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Treatment Effects

Paper Session

Saturday, Jan. 4, 2025 8:00 AM - 10:00 AM (PST)

Hilton San Francisco Union Square, Union Square 3 and 4
Hosted By: Econometric Society
  • Chair: Haoge Chang, Microsoft

Statistical Inference of Optimal Allocations I: Regularities and their Implications

Kai Feng
,
Tsinghua University
Han Hong
,
Stanford University

Abstract

In this paper, we develp a functional differentiability approach for solving statistical optimal allocation problems. We first derive Hadamard differentiability of the value function through a detailed analysis of the general properties of the sorting operator. Central to our framework are the concept of Hausdorff measure and the area and coarea integration formulas from geometric measure theory. Building on our Hadamard differentiability results, we demonstrate how the functional delta method can be used to directly derive the asymptotic properties of the value function process for binary constrained optimal allocation problems, as well as the two-step ROC curve estimator. Moreover, leveraging profound insights from geometric functional analysis on convex and local Lipschitz functionals, we obtain additional generic Fréchet differentiability results for the value functions of optimal allocation problems. These compelling findings motivate us to study carefully the first order approximation of the optimal social welfare. In this paper, we then present a double / debiased estimator for the value functions. Importantly, the conditions outlined in the Hadamard differentiability section validate the margin assumption from the statistical classification literature employing plug-in methods that justifies a faster convergence rate.

Randomization-Based Confidence Intervals for the Local Average Treatment Effect

P Aronow
,
Yale University
Haoge Chang
,
Microsoft
Patrick Lopatto
,
Brown University

Abstract

We consider the problem of generating confidence intervals in randomized
experiments with noncompliance. We show that a refinement of a randomization-based
procedure proposed by Imbens and Rosenbaum (2005) has desirable properties. Namely,
we show that using a studentized Anderson–Rubin-type statistic as a test statistic yields
confidence intervals that are finite-sample exact under treatment effect homogeneity, and
remain asymptotically valid for the Local Average Treatment Effect when the treatment
effect is heterogeneous. We provide a uniform analysis of this procedure.

Assessing Heterogeneity of Treatment Effects

Tetsuya Kaji
,
University of Chicago
Jianfei Cao
,
Northeastern University

Abstract

Treatment effect heterogeneity is of major interest in economics, but its assessment is often hindered by the fundamental lack of identification of the individual treatment effects. For example, we may want to assess the effect of insurance on the health of otherwise unhealthy individuals, but it is infeasible to insure only the unhealthy, and thus the causal effects for those are not identified. Or, we may be interested in the shares of winners from a minimum wage increase, while without observing the counterfactual, the winners are not identified. Such heterogeneity is often assessed by quantile treatment effects, which do not come with clear interpretation and the takeaway can sometimes be equivocal. We show that, with the quantiles of the treated and control outcomes, the ranges of these quantities are identified and can be informative even when the average treatment effects are not significant. Two applications illustrate how these ranges can inform us about heterogeneity of the treatment effects.
JEL Classifications
  • C10 - General