Why does “OLS” mean a linear function of X? Are you assuming empirical researchers never think to try quadratics or cubics after graphing their data? Isn’t a regression Y on 1, X, X^2, X^3 estimated by OLS?
And, how realistic is that pattern of treatment effects, especially in social sciences?
And, how realistic is that pattern of treatment effects, especially in social sciences?
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The point here is not about the estimation method or about fitting the cef but only to highlight how wrong you can go if use reg y x to estimate an ate when x is continuous
Y on X targets ATE when X is randomized and binary; but the results on what the 'YonX estimand' (argh) is when X is continuous seem less well appreciated
https://macartan.github.io/assets/htmls/continuous_ols.html