Symmetric Difference in Difference Dominates Matching in a Realistic Selection Model∗

Matching and Difference in Difference (DID) are two widespread methods that use pre-treatment outcomes to correct for selection bias. I use a model of earnings dynam-ics and entry into a Job Training Program (JTP) calibrated with realistic parameter values to assess the performances of both estimators. I find that Matching generally underestimates the average causal effect of the program and gets closer to the true effect when conditioning on an increasing number of pre-treatment outcomes. Apply-ing DID symmetrically around the treatment date is consistent when selection bias forms and dissipates at the same pace. When selection bias is not symmetric, Monte Carlo simulations show that Symmetric DID still performs better than Matching, especially in the middle of the life-cycle. These results are consistent with estimates of the bias of Matching and DID from randomly assigned JTPs. Some of the virtues of Symmetric DID extend to programs allocated according to a cutoff eligibility rule