Properties of the Social Discount Rate in a Benthamite Framework with Heterogeneous Degrees of Impatience

This paper derives the properties of the discount rate that should be applied to a public-sector project when the affected population has heterogeneous degrees of impatience. We show that, for any distribution of discount rates, the social discount rate has the following properties: it decreases over time, it is lower than the average of the discount rates in the population, and it converges to the discount rate of the most patient individual in the economy. These properties hold for both constant and decreasing individual discount rates. Finally, we evaluate how changes in the distribution of individual discount rates affect the social discount rate.social discount rate; hyperbolic discounting; cost-benefit analysis

Discounting and Divergence of Opinion

The objective of this paper is to adopt a general equilibrium model and determine the socially efficient discount factor, risk free rate and discount rate when there are heterogeneous anticipations about the growth of the economy as well as heterogeneous time preference rates. Among others we tackle the following questions. Is the socially efficient discount factor an arithmetic average of the individual subjectively anticipated discount factors? More generally, can the Arrow-Debreu prices, the risk free rates, the subjectively expected socially efficient discount factors and discount rates be obtained as an average of the individual subjectively anticipated ones? Can beliefs dispersion be analyzed as a sort of additional risk or uncertainty leading to possibly lower discount rates? Is it socially efficient, when diversity of opinion is taken into account, to reduce the discount rate per year for more distant horizons? If so, what is the trajectory of the decline?discount rate, risk free rate

Discounting and Divergence of Opinion

The objective of this paper is to adopt a general equilibrium model and determine the socially efficient discount factor, risk free rate and discount rate when there are heterogeneous anticipations about the growth of the economy as well as heterogeneous time preference rates. Among others we tackle the following questions. Is the socially efficient discount factor an arithmetic average of the individual subjectively anticipated discount factors? More generally, can the Arrow-Debreu prices, the risk free rates, the subjectively expected socially efficient discount factors and discount rates be obtained as an average of the individual subjectively anticipated ones? Can beliefs dispersion be analyzed as a sort of additional risk or uncertainty leading to possibly lower discount rates? Is it socially efficient, when diversity of opinion is taken into account, to reduce the discount rate per year for more distant horizons? If so, what is the trajectory of the decline?discount rate, risk free rate

Cognitive biases and the representative agent

In this paper, we show that behavioral features can be obtained at a group level when the individuals of the group are heterogeneous enough. Starting from a standard model of Pareto optimal allocations, with expected utility maximizers and exponential discounting, but allowing for heterogeneity among individual beliefs and individual time preference rates, we show that the representative agent has an inverse S-shaped probability distortion function and hyperbolic discount rates. As an application of this result, we show that an agent with a probability weighting function as in Cumulative Prospect Theory (resp. an ambiguity averse agent, resp. an hyperbolic discounting agent) may be represented as a collection of agents with noisy beliefs (resp. heterogeneous beliefs, resp. heterogeneous constant discount rates)

La valeur psychologique du temps : Une synthèse de la littérature

International audienceCet article procède à une synthèse de la littérature sur la question de la valeur psychologique du temps. Il discute des différents déterminants du taux d'actualisation et la possibilité d'avoir une fonction d'escompte de type hyperbolique. L'approche historique permet de retracer les origines du concept de valeur psychologique du temps. Ce concept est ensuite rediscuter dans le cadre de la théorie des perspectives, en considérant que l'utilité ressentie de l'agent vient modifier la structure de leur valeur psychologique du temps. L'analyse des résultats empiriques et des méthodologies d'identification permet de mettre en évidence que motifs individuels et psychologiques conditionnent le caractère intertemporel des choix

Shareholder heterogeneity, asymmetric information, and the equilibrium manager

Consider a Örm owned by shareholders with heterogeneous beliefs and discount rates who delegate to a manager the choice of a production plan. The shareholders and the manager can trade contingent claims in a complete asset market. Shareholders cannot observe the chosen production plan and design a compensation scheme so that at equilibrium the manager chooses the plan they prefer and reveals it truthfully. We show that at equilibrium i) proÖt is maximized, ii) the manager gets a constant share of production, iii) she has no incentive to trade. We then show that such equilibrium exists if and only if the manager has the same belief and discount rate as the representative shareholder. This allows us to characterize the required characteristics of the manager as a function of shareholdersí characteristics

Report Contrasting CRESSI’s Approach of Social Innovation with that of Neoclassical Economics

Deliverable 1.

