Specification of placebo regressions (add vs replace)

Ascertain a principled specification for placebo regression experiments in clustered settings—specifically, whether placebo regressors should replace the actual regressor of interest or be added alongside it—and delineate the conditions under which each approach yields valid and interpretable diagnostics of inferential reliability.

Background

Placebo regressions serve as a diagnostic to assess the reliability of inference by simulating regressors unrelated to the outcome. There are at least two variants—adding the placebo regressor or replacing the original regressor—and model misspecification concerns can affect interpretations. The paper notes ambiguity about how to specify these experiments, indicating a methodological gap.