Unobservable Selection and Coefficient Stability: Theory and Validation
A common heuristic for evaluating the problem of omitted variable bias in economics is to look at coefficient movements after inclusion of controls. The theory under which this is informative is one in which the selection on observables is proportional to selection on unobservables. However, this connection is rarely made explicit and the underlying assumption is rarely tested. In this paper I first show how, under proportional selection, coefficient movements, along with movements in r-squared values, can be used to calculate a measure of omitted variable bias. I discuss practical details of implementation. I then undertake two empirical exercises to explore the performance of this adjustment in the data. First, I relate maternal behavior on child birth weight and IQ. Simple controlled regressions give misleading estimates; estimates adjusted with a proportional selection adjustment do significantly better. Second, I match observational and randomized trial data for 23 relationships in public health. I show that on average bias-adjusted coefficients perform much better than simple controlled coefficients and I suggest that a simple form of this adjustment could dramatically improve inference in many public health contexts.
You may purchase this paper on-line in .pdf format from SSRN.com ($5) for electronic delivery.
This paper was revised on August 21, 2013