Primary Submission Category: Difference in Differences, Synthetic Control, Methods for Panel and Longitudinal Data
Semi-parametric Estimation Under a Stationarity Assumption With Applications to Quasi-Experimental Designs
Authors: Gary Hettinger,
Presenting Author: Gary Hettinger*
Semi-parametric causal inference typically relies on assumptions that connect causal estimands to directly observable data, enabling non-parametric estimation of nuisance functions and the construction of doubly robust estimators. However, many important problems such as positivity violations, transportability across populations, and controlled interrupted time series, require extrapolation beyond the observed data support, making fully non-parametric identification impossible. In these settings, part of the data-generating process must be specified parametrically, often through assumptions such as stationarity or stable trends, while other components remain non-parametrically estimable.
In this work, we formulate such problems as a semi-parametric estimation problem under required extrapolation and provide formal theory to what is done often implicitly in practice. Further, we propose a unified semi-parametric framework that separates parametric extrapolation components from nonparametric confounding mechanisms and characterize the resulting efficiency-robustness tradeoffs. The framework is illustrated via a controlled interrupted time series analysis evaluating a nutritional excise tax policy. Our results clarify attainable bounds on robustness and efficiency under extrapolation and provide practical guidance for causal inference in modern observational studies.