Most economics papers exclusively fit linear models to the data. There’s no discussion of potential outcomes. It’s just hears a linear model and the error term is uncorrelated with the covariates so we’re indentified.

dentification assumptions are typically stated not with regards to potential outcomes but with respect to linear models: $\text{Cov}(X_i, \varepsilon_i) = 0$. The linear model is so ingrained that papers will occasionally initially frame methods under the assumption of constant treatment effects. I have yet to see why it’s helpful to think of anything under a constant treatment effect assumption, but perhaps I am naive!

But given our approach to causal inference, where causal effects are defined with respect to the potential outcome framework, it is a bit surprising that so many papers, so many “robustness” checks restrict themselves to linear models.