ALT We measure firms’ wage-setting power in 16 Latin American and Caribbean countries. Exploiting variation in firms’ exposure to trade and exchange rates, we generate shocks to labor demand to trace out firm-level labor supply curves and quantify labor market power. We estimate an inverse labor supply elasticity of 0.82, implying that workers receive 55 cents per additional dollar produced. Wage-setting power is significantly higher among firms in countries with lower union density, limited collective bargaining, and no unemployment protection. This underscores the role of labor market institutions in shaping firms’ wage-setting power and the distribution of the gains from trade.