Testing for coefficient differences across nested linear regression specifications

Statistical applications often involve a comparison of coefficients across two different nested linear regression specifications. However, these comparisons are rarely accompanied by a hypothesis test for the coefficients being equal. Standard specification tests from econometrics, while easy to apply, are not useful in this case. Generalized versions of these tests can be seen as essentially applying the delta method to the omitted-variable-bias formula, but have a tendency to over-reject, especially in small samples when errors are heteroskedastic. Resampling procedures can be helpful in this case, with approaches associated with the jackknife performing particularly well in conducting this test.