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 errors, and this in turn limits the applicability of the existing estimators whose essential asymptotic properties, such as consistency, are developed under the exogeneity condition. To resolve this issue, this paper proposes new instrumental variable estimators for functional endogenous linear models, and establishes their asymptotic properties. We also develop a novel test for examining if various characteristics of the response variable depend on the explanatory variable in our model. Simulation experiments under a wide range of settings show that the proposed estimators and test perform considerably well. We apply our methodology to estimate the impact of immigration on native wages.
翻译:功能线性回归作为一种统计工具,研究功能价值反应与外部解释变量之间的关系,其受人欢迎。然而,在实践中,很难期望有关解释变量完全具有外在性,例如,由于存在省略变量和测量错误,这反过来又限制了现有估测器的适用性,这些估测器在外异性条件下开发了基本的亚光性特性,例如一致性。为解决这一问题,本文件为功能内源线性模型提出了新的工具变量估测器,并确定了其消化特性。我们还开发了一个新测试,以检查响应变量的各种特性是否取决于我们模型中的解释变量。在广泛环境下进行的模拟实验表明,拟议的估测器和测试效果相当良好。我们运用我们的方法来估计移民对本地工资的影响。