Now or Never: Environmental Protection under Hyperbolic Discounting

In this paper, we extend the well known result that hyperbolically discounting agents tend to postpone costs into the future. In a simple model we show that, without commitment to the ex ante optimal plan, no investment in environmental protection is undertaken over the whole time horizon, no matter whether the decision makers are naive or sophisticated, although investment seems optimal in the long run from every generations point of view. This result questions the application of hyperbolic discounting in cost-benefit analysis and gives rise to concern, as it is consistent with unsatisfactory policy performance in solving long-term environmental problems.environmental policy, environmental protection, hyperbolic discounting, intertemporal decision theory, procrastination, time-(in)consistency

CLIMATE POLICY WHEN THE DISTANT FUTURE MATTERS: CATASTROPHIC EVENTS WITH HYPERBOLIC DISCOUNTING

Low probability catastrophic climate change can have a signifcant influence on policy under hyperbolic discounting. We compare the set of Markov Perfect Equilibria (MPE) to the optimal policy under time-consistent commitment. For some initial levels of risk there are multiple MPE; these may involve either excessive or insufficient stabilization effort. These results imply that even if the free-rider problem amongst contemporaneous decision-makers were solved, there may remain a coordination problem amongst successive generations of decision-makers. A numerical example shows that under plausible conditions society should respond vigorously to the threat of climate change.abrupt climate change, event uncertainty, catastrophic risk, hyperbolic discounting, Markov Perfect Equilibria, Environmental Economics and Policy, C61, C73, D63, D99, Q54,

Resource Management with Stochastic Recharge and Environmental Threats

Exploitation diminishes the capacity of renewable resources to with-stand environmental stress, increasing their vulnerability to extreme conditions that may trigger abrupt changes. The onset of such events depends on the coincidence of extreme environmental conditions (environmental threat) and the resource state (determining its resilience). When the former is uncertain and the latter evolves stochastically, the uncertainty regarding the event occurrence is the result of the combined effect of these two uncertain components. We analyzed optimal resource management in such a setting. Existence of an optimal stationary policy is established and long run properties are characterized. A numerical illustration based on actual data is presented.Stochastic stock dynamics, event uncertainty, Markov decision process, optimal stationary policy, Environmental Economics and Policy,

Intergenerational interactions in human capital accumulation

We analyze an economy populated by a sequence of generations who decide over their consumption and investment in human capital of their immediate descendants. The objective of the paper is twofold: firstly, to identify the impact of strategic interactions between consecutive generations on the time path of human capital accumulation. To this end, we characterize the Markov perfect equilibrium (MPE) in such an economy and derive the sufficient conditions for its existence and uniqueness. We then benchmark our results against an optimal but time-inconsistent policy which abstracts from strategic interactions between generations. We prove analytically that human capital accumulation is unambiguously lower in the “strategic” case than in the optimal, “non-strategic” case. The second objective of the current paper is to work out a functional parametrization of the model, suitable for obtaining clear-cut results on the monotonicity of the (unique) Markov perfect equilibrium policy and the optimal policy. We then carry out a sensitivity analysis under this parametrization, thereby assessing quantitatively the magnitude of discrepancies between human capital accumulation paths whether strategic interactions between consecutive generations are taken into account or not.human capital, intergenerational interactions, Markov perfect equilibrium, stochastic transition, constructive approach

Theory of Stochastic Optimal Economic Growth

This paper is a survey of the theory of stochastic optimal economic growth.International Development,

QDQD-Learning: A Collaborative Distributed Strategy for Multi-Agent Reinforcement Learning Through Consensus + Innovations

The paper considers a class of multi-agent Markov decision processes (MDPs), in which the network agents respond differently (as manifested by the instantaneous one-stage random costs) to a global controlled state and the control actions of a remote controller. The paper investigates a distributed reinforcement learning setup with no prior information on the global state transition and local agent cost statistics. Specifically, with the agents' objective consisting of minimizing a network-averaged infinite horizon discounted cost, the paper proposes a distributed version of $Q$-learning, $\mathcal{QD}$-learning, in which the network agents collaborate by means of local processing and mutual information exchange over a sparse (possibly stochastic) communication network to achieve the network goal. Under the assumption that each agent is only aware of its local online cost data and the inter-agent communication network is \emph{weakly} connected, the proposed distributed scheme is almost surely (a.s.) shown to yield asymptotically the desired value function and the optimal stationary control policy at each network agent. The analytical techniques developed in the paper to address the mixed time-scale stochastic dynamics of the \emph{consensus + innovations} form, which arise as a result of the proposed interactive distributed scheme, are of independent interest.Comment: Submitted to the IEEE Transactions on Signal Processing, 33 page

Job Search and Impatience

How does impatience affect job search? More impatient workers search less intensively and set a lower reservation wage. The effect on the exit rate from unemployment is unclear. In this paper we show that, if agents have exponential time preferences, the reservation wage effect dominates for sufficiently patient individuals, so increases in impatience lead to higher exit rates. The opposite is true for agents with hyperbolic time preferences: more impatient workers search less and exit unemployment later. Using two large longitudinal data sets, we find that various measures of impatience are negatively correlated with search effort and the exit rate from unemployment, and are orthogonal to reservation wages. Overall, impatience has a large effect on job search outcomes in the direction predicted by the hyperbolic discounting model.