Research

How does being time-inconsistent affect economic growth, the extraction of natural resources, and pollution? In this paper we study an endogenous growth model of the expanding variety class, with exhaustible natural resources and pollution under non-constant discounting. We study the naive agent case, who is time-inconsistent under a general discount function and tends to procrastinate. We compare the solutions obtained with a general discount function versus the canonical time-consistent exponential discounting. This self-control component leads the analysis to a Behavioral Macroeconomics problem (willpower and the planner-doer). A firm in the resource sector extracts the non-renewable natural resource needed to produce the final good. Final producer uses labor, non-renewable resource, and a different number of intermediate inputs (machines) produced by different monopolists. Both economic activity and the extraction of the resource generate pollution,  which negatively affects households. We then compare the behaviors under different discount functions and the implications on the sum of discounted utilities under the strong observational equivalence principle. We show that time-inconsistent agents with constant elasticity of intertemporal substitution (CEIS) greater than one have higher levels of economic growth, extract the resource less aggressively, and experience higher growth rate of the creation of new ideas. Moreover, if pollution is reduced, time-inconsistent agents have a slower reduction rate, and if pollution increases, it increases faster for time-incosistent agents. However, if households have a CEIS lower than one, the story is reversed, and the economy with time-consistent decision-makers has higher growth rates, extracts the resource more gently and experiences a higher growth rate in the creation of new ideas. Paradoxically, we find that for any CEIS level, agents behaving time-inconsistently have a higher sum of discounted utilities than time-consistent agents. This gap becomes more significant as the CEIS level increases.

A two-stage non-standard optimal control problem with time inconsistent preferences is studied. In an infinite horizon setting, a time consistent (sophisticated) decision maker chooses the time of switching between two consecutive regimes. The second regime corresponds to the implementation of a new technology, and a cost must be paid at the switching time. Although the problem is formulated for a general discount function, special attention is devoted to models with nonconstant discounting and heterogeneous discounting. The problem is solved by transforming it into a problem in a finite horizon and free terminal time. The corresponding dynamic programming equations are presented, and conditions for the derivation of the switching time by decision makers with different degrees of sophistication are studied. A resource extraction model with technology adoption is solved in detail. Effects of the adoption of different discount functions are illustrated numerically