Hengjie Ai and Rui Li
CQER Working Paper 12-01
February 2012
We present a dynamic general equilibrium model with heterogeneous firms. Owners of firms delegate investment decisions to managers, whose consumption and investment decisions are private information. We solve the optimal contracts and characterize the implied general equilibrium. Our calibrated model has implications on the cross-sectional distribution and time-series dynamics of firms' investment, managers' compensation, and dividend payout policies. Risk sharing requires that managers' equity shares decrease with firm sizes. That, in turn, implies it is harder to prevent private benefit in larger firms, where managers have a lower equity stake under the optimal contract. Consequently, small firms invest more, pay less dividends, and grow faster than large firms. Despite the heterogeneity in firms' decision rules and the failure of Gibrat's law, we show that the size distribution of firms in our model resembles a power law distribution with a slope coefficient about 1.06, as in the data.
JEL classification: C68, D82, D86, D92, G32
Key words: principal-agent, moral hazard, investment, firm dynamics
The authors would like to thank Ravi Bansal, Dean Corbae, Steven Durlauf, Kenichi Fukushima, Antonio Mello, Adriano Rampini, Marzena Rostek, Vish Viswanathan, Noah Williams, Tao Zha, and seminar participants at the Fuqua School of Business at Duke University, Federal Reserve Bank of Atlanta, University of Calgary, University of Minnesota, and University of Wisconsin-Madison for useful conversations on the topic. The authors also thank Song Ma for his excellent research assistance. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.
Please address questions regarding content to Hengjie Ai, The Fuqua School of Business, Duke University, 100 Fuqua Drive, Durham, North Carolina 27708, 919-660-2900, hengjie.ai@duke.edu or Rui Li, Department of Economics, University of Wisconsin, Sewell Social Sciences Building, Office 7234, 1180 Observatory Drive, Madison, Wisconsin 53706, 608-262-0200, rli2@wisc.edu.
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