Unobservable Selection and Coefficient Stability: Theory and Validation

A common heuristic for evaluating robustness of results to omitted variable bias is to look at coefficient movements after inclusion of controls. This heuristic is informative only if selection on observables is proportional to selection on unobservables. I formalize this link, drawing on theory in Altonji, Elder and Taber (2005) and show how, with this assumption, coefficient movements, along with movements in R-squared values, can be used to calculate omitted variable bias. I discuss empirical implementation and describe a formal bounding argument to replace the coefficient movement heuristic. I show two validation exercises suggesting that this bounding argument would perform well empirically. I discuss application of this procedure to a large set of publications in economics, and use evidence from randomized studies to draw guidelines as to appropriate bounding values.