Endogenous Discounting and Economic Dynamics (with Kirill Borissov, Stefano Bosi, Van-Quy Nguyen and Mikhail Pakhnin)
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.
Poverty traps under endogenous discounting (with Stefano Bosi)
We consider a general Ramsey model with endogenous discounting, depending on current consumption or future capital, study the monotonicity properties of the optimal path, and provide a new narrative for the existence of a poverty trap, alternative to the literature on convex-concave production functions. We prove the continuity and differentiability properties of the value function, as well as the monotonicity of the policy correspondence, which in turn entails the strict monotonicity of the optimal path. Importantly, the existence of a poverty trap relies on the existence of a critical level of capital such that, if the initial condition is lower, the optimal path converges to the origin, while, if it is higher, this path converges to a positive steady state. Since it is impossible to compute this critical level under endogenous discounting when the discount factor is a general function of current consumption or future capital, in both these cases, we complement the theoretical analysis with robust corresponding examples and, showing that a poverty trap exists for a nonzero-measure set of parameter values, we demonstrate that the poverty trap is a pervasive feature under endogenous discounting.
Subjective Expected Utility on Arbitrary State Spaces
This article considers Savage's theorem in a configuration relaxing the \textit{technical} axioms P6 and P7 that ensure a continuum nature on the set of states. With the only enrichment on fundamentals being the connectivity of the outcomes set, we show that a weakened version of the Independence property is sufficient to establish a utility function, a subjective probability, and an expected utility behavior. The proof does not require the existence of a pair event, an idea initiated by Ramsey (1926) and applied by Gul (1992).
On Ramsey equilibrium with dependent preferences (with Jean-Paul Barinci).
This paper introduces consumption externalities in a one-sector Ramsey economy featuring heterogeneous households and borrowing constraints. Externalities are taken into account by writing that the felicity functions depend upon the consumption of all the households in the economy. Focusing on the class of equilibria in which the most patient household owns the whole capital stock, it is proved that there exist non-convergent Ramsey equilibria even though the Maximum Income Monotonicity (MIM) condition holds.
On Multiple Time-Varying Discount Rates with Recursive Time-Dependent Orders (with Jean-Pierre Drugeon).
This study addresses time-dependent orders that lead to recursive representations based on a Max-Min configuration. The article introduces and analyzes a structure that is combined with a time-varying multiple discounts. This setup contributes to the understanding of the much discussed present biases. A representation result for robust orders is also presented.