In this paper we study the effect of unions on product and process innovation both theoretically and empirically. We propose a Cournot duopoly model where labor productivity is allowed to differ across unionized and non-unionized sectors due to collective voice mechanism. Our findings suggest that the traditional hold-up view whereby unions discourage innovation does not necessarily survive. When the voice effect is neither too strong nor too low, the unionized sector outperforms the market in terms of process innovation, while the effect on product innovation is strictly increasing in the voice power. Our empirical analysis of a large representative sample of Italian firms supports the model's predictions in both pooled OLS, fixed effects and IV.