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Heterogeneous Treatment Effects for Networks, Panels, and other Outcome Matrices

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  • Eric Auerbach
  • Yong Cai

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.

Suggested Citation

  • Eric Auerbach & Yong Cai, 2022. "Heterogeneous Treatment Effects for Networks, Panels, and other Outcome Matrices," Papers 2205.01246, arXiv.org, revised Oct 2022.
    • Handle: RePEc:arx:papers:2205.01246
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    References listed on IDEAS

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