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

aggregate social discount rate derived from individual discount rates in the economic evaluation of large public sector projects an aggregate social discount rate may be used in present worth comparison of alternatives this paper uses the assumptions that individual discount rates are constant over time and approximately normally distributed across the affected population with mean and variance i 2 to derive an aggregate discount function that is exponential in form but with time dependent aggregate discount rate i t i 2t 2 where t is the time of occurrence of the cost or benefit this equation agrees with numerical simulations if i 2 0 then the aggregate discount rate is less than the mean individual discount rate and use of the time dependent aggregate discount rate i t i 2t 2 instead of the constant discount factor i t would result in larger discounted present values for public sector projects for which the benefits lie far in the future this could mean that public sector investments that would be rejected under the assumption i t might be justified using the time dependent aggregate discount rate i t i 2t 2

communication in repeated games with private monitoring abstract the paper considers repeated games where each player can be observed by only a subset of the other players and where players can make public announcements about the behavior of the players they observed we address the following question what is the minimal level of observability that is required to obtain efficient outcomes the main result is that the limit set of sequential equilibrium payoffs when the discount factor tends to one contains the set of individual rational payoffs whenever each player is observed by at leasttwoother players journal of economic literatureclassification number c73

repeated partnership games with imperfect monitoring and no discounting in a partnership game each player s utility depends on the other players actions through a commonly observed consequence e g output profit price which is itself a function of the players actions and an exogenous stochastic environment if a partnership game is repeated infinitely and each player s payoff in the infinite game supergame is the long run average of his expected one period utilities then efficient combinations of one period actions can be sustained as nash equilibria of the supergame even if the players cannot observe other players actions or information but can only observe the resulting consequences

investment under uncertainty and time inconsistent preferences abstract while standard real options models assume that agents possess a constant rate of time preference there is substantial evidence that agents are impatient about choices in the short term but are patient when choosing between long term alternatives we extend the real options framework to model the investment timing decisions of entrepreneurs with time inconsistent preferences the impact on investment timing depends on such factors as whether entrepreneurs are sophisticated or naive in their expectations regarding their future time inconsistent behavior and whether the payoff from investment occurs all at once or over time the model is extended to the case of a competitive equilibrium

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

anomalies in intertemporal choice evidence and an interpretation research on decision making under uncertainly has been strongly influenced by the documentation of numerous expected utility eu anomalies behaviors that violate the expected utility axioms the relative lack of progress on the closely related topic of intertemporal choice is partly due to the absence of an analogous set of discounted utility du anomalies we enumerate a set of du anomalies analogous to the eu anomalies and propose a model that accounts for the anomalies as well as other intertemporal choice phenomena incompatible with du we discuss implications for savings behavior estimation of discount rates and choice framing effects

aggregation of heterogeneous time preferences we examine an economy whose consumers have different discount factors for utility possibly not exponential we characterize the properties of efficient allocations of resources and of the shadow prices that would decentralize such allocations we show in particular that the representative agent has a decreasing discount rate when as is usually posited all of a group s members have a constant discount rate and decreasing absolute risk aversion preferences we also identify conditions that lead the representative agent to have a rate of impatience that decreases with gross domestic product per capita

on abel s concept of doubt and pessimism abstract in this paper we characterize subjective probability beliefs leading to a higher equilibrium market price of risk we establish that abel s result on the impact of doubt on the risk premium is not correct in general see abel 2002 an exploration of the effects of pessimism and doubt on asset returns journal of economic dynamics and control 26 1075 1092 we introduce on the set of subjective probability beliefs market price of risk dominance concepts and we relate them to well known dominance concepts used for comparative statics in portfolio choice analysis in particular the necessary first order conditions on subjective probability beliefs in order to increase the market price of risk for all nondecreasing utility functions appear as equivalent to the monotone likelihood ratio property

mean preserving portfolio dominance consider risk averse agents with utility functions u and v holding portfolios composed of the same two risky and riskless assets then v is arrow more risk averse if in all such portfolios v invests less in the risky asset a natural extension of this analysis of attitudes towards risk to risk itself is to establish a relation between distributions which is necessary and sufficient to induce such investment patterns in the class of all risk averse agents this characterization is established in this paper for distributions with equal means second degree dominance performs a similar role for the notion of more risk averse introduced by pratt but it is too weak for the arrow concept

r d investment under time inconsistent preferences abstract we extend the real options model of r d by incorporating time inconsistent preferences we show that time inconsistent preferences can lead to both under investment and over investment in r d which depends on the magnitude of technological uncertainty when the technological uncertainty is low the sophisticated entrepreneurs exercise earlier than the time consistent entrepreneur however the sophisticated entrepreneurs invest later when the technological uncertainty is high