Essays on real business cycle modelling under adaptive learning

The thesis consists on three chapters aiming to contribute to a growing literature on adaptive learning, a form of bounded rationality that has been attracting increasing interest both in the theoretical and practical fields, as an alternative to the commonly used rational expectations hypothesis on how expectations are formed among economic agents. The first chapter investigates whether it is possible to improve the ability of the standard real business cycle model to match the main stylised facts of emerging economies, taking the case of Mexico as an illustration, by assuming that agents are not fully rational and instead form expectations according to an adaptive learning rule. Two well-known rules - recursive least squares and its constant gain variant - are considered for this purpose. The degree of difficulty of the learning process is characterised by different starting values of the algorithms as well as different constant gains. The simulations show that the model under learning generally outperforms its rational expectations counterpart. Therefore, policymakers should take into account the fact that the expected welfare gains/losses of a particular policy reform, conceived assuming a fully-rational environment, might be significantly different if, in practice, agents behave as learners. Using a heterogeneous-agent model with three types of agents, namely capitalists, skilled workers and unskilled workers - assuming constant population shares suggesting low social mobility -, and allowing for different degrees of complementarity among these within the productive structure, the second chapter welfare-evaluates tax reforms consistent with a lower long run debt-to-output ratio for the United Kingdom, both under rational expectations and heterogenous learning. This chapter shows that, relative to the other tax reforms, capital tax cuts lead to the highest aggregate welfare but are skill-biased and can thus increase inequality in the long run. That is, depending on the elasticity of substitution between capital and unskilled labour, falls in the capital tax can result in higher levels of welfare inequality, even in the absence of other frictions and increases in other forms of taxation. On the other hand, reductions in labour taxes can hurt the capitalists. This chapter shows too that including the transition period in the welfare evaluation lowers the inequality effects of capital tax reductions since the complementarity between capital and all labour inputs is higher in the short- than in the long-run. Finally, while heterogeneous learning in the shape of differing initial beliefs after the reform can lead to a form of "irrational exuberance" after a tax cut, it can also exacerbate welfare inequality. Finally, the third chapter presents an heterogeneous-agent model with two types of agents, capitalists and workers - with constant population shares given the strong evidence on low social mobility -, calibrated to Bolivia´s data in order to examine the short and long-run effectiveness and distributional effects of various fiscal rules designed to impose restrictions on the evolution of public debt as a share of output, in response to two different sources of exogenous volatility (i.e. productivity and commodity shocks) and under different ways of forming expectations, namely rational expectations and heterogenous learning. The results show that under full rationality the fiscal rules generate a trade-off between debt-stabilisation and higher income inequality while, under some conditions, heterogenous learning can help to break such trade-off so that some of the rules can perform well in both fields. However, given the significantly high levels of income inequality and dependence on commodity revenues experienced by Bolivia, finding the best performing rule in response to all the relevant exogenous shocks this economy might face, appears to be a challenging task

Statement from the Editor Regarding "Properties of the Social Discount Rate in a Benthamite Framework with Heterogeneous Degrees of Impatience"

In the original version of the paper "Properties of the Social Discount Rate in a Benthamite Framework with Heterogeneous Degrees of Impatience" by Diego Nocetti (Management Science, Articles in Advance, January 25, 2008), Proposition 2 stated that "First and second order stochastically dominated shifts in the distribution of the individual discount rates reduce the SDR." However, Elyès Jouini and Clotilde Napp pointed out that this is not always the case, noting that "although first and second order stochastically dominated shifts in the distribution of discount rates increase the present value of the project, they are neither necessary nor sufficient to decrease the SDR for all horizons." Consequently, the original paper was replaced by a new version by Nocetti, Jouini, and Napp, which corrects this result by introducing stronger notions of stochastic dominance (maximum likelihood ratio dominance and portfolio dominance) to determine conditions under which the SDR unambiguously increases or decreases given a shift in the distribution of individual discount rates. The online appendix, which includes all formal proofs, was also revised accordingly. The new version of "Properties of the Social Discount Rate in a Benthamite Framework with Heterogeneous Degrees of Impatience" by Diego Nocetti, Elyès Jouini, and Clotilde Napp appears on pp. 1822-1826 in this issue of Management Science.