# Econometrica

## Journal Of The Econometric Society

### An International Society for the Advancement of Economic Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Jan, 1998, Volume 66, Issue 1

# Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors

Arthur Lewbel

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.