Has distance died in trade? Year-by-year gravity, 1995 to 2024

Disdier & Head (2008, Review of Economics and Statistics 90(1)) ran a meta-analysis of 1,467 distance elasticities from 103 gravity studies and found the puzzle that the coefficient had, if anything, risen over the post-war period despite the container revolution and the Internet. The obvious question — does that still hold in the BACI + digital era? — is what we re-run here on one consistent pipeline: CEPII BACI 202501, CEPII Gravity V202411, and WDI, from 1995 through 2024.

Method note. Our specification is the simple Tinbergen (1962) log-linear cross-section, ln X_ij,t = α_t + β_t · ln dist_ij + γ_t · ln(Y_i,t · Y_j,t) + ε_ij,t, estimated separately by year. It is deliberately descriptive: no origin / destination fixed effects, no pair fixed effects, no multilateral-resistance iteration (Anderson & van Wincoop 2003), and therefore no identification of a structural trade-cost elasticity. Zero-trade pairs are dropped by the log, biasing β toward zero (Silva & Tenreyro 2006, REStat 88(4)); the PPML fix (Yotov, Piermartini, Monteiro & Larch 2016, WTO-UN manual) is the modern answer and is not implemented on this page. Standard errors are cluster-robust on exporter ISO3 (CR1), computed in closed form via the Frisch-Waugh-Lovell partialled regressor. Our β_t values should be read as the time-series evolution of a reduced-form correlation, directly comparable to Disdier & Head’s meta-range but not to FE-PPML structural estimates.

The year-by-year distance coefficient

Each dot in Figure 1 is one annual cross-section. The 95% interval uses cluster-robust standard errors on exporter, so that the within-exporter correlation of residuals (every exporter trades with many partners) does not understate uncertainty (Cameron & Miller 2015, Journal of Human Resources 50(2)). If containerisation and digital commerce were hollowing out distance, we would expect β̂_t to drift toward zero. The opposite shows up in the raw data.

Distance by what exporters sell

If container shipping matters asymmetrically — a ton of soybeans moves more cheaply than a ton of medical devices — then distance elasticities should differ by sector. BACI is HS6-coded but our bilateral extract is aggregated across products, so we approximate by classifying each exporter into its dominant HS Section in 2024 exports and running the same gravity within each exporter-specialization group. This is not the cleanest cut (a commodity exporter also sells some machinery), but it preserves the gravity identity. A fully bilateral-by-HS6 PPML would be the right fix; see Head & Mayer (2014) §4 and Yotov et al. (2016) ch. 2 for the recipe.

Digital-intensive exporters vs everyone else

A cleaner test of the digital-trade hypothesis would track services flows — software, streaming, cloud, professional services — that cross borders without incurring physical freight cost. BACI tracks goods only, so we use a goods-side proxy: exporters whose largest HS Section in 2024 falls in chapters 49 (printed matter), 84 (computers and machinery), or 85 (electrical and telecom) — the ICT hardware and information-goods bloc identified as “digital-intensive” in Freund, Mulabdic & Ruta (2024, World Bank Policy Research WP 9719). If digital infrastructure were genuinely lowering the distance wedge in goods, we would expect the distance coefficient on trade from these exporters to be less negative than the all-exporter benchmark.

HS Section heterogeneity: all 21 sections

Figure 2 pooled HS Sections into four groups; Figure 3b is the full heterogeneity read at the WCO HS Section level. Each bar is the estimated β̂_dist in the 2024 cross-section for exporters whose dominant HS Section equals that Section, with CR1 cluster-robust SE on exporter iso3. Sections with fewer than 300 bilateral pairs are dropped. Sorted from steepest decay (most negative β) at the top to shallowest at the bottom. Blue = Sections I–V (commodities / animal / vegetable / food / mineral), green = Sections VI–XV (intermediate manufactures), orange = Sections XVI–XXI (machinery, transport, instruments, arts). This is the sector-level version of the Feyrer (2019, AER: Insights) finding that bulk commodities have fallen in per-unit freight cost more than high-value manufactures — if shipping-cost declines were uniform, β̂ should look flat across sections; it does not.

Distance elasticity by BEC-style sector block

Figure 4 collapses the 21-section heterogeneity in Figure 3b into the three UN Broad Economic Categories (Rev.5, United Nations Statistics Division 2016) that matter most for the distance-trade literature: consumption goods (HS 16–24, 50–67, 94–97), capital goods (HS 84, 88), and intermediates (HS 25–40, 72–83). This is the Johnson & Noguera (2012, Journal of International Economics 86(2)) intermediate-vs-final split at HS-chapter granularity, but with an additional capital-goods cut because Bown & Crowley (2016, Handbook of Commercial Policy) and Antràs & Chor (2022, Handbook of International Economics vol. 5) find capital goods to behave distinctly: high value-to-weight, long investment horizons, and tariff regimes that systematically treat capital equipment more leniently than consumer or intermediate goods. If trade composition drives the distance coefficient (rather than the technology of shipping), we would expect the three blocks to sort in a predictable order on β̂.

