Correlation Is Not Causation, Yet… Matching and Weighting for Better Counterfactuals

Anyone who has attended a statistics class has heard the old adage “correlation does not imply causation,” usually followed by a series of hilarious graphs showing spurious correlations. Even if we strongly agree with it, this reminder has been taken a little too far: it is repeated like a mantra to criticize every observational study as being unable to detect causation behind statistical association. This chapter helps the reader go beyond the mantra, firstly, by explaining that “correlation does not imply causation” in observational studies because of selection bias (i.e. the composition of treatment and control groups follows a non-random selection) and parametric model dependence. Then, it introduces readers to weighting and matching techniques, smart statistical tools for reducing imbalance in the empirical distribution of pretreatment covariates between the treatment and control groups. Lastly, it provides an empirical illustration by focusing on two powerful algorithms: the entropy balancing (EB) and the coarsened exact matching (CEM). The chapter ends with caveats.