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KITE.jl

Quantitative multi-sector Ricardian trade models, solved in changes ("exact hat algebra").

KITE.jl evaluates counterfactual trade policy — tariffs, non-tariff barriers, sanctions, export subsidies — in the framework of Caliendo & Parro (2015) and the sanctions-coalition extension of Chowdhry, Hinz, Kamin & Wanner (2022). It is a Julia translation of the public R package KITE (Kiel Institute Trade Policy Evaluation). Please cite the model suite as Hinz, Mahlkow & Wanner (2025); see CITATION.bib.

Installation

using Pkg
Pkg.develop(path = "path/to/KITE.jl")   # not yet registered

Quick start

using KITE

b = load_baseline(year = 2022)          # 81 countries × 50 sectors

sc = Scenario(b; label = "25% US tariff on China")
set_tariff!(sc, b, 1.25; from = "CHN", to = "USA", mode = :multiply)

r = update_equilibrium(CaliendoParro2015(), b, sc)
results(r; level = :country)

The model

Households in each country d consume a Cobb–Douglas bundle over J sectors. Each sector produces with labour and intermediates from every sector, under Fréchet productivity with shape θ_j — the trade elasticity. Trade costs combine tariffs τ, iceberg/non-tariff barriers κ and export taxes or subsidies ζ.

Everything is solved in changes, so the technology and geography terms drop out. Writing x̂ = x′/x and φ̂ = τ̂ κ̂ ζ̂:

\[\hat c_d^j = \hat z_d^{j\,-1}\,\hat w_d^{\beta_d^j} \Bigl(\prod_k (\hat P_d^k)^{\gamma_d^{kj}}\Bigr)^{1-\beta_d^j}\]

\[\hat P_d^j = \Bigl(\sum_o \pi_{od}^j \bigl(\hat\varphi_{od}^j\,\hat c_o^j\bigr)^{-\theta_j}\Bigr)^{-1/\theta_j}\]

\[\pi_{od}^{j\prime} = \pi_{od}^j \Bigl(\frac{\hat\varphi_{od}^j\,\hat c_o^j}{\hat P_d^j}\Bigr)^{-\theta_j}\]

with expenditure, income and output closing the system:

\[X_d^{j\prime} = \alpha_d^j I_d' + \sum_k (1-\beta_d^k)\gamma_d^{jk} Y_d^{k\prime}, \qquad Y_o^{j\prime} = \sum_d \frac{\pi_{od}^{j\prime}}{\tau_{od}^{j\prime}\zeta_{od}^{j\prime}} X_d^{j\prime}\]

The solver iterates on the wage change ŵ. CaliendoParro2015 updates it from labour-market clearing; ChowdhryHinzKaminWanner2022 from the trade-balance excess-demand function, and additionally computes transfers that equalise the welfare cost across a sanctioning coalition.

Extensions

Two further models from the KITE whitepaper that are not in the public R package (the closed KITE suite implements many more):

MahlkowWanner2023 adds energy. Primary fossil-fuel sectors extract a natural resource in fixed supply, so its rental price is solved for alongside wages and rents are part of income. Secondary fuels combine their complementary primary fuel with the rest of their inputs in Leontief rather than Cobb-Douglas fashion — fuel cost shares then move with relative prices instead of being pinned by a fixed exponent, which is what lets fuel use, and so emissions, respond to a trade shock. Use fossil_use and resource_price_change.

AntrasChor2018 makes sourcing use-specific: π[o,d,j,k] for sector-j goods bought by sector k, plus π[o,d,j,C] for final consumption, each with its own price index. It takes a GVCBaseline. Tariffs stay product-specific, matching how trade policy actually applies. Be aware of the memory: π[o,d,j,k] is 125 MB at 81 countries and 50 sectors.

Both reduce exactly to CaliendoParro2015 in their degenerate case — no fossil sectors designated, or use-independent sourcing — which is how they are tested.

Trade elasticity convention

θ is the standard Fréchet shape parameter: larger θ means more responsive trade. The R implementation inverts the exponents, so its trade_elasticity argument behaves as 1/θ. See Differences from the R implementation.

Model-consistent baselines

A KiteBaseline satisfies the equilibrium identities at the baseline itself:

Y[o,j] = Σ_d π[o,d,j] · X[d,j] / (τ[o,d,j] · ζ[o,d,j])          goods market
X[d,k] = α[d,k] · I[d] + Σ_j input_share[d,k,j] · Y[d,j]        expenditure
I[d]   = VA[d] + R[d] − D[d]                                    income

The constructor rejects data that violates them. This is what makes a no-change scenario return every hat equal to one, in a single iteration:

r = update_equilibrium(CaliendoParro2015(), b)
r.iterations           # 1
maximum(abs, r.ŵ .- 1) # ~1e-16

Raw MRIO data does not satisfy the identities — published final demand, value added and trade balances are not mutually consistent once run through an input-output loop. calibrate resolves this by making final demand residual (so α reproduces observed final demand by construction) and letting the trade balance close the income identity. Inspect the result with residuals.

Bringing your own data

The long CSV interchange format matches the R package's initial conditions, one file per variable with its index columns plus value:

b = read_baseline_csv("my_data")   # trade_share.csv, intermediate_share.csv, factor_share.csv,
                                   # expenditure.csv, trade_elasticity.csv, tariff.csv, …

Tables may be sparse: absent cells take a documented fill and the number filled is reported. write_baseline writes the same format back.

Differences from the R implementation

Several issues in the public R package can change the numbers it produces; they are fixed here. In brief:

  1. The outer convergence criterion monitored only wages, so shocks that move prices but not wages could stop early with inconsistent prices.
  2. The trade-elasticity exponents are inverted relative to the shipped data and docs, so it solves a model with elasticity 1/θ.
  3. The baseline is not required to be model-consistent, so a no-change scenario does not reproduce it.
  4. cast_variable() reshapes long tables positionally — harmless for square initial conditions, but silently recycles values when a table is sparse.

Plus several smaller corrections to ChowdhryHinzKaminWanner2022. See NEWS.md for the full account with measured magnitudes.

Validation

The no-change scenario returning unity in one iteration is the headline test. Beyond it: the R solver, with its inverted exponents patched out, serves as an independent second implementation and agrees to 1e-15 on wages, prices and trade shares across three scenarios with identical iteration counts. The suite also checks homogeneity of degree one, market clearing and Walras' law, numéraire invariance, monotonicity in θ, trade diversion, the autarky limit, and agreement between the iterative and direct inner solvers.

References

  • Hinz, J., Mahlkow, H. and Wanner, J. (2025). The KITE Model Suite: A Quantitative Framework for International Trade Analysis. White Paper, Kiel Institute for the World Economy. https://trade.ifw-kiel.de/KTTM/KITE_whitepaper.pdf
  • Caliendo, L. and Parro, F. (2015). Estimates of the Trade and Welfare Effects of NAFTA. Review of Economic Studies, 82(1), 1–44.
  • Chowdhry, S., Hinz, J., Kamin, K. and Wanner, J. (2024). Brothers in arms: The value of coalitions in sanctions regimes. Economic Policy, 39(118), 471–512.
  • Fontagné, L., Guimbard, H. and Orefice, G. (2022). Tariff-based product-level trade elasticities. Journal of International Economics, 137.