Robust Inference for the Frisch Labor Supply Elasticity

There is a long standing controversy over the magnitude of the Frisch labor supply elasticity. Macro economists using DSGE models often calibrate it to be large, while many micro data studies find it is small. Several papers attempt to reconcile the micro and macro results. We offer a new and simple explanation: Most micro studies estimate the Frisch using a 2SLS regression of hours changes on wage changes. However, due to a little appreciated power asymmetry property of 2SLS that we clarify, estimates of the Frisch will (spuriously) appear more precise when they are more shifted in the direction of the OLS bias, which is negative. As a result, Frisch elasticity estimates near zero appear (spuriously) precise, while large positive estimates appear (spuriously) imprecise. This pattern makes it difficult for a 2SLS t-test to detect a true positive Frisch elasticity. Fortunately, the Anderson-Rubin (AR) test does not suffer from this power asymmetry problem. The AR test leads us to conclude the Frisch elasticity is large and significant in the NLSY97 data. In contrast, a conventional 2SLS t-test would lead us to conclude it is not significantly different from zero. Our application illustrates a fundamental problem with 2SLS t-tests that arises quite generally. This problem is severe when instruments are weak, but persists even if they are strong. Thus, we argue the AR test should be widely adopted in lieu of the t-test.