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original research
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 (retrieved 2026-04-28), CEPII Gravity V202411, and WDI, from 1995 through 2024.
Method note. Our specification is the simple Tinbergen (1962) log-linear cross-section, ln Xij,t = αt + βt · ln distij + γt · ln(Yi,t · Yj,t) + εij,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 βtvalues 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.
year range1995-2024
pairs per year (avg)24,137
β̂(dist) first yr-1.31
β̂(dist) last yr-1.52
mean β̂(dist)-1.47
trend per decade-0.086
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 β̂t to drift toward zero. The opposite shows up in the raw data.
Figure 1
Annual distance elasticity of bilateral trade, 1995-2024
The conditional distance elasticity moves between -1.57 (2021) and -1.31 (1995), averaging -1.47 across the 30 annual cross-sections. A linear OLS trend on β̂t vs year gives -0.086 log-points per decade, essentially flat, and if anything the coefficient has become slightly more negative since the mid-2000s. This is the Disdier & Head (2008) puzzle on updated data: three decades of container-ship scaling, air freight, and digital trade have not killed distance in a pre-FE gravity regression. The same qualitative pattern is found in structural re-estimates (Yotov 2012, Economics Letters117(3); Head & Mayer 2014), so the result is not simply an artefact of omitted fixed effects; however the level of our β̂ (around −1.5) is larger in magnitude than typical FE-PPML estimates (around −0.8 to −1.1) because dropping zeros and omitting origin/destination FE both inflate the log-OLS slope, as Silva & Tenreyro (2006) demonstrated.
Method: annual log-OLS gravity, β̂ conditional on ln(Y_o · Y_d), CR1 cluster-robust SE on exporter iso3. Sources: CEPII BACI 202501 (retrieved 2026-04-28) (trade, via bilateral_year); CEPII Gravity V202411 (distance, pair-averaged); World Bank WDI NY.GDP.MKTP.CD (GDP). Authors calcs.Figure 1b
Annual GDP-product elasticity, 1995-2024
The size coefficient γ̂t averages 1.07 across the window, above the theoretical unit value predicted by a symmetric CES Armington model with multilateral-resistance terms (Anderson & van Wincoop 2003, AER 93(1)). Without fixed effects the GDP product absorbs part of the omitted MR variation (Head & Mayer 2014, §3.2), which is why the coefficient drifts above one; it is a descriptive size-trade correlation, not the structural size elasticity.
Method: same as Figure 1 but returning γ̂(ln GDPₒ·GDPᵢ) conditional on ln dist.
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 2024exports 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.
Figure 2
Distance elasticity by exporter sector specialization, 2024
Commodity exporters, agri, minerals, fuels (HS Sections 1-5), show the steepest distance decay at -1.71. Complex-manufacturing exporters (HS Sections 16-17: machinery, electrical, vehicles, aircraft, ships) show the shallowest decay at -1.26, with intermediate manufacturing (Sections 6-15) between the two. This ordering lines up with Duranton & Storper (2008, Canadian Journal of Economics 41(1)) on higher-margin sorted manufactures being less distance-sensitive, and with Feyrer (2019, AEJ: Applied Economics 11(4)) on trade-cost declines being concentrated in the heavier bulk-commodity lines. Each group uses CR1-clustered SE on exporter. Cluster means beyond the fifth decimal shown here: see the source CSV for full precision.
A cleaner test of the digital-trade hypothesis would track services flows: software, streaming, cloud, professional services. 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). This is the ICT hardware and information-goods bloc, a chapter-level approximation rather than a paper-derived classification. If digital infrastructure were genuinely lowering the distance wedge in goods, we would expect the distance coefficient on trade fromthese exporters to be less negative than the all-exporter benchmark.
Figure 3
Distance elasticity, digital-intensive exporters vs non-digital, 2024
β̂dist for digital-intensive exporters is -1.21 versus -1.65 for non-digital exporters. The gap is 0.43 log points. A positive gap (less-negative β̂ for digital-intensive) would support 'digital kills distance'; a negative or near-zero gap argues it does not, at least in the subset of trade that BACI captures. The result here is consistent with Hortaçsu, Martínez-Jerez & Douglas (2009, AEJ: Micro 1(1)), who find distance survives as a determinant even of online-platform trade. Caveat: this uses the dominant-exporter-chapter proxy rather than bilateral-by-HS flows; re-running on bilateral HS6 trade with PPML would be the next step.
Method: log-OLS gravity within exporter's digital-intensive status; classification = HS92 chapter in {49, 84, 85} as dominant 2024 export chapter. Sources: CEPII BACI 202501 (retrieved 2026-04-28); CEPII Gravity V202411; WDI. Digital chapter set follows Freund, Mulabdic & Ruta (2024) ICT-hardware bloc.
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 β̂dist 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.
Figure 3b
Distance elasticity by dominant HS Section of exporter, 2024
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 Economics86(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.
Figure 4
Distance elasticity by BEC-style sector block, 2024
β̂dist for consumption goods sits at -1.73 (95% CI ± 0.18), for capital goods at -1.22 (95% CI ± 0.48), and for intermediates at -1.37 (95% CI ± 0.15). Capital goods carry the shallowest decay: they are tariff-light, high value-to-weight, and shipped air-freight more often than the other two blocks. Intermediates sit between the two, as the Johnson & Noguera (2012) value-added read predicts: intermediates are shipped multiple times across borders before final demand, so each leg's distance matters more than a single-ship final-goods flow. Consumption goods fall closest to the all-sector benchmark from Figure 1. The spread across the three blocks is 0.51 log-points, smaller than the cross-section spread across all 21 HS Sections (Figure 3b) but meaningfully larger than the year-to-year time-series noise in Figure 1. Policy implication: trade facilitation and logistics investment have the largest proportional β̂-tightening potential on the intermediates block; consumer-price-pass-through policy bites hardest on the consumption-goods block.
