Econometrica: Jan 1998, Volume 66, Issue 1

Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors

https://doi.org/0012-9682(199801)66:1<105:SLVMEW>2.0.CO;2-E
p. 105-121

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.

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