We measure firms’ wage-setting power in 16 countries across Latin America and the Caribbean. Exploiting variation in firms’ exposure to trade and exchange rates, we generate idiosyncratic 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 for every additional dollar they produce. Wage-setting power is significantly higher among firms in countries with lower union density, limited collective bargaining, and no unemployment protection. These findings underscore the role of labor market institutions in shaping firms’ wage-setting power and the distribution of the gains from trade.