Abstract
Outliers can be particularly hard to detect, creating bias and inconsistency in the semi-parametric estimates. In this paper, we use Monte Carlo simulations to demonstrate that semi-parametric methods, such as matching, are biased in the presence of outliers. Bad and good leverage point outliers are considered. Bias arises in the case of bad leverage points because they completely change the distribution of the metrics used to define counterfactuals; good leverage points, on the other hand, increase the chance of breaking the common support condition and distort the balance of the covariates, which may push practitioners to misspecify the propensity score or the distance measures. We provide some clues to identify and correct for the effects of outliers following a reweighting strategy in the spirit of the Stahel-Donoho (SD) multivariate estimator of scale and location, and the S-estimator of multivariate location (Smultiv). An application of this strategy to experimental data is also implemented.
Highlights
Centro de Investigaciones Económicas y Empresariales (CIEE), Universidad Privada Boliviana, División de Economía, Centro de Investigación y Docencia Económicas, A.C. (CIDE), Aguascalientes CP20313, Mexico
Control observations with outlying covariate values, on the other hand, will likely have little effect on the estimates of average treatment effect for the treated, since such observations are unlikely to be used as matches
We focus on (i) the effect of these outliers in the estimates of the metric, propensity score, and Mahalanobis distance; (ii) the effect of those metrics contaminated by outliers in the matching procedure when finding counterfactuals; and (iii) the effect of these matches on the estimates of the average treatment effect on the treated (TOT)
Summary
Treatment effect techniques are the workhorse tool when examining the causal effects of interventions, i.e., whether the outcome for an observation is affected by the participation in a program or policy (treatment). The bias emerges because this type of outlier completely changes the distribution of the metrics used to define good counterfactuals, and changes the matches that had initially been undertaken, assigning as matches observations with very different characteristics This effect is independent of the location of the outlier observation. Good leverage points in the control sample do not affect the estimates of treatment effects, because they are unlikely to be used as matches Fourth, these outliers distort the balance of the covariates criterion used to specify the propensity score. Monte Carlo simulations support the utility of these tools for overcoming the effects of outliers in the semi-parametric estimation of treatment effects An application of these estimators to the data of LaLonde (1986) allows us to understand the failure of the matching estimators of Dehejia and Wahba (1999, 2002) to overcome. An application to LaLonde’s data is presented in Section 6, and in Section 7, we conclude
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