The evaluation of the possible effects of a treatment on an outcome plays a central role in both theoretical and applied statistical and econometrical literature. This paper focuses on nonparametric tests for possible difference in the distribution of potential outcomes due to receiving or not receiving a treatment. The approach is based on weighting observed data on the basis on the estimated propensity score. Kolmogorov–Smirnov type and Wilcoxon–Mann–Whitney type tests are constructed, and their limiting distributions are studied. Rejection regions are obtained by inverting confidence intervals. This involves the study of appropriate estimators of the limiting variance of test statistics. Approximations of quantiles via subsampling are also considered. The merits of the different tests are studied by Monte Carlo simulation. An application to the construction of tests for stochastic dominance is provided.

Testing for the presence of treatment effect under selection on observables / De Giovanni, Livia; Conti, Pier Luigi. - In: ASTA ADVANCES IN STATISTICAL ANALYSIS. - ISSN 1863-8171. - (In corso di stampa), pp. 1-29. [10.1007/s10182-022-00454-8]

Testing for the presence of treatment effect under selection on observables

Livia De Giovanni
;
Pier Luigi Conti
In corso di stampa

Abstract

The evaluation of the possible effects of a treatment on an outcome plays a central role in both theoretical and applied statistical and econometrical literature. This paper focuses on nonparametric tests for possible difference in the distribution of potential outcomes due to receiving or not receiving a treatment. The approach is based on weighting observed data on the basis on the estimated propensity score. Kolmogorov–Smirnov type and Wilcoxon–Mann–Whitney type tests are constructed, and their limiting distributions are studied. Rejection regions are obtained by inverting confidence intervals. This involves the study of appropriate estimators of the limiting variance of test statistics. Approximations of quantiles via subsampling are also considered. The merits of the different tests are studied by Monte Carlo simulation. An application to the construction of tests for stochastic dominance is provided.
Potential outcomes, Propensity score, Nonparametric tests, Two sample comparison
Testing for the presence of treatment effect under selection on observables / De Giovanni, Livia; Conti, Pier Luigi. - In: ASTA ADVANCES IN STATISTICAL ANALYSIS. - ISSN 1863-8171. - (In corso di stampa), pp. 1-29. [10.1007/s10182-022-00454-8]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/220458
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