When Do Treatment Changes Identify Causal Effects?

2026-06-01

AI Summary

This study investigates the validity conditions for identifying causal effects using changes in treatment variables rather than their levels, and examines the relationship between this approach and conventional methods. By developing two non-nested structural models and integrating structural causal modeling with difference-in-differences and two-period fixed-effects regression, the authors theoretically demonstrate that strategies based on treatment changes and treatment levels are generally non-nested but become equivalent under specific conditions. They propose a corresponding overidentification test to assess these conditions. Simulation evidence confirms the favorable finite-sample performance of the proposed method, and an empirical application to cigarette demand estimation supports its practical validity. The work clarifies the fundamental distinctions and connections between these two causal identification strategies, thereby extending the methodological foundations of causal inference.

Abstract

This paper clarifies the identifying assumptions underlying causal inference based on treatment changes rather than treatment levels, and their relationship to conventional identification strategies. We characterize two distinct structural models, with non-nested identifying assumptions, under which treatment-change identification is valid conditional on observed covariates. We demonstrate that the identifying assumptions relying on treatment changes are generally not nested with those of methods relying on treatment levels, such as selection-on-observables strategies that control for past outcomes, treatments, and covariates, or difference-in-differences approaches that difference outcomes rather than treatments over time. We show, however, that under a random-walk restriction on the treatment process, conditioning on treatment changes is equivalent to conditioning on treatment levels given lagged treatment. This and other equivalence results motivate overidentification tests by jointly considering methods based on treatment levels and changes. Beyond these tests, the non-nesting results carry a structural double robustness implication: an estimator that differences both the outcome and the treatment over time, such as two-way fixed effects regression, remains consistent if either the treatment-change assumption or the parallel-trends assumption holds, without requiring both simultaneously. We characterize the causal models consistent with each method, investigate finite-sample behavior in a simulation study, and present an empirical application to cigarette demand.

Problem

• causal inference
• treatment changes
• identification assumptions
• treatment levels
• non-nested assumptions

Innovation

• treatment changes
• causal identification
• non-nested assumptions
• structural double robustness
• random walk treatment process