02761cam a22002657 4500001000600000003000500006005001700011008004100028100002300069245015600092260006600248490005100314500001400365520153100379530006101910538007201971538003602043690009902079690009702178700001902275710004202294830008602336856003702422856003602459t0241NBER20180422221034.0180422s1999 mau||||fs|||| 000 0 eng d1 aAngrist, Joshua D.10aWhen to Control for Covariates? Panel-Asymptotic Results for Estimates of Treatment Effectsh[electronic resource] /cJoshua D. Angrist, Jinyong Hahn. aCambridge, Mass.bNational Bureau of Economic Researchc1999.1 aNBER technical working paper seriesvno. t0241 aMay 1999.3 aThe problem of how to control for covariates is endemic in evaluation research. Covariate-matching provides an appealing control strategy, but with continuous or high-dimensional covariate vectors, exact matching may be impossible or involve small cells. Matching observations that have the same propensity score produces unbiased estimates of causal effects whenever covariate-matching does, and also has an attractive dimension-reducing property. On the other hand, conventional asymptotic arguments show that covariate-matching is (asymptotically) more efficient that propensity score-matching. This is because the usual asymptotic sequence has cell sizes growing to infinity, with no benefit from reducing the number of cells. Here, we approximate the large sample behavior of difference matching estimators using a panel-style asymptotic sequence with fixed cell sizes and the number of cells increasing to infinity. Exact calculations in simple examples and Monte Carlo evidence suggests this generates a substantially improved approximation to actual finite-sample distributions. Under this sequence, propensity-score-matching is most likely to dominate exact matching when cell sizes are small, the explanatory power of the covariates conditional on the propensity score is low, and/or the probability of treatment is close to zero or one. Finally, we introduce a random-effects type combination estimator that provides finite-sample efficiency gains over both covariate-matching and propensity-score-matching. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aC14 - Semiparametric and Nonparametric Methods: General2Journal of Economic Literature class. 7aC23 - Panel Data Models • Spatio-temporal Models2Journal of Economic Literature class.1 aHahn, Jinyong.2 aNational Bureau of Economic Research. 0aTechnical Working Paper Series (National Bureau of Economic Research)vno. t0241.4 uhttp://www.nber.org/papers/t024141uhttp://dx.doi.org/10.3386/t0241