COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1292

The Financing of Innovation: Learning and Stopping

Dirk Bergemann and Ulrich Hege

January 2001

This paper considers the financing of a research project under uncertainty about the time of completion and the probability of eventual success. The uncertainty about future success gradually diminishes with the arrival of addtional funding. The entrepreneur controls the funds and can divert them. We distinguish between relationship financing, meaning that the entrepreneur's allocation of the funds is observable, and arm's length financing, where it is unobservable.

We find that equilibrium funding stops altogether too early relative to the efficient stopping time in both financing modes. We characterize the optimal contracts and equilibrium funding decisions. The financial constraints will typically become tighter over time under relationship finance, and looser under arm's length financing. The trade-off is that while relationship financing may require smaller information rents, arm's length financing amounts to an implicit commitment to a finite funding horizon. The lack of such a commitment under relationship financing implies that the sustainable release of funds eventually slows down. We obtain the surprising result that arm's length contracts are preferable in a Pareto sense.

Keywords: innovation, venture capital, relationship financing, arm's length financing, learning, time-consistency, stopping, renegotiation, Markov perfect equilibrium

JEL Classification: D83, D92, G24, G31