Aer identification

AER Identification

Overview

In AER-track empirical economics, identification is the paper. This skill routes among canonical designs, modern defaults, and referee-facing diagnostics.

If the design is fragile, return to aer-topic-selection; writing cannot save it.

When to Use

• Designing the empirical strategy for a new project
• The current strategy is TWFE / first-stage F / naive RDD and the referee will flag it
• A prior submission was rejected on identification grounds and the design needs rebuilding
• Choosing between two candidate identification strategies for the same question

Master Decision Tree

Is treatment assignment plausibly random conditional on observables?
├── Yes, by design (RCT, lottery) → run the RCT analysis; register PAP via AEA RCT Registry
└── No → identification must come from variation
    ├── Sharp threshold in a running variable → RDD (sharp or fuzzy)
    ├── Discrete policy change in some units, not others, over time → DiD
    │     ├── Single treatment date → canonical 2×2 DiD
    │     └── Staggered adoption → Callaway-Sant'Anna or Borusyak-Jaravel-Spiess
    ├── Endogenous regressor + plausibly exogenous shifter → IV
    │     ├── Shifter × pre-existing exposure shares → shift-share / Bartik
    │     └── Single instrument → weak-IV-robust inference if F < 50
    ├── One treated unit / aggregate intervention → synthetic control
    └── None of the above → reconsider the question

Difference-in-Differences

Canonical 2×2 (single treatment date, two groups)

Use TWFE if and only if:

• Treatment timing is simultaneous for all treated units
• The control group is never treated
• Treatment-effect heterogeneity is implausible

Otherwise, TWFE produces biased and often sign-flipped estimates.

Staggered Adoption (most modern applications)

Do not use TWFE. Use one of:

• Callaway and Sant'Anna (2021) — csdid (Stata), did (R). Identifies group-time average treatment effects (ATT(g,t)); estimands are doubly robust; supports event-study aggregation.
• Borusyak, Jaravel, and Spiess (2024) — imputation estimator.
• de Chaisemartin and D'Haultfœuille (2020) — did_multiplegt.
• Sun and Abraham (2021) — interaction-weighted estimator for event studies.

Required diagnostics:

1. Goodman-Bacon decomposition to show the share of weight from "forbidden" comparisons under TWFE
2. Event-study plot with the imputation or Callaway-Sant'Anna estimator
3. Pre-trends test reported as the joint test, not just the visual
4. Heterogeneity by treatment cohort

Pre-Trends

A flat pre-trend is necessary but not sufficient. Report:

• Visual event-study plot with 95% confidence intervals
• Formal joint test of pre-period coefficients (p-value)
• Honest DiD (Rambachan-Roth 2023) sensitivity bounds for the post-period

Instrumental Variables

Weak Instruments

The first-stage F > 10 rule is obsolete. Modern conventions:

• Just-identified models: report Anderson-Rubin (AR) confidence sets as primary inference; AR keeps size under weak instruments.
• For F < 50: 2SLS confidence intervals are unreliable; AR is required, not optional.
• Stock-Yogo TSLS-bias critical values assume homoskedasticity and rarely fit clustered settings.

Use weakivtest (Stata), ivDiag (R), or the Olea-Pflueger effective F statistic.

Exclusion Restriction

The IV's credibility depends on a story, not a test. State the exclusion restriction in one sentence in the introduction and defend it with:

• Institutional narrative (one paragraph)
• A placebo regression where the instrument predicts an outcome it should not affect
• Sensitivity analysis: how much exclusion-restriction violation would overturn the result (Conley et al. 2012)

Shift-Share / Bartik

Two valid sources of identification, with very different implications:

1. Exogenous shares (Goldsmith-Pinkham, Sorkin, Swift 2020) — argue that pre-existing exposure shares are conditionally exogenous; report the Rotemberg weights and inspect the top-5 industries driving identification.
2. Exogenous shocks (Borusyak, Hull, Jaravel 2022; Adão, Kolesár, Morales 2019) — argue that aggregate shocks are as-good-as-random; report shock-level inference.

Pick one explicitly. Do not hand-wave between the two.

Regression Discontinuity

Modern Defaults

• Local linear regression with a triangular kernel. Polynomials of order > 1 are discouraged (Gelman-Imbens 2019).
• MSE-optimal bandwidth (Calonico-Cattaneo-Titiunik 2014) with the robust bias-corrected confidence interval. Use rdrobust.
• Donut RDD if bunching near the cutoff is a concern.
• Covariate adjustment for efficiency; main result must hold without it.

Required Diagnostics

1. McCrary (2008) / Cattaneo-Jansson-Ma (2020) density test for manipulation of the running variable
2. Balance tests on predetermined covariates at the cutoff
3. Placebo cutoffs away from the true threshold
4. Bandwidth sensitivity — show the estimate across at least three bandwidths
5. Visual RD plot using rdplot with the binning method explicitly stated

Synthetic Control

When Appropriate

• One (or few) treated units
• Long pre-treatment outcome series (≥ 10 periods)
• A large donor pool of plausibly comparable untreated units
• Aggregate intervention (policy at the country, state, city level)

Modern Extensions

• Generalized synthetic control (Xu 2017) for multiple treated units
• Augmented synthetic control (Ben-Michael, Feller, Rothstein 2021) for bias correction
• Synthetic DiD (Arkhangelsky et al. 2021) combining SCM and DiD weighting

