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Silva & Tenreyro's 2006 Review of Economics and Statistics paper, 'The Log of Gravity,' showed that running bilateral trade on OLS-in-logs systematically inflates the distance elasticity in absolute value and biases the income elasticities downward, because the log transformation interacts badly with heteroskedasticity and because it silently drops zero-trade pairs. Their remedy, Poisson pseudo maximum likelihood on the multiplicative form, has become the modern default. Twenty years later, with BACI 2024 now available and global trade patterns reshaped by China's rise, the 2018 tariff war, and the pandemic supply break, it is worth asking: do OLS and PPML still diverge in the same direction, by the same order of magnitude, when we re-run the race on today's data? We estimate both on four annual cross-sections (1996, 2005, 2015, 2024) on a consistent universe of 120 economies and report the gap.
The classic Silva & Tenreyro (2006, REStat) Table 3 result on their 1990 sample is a distance elasticity of about −1.35 under OLS-in-logs and −0.75under PPML, PPML at roughly 56% of OLS in absolute value. Head & Mayer (2014, Handbook of International Economics, chapter 3) survey the downstream literature and place the modal PPML distance elasticity between −0.8 and −1.1 under origin & destination fixed effects. Yotov, Piermartini, Monteiro & Larch (2016, An Advanced Guide to Trade Policy Analysis, UN/WTO) recommend PPML with exporter-year, importer-year and pair fixed effects as the structural-gravity workhorse. Our question here is narrower and descriptive: on pooled cross-sections without fixed effects, does the OLS/PPML wedge on distance, GDP-origin, GDP-destination, and contiguity persist in 2024 data, and how does it move from 1996 to 2024?
For each of the four years we build a balanced panel of directed pairs across a fixed universe of 120 economies (the top 120 by average nominal GDP 1996-2024, intersected with the country universe in Legacy gravity_bilateral table (exact release provenance unverified) so all covariates are present). Bilateral trade comes from CEPII BACI release 202601, aggregated across all HS6 products to a single exporter-importer flow in thousands of USD and multiplied by 1000 for the analysis; pairs with no BACI record are coded as zero. GDP at current USD comes from the World Bank WDI NY.GDP.MKTP.CD indicator; distance and contiguity come from Legacy gravity_bilateral table (exact release provenance unverified), using population-weighted values taken from year 2020 (time-invariant geography). We then run two specifications on every year:
IRLS iterates βt+1 = (X′ Wt X)−1 X′ Wtzt with weights Wt = diag(μt) and working response zt = ηt + (y − μt) / μt, μt = exp(X βt), starting from the OLS solution and converging to tolerance 10−6 in typically fewer than 30 steps on every year in our sample. We do notinclude origin-year, destination-year, or pair fixed effects: this is deliberately the same no-FE specification Silva & Tenreyro compare in their Table 3, so the OLS-vs-PPML wedge here is apples-to-apples with their 1990 benchmark. A fully-specified structural gravity would add three-way fixed effects and is outside the scope of this page. Robust (Eicker-Huber-White) standard errors are reported in parentheses: the sandwich estimator at the converged IRLS weights for PPML, HC1 for OLS, both heteroskedasticity-consistent and unclustered.
Anderson & van Wincoop (2003, AER) show that the Armington-CES structural-gravity model implies unit elasticities on both origin and destination GDP once multilateral-resistance terms are absorbed by fixed effects. Without fixed effects, both OLS and PPML coefficients are reduced-form; the question is which estimator lands closer to the theoretical unit benchmark.
Table 1 puts our estimates next to the canonical Silva-Tenreyro (2006) Table 3 numbers for 1990 and our replication of the same model on 1996 (the earliest BACI year) and 2024. The 1996 column is not a true replication of the SST sample, they used a different country set and a simpler covariate list, but it is the closest apples-to-apples we can build from Legacy gravity_bilateral table (exact release provenance unverified) and CEPII BACI 202601 (retrieved 2026-06-01).
Head & Mayer (2014, Handbook of International Economics, ch. 3) survey 159 papers and report a modal 'border coefficient' of about +0.5 under OLS-in-logs and +0.3 under PPML, the wedge Silva & Tenreyro (2006) attribute to heteroskedasticity in the tail of pairs that happen to share a border and have small absolute flows.
The four-cross-section view of Figure 1 hides the year-by-year path. The 'slowbalisation' hypothesis (popularised in The Economist, January 2019, and formalised in Antràs 2020, NBER Working Paper 28115) claims that the trade-distance relationship has weakened (elasticity moving toward zero) since the 2008 global financial crisis, as global value chains stopped lengthening and China-centred production consolidated. We re-estimate PPML and OLS on 11 roughly-evenly-spaced years between 1996 and 2024 on the same 120-country universe and read the trajectory off.
Anderson & van Wincoop (2003, AER93(1)) derive the canonical structural gravity prediction: unit elasticities on both GDP sides (β=1) and a distance elasticity of roughly −1. A compact cross-section-invariant test is the RELATIVE magnitude |β(dist)| / avg(β(GDPo), β(GDPd)), the 'distance tax' expressed in GDP-elasticity units. If both the numerator and the denominator are near unity, the ratio is near one and the 'slowbalisation' claim that relative frictions have fallen can be tested by whether the ratio declines. We plot the PPML and OLS versions across the four cross-sections.
