# Efficiency Bounds for Estimating Linear Functionals of Nonparametric Regression Models with Endogenous Regressors

*Thomas A. Severini* and
*Gautam Tripathi* ()

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Thomas A. Severini: Northwestern University

No 2007-18, Working papers from University of Connecticut, Department of Economics

**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.

**Keywords:** Efficiency bounds; Linear functionals; Nonparametric regression; Endogenous regressors (search for similar items in EconPapers)

**JEL-codes:** C14 (search for similar items in EconPapers)

**New Economics Papers:** this item is included in nep-ecm

**Date:** 2007-05

**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.

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**Related works:**

Journal Article: Efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors (2012)

Working Paper: Efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors (2007)

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**Persistent link:** http://EconPapers.repec.org/RePEc:uct:uconnp:2007-18

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