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

Fig. 3. Estimated trade volume and unit price effects of VSS-specific coverage.

Fig. 3

a, b Estimated effects (%) of a one-percentage-point (pp) increase in VSS-specific certified production area on (a) trade volume and (b) 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 interval. Trade volume effects (a) estimated for the full sample (N = 961,664 exporter-importer-product-time trade flow observations) using PPML and IV-PPML, and trade volume effects (a) and unit price effects (b) estimated for the non-zero sample (N = 120,800 exporter-importer-product-time trade flow observations) using PPML, IV-PMML, OLS, and 2SLS. ProTerra full-sample IV-PPML volume effects 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 S5–S7. VSS voluntary sustainability standards, RA Rainforest Alliance, Fairtrade Fairtrade International, RSPO Roundtable on Sustainable Palm Oil, IFOAM IFOAM Organics International, PPML Poisson pseudo-maximum likelihood, IV-PPML instrumental variable PPML, OLS ordinary least squares, 2SLS two-stage least squares.