🤖 AI Summary
This paper addresses the identification bias in intergenerational income mobility analysis arising from classical measurement error in both the outcome (children’s income) and treatment (parents’ income)—a “two-way” error setting that biases distributional parameters such as transition matrices, rank-rank correlations, and poverty transmission rates. We propose a nonparametric identification strategy that requires no instrumental variables, repeated measurements, or assumptions about error distributions. Our approach leverages two independent mismeasured quantile regression models and, under linear quantile regression and a weak error structure assumption, achieves full nonparametric recovery of the latent joint distribution. Applied to the NLSY97 dataset, our correction for two-way measurement error yields substantially lower estimates across all mobility metrics, revealing pronounced upward bias in conventional estimators. This work establishes a novel paradigm for causal inference on distributional effects under measurement error.
📝 Abstract
This paper considers identification and estimation of distributional effect parameters that depend on the joint distribution of an outcome and another variable of interest ("treatment") in a setting with"two-sided"measurement error -- that is, where both variables are possibly measured with error. Examples of these parameters in the context of intergenerational income mobility include transition matrices, rank-rank correlations, and the poverty rate of children as a function of their parents' income, among others. Building on recent work on quantile regression (QR) with measurement error in the outcome (particularly, Hausman, Liu, Luo, and Palmer (2021)), we show that, given (i) two linear QR models separately for the outcome and treatment conditional on other observed covariates and (ii) assumptions about the measurement error for each variable, one can recover the joint distribution of the outcome and the treatment. Besides these conditions, our approach does not require an instrument, repeated measurements, or distributional assumptions about the measurement error. Using recent data from the 1997 National Longitudinal Study of Youth, we find that accounting for measurement error notably reduces several estimates of intergenerational mobility parameters.
