Gravity model of bilateral trade

Method

The gravity_residual column served by /gravity and /api/gravity/* comes from a per-year OLS on log-linearised trade, positive flows only, with three regressors and no fixed effects: ln(trade) = b0 + b_d ln(dist) + b_o ln(gdp_o) + b_m ln(gdp_d). BACI trade values are stored in thousands of USD, so the fitted intercept reflects that unit. Reproduced exactly from the stored column on 2026-08-27 (maximum absolute deviation 0.0 for every year tested). Adding contiguity, common language and FTA breaks the reproduction, so those variables are displayed on the page but are not regressors.

Fitted values, re-derived: 2020 gives b_d = -1.5005, b_o = +1.3343, b_m = +0.9728, intercept -20.8546, R-squared 0.6389 on 23,795 pairs. 1996 gives b_d = -1.1483, R-squared 0.6848 on 11,203 pairs. The distance elasticity steepens from about -1.15 in 1996 to about -1.53 in 2019.

A separate, genuine PPML estimation lives at /research/gravity-ppml: Poisson pseudo-maximum-likelihood by hand-written IRLS in TypeScript (fitPPML() at lines 167-215), regressors [1, ln dist, ln gdp_o, ln gdp_d, contig], zero-inclusive sample built from bilateral_year with COALESCE(trade, 0), top 120 economies by mean nominal GDP, years 1996, 2005, 2015 and 2024, Eicker-Huber-White sandwich standard errors, unclustered, no fixed effects.

The card links /gravity for the residuals and /research/gravity-ppml for the PPML estimates. They are separate estimators.

Equations

Validation

• src/app/replications/silva-tenreyro-2006/page.tsx re-estimates OLS and PPML on the same table with seven regressors and compares to the published paper. Re-derived independently on 2026-08-27: OLS distance elasticity -1.1991, PPML -0.4971, n = 23,795 for both, PPML converging in 8 IRLS iterations. The gallery card at src/app/replications/page.tsx states the same figures.
• The published Silva and Tenreyro benchmarks the replication carries are -1.166 (OLS) and -0.776 (PPML) for the traditional-gravity table, and -1.347 / -0.750 for the fixed-effects table.
• The direction replicates: PPML attenuates the distance elasticity relative to OLS in logs, which is the paper's central result.

Limitations

• The residual model has no multilateral resistance and no fixed effects, so it is not an Anderson and van Wincoop specification. src/app/gravity/page.tsx currently claims it is. This card does not repeat that claim.
• No estimation script for gravity_bilateral exists in this repository; the parquet ships with the residual precomputed and no standard errors are stored. The specification above was recovered by reproducing the column.
• Absent flows are stored as NULL, never as 0: the table contains no zero-valued rows in any year. The residual model and the Silva-Tenreyro replication are therefore positive-flows-only and do not exercise the zeros channel. Only /research/gravity-ppml builds a zero-inclusive sample.
• year=1995 and year=2021 partitions carry geography and partial GDP but no trade and no residuals. Effective residual coverage is 1996-2020, and /api/v1/gravity accepts 1995 and 2021 regardless.
• The table is on the pinned legacy vintage (HS92). BACI_LEGACY_LABEL interpolates the live BACI_YEAR_MAX and therefore renders a tail later than this table. Residual coverage is 1996-2020 and covariate coverage is 1996-2021.
• Neither gravity surface reports clustered standard errors.

References

• Tinbergen (1962), Shaping the World Economy.
• Silva and Tenreyro (2006), The Log of Gravity, Review of Economics and Statistics 88(4): 641-658.
• Head and Mayer (2014), Gravity Equations: Workhorse, Toolkit, and Cookbook.
• Yotov, Piermartini, Monteiro and Larch (2016), An Advanced Guide to Trade Policy Analysis.
• TradeWeave PPML estimation surface.

Endpoints