When is it really justifiable to ignore explanatory variable endogeneity in a regression model?

•Examines corrections to least-squares to render it consistent under simultaneity.•Derives the limiting distribution of estimators corrected for inconsistency.•Exploits this to indicate the sensitivity of t-tests when one regressor is endogenous.•Explains the flaws in an alternative approach published in Ashley and Parmeter (2015).

A procedure that aims to pinpoint the sensitivity of ordinary least-squares based inferences regarding the degree of endogeneity of some regressors has been put forward in Ashley and Parmeter (2015a). Here it is demonstrated that this procedure is based on an incorrect and systematically too optimistic asymptotic approximation to the variance of inconsistent least-squares. Therefore, and because the suggested sensitivity findings pertain to a random set of estimated endogeneity correlations, the claimed significance levels are misleading. For a very basic one coefficient model it is demonstrated why much more sophisticated asymptotic expansions under a stricter set of assumptions are required. This enables to replace some of the flawed earlier sensitivity analysis results for an empirical growth model by asymptotically valid findings.