Fannie Mae and Freddie Mac Regulation

Charles Calomiris has a WSJ op-ed (with someone else) on Fannie Mae and Freddie Mac's role in the subprime mortgage market and the Republicans' attempt to stop them. The Democrats are squarely to blame, it seems. The op-ed also points out that deregulation has played no role in this crisis. The problem on Wall Street is that we've never regulated investment banks' capital levels, not that we've deregulated them, and that financial innovations have created a need for regulation.

Power Law-- A New Gabaix Paper

Xavier Gabaix has a new paper, "Power Laws in Economics and Finance" that surveys research on when and why variables such as city size or executive pay follow the power law distribution. One gets a power law distribution if a city's relative population (its population relative to the average city) grows proportionally to its relative population except for a small absolute increase that gives small cities a bit of an advantage. Even writing that first step is tricky, alas, and I don't think I'll be able to understand well enough to do research in the area. The reason the power law is useful seems to be that when it applies, the same laws are at work for big values and little values of variables, so, for example, one wouldn't need a special theory of stock price plunges-- it would just be a chance occurrence from the same distribution as small price declines.

Longer Sale Times in Depressed Housing Markets

Why should it take longer to sell a house in a depressed market? The answer may seem obvious-- nobody wants to buy-- but it is not. If the price fell enough, somebody would buy. The question is why the weak market is reflected in both lower prices and longer waiting times, rather than just lower prices.

I think there is a 1995 Jeremy Stein article on this where he thinks about the financing of housebuying. Christopher Mayer has some papers too. But I wonder whether the answer may not lie in transaction costs.

Suppose too many houses have been built by mistake. It will take a few years before population growth catches up. We can forecast the house price will recover by that date. We could sell now, though, and somebody now renting could live in the house until demand recovered. If transaction costs were zero, that is what would happen. The person would buy the house, live in it cheaply until demand recovered, and then move out when a house that size became expensive again. But if there is a fixed cost to moving in and out (or to arranging sale or rental) then that won't happen.

This seems too obvious an explanation, but I haven't heard it mentioned. It could be modelled by assuming that there are big houses and little houses, with two types of people who prefer each at their construction cost. Everyone prefers a big house, but poor people would prefer a small house if they must pay the cost of building a house. Population grows steadily, but then there is a shock and not enough rich people enter in one year. If there is no transaction cost, then some poor people move into big houses, and some small houses stay empty. If there is a big enough transaction cost, big house prices fall somewhat, but no poor people move into big houses. The best model might have a distribution of moving costs across people, so that there would be some poor people moving into big houses, but some big houses staying empty. Note that the price of small houses would fall too, because of poor people's demand for them falling as some move into big houses.

Semi-elasticities in Regressions

Suppose you have a log-linear regression like this:

log(y) = beta*x

The way to interpret beta is as the percentage change in y that we get from a 1 unit change in x. To see that note that the regression equatino is the same as y = exp(beta*x), in which case dy/dx = beta*exp(beta*x). Thus, the percentage change in y when x changes is (dy/dx)/y = (beta*exp(beta*x))/exp(beta*x) = beta.

This contrasts with the log-log form, log(y) = beta*log(x), in which case beta is the elasticity of y with respect to x, i.e., the percentage change in y that we get from a 1 percent change in x.