This paper develops estimators for quantile treatment effects under the identifying restriction that selection to treatment is based on observable characteristics. Identification is achieved without requiring computation of the conditional quantiles of the potential outcomes. Instead, the identification results for the marginal quantiles lead to an estimation procedure for the quantile treatment effect parameters that has two steps: nonparametric estimation of the propensity score and computation of the difference between the solutions of two separate minimization problems. Root-N consistency, asymptotic normality, and achievement of the semiparametric efficiency bound are shown for that estimator. A consistent estimation procedure for the variance is also presented. Finally, the method developed here is applied to evaluation of a job training program and to a Monte Carlo exercise. Results from the empirical application indicate that the method works relatively well even for a data set with limited overlap between treated and controls in the support of covariates. The Monte Carlo study shows that, for a relatively small sample size, the method produces estimates with good precision and low bias, especially for middle quantiles.

Despite rising inequality in rich countries, many developing economies have experienced a decline in inequality in recent decades. Brazil is a notable example. From 1995 to 2015, its Gini index decreased from 58 to 48 points. An extensive body of research has investigated a diverse set of explanations for this reduction. This article reviews this literature, using Brazil as a privileged case study to understand the broader phenomenon of inequality decline in many parts of the developing world. We present stylized facts about inequality during this period, focusing on the results of decomposition methods. We then examine research that employs quasi-experiments and structural models to assess mechanisms related to labor supply and demand, trade, technological changes, and institutional factors such as the minimum wage and race and gender discrimination. We end by discussing some unanswered questions. (JEL D31, D63, J22, J23, J31, O15)

We propose a new regression method to evaluate the impact of changes in the distribution of the explanatory variables on quantiles of the unconditional (marginal) distribution of an outcome variable. The proposed method consists of running a regression of the (recentered) influence function (RIF) of the unconditional quantile on the explanatory variables. The influence function, a widely used tool in robust estimation, is easily computed for quantiles, as well as for other distributional statistics. Our approach, thus, can be readily generalized to other distributional statistics.