Theory & Model for Interpretation (aeja-theory-model)

When to trigger

• A referee asks "what is the mechanism / what model rationalizes this?"
• The reduced-form estimate is credible but its economic meaning is ambiguous
• You want a welfare statement, an elasticity, or a counterfactual the raw estimate cannot deliver
• You are tempted to lead the paper with a full structural model and need to right-size it for AEJ: Applied

The AEJ: Applied theory dial

AEJ: Applied is empirical-first. Theory earns its place only when it interprets the estimate, sharpens the estimand, or unlocks a magnitude the design cannot deliver alone — never as the headline. Pick the lightest tool that does the job and keep the empirical estimate the star.

Theory's job	Right amount of model	Where it goes
Name the mechanism	a few equations / a conceptual framework	short section before results
Map a reduced-form coefficient to a structural parameter	a sufficient-statistic / envelope argument	inline derivation + appendix
Deliver a welfare or counterfactual number	a calibrated or partially-structural model	a dedicated section, clearly bounded
Discipline heterogeneity / sign predictions	a simple model generating testable comparative statics	framework section, tested in results

Sufficient-statistic style (often the AEJ: Applied sweet spot)

Where possible, express the welfare/policy object as a function of estimable elasticities (a Harberger/Chetty-style sufficient statistic) rather than estimating a full structural model. This keeps the credibility in the reduced-form design while delivering an economic magnitude. State the assumptions under which the sufficient statistic is valid and what it omits.

When a fuller model is warranted

If the question genuinely requires out-of-sample counterfactuals or unobservable primitives, a small structural model is acceptable — but tie each parameter to a data feature, validate against an untargeted moment, and never let the model's assumptions silently replace the identification the design provided.

Checklist

• Theory's job named (mechanism / mapping / welfare / comparative statics)
• Lightest adequate tool chosen; model does not upstage the empirical estimate
• If a sufficient statistic: the estimable elasticities and validity assumptions stated
• If structural: each parameter tied to a data feature; an untargeted-moment validation shown
• Comparative statics / sign predictions made before they are tested
• Welfare/counterfactual numbers carry their own uncertainty and stated scope

Anti-patterns

• Leading an empirical AEJ: Applied paper with a full structural model (reads as a different journal)
• A "model" section that is decorative — adds notation but no testable prediction or magnitude
• Letting model assumptions quietly substitute for the identification the design was supposed to provide
• A welfare number with no uncertainty and no statement of what the model omits
• Comparative statics derived after seeing the results (HARKing the theory)

Worked vignette (illustrative)

A clean RD shows a tuition subsidy raises enrollment by 4.2pp (s.e. 1.1). The number is credible but the policy question is the welfare gain. Instead of building a full college-choice model, the paper uses a sufficient-statistic argument: the marginal value of public funds depends on the enrollment elasticity (estimated) and the fiscal externality of an extra graduate (calibrated from administrative tax data). This yields an MVPF of ~1.3 (illustrative) with a stated range, while the credibility still rests on the RD — the AEJ: Applied ideal.

Referee pushback mapped to the theory fix

• "What is the mechanism behind this reduced-form effect?" → Add a short framework with a sign prediction you then test, or a channel-distinguishing test in the data — not more notation.
• "This number is not policy-relevant without a welfare interpretation." → Express the welfare object as a sufficient statistic of estimable elasticities; state the assumptions that make it valid.
• "Your structural model just assumes the result." → Tie each parameter to a data feature and validate against an untargeted moment; keep the credibility anchored in the reduced-form design.

Output format

【Theory's job】mechanism / reduced-to-structural mapping / welfare / comparative statics
【Tool chosen】framework / sufficient statistic / small structural model
【Key relation】estimand = f(estimable elasticities / parameters): ___
【Validity assumptions + what it omits】[...]
【Magnitude delivered】[number + uncertainty + scope], or "none — interpretation only"
【Next step】aeja-robustness