This paper investigates the nite sample properties of a range of inference methods for propensity score-based matching and weighting estimators frequently applied to evaluate the average treatment eect on the treated. We analyse both asymptotic approximations and bootstrap methods for computing variances and condence 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, eect heterogeneity, share of treated, and sample size. The results suggest that in general, theoretically justied bootstrap procedures (i.e. wild bootstrapping for pair matching and standard bootstrapping for`smoother' treatment eect estimators) dominate the asymptotic approximations in terms of coverage rates for both matching and weighting estimators. Most ndings are robust across simulation designs and estimators.

We study the validity of the pairs bootstrap for lasso estimators in linear regression models with random covariates and heteroscedastic error terms. We show that the naive pairs bootstrap does not provide a valid method for approximating the distribution of the lasso estimator. To overcome this deficiency, we introduce a modified pairs bootstrap procedure and prove its consistency. Finally, we consider the adaptive lasso and show that the modified pairs bootstrap consistently estimates the distribution of the adaptive lasso estimator.

We derive new theoretical results on the properties of the adaptive least absolute shrinkage and selection operator (adaptive lasso) for time series regression models. In particular, we investigate the question of how to conduct finite sample inference on the parameters given an adaptive lasso model for some fixed value of the shrinkage parameter. Central in this study is the test of the hypothesis that a given adaptive lasso parameter equals zero, which therefore tests for a false positive. To this end we construct a simple testing procedure and show, theoretically and empirically through extensive Monte Carlo simulations, that the adaptive lasso combines efficient parameter estimation, variable selection, and valid finite sample inference in one step. Moreover, we analytically derive a bias correction factor that is able to significantly improve the empirical coverage of the test on the active variables.Finally, we apply the introduced testing procedure to investigate the relation between the short rate dynamics and the economy, thereby providing a statistical foundation (from a model choice perspective) to the classic Taylor rule monetary policy model. JEL classifications: C12; C22; E43.

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We characterize the robustness of subsampling procedures by deriving a formula for the breakdown point of subsampling quantiles. This breakdown point can be very low for moderate subsampling block sizes, which implies the fragility of subsampling procedures, even when they are applied to robust statistics. This instability arises also for data driven block size selection procedures minimizing the minimum confidence interval volatility index, but can be mitigated if a more robust calibration method can be applied instead. To overcome these robustness problems, we introduce a consistent robust subsampling procedure for M-estimators and derive explicit subsampling quantile breakdown point characterizations for MM-estimators in the linear regression model. Monte Carlo simulations in two settings where the bootstrap fails show the accuracy and robustness of the robust subsampling relative to the subsampling