Matching estimators are widely used in statistical data analysis. However, the distribution of matching estimators has been derived only for particular cases (Abadie and Imbens, 2006). This article establishes a martingale representation for matching estimators. This representation allows the...

We investigate the problem of optimal choice of the smoothing parameter (bandwidth) for the regression discontinuity estimator. We focus on estimation by local linear regression, which was shown to be rate optimal (Porter, 2003). Investigation of an expected-squared-error-loss criterion reveals...

There is a large theoretical literature on methods for estimating causal effects under unconfoundedness, exogeneity, or selection-on-observables type assumptions using matching or propensity score methods. Much of this literature is highly technical and has not made inroads into empirical...

Estimation of average treatment effects under unconfoundedness or exogenous treatment assignment is often hampered by lack of overlap in the covariate distributions. This lack of overlap can lead to imprecise estimates and can make commonly used estimators sensitive to the choice of...

This paper develops a new efficient estimator for the average treatment effect, if selection for treatment is on observables. The new estimator is linear in the first-stage nonparametric estimator. This simplifies the derivation of the means squared error (MSE) of the estimator as a function of...

This paper develops a new nonparametric series estimator for the average treatment effect for the case with unconfounded treatment assignment, that is, where selection for treatment is on observables. The new estimator is efficient. In addition we develop an optimal procedure for choosing the...

Matching estimators are widely used in statistical data analysis. However, the distribution of matching estimators has been derived only for particular cases (Abadie and Imbens, 2006). This article establishes a martingale representation for matching estimators. This representation allows the...

We investigate the problem of optimal choice of the smoothing parameter (bandwidth) for the regression discontinuity estimator. We focus on estimation by local linear regression, which was shown to be rate optimal (Porter, 2003). Investigation of an expected-squared-error-loss criterion reveals...

Many empirical studies use Fuzzy Regression Discontinuity (FRD) designs to identify treatment effects when the receipt of treatment is potentially correlated to outcomes. Existing FRD methods identify the local average treatment effect (LATE) on the subpopulation of compliers with values of the...

Many empirical studies use Fuzzy Regression Discontinuity (FRD) designs to identify treatment effects when the receipt of treatment is potentially correlated to outcomes. Existing FRD methods identify the local average treatment effect (LATE) on the subpopulation of compliers with values of the...