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. 2026 Apr 2;17:4752. doi: 10.1038/s41467-026-71245-x

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© The Author(s) 2026

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

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Fig. 2 — a, b Estimated effects (%) of a one-percentage-point (pp) increase in overall certified production area on (a) trade volume and (b) unit price. c, d Estimated effects (%) of a one-pp increase in commodity-specific certified production area on (c) trade volume and (d) unit price. Notes: Bars indicate regression estimates derived from augmented gravity models at the exporter-importer-product-time level, and error bars present 90% confidence intervals. Trade volume effects (a, c) estimated for the full sample (N = 961,664 exporter-importer-product-time trade flow observations) using PPML and IV-PPML. Trade volume effects (a, c) and unit price effects (b, d) estimated for the non-zero sample (N = 120,800 exporter-importer-product-time trade flow observations) using PPML, IV-PMML, OLS, and 2SLS. Soy-specific IV-PPML and 2SLS and oil palm non-zero volume IV-PPML estimates could not be estimated. Significance is based on unadjusted two-sided z-tests (PPML, IV-PPML) or t-tests (OLS, 2SLS) and indicated as ***p < 0.01, **p < 0.05, *p < 0.1. Regression results with exact p-values are reported in Supplementary Tables S2–S4. VSS voluntary sustainability standards, PPML Poisson pseudo-maximum likelihood, IV-PPML instrumental variable PPML, OLS ordinary least squares, 2SLS two-stage least squares.