Given two sets of random variables, how can one determine whether the former variables are more interdependent than the latter?
This question is of major importance to economists, for example, in comparing how various policies affect systemic risk or multidimensional income inequality. Moreover, the familiar correlation coefficient is ill-suited to this task as it is typically not justified by any economic objective.
Since economists’ interest in interdependence often stems from complementarities (or substitutabilities) in the environments analysed, and since supermodular functions treat their arguments as complements, we propose an economically-grounded ordering of dependence based on comparing expectations of supermodular objective functions.
The first part of the project (joint work with Bruno Strulovici, Northwestern University) characterizes the “supermodular stochastic ordering” and develops methods for determining when one set of random variables is more interdependent than another according to this concept.
The second part will explore selected applications in detail. We will examine how a strategic individual or organization can influence the actions of multiple, heterogeneous “listeners”, by providing different information to different listeners - such a problem is formally one of choosing a dependence structure. We will also use the supermodular ordering to compare the efficiency of different matching or assignment protocols when information about the quality of the individuals or items to be matched is observed only imperfectly.