Instrumental variable estimation for functional concurrent regression models

Abstract

In this work we propose a functional concurrent regression model to estimate labor supply elasticities over the years 1988 through 2014 using Current Population Survey data. Assuming, as is common, that individuals' wages are endogenous, we introduce instrumental variables in a two-stage least squares approach to estimate the desired labor supply elasticities. Furthermore, we tailor our estimation method to sparse functional data. Though recent work has incorporated instrumental variables into other functional regression models, to our knowledge this has not yet been done in the functional concurrent regression model, and most existing literature is not suited for sparse functional data. We show through simulations that this two-stage least squares approach greatly eliminates the bias introduced by a naive model (i.e. one that does not acknowledge endogeneity) and produces accurate coefficient estimates for moderate sample sizes.

Keywords:

• Functional concurrent regression
• sparse functional data
• instrumental variable
• labor supply elasticity

Acknowledgments

The authors would like to thank the two anonymous referees as well as the Associate Editor, whose comments and suggestions helped to make the paper more technically sound and more accessible to a broader audience. We would also like to thank Matthew Reimherr for his helpful suggestions about the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Note that the technical discussion about the $L^2$ space of functions, found in Section 3, applies to this condition as well.

Additional information

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.