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.
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Paper provided by University of Connecticut, Department of Economics in its series Working papers with number
2007-18.
Length: 23 pages Date of creation: May 2007 Date of revision: Handle: RePEc:uct:uconnp:2007-18
Note: We thank Gary Chamberlain, Enno Mammen, Whitney Newey, and participants at several seminars for helpful suggestions and conversations. The first author also thanks the NSF for financial support. Contact details of provider: Postal: University of Connecticut 341 Mansfield Road, Unit 1063 Storrs, CT 06269-1063 Phone: (860) 486-4889 Fax: (860) 486-4463 Web page: http://www.econ.uconn.edu/ More information through EDIRC
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Find related papers by JEL classification: C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
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