Bootstrap Tests for Overidentification in Linear Regression Models

Russell Davidson (1, 2) , James G. Mackinnon

1 GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille
2 Department of Mining and Materials Engineering [Montréal]

We study the finite-sample properties of tests for overidentifying restrictions in linear regression models with a single endogenous regressor and weak instruments. Under the assumption of Gaussian disturbances, we derive expressions for a variety of test statistics as functions of eight mutually independent random variables and two nuisance parameters. The distributions of the statistics are shown to have an ill-defined limit as the parameter that determines the strength of the instruments tends to zero and as the correlation between the disturbances of the structural and reduced-form equations tends to plus or minus one. This makes it impossible to perform reliable inference near the point at which the limit is ill-defined. Several bootstrap procedures are proposed. They alleviate the problem and allow reliable inference when the instruments are not too weak. We also study their power properties.

Mots clés: Anderson-Rubin test; Basmann test; Sargan test; weak instruments

Domaines: Sciences de l'Homme et Société; Economies et finances

Russell Davidson, James G. Mackinnon. Bootstrap Tests for Overidentification in Linear Regression Models. Econometrics, 2015, 3 (4), pp.825--863. ⟨10.3390/econometrics3040825⟩. ⟨hal-01456100⟩