Identification & Asymptotic Strategy (joe-identification-strategy)

When to trigger

• The estimand is not formally identified, or identification is asserted not proved
• Regularity conditions are stated loosely or are non-primitive (they smuggle in the conclusion)
• The limiting distribution / convergence rate is claimed without a derivation path
• You are unsure the result is general enough, or whether the conditions are verifiable

The JoE formal bar

At the Journal of Econometrics, "identification strategy" means the formal core: the assumptions under which the estimand is identified, the estimator is consistent, and inference is valid. The house norm is mathematical rigor — proofs and asymptotic derivations are expected, and referees probe whether conditions are primitive and verifiable, whether the asymptotics are honest, and whether the result generalizes beyond a convenient special case. This is methodology, not applied causal design: the deliverable is theorems plus the Monte Carlo that shows the asymptotics bite in finite samples.

The formal-core checklist

1. Identification

• State the estimand and the model precisely. Prove identification (the map from the distribution of observables to the parameter is unique) before estimation. Distinguish point vs. partial identification.
• If identification is weak or fails on a boundary (weak instruments, near-unit-root, near-singular Jacobian), say so and provide identification-robust inference rather than hiding it.

2. Assumptions / regularity conditions

• List each assumption and label it (moment existence, smoothness, mixing/dependence, bandwidth/rate conditions, rank/full-rank, parameter-space compactness).
• For each: is it primitive (on the DGP/data) or high-level (on objects derived from the estimator)? Prefer primitive; justify any high-level condition and verify it for a leading example.
• Check none of them silently assume the conclusion (e.g., assuming the very uniform convergence you need).

3. Asymptotic theory

• Lay out the proof path: consistency (ULLN / argmax) → rate → asymptotic distribution (CLT / Delta method / empirical-process tools) → variance estimator.
• State the convergence rate and the limiting distribution; derive or cite the standard-error / variance estimator and prove it is consistent.
• Handle nuisance parameters, tuning (bandwidth, lag length, penalty), and any first-stage estimation (Neyman-orthogonality / influence-function corrections) explicitly.

4. Generality

• State the class of models/DGPs the result covers; flag what is excluded and why.
• Show the result nests or extends known cases (a sanity check and a positioning device).

5. Proof exposition

• Map theorems → lemmas; keep the main text's intuition, push routine algebra to an appendix.
• Make each step auditable; a referee should reconstruct the argument without guessing.

Numerical / Monte Carlo confirmation (light here, full in joe-data-analysis)

• Cross-check a derived asymptotic variance against a high-replication Monte Carlo; a mismatch usually signals an algebra error. The full size/power design lives in joe-data-analysis.

Assumption audit

Turn the formal core into an assumption audit table:

Use the table to police the paper's language. If an assumption is high-level, either verify it for a leading example or state clearly that it is a sufficient technical condition. If a theorem relies on an assumption that is never invoked in the proof map, delete or relocate it.

Execution bridge (StatsPAI / Stata MCP)

Estimate and audit the design, don't only describe it. Full map: execution-with-mcp. Journal of Econometrics is a methods venue — estimator validity + simulation evidence are the contribution; pair estimates with diagnostics and Monte-Carlo where relevant.

• detect_design → recommend → fit with as_handle=true → audit_result.
• Observational causal claims: staggered DiD (callaway_santanna / sun_abraham + bacon_decomposition + honest_did_from_result); IV (effective_f_test + anderson_rubin_ci); RDD (rdrobust + mccrary_test).
• Experiments: randomization-based inference + romano_wolf for many-outcome control.
• Sensitivity: oster_delta / sensemakr for observational claims.

Report the magnitude in interpretable units; route the full battery to the appendix. A run end-to-end (synthetic data, real returns) is in the JF execution walkthrough.

Anti-patterns

• "Under standard regularity conditions" with no list and no verification
• High-level assumptions chosen so the theorem is one line — but unverifiable in any real model
• Asserting asymptotic normality with no derivation or no consistent variance estimator
• Ignoring weak/partial identification when the design is on its boundary
• Treating assumptions as a preamble rather than linking each one to a theorem step

Output format

【Estimand & model】...
【Identification】point/partial; proof sketch
【Assumptions】[A1 primitive, A2 high-level (justified), ...]
【Assumption audit】primitive/high-level, theorem use, failure mode
【Asymptotics】rate + limiting distribution + variance estimator
【Generality】class covered; what is excluded; nested cases
【Proof plan】theorems → lemmas → appendix
【Next step】joe-data-analysis