restat-theory-model

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?

| Situation | Theory dose | Form |

|-----------|-------------|------|

| Clean causal estimate of broad interest | Minimal | A paragraph mapping the coefficient to an economic object; estimand stated |

| Coefficient is ambiguous without a frame | Light model | A simple model giving a sign/comparative-static prediction the data test |

| Question demands a counterfactual / welfare number | Structural-light | A parsimonious model estimated/calibrated to deliver the counterfactual, validated out of sample |

| Mechanism is the contribution | Mechanism model + tests | Model that generates distinguishing predictions; test them against rival mechanisms |

| You want to publish the model itself | Wrong journal | Redirect to a theory/structural venue |

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