Moment Conditions for the Quadratic Regression Model With Measurement Error

Abstract

We propose a new identification strategy for the quadratic regression model with classical measurement error, based on higher-order moment conditions. Our novel approach contributes to the literature in two ways: by not requiring any side information (such as a known measurement-error variance, replicate measurements, or instrumental variables) and by straightforwardly allowing for one or more error-free control variables. We derive the asymptotic properties of the proposed method-of-moments estimator and illustrate its finite-sample properties by means of a simulation study and an empirical application to existing data from the literature. The simulation study shows that the method-of-moments estimator outperforms the OLS estimator, even if certain assumptions are violated. The method-of-moments estimator also performs well relative to a more general semi-parametric estimator.