Martin Mugnier - Paris School of Economics

Abstract

We consider the problem of inference on the mathematical expectation of unknown quantile-cdf transforms of a random variable. A prominent example is the Changes-in-Changes causal inference model developed by Athey and Imbens (2006, Econometrica), where the average treatment effect takes this form. Instead of relying on possibly restrictive differentiability conditions, bounded densities, and the functional delta method, we propose a novel large sample theory for a simple plug-in estimator. Our approach is based on weaker regularity assumptions, leveraging existing results from the theory of L-statistics and developing new results on the empirical process that may be of independent interest. Asymptotic normality is proven, and a new semiparametric estimator for the asymptotic variance is shown to be consistent under Hölder-type smoothness conditions on the densities. Monte Carlo simulations indicate that such sufficient conditions may also be necessary.

Additional information:

• Speaker: Martin Mugnier
• Time: Thursday, 26.06.2025, 16:00 - 17:00
• Location: Faculty Lounge, Room 0.036
• Further links:
  • Martin Mugnier's webpage¹
• Organizer: Statistics Group
• Contact:
  • Almut Lunkenheimer
  • +49 228 73-9228
  • ifs@uni-bonn.de