Specification testing in nonparametric instrumental variable estimation

Joel L. Horowitz

Journal of Econometrics, 2012, vol. 167, issue 2, 383-396

Abstract: In nonparametric instrumental variable estimation, the function being estimated is the solution to an integral equation. A solution may not exist if, for example, the instrument is not valid. This paper discusses the problem of testing the null hypothesis that a solution exists against the alternative that there is no solution. We give necessary and sufficient conditions for existence of a solution and show that uniformly consistent testing of an unrestricted null hypothesis is not possible. Uniformly consistent testing is possible, however, if the null hypothesis is restricted by assuming that any solution to the integral equation is smooth. Many functions of interest in applied econometrics, including demand functions and Engel curves, are expected to be smooth. The paper presents a statistic for testing the null hypothesis that a smooth solution exists. The test is consistent uniformly over a large class of probability distributions of the observable random variables for which the integral equation has no smooth solution. The finite-sample performance of the test is illustrated through Monte Carlo experiments.

Keywords: Inverse problem; Instrumental variable; Series estimator; Linear operator (search for similar items in EconPapers)
JEL-codes: C12 C14 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (15)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:167:y:2012:i:2:p:383-396

DOI: 10.1016/j.jeconom.2011.09.023

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