  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.
