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 income changes. But available instruments are typically "weak." In that case, we show it is an inherent property of 2SLS that 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 elasticities near zero will (spuriously) appear to be precisely estimated, while large estimates will appear to be imprecise. This pattern makes it difficult for a 2SLS t-test to detect a true positive Frisch elasticity. We show how the use of a weak instrument robust hypothesis test, the Anderson-Rubin (AR) test, leads us to conclude the Frisch elasticity is large and signiï¬ cant 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, even with strong instruments. Thus, we argue the AR test should be widely adopted in lieu of the t-test.