Root-N-Consistent Semiparametric Regression

One type of semiparametric regression is b8X A u(Z), where b and u(Z) are an unknown slope coefficient vector and function. Estimates of b based on incorrect parametrization of u are generally inconsist ent, whereas consistent nonparametric estimates converge slowly. An e stimate, bC, is constructed by inserting nonpar-ametric regression es timates in the nonlinear orthogonal projection on Z. Under regularity conditions bC is shown to be N1/2-consistent for b and asymptoticall y normal, and a consistent estimate of its limiting covariance matrix is given. The author discusses the identification problem and bC's e fficiency. Extensions to other econometric models are described.