Nonlinear Approaches to Intergenerational Income Mobility allowing for Measurement Error.

This paper considers nonlinear measures of intergenerational income mobility such as (i) the effect of parents' permanent income on the entire distribution of their child's permanent income, (ii) transition matrices, and (iii) rank-rank correlations, among others. A central issue in the literature on intergenerational income mobility is that the researcher typically observes annual income rather than permanent income. Following the existing literature, we treat annual income as a measured-with-error version of permanent income. Studying these types of distributional effects, which are inherently nonlinear, while simultaneously allowing for measurement error requires developing new methods. In particular, we develop a new approach to studying distributional effects with "two-sided" measurement error -- that is, measurement error in both an outcome and treatment variable in a general nonlinear model. Our idea is to impose restrictions on the reduced forms for the outcome and the treatment separately, and then to show that these restrictions imply that the joint distribution of the outcome and the treatment is identified, and, hence, any parameter that depends on this joint distribution is identified -- this includes essentially all parameters of interest in the intergenerational mobility literature. Importantly, we do not require an instrument or repeated observations to obtain identification. These results are new, and this part of the paper provides an independent contribution to the literature on nonlinear models with measurement error. We use our approach to study intergenerational mobility using recent data from the 1997 National Longitudinal Study of Youth. Accounting for measurement error notably reduces various estimates of intergenerational mobility relative to estimates coming directly from the observed data that ignore measurement error.