Theory & Model Right-Sizing (restat-theory-model)

When to trigger

• A reduced-form result needs an economic interpretation a referee will ask for
• The draft has a sprawling model section that overshadows the empirical contribution
• You are unsure whether to estimate a structural model or stay reduced-form
• A referee asked "what is the mechanism?" or "what is the model behind this regression?"

The REStat theory bar

REStat is empirical-first: theory is in service of the estimate, not the headline. The right amount of model is the amount that (1) defines the estimand — names the parameter the design recovers and why it is interesting; (2) disciplines the interpretation — maps the coefficient to an economic object (an elasticity, a welfare-relevant margin, a structural parameter); or (3) delivers a counterfactual the reduced form cannot. Anything more risks turning the paper into a theory or pure-structural paper that belongs elsewhere. A short, transparent model that yields a testable prediction or an interpretable parameter is worth more at REStat than an elaborate one that buries the empirics.

Decision: how much theory?

Right-sizing moves

• Lead with the estimand, not the equations. State the parameter the design identifies before any model algebra.
• Make every modeling assumption earn its place — if removing it does not change the interpretation, cut it.
• Tie structure to data features. If you estimate a structural parameter, name what in the data identifies it (hand to restat-identification Branch on measurement/identification logic).
• Validate, don't just calibrate. Show fit to an untargeted moment when the model does real work.
• Keep the counterfactual honest. State the policy-invariance assumption a counterfactual relies on.

Checklist

• The estimand is named and economically interpreted (elasticity / margin / structural parameter)
• Theory dose matched to the question (minimal / light / structural-light / mechanism)
• Every modeling assumption is load-bearing; non-essential ones cut
• If structural: identification of each parameter named; an untargeted moment validates fit
• If a counterfactual is run: policy-invariance / extrapolation assumptions stated
• The model does not overshadow the empirical contribution (page budget reflects priorities)

Anti-patterns

• A 10-page model section in front of a reduced-form paper — reads as a theory paper REStat will redirect
• Equations with no estimand stated, leaving the referee to guess what is identified
• A structural model calibrated, not validated, then used for a bold counterfactual
• Theory used decoratively (a model that predicts nothing the empirics test)
• Hiding a weak design behind structural machinery

Worked vignette: right-sizing a model to an estimate (illustrative)

A reduced-form paper finds that a transport-subsidy raised rural employment. A referee asks "what is the welfare implication?" — the reduced form alone cannot say. The wrong response is to bolt on a full spatial general-equilibrium model that takes over the paper. The right REStat response is a structural-light addition: a parsimonious model whose one new parameter (the commuting elasticity) is identified by the estimated employment response itself, validated against an untargeted moment (the change in commuting distance), and used to deliver a single welfare number with its uncertainty. The model earns exactly its keep — it converts the credible estimate into a welfare statement — without becoming the contribution.

Output format

【Theory role】define estimand | discipline interpretation | deliver counterfactual | model mechanism
【Theory dose】minimal | light | structural-light | mechanism-model
【Estimand】[parameter] = [economic object]; identified by [data feature]
【Counterfactual assumptions】[policy-invariance / extrapolation] — or "n/a"
【Cut】assumptions/sections removed as non-load-bearing: [...]
【Next step】restat-robustness