8.6 What should I match on?
- Selection on observables assumption: Assignment random conditional on covariates
- Match on quadratic/polynomial terms etc. where it makes sense theoretically (e.g. age X, education D and income Y)
- Ultimate benchmark is balance of controls X across values of treatment D
- Does it make sense to combine matching with regression?
- Yes, conceptually you induce independence between X and D in the matched sample. But there may still be a direct path from X on Y, i.e. X may explain some of the variation in Y independently from D
- Adding X decreases the amount of unexplained variance in Y, you get more precise estimates (decreases S.E.)
References
Elwert, Felix, and Christopher Winship. 2014b. “Endogenous Selection Bias: The Problem of Conditioning on a Collider Variable.” Annu. Rev. Sociol. 40 (1): 31–53.
Tam Cho, Wendy K, Jason J Sauppe, Alexander G Nikolaev, Sheldon H Jacobson, and Edward C Sewell. 2013. “An Optimization Approach for Making Causal Inferences.” Stat. Neerl. 67 (2): 211–26.