Identification & What Makes the Result Tight (aejmic-identification)

AEJ: Micro is theory-first, so "identification" here is two things. For pure theory it means: which assumptions are doing the work, and how tight/robust the mechanism is. For structural and experimental work it means the standard data-to-object mapping. Pick the branch.

When to trigger

• (Theory) A referee asks whether the result is a knife-edge artifact of one assumption
• (Theory) You cannot say cleanly which primitive drives the comparative static
• (Structural) Parameters are estimated but it is unclear what in the data identifies them
• (Experimental) The estimand or the assumptions behind the treatment effect are not pinned down

Branch A: Pure theory — what makes the result tight

The AEJ: Micro bar is that the reader sees exactly which assumption is load-bearing and how far the mechanism extends.

• Decompose the assumptions. For each substantive assumption, ask: is the result false without it, weaker without it, or unchanged (then it was WLOG — say so)? The result is "tight" when you can name the assumption that breaks it.
• Comparative statics as identification. Show the sign/magnitude of the key comparative static and what primitive drives it (single-crossing? a supermodularity? a curvature condition?). Monotone-comparative-statics tools (Topkis, Milgrom–Shannon) make the driver explicit.
• Necessity, not just sufficiency. Where you can, show the assumption is necessary (a counterexample when it fails), not merely sufficient — this is what makes a characterization tight.
• Robustness of the mechanism (then hand to aejmic-robustness for full extensions): does the result survive a small perturbation of the information structure, the timing, or the type distribution?

Branch B: Structural / empirical IO

• Name what identifies each parameter. Tie parameters to specific data features / moments; argue identification from the model's structure, not "the estimator converged."
• Targeted vs. untargeted moments; report a sensitivity/informativeness measure so readers see which data move which parameters.
• Estimation regularity: objective (MLE/GMM/MSM), starting values, tolerances, multi-start; Monte Carlo recovery of known parameters.
• Counterfactual validity: argue the estimated parameters are policy-invariant enough for the counterfactual (Lucas critique).
• For reduced-form companions, use design-appropriate diagnostics (pre-trends, first-stage strength, density tests) and report SEs, not asterisks.

Branch C: Experimental (theory-grounded)

• Design maps to the model: each treatment isolates a model primitive or prediction; state the estimand.
• Pre-registration in a recognized registry where applicable; report deviations; include instructions/transcripts.
• Randomization balance; attrition (Lee bounds if differential); multiple-hypothesis adjustment; external-validity scope.

Execution bridge (StatsPAI / Stata MCP)

Estimate and audit the identification claim, don't only argue 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.

1. detect_design → recommend → fit with as_handle=true → audit_result to list the checks the design still owes.
2. Staggered DiD: callaway_santanna / sun_abraham + bacon_decomposition + honest_did_from_result (the pre-trend test is low-power, Roth 2022).
3. IV: effective_f_test + an anderson_rubin_ci (valid under weak instruments), not a 2SLS t-stat alone.
4. RDD: rdrobust (bias-corrected) + rddensity / mccrary_test for manipulation.
5. OVB: oster_delta / sensemakr — how strong a confounder would have to be.

Report the economic magnitude; route the full battery to the appendix; keep every number reproducible. A run end-to-end (synthetic data, real returns) is in the JF execution walkthrough. If StatsPAI/Stata are not connected, adapt the vendored resources/code/ skeleton and flag any unverified number.

Checklist

• Branch chosen; the "what makes it tight / what identifies it" question answered in one sentence
• Theory: each substantive assumption classified (false/weaker/WLOG without it); the load-bearing one named
• Theory: key comparative static signed with its driving primitive; necessity shown where possible
• Structural: each parameter tied to identifying moments; sensitivity + Monte Carlo recovery
• Experimental: estimand stated; pre-registered; balance/attrition/MHT handled
• Inference (applied): SEs / coverage sets, never asterisks; clustering correct

Anti-patterns

• (Theory) A result whose driving assumption is never identified — "it just works"
• (Theory) Claiming a characterization is tight without a counterexample when the assumption fails
• (Structural) "The estimator converged" presented as identification
• (Structural) A counterfactual on calibrated parameters with no policy-invariance argument
• (Experimental) No pre-registration or no stated estimand; significance asterisks instead of SEs

Worked vignette (illustrative)

A matching paper proves stability is preserved under a new preference domain. A referee suspects it rides on a substitutability condition. The AEJ: Micro answer names it: "Substitutability is load-bearing — without it, Example 3 exhibits an empty core; with the weaker 'unilateral substitutes' condition the existence result survives but uniqueness fails." That sentence makes the result tight: the necessary assumption is named, and the cost of relaxing it is shown.

Output format

【Branch】theory / structural / experimental
【What makes it tight / data-to-object】one sentence
【Load-bearing assumption(s) or identifying moments】[...]
【Tightness evidence】counterexample-on-failure / sensitivity+Monte Carlo / balance+estimand
【What it does NOT establish】[...]
【Next step】aejmic-robustness (extensions/edge cases)