Ier Theory Model

Theory and Model Craft (ier-theory-model)

When to trigger

• The model "works" numerically but you cannot say which assumption is doing the work
• Existence/uniqueness of equilibrium is asserted rather than proved, or relies on a knife-edge condition
• A referee suspects the headline result is an artifact of a functional-form or parametric choice
• The comparative statics are stated but the sign of a key derivative is not signed cleanly
• You are unsure the model is general enough — does the result survive perturbing the convenient assumption?

Why theory is central at IER

IER tilts theory/structural, and for theory and structural papers the model is the contribution — so the bar is not "is the model plausible" but "is the result tight and general." A tight result names exactly which assumptions are load-bearing and shows the conclusion is not an accident of a convenient functional form. This is the difference an IER referee looks for between a paper that teaches a general lesson and one that re-derives a known fact under new notation.

What makes a result "tight" at IER

The discipline sequence for an IER model

1. Write the assumptions as a ranked list, not a block — order them by how much the result depends on each. The top one or two are your load-bearing assumptions; the rest are for tractability.
2. For each load-bearing assumption, run the perturbation test: relax it slightly and report whether the result survives, weakens, or flips. If it flips, that is the paper's real boundary — state it as a result, not a limitation buried in a footnote.
3. Prove (or cleanly bound) existence and uniqueness, and translate the condition into economics. A condition like "the demand elasticity exceeds 1" must be explained, not just stated.
4. Sign the comparative statics analytically wherever possible; where a sign is ambiguous, decompose it into competing forces and say which dominates and when. This is the comparative-statics craft IER readers expect.
5. Lead each formal result with intuition. The model serves a general audience; the proof goes to the appendix (see ier-replication-package for the proof-appendix contract), the economics stays in the text.
6. For structural/quantitative work, hand the parameter-identification question to ier-identification — "what in the data pins this parameter" is a different question from "is the model tight."

Worked vignette: making a uniqueness claim tight (illustrative)

A general-equilibrium model with externalities asserts "an equilibrium exists and is unique." A referee flags this as the soft spot — multiplicity would undermine the comparative statics the paper builds on. The loose draft cites "standard fixed-point arguments." The tight IER version states a sufficient condition (say, the externality elasticity is below a threshold), proves uniqueness under it, and then explains the economics: below the threshold the feedback from the externality does not overpower the price mechanism, so the equilibrium map is a contraction. Now the condition is not a technicality — it is the economic boundary of the result, and the comparative statics are safe inside it. If the referee asks "what if the elasticity is above the threshold?", the paper already answers: multiplicity, and the paper says so as a result, not a caveat.

Why theory craft is judged harder at IER than at applied venues

At an applied journal a model is often a framing device for the empirics, and a referee tolerates a convenient functional form. At IER, when the model is the contribution, the same functional-form shortcut is a rejection risk: the referee asks whether the result is a property of the economics or an artifact of the algebra. The perturbation test and the analytical comparative static are how you demonstrate it is the economics — they are not optional polish but the core evidence that the result is real and general.