Nonclassical Measurement Error in the Outcome Variable

Abstract: We study a semi-/nonparametric regression model with a general form of nonclassical measurement error in the outcome variable. We show equivalence of this model to a generalized regression model. Our main identifying assumptions are a special regressor type restriction and monotonicity in the nonlinear relationship between the observed and unobserved true outcome. Nonparametric identification is then obtained under a normalization of the unknown link function, which is a natural extension of the classical measurement error case. We propose a novel sieve rank estimator for the regression function and establish its rate of convergence. In Monte Carlo simulations, we find that our estimator corrects for biases induced by nonclassical measurement error and provides numerically stable results. We apply our method to analyze belief formation of stock market expectations with survey data from the German Socio-Economic Panel (SOEP) and find evidence for nonclassical measurement error in subjective belief data.