Instrument approval by the Sargan test and its consequences for coefficient estimation

Empirical econometric findings are often vindicated by supplementing them with the p-values of Sargan–Hansen tests for overidentifying restrictions, provided these exceed a chosen small nominal significance level. It is illustrated here that the probability that such tests reject instrument validity may often barely exceed small levels, even when instruments are seriously invalid, whereas even minor invalidity of instruments can severely undermine inference on regression coefficients by instrumental variable estimators. These uncomfortable patterns may be aggravated when particular valid or invalid instruments are relatively weak or strong.