Optimal Pre-Analysis Plans: Statistical Decisions Subject to Implementability

What is the purpose of pre-analysis plans, and how should they be designed? We model the interaction between an agent who analyzes data and a principal who makes a decision based on agent reports. The agent could be the manufacturer of a new drug, and the principal a regulator deciding whether the drug is approved. Or the agent could be a researcher submitting a research paper, and the principal an editor deciding whether it is published. The agent decides which statistics to report to the principal. The principal cannot verify whether the analyst reported selectively. Absent a pre-analysis message, if there are conflicts of interest, then many desirable decision rules cannot be implemented. Allowing the agent to send a message before seeing the data increases the set of decisions rules that can be implemented, and allows the principal to leverage agent expertise. The optimal mechanisms that we characterize require pre-analysis plans. Applying these results to hypothesis testing, we show that optimal rejection rules pre-register a valid test, and make worst-case assumptions about unreported statistics. Optimal tests can be found as a solution to a linear-programming problem.