"Post" Pre-Analysis Plans: Valid Inference for Non-Preregistered Specifications

Pre-analysis plans (PAPs) have become standard in experimental economics research, but it is nevertheless common to see researchers deviating from their PAPs to supplement preregistered estimates with non-prespecified findings. While such ex-post analysis can yield valuable insights, there is broad uncertainty over how to interpret -- or whether to even acknowledge -- non-preregistered results. In this paper, we consider the case of a truth-seeking researcher who, after seeing the data, earnestly wishes to report additional estimates alongside those preregistered in their PAP. We show that, even absent "nefarious" behavior, conventional confidence intervals and point estimators are invalid due to the fact that non-preregistered estimates are only reported in a subset of potential data realizations. We propose inference procedures that account for this conditional reporting. We apply these procedures to Bessone et al. (2021), which studies the economic effects of increased sleep among the urban poor. We demonstrate that, depending on the reason for deviating, the adjustments from our procedures can range from having no difference to an economically significant difference relative to conventional practice. Finally, we consider the robustness of our procedure to certain forms of misspecification, motivating possible heuristic checks and norms for journals to adopt.