Distributional counterfactual analysis with (common) deterministic trend units

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The goal of this paper is to extend the counterfactual methodologies in particular Carvalho et al. (2016), by considering the estimation of quantile counterfactuals in the presence of trend units. We derive an asymptotically normal test statistics for the quantile intervention effect and for the distribution effect as a whole. As a by-product, we show the consistency of the quantile regression under heterogeneity and temporal dependence. More importantly, the consistency is obtained without relying on common assumptions of compactness and uniform convergence of the objective function. In fact due to the deterministic trend the objective function fails to be stochastically equicontinuos, which provided that the parameter space is totally bounded, is necessary for uniform convergence. Our procedure is illustrated in a detailed simulation experiment as well as in an empirical application in Corporate Finance.

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