Identification and estimation of polynomial errors-in-variables models

Methods of estimation of regression coefficients are proposed when the regression function includes a polynomial in a 'true' regressor which is measured with error. Two sources of additional information concerning the unobservable regressor are considered: either an additional indicator of the regressor (itself measured with error) or instrumental variables which characterize the systematic variation in the true regressor. In both cases, estimators are constructed by relating moments involving the unobserved variables to moments of observables; these relations lead to recursion formulae for computation of the regression coefficients and nuisance parameters (e.g., moments of the measurement error). Consistency and asymptotic normality of the estimated coefficients is demonstrated, and consistent estimators of the asymptotic covariant matrices are provided.