Check out the interesting new paper by Bentley MacLeod at Columbia ("The Human Capital Approach to Inference"), on using economic theory in combination with machine learning to estimate conditional average treatment effects better than can be done with randomized control trials.
Quite apart from new methods for accurate estimation of conditional average treatment effects, the paper's intro contains some interesting tidbits on causal econometric inference. Here's one sequence in yellow, with my reactions:
BM: "There are two distinct approaches to modern empirical economics."
-- The MacLeod paper is exclusively about causal inference, so it should say "two distinct approaches to causal inference in modern empirical economics." Equating causal inference to all of empirical economics is simply wrong. Causal inference is a large and very important part of modern empirical economics, but far from its entirety. The booming field of financial econometrics, for example, is largely and intentionally reduced-form. See this.
BM: "First, there is research using structural models that begins by assuming individuals make utility maximizing decisions within a well defined environment, and then proceeds to measure the value of the unknown parameters..."
-- There is some unsettling truth here. A cynical but not-entirely-false view is that structural causal inference effectively assumes a causal mechanism, known up to a vector of parameters that can be estimated. Big assumption. And of course different structural modelers can make different assumptions and get different results.
BM: "The second approach addresses the self-selection of individuals into different observed treatments or choices by either explicitly randomizing treatments/choices in the context of an experiment...or through the use of a natural experiment that allows for an instrumental variables strategy. There is general agreement that explicit randomization provides one of the cleanest ways to obtain a measure of the effect of choice."
-- There's rarely general agreement about anything in economics. But yes, randomization is arguably the gold standard for causal effect estimation, if and when it can be done credibly.