2SLS Using Weak Instruments: Implications for Estimating 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 numerous micro data studies estimate it is near zero. A large literature has emerged that attempts to reconcile the micro and macro results. We o ff er a new and simple explanation: Most micro studies estimate the Frisch using a 2SLS regression of hours changes on income changes. But the available instruments are typically "weak." In that case, 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 very imprecise. This will naturally bias micro data studies toward concluding the Frisch is small. We show how the use of a weak instrument robust hypothesis test, the Anderson-Rubin 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 signiï¬ cantly greater then zero.