  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.
