Networks Webinar - Eric Auerbach

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.