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.

In this paper we analyze the estimation of coefficients in regression models under moment restrictions in which the moment restrictions are derived from auxiliary data. The moment restrictions yield weights for each observation that can subsequently be used in weighted regression analysis. We discuss the interpretation of these weights under two assumptions: that the target population (from which the moments are constructed) and the sampled population (from which the sample is drawn) are the same, and that these populations differ. We present an application based on omitted ability bias in estimation of wage regressions. The National Longitudinal Survey Young Men's Cohort (NLS)—in addition to containing information for each observation on wages, education, and experience—records data on two test scores that may be considered proxies for ability. The NLS is a small dataset, however, with a high attrition rate. We investigate how to mitigate these problems in the NLS by forming moments from the joint distribution of education, experience, and log wages in the 1% sample of the 1980 U.S. Census and using these moments to construct weights for weighted regression analysis of the NLS. We analyze the impacts of our weighted regression techniques on the estimated coefficients and standard errors of returns to education and experience in the NLS controlling for ability, with and without the assumption that the NLS and the Census samples are random samples from the same population.