Economics and similar, for the sleep-deprived

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Monday, March 24, 2003

Insuring the uninsurable

Bit of an unplanned hiatus there, as I find myself quite literally too exhausted to write anything for a week ... sorry.
Historical note: this excuse was true when I wrote it; then my broadband crash intervened and since then I haven't got round to posting this. etc etc.

Anyway, I'm sorry to inflict another rambling go-nowhere post on my long-suffering readers (recent arrivals: suck it in), but before we get going on the application of the principles of insurance to a few important economic topics, I think I need to set out a couple more concepts. Don't worry, we'll be having fun with these soon.

The general topic of these notes is that of how the world deals with uninsurable risks, the point being that risks don't go away just because they're large, non-accidental or actuarially ill-behaved.

(By the way, at this point, I'd like to correct what looks like a mistake in the post below, which was pointed out to me in comments. I've been using the term "nonergodic" in lots of previous posts to describe certain properties of economic systems which operate on the basis of positive feedback, and which for that reason don't have the property of having well-defined expectations. Because this topic has been on my mind while I've been working through Paul Davidson's excellent book "Money, Financial Markets and the Real World", I've been overusing it somewhat. Specifically, I seem to have misused it below in a way which implies that nonergodicity of the underlying system is one of the most important ways in which a phenomenon can be actuarially ill-behaved. This is not really right; in general, the problem with actuarially ill-behaved processes is that the underlying risk factor is non-stationary. Non-stationary processes are by definition nonergodic in a fairly weak technical sense, but they can often be modelled (to take a simple example, by conditioning on a linear time trend) in a way which leaves residuals which follow an ergodic process. The problem with respect to actuarially ill-behaved series is usually that the non-stationarity of the underlying process is quite important and the risk event is uncommon, meaning that the sampling distribution of risk events doesn't converge on the underlying process anything like quick enough to build a model you can have any confidence in; in other words, it's a problem of sampling theory which could in principle be solved by having an infinitely large risk pool, rather than a problem of "deep" nonergodicity, under which there is no model at all under which the sampling space represents the underlying process.)

But anyway, there are a lot of uninsurable risks out there, and we need to live with them. The following methods are all ways of making financial sense of an uncertain future ("making financial sense of an uncertain future" is the motto of the UK's Faculty and Institute of Actuaries, if you care), and they are in general important because they tell us a bit about the different ways in which economic agents behave when faced with what Frank Knight called "uncertainty" as opposed to "risk" (the distinction here being that "risk" is what you face if your economic welfare depends on a random variable for which your expectation has a well-defined probability measure and "uncertainty" being the case in which you just generally don't know what�s going to happen -- a distinction which might have been made in terms of ergodic and nonergodic systems if the history of probability had been a bit different). As a result, given that the official editorial position of D2D is that the economic world is full of actuarially ill-behaved (because nonergodic) processes, the concepts that we find in close observation of the disreputable end of the insurance industry probably have a lot to do with a lot of otherwise inexplicable human behaviour in everyday economic life. On with the show ... I've italicized and/or bolded most of the terms of art, but not in any particularly systematic way.

The first way in which the world deals with uninsurable risks is to use insurance. Sounds paradoxical but isn't really. Basically, there are two ways in which insurance companies cover uninsurable risks. In the first place they are often prepared to write speculative insurance (remember that in the post below we remarked that speculative risks were uninsurable), either because they can hedge that speculative risk by dealing in an open market (oh God, I fear that I will have to write yet a third "concepts" post on the difference between insurance and hedging before we can go on to bloody anything interesting.). The basic idea here is that if you're a big and well-capitalised insurance company, you can take a gamble on something that's more or less uninsurable, but if you think that the actual risk of paying out is small, you'll probably make money. Thus, insurance against alien abduction, etc, which isn't based on sound actuarial principles, but which is just basically a fancy form of bookmaking (note that when you see a bookmaker offering an outrageous bet on whether Elvis will be found alive, etc, they will usually be laying the risk off with an insurance company. On a related note, if your firm wants to spice up your annual golf tournament by offering a $1,000,000 prize for anyone scoring a hole-in-one, these guys will do you insurance against someone scoring it, and given the number of such tournaments held in the world, this risk is surprisingly diversified and actuarially well-behaved).

The other way in which insurance companies write insurance on uninsurable risks is by accident. This happens all the time and there's nothing much that anyone can do about it. All manner of risks which look on the face of them to be decent insurance propositions can turn out on deeper analysis to be large (like asbestos), or not really accidental (like medical negligence) or actuarially ill-behaved (like insurance against terrorist attack), and mistakes are bound to be made by overworked actuary's departments when under pressure from hard-charging underwriters. It's also possible to write a lot more insurance on a particular risk factor than you believe yourself to be writing if you happen to have mispriced a given category of insurance, something which also happens all the time, but which probably deserves a section of its own in a future post.

Any road up, if you can't get an insurance company to take on your risk at what you consider to be a reasonable rate of premium, you have two choices;
Self-insurance. This is where you set aside an amount of capital roughly equal to what you think your risk will cost to sort out. You then go about your business, taking the investment income on the capital you've set aside and (we shall assume) spending it on sweets, and then one day when the catastrophe occurs, you�ve got the cash set aside to pay for it. Note that setting aside the capital for self-insurance isn't really a cost to you, because the investment is still yours and you get the income from it despite the fact that the assets are also being used to support the insurance of risks (this "double-gearing" was one of the attractions of being a Lloyd's name, back in the day, which gives you a clue that there is some economic sense in which there is a cost after all). But in order to self-insure, you've got to have the capital lying around in the bank. Which is why under Marxist economics, insurance premium is not a cost of doing business; it's part of the return on "surplus-value" in the same way in which coupon payments to a rentier are, and for this reason, insurance premiums weren't a tax-deductible expense in Russia for a long time. But I digress. The other way of dealing with an uninsurable risk that happens to take up residence in your house is ...

Non-insurance. This is the same as self-insurance, except that you don't put the money aside in a dedicated fund, either because you can't or because you don't want to. When the shit heads fanward, you just suck it in and pay for the clean-up bill out of your current income. This makes sense for small risks, particularly which the insurance industry regards as uninsurable for reasons of moral hazard; for example, unless you have a bizarrely generous motor insurance policy, you yourself are currently following a non-insurance strategy for small bumps and dents, through the excess on your policy. For large uninsurable risks, however, non-insurance shades into ...

Socialisation. I'm using this as a catch-all term for the time-honoured procedure of taking your risk event and chucking it onto an arbitrary group of people who basically don't know anything about it, don't want it, but who have the attractive property of being able to pay for it when you can't. The two most common groups of people to hit up for an uninsured risk event are 1) your creditors (including your employees), through declaring bankruptcy and 2) the government, if you can make a decent political or moral case for not being allowed to actually die or be forced into penury through an unfortunate event.

Anyway, that's my taxonomy and I'm sticking to it. Sorry for the lack of interesting applications of these principles to interesting economic cases, but bear with me ... we're on a journey here. Applications of these categories to such cases as health insurance, unemployment insurance and retirement insurance (which can be analysed as "insurance against living too long for your savings") are for the moment left as exercises for the reader, out of a probably forlorn hope of having the only comments board on the whole internet used for purposes other than calling people bastards for having views on Israel which differ from one's own.

1 comments this item posted by the management 3/24/2003 02:36:00 PM

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