  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.
