This paper introduces and proves asymptotic normality for a new semi-parametric estimator of continuous treatment effects in panel data. Specifically, we estimate the average derivative. Our estimator uses the panel structure of data to account for unobservable time-invariant heterogeneity and machine learning (ML) methods to preserve statistical power while modeling high-dimensional relationships. We construct our estimator using tools from double de-biased machine learning (DML) literature. Monte Carlo simulations in a nonlinear panel setting show that our method estimates the average derivative with low bias and variance relative to other approaches. Lastly, we use our estimator to measure the impact of extreme heat on United States (U.S.) corn production, after flexibly controlling for precipitation and other weather features. Our approach yields extreme heat effect estimates that are 50% larger than estimates using linear regression. This difference in estimates corresponds to an additional $3.17 billion in annual damages by 2050 under median climate scenarios. We also estimate a dose-response curve, which shows that damages from extreme heat decline somewhat in counties with more extreme heat exposure.

翻译：本文提出一种新的半参数估计量，用于估计面板数据中的连续处理效应，并证明其渐近正态性。具体地，我们估计平均导数。该估计量利用面板数据的结构来处理不可观测的时不变异质性，并采用机器学习方法来保持统计功效，同时建模高维关系。我们基于双去偏机器学习（DML）文献中的工具构建该估计量。在非线性面板设置下的蒙特卡洛模拟表明，与其他方法相比，我们的方法能以低偏差和低方差估计平均导数。最后，我们利用该估计量衡量极端高温对美国玉米产量的影响，并灵活控制降水及其他天气特征。我们的方法得到的极端高温效应估计值比线性回归估计值高出50%。根据中位数气候情景，这一估计差异意味着到2050年每年额外增加31.7亿美元的损失。我们还估计了剂量-反应曲线，结果表明，在极端高温暴露较多的县，极端高温造成的损失有所下降。