finish a

Oops... forgot to finish a thought up there. It should have read something like this:

But, naturally, when the distribution is heavily skewed, i.e., when the average is not representative of the entire distribution, as is the case with a power law (I truly loathe the term “hockey-stick” to describe it; when people use that term, they’re actually meaning a bimodal distribution, but a power law is quite different), I'm not sure that these decentralized processes are capable of planning appropriately. The most catastrophic events are typically the ones with the longest lag-time between them, and people forget very easily that these things happen with a certain statistical regularity (indeed, the regularity is surprisingly robust for disasters of all kinds, eg., the "big" floods, earthquakes, forest fires, wars and terrorist attacks). When there's pressure to always reduce expenses or otherwise improve the bottom line, money being devoted for long-term planning, whether by a government or by a business, which isn't obviously returning any benefit in the near-term, is one of the first casualties.