We examine whether standards raise the quality of traded products by correcting market failures associated with information asymmetry on product attributes. Matching a panel of French firmproduct- destination export data with a dataset on sanitary and phytosanitary (SPS) measures and technical barriers to trade (TBTs), we find that such quality standards enforced on products by destination countries: (i) favor 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; (iii) improve the average quality of consumption goods exported by France. We then develop a simple new trade model under uncertainty about product quality, in which heterogeneous firms can strategically invest in quality signaling, to rationalize these empirical results on quality and selection effects.