We examine whether standards raise the quality of traded products by correcting mar-ket failures associated with information asymmetry on product attributes. Our predictionson their quality and selection effects are based on a new trade model under uncertaintyabout product quality in which heterogeneous firms can strategically invest in quality sig-naling. Using French firm-level data, we exploit information on prices and productivity toestimate the quality of exported products. Higher quality is assigned to products suppliedby an exporter with higher marginal costs conditional on productivity. In accordance withour theory, quality standards enforced on products by destination countries (i) reduce theexport probability of low-quality firms but also that of high-quality low-productivity firms;(ii) increase the export participation and sales of high-productivity high-quality firms; (iii)improve the average quality of consumption goods exported by France.