Distributional Effects with Two-Sided Measurement Error: An Application to Intergenerational Income Mobility

TL;DR

This paper develops a method to identify and estimate distributional effects in the presence of two-sided measurement error, applied to intergenerational income mobility, without requiring instruments or repeated measures.

Contribution

It introduces a novel approach using quantile regression models to recover joint distributions under two-sided measurement error without additional distributional assumptions.

Findings

Measurement error significantly affects mobility estimates.

Accounting for measurement error reduces mobility parameter estimates.

Method does not require instruments or repeated measurements.

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.