Date of Award
Doctor of Philosophy (PhD)
Carlos Martins Filho
I propose a multi-stage mixed sieve and kernel estimator for a partially linear regression model in a triangular system of equations. The model consists of D+1 equations; a single partially linear primary equation having a mixture of endogenous and exogenous regressors, as well as D fully nonparametric secondary equations with exogenous regressors. Regressor endogeneity in the primary equation is handled using the control function approach of Newey et al. (1999). The estimator realizes effciency gains by imposing an additive structure on the nonparametric component functions of the primary equation and secondary equations of the system (Yu et al. (2011)). As an added benefit, the additive structure circumvents the curse of dimensionality associated with nonparametric estimators. In particular, I show that the estimator of the parametric component β1 is consistent, square root of n asymptotically normally distributed, and Oracle effcient having an asymptotic covariance matrix equal to one derived from an identical estimation procedure for a model consisting solely of the primary equation where all regressors are exogeneous. Furthermore, I propose a consistent and easy to compute estimator for the asymptotic covariance matrix of the estimator for β1. I subsequently plug my estimator for the parametric component into a two stage estimation procedure for the nonparametric component functions of the primary equation developed in Ozabaci et al. (2014) which results in estimates which are consistent, asymptotically normal, and Oracle efficient in the traditional nonparametric sense.
Penner, Eric Matthew, "An Essay in Semiparametric Structural Estimation" (2017). Economics Graduate Theses & Dissertations. 76.