risk averse decision making under catastrophic risk abstract a nonstandard probabilistic setting for modeling of the risk of catastrophic events is presented it allows random variables to take on infinitely large negative values with non zero probability which correspond to catastrophic consequences unmeasurable in monetary terms e g loss of human lives thanks to this extension the safety first principle is proved to be consistent with traditional axioms on a preference relation such as monotonicity continuity and risk aversion also a robust preference relation is introduced and an example of a monotone robust preference relation sensitive to catastrophic events in the sense of chichilnisky 2002 is provided the suggested setting is demonstrated in evaluating nuclear power plant projects when the probability of a catastrophe is itself a random variable

empirical and public choice evidence for hyperbolic social discount rates and the implications for intergenerational discounting the derivation of the correct discount rate for intergenerational projects in cost benefit analysis is particularly contentious public choice has resulted in lower discretionary exponential discount rates for many intergenerational projects in britain and the usa this is shown to be strong indirect evidence that the true social discount rate may be a hyperbolic rather than an exponential function there is also empirical evidence for this hypothesis the hyperbolic nature of discounting is also a standard finding in the behavioural sciences for intergenerational time frames hyperbolic discount rates should be employed together with exponential discount rates in cost benefit sensitivity analyses

why the far distant future should be discounted at its lowest possible rate abstract a critical feature of the distant future is currently unresolvable uncertainty about what will then be the appropriate rate of return on capital to use for discounting this paper shows that there is a well defined sense in which the lowest possible interest rate should be used for discounting the far distant future part of any investment project some implications are discussed for evaluating long term environmental projects or activities like measures to mitigate the possible effects of global climate change

communication in repeated games with imperfect private monitoring this paper examines repeated games in which each player observes a private and imperfect signal on the actions played and in which players are allowed to communicate using public messages providing incentives for players to reveal their observations generates revelation constraints that combined with signal imperfections may be a source of inefficiencies however by delaying the revelation of their observations players may economize on the cost of deterring deviations and thereby avoid these inefficiencies because a player would not want to trigger a sanction that would penalize him too revelation constraints also tend to make sanctions difficult to enforce however with at least three players detecting deviations may not require that all the players reveal their observations in that case we obtain a nash threat version of the folk theorem with two players we do not obtain a similar result nevertheless we show that an efficient outcome can almost always be approximated

optimal capital structure and investment decisions under time inconsistent preferences based on a continuous time model of quasi hyperbolic discounting this paper provides an analytically tractable framework of entrepreneurial firms capital structure and investment decisions under time inconsistent preferences inefficiency in both investment and default is caused due to time inconsistency if we view the time consistent benchmark as efficient compared to the standard trade off theory in corporate finance we clarify that debt financing under time inconsistent preferences brings a new trade off between the alleviation effect on investment inefficiency and the aggravation effect on default inefficiency the impact of time inconsistent preferences depends on the entrepreneurs belief regarding their future time inconsistent behavior i e sophisticated or naive concretely we find that naive entrepreneurs always choose higher leverages while sophisticated ones are more likely to choose lower leverages compared to the time consistent benchmark therefore time inconsistency can explain the observed leverage puzzle i e why firms choose different leverages even with similar fundamentals moreover we demonstrate that time inconsistent preferences delay investment and hasten default due to the interaction among the three effects option value effect payoff value effect and leverage effect in particular naive entrepreneurs invest later and default earlier than sophisticated ones leading to a shorter operating period these results support the empirical findings in entrepreneurial finance

optimal dividend strategies with time inconsistent preferences abstract this paper studies the optimal dividend strategies of an insurance company when the manager has time inconsistent preferences we consider the problem for a naive manager and a sophisticated manager and analytically derive the optimal dividend strategies when claim sizes follow an exponential distribution our results show that the manager with time inconsistent preferences tends to pay out dividends earlier than her time consistent counterpart and that the sophisticated manager is more inclined to pay out dividends than the naive manager furthermore we extend these results to the case with claim sizes following a mixed exponential distribution and provide a numerical analysis to reveal the sensitivity of the optimal dividend strategies to changes in the premium claims and surplus volatility

discounting the distant future how much do uncertain rates increase valuations abstract we demonstrate that when the future path of the discount rate is uncertain and highly correlated the distant future should be discounted at significantly lower rates than suggested by the current rate we then use two centuries of us interest rate data to quantify this effect using both random walk and mean reverting models we compute the certainty equivalent rate that summarizes the effect of uncertainty and measures the appropriate forward rate of discount in the future under the random walk model we find that the certainty equivalent rate falls continuously from 4 to 2 after 100 years 1 after 200 years and 0 5 after 300 years at horizons of 400 years the discounted value increases by a factor of over 40 000 relative to conventional discounting applied to climate change mitigation we find that incorporating discount rate uncertainty almost doubles the expected present value of mitigation benefits

