Bertrand Wigniolle

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.

Imagine a cohort of economic experts appraising long-term projects through the quasi-hyperbolic discounting criterion. The parameters (long-run and short-run discount rates) used by each expert may differ, which implies different policy recommendations. Subsequently, a decision maker is faced with the task of selecting an efficient aggregation from these varied opinions. This paper proposes a solution to reconcile these conflicting recommendations, taking into account the decision maker’s adoption of a “prudent” behavior.

In this paper, we give axiomatic foundations for a social planner objective function that takes the form of the maxmin of quasi-hyperbolic criteria. The minimum is taken over a set Q of possible pairs of discount rates δ and present bias parameters p0. When there is no present bias, we recover Chambers and Echenique’s axiomatization of maxmin exponential preferences, and when Q reduces to a singleton, we get Montiel Olea and Strzalecki’s axiomatization of quasi-hyperbolic preferences. To prove our main result, we provide some intertemporal variational representation results of interest for its own sake.

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 paper emphasizes the role of land and technological progress in economic and population growth. The model is calibrated using historical data on England concerning both economic growth rate and the factor shares (land, capital, and labor) in total income, as well as mortality tables. It is able to reproduce the dynamics of population since 1760. Moreover, it is possible to disentangle the relative effect of technical changes and mortality fall on the evolution of population. We conduct a counterfactual analysis eliminating successively the increase in life expectancy and the technological bias. With no increase in life expectancy, population would have been respectively 10% and 30% lower in 1910 and in the long run. The figures would have been respectively 40% and 60% lower, with no bias in the technical progress. Finally, population would have been 45% smaller in 1910 and 70% smaller in the long run, neutralizing both the effect of life expectancy and technological bias. So the major part of population increase is due to the technological bias evolution between land and capital.

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 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 is generically 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 paper emphasizes the role of land and technological progress in economic and population growth. The model is calibrated using historical data on England concerning both economic growth rate and the factor shares (land, capital, and labor) in total income, as well as mortality tables. It is able to reproduce the dynamics of population since 1760. Moreover, it is possible to disentangle the relative effect of technical changes and mortality fall on the evolution of population. We conduct a counterfactual analysis eliminating successively the increase in life expectancy and the technological bias. With no increase in life expectancy, population would have been respectively 10% and 30% lower in 1910 and in the long run. The figures would have been respectively 40% and 60% lower, with no bias in the technical progress. Finally, population would have been 45% smaller in 1910 and 70% smaller in the long run, neutralizing both the effect of life expectancy and technological bias. So the major part of population increase is due to the technological bias evolution between land and capital.

A general setup is considered where agents are characterised by quasi-hyperbolic discounting and by heterogeneous bias for the present and heterogenous discounting parameters. Consumptions are moreover subject to a standard feasibility constraint. A collective utility function is defined as a function of the intertemporal utilities of the selves of the different agents, the elementary unit being thus the self of a given period for a given agent. The analysis is further specialized to time-independent collective utility functions. Such a framework generating a tension between Pareto-optimality and time-consistency for the optimal allocations, two approaches are suggested in order to tackle this issue. The first one imposes restrictions on the collective utility function that ensure the timeconsistency of the optimal decisions. The second one builds from an a priori time-inconsistent collective utility function. The benevolent planner is then to be considered as 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. The results obtained for both solution concepts are compared through an example that also shows how they can be recovered through a competitive equilibrium.