Achdou, Yves. <br/><br/>
Income and Wealth Distribution in Macroeconomics:  A Continuous-Time Approach / 
Yves Achdou, Jiequn Han, Jean-Michel Lasry, Pierre-Louis Lions, Benjamin Moll. 
 - Cambridge, Mass.  National Bureau of Economic Research  2017. 
 - 1 online resource:  illustrations (black and white); 
 - NBER working paper series  no. w23732 .
 - Working Paper Series (National Bureau of Economic Research)  no. w23732. .
<br/><br/> August 2017. 
<br/><br/> 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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