When Do Treatment Changes Identify Causal Effects?

Economics > Econometrics [Submitted on 1 Jun 2026] Title:When Do Treatment Changes Identify Causal Effects? View PDF HTML (experimental)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. Current browse context: econ.EM References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.