Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors

A simple root n consistent, asymptotically normal semiparametric estimator of the coefficient vector beta in the latent variable specification y = L (beta'x + e) is constructed. The distribution of e is unknown and may be correlated with x or be conditionally heteroscedastic, e.g., x can contain measurement error. The function L can also be unknown. The identification assumption is that e is uncorrelated with instruments u and that the conditional distribution of e given x and u does not depend on one of the regressors, which has some special properties. Extensions to more general latent variable specifications are provided.