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.
- Broadens the contribution — the result now covers a setting readers care about (continuum types, dynamics, asymmetry) that the base model excluded.
- Defends a load-bearing assumption — it answers the specific "is this knife-edge?" objection that
aejmic-identificationflagged.
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) orbenjamini_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 exactsuggest_functionfor each — no guessing the battery. - Exhibits:
etable/did_summary_to_latexfrom 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
Source: brycewang-stanford/Awesome-Journal-Skills → AEJ-Microeconomics-Skills/skills/aejmic-robustness/SKILL.md