perfect communication equilibria in repeated games with imperfect monitoring this paper introduces an equilibrium concept called perfect communication equilibrium for repeated games with imperfect private monitoring this concept is a refinement of myerson s myerson r b 1982 optimal coordination mechanisms in generalized principal agent problems j math econ 10 67 81 communication equilibrium a communication equilibrium is perfect if it induces a communication equilibrium of the continuation game after every history of messages of the mediator we provide a characterization of the set of corresponding equilibrium payoffs and derive a folk theorem for discounted repeated games with imperfect private monitoring

cross disciplinary evidence for hyperbolic social discount rates researchers in different disciplines have independently found evidence to suggest that the social discount rate may be hyperbolic rather than exponential in nature both behaviorist research and some empirical economics studies support the hyperbolic discounting hypothesis u s and u k government discounting dispensations for some long run public development projects are explicable in terms of an underlying hyperbolic social discount rate a statistical aggregation argument demonstrates that even if the behaviorist economics and public choice evidence for hyperbolic discounting is not conclusive the social discount rate of a set of people who individually express time preferences best modeled by exponential discounting functions is nonetheless hyperbolic further empirical economics studies of discounting preferences are required comparisons of different national discounting practices would also be useful to see how widespread is the use of unusually low exponential rates of discount for long run projects the application of hyperbolic discounting would have most impact in long run benefit cost analyses however government agencies would require overwhelming evidence before switching from exponential to hyperbolic discounting

optimal cartel equilibria with imperfect monitoring abstract there exist optimal symmetric equilibria in the green porter model 4 8 having an elementary intertemporal structure such an equilibrium is described entirely by two subsets of price space and two quantities the only production levels used by firms in any contingency the central technique employed in the analysis is the reduction of the repeated game to a family of static games

discount rates inferred from decisions an experimental study two hundred and four students of economics and finance participated in an intertemporal choice experiment which manipulated three dimensions in a 4 4 4 factorial design scenario postponing a receipt postponing a payment expediting a receipt expediting a payment time delay 0 5 1 2 and 4 years and size of cashflow 40 200 1000 and 5000 individual discount rates were inferred from the responses and then used to test competitively four hypotheses regarding the behavior of discount rates the classical hypothesis asserting that the discount rate is uniform across scenarios time delays and sums of cashflow was flatly rejected a market segmentation approach was found lacking the results support an implicit risk hypothesis according to which delayed consequences are associated with an implicit risk value and an added compensation hypothesis which asserts that individuals require compensation for a change in their financial position

demand for risky financial assets a portfolio analysis abstract demand for risky financial assets takes place in portfolio settings the common stochastic orders applied in economics fail to rank demand for assets in such situations even for risk averse investors therefore the evaluation of the relative desirability of risky financial assets requires the establishment of new orders we prove that if returns on risky assets are ordered by the monotone likelihood ratio order then dominating assets will be more desired by all investors with nondecreasing utility functions

an example of a repeated partnership game with discounting and with uniformly inefficient equilibria in this note we present an example of a repeated partnership game with imperfect monitoring in which all supergame equilibria with positive discount rates are bounded away from full efficiency uniformly in the discount rate provided the latter is strictly positive on the other hand if the players do not discount the future then every efficient one period payoff vector that dominates the one period equilibrium payoff vector can be attained by an equilibrium of the repeated game thus the correspondence that maps the players discount rate into the corresponding set of repeated game equilibrium payoff vectors is discontinuous at the point at which the discount rate is zero

discounting inside the washington d c beltway places more weight on costs and benefits in the near term over costs and benefits in the future the choice of the discount rate is therefore critical in evaluating the merits of many public policy proposals this article focuses on how the choice of discount rate can dramatically affect policy choices these policies include whether to build a bridge whether to privatize a power marketing administration which sells electricity generated by government owned facilities such as dams how much money should be spent on early childhood education or options for reforming social security the ongoing challenge is to discount future costs or benefits in a way that matches the project s level of riskiness we begin by discussing the underlying issues in choosing an appropriate discount rate we then discuss the variety of different discount rates that are actually used by various washington policymakers and the biases they often generate

communication in repeated games with costly monitoring abstract we study repeated games with discounting where perfect monitoring is possible but costly it is shown that if players can make public announcements then every payoff vector which is an interior point in the set of feasible and individually rational payoffs can be implemented in a sequential equilibrium of the repeated game when the discount factor is high enough thus efficiency can be approximated even when the cost of monitoring is high provided that the discount factor is high enough

a note on portfolio dominance dominated if it reduces the demand for the risky asset by all risk averse agents irrespective of the risk fiee rate we show that the condition obtained by landsberger and meilijson 1993 while necessary is not sufficient for portfolio dominance and we present an exact necessary and sufficient condition