10 - Retrospect and Prospect

Summary

Nonparametric (NP) and semiparametric (SP) methods potentially offer a very high return to applied researchers, owing to their ability to adapt to many unknown features of the data. Moreover, it can now be said with some confidence that there exists an NP or SP technique capable of handling any situation an applied researcher would encounter. Such breadth may not be fully evident from this book in that its table of contents reflects the typical set of topics covered in a first-year graduate course in econometrics. But, just as such courses aim to establish principles in parametric econometrics that can be applied in a more general context, so too does this book attempt to perform the same function for the NP and SP approaches. Topics dealt with, such as kernel and series estimation, choice of window widths, bias adjustments, and efficiency bounds, recur in many areas that we have left untouched; examples include the literatures on broad areas such as panel data and hazard function estimation as well as some more restricted topics, such as frontier production functions and dynamic optimal decisions. A knowledge of the basic principles of NP and SP estimation sets a vital foundation for understanding this latter literature.

As should be apparent from the book there is a well-defined asymptotic theory for most estimators, and one can generally find one that is consistent and asymptotically normal, at least under particular assumptions. How useful this feature really is remains to be decided. Although there have been simulation studies of estimators, these tend to be in the original papers justifying them, and little comparative work has appeared.