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This paper considers identification and estimation of distributional effectparameters that depend on the joint distribution of an outcome and anothervariable of interest ("treatment") in a setting with "two-sided" measurementerror -- that is, where both variables are possibly measured with error.Examples of these parameters in the context of intergenerational incomemobility include transition matrices, rank-rank correlations, and the povertyrate of children as a function of their parents' income, among others. Buildingon recent work on quantile regression (QR) with measurement error in theoutcome (particularly, Hausman, Liu, Luo, and Palmer (2021)), we show that,given (i) two linear QR models separately for the outcome and treatmentconditional on other observed covariates and (ii) assumptions about themeasurement error for each variable, one can recover the joint distribution ofthe outcome and the treatment. Besides these conditions, our approach does notrequire an instrument, repeated measurements, or distributional assumptionsabout the measurement error. Using recent data from the 1997 NationalLongitudinal Study of Youth, we find that accounting for measurement errornotably reduces several estimates of intergenerational mobility parameters.

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