While many studies analyzed effects of sustainability standards - such as Fairtrade or Rainforest Alliance - on smallholder farmers in developing countries, most did not sufficiently account for systematic differences between certified and non-certified farmers. Certified farmers are typically organized in cooperatives. When sampling only from a small number of cooperatives, as previous studies did, it is not easy to disentangle certification effects from possible cooperative effects. Here, we address this shortcoming by randomly sampling from a large number of cooperatives, thus capturing a wide range of institutional heterogeneity. In particular, we collect and use data from cocoa farmers in Cote d'Ivoire that are organized in Fairtrade-certified and non-certified cooperatives. Regression models with instrumental variables show that Fairtrade has positive and significant effects on cocoa yields, prices, and living standards. These effects remain significant also after controlling for cooperative characteristics, but the magnitude of the estimates changes. We draw two conclusions. First, in Cote d'Ivoire Fairtrade certification benefits farmers economically. Second, and more generally, cooperative characteristics are jointly correlated with certification and relevant outcomes, which needs to be accounted for to avoid bias when evaluating the benefits of sustainability standards in the small farm sector.