Benchmark against the literature

Table 1 places our workbench estimate next to the three main reference points in the distance-gravity literature. Comparability is not one-for-one because each study uses a different regressor set, fixed-effect structure, and time window, but the ordering and range are instructive.

What we learn

Three decades of container shipping scaling up, freight costs falling, and digital infrastructure expanding have not visibly pulled the distance coefficient in a standard cross-sectional gravity toward zero. Our trend per decade on β̂_t is -0.086 log points — inside noise. The sector decomposition suggests where the action is: complex manufacturing, the category most exposed to containerised and air-freight logistics, shows the shallowest distance decay, while bulk-commodity specialisation shows the steepest. The digital-intensive-exporter cut does not reveal a pro-digital flattening in goods, consistent with the prior that digital kills distance in services rather than in BACI-tracked physical goods — a test we cannot run without bilateral services-trade data of comparable quality.

The limitations are stated up front: this is descriptive gravity without fixed effects or MR iteration, so the absolute magnitude of β̂_t should not be compared one-for-one with Anderson-van Wincoop structural elasticities, and the log transform drops zero-trade pairs. For each of those biases the likely direction is known (Silva & Tenreyro 2006; Head & Mayer 2014), and neither reverses the time-series flatness of β̂_treported in Figure 1. The puzzle is still a puzzle.

Open questions

• PPML re-estimation. The canonical Anderson & van Wincoop (2004) and Yotov (2012, Economics Letters) argument is that zero-trade pairs carry information; dropping them biases β. PPML with origin-time, destination-time, and pair FEs (Yotov et al. 2016) is the next step. Our log-OLS β sits above the typical PPML range (around −0.8), consistent with the well-known Silva-Tenreyro direction-of-bias.
• Sector-level distance within bilateral HS6. The sector cut here uses exporter specialization as a proxy. A true sector test requires bilateral HS6 flows (the BACI long form is hosted; a partitioned bilateral-by-HS6 extract is not). The prior is that bulk commodities and heavy chemicals carry the steepest distance decay (Feyrer 2019 identification via the Suez closure).
• Services-trade counterpart. The “digital kills distance” hypothesis lives in services. BACI is goods-only; an OECD-WTO BaTiS ingest would close this gap.
• Policy read. Trade facilitation, customs modernization, and logistics-performance investment all raise the intercept α of the gravity fit; they do not tilt β. The distance puzzle’s policy corollary is that shipping-cost falls and digital penetration, individually, do not produce a flatter β without deep changes in what is traded. The composition effect (more manufactures, fewer bulk commodities) matters at least as much as the logistics technology itself.

References

• Anderson, J. E., & van Wincoop, E. (2003). “Gravity with Gravitas: A Solution to the Border Puzzle.” American Economic Review 93(1): 170–192.
• Cameron, A. C., & Miller, D. L. (2015). “A Practitioner’s Guide to Cluster-Robust Inference.” Journal of Human Resources 50(2): 317–372.
• Conte, M., Cotterlaz, P., & Mayer, T. (2022). “The CEPII Gravity Database.” CEPII Working Paper 2022-05.
• Disdier, A.-C., & Head, K. (2008). “The Puzzling Persistence of the Distance Effect on Bilateral Trade.” Review of Economics and Statistics 90(1): 37–48.
• Duranton, G., & Storper, M. (2008). “Rising Trade Costs? Agglomeration and Trade with Endogenous Transaction Costs.” Canadian Journal of Economics 41(1): 292–319.
• Feyrer, J. (2019). “Trade and Income — Exploiting Time Series in Geography.” American Economic Journal: Applied Economics 11(4): 1–35.
• Freund, C., Mulabdic, A., & Ruta, M. (2024). “Is 3D Printing a Threat to Global Trade? The Trade Effects You Didn’t Hear About.” World Bank Policy Research Working Paper 9719.
• Head, K., & Mayer, T. (2014). “Gravity Equations: Workhorse, Toolkit, and Cookbook.” In Handbook of International Economics, vol. 4, ch. 3.
• Hortaçsu, A., Martínez-Jerez, F. A., & Douglas, J. (2009). “The Geography of Trade in Online Transactions.” American Economic Journal: Microeconomics 1(1): 53–74.
• Silva, J. M. C. Santos, & Tenreyro, S. (2006). “The Log of Gravity.” Review of Economics and Statistics 88(4): 641–658.
• Tinbergen, J. (1962). Shaping the World Economy. Twentieth Century Fund.
• Yotov, Y. V. (2012). “A Simple Solution to the Distance Puzzle in International Trade.” Economics Letters 117(3): 794–798.
• Yotov, Y. V., Piermartini, R., Monteiro, J.-A., & Larch, M. (2016). An Advanced Guide to Trade Policy Analysis: The Structural Gravity Model. WTO and UNCTAD.