Muliere, Pietro; Suverato, Davide (28. May 2014): Income and Wealth Distributions in a Population of Heterogeneous Agents. Discussion Papers in Economics 201421 

257kB 
Abstract
This paper develops a simple framework to characterize the distribution of income and wealth in a real business cycle model. Agents are of two types depending on the human factor of production they own and they are located in separated markets, cities. In each city the two types of agent match to produce a composite factor, human service. We show that if the population is an exchangeable sequence of agents' types generated according to a Pòlya urn then (i) the share of agents' type follows a Beta distribution and (ii) the functional form of the matching function belongs to the family of the constant elasticity of substitution, with agent shares that depend on the composition of the population. We nest this structure into a standard Bewley economy, in which the aggregate supply of human service is combined with physical capital to produce the homogeneous output. Given the results (i)(ii) we perform the exact aggregation of income, consumption and asset holding across agents, leading to the solution of the real business cycle model with heterogeneous agents. Our framework predicts that the theoretical distributions of income and wealth are known real valued transformations of a Beta distribution. This result provides a simple way to characterize the equilibrium of macroeconomic models with heterogeneous agents.
Item Type:  Paper (Discussion Paper) 

Faculties:  Economics Economics > Munich Discussion Papers in Economics 
Subjects:  300 Social sciences > 330 Economics 
URN:  urn:nbn:de:bvb:19epub209289 
Language:  English 
ID Code:  20928 
Deposited On:  02. Jun 2014 10:56 
Last Modified:  13. Oct 2016 15:56 
References:  Aiyagari, S. (1994). Uninsured idiosyncratic risk and aggregate saving. The Quarterly Journal of Economics, 109(3):659684. Aoki, M. (1998). Simple model of asymmetrical business cycles: Interactive dynamics of a large number of agents with discrete choices. Macroeconomic Dynamics, 2(04):427442. Aoki, M. and Yoshikawa, H. (2007). Reconstructing Macroeconomics. Cambridge edition. Brock, W. A. and Mirman, L. J. (1972). Optimal economic growth and uncertainty: The discounted case. Journal of Economic Theory, 4(3):479513. Durlauf, S. N. (2012). Complexity, economics, and public policy. Politics, Philosophy & Economics, 11(1):4575. Durlauf, S. N. and Ioannides, Y. M. (2010). Social Interactions. Annual Review of Economics, 2(1):451478. Gaffeo, E., Gatti, D. D., Desiderio, S., and Gallegati, M. (2008). Adaptive microfoundations for emergent macroeconomics. Eastern Economic Journal, 34(4):441463. Heathcote, J., Storesletten, K., and Violante, G. L. (2009). Quantitative Macroeconomics with Heterogeneous Households. Annual Review of Economics, 1(1):319354. Hill, B. M. (1970). Zipf' s Law and Prior Distributions for the Composition of a Population. Journal of the American Statistical Association, 65(331):12201232. Houthakker, H. (1955). The Pareto distribution and the CobbDouglas production function in activity analysis. The Review of Economic Studies, 23(1):2731. Huggett, M. (1993). The riskfree rate in heterogeneousagent incompleteinsurance economies. Journal of Economic Dynamics and Control. Johnson, N. L. and Kotz, S. (1997). Urn Models and Their Application. John Wiley, 1 edition. Jones, C. (2005). The shape of production functions and the direction of technical change. The Quarterly Journal of Economics, (May):517549. Kirman, A. P. (1992). Whom or What Does the Representative Individual Represent? Journal of Economic Perspectives, 6(2):117136. Kortum, S. (1997). Research, Patenting, and Technological Change. Econometrica, 65(6):13891419. Lengnick, M. (2013). Agentbased macroeconomics: A baseline model. Journal of Economic Behavior & Organization, 86(C):102120. Mahmoud, H. (2008). Polya Urn Models. Chapman & Hall/CRC, 1 edition. McCall, J. J. (1991). Exchangeability and its economic applications. Journal of Economic Dynamics and Control, 15(3):549568. Muliere, P., Secchi, P., and Walker, S. (2005). Partially exchangeable processes indexed by the vertices of a ktree constructed via reinforcement. Stochastic Processes and their Applications, 115(4):661677. 