2 A Model of Sequential Production with Incomplete Contracts

Existing incomplete contracting models of the boundaries of the firm have largely focused on production functions in which all tasks are executed simultaneously: All suppliers provide their customized inputs and these are combined at the same time to generate the final good. In practice, however, production processes often take on a sequential nature, with a distinction between upstream stages (such as the procurement or manufacture of basic components) and downstream stages (such as complex assembly or distribution). In this setting, the relationshipspecific investments made by suppliers in upstream stages can affect the incentives of parties involved in later downstream stages. To capture these interactions, we develop a model of firm production with a continuum of uniquely sequenced production stages. In each stage, the firm contracts with a distinct supplier for the procurement of a customized stage-specific input. This setup yields predictions regarding the organizational choices of the firm along its production line. We find that when productionstage inputs are sufficiently close complements, the optimal choice involves the outsourcing of upstream stages and the integration of downstream stages. Intuitively, outsourcing elicits high levels of investment from upstream suppliers. The complementarity of upstream with downstream inputs in turn alleviates the under-investment problem for downstream suppliers, and the firm instead chooses integration downstream to retain a larger share of the realized output. On the other hand, when production stage inputs are sufficiently strong substitutes, the optimal choice involves integration of early production stages and possibly outsourcing of the later ones. ∗We thank Nathan Nunn for generously providing data. Gurmeet Singh Ghumann, Frank Schilbach, and Zhicheng Song provided excellent research assistance. All errors are our own. †Department of Economics, Harvard University, Littauer 230, Cambridge, MA 02138, National Bureau of Economic Research, and Centre for Economic Policy Research. Email: [email protected] ‡School of Economics, Singapore Management University. Address: 90 Stamford Road, Singapore 178903. E-mail: [email protected]