When can we determine the direction of omitted variable bias of OLS estimators?

Omitted variable bias (OVB) of OLS estimators is a serious and ubiquitous problem in social science research. Often researchers use the direction of the bias in substantive arguments or to motivate estimation methods to deal with the bias. This paper offers a geometric interpretation of OVB that highlights the difficulty in ascertaining its sign in any realistic setting and cautions against the use of direction-of-bias arguments. This analysis has implications for comparison of OLS and IV estimators too.