AI 中文总结
该研究针对协变量需先估计的非参数回归问题，提出两种去偏方法并验证其收敛优势，应用于1997年全国青年纵向调查数据，发现低大学入学概率者完成大学后失业减少更显著。
AI 中文摘要
受Brand & Xie 2010年关于教育异质性回报研究的启发，该研究探讨完成大学教育对收入的影响如何随（未知的）完成大学教育的概率变化，我们分析了当某些协变量在第一步被估计时非参数回归函数的估计问题。将估计的协变量视为已知的插件估计量通常会遭受第一阶段估计误差的影响。为缓解该问题，我们在不依赖第一阶段估计方法选择的框架内分析了两种去偏方法，该框架依赖于第二阶段回归的局部平滑或筛方法。具体而言，我们考虑：（i）路径可微参数的影响函数型估计量，其近似目标估计量；（ii）插件估计量的一种变体，其直接旨在校正其偏差。对于每种方法，我们对估计误差进行上界估计，并刻画可达到先验速率的条件，突出了相对于插件估计量在收敛速率方面的潜在收益。模拟研究说明了这些方法的有限样本行为。我们将我们的方法应用于1997年全国青年纵向调查的数据，发现有证据表明，最不可能完成大学教育的个体从完成大学教育中获得的失业减少幅度最大，这与文献中早期的研究结果（Brand & Xie 2010；Brand 2023）一致。
英文摘要
Motivated by the study of heterogeneous returns to education in Brand & Xie 2010, which considers how the effect of completing college on earnings varies with the (unknown) probability of completing college, we analyze the problem of estimating a nonparametric regression function when certain covariates are estimated in a first step. Plug-in estimators that treat the estimated covariates as known generally suffer from first-stage estimation error. To mitigate this issue, we analyze two debiasing approaches within a framework that is agnostic to the choice of the first-stage estimation method and relies on either local-smoothing or sieve-based methods for the second-stage regression. In particular, we consider: (i) influence function-based estimators of pathwise differentiable parameters that approximate the target estimand, and (ii) a variant of plug-in estimators that directly aims to correct their bias. For each method, we upper bound the estimation error and characterize conditions under which oracle rates can be approached, highlighting the possible gains in terms of convergence rates relative to the plug-ins. Simulation studies illustrate the finite-sample behavior of the methods. We apply our methodology to data from the National Longitudinal Survey of Youth 1997 and find evidence that completing college yields the largest reductions in unemployment for individuals least likely to do so, consistent with earlier findings in the literature (Brand & Xie 2010; Brand 2023).
