Generalized Difference in Difference Models with Gaussian Processes

• Activity Number: 609
• Type: Contributed
• Date/Time: Wednesday, August 3, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): William Herlands* and Daniel B. Neill and Akshaya Jha and Seth Flaxman and Kun Zhang
• Companies: Carnegie Mellon University and Carnegie Mellon University and Carnegie Mellon University and University of Oxford and Carnegie Mellon University
• Keywords: Econometrics ; Gaussian process ; Difference in Difference ; Spatio-temporal ; Machine learning

Abstract

Difference in Difference (DD) is a popular econometric technique for identifying and quantifying causal effects in observational data. We introduce GP-DD: a generalization of DD using Gaussian processes for a nonparametric prior over smooth functions. We use maximum marginal likelihood optimization to obtain estimates for the causal effect and a bootstrapping procedure to yield confidence intervals. Using synthetic data we demonstrate that for fixed effects data with iid noise, GP-DD has equivalent accuracy to traditional DD. However, with highly correlated noise, GP-DD is a more efficient estimator than traditional DD. This indicates that GP-DD is particularly well suited for non-iid domains such as spatio-temporal data. Additionally, we develop scalable inference GP-DD models using Kronecker methods to significantly reduce the naive O(N^3) computational burden for Gaussian process optimization, allowing GP-DD to be scaled to massive datasets.