Robustness, Extensions & Edge Cases (aejmic-robustness)

When to trigger

• The main result is proved but referees will ask "does it survive [relaxation]?"
• You have many possible extensions and must decide which belong in the paper
• A knife-edge or boundary case is unaddressed
• (Applied) The empirical/experimental result needs a robustness battery

What robustness means at AEJ: Micro

For a theory paper, robustness is about the mechanism's reach: which relaxations preserve the result, which break it, and which boundary cases need care. AEJ: Micro values knowing the edges of a result as much as the result. For structural/experimental work, it is the standard robustness battery. The discipline is the same: every extension must earn its place — it either broadens the contribution or defends a load-bearing assumption flagged in aejmic-identification.

Theory extensions — the menu (include only what earns its place)

• Relax a substantive assumption: continuum vs. finite types, asymmetric vs. symmetric players, correlated vs. independent values. Show the qualitative result survives or pin down where it changes.
• Alternative solution concept / refinement: does the result hold under a coarser or finer equilibrium notion? If it is concept-specific, say so.
• Perturbations: small changes to the information structure, timing, or commitment level (full → partial). Continuity/upper-hemicontinuity arguments belong here.
• Boundary and knife-edge cases: tie-breaking, measure-zero events, corner solutions — handle explicitly, do not hand-wave.
• Negative extensions are informative: an extension that fails and explains why sharpens the contribution and pre-empts a referee.

Applied / experimental robustness

• Alternative specifications/estimators; sensitivity to grids, tuning, and seeds (structural/simulation).
• Placebo / falsification; multiple-testing adjustment; subsample stability.
• Report as SEs / coverage sets, never significance asterisks.

The "earns its place" test

Before adding an extension, ask which of two jobs it does. If it does neither, cut it.

1. Broadens the contribution — the result now covers a setting readers care about (continuum types, dynamics, asymmetry) that the base model excluded.
2. Defends a load-bearing assumption — it answers the specific "is this knife-edge?" objection that aejmic-identification flagged.

An extension that merely re-derives the base result under a cosmetic re-parameterization fails the test and dilutes the paper.

Placement discipline

• Core extensions that change the reading: main text. Supporting extensions: online appendix. Do not bury a result-defining extension in supplementary material, and do not pad the main text with extensions that add nothing.
• A negative extension that explains a boundary of the result often belongs in the main text precisely because it sharpens the contribution; a routine confirmation belongs in the appendix.

Execution bridge (StatsPAI / Stata MCP)

Run the battery, don't just enumerate it. Full map: execution-with-mcp. AEJ: Micro spans applied and structural micro; the chain below is for the reduced-form / causal lane — structural estimation uses the field's own solvers.

• Many outcomes / specifications: romano_wolf (step-down FWER, accounts for cross-test correlation) or benjamini_hochberg — report the adjusted threshold.
• OVB sensitivity: oster_delta / sensemakr — the confounder strength that would overturn the headline.
• Inference: wild_cluster_bootstrap (few clusters), twoway_cluster / conley.
• Re-fit off one handle: audit_result(result_id) lists the missing checks and the exact suggest_function for each — no guessing the battery.
• Exhibits: etable / did_summary_to_latex from the handle — no retyped numbers.

Keep the decisive checks in the body and the exhaustive (now actually-run) battery in the appendix. See the executed chain in the JF execution walkthrough.

Checklist

• Listed candidate extensions; kept only those that broaden the contribution or defend a load-bearing assumption
• At least one substantive relaxation shows the qualitative result survives (or pins down where it changes)
• Boundary / knife-edge / tie-breaking cases handled explicitly
• Concept-dependence stated if the result is specific to one equilibrium notion
• (Applied) specification/placebo/seed-sensitivity battery run; SEs not asterisks
• Placement decided: result-defining → main text; supporting → appendix

Anti-patterns

• An extensions section that adds robustness checks no referee asked for and the result does not need (padding)
• Hand-waving a knife-edge assumption ("generically this does not matter") without argument
• Hiding a result-defining extension in the online appendix
• A robustness table with significance stars
• Claiming the mechanism is general while every extension quietly re-imposes the key assumption

Worked vignette (illustrative)

A contest-design paper proves the optimal prize structure is winner-take-all under risk-neutral, symmetric players. The earned extensions: (1) risk aversion — show winner-take-all survives up to a curvature threshold, beyond which prizes spread (broadens contribution and locates the edge); (2) asymmetry — show the result fails and explain why (a negative extension that sharpens the mechanism). A non-earned extension would be re-deriving the symmetric case with a trivially different payoff normalization — drop it.

Output format

【Extension menu considered】[...]
【Kept (and why)】broadens contribution / defends load-bearing assumption
【Survives】[relaxation → result holds, with any new condition]
【Breaks / boundary】[case → what changes, handled how]
【Applied robustness】[specs / placebo / seeds] — SEs not asterisks
【Placement】main text: [...]; appendix: [...]
【Next step】aejmic-tables-figures