Nonlinear modeling has become popular in applied macroeconomics. Successful attempts include Beaudry and Koop's CDR (current depth of the recession) model of real GNP, and various STAR (smooth transition autoregression) models of industrial production. However, these models have not been directly compared. We compare CDR and STAR models of U.S. real GNP and industrial production. We find (i) within sample, the CDR model fits slightly better than the STAR model; (ii) out of sample, the CDR model forecasts better than the STAR model; and (iii) the CDR model generates very different dynamics than the STAR model.

Numerous articles have investigated the distribution of share prices, and find that the returns are fat tailed. Nevertheless, there is still controversy about the amount of probability mass in the tails, and hence about the most appropriate distribution to use in modeling returns. This controversy has proven hard to resolve, as the alternatives are non-nested. We employ extreme value theory, focusing exclusively on the larger observations in order to assess the tail shape within a unified framework. We find that at least the first two moments exist. This enables one to generate robust probabilities on large returns, which put the recent stock market swings into historical perspective.