The Factor Bias of External Inputs: Implications for Substitution between Capital and Labor

This paper reevaluates the longstanding debate on capital-labor substitution by examining the role of external inputs: commodities, intermediate goods and services, imports, offshoring. With more than two factors of production, there is more than one relative price. This paper shows that consequently—and in contrast to many workhorse models—external inputs can lead the capital-labor ratio to respond differently to changes in labor and to changes in capital prices. Both indirect inference (based on a meta analysis of existing studies) and direct estimates (using U.S. data for 1963-2016) indicate that external inputs disproportionately displace labor. These findings imply (1) that the capital-labor ratio responds 40-80% more strongly to the price of labor than to the price of capital, (2) that capital and labor are not separable from external inputs in modeling production, and (3) that historical disagreements regarding substitution can be recast as an omitted variable bias involving external inputs.