Notes on Causation, Comparison, and Regression
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Comparison and contrast are the basic means to unveil causation and learn which treatments work. To build good comparisons that isolate the average effect of treatment from confounding factors, randomization is key, yet often infeasible. In such non-experimental settings, we illustrate and discuss how well the common linear regression approach to causal inference approximates features of randomized experiments, such as covariate balance, study representativeness, sample-grounded estimation, and unweighted analyses. We also discuss alternative regression modeling, weighting, and matching approaches. We argue they should be given strong consideration in empirical work.
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