FUNCTIONAL INSTRUMENTAL VARIABLE REGRESSION WITH AN APPLICATION TO ESTIMATING THE IMPACT OF IMMIGRATION ON NATIVE WAGES
针对函数型线性回归中解释变量内生性问题，提出基于函数主成分分析的工具变量估计量，推导其渐近性质，并通过模拟和移民对本地工资影响的实证研究验证方法有效性。
Functional linear regression has gained popularity as a statistical tool for studying the relationship between function-valued variables. However, in practice, it is hard to expect that the explanatory variables of interest are strictly exogenous, due to, for example, the presence of omitted variables and measurement error. This issue of endogeneity remains insufficiently explored, in spite of its empirical importance. To fill this gap, this article 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 labor market outcomes in the US.