Do larger firms exert more market power? Markups and markdowns along the size distribution

Several models posit a positive cross-sectional correlation between markups and firm size, which characterizes misallocation, factor shares, and gains from trade. Accounting for labor market power in markup estimation, we find instead that larger firms have lower product markups but higher wage markdowns. The negative markup-size correlation turns positive when conditioning on markdowns, suggesting interactions between product and labor market power. Our findings are robust to common criticism (e.g., price bias, non-neutral technology) and hold across 19 European countries. We discuss possible mechanisms and resulting implications, highlighting the importance of studying input and output market power in a unified framework.