Abstract

We propose a simple procedure based on an existing “debiased” l₁-regularized method for inference of the average partial effects (APEs) in approximately sparse probit and fractional probit models with panel data, where the number of time periods is fixed and small relative to the number of cross-sectional observations. Our method is computationally simple and does not suffer from the incidental parameters problems that come from attempting to estimate as a parameter the unobserved heterogeneity for each cross-sectional unit. Furthermore, it is robust to arbitrary serial dependence in underlying idiosyncratic errors. Our theoretical results illustrate that inference concerning APEs is more challenging than inference about fixed and low-dimensional parameters, as the former concerns deriving the asymptotic normality for sample averages of linear functions of a potentially large set of components in our estimator when a series approximation for the conditional mean of the unobserved heterogeneity is considered. Insights on the applicability and implications of other existing Lasso-based inference procedures for our problem are provided. We apply the debiasing method to estimate the effects of spending on test pass rates. Our results show that spending has a positive and statistically significant average partial effect; moreover, the effect is comparable to found using standard parametric methods.

摘要

我们基于现有的“去偏” l ₁提出了一个简单的程序-使用面板数据推断近似稀疏概率模型和分数概率模型中的平均局部效应（APE）的正规化方法，其中时间段的数量是固定的，并且相对于横截面观察的数量而言较小。我们的方法计算简单，不会遇到偶然参数问题，这些问题是由于尝试将每个横截面单元的未观察到的异质性估计为参数而引起的。此外，它对于潜在的特质错误中的任意串行依赖性是鲁棒的。我们的理论结果表明，关于APE的推理要比关于固定和低维参数的推理更具挑战性，因为前者关注的是，当考虑未观察到的异质性的条件均值的序列逼近时，我们的估计器中潜在的大量组件的线性函数的样本平均值的渐近正态性。提供了对其他现有基于套索的推理程序对我们问题的适用性和含义的见解。我们采用去偏方法来估算支出对考试合格率的影响。我们的结果表明，支出具有积极且具有统计学意义的平均部分效果；此外，其效果可与使用标准参数方法获得的效果相媲美。提供了对其他现有基于套索的推理程序对我们问题的适用性和含义的见解。我们采用去偏方法来估算支出对考试合格率的影响。我们的结果表明，支出具有积极且具有统计学意义的平均部分效果；此外，其效果可与使用标准参数方法获得的效果相媲美。提供了对其他现有基于套索的推理程序对我们问题的适用性和含义的见解。我们采用去偏方法来估算支出对考试合格率的影响。我们的结果表明，支出具有积极且具有统计学意义的平均部分效果；此外，其效果可与使用标准参数方法获得的效果相媲美。