Is Software Eating the World?

When explaining the declining labor income share in advanced economies, the macro literature finds that the elasticity of substitution between capital and labor is greater than one. However, the vast majority of micro-level estimates shows that capital and labor are complements (elasticity less than one). Using firm- and establishment-level data from Korea, we divide capital into equipment and software, as they may interact with labor in different ways. Our estimation shows that equipment and labor are complements (elasticity 0.6), consistent with other micro-level estimates, but software and labor are substitutes (1.6), a novel finding that helps reconcile the macro vs. micro-literature elasticity discord. As the quality of software improves, labor shares fall within firms because of factor substitution and endogenously rising markups. In addition, production reallocates toward firms that use software more intensively, as they become effectively more productive. Because in the data these firms have higher markups and lower labor shares, the reallocation further raises the aggregate markup and reduces the aggregate labor share. The rise of software accounts for two-thirds of the labor share decline in Korea between 1990 and 2018. The factor substitution and the markup channels are equally important. On the other hand, the falling equipment price plays a minor role, because the factor substitution and the markup channels offset each other.