Hat algebra, end‑to‑end.
KITE solves for changes relative to an observed equilibrium (Dekle, Eaton & Kortum, 2008). Each application starts from a calibrated baseline; hat algebra lets us sidestep estimation of unobserved levels and recover counterfactuals from observed data and a small set of elasticities.
HAT ALGEBRA, IN ONE BREATH
Hat algebra is a re-parameterisation: we solve the model in terms of changes relative to today's observed equilibrium, not in absolute levels. That means the counterfactual depends only on a small set of trade elasticities — fundamental productivity, trade costs, and preferences cancel out, and we don't have to estimate them.
- ONE API The 13 KITE models share the same scenario and result conventions across the API and web workflows.
- SAME PIPELINE Switch model at runtime depending on the policy question — no rebuild.
- SCENARIO GRIDS Run repeated policy scenarios, sensitivity checks, and publication pipelines without rebuilding the workflow.
- YAML CONTRACTS Model interfaces are documented with YAML contracts, automated tests, and contract audits.
The core mechanism.
Cost changes propagate through input-output linkages; price indices aggregate across origins. The system is solved simultaneously for wages, prices and trade shares — every feedback loop included.
A tariff raises the landed price of imported intermediates. Through the IO matrix, that cost spreads to every downstream sector that uses them — directly and recursively.
Higher input costs reshuffle origin shares; reshuffled trade reshapes wages; new wages feed back into costs. KITE solves the fixed point — every loop closed, no sequential approximation.
EXACT HAT ALGEBRA · THE FIVE EQUATIONS
For any variable x, write its relative change as x̂ = x′/x. Following Dekle, Eaton & Kortum (2008), the Caliendo–Parro counterfactual reduces to a system of five equations in changes — no estimation of unobserved levels required.
- INPUT COSTS
Cobb–Douglas in wages and intermediate prices, with labour share β and IO shares γ.
$\hat{c}_d^{\,j} \;=\; \hat{w}_d^{\,\beta_d^{\,j}} \prod_{k=1}^{J} \bigl(\hat{P}_d^{\,k}\bigr)^{\gamma_d^{\,k,j}(1-\beta_d^{\,j})}$ - PRICE INDEX
Sectoral price changes aggregate over origins, weighted by trade shares and the trade elasticity θ.
$\hat{P}_d^{\,j} \;=\; \Bigl[\, \sum_{o=1}^{N} \pi_{od}^{\,j}\,\bigl(\hat{\phi}_{od}^{\,j}\,\hat{c}_o^{\,j}\bigr)^{-\theta^{\,j}} \Bigr]^{-1/\theta^{\,j}}$ - TRADE SHARES
Bilateral expenditure shares update as relative landed costs shift — the gravity backbone of the model.
$\pi_{od}^{\,j\prime} \;=\; \pi_{od}^{\,j}\,\Bigl(\dfrac{\hat{c}_o^{\,j}\,\hat{\phi}_{od}^{\,j}}{\hat{P}_d^{\,j}}\Bigr)^{-\theta^{\,j}}$ - OUTPUT
Sectoral output sums final-consumption demand and intermediate-input demand from every downstream sector.
$Y_o^{\,j\prime} \;=\; \sum_{d=1}^{N} \dfrac{\pi_{od}^{\,j\prime}}{\tau_{od}^{\,j\prime}\,\zeta_{od}^{\,j\prime}} \Bigl[\, \alpha_d^{\,j} I_d^{\,\prime} + \sum_{k=1}^{J}(1-\beta_d^{\,k})\,\gamma_d^{\,j,k}\,Y_d^{\,k\prime} \Bigr]$ - INCOME
Wage income plus net tariff and export-tax revenue, less the (exogenous) trade-balance position.
$I_d^{\,\prime} \;=\; \hat{w}_d\,w_d L_d \;+\; R_d^{\,\prime} \;-\; D_d^{\,\prime}$
Solved as a fixed point in ŵ: every loop closed, no sequential approximation. See white paper §2.2.6 for the full derivation, including the trade-balance specifications and revenue accounting.
CALIBRATION
Trade elasticities θj from Fontagné, Martin & Orefice (2018). Sectoral input-output shares commonly use GTAP 12 base-year tables. Public package examples are synthetic; calibrated application baselines are released where licensing permits or made available through the project team.
Thirteen models.
13 API + WEB MODELS · 2 OPEN SOURCE NOWEquations, derivations, calibration notes.
The white paper documents the shared framework and public package references. Application pages link public results and data where available; API and web models are documented with model contracts.
CAVEATS & LIMITATIONS
- Parameter uncertainty. Trade elasticities are estimated and carry uncertainty; public charts on this site report point estimates or published headline ranges unless an interval is explicitly shown.
- Calibration is to observed flows. Counterfactuals describe deviations from the calibration year; structural breaks during a long horizon are not captured.
- Trade-balance specification. Closure choice (fixed deficits, balanced trade, endogenous deficits) materially affects long-run welfare numbers; we default to the white paper's specification and document deviations per application.
- Short- vs. long-run definitions. Short-run holds factors and capital fixed; long-run lets labour and trade shares fully reallocate. Pick the horizon that matches the policy question.
- What KITE does not model. No nominal rigidities, no household heterogeneity, no time dynamics, no labour-market frictions in the headline specification. Specific extensions exist for several of these.
WHAT KITE DOESN'T DO (YET)
- No nominal block — prices and wages are real.
- No household heterogeneity — representative agent per country.
- No time dynamics in the headline specification — comparative statics on changes.
- No labour-market frictions — labour reallocates frictionlessly.
Specific extensions exist for several of these — see the model table. Need a related question that is not covered yet? Tell us what you need.