Three-stage least-squares estimation for a system of simultaneous, nonlinear, implicit equations

The article describes a nonlinear three-stage least-squares estimator for the parameters of a system of simultaneous, nonlinear, implicit equations; the method allows the estimation of these parameters subject to nonlinear parametric restrictions across equations. The estimator is shown to be strongly consistent, asymptotically normally distributed, and more efficient than the nonlinear two-stage least-squares estimator. Some practical implications of the regularity conditions used to obtain these results are discussed from the point of view of one whose interest is in applications, Also, computing methods using readily available nonlinear regression programs are described.