Sparse Functional Concurrent Regression with Instrumental Variables

Abstract

In economic theory, labor supply elasticities measure a person’s response, in terms of hours worked, to a change in that person’s hourly wage. Labor supply elasticities signal attitudes about working which can contribute to policy decisions. In this project, we show how to estimate labor supply elasticities using an instrumental variables estimator in functional concurrent regression models. Though some recent works have adapted instrumental variables estimation to functional regression models, they have focused on scalar-on-function and function-on-function regression models. Our estimation method is novel in that it applies to functional concurrent regression with longitudinal, or sparsely observed functional data. We illustrate the accuracy of our estimation strategy through a detailed simulation study and apply it to data from the Current Population Survey to estimate labor supply elasticities for different demographic groups of the U.S. population.