
In this paper we consider estimation of the parameters of a single equation of a simultaneous equations model which is nonlinear both in variables and paarmeters. Such a model has never been analyzed in the literature to the best of our knowledge. Models in which the nonlinearity appears only in variables or only in parameters have been previously considered. For the former case see Kelejian (1971) and other references cited in Goldfeld and Quandt (1972), and for the latter case see, for example, Zellner, Huang and Chau (1965.) We define the nonlinear two-stage least-squares estimator (NL2SLS) for our model and derive its asymptotic distribution. Our estimator reduces to the NL2SLS of Kelejian if the nonlinearity exists only in variables, to the NL2SLS of Zellner and others if the nonlinearity exists only in parameters, and to the usual 2SLS estimator if the regression function is linear both in variables and parameters. We show that the well-known optimality properties of 2SLS extend to NL2SLS in the model that is linear in variables and nonlinear in parameters. The question of whether they extend to NL2SLS in the general nonlinear model is left for further study.
Linear regression; mixed models, Applications of statistics to economics
Linear regression; mixed models, Applications of statistics to economics
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