Journal article: We examine whether standards raise the quality of traded products. Matching a panel of French firm–product–destination export data with a data set on sanitary and phytosanitary measures and technical barriers to trade, we find that such quality standards enforced on products by destination countries: (i) favour the export probability of high-quality firms provided that their productivity is high enough, (ii) raise the export sales of high-productivity, high-quality firms at the expense of low-productivity and low-quality firms and (iii) increase the quality supplied by firms if their productivity is high enough. We then develop a simple new trade model under uncertainty about product quality in which heterogeneous firms can strategically invest in quality signalling to rationalize these empirical results on quality and selection effects.