On the Foundations of the Design-Based Approach
The design-based paradigm may be adopted in causal inference and survey sampling when we assume Rubin's stable unit treatment value assumption (SUTVA) or impose similar frameworks. While often taken for granted, such assumptions entail strong claims about the data generating process. We develop an alternative design-based approach: we first invoke a generalized, non-parametric model that allows for unrestricted forms of interference, such as spillover. We define an associated set of inferential targets and discuss their interpretation under SUTVA and a weaker assumption that we call the No Unmodeled Revealable Variation Assumption (NURVA). We then reconstruct the standard paradigm, reconsidering SUTVA at the end rather than assuming it at the beginning. Despite its similarity to SUTVA, we demonstrate the practical limitations of NURVA alone for identifying substantively interesting quantities. In so doing, we provide clarity on the nature and importance of SUTVA for applied research.