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 probability such reject instrument validity may barely levels, even when instruments seriously invalid, whereas minor invalidity can severely undermine inference on regression coefficients instrumental variable estimators. These uncomfortable patterns be aggravated particular valid or invalid relatively weak strong.