  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.
