IDENTIFICATION OF PAIRED NONSEPARABLE MEASUREMENT ERROR MODELS

Abstract

This paper studies the paired nonseparable measurement error models, where two measurements, X and Y, are produced by mutually independent unobservables, U, V, and W, through the system, X = g(U,V) and Y = h(U,W). We propose restrictions to identify the marginal distribution of the common component U and the conditional distributions of X and Y given U. Applying this method to twin panel data, we find the following robust reporting patterns for years of education: (1) self reports are accurate only when the true years of education are 16 or 18, typically corresponding to advanced university degrees in the US education system; (2) sibling reports are accurate whenever the true years of education are 12, 14, 16, and 18, which are typical diploma years.