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This article investigates the finite sample properties of a range of inference methods for propensity score-based matching and weighting estimators frequently applied to evaluate the average treatment effect on the treated. We analyze both asymptotic approximations and bootstrap methods for computing variances and confidence intervals in our simulation designs, which are based on German register data and U.S. survey data. We vary the design w.r.t. treatment selectivity, effect heterogeneity, share of treated, and sample size. The results suggest that in general, theoretically justified bootstrap procedures (i.e., wild bootstrapping for pair matching and standard bootstrapping for “smoother” treatment effect estimators) dominate the asymptotic approximations in terms of coverage rates for both matching and weighting estimators. Most findings are robust across simulation designs and estimators.

We describe R package “causalweight” for causal inference based on inverse probability weighting (IPW). The “causalweight” package offers a range of semiparametric methods for treatment or impact evaluation and mediation analysis, which incorporates intermediate outcomes for investigating causal mechanisms. Depending on the method, identification relies on selection on observables assumptions or on instrumental variables when selection is on unobservables, approaches that may also be applied to tackle non-random outcome attrition and sample selection. Inference is based on the bootstrap.

We introduce a wild bootstrap algorithm for the approximation of the sampling distribution of pair or one-to-many propensity score matching estimators. Unlike the conventional iid bootstrap, the proposed wild bootstrap approach does not construct bootstrap samples by randomly resampling from the observations with uniform weights. Instead, it fixes the covariates and constructs the bootstrap approximation by perturbing the martingale representation for matching estimators. We also conduct a simulation study in which the suggested wild bootstrap performs well even when the sample size is relatively small. Finally, we provide an empirical illustration by analyzing an information intervention in rural development programs.

This paper investigates the finite sample properties of a range of inference methods for propensity score-based matching and weighting estimators frequently applied to evaluate the average treatment effect on the treated. We analyse both asymptotic approximations and bootstrap methods for computing variances and confidence intervals in our simulation design, which is based on large scale labor market data from Germany and varies w.r.t. treatment selectivity, effect heterogeneity, the share of treated, and the sample size. The results suggest that in general, the bootstrap procedures dominate the asymptotic ones in terms of size and power for both matching and weighting estimators. Furthermore, the results are qualitatively quite robust across the various simulation features.

We introduce a wild bootstrap algorithm for the approximation of the sampling distribution of pair or one-to-many propensity score matching estimators. Unlike the conventional iid bootstrap, the proposed wild bootstrap approach does not construct bootstrap samples by randomly resampling from the observations with uniform weights. Instead, it fixes the covariates and constructs the bootstrap approximation by perturbing the martingale representation for matching estimators. We also conduct a simulation study in which the suggested wild bootstrap performs well even when the sample size is relatively small. Finally, we provide an empirical illustration by analyzing an information intervention in rural development programs.

This paper investigates the finite sample properties of a range of inference methods for propensity score-based matching and weighting estimators frequently applied to evaluate the average treatment effect on the treated. We analyse both asymptotic approximations and bootstrap methods for computing variances and confidence intervals in our simulation design, which is based on large scale labor market data from Germany and varies w.r.t. treatment selectivity, effect heterogeneity, the share of treated, and the sample size. The results suggest that in general, the bootstrap procedures dominate the asymptotic ones in terms of size and power for both matching and weighting estimators. Furthermore, the results are qualitatively quite robust across the various simulation features.

We describe R package “causalweight” for causal inference based on inverse probability weighting (IPW). The “causalweight” package offers a range of semiparametric methods for treatment or impact evaluation and mediation analysis, which incorporates intermediate outcomes for investigating causal mechanisms. Depending on the method, identification relies on selection on observables assumptions or on instrumental variables when selection is on unobservables, approaches that may also be applied to tackle non-random outcome attrition and sample selection. Inference is based on the bootstrap.

This article investigates the finite sample properties of a range of inference methods for propensity score-based matching and weighting estimators frequently applied to evaluate the average treatment effect on the treated. We analyze both asymptotic approximations and bootstrap methods for computing variances and confidence intervals in our simulation designs, which are based on German register data and U.S. survey data. We vary the design w.r.t. treatment selectivity, effect heterogeneity, share of treated, and sample size. The results suggest that in general, theoretically justified bootstrap procedures (i.e., wild bootstrapping for pair matching and standard bootstrapping for “smoother” treatment effect estimators) dominate the asymptotic approximations in terms of coverage rates for both matching and weighting estimators. Most findings are robust across simulation designs and estimators.