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
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
1---2name: aejmic-tables-figures3description: Result Presentation: Propositions, Examples & Exhibits (aejmic-tables-figures)4---56# Result Presentation: Propositions, Examples & Exhibits (aejmic-tables-figures)78## When to trigger910- Propositions are buried in prose or stated imprecisely11- A numerical example would make an abstract result concrete but is missing or cluttered12- A schematic figure (timeline, type space, equilibrium region) would help but is not drawn13- (Applied/experimental) tables are dense or carry significance asterisks1415## Presenting a theory-first result1617AEJ: Micro results are mostly **propositions, characterizations, and numerical examples**, not regression tables. The exhibit job is to make a formal result **legible and concrete**.1819### Propositions and theorems20- State each as a **numbered, self-contained** Proposition/Theorem/Lemma: a reader should grasp it without re-reading the model.21- Put the **economic content first** in surrounding prose ("Higher search costs *raise* equilibrium prices because…"), then the formal statement.22- Define every symbol at first use; keep notation consistent across statements; minimize ad-hoc subscripts.2324### Numerical examples (the AEJ: Micro workhorse)25- Use a small, transparent parameterization to **illustrate the mechanism**, not to "test" it — say which proposition it instantiates.26- Show the moving part: a table or plot of the key object (optimal mechanism, equilibrium strategy, welfare) as a primitive varies.27- Report enough to reproduce (parameter values, grid) — these go in the replication package.2829### Schematic theory figures30- Timelines for extensive-form games; **type-space / signal partitions** for information design; **equilibrium-region** plots in parameter space; best-response diagrams.31- Vector output; readable labels; no chartjunk. A figure should carry one idea.3233### Applied / experimental tables34- Three-line tables; **report standard errors and confidence sets, not significance asterisks** (AEA house norm for inference presentation).35- Place exhibits near their discussion; self-contained notes (sample, units, what each column is).3637### Choosing the right exhibit for the result3839| What you want to convey | Best exhibit |40|---|---|41| A characterization holds | A numbered Proposition + an intuition sentence; rarely a table |42| How an optimum moves with a primitive | A numerical-example plot (object vs. primitive) |43| The structure of an equilibrium | A schematic (timeline, partition, region plot) |44| A magnitude from estimation/experiment | A three-line table with SEs / coverage sets |45| Model fit (structural) | Data vs. model overlay, not a fit statistic alone |4647Pick 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.4849## Execution bridge (StatsPAI / Stata MCP)5051Generate exhibits from the fitted result, not by retyping numbers (the usual source of52body-vs-appendix drift). Full map: [`execution-with-mcp`](../../../shared-resources/empirical-methods/execution-with-mcp.md).5354- **Tables:** `etable` (multi-model columns) or `did_summary_to_latex` straight from the55 `result_id` — one variable definition, one set of numbers, body and appendix in sync.56- **Figures:** `plot_from_result` / `enhanced_event_study_plot` / `event_study_table` —57 axis units and the SE/clustering note baked in.58- **Every note** names the estimator + clustering (from the result's diagnostics) and59 states the magnitude in interpretable units.6061See a full fitted-result → exhibit chain in the [JF execution walkthrough](../../../Journal-of-Finance-Skills/resources/worked-examples/02-execution-walkthrough.md).62## Checklist6364- [ ] Every formal result is a numbered, self-contained Proposition/Theorem/Lemma65- [ ] Economic content precedes the formal statement in prose66- [ ] Notation defined at first use and consistent across exhibits67- [ ] Numerical example states which proposition it illustrates and is reproducible68- [ ] Schematic figures carry one idea each; vector output; clean labels69- [ ] (Applied) tables report SEs / coverage sets, no significance asterisks70- [ ] Exhibits placed near discussion; notes self-contained7172## Anti-patterns7374- A proposition stated only inside a paragraph, un-numbered and un-restated75- A numerical example with a dozen parameters and no statement of what it shows76- Overloaded figures (multiple unrelated panels, dense legends, chartjunk)77- Inconsistent or ad-hoc notation across statements78- Significance asterisks in an empirical/experimental table7980## Worked vignette (illustrative)8182An 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.8384## Output format8586```87【Formal results】numbered propositions/theorems, each self-contained? [Y/N]88【Economic-content-first prose】present for each? [Y/N]89【Numerical example】illustrates which proposition; reproducible? [Y/N]90【Schematic figures】one idea each; vector; clean labels? [Y/N]91【Applied tables】SEs/coverage, no asterisks? [Y/N or N/A]92【Next step】aejmic-writing-style93```
gabrielmoreira