Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities

Borovička, Jaroslav; Stachurski, John

doi:10.3386/w24162

“…To attack this problem, I use a technique recently introduced by Borovička and Stachurski (2017), who give a necessary and sufficient condition for existence, uniqueness, and computability of a fixed point of a certain monotone operator. Because their condition is necessary and sufficient, we can study the behavior of the fixed point as the interest rate tends to the upper bound for the existence of a solution, which enables me to show that the excess demand function crosses zero.…”

Section: Introductionmentioning

confidence: 99%

Wealth Distribution with Random Discount Factors

Toda

¹

2017

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It is well-known that empirical wealth distributions have Pareto tails. To explain this fact, the quantitative macro literature has occasionally assumed that agents have random discount factors. However, the fact that random discounting generates Pareto tails is a 'folk theorem' that has been shown only in very particular settings (e.g., i.i.d. environment or affine rule-of-thumb consumption rule). Using a highly stylized but fully specified heterogeneous-agent dynamic general equilibrium model of consumption and savings with an arbitrary Markovian dynamics for the discount factor, I prove that the upper and lower tails of the wealth distribution obey power laws and characterize the Pareto exponents. I also discuss a numerical example and show that there is no clear relationship between the return on wealth and inequality and that the Pareto exponent is highly sensitive to the persistence of the discount factor process.

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Wealth distribution with random discount factors

Toda

¹

2019

Journal of Monetary Economics

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It is well-known that empirical wealth distributions have Pareto tails. To explain this fact, the quantitative macro literature has occasionally assumed that agents have random discount factors. However, the fact that random discounting generates Pareto tails is a 'folk theorem' that has been shown only in very particular settings (e.g., i.i.d. environment or affine rule-of-thumb consumption rule). Using a highly stylized but fully specified heterogeneous-agent dynamic general equilibrium model of consumption and savings with an arbitrary Markovian dynamics for the discount factor, I prove that the upper and lower tails of the wealth distribution obey power laws and characterize the Pareto exponents. I also discuss a numerical example and show that there is no clear relationship between the return on wealth and inequality and that the Pareto exponent is highly sensitive to the persistence of the discount factor process.

show abstract