Many recent contributions to the econometrics literature have proposed and analyzed "plug-in" semiparametric estimators. Such estimators replace unknown density or regression functions by nonparametric estimators of those functions. While theory states that these nonparametric estimators are "better" because they are able to capture all nuances in the structure of econometric relationships in large samples, this does not assure that they will always produce better answers in either small or moderately sized samples. In particular, since an infinite series expansion must always be truncated, or a finite approximation region chosen for a local average estimator, there is the real possibility that nonparametric estimators can contain systematic biases, because of their construction. In other words, the remainder terms that modern theorists easily show vanish in large samples could actually be large, and systematic in onerous ways. This is a particularly dangerous possibility for econometric results, since such semiparametric estimators could naturally be interpreted as less biased than their more restricted parametric counterparts. The contribution of this project comes from measuring the significance of the biases in these estimators and developing ways of correcting for them. In particular, this research will show how derivatives or elasticities computed from local smoothing estimators display systematic downward bias. As such, measured derivatives from kernel regression and kernel density estimators are too small on average. The project demonstrates how large such bias will typically be, and proves theoretically why such biases arise naturally. Corrections for this bias are studied. This work involves both theoretical development and computer simulation. The project also continues research on average derivative estimation, a particular semiparametric approach. Questions to be addressed include the calculation and implementation of optimal bandwidths for average derivatives, as well as how to measure discrete variable coefficients in index models.
