We contribute to the growing literature which aims to link product market regulation and competition to labor market outcomes, in an attempt to explain the divergent US and continental European labor market performance over the past two decades. The main contributions of this paper are threefold. First, we show that the choice of bargaining regime is crucial for the effect of product market competition on unemployment rates, being substantial under collective bargaining and considerably more modest under individual bargaining. Since the choice of bargaining institution is so important, we endogenize it. We find that the bargaining regime which emerges endogenously depends crucially on the degree of product market competition. When product market competition is low, collective bargaining is stable, while individual bargaining emerges as the stable institution under high degrees of product market competition. This also allows us to link product market competition and collective bargaining coverage rates. Our results suggest that the strong decline in collective bargaining coverage and unionization in the US and UK over the last two decades might have been a direct consequence of the Reagan/Thatcher product market reforms of the early 80's. Finally, we calibrate the model to assess the quantitative magnitude of our results. We find that moving from the US low regulation-individual bargaining economy to the EU high regulation-collective bargaining economy leads to a substantial increase in equilibrium unemployment rates from 5.5% to 8.9 % in the model economy.