I first came across this paper while writing the Machine Learning Using IV chapter of the Causal Book. Revisiting it today, I remain struck by its central finding: about 95% of the empirical TSLS (Two-Stage Least Squares) models surveyed here claim to estimate the Local Average Treatment Effect (LATE), but they fail to meet the necessary conditions to do so.
The failure is mainly due to not controlling for covariates nonparametrically. That is to say, in attempting to correct for selection bias (endogeneity) using IVs, causal modelers inadvertently introduce significant specification bias, thereby theoretically nullifying the LATE interpretation.
On a different note, I’ve resumed work on Causal Book. Updates are on the way!