Heterogeneous Treatment Effects for Networks, Panels, and other Outcome Matrices
Abstract
We are interested in the distribution of treatment effects for an experiment where units are randomized to a treatment but outcomes are measured for pairs of units. For example, we might measure risk sharing links between households enrolled in a microfinance program, employment relationships between workers and firms exposed to a trade shock, or bids from bidders to items assigned to an auction format. Such a double randomized experimental design may be appropriate when there are social interactions, market externalities, or other spillovers across units assigned to the same treatment. Or it may describe a natural or quasi experiment given to the researcher. In this paper, we propose a new empirical strategy that compares the eigenvalues of the outcome matrices associated with each treatment. Our proposal is based on a new matrix analog of the Fr\'echet-Hoeffding bounds that play a key role in the standard theory. We first use this result to bound the distribution of treatment effects. We then propose a new matrix analog of quantile treatment effects that is given by a difference in the eigenvalues. We call this analog spectral treatment effects.
Keywords
Cite
@article{arxiv.2205.01246,
title = {Heterogeneous Treatment Effects for Networks, Panels, and other Outcome Matrices},
author = {Eric Auerbach and Yong Cai},
journal= {arXiv preprint arXiv:2205.01246},
year = {2022}
}
Comments
An R package can be found at \url{https://github.com/yong-cai/MatrixHTE}