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Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach

Listed author(s):
  • Yves Achdou
  • Jiequn Han
  • Jean-Michel Lasry
  • Pierre-Louis Lions
  • Benjamin Moll

We recast the Aiyagari-Bewley-Huggett model of income and wealth distribution in continuous time. This workhorse model – as well as heterogeneous agent models more generally – then boils down to a system of partial differential equations, a fact we take advantage of to make two types of contributions. First, a number of new theoretical results: (i) an analytic characterization of the consumption and saving behavior of the poor, particularly their marginal propensities to consume; (ii) a closed-form solution for the wealth distribution in a special case with two income types; (iii) a proof that there is a unique stationary equilibrium if the intertemporal elasticity of substitution is weakly greater than one; (iv) characterization of “soft” borrowing constraints. Second, we develop a simple, efficient and portable algorithm for numerically solving for equilibria in a wide class of heterogeneous agent models, including – but not limited to – the Aiyagari-Bewley-Huggett model.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 23732.

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Date of creation: Aug 2017
Handle: RePEc:nbr:nberwo:23732
Note: AP EFG ME
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  1. Olivier Guéant & Pierre Louis Lions & Jean Michel Lasry, 2011. "Mean Field Games and Applications," Post-Print hal-01393103, HAL.
  2. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, January.
  3. Francesco Lippi & Stefania Ragni & Nicholas Trachter, 2013. "State Dependent Monetary Policy," EIEF Working Papers Series 1324, Einaudi Institute for Economics and Finance (EIEF), revised Sep 2013.
  4. Carroll, Christopher D., 2006. "The method of endogenous gridpoints for solving dynamic stochastic optimization problems," Economics Letters, Elsevier, vol. 91(3), pages 312-320, June.
  5. Charles I. Jones, 2015. "Pareto and Piketty: The Macroeconomics of Top Income and Wealth Inequality," Journal of Economic Perspectives, American Economic Association, vol. 29(1), pages 29-46, Winter.
  6. Greg Kaplan & Giovanni L. Violante, 2014. "A Model of the Consumption Response to Fiscal Stimulus Payments," Econometrica, Econometric Society, vol. 82(4), pages 1199-1239, 07.
  7. Francisco Buera, 2009. "A dynamic model of entrepreneurship with borrowing constraints: theory and evidence," Annals of Finance, Springer, vol. 5(3), pages 443-464, June.
  8. Conze, Antoine & Lasry, Jean Michel & Scheinkman, Jose, 1993. "2. Borrowing Constraints and International Comovements," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 34(Special I), pages 23-47, December.
  9. Wang, Neng, 2007. "An equilibrium model of wealth distribution," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 1882-1904, October.
  10. Charles I. Jones & Jihee Kim, 2014. "A Schumpeterian Model of Top Income Inequality," NBER Working Papers 20637, National Bureau of Economic Research, Inc.
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