Publications by PSE researchers

The importance of the literature on present bias may have overlooked some other forms of temporal inconsistencies anchored in the smoothing properties of consumption. The article first clarifies how a list of axioms enable the obtention of time-dependent recursive utility functions. The properties of the latters are analysed in light of the well-known present bias but also through a temporal smoothing bias that emerges when two successives selves do no share the same aversion to fluctuations. It is shown that this new concept relates to a time-varying Morishima intertemporal elasticity of substitution. The second part of the article brings an axiomatic construction providing a parametric representation that is aimed at a careful account of future and present bias, how they relate to each other or to substitution mechanisms and is finally concerned with the testable implications of the current framework. The theory is finally applied by considering intertemporal choices with Markovian strategies and temporally consistent solutions. For some parameters configurations, there exists a multiplicity of Nash equilibria, and then an indeterminacy in the agent behaviour.

This article is interested in future allocations of scarce resources in an environment where upper bounds and lower bounds are fixed on the stream of consumptions or extractions of the scarce resource. It is shown that we can compute the optimal planning of consumptions independently from an explicit sequence of discounting factors as soon as they are decreasing at a rate smaller than a bound linked to the concavity of the utility function and the choice of the sequences of lower and upper bounds. The optimal solution is unique and exhibits two regimes with a pivotal period in the middle. Therefore, one gets plans satisfying some kind of intergenerational fairness: while the highest e ort is supported by the first generations, it then decreases for the remaining ones. The argument is then extended to partially renewable resources. Finally, we consider the role of the horizon and of a potential regret after a revision for the bounds.

This article considers a three-period-lived pure exchange overlapping generations economy and clarifies the role of market complementarities in the scope for Kehoe & Levine’s convergence criterion in order to reduce the size of continuation equilibria and establish uniqueness and determinacy. The argument is based upon the price-relatedness of dated goods and the way the law of demand, gross substitutability and the scope for asymmetric complementarities come into play when three periods lifespans are considered. The nature of these restriions is clarified in the context of stationary economies and the way it relates to equilibrium continuation and Kehoe & Levine’s determinacy is made precise. A detailed articulation between complementarities and determinacy is finally provided in the context of Samuelson intermediate economies. The key role of dated goods spaced one period apart and entering in an additive way is emphasised in the determinacy result while the importance of asymetric complementarities between isolated goods spaced two periods apart is also pointed out.

This article introduces an axiomatic approach of utilities streams based upon three preference relations, namely the close future order, the distant future order, and the main order. Assuming all these preferences to be bi-separable, the article derives a unanimous representation for weights over periods. The analysis of two categories of a emph{potentially better} property allows for the establishment of textit{MaxMin}, textit{MaxMax}, and $alpha-$textit{MaxMin} representations. This is followed by the presentation of a multiple discounts rates version of $T^{*}$-temporally biased, generalizing quasi-hyperbolic discounting for the close future order. A similar analysis for the distant future is also performed, where it is proved that Banach limits can be considered as the distant future counterpart of exponential discounting in the evaluation of the close future.

This paper provides a framework for understanding preferences over utility streams across different time periods. We analyze preferences for the close future, for the distant future, and a synthesis of both, establishing a representation involving weights over time periods. Examining scenarios where two utility streams cannot be robustly compared to each other, we introduce notions in which one has more “potential” to be preferred over another, which lead to MaxMin, MaxMax, and -MaxMin representations. Finally, we consider temporal bias in the form of violations of stationarity. For close future preferences, we obtain a generalization of quasi-hyperbolic discounting. For distant future preferences, we obtain Banach limits and discuss the relationship with exponential discounting.

This article builds an axiomatization of inter-temporal trade-offs that takes an explicit account of the distant future. The focus is on separable representations and the approach is completed following a decision-theory index based approach that is applied to utility streams understood as the well-being of future generations. The introduction of some new axioms is herein shown to lead to the emergence of two distinct orders that respectively relate to the distant future and close future components of some utility stream. This enlightens the limits of the commonly used fat tail intensity requisites for the evaluation of utility streams. These are replaced by an axiomatic approach to myopia degrees.

