Tuesday, September 23, 2008
Monday, September 22, 2008
Power Law-- A New Gabaix Paper
Monday, September 15, 2008
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.
Wednesday, September 10, 2008
Semi-elasticities in Regressions
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.