A Theory of Factor Shares∗

This paper presents a theory of how factor shares are determined. I first develop microfoundations for a unified aggregate production function that incorporates a frictional process of matching workers and firms. Firms with productivities drawn from a Pareto distribution hire capital and compete for workers. Wages are determined by Bertrand competition. In contrast with Houthakker’s classic result, the aggregate production function derived here is Cobb-Douglas only in the limit as unemployment goes to zero. In general, the elasticity of substitution between capital and labor is less than one. Factor shares are asymptotically constant when unemployment disappears and also when workers’reservation wage exceeds the minimum firm productivity. In general, factor shares are variable and depend on unemployment and workers’ reservation wage, as well as the firm productivity distribution. Using annual data on unemployment and eligibility for unemployment insurance, I calibrate the model and test its quantitative predictions. The theory can explain much of the behavior of factor shares in the U.S. from 1951-2003. The correlation between the data and the model’s predictions during this period of over fifty years is 0.69 for the perfect foresight equilibrium and 0.73 when workers are myopic. JEL Codes: E23, E24, E25, J64. ∗I would particularly like to thank my PhD advisors Chris Edmond, Ian King, and John Creedy, and my thesis examiners Rob Shimer and Ricardo Lagos, for helpful feedback and advice. I thank seminar participants at the University of Edinburgh, the Capital Theory Working Group at the University of Chicago, the Chicago Fed, the Philadelphia Fed, the St Louis Fed, the University of Wisconsin-Madison, Melbourne, Adelaide, Queensland, Monash, ANU, Deakin, the SED Annual Meeting 2012, the Search and Matching Annual Meeting 2012, the MEA Meeting 2012, the Midwest Macro Meeting 2012, and the Workshop on Macroeconomic Dynamics 2013. I am grateful to Richard Paris for his assistance in proving Lemma 1 and to Klaus Ackermann for providing excellent research assistance. An early predecessor of this paper was titled "A Unified Production and Matching Function: Implications for Factor Shares". †Monash University, Melbourne. Contact email: [email protected]. Phone: +61 3 9903 2384