Required Diagnostics

1. Placebo (in-time): apply SCM to pre-treatment fake intervention dates
2. Placebo (in-space): apply SCM to every donor as if it were treated; report the distribution of placebo effects
3. Permutation inference / Fisher exact p-value
4. Weight vector reported in the appendix; donors with > 10% weight discussed

Field Experiments and RCTs

If the paper uses a field experiment:

• Register with AEA RCT Registry before the intervention begins. AEA journals require this prior to submission.
• Pre-analysis plan (PAP) posted before unblinding. Per Olken and others, keep the PAP moderate in scope — pre-specify primary outcomes and the analysis specification, leave exploratory work clearly labeled as such.
• Power calculations in the manuscript or appendix.
• Multiple-hypothesis correction if more than one primary outcome.
• Attrition documented and tested for differential attrition by treatment arm.

Mechanism vs. Identification

A common confusion: identification answers whether X causes Y; mechanism answers why. Mechanism evidence should not weaken the identification of the main effect. Run:

• Subgroup heterogeneity (does the effect concentrate where theory predicts?)
• Mediation analysis only if the mediator is itself plausibly exogenous (rare)
• Auxiliary outcomes consistent with the proposed channel

Red Flags for Referees

• TWFE on staggered data with no Goodman-Bacon decomposition
• First-stage F = 12 cited as evidence of instrument strength
• RDD with a polynomial of order 4
• Synthetic control with no placebo inference
• DiD with a "control group" of eventually-treated units
• IV exclusion restriction defended only by "we control for X"
• Quoting an Angrist-Pischke citation as a substitute for showing the diagnostic

StatsPAI Tool Bindings

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When a StatsPAI MCP server is connected, select the validated tool, then let it run the estimator — do not hand-roll the design. The methodological choice still comes from the decision tree above; this table is only the execution surface. The full registry and chained workflow live in skills/aer-statspai/SKILL.md.

Design / diagnostic	Call (StatsPAI)	Do not hand-roll
Staggered DiD ATT(g,t)	callaway_santanna then aggte	a pooled two-way fixed-effects regression
Imputation / dCDH variants	did_imputation, sun_abraham, did_multiplegt	event-study leads and lags assembled by hand on staggered data
Forbidden-comparison weight	bacon_decomposition	eyeballing whether TWFE is "probably fine"
Pre-trends (joint, not visual)	event_study, pretrends_test	declaring parallel trends from a plot alone
IV under weak instruments	ivreg with anderson_rubin_ci, effective_f_test	a first-stage-F-only 2SLS table
Shift-share / Bartik	bartik	a Bartik IV with no Rotemberg-weight report
RDD (local-linear, RBC)	rdrobust, rdbwselect, rdplot, rddensity	a high-order global-polynomial RDD
Synthetic control	synth, augsynth, gsynth, sdid, synth_time_placebo, synth_loo	SCM with no placebo or leave-one-out inference
Design / estimator selection	detect_design, preflight, recommend	guessing the estimator before profiling the data

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Repository Resources

Bundled with the installed skill, no repository checkout needed --- read it before the repo resources below:

• references/estimator-playbook.md --- per-design estimands, modern defaults, diagnostics, and referee-objection response scripts

When working from the repo or plugin bundle, load only the relevant resource:

• Estimator defaults, package calls, diagnostics, and citations: docs/methods-reference.md
• Staggered DiD implementation: templates/stata/03_main_did.do, templates/r/03_main_did.R, or templates/python/main_did.py
• Worked empirical examples: examples/aer-exemplars.md and examples/modern-aer-exemplars.md

Use the methods reference before prose: it fixes the estimand, diagnostic, inference method, and citation that the manuscript must report.

Identification Gate

Do not advance to robustness or writing until, for the chosen design, all are true:

• A modern estimator is used — no TWFE on staggered data, no first-stage-F-only IV, no high-order-polynomial RDD
• Every required diagnostic for the design (see the per-design lists above) is run and reported
• Inference matches the design — cluster-robust / AR / wild bootstrap / permutation, not default OLS SEs by reflex
• The identifying assumption is stated in one sentence, ready to drop into the introduction
• No item in "Red Flags for Referees" is present

Gate Record Mini-Example

Write the gate decision before routing onward:

STRATEGY: IV
FIRST STAGE: effective F = 7.8; 2SLS CI is not primary
ROBUST INFERENCE: AR 95% CI = [-0.14, 0.52]
PLACEBO: beta = 0.003 (p = 0.71)
DECISION: advance with directional headline only

Handoff

STRATEGY: <DiD | IV | RDD | SCM | shift-share | RCT>
MODERN ESTIMATOR USED: <yes / no / which>
REQUIRED DIAGNOSTICS REPORTED: <list>
INFERENCE METHOD: <robust / cluster-robust / AR / wild bootstrap / permutation>
WEAK-IV / TWFE / POLY-ORDER RED FLAGS: <list or "none">
NEXT SKILL: aer-robustness

Anti-Patterns

• Defending an old design ("the prior literature used TWFE") when modern estimators exist
• Reporting OLS-with-controls as the main specification and IV/RD as "robustness"
• Using more than one identification strategy as if they were independent confirmations when they share identifying variation
• Footnoting the identifying assumption instead of stating it in the introduction