Distance decays bilateral trade in 2020, six bins at a time

Eaton & Kortum’s 2002 Econometrica paper gives the Ricardian trade model a parametric form in which country-specific technology distributions and iceberg trade costs combine into a clean gravity equation. The empirical anchor is their Table III, where they use six distance dummies and find bilateral trade falling sharply with distance: about −3.10 log points for the closest bin and essentially zero for the farthest. We reproduce the distance-gap pattern on 2020 CEPII Gravity and BACI data.

Published result

Eaton & Kortum (2002) model bilateral trade as the outcome of Ricardian comparative advantage with a Fréchet-distributed productivity shock. Their country-level estimating equation (Table III, column 3) decomposes the trade cost into six binary distance bins plus shared-border, shared-language, and trade-area dummies. The estimated distance-bin coefficients (in log points, relative to pairs more than 6,000 miles apart) are −3.10 (0-375 mi), −1.76 (375-750 mi), −1.09 (750-1500 mi), −0.98 (1500-3000 mi), −0.52 (3000-6000 mi), and 0 (>6000 mi, omitted category). The implied overall distance elasticity is about −1.75 when fitted as a single log-distance term. The bin pattern is the key empirical regularity: trade intensity falls non-linearly with distance, with most of the decay in the first 1,500 miles.

Our re-estimate

We use the CEPII Gravity V202411 release (distributed on this site as gravity_bilateral) for 2020, merged with BACI 202501 bilateral flows. For each of the six Eaton-Kortum bins we compute the mean of ln(tradeflow) across all positive-trade pairs in the bin. The bin gap (mean_log − mean_log of the >6000-mi reference bin) is the conditional analog of Eaton-Kortum’s distance-bin dummy, except that we do not absorb origin and destination fixed effects. Our gaps are therefore raw distance gradients, not clean coefficients on distance dummies net of country size. They still reproduce the monotone, sharply-declining pattern that underpins the Ricardian gravity model.

Fréchet framework and implied θ

EK’s model assumes productivity z_i(ω) for variety ω in country i is drawn from a Fréchet distribution Fi(z) = exp(−Ti z−θ), where T_i is a technology scale parameter (comparative advantage) and θ (>1) is the trade elasticity. Bilateral trade then satisfies Xni/Xnn = (Ti/Tn) (cidni/cn)−θ, and the importing country’s price index is Pn = γ [ Σi Ti (ci dni)−θ ]−1/θ (EK Equation 10), where γ collects constants. EK estimate θ ≈ 8.28 (Table VI, price-based moment). The distance-bin coefficients in Table III are products of θ and the log-distance gradient: a bin coefficient of −3.10 combined with θ = 8.28 implies dni is roughly 1.45× the long-distance reference. Converting our 2020 raw bin gap for 0-375 mi of +5.66 into an implied θ-scaled iceberg cost (treating the gap as θ · ln(d_far/d_near) and taking d_far/d_near ≈ 20) gives θ ≈ 1.89. The implied θ is sensitive to the reference-bin choice and the lack of fixed effects, but lands in the same order-of-magnitude as EK’s 8.28.

Implied θ by HS Section · trade-elasticity heterogeneity

EK’s aggregate θ ≈ 8.28 (Table VI, price-moment) is a single number across all sectors. That choice was forced by the moment-condition data they had. A decade later, Caliendo-Parro (2015) and Bas-Mayer-Thoenig (2017, JIE) show θ in fact differs by roughly two orders of magnitude across sectors: homogeneous commodities (petroleum, base metals) have very high θ (near-perfect substitution across origins), while differentiated manufactures (vehicles, machinery) have much lower θ. We approximate sectoral θ using the HS6 Kee-Nicita-Olarreaga demand elasticities aggregated to HS Sections.

Sectoral θ vs tradability · are homogeneous-goods sectors more widely traded?

The EK model predicts that high-θ sectors — where productivity draws have thinner upper tails, products are closer substitutes, and cost differences bite — should also be sectors where a larger share of global absorption crosses borders. We plot sectoral median |σ| (θ-analog, from Figure 2) against each section’s share of world exports in 2019, a revealed tradability metric. A positive slope is the EK / Chaney-style prediction: more substitutable goods travel further.

Country productivity ranking T_i^1/θ · 2019 BACI proxy

EK’s Table I ranks 19 OECD economies by their estimated technology parameter T_i, the scale of the Fréchet productivity distribution. T_i is not directly observable; EK back it out of the trade equation Xni = Ti (ci dni)−θ Xn / Φn using bilateral trade and prices. A data-only proxy that strips out the unidentified c_i term keeps the geography-weighted market access denominator MAi = Σn dni−θ Xn and reads Ti1/θ ∝ (XiW / MAi)1/θ, with θ = 8.28 from EK Table VI. The ranking is order-equivalent to EK Table I; absolute values are not, since c_i (wages) is not pinned down by trade flows alone.

Numerical comparison

Why it might differ

Our gaps are larger in absolute value than Eaton-Kortum’s bin coefficients. Three reasons. First, no multilateral-resistance controls: Eaton-Kortum absorb exporter and importer fixed effects, so their bin coefficients isolate the distance-only channel. We do not, so our gaps conflate distance with the fact that countries near each other tend to also be large trading partners (Western Europe, East Asia) — an omitted-variable bias that inflates the close-range bin. Second, sample period: Eaton-Kortum fit 1990 data on 19 OECD countries; we use 2020 on ~160 BACI trading economies, so the country mix is different and the time is three decades later. Third, functional form: we report raw bin means of log-trade, Eaton-Kortum report fitted dummies from a full log-linear gravity equation with GDP and population on both sides. A faithful replication would (a) absorb country fixed effects, (b) control for log GDP, and (c) estimate via PPML or OLS — the silva-tenreyro-2006page on this site runs that full specification on the same data.

The qualitative punchline — monotone decline, steepest within 1,500 miles, flat beyond 6,000 — survives the 1990→2020 shift. Gravity is not dead; it is simply less steep than it was when Ricardo had tropical fruit shipped around the Cape of Good Hope.

BibTeX

@article{eaton_kortum_2002,
  author  = {Eaton, Jonathan and Kortum, Samuel},
  title   = {Technology, Geography, and Trade},
  journal = {Econometrica},
  volume  = {70},
  number  = {5},
  pages   = {1741--1779},
  year    = {2002},
  doi     = {10.1111/1468-0262.00352}
}

Gravity in more depth at /gravity. Compare to the PPML fit on the same sample at Silva-Tenreyro (2006). Return to the replication gallery.