Monte Carlo and Finite-Sample Evidence (ecta-robustness)

When to trigger

• The paper reports asymptotic theory but contains no finite-sample (Monte Carlo) check
• Coverage / size / power of a proposed test or interval is claimed but never simulated
• You have not probed where the regularity conditions bind or where the method breaks
• A theory result needs numerical illustration of comparative statics or equilibrium behavior

For methods papers, asymptotics without finite-sample evidence is a standard rejection reason. The Monte Carlo is not decoration — it is how the reader learns whether the asymptotic approximation is usable at realistic sample sizes.

Econometrica-specific: simulation results fall inside the Econometric Society Data and Code Availability Policy (which covers "empirical, experimental, and/or simulation results"). The ES Data Editor will run a pre-acceptance reproducibility check on your Monte Carlo, so every table must regenerate bit-for-bit from seeded code (see ecta-replication-package). This is a sharper bar than at applied siblings where simulation appendices are rarely re-run. A pure-theory paper with no simulations is exempt from that policy, but numerical illustration is still expected where it sharpens a result.

Designing the Monte Carlo

1. Designs that mirror the theory. Include DGPs where assumptions hold (to show the method works) and designs that approach the boundary of each assumption (to show how it degrades). One favorable design proves nothing.
2. Sample sizes that show convergence. Use several n (e.g., small, moderate, large) so the reader sees the asymptotics kicking in; report how fast.
3. Competitors. Compare against the natural existing method(s). A new estimator must beat or at least match what it replaces on bias, RMSE, size, or power.
4. Replications and Monte Carlo error. Use enough replications that reported size/coverage has small simulation error; report the number of replications and, where relevant, the Monte Carlo standard error so a 0.06 is distinguishable from 0.05.
5. Seeds. Fix and record seeds; the tables must be reproducible bit-for-bit (see ecta-replication-package).

What to report

Regularity and edge-case stress tests

• Assumption boundaries. For each key assumption, build a design that violates it slightly and show the consequence. This both demonstrates necessity and warns practitioners.
• Degenerate cases. Ties, empty cells, near-singular design matrices, heavy tails, serial dependence, heteroskedasticity — whichever your conditions rule out, probe the boundary.
• Tuning robustness. Vary every tuning parameter; if results are knife-edge in a knob, say so and give a data-driven choice.
• Misspecification. If the method is supposed to be robust to some misspecification, simulate it; if it is not, be explicit about that limitation.

For theory papers

A theory paper still benefits from numerical illustration: plot the equilibrium / value function / comparative-static across the parameter range, show the representation on a worked example, or compute the solution where closed forms are unavailable. Make clear this is illustration, not evidence of generality (the proof carries generality).

Execution bridge (StatsPAI / Stata MCP)

Run the battery, don't just enumerate it. Full map: execution-with-mcp. Econometrica publishes econometric theory and applied micro; the chain below serves its applied/empirical papers (weak-IV-robust and modern-DiD reporting expected) — pure theory uses its own apparatus.

• Many outcomes / specifications: romano_wolf (step-down FWER) or benjamini_hochberg.
• OVB sensitivity: oster_delta / sensemakr.
• Inference: wild_cluster_bootstrap (few clusters), twoway_cluster / conley.
• Re-fit off one handle: audit_result(result_id) lists missing checks + the exact suggest_function for each.
• Exhibits: etable / did_summary_to_latex from the handle — no retyped numbers.

Decisive checks in the body, exhaustive battery in the appendix. JF execution walkthrough.

Checklist

• At least one favorable design and one boundary / adverse design
• Multiple sample sizes showing the asymptotics engage
• Comparison against the natural competitor method(s)
• Number of replications stated; Monte Carlo error small / reported
• Size, power (size-adjusted), coverage, and length reported as relevant
• Tuning-parameter sensitivity examined
• Weak / near-boundary identification behavior shown if the theory has that regime
• Seeds fixed and recorded; tables reproducible

Anti-patterns

• Asymptotics with no finite-sample evidence at all
• A single, conveniently favorable DGP presented as comprehensive
• Reporting power without size control (or without size adjustment) so the comparison is unfair
• Too few replications, so a reported 0.05 size is within noise of 0.08
• Cherry-picking the tuning parameter that makes the method look best
• Comparing only to a strawman, not to the genuinely competitive existing method
• Claiming robustness to misspecification that is never simulated

Output format

【Designs】favorable: ...; boundary/adverse: ...
【Sample sizes】[...]   【Replications】...   【MC error reported】yes/no
【Competitors】[...]
【Metrics】bias/RMSE, size, power, coverage, length — [which reported]
【Tuning sensitivity】...
【Weak/boundary regime】examined / n.a.
【Gaps】[...]
【Next step】ecta-tables-figures