Why Wasserstein Metric Is Useful in Econometrics

Abstract

In many practical situations, we need to change the spatial distribution of some goods. In such situations, it is desirable to minimize the overall transportation costs. In the 1-D case, the smallest transportation cost of such a change is proportional to what is known as the Wasserstein metric. The same metric can be used to describe the distance between two probability distributions. In the last decades, it turned out that this metric can be successfully used in many economic applications beyond transportation. These successes are somewhat of a mystery: in principle, there are many different metrics on the set of all probability distributions, and it is not immediately clear why namely Wasserstein metric is so successful. In this paper, we show that the Wasserstein metric naturally appears in decision making situations. This fact explains the usefulness of the Wassterstein’s metric in economic applications.