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- handle: 10670/1.td7bue
- hal: hal-01456100
- doi: 10.3390/econometrics3040825
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Russell Davidson et al., « Bootstrap Tests for Overidentification in Linear Regression Models », HAL-SHS : économie et finance, ID : 10.3390/econometrics3040825
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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.