Control variables provide an important means of controlling for endogeneity in econometric models with nonseparable and/or multidimensional heterogeneity. We allow for discrete instruments, giving identi cation results under a variety of restrictions on the way the endogenous variable and the...

We propose robust methods for inference on the effect of a treatment variable on a scalar outcome in the presence of very many controls. Our setting is a partially linear model with possibly non-Gaussian and heteroscedastic disturbances where the number of controls may be much larger than the...

The fundamental problem of external validity is not to generalize from one experiment, so much as to experimentally test generalizable theories. That is, theories that explain the systematic variation of causal effects across contexts. Here we show how the graphical language of causal diagrams...