The new training literature argues that imperfect labour markets (i.e. less competition) lead to an increasing productivity-wage wedge. We show that this relation does not hold for all institutional and market environments. We use representative establishment panel data for Germany and apply a control function approach for estimating the production function to correct for endogeneity in input factors. We show that the skill-productivity gradient responds stronger to increases in product market competition and labour market density than the skill-wage gradient. This leads to an increasing productivity-wage wedge in more competitive environments. Similarly, works councils have a stronger effect on the skill-productivity than on the skill-wage gradient while both gradients are similar in the presence of union wage bargaining. Our results call for a more nuanced interpretation of the exposition of the new training literature to understand company-sponsored training across institutional and market environments.