## Abstract

This paper is concerned with inference about a function g that is identified by a conditional moment restriction involving instrumental variables. The paper presents a test of the hypothesis that g belongs to a finite-dimensional parametric family against a nonparametric alternative. The test does not require nonparametric estimation of g and is not subject to the ill-posed inverse problem of nonparametric instrumental variables estimation. Under mild conditions, the test is consistent against any alternative model. In large samples, its power is arbitrarily close to 1 uniformly over a class of alternatives whose distance from the null hypothesis is O(n^{-1/2}), where n is the sample size. In Monte Carlo simulations, the finite-sample power of the new test exceeds that of existing tests.

Original language | English (US) |
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Pages (from-to) | 521-538 |

Number of pages | 18 |

Journal | Econometrica |

Volume | 74 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1 2006 |

## Keywords

- Consistent testing
- Hypothesis test
- Instrumental variables
- Specification testing

## ASJC Scopus subject areas

- Economics and Econometrics