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Several approaches have been proposed to evaluate treatment effect, relying on matching methods propensity score, quantile regression, influence function, bootstrap and various combinations of the above. This paper considers two of these approaches to define the quantile double robust (DR) estimator: the inverse propensity score weights, to compare potential output of treated and untreated groups; the Machado and Mata quantile decomposition approach to compute the unconditional quantiles within each group – treated and control. Two Monte Carlo studies and an empirical application for the Italian job labor market conclude the analysis. The paper aims to discuss these issue.

The DR estimator is extended to analyze the tails of the distribution comparing treated and untreated groups, thus defining the quantile based DR estimator. It allows us to measure the treatment effect along the entire outcome distribution. Such a detailed analysis uncovers the presence of heterogeneous impacts of the treatment along the outcome distribution. The computation of the treatment effect at the quantiles, points out variations in the impact of treatment along the outcome distributions. Indeed it is often the case that the impact in the tails sizably differs from the average treatment effect.

Two Monte Carlo studies show that away from average, the quantile DR estimator can be profitably implemented. In the real data example, the nationwide results are compared with the analysis at a regional level. While at the median and at the upper quartile the nationwide impact is similar to the regional impacts, at the first quartile – the lower incomes – the nationwide effect is close to the North-Center impact but undervalues the impact in the South.

The computation of the treatment effect at various quantiles allows to point out discrepancies between treatment and control along the entire outcome distributions. The discrepancy in the tails may differ from the divergence between the average values. Treatment can be more effective at the lower/higher quantiles. The simulations show the performance at the quartiles of quantile DR estimator. In a wage equation comparing long and short term contracts, this estimator shows the presence of an heterogeneous impact of short term contracts. Their impact changes depending on the income level, the outcome quantiles, and on the geographical region.