Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach / Yves Achdou, Jiequn Han, Jean-Michel Lasry, Pierre-Louis Lions, Benjamin Moll.

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Achdou, Yves

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TextSeries: Working Paper Series (National Bureau of Economic Research) ; no. w23732.Publication details: Cambridge, Mass. National Bureau of Economic Research 2017.Description: 1 online resource: illustrations (black and white)Subject(s):

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Abstract: 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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August 2017.

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.