Multicollinearity in the presence of errors-in-variables can increase the probability of type-I errors

The conventional view of multicollinearity is that it inflates the estimated standard errors of regression coefficients, thereby reducing statistical power. Much less widely recognised is that, in combination with errors-in-variables, multicollinearity can also increase the likelihood of a type-I error by inflating coefficient estimates more than their estimated standard errors, thus generating spurious statistical significance. This implies that variance-inflation factors should be routinely computed, even when coefficients appear significant, in order to avoid false inferences. We illustrate this problem using a study in anthropometric history, in which extreme multicollinearity combined with measurement error produced misleadingly significant results. This example demonstrates the need to take multicollinearity seriously in empirical research.