Put spend on the right-hand side of a fixed effects regression and the coefficient looks like marginal return. On simulated data with randomly assigned dose, it overstates the true marginal return by 31%. Here is why, and how the new contdid package fixes it.
The two-way fixed effects regression is the default for staggered geo rollouts. On simulated data where the true lift is known, it understates the effect by 41%. Here is why, and the estimator that fixes it, in R and Python.