Optimal transport theory in incomplete econometric models

This talk focuses on the central role played by optimal transport theory in the study of incomplete econometric models. Incomplete econometric models are designed to analyze microeconomic data within the constraints of microeconomic theoretic principles, such as maximization, equilibrium and stability. These models are called incomplete because they do not predict a single distribution for the variables observed in the data. Incompleteness arises because of multiple equilibria in game theoretic solutions, unobserved heterogeneity in choice sets, interval predictions in auctions, and unknown sample selection mechanisms. The problem of confronting the model parameters (possibly infinite dimensional) and the data can be formulated as an optimal transport problem, where the transport cost is some measure of departure from the microeconomic theoretic principles. We will discuss a selection of inference methodologies on the model parameter based on different choices of transport cost, and applications to industrial organization, consumer demand theory and network formation.