Ier Identification

Identification Strategy (ier-identification)

When to trigger

• A structural model's parameters are estimated but it is unclear what in the data identifies each one
• The headline counterfactual is suspected to be driven by a calibrated elasticity nobody defends
• An empirical causal claim rests on OLS + controls, or TWFE on staggered timing
• A referee says the result is "calibration in disguise" or "not credibly identified"
• For a theory paper, you need to confirm the result is pinned (which assumption identifies it) — though the tightness craft lives in ier-theory-model

The IER identification bar

IER prizes a clean model-to-evidence link, so identification is judged by one test: is the mapping from data to the object of interest explicit and defended? The object differs by branch, and so does what "identified" means. Pick the branch and make the mapping transparent — a referee should be able to point at the data feature that moves each estimate.

Branch A: Structural / quantitative (the IER core)

This is where most IER identification debates happen. The failure mode is treating "the estimator converged" as if it were identification.

• Name what identifies each parameter. Tie every structural parameter to a specific data moment or feature, and argue identification from the model's structure — e.g., "the trade elasticity is identified by the response of bilateral flows to tariff variation," not "by the GMM objective."
• Targeted vs. untargeted moments. Report fit to targeted moments; then show untargeted moments the model was not fit to but still matches — this is the out-of-sample discipline IER readers want.
• Sensitivity / informativeness. Report a sensitivity matrix (à la Andrews–Gentzkow–Shapiro) so readers see which moment moves which parameter, and by how much.
• Estimation regularity. State the objective (MLE / GMM / MSM / SMM / indirect inference), starting values, tolerances, and global-optimum evidence (multi-start). Show Monte Carlo recovery of known parameters.
• Counterfactual validity. Argue the estimated parameters are policy-invariant enough for the counterfactual you run (the Lucas critique applies); show they are not functions of the policy you change.

Branch B: Empirical causal design (applied micro)

• DID / event study. With staggered adoption, move beyond TWFE (Callaway–Sant'Anna, Sun–Abraham, de Chaisemartin–D'Haultfœuille); show a clean event study with leads; report a Goodman-Bacon decomposition.
• IV. Strong first stage; with weak instruments use Anderson–Rubin / weak-IV-robust sets; defend exclusion in theory, institutions, and falsification.
• RDD. Density test (McCrary / Cattaneo–Jansson–Ma); optimal bandwidth + robustness; covariate smoothness; bias-corrected CIs.
• Cluster at the assignment level; address few-cluster issues (wild-cluster bootstrap).

Branch C: Econometric method / theory

• Identification here means the conditions under which the estimand is point- (or partially-) identified. State them as assumptions, show what the data must satisfy, and connect to the tightness craft in ier-theory-model.
• Where point identification fails, do not abandon the object — characterize the identified set and show how it shrinks with stronger but credible assumptions. IER referees respect honest partial identification over an overclaimed point estimate.

The boundary with ier-theory-model

These two skills divide one question. ier-theory-model asks "is the result tight and general as a theoretical object" — which assumptions are load-bearing, is the comparative static signed. ier-identification asks "is the object recoverable from data" — what moment moves the parameter, what variation supports the causal claim. A structural paper needs both: a tight model whose parameters are also empirically pinned. When a referee says "this is calibration in disguise," that is an identification failure even if the model is theoretically immaculate — route it here, not to ier-theory-model.

The sensitivity matrix as the IER identification exhibit

For structural papers, the most persuasive single piece of identification evidence is a sensitivity matrix (Andrews–Gentzkow–Shapiro) showing, for each parameter, how its estimate would move if each targeted moment shifted. This converts the abstract claim "the model is identified" into a checkable map: the referee sees that the trade elasticity is driven mainly by the tariff-flow moment, the fixed cost by the extensive-margin moment, and so on. When a parameter's row shows it responds to every moment a little and no moment a lot, that is the data signature of weak identification — and reporting it honestly, with the corrective (a better moment, or a partial-identification statement), is far stronger than hiding it behind a converged objective.

Distinguishing calibration from estimation cleanly

IER's structural readers draw a sharp line between estimated parameters (recovered from data with stated identification) and calibrated/external parameters (set from outside the model). Both are legitimate, but conflating them invites the "calibration in disguise" reject. State explicitly which parameters are estimated and which are external; for each external one, cite the source and carry it into the ier-robustness range analysis. The failure mode is presenting an externally-set parameter as if the model estimated it — referees notice, and the credibility of the whole exercise drops.

Execution bridge (StatsPAI / Stata MCP)

Estimate and audit the identification claim, don't only argue it. Full map: execution-with-mcp. IER is theory-forward and quantitative; the chain below serves its empirical lane — structural / quantitative 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 data-to-object mapping stated in one sentence
• Structural: each parameter tied to an identifying moment/feature; sensitivity matrix + Monte Carlo recovery shown
• Structural: untargeted-moment validation reported; counterfactual policy-invariance argued
• Empirical: design-appropriate diagnostics (pre-trends / density / first-stage / balance); modern estimator where TWFE would bias
• Inference: clustering at the assignment level; few-cluster correction if needed
• The claim never exceeds what the identification supports; what it does NOT identify is stated

Anti-patterns

• "The estimator converged" or "the likelihood is maximized" presented as identification (structural)
• A headline counterfactual driven by a calibrated parameter with no identifying argument
• TWFE on staggered treatment with no heterogeneity-bias discussion (empirical)
• Running a policy counterfactual without arguing the parameters are policy-invariant
• Reporting only targeted-moment fit and calling the model validated

Worked vignette: identifying a trade elasticity (illustrative)

A quantitative trade model is estimated and the welfare gain from a tariff cut is the headline. A referee asks what identifies the trade elasticity. A weak answer points at the GMM objective. An IER answer points at a data feature: the elasticity is identified by how bilateral flows respond to plausibly-exogenous tariff variation, and the sensitivity matrix shows that this moment moves the elasticity from, say, 4.0 to 5.5 (illustrative) — making identification visible. Pair it with Monte Carlo recovery (simulated data returns the true elasticity within a few percent) and an untargeted moment the model still matches.

Referee pushback mapped to the identification fix

• "This is calibration in disguise — not credibly identified." → Show the sensitivity matrix tying each parameter to a moment; report untargeted-moment fit.
• "Your counterfactual assumes policy-invariant parameters you never defend." → Argue invariance (Lucas critique); show the parameters are not functions of the policy you change.
• "Staggered TWFE is biased here." → Re-estimate with Callaway–Sant'Anna / Sun–Abraham; show flat event-study leads and a Goodman-Bacon decomposition.
• "The exclusion restriction is asserted, not defended." → Defend it in theory, institutions, and a falsification test; if instruments are weak, report Anderson–Rubin sets.

Output format

【Journal】International Economic Review
【Skill】ier-identification
【Branch】structural / empirical-causal / econometric-method
【Data-to-object mapping】one sentence: what feature identifies the key object
【Identification evidence】[sensitivity matrix + Monte Carlo / pre-trends+first-stage+density / formal conditions]
【Out-of-sample / falsification】untargeted moments or placebo/falsification shown? [Y/N]
【Counterfactual / external validity】policy-invariance or generalizability argued? [Y/N]
【What it does NOT identify】the object(s) out of reach
【Verdict】credible / needs-work
【Next skill】ier-robustness