Working Paper: NBER ID: w24162
Authors: Jaroslav Borovika; John Stachurski
Abstract: We study existence, uniqueness and stability of solutions for a class of discrete time recursive utilities models. By combining two streams of the recent literature on recursive preferences - one that analyzes principal eigenvalues of valuation operators and another that exploits the theory of monotone concave operators - we obtain conditions that are both necessary and sufficient for existence and uniqueness. We also show that the natural iterative algorithm is convergent if and only if a solution exists. Consumption processes are allowed to be nonstationary.
Keywords: recursive utility; existence; uniqueness; consumption; macroeconomics
JEL Codes: D81; G11
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| spectral radius (r_k) < 1 (C62) | unique globally attracting solution exists (C62) |
| r_k ≥ 1 (C29) | no finite solution exists (C62) |
| solution exists (C62) | iterative algorithm converges (C69) |