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Exchangeable Gaussian Processes for Staggered-Adoption Policy Evaluation

Hayk Gevorgyan, Konstantinos Kalogeropoulos, Angelos Alexopoulos

Abstract

We study the use of exchangeable multi-task Gaussian processes (GPs) for causal inference in panel data, applying the framework to two settings: one with a single treated unit subject to a once-and-for-all treatment and another with multiple treated units and staggered treatment adoption. Our approach models the joint evolution of outcomes for treated and control units through a GP prior that ensures exchangeability across units while allowing for flexible nonlinear trends over time. The resulting posterior predictive distribution for the untreated potential outcomes of the treated unit provides a counterfactual path, from which we derive pointwise and cumulative treatment effects, along with credible intervals to quantify uncertainty. We implement several variations of the exchangeable GP model using different kernel functions. To assess prediction accuracy, we conduct a placebo-style validation within the pre-intervention window by selecting a ``fake'' intervention date. Ultimately, this study illustrates how exchangeable GPs serve as a flexible tool for policy evaluation in panel data settings and proposes a novel approach to staggered-adoption designs with a large number of treated and control units.

Exchangeable Gaussian Processes for Staggered-Adoption Policy Evaluation

Abstract

We study the use of exchangeable multi-task Gaussian processes (GPs) for causal inference in panel data, applying the framework to two settings: one with a single treated unit subject to a once-and-for-all treatment and another with multiple treated units and staggered treatment adoption. Our approach models the joint evolution of outcomes for treated and control units through a GP prior that ensures exchangeability across units while allowing for flexible nonlinear trends over time. The resulting posterior predictive distribution for the untreated potential outcomes of the treated unit provides a counterfactual path, from which we derive pointwise and cumulative treatment effects, along with credible intervals to quantify uncertainty. We implement several variations of the exchangeable GP model using different kernel functions. To assess prediction accuracy, we conduct a placebo-style validation within the pre-intervention window by selecting a ``fake'' intervention date. Ultimately, this study illustrates how exchangeable GPs serve as a flexible tool for policy evaluation in panel data settings and proposes a novel approach to staggered-adoption designs with a large number of treated and control units.
Paper Structure (37 sections, 41 equations, 9 figures, 7 tables)

This paper contains 37 sections, 41 equations, 9 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Causal Inference with panel data
  3. Panel structure and potential outcomes
  4. Causal estimands
  5. Assumptions
  6. Assumption 1 (Single sharp intervention).
  7. Assumption 2 (Temporal no-interference).
  8. Assumption 3 (Covariates unaffected by treatment).
  9. Assumption 4 (Non-anticipation of outcomes).
  10. Assumption 5 (Non-anticipating treatment).
  11. State-of-the-art methods for panel data causal inference
  12. Gaussian Processes for Causal Inference in Panel Data
  13. Exchangeable Gaussian Processes for Panel Data Causal Inference
  14. Decomposition into common and idiosyncratic components.
  15. Extension with covariates.
  16. ...and 22 more sections

Figures (9)

  • Figure 1: Per-capita cigarette sales in California and other U.S. states (1970--1999).
  • Figure 2: Example run of the GP--OU--time--covariates model for five randomly chosen pseudo-treated states in the pre-treatment validation step. The bold lines show the posterior predictive means, and the transparent bands show the corresponding 95% prediction intervals.
  • Figure 3: Validation example for California with a fake treatment in 1981: observed outcomes and posterior predictive counterfactual path over 1982--1988.
  • Figure 4: Predicted versus observed outcomes in the validation exercise, by method.
  • Figure 5: California post-intervention comparison (1989--1999): exchangeable GP (OU--time--covariates) vs. SynthDiD benchmark.
  • ...and 4 more figures