A general setup is considered where quasi-hyperbolic discounting agents differ in assuming heterogeneous bias for the present as well as heterogeneous discounting parameters, consumptions being, moreover, subject to a standard feasibility constraint. A collective utility function is defined as a linear combination of the inter-temporal utilities of the selves of the different agents, the elementary unit being thus the self of a given period of a given agent. Such a framework generating a tension between Pareto-optimality and time consistency for the optimal allocations, a new approach is introduced in order to tackle this issue. This builds from an a priori time-inconsistent collective utility function where the benevolent planner is to be apprehended in terms of a sequence of successive incarnations, any of these incarnations being endowed with its own objective. The associated optimal policy is the equilibrium of a game between the successive incarnations of the planner when the players follow Markovian strategies. This is compared with a more standard approach where restrictions would be imposed on the collective utility function that ensure the time consistency of the optimal decisions.

This contribution1 introduces a sectoral supply functions approach of equilibrium dynamics in the context of a simple model of overlapping generations with heterogeneous goods. The class of preferences that is here considered hinges upon an endogenous leisure motive and an elementary savings behaviour, that comes as a simpler alternative to the Diamond tradition in the benchmark contributions about the properties of overlapping generations economies with two industries. The presence of some institution making possible intergenerational transfers is shown to influence both the equilibrium aggregate factors shares and elasticity of substitution along a stationary equilibrium. Both Wealth-to-Capital and Golden Rule steady state equilibria being considered, the economies are categorised, either as Samuelsonian or classical, according to the sign of the transfers between generations at the Golden Rule steady state. The local stability properties of the various types of equilibria are successively investigated, the elasticities of substitution between the two inputs being emphasised to play a key-role for that purpose. Interestingly, the smoothing properties of factors substitution and their respective contribution to the obtention of the local uniqueness property may differ between the Samuelsonian and classical economies.

The purpose of this contribution is to consider a discrete time formulation that would allow for clarifying some salient features of a vintage based understanding of the capital stock..ree main lines of conclusions are established on an analytical basis. First and for an elementary configuration with linear utility, it is proved that the rate of growth of investment is prone to andoscillating—convergent, sustained or unstable—motions. Second and for an environment with a linear production technology and a AK setup, the dynamics of investment is explicitly solved and it is established that the rate of growth of investment may either converge to the steady growth solution in oscillating way, diverge from that solution in a oscillating way, or even undergo permanent sustained oscillations with a periodicity of two. .ird, it is proved that no perennial .uctuations can emerge within a benchmark environment with strictly concave utilities and production technologies. On a methodological basis, few restrictions are superimposed, the arguments remain fairly general and the proofs are elementary.

This article considers the long-run equilibrium distribution of an economy populated by heterogenous and present biased quasi-hyperbolic discounting agents. In a first configuration with logarithmic utility functions and Cobb-Douglas production technologies, this article establishes the existence and the uniqueness of the equilibrium : only one agent, determined by the highest value of a coefficient building from both the degree of present bias and the rate of discount, will have a positive long-run consumption and a positive long-run wealth. A second configuration with constant elasticities of substitution utilities and linear production technologies is then considered. This article similarly establishes the existence and the uniqueness of the equilibrium. There generically is a unique agent with the highest growth rate for his consumption and his wealth. This agent is determined by both preferences and technology parameters and may change following a technological shock.

This article establishes a dynamic programming argument for a maximin optimization problem where the agent completes a minimization over a set of discount rates. Even though the consideration of a maximin criterion results in a program that is not convex and not stationary over time, it is proved that a careful reference to extended dynamic programming principles and a maxmin functional equation however allows for circumventing these difficulties and recovering an optimal sequence that is time consistent.

This article builds an axiomatization of inter-temporal trade-offs that makes an explicit account of the distant future and therefore encompasses motives related to sustainability, transmission to offsprings and altruism. The focus is on separable representations and the approach is completed following a decision-theory index based approach that is applied to utility streams. This enlightens the limits of the commonly used tail intensity requesites for the evaluation of utility streams: in this article, these are supersed and replaced by an axiomatic approach to optimal myopia degrees that in its turn precedes the determination of optimal discount. The overall approach is anchored in the new and explicit proof of a temporal decomposition of the preference orders between the distant future and the close future itself directly related to the determination of the optimal myopia degrees. The argument is shown to provide a novel understanding of temporal biases with the scope for a distant future bias when the finite dimensional gets influenced by the infinite dimensional. The reference to robust orders and pessimism-like axioms finally allows for determining tractable representations for the indexes.