Return of the Phantom Menace

Scholars often assume that the danger posed by omitted variable bias can be ameliorated by the inclusion of large numbers of relevant control variables. However, there is nothing in the mathematics of regression analysis that supports this conclusion. This paper goes beyond textbook treatments of omitted variable bias and shows, both for OLS and for generalized linear models, that the inclusion of additional control variables may increase or decrease the bias, and we cannot know for sure which is the case in any particular situation. The last section of the paper shows how formal sensitivity analysis can be used to determine whether omitted variables are a problem. A substantive example demonstrates the method.