Result Presentation: Propositions, Examples & Exhibits (aejmic-tables-figures)

When to trigger

• Propositions are buried in prose or stated imprecisely
• A numerical example would make an abstract result concrete but is missing or cluttered
• A schematic figure (timeline, type space, equilibrium region) would help but is not drawn
• (Applied/experimental) tables are dense or carry significance asterisks

Presenting a theory-first result

AEJ: Micro results are mostly propositions, characterizations, and numerical examples, not regression tables. The exhibit job is to make a formal result legible and concrete.

Propositions and theorems

• State each as a numbered, self-contained Proposition/Theorem/Lemma: a reader should grasp it without re-reading the model.
• Put the economic content first in surrounding prose ("Higher search costs raise equilibrium prices because…"), then the formal statement.
• Define every symbol at first use; keep notation consistent across statements; minimize ad-hoc subscripts.

Numerical examples (the AEJ: Micro workhorse)

• Use a small, transparent parameterization to illustrate the mechanism, not to "test" it — say which proposition it instantiates.
• Show the moving part: a table or plot of the key object (optimal mechanism, equilibrium strategy, welfare) as a primitive varies.
• Report enough to reproduce (parameter values, grid) — these go in the replication package.

Schematic theory figures

• Timelines for extensive-form games; type-space / signal partitions for information design; equilibrium-region plots in parameter space; best-response diagrams.
• Vector output; readable labels; no chartjunk. A figure should carry one idea.

Applied / experimental tables

• Three-line tables; report standard errors and confidence sets, not significance asterisks (AEA house norm for inference presentation).
• Place exhibits near their discussion; self-contained notes (sample, units, what each column is).

Choosing the right exhibit for the result

What you want to convey	Best exhibit
A characterization holds	A numbered Proposition + an intuition sentence; rarely a table
How an optimum moves with a primitive	A numerical-example plot (object vs. primitive)
The structure of an equilibrium	A schematic (timeline, partition, region plot)
A magnitude from estimation/experiment	A three-line table with SEs / coverage sets
Model fit (structural)	Data vs. model overlay, not a fit statistic alone

Pick one exhibit per idea. If a sentence does the job, do not add a figure; an AEJ: Micro theory paper can be exhibit-light without penalty.

Execution bridge (StatsPAI / Stata MCP)

Generate exhibits from the fitted result, not by retyping numbers (the usual source of body-vs-appendix drift). Full map: execution-with-mcp.

• Tables: etable (multi-model columns) or did_summary_to_latex straight from the result_id — one variable definition, one set of numbers, body and appendix in sync.
• Figures: plot_from_result / enhanced_event_study_plot / event_study_table — axis units and the SE/clustering note baked in.
• Every note names the estimator + clustering (from the result's diagnostics) and states the magnitude in interpretable units.

See a full fitted-result → exhibit chain in the JF execution walkthrough.

Checklist

• Every formal result is a numbered, self-contained Proposition/Theorem/Lemma
• Economic content precedes the formal statement in prose
• Notation defined at first use and consistent across exhibits
• Numerical example states which proposition it illustrates and is reproducible
• Schematic figures carry one idea each; vector output; clean labels
• (Applied) tables report SEs / coverage sets, no significance asterisks
• Exhibits placed near discussion; notes self-contained

Anti-patterns

• A proposition stated only inside a paragraph, un-numbered and un-restated
• A numerical example with a dozen parameters and no statement of what it shows
• Overloaded figures (multiple unrelated panels, dense legends, chartjunk)
• Inconsistent or ad-hoc notation across statements
• Significance asterisks in an empirical/experimental table

Worked vignette (illustrative)

An information-design paper proves the sender-optimal signal is a two-message partition. The presentation: state Proposition 2 cleanly ("The sender-optimal signal partitions the state into {low, high} with cutoff x*"), precede it with the intuition (pooling above x* maximizes the receiver's action while preserving credibility), then a schematic figure of the state line with the cutoff and a small numerical example showing how x* moves with the sender's bias. No regression table, no asterisks — the exhibits make the mechanism visible.

Output format

【Formal results】numbered propositions/theorems, each self-contained? [Y/N]
【Economic-content-first prose】present for each? [Y/N]
【Numerical example】illustrates which proposition; reproducible? [Y/N]
【Schematic figures】one idea each; vector; clean labels? [Y/N]
【Applied tables】SEs/coverage, no asterisks? [Y/N or N/A]
【Next step】aejmic-writing-style