Weak instrumental variables due to ignored nonlinearities in panel data: A Super Learner Control Function estimator
忽略面板非线性导致的弱工具变量：Super Learner 控制函数估计AI 解读 ↓
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忽略面板非线性导致的弱工具变量：Super Learner 控制函数估计
- 研究问题
- 面板模型中若将内生变量的非线性约化式误设为线性，是否会削弱工具变量关联，以及如何据此估计结构因果参数？
- 方法与思路
- 作者在可加个体固定效应的三角模型中，以 Super Learner 估计控制函数，再代入线性结构方程，并沿个体维度交叉拟合。
- 材料陈述的贡献
- 摘要称，论文用广义集中参数刻画误设导致的弱工具问题，并提出具有参数收敛率的估计器，说明其与两类朴素插件方法的差别。
- 阅读关注点
- 应核对排除限制、控制函数识别及固定效应处理，检查学习器收敛条件、个体维度渐近设定，以及插件方法不一致结论的范围。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未经核实；摘要未列明完整正则条件，不能推断该方法消除了所有弱工具或识别问题。
原文摘要
A triangular structural panel data model with additive separable individual-specific effects is used to model the causal effect of a covariate on an outcome variable when there are unobservable confounders with some of them time-invariant. In this setup, a linear specification for the reduced-form equation might be problematic when the conditional mean of the endogenous covariate and the instrumental variables is nonlinear in the population. The reason is that ignoring the nonlinearity could lead to weak instruments (instruments are weakly correlated with the endogenous covariate) due to misspecification as shown using a generalized concentration parameter for panel data. As a solution, we propose a triangular simultaneous equation model for panel data with additive separable individual-specific fixed effects composed of a linear structural equation with a nonlinear reduced form equation. The parameter of interest is the structural parameter of the endogenous variable. The identification of this parameter is obtained under the assumption of available exclusion restrictions and using a control function approach. We provide an estimator that we call Super Learner Control Function estimator (SLCFE). The estimation procedure is composed of two main steps and cross-fitting. First, we estimate the control function using a super learner. In the following step, we use the estimated control function to control for endogeneity in the structural equation. Cross-fitting is done across the individual dimension. The estimator is consistent and asymptotically normal achieving a parametric rate of convergence. We show that the SLCF estimator differs from both the plug-in IV estimator and a naive plug-in 2SLS estimator, with the former not being consistent without cross-fitting, and the latter not being consistent even with cross-fitting.