Endogenous Discounting and Economic Dynamics
(with Kirill Borissov, Stefano Bosi, Thai Ha-Huy and Van-Quy Nguyen), CESifo Working Paper No. 12156, 2025.

Abstract: We study a discrete-time optimal growth model with endogenous discounting. The discount factor may depend on both consumption and the capital stock, and intertemporal utility is modeled as a discounted sum of instantaneous utilities, with the sum of discount factors equal to one. We show that this specification preserves the invariance of optimal paths and steady states to affine transformations of the instantaneous utility function, providing a general and flexible framework for analyzing economic dynamics under endogenous time preference. We prove that optimal capital paths are monotonic, and steady states depend on initial conditions. We also show the robustness of poverty traps under endogenous discounting: in several examples, for a set of parameters with positive measure, the optimal path converges to a positive steady state only if the initial capital stock exceeds a critical level and otherwise converges to the origin.

Envy Today, Inequality Tomorrow: How Present Bias Shapes the Wealth Distribution
(with Kirill Borissov and Ronald Wendner), Graz Economics Papers 2025-02, University of Graz, Department of Economics, 2025.

Abstract: We study the effects of envy (relative consumption concerns), drawing on evidence that preferences typically exhibit present bias. We employ a Ramsey-type model with agents who differ in initial capital endowments and account for present-biased envy: agents are naive and care about how their consumption levels compare to those of others only in the current period. Present-biased envy, unlike permanent envy, significantly affects both the level of inequality and the aggregate income level in an economy. First, it generates the Matthew effect (the relatively rich get richer while the relatively poor get poorer), and after a finite time, only the initially wealthiest agents own the entire capital stock and the debts of others who are in the maximum borrowing state. Second, in contrast to both an economy without envy or with permanent envy, present-biased envy makes agents effectively more impatient, reducing the long-run capital stock and aggregate income level.

Earlier version: Present-Biased Envy, Inequality, and Growth