Distributional Counterfactual Analysis in High-Dimensional Setup

by   Ricardo Masini, et al.

In the context of treatment effect estimation, this paper proposes a new methodology to recover the counterfactual distribution when there is a single (or a few) treated unit and possibly a high-dimensional number of potential controls observed in a panel structure. The methodology accommodates, albeit does not require, the number of units to be larger than the number of time periods (high-dimensional setup). As opposed to model only the conditional mean, we propose to model the entire conditional quantile function (CQF) in the absence of intervention and estimate it using the pre-intervention period using a penalized regression. We derive non-asymptotic bounds for the estimated CQF valid uniformly over the quantiles, allowing the practitioner to re-construct the entire contractual distribution. Moreover, we bound the probability coverage of this estimated CQF which can be used to construct valid confidence intervals for the (possibly random) treatment effect for every post-intervention period or simultaneously. We also propose a new hypothesis test for the sharp null of no-effect based on the ℒ^p norm of deviation of the estimated CQF to the population one. Interestingly, the null distribution is quasi-pivotal in the sense that it only depends on the estimated CQF, ℒ^p norm, and the number of post-intervention periods, but not on the size of the post-intervention period. For that reason, critical values can then be easily simulated. We illustrate the methodology is by revisiting the empirical study in Acemoglu et al (2016).


page 1

page 2

page 3

page 4


Uniformly valid confidence intervals for conditional treatment effects in misspecified high-dimensional models

Eliminating the effect of confounding in observational studies typically...

hdm: High-Dimensional Metrics

In this article the package High-dimensional Metrics (hdm) is introduced...

High-Dimensional Metrics in R

The package High-dimensional Metrics (hdm) is an evolving collection of ...

Non-asymptotic confidence bands on the probability an individual benefits from treatment (PIBT)

The premise of this work, in a vein similar to predictive inference with...

Randomization Tests in Observational Studies with Staggered Adoption of Treatment

This paper studies inference in observational studies with time-varying ...

Least Squares with Error in Variables

Error-in-variables regression is a common ingredient in treatment effect...

Do We Exploit all Information for Counterfactual Analysis? Benefits of Factor Models and Idiosyncratic Correction

The measurement of treatment (intervention) effects on a single (or just...