OLS versus PPML gravity, revisited on BACI 2024

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 (1995, 2005, 2015, 2024) on a consistent universe of 120 economies and report the gap.

Research question

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 −0.75 under 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 1995 to 2024?

Method

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 1995–2024, intersected with the CEPII Gravity V202411 country universe so all covariates are present). Bilateral trade comes from CEPII BACI release 202501, 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 are the CEPII Gravity population-weighted values taken from 2020 (time-invariant geography). We then run two specifications on every year:

1. OLS-in-logs on positive-trade pairs only: ln X_ij = β₀ + β_d ln dist_ij + β_o ln GDP_i + β_m ln GDP_j + γ contig_ij + ε_ij.
2. PPML on the full zero-inclusive sample: X_ij = exp(β₀ + β_d ln dist + β_o ln GDP_i+ β_m ln GDP_j + γ contig) · ν_ij, estimated by iteratively-reweighted least squares on the Poisson quasi-likelihood (Gourieroux, Monfort & Trognon 1984; Silva & Tenreyro 2006; Yotov et al. 2016, §2.3).

IRLS iterates β_t+1 = (X′ W_t X)⁻¹ X′ W_tz_t with weights W_t = diag(μ_t) and working response z_t = η_t + (y − μ_t) / μ_t, μ_t = exp(X β_t), starting from the OLS solution and converging to tolerance 10⁻⁶ in under 30 steps on every year. We do not include 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. Standard errors are not reported; point estimates only.

Distance: the classic OLS bias still lives

GDP-origin and GDP-destination: closer to unity under PPML

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.

How much do we throw away by running OLS?

Benchmark: Silva-Tenreyro 1990 vs our 1995 and 2024

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 1995 (the earliest BACI year) and 2024. The 1995 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 CEPII Gravity V202411 and BACI 202501.

Contiguity: where OLS most overstates the border effect

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.

Has globalisation “slowed”? The annual PPML distance elasticity, 1995–2024

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, Journal of Economic Perspectives) 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 1995 and 2024 on the same 120-country universe and read the trajectory off.

Figure 6: Relative stability of the distance and GDP elasticities

Anderson & van Wincoop (2003, AER 93(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(GDP_o), β(GDP_d)) — 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.

Heterogeneity: PPML distance elasticity by exporter income tertile, 2024

Figures 1–6 estimate one PPML coefficient per cross-section and treat the world of exporters as homogeneous. Head & Mayer (2014, Handbook of International Economics ch. 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.

What we learn

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 1995, 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 not done: 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, JIE) 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 — OLS-in-logs bias is real, in a specific and quantifiable direction — still holds on BACI 2024 with 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 (2019) ppmlhdfe iterative-reweighting algorithm, which is the right tool for that enlarged specification.

Open questions

• With three-way fixed effects (exporter-year, importer-year, pair) as in Yotov et al. (2016), does the OLS/PPML distance-elasticity wedge compress, widen, or invert? The answer determines whether the Silva–Tenreyro critique is a fixed-effect artefact or a structural heteroskedasticity result.
• Does the rising zero-trade share in tail economies since 2018 (pandemic+sanctions) reinstate the Helpman, Melitz & Rubinstein (2008) extensive-margin correction that had been fading as globalisation progressed?
• How do PPML distance elasticities move when estimated separately on services gravity (WTO BaTIS) versus goods (BACI)? Head & Mayer (2014) note that services distance elasticities are typically closer to zero, consistent with the digital-trade cost literature.

References

• Anderson, J. E., & van Wincoop, E. (2003). “Gravity with Gravitas: A Solution to the Border Puzzle.” American Economic Review 93(1): 170–192.
• Anderson, J. E., Larch, M., & Yotov, Y. V. (2018). “GEPPML: General Equilibrium Analysis with PPML.” The World Economy 41(10): 2750–2782.
• Correia, S., Guimarães, P., & Zylkin, T. (2019). “ppmlhdfe: Fast Poisson Estimation with High-Dimensional Fixed Effects.” Stata Journal 20(1): 95–115.
• Gourieroux, C., Monfort, A., & Trognon, A. (1984). “Pseudo Maximum Likelihood Methods: Applications to Poisson Models.” Econometrica 52(3): 701–720.
• Head, K., & Mayer, T. (2014). “Gravity Equations: Workhorse, Toolkit, and Cookbook.” In Handbook of International Economics, vol. 4, ch. 3, 131–195.
• Helpman, E., Melitz, M., & Rubinstein, Y. (2008). “Estimating Trade Flows: Trading Partners and Trading Volumes.” Quarterly Journal of Economics 123(2): 441–487.
• Santos Silva, J. M. C., & Tenreyro, S. (2006). “The Log of Gravity.” Review of Economics and Statistics 88(4): 641–658.
• Yotov, Y. V., Piermartini, R., Monteiro, J.-A., & Larch, M. (2016). An Advanced Guide to Trade Policy Analysis: The Structural Gravity Model. UNCTAD/WTO.
• Yotov, Y. V. (2022). “On the Role of Domestic Trade Flows for Estimating the Gravity Model of Trade.” Contemporary Economic Policy 40(2): 526–540.

BibTeX

@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}
}