Optimal Transport Meets Econometrics
Friday, Jan. 6, 2023 8:00 AM - 10:00 AM (CST)
- Chair: Timothy Christensen, New York University
Optimal Transport as a Regression Tool
AbstractWe are concerned with program evaluation when the data is observed, before and after treatment, in the form of empirical distributions. We are interested in treatment impact on features other than the mean. For instance, we are interested in the number of subjects impacted by the treatment. We produce methodology based on optimal transport to estimate such quantities. In one main application of interest, we produce a lower bound on the number of drivers purchasing their license to buy a new car on the black market in Beijing.
Counterfactual Identification and Latent Space Enumeration in Discrete Outcome Models
AbstractThis paper considers partial identification of counterfactual parameters in a general class of discrete outcome models allowing for endogenous regressors and multi-dimensional latent variables, all without parametric distributional assumptions. Our main theoretical result is that, when the covariates are discrete, the infinite-dimensional latent variable distribution can be replaced with a finite-dimensional version that is equivalent from an identification perspective. Practically constructing the finite-dimensional latent variable distribution is done by enumerating regions of the latent variable space with a new and efficient cell enumeration algorithm for hyperplane arrangements. We then show that bounds on a certain class of counterfactual parameters can be computed by solving a sequence of linear programming problems, and show how the researcher can introduce additional assumptions as constraints in the linear programs. Finally, we apply the method to an airline entry game example and a dynamic panel data discrete response model of labor market participation.
Existence of a Competitive Equilibrium with Substitutes, with Applications to Matching and Discrete Choice Models
AbstractWe propose novel results for the existence of a competitive equilibrium with substitutes. An algorithm is provided. Two applications are given: one to the existence of a stable matching without unassigned agents, and one to the identification of discrete choice models.
- C10 - General
- C61 - Optimization Techniques; Programming Models; Dynamic Analysis