Estimating Continuous Treatment Effects in Panel Data using Machine Learning with an Agricultural Application

This paper introduces and proves asymptotic normality for a new semi-parametric estimator of continuous treatment effects in panel data. Specifically, we estimate an average derivative of the regression function. Our estimator uses the panel structure of data to account for unobservable time-invariant heterogeneity and machine learning methods to flexibly estimate functions of high-dimensional inputs. We construct our estimator using tools from double de-biased machine learning (DML) literature. We show the performance of our method in Monte Carlo simulations and also apply our estimator to real-world data and measure the impact of extreme heat in United States (U.S.) agriculture. We use the estimator on a county-level dataset of corn yields and weather variation, measuring the elasticity of yield with respect to a marginal increase in extreme heat exposure. In our preferred specification, the difference between the estimates from OLS and our method is statistically significant and economically significant. We find a significantly higher degree of impact, corresponding to an additional $1.18 billion in annual damages by the year 2050 under median climate scenarios. We find little evidence that this elasticity is changing over time.