Mons Chan, University of Minnesota
"How Substitutable Are Labor and Intermediates?"
Empirical models of production often impose input complementarity and rule out an extensive margin in the decision to “make or buy” inputs. This paper develops a simple model of production which generalizes the standard Cobb-Douglas approach and allows labor and intermediates of similar types (or “tasks”) to be complements, substitutes, or (importantly) outsourced entirely. Modeling this make-or-buy decision directly allows me to correct for the selection bias resulting from the endogenous outsourcing decision and to characterize the extensive margin of factor demand. I take the model to unique Danish data on task-level purchases of disaggregated labor (e.g., truck drivers), goods, and services (e.g., shipping) and find that labor and intermediates are gross substitutes. Estimated elasticities of substitution range from 1.5 to 4, with positive cross-price elasticities between 0 to 2 across inputs and industries.
These results also hold in standard firm data using total labor and intermediate expenditure variables. Aggregating across firms, I show that demand for labor is becoming increasingly price elastic over time, driven by growing outsourcing and specialization. To illustrate the importance of allowing for flexible substitutability, I examine the effect of an increase in minimum wages in the Danish manufacturing industry, finding that ignoring outsourcing underestimates disemployment by 40%. This finding also has important implications for estimating productivity. I estimate the effect of recent decreases in Danish import tariffs on firm productivity and show that controlling for substitution triples the results relative to benchmark models, which only control for price effects.
Contact person: Jakob Roland-Munch