Nonlinear difference-in-differences with cocycles: idea and some simulation experiments

Recovering counterfactual distributions is an important goal in causal inference. In recent years, there has been a growing literature on transport-based models that directly model transport maps between outcome distributions. These methods avoid specifying full data-generating processes and are therefore more robust to mis-specification. The multivariate nonlinear difference-in-differences (DiD) model is one such example. It recovers counterfactual distributions using optimal transport when the treatment is discrete. This approach, however, does not readily generalize to continuous treatments. In this talk, we extend the nonlinear DiD to a continuous treatment setting using cocycles, which are constructed using a different class of transport maps. We propose an estimator for the average treatment effect on the treated and conduct simulation experiments to empirically study its convergence. We also investigate whether having anchoring treatment groups can result in faster convergence and answer that in the negative based on the simulation results.

To join this seminar virtually, please request Zoom connection details from hr.ops@stat.ubc.ca.