Abstract
Consider a nonparametric regression model Y=mu*(X) + e, where the explanatory variables X are endogenous and e satisfies the conditional moment restriction E[e|W]=0 w.p.1 for instrumental variables W. It is well known that in these models the structural parameter mu* is 'ill-posed' in the sense that the function mapping the data to mu* is not continuous. In this paper, we derive the efficiency bounds for estimating linear functionals E[p(X)mu*(X)] and int_{supp(X)}p(x)mu*(x)dx, where p is a known weight function and supp(X) the support of X, without assuming mu* to be well-posed or even identified.
Recommended Citation
Severini, Thomas A. and Tripathi, Gautam, "Efficiency Bounds for Estimating Linear Functionals of Nonparametric Regression Models with Endogenous Regressors" (2007). Economics Working Papers. 200718.
https://digitalcommons.lib.uconn.edu/econ_wpapers/200718