Method: log-OLS gravity with exporter-specialization proxy by BEC bucket, CR1-clustered SE on exporter iso3, same FWL/CR1 machinery as Figure 1. BEC buckets follow UNSD BEC Rev.5 (United Nations 2016) but aggregated at HS chapter granularity to match the workbench Parquet (no bilateral-HS6 table yet). Sources: CEPII BACI 202501 (retrieved 2026-04-28); CEPII Gravity V202411; WDI.Figure 5
Trade-weighted mean great-circle distance, 1995-2024
The dollar-weighted average great-circle distance of world bilateral merchandise trade rose from 5,362 km in 1995 to 5,702 km in 2024, a change of +6.3%. The series peaks at 5,702 km (2024) and bottoms at 4,972 km (2003). Carrere & Schiff (2005, Annales d'Economie et de Statistique 77) proposed this measure as a model-free companion to the gravity coefficient and concluded distance was 'alive and well' for 1962-1996 because d-bar was falling. The 2024 read is consistent with the post-2018 regionalisation evidence in Antras (2020, Journal of Economic Perspectives 34(3)) and Alfaro & Chor (2023, NBER WP 31755): containerised long-haul trade has not lengthened the average dollar's journey, even as the gravity coefficient itself stays flat in Figure 1. The two series are complementary: a flat beta with a flat d-bar tells us that the geographic composition of trade is changing inside a stable distance-elasticity envelope, not that frictions per kilometre are falling.
Sources: CEPII BACI 202501 (retrieved 2026-04-28) (bilateral_year, total_value in thousands USD); CEPII Gravity V202411 (great-circle distance dist, pair-averaged across years). Method: weighted mean d-bar = Σ X·dist / Σ X by year. Authors calcs.
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.
Table 1
Distance elasticity: this workbench vs. the canonical literature
Study
Method
Coverage
β̂(ln dist)
Note
Disdier & Head (2008), REStat 90(1)
Meta-analysis, OLS/Tobit
1,467 estimates, 103 papers, 1870-2001
−0.89 (s.e. 0.40 across studies)
No evidence of decline over time; mildly increasing post-1950.
Head & Mayer (2014), Handbook ch. 3
Structural and FE-OLS, PPML
Review of 159 papers; new ALADIN-style re-estimates
−1.10 (mean), −0.89 (median)
Range [−1.27, −0.89] across FE-OLS and PPML with MR-consistent FEs.
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 β̂t 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 β̂tshould 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 β̂treported 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.
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.
Steepest decay sits in IV. Prepared food, beverages, tobacco at β̂ = -2.22 (95% CI ± 0.42), shallowest in XVI. Machinery, electrical at β̂ = -1.23 (95% CI ± 0.19). The spread across 9 sections is -0.99 log-points, which is much larger than the year-to-year time-series variation in Figure 1 (inside ±0.2). The within-cross-section sectoral dispersion swamps the between-year dispersion: where Disdier & Head (2008) asked why β has not moved across decades, the updated answer in Figure 3b is that the sectoral composition of what a country exports is the dominant determinant of its effective β, not the technology of shipping itself. Bulk mineral, stone, and base-metal sections carry the steepest decay (consistent with Feyrer's Suez-closure elasticity); arms, instruments, and works-of-art sit at the shallow end (very high value-to-weight, insurance-grade logistics). The manufacturing complex (machinery, vehicles) sits in the middle, consistent with Head & Mayer (2014) §3.2.
Method: per-HS Section log-OLS gravity within exporter-specialization group; section = WCO HS Sections I-XXI. Bilateral flows in bilateral_year regressed on log dist (CEPII Gravity V202411, pair-averaged) and log GDP product (WDI NY.GDP.MKTP.CD), with CR1-clustered SE on exporter iso3. Sections with <300 pairs dropped. Sources: CEPII BACI 202501 (retrieved 2026-04-28) (country_year_product_ext, bilateral_year); CEPII Gravity V202411; WDI.
−1.55 to −1.40 by year, −1.52 in 2024
Descriptive, no multilateral-resistance terms. Larger magnitude than structural estimates because no origin/destination FE; drops zeros so Silva-Tenreyro PPML bias applies. See Figure 1 note.
All four rows locate the distance elasticity in the −0.8 to −1.6 range. Our log-OLS coefficient is more negative than the FE-PPML estimates in Head & Mayer (2014) and Yotov et al. (2016), which is the expected log-OLS bias (Silva & Tenreyro 2006) plus the absence of origin/destination fixed effects to purge multilateral-resistance correlation. What survives the methodological differences is the qualitative finding: distance elasticity is firmly negative, large, and, over 1995-2024, not visibly declining, matching the Disdier & Head (2008) conclusion almost two decades on.
Primary-source quotes only. Disdier & Head (2008): REStat 90(1), Table 1 meta means. Head & Mayer (2014): Handbook of International Economics vol. 4, ch. 3, Table 3.4. Yotov et al. (2016): Advanced Guide to Trade Policy Analysis, WTO/UN, ch. 2 applications. Workbench row: this page.