To Control or Not to Control? Bias of Simple Matching vs Difference-in-Difference Maching in a Dynamic Framework

Mardi | 2010-11-09

Sylvain CHABE-FERRET – libre

In this paper, I examine whether the claim “the more control variables, the better” holdswhen matching in a dynamic context. I exhibit three situations where it is better todifference with respect to past outcomes rather than to control for them: DID-matchingis unbiased whereas matching on past outcomes is biased. I also study the special caseof evaluating a job training program, borrowing a credible selection rule from Heckman,LaLonde, and Smith (1999) and relying on the parameters of the wage process estimatedby MaCurdy (1982). I derive closed forms for the bias terms of the two estimators whenthe error terms are normally distributed. I show that DID matching is unbiased whenapplied symmetrically around the period of enrollment, as implemented by Heckman,Ichimura, Smith, and Todd (1998). DID-matching is more robust than matching to misspecificationboth of the amount of information individuals have when deciding to enterthe program and of the control period. I finally point to previously unnoticed experimentalresults that confirm the claim that DID-matching is less biased than matching.