Functional instrumental variable regression with an application to estimating the impact of immigration on native wages

TL;DR

This paper introduces new functional instrumental variable estimators to address endogeneity in functional linear regression, demonstrating their effectiveness through simulations and an application to immigration's impact on wages.

Contribution

It develops consistent FPCA-based instrumental variable estimators for functional regression with endogeneity, filling a gap in theoretical understanding and practical application.

Findings

Estimators perform well in simulation studies.

Application estimates the impact of immigration on wages.

Asymptotic properties are thoroughly derived.

Abstract

Functional linear regression gets its popularity as a statistical tool to study the relationship between function-valued response and exogenous explanatory variables. However, in practice, it is hard to expect that the explanatory variables of interest are perfectly exogenous, due to, for example, the presence of omitted variables and measurement error. Despite its empirical relevance, it was not until recently that this issue of endogeneity was studied in the literature on functional regression, and the development in this direction does not seem to sufficiently meet practitioners' needs; for example, this issue has been discussed with paying particular attention on consistent estimation and thus distributional properties of the proposed estimators still remain to be further explored. To fill this gap, this paper proposes new consistent FPCA-based instrumental variable estimators and develops their asymptotic properties in detail. Simulation experiments under a wide range of settings show that the proposed estimators perform considerably well. We apply our methodology to estimate the impact of immigration on native wages.