Wednesday, September 30, 2009

clever people

Robert Shiller has long been a fan of increasing the "completeness" of markets, creating more and more derivatives to require that "the market" be explicit about its beliefs; for example, in his 2000 book Irrational Exuberance, he proposed long-dated S&P dividend futures so as to require a market forecast of future dividends and their growth, after which one could see whether anyone really bought the implications of the levels of stock prices. In principle, there are all kinds of problems of both self-delusion and private information that could be solved by more and more derivatives.

Of course, in the last few years it has become clear that relatively simple derivatives, like MBS tranches (or even credit default swaps), seem to have befuddled people well smarter than the median. It's not that a large number of people who do understand the derivatives is necessarily needed for them to have their benign effect — up to some solvency limits, some people out there can arbitrage really bad mispricings and should keep things grossly in-line. The problem, though, is the amount of damage people seem to be able to do to themselves and then, transitively, to their creditors, or to people whose reputation may be tied up with theirs, that is on some level independent of the good these things do. Mortgage credit derivatives did create a market price for mortgage credit risk, and even did help spread and diversify it, and yet some people got themselves into a lot of trouble taking on too much risk that they didn't understand, and a lot of other people got in trouble.

It's possible the mispriced supersenior mortgage tranches would have been better priced with even more complete markets, but we will never have complete markets (and we wouldn't have the solvency to correct them if we did). I'm a fan of more complete markets in general, but expecting them to solve all of our problems strikes me a bit like some leftist beliefs in government; the problem, we're told, is that our problems haven't been dealt with by sufficiently clever people, and yet neither the government nor the financial markets are populated entirely, or even mostly, by particularly clever people. Mankind is not perfectable, whether by government or by market.

Tuesday, September 29, 2009

monopolies and consumer surplus

In a competitive market, each firm faces an inelastic demand curve; this means that the consumer surplus due to the existence of this firm is zero, so that having profitable firms stay in business and unprofitable ones exit passes a social cost-benefit analysis; the marginal benefit and cost of the firm's being in business are internalized to the firm. In a situation in which the firm has some monopoly power, however, the firm creates consumer surplus; from a social cost-benefit perspective, any profitable company produces net benefits, but so too may a somewhat unprofitable company, insofar as the consumers have fewer good places to turn if the company goes out of business.

Gerrymandering and equal-population districts

On constraining gerrymanderers with convexity requirements (pdf):
a gerrymanderer can always create equal sized convex constituencies that translate a margin of k voters into a margin of at least k constituency wins. Thus even with a small margin a majority party can win all constituencies. Moreover there always exists some population distribution such that all divisions into equal sized convex constituencies translate a margin of k voters into a margin of exactly k constituencies. Thus a convexity constraint can sometimes prevent a gerrymanderer from generating any wins for a minority party.
The current congressional districts in Iowa are a bit wrapped around each other; an initial districting proposal with more "compact" districts was replaced with this one, which had more nearly equal numbers of voters in each district as of the 2000 census. (The numbers in the initial plan were themselves so close that there's simply no way that 10 years of population movements wouldn't expand the variance by a large factor.) As long as we have single-member districts, and political minorities are going to be stuck with a single representative chosen by others in their district, it seems proper to me to favor a bit of homogeneity in each district, and "compactness" may function as a proxy for that. (The "population distribution such that all divisions into equal sized convex constituencies translate a margin of k voters into a margin of exactly k constituencies" is a theoretical curiosity, and is not likely in the world of geographical homophily in which we actually live.)

The absolute equality of district size is something of a misguided fetish. If you drew congressional districts largely at random with only a vague interest in keeping populations within about 50% of each other, I expect that congressional elections would play out similarly to districts that were more punctiliously equalized; if the former were able to be drawn with more homogeneity than the latter, they would leave most people better represented by "their" representative. In actual practice, of course, you would have Democrats drawing more populous Republican districts and vice versa; I think the best argument for keeping Congressional districts approximately the same size is that it places a constraint on gerrymandering. In addition to the homogeneity motive, "compactness" has the virtue of creating an — in some sense random — additional constraint on people who are likely, left to their own devices, to be worse than random. While this paper shows that convexity and equal populations aren't themselves sufficient constraints, I'm still tempted by the intuition that something like convexity, combined with other constraints — probably related to other political lines — would have a salutary effect on protecting us from a self-propagating political class. (That intuition wouldn't have expected the results of this paper, though. If I were precise in my statement, I could well be proved wrong.)