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,

Multiple solutions under quasi-exponential discounting

We consider a group or committee that faces a binary decision under uncertainty. Each member holds some private information. Members agree which decision should be taken in each state of nature, had this been known, but they may attach different values to the two types of mistake that may occur. Most voting rules have a plethora of uninformative equilibria, and informative voting may be incompatible with equilibrium. We analyze an anonymous randomized majority rule that has a unique equilibrium. This equilibrium is strict, votes are informative, and the equilibrium implements the optimal decision with probability one in the limit as the committee size goes to infinity. We show that this also holds for the usual majority rule under certain perturbations of the behavioral assumptions: (i) a slight preference for voting according to one's conviction, and (ii) transparency and a slight preference for esteem. We also show that a slight probability for voting mistakes strengthens the incentive for informative voting.: time-consistency, hyperbolic discounting, stochastic dynamic programming, multiplicity, uniqueness.

Heterogeneous discounting in consumption-investment problems. Time consistent solutions

In this paper we analyze a stochastic continuous time model in finite horizon in which agents discount the instantaneous utility function and the final function at constant but different instantaneous discount rates of time preference. Within this context we can model problems in which, when the time t approaches to the final time, the valuation of the final function increases compared with previous valuations in a way that cannot be explained by using a unique constant or a variable discount rate. We derive a dynamic programming equation whose solutions are time-consistent Markov equilibria. For this class of time preferences, we study the classical consumption and portfolio rules model (Merton, 1971) for CRRA and CARA utility functions for time- consistent agents, and we compare the different equilibria with the time-inconsistent solutions. The introduction of stochastic terminal time is also discussed.dynamic programming, consumption and portfolio rules, heterogeneous discounting, time consistency

Credible Communication in Dynastic Government

It has been suggested that ``horizontal accountability," i.e., a system of governance where auditing functions lie outside the executive branch, can ensure credible disclosure of information. This paper examines a model of intertemporal information provision in government that suggests a cautious approach to that view. Government consists of a succession of regimes, each ruling for one period before relinquishing power to a successor. Without external auditing, credible communication cannot be sustained. Hence, expenditure policies are suboptimal. Even with external auditing, credible communication requires ideological conflicts between the auditor and the regime. Moreover, because information transmission stops when the auditor's and the regime's biases coincide, effective deterrents even in the ``good" periods (when the auditor's and the regime's biases differ) are difficult to construct. As a result, in standard constructions of equilibrium, efficient policy choices are shown to be unsustainabledynastic government, dynamic policy bias, auditor neutrality, credible communication

Credible Communication in Dynastic Government

This paper examines the mechanics of intertemporal information provision in dynastic governments. It has been suggested that "horizontal accountability," i.e., a system of governance where auditing functions lie outside the executive branch, can ensure credible disclosure of information. The results here suggest a cautious approach to that view. Government is modelled as a dynastic sequence of regimes. Each regime rules for one period, chooses an expenditure level, then relinquishes power to its successor. When information about past policy choices comes exclusively from the reports of previous regimes, each regime has an incentive to choose its (suboptimal) one shot expenditure policy, and then misrepresent its choice to its successor. I examine the credible communication equilibria taking into account the reporting incentives of an auditor who can independently verify the information each period. In an environment where "liberal" (i.e., those prefering larger government expenditures) and "conservative" (those prefering smaller expenditures) regimes and auditors evolve over time, it is shown that: "conservative" ("liberal") auditors are not credible when the current regime is also "conservative" ("liberal"). Moreover, because information transmission stops when the auditor's and the regime's biases coincide, e_ective deterrents even in the "good" periods (when the auditor's and the regime's biases di_er) are di_cult to construct. In all periods the equilibrium requirement of auditor neutrality constrains the dynamic incentives for e_cient policy choices. The main result shows that these constraints typically bind away from optimal policies in standard constructions of equilibrium.dynastic government, dynamic policy bias, auditor neutrality, credible communication.

Time inconsistent preferences and Social Security

In this paper we examine the role of social security in an economy populated by overlapping generations of individuals with time-inconsistent preferences who face mortality risk, individual income risk, and borrowing constraints. Agents in this economy are heterogeneous with respect to age, employment status, retirement status, hours worked, and asset holdings. We consider two cases of time-inconsistent preferences. First, we model agents as quasi-hyperbolic discounters. They can be sophisticated and play a symmetric Nash game against their future selves; or they can be naive and believe that their future selves will exponentially discount. Second, we consider retrospective time inconsistency. We find that (1) there are substantial welfare costs to quasi-hyperbolic discounters of their time-inconsistent behavior, (2) social security is a poor substitute for a perfect commitment technology in maintaining old-age consumption, (3) there is little scope for social security in a world of quasi-hyperbolic discounters (with a short-term discount rate up to 15%), and, (4) the ex ante annual discount rate must be at least 10% greater than seems warranted ex post in order for a majority of individuals with retrospective time inconsistency to prefer a social security tax rate of 10% to no social security. Our findings question the effectiveness of unfunded social security in correcting for the undersaving resulting from time-inconsistent preferences.Social security

Repeated Games with Present-Biased Preferences

We study infinitely repeated games with observable actions, where players have present-biased (so-called beta-delta) preferences. We give a two-step procedure to characterize Strotz-Pollak equilibrium payoffs: compute the continuation payoff set using recursive techniques, and then use this set to characterize the equilibrium payoff set U(beta,delta). While Strotz-Pollak equilibrium and subgame perfection differ here, the generated paths and payoffs nonetheless coincide. We then explore the cost of the present-time bias. Fixing the total present value of 1 util flow, lower beta or higher delta shrinks the payoff set. Surprisingly, unless the minimax outcome is a Nash equilibrium of the stage game, the equilibrium payoff set U(beta,delta) is not separately monotonic in beta or delta. While U(beta,delta) is contained in payoff set of a standard repeated game with smaller discount factor, the present-time bias precludes any lower bound on U(beta,delta) that would easily generalize the beta=1 folk-theorem.beta-delta preferences, repeated games, dynamic programming, Strotz-Pollak equilibrium

Persuasion Against Self-Control Problems

I derive a social planner's optimal information design in an environment with quasi-hyperbolic discounting consumers without commitment. Consumption induces instantaneous utility, but unknown delayed cost. Consumers may or may not acquire additional costless information on the cost parameter. The planner's optimal signal can be interpreted as an incentive compatible consumption recommendation whenever the cost parameter is below some cut-off. Welfare strictly exceeds the one under full information. I characterize distributional conditions under which welfare attains first best