jue-theory-model

Spatial Theory & Model Craft (jue-theory-model)

When to trigger

• A reduced-form spatial result needs a mechanism that interprets the magnitude
• A referee asks "what does this estimate mean in equilibrium, once agents re-sort?"
• The paper wants counterfactuals (a policy, an infrastructure change) that require a quantitative spatial model
• The empirical object (a density-wage elasticity, a capitalization rate) maps to a structural parameter you have not named
• You are choosing how much model the paper needs: a one-equation Rosen–Roback wedge or a full QSM

How much model does a JUE paper need?

JUE is empirically led, but referees expect theory to discipline interpretation, not decorate it. Match the model to the claim:

The claim is...	The model you need	Pitfalls
"this amenity/disamenity is valued at X"	Rosen–Roback capitalization, wages + rents jointly	using only prices ignores the wage margin and the worker indifference condition
"agglomeration raises productivity by Y"	sharing/matching/learning micro-foundation; sorting vs spillover decomposition	attributing sorting of high types to true agglomeration
"policy/infrastructure changes welfare by Z"	quantitative spatial model with mobility, trade/commuting, housing	counterfactual not invariant to the policy; ignored general-equilibrium reallocation
"households sort on local public goods"	Tiebout / discrete-choice sorting model	treating sorting as exogenous; no equilibrium in prices
"market access drives outcomes"	gravity/market-access (Donaldson–Hornbeck, ARSW)	endogenous network; access measured without the structural weight

Spatial-equilibrium discipline

1. Respect the indifference/zero-profit conditions. In a Rosen–Roback world a local change that looks like a pure benefit is partly capitalized into rents and partly offset by wage adjustment. A JUE referee will ask where the incidence falls — land, labor, or firms.
2. Close the model where agents move. If your empirical comparison holds location fixed but theory says agents re-sort, the reduced form is a short-run object; say so and bound the long-run.
3. For a QSM, tie every parameter to data. State which moment or reduced-form estimate identifies each elasticity (migration, commuting, housing supply, agglomeration). Report sensitivity of counterfactuals to the parameters that are least well identified.
4. Argue invariance for counterfactuals. The estimated elasticities must be policy-invariant enough for the experiment you run (a spatial Lucas critique).
5. Use theory to sign and bound, not to over-claim. The most persuasive JUE theory section delivers a comparative static the data then confirms.

Checklist

• The model is matched to the claim (capitalization / agglomeration / QSM / sorting / market access)
• Spatial-equilibrium conditions (indifference, zero-profit, market clearing) are respected
• Incidence is located: who bears the change — land, labor, or firms
• Short-run (location fixed) vs long-run (re-sorting) is distinguished
• QSM: each structural parameter is tied to an identifying moment/estimate; counterfactual sensitivity reported
• Counterfactual parameters argued policy-invariant
• Open-city vs closed-economy assumption stated and defended for the geographic scale
• The model is load-bearing (removing it makes an estimate uninterpretable), not decorative
• Theory yields a comparative static the empirics actually test

Anti-patterns

• A reduced-form result with no mechanism, leaving the magnitude uninterpretable
• Reading a capitalization estimate from prices alone, ignoring the wage and the worker indifference margin
• Attributing the density-wage elasticity to agglomeration when it is sorting of high-productivity workers
• A QSM whose counterfactual rests on parameters never tied to data, or whose elasticities are not policy-invariant
• Decorative theory: a model that does not change how any estimate is read
• Ignoring general-equilibrium reallocation, so a local gain is reported as a national welfare gain

Referee pushback mapped to the theory fix

• "What does this mean once households re-sort?" → Embed the estimate in a spatial-equilibrium model; report the short-run (location fixed) vs long-run (re-sorting) effect and where incidence lands.
• "Is this agglomeration or sorting of high types?" → Add the sharing/matching/learning micro-foundation and a decomposition that separates true spillovers from compositional sorting.
• "Your counterfactual parameters are not policy-invariant." → Argue invariance explicitly (spatial Lucas critique); show the elasticities are primitives, not functions of the policy.
• "The model is decorative." → Derive a comparative static the data then tests; if the model changes no estimate's interpretation, cut it.

Calibrate vs estimate

JUE accepts both calibrated and estimated spatial models, but the referee asks the same question: what disciplines the parameters? For a calibrated QSM, cite the external estimates each elasticity comes from and report counterfactual sensitivity to the least-credible one. For an estimated model, name the moment or reduced-form variation that identifies each parameter (this hands off to jue-identification). Either way, the counterfactual's credibility is only as strong as the weakest-identified elasticity — surface it rather than hiding it in an appendix.

Open vs closed city, and why it matters here

A recurring JUE referee question is whether your setting is an open city (migration equalizes utility, so local shocks capitalize into land and dissipate in welfare terms) or a closed economy (population fixed, effects fall on prices and quantities differently). The choice changes the sign and incidence of your comparative statics: in an open-city model a local amenity gain is fully capitalized into rents with no utility change, whereas in a closed model it raises resident welfare. State which assumption you make and defend it for your geographic scale — a single metro is more open than a national system. Getting this wrong is a common interpretation error referees flag.

Worked vignette (illustrative)

A paper estimates that a zoning relaxation raised housing units in treated tracts. Reduced form alone cannot say whether welfare rose, because households re-sort and rents adjust elsewhere. The JUE theory move: embed the estimate in a small spatial-equilibrium model with mobility and housing supply, calibrate the supply elasticity to the reduced-form response and the migration elasticity to prior estimates, and report the welfare counterfactual with sensitivity to the migration elasticity (the least-identified parameter). The model shows the local rent decline is partly undone by in-migration — a comparative static the data then supports.

Where the model lives in the paper

JUE referees punish theory that is either missing or overgrown. A reduced-form paper usually needs only a compact framework — a few equations stating the indifference/zero-profit conditions and the comparative static the data tests — placed before the empirics so the estimate has meaning when it arrives. A structural paper carries a fuller model but should still front-load the intuition and relegate derivations to an appendix. The test in both cases: remove the model and ask whether any estimate changes meaning. If nothing changes, the model is decoration; if the magnitude becomes uninterpretable, the model is load-bearing and belongs in the main text.

Output format

【Claim type】capitalization / agglomeration / QSM-counterfactual / sorting / market-access
【Model chosen】one line — and why this much model
【Equilibrium conditions】indifference / zero-profit / clearing respected? [Y/N]
【Incidence】land / labor / firms
【Run vs long-run】short-run (fixed location) vs long-run (re-sorting)
【QSM params → data】each elasticity tied to a moment; sensitivity reported?
【Comparative static tested】[...]
【Next skill】jue-robustness