Figures 1-6 estimate one PPML coefficient per cross-section and treat the world of exporters as homogeneous. Head & Mayer (2014, Handbook of International Economicsch. 3, §3.2) flag exporter heterogeneity as a first-order omitted dimension in pooled gravity, and Anderson & van Wincoop (2003, AER 93(1)) absorb it into multilateral-resistance terms in modern fixed-effects specifications. Figure 7 keeps the same bare-bones design (no fixed effects) but splits the 2024 cross-section into exporter-GDP tertiles and refits PPML on each. If the headline elasticity is masking heterogeneity (rich-country exporters less distance-sensitive than poor-country exporters, the prediction in Hummels 2007 JEP 21(3) on air-cargo penetration), the three bars should fan out.
Three findings emerge from this re-run. First, the direction of the OLS-vs-PPML distance wedge is identical to what Silva & Tenreyro documented twenty years ago on 1990 data: OLS on positive-trade pairs returns a more-negative distance elasticity than PPML on the zero-inclusive sample, in every year we estimate. Second, the ratio of the two is roughly 0.5-0.7 across 1996, 2005, 2015 and 2024, broadly consistent with the 0.56 ratio SST reported, though not identical. Third, the zero-trade share is still economically meaningful in 2024 (6.7% of directed pairs within our universe), which means OLS-in-logs is still discarding real information about the extensive margin that PPML retains, the Helpman-Melitz-Rubinstein (2008) point about the extensive margin has not gone away.
What we have notdone: we omit exporter-year, importer-year, and pair fixed effects. The modern best-practice structural-gravity specification of Yotov et al. (2016, UN/WTO) or Anderson, Larch & Yotov (2018, The World Economy) would add those, and the distance elasticities under three-way FE would typically land in the −0.8 to −1.1 range (Head & Mayer 2014). The point of this page is narrower: to demonstrate that the Silva-Tenreyro message that OLS-in-logs bias is real, in a specific and quantifiable direction, still holds on BACI 2024with the same bare-bones covariate set they used. A future page on this workbench will re-run the exercise with three-way fixed effects and the Correia, Guimarães & Zylkin (2020) ppmlhdfe iterative-reweighting algorithm, which is the right tool for that enlarged specification.
@misc{hossen_2026_gravity_ppml_baci2024,
author = {Md Deluair Hossen},
title = {OLS versus PPML gravity, revisited on BACI 2024},
year = {2026},
howpublished = {TradeWeave Workbench},
url = {https://tradeweave.org/research/gravity-ppml}
}-- per year t in {1996, 2005, 2015, 2024}
WITH pairs AS (
SELECT o.iso3 AS iso3_o, d.iso3 AS iso3_d
FROM universe o CROSS JOIN universe d
WHERE o.iso3 <> d.iso3
), trade AS (
SELECT exporter.iso3 AS iso3_o, importer.iso3 AS iso3_d,
SUM(total_value) AS trade_kusd
FROM 'bilateral_year/year=${t}/*.parquet'
GROUP BY exporter.iso3, importer.iso3
)
SELECT p.iso3_o, p.iso3_d,
COALESCE(trade.trade_kusd, 0) AS trade_kusd,
wdi_o.value AS gdp_o, wdi_d.value AS gdp_d,
g.dist, g.contig
FROM pairs p
JOIN wdi wdi_o ON wdi_o.iso3 = p.iso3_o AND wdi_o.year = ${t}
JOIN wdi wdi_d ON wdi_d.iso3 = p.iso3_d AND wdi_d.year = ${t}
JOIN 'gravity_bilateral/year=2020/*.parquet' g
ON g.iso3_o = p.iso3_o AND g.iso3_d = p.iso3_d
LEFT JOIN trade ON trade.iso3_o = p.iso3_o AND trade.iso3_d = p.iso3_d;
-- OLS on rows with trade_kusd > 0, PPML IRLS on full sample.| OLS β on contiguity | +0.470 | +0.804 (0.140) | +0.755 (0.137) |
| PPML β on contiguity | +0.349 | +0.862 (0.153) | +0.718 (0.182) |
| sample (OLS / PPML) | ~18k / ~18k | 6,454 / 11,772 | 10,382 / 11,130 |
-- Re-fit PPML on each year in {1996, 1999, 2002, 2005, 2008, 2011, 2014, 2017, 2020, 2023, 2024} with identical universe.
-- Same data-construction CTE as Figure 1; IRLS iteration same as earlier figures.
-- Reads out PPML β on ln(distance) only; see Figures 1-4 for the full coefficient vector.-- Per-year OLS + PPML coefficients from the same construction as Figures 1-4; -- ratio computed in-app as |β(ln dist)| / ((β(ln GDP_o) + β(ln GDP_d)) / 2).
-- PPML β(ln dist) on each exporter-GDP tertile, 2024 cross-section -- Subset latest cross-section by tertile of exporter contemporaneous GDP, -- refit IRLS PPML with the same 5-column design as Figures 1-2.