2-STAGE INSTRUMENTAL VARIABLE ESTIMATORS FOR THE NONLINEAR ERRORS-IN-VARIABLES MODEL

Estimation for the nonlinear functional errors-in-variables model is considered under the assumption that instrumental variables are available. The approximate bias in the ordinary instrumental variable estimator due to the nonlinearity of the relationship is derived. Utilizing the nonlinearity of the relationship, an estimator of the error covariance matrix is introduced. Using the error covariance matrix estimator, two types of two-stage instrumental variable estimators are proposed. The two two-stage estimators do not have the asymptotic bias due to the nonlinearity. A Monte Carlo experiment also shows the superiority of the two-stage estimators over the ordinary estimator. © 1990.