In this short course, we first provide some empirical examples that motivate the usefulness of semi-nonparametric techniques in modelling economic and financial data. We describe popular classes of semi-nonparametric models. We then present penalized sieve extremum (PSE) estimation as a general method for semi-nonparametric models with cross-sectional, panel, time series, or spatial data. The method is especially powerful in estimating difficult ill-posed inverse problems such as semi-nonparametric mixtures or conditional moment restrictions.
We discuss recent advances on inference and large sample properties of the PSE estimators, which include:
(1) consistency and convergence rates of the PSE estimators of the nonparametric part;
(2) limiting distributions of plug-in PSE estimators of functionals that are either regular (i.e., root-n estimable) or irregular (i.e., slower than root-n estimable);
(3) simple criterion-based inference for plug-in PSE estimation of regular or irregular functionals;
(4) root-n asymptotic normality of semiparametric two-step estimators and their consistent variance estimators; and
(5) bootstrap based inference for semi-nonparametric models.
Examples from industrial organization, labor economics, dynamic asset pricing, and nonlinear semi-parametric multivariate financial models are used to illustrate the general results.