A note on generalized hyperbolic discounting

In a major contributions to behavioral economics, Loewenstein and Prelec (1992) set the foundations for the behavioral approach to decision making over time and derive the generalized hyperbolic discounting formula. Here we show that their assumption ‘common difference effect with quadratic delay’ cannot be weakened to ‘common difference effect

Increasing elasticity of the value function in the Loewenstein-Prelec Theory of intertemporal choice

In a critique of the Loewenstein and Prelec (1992) theory of intertemporal choice, al-Nowaihi and Dhami (2006) point out to four errors. One of the alleged errors was that the value function in prospect theory is decreasing. But it is in fact increasing. We provide a correction and a formal proof. As a corollary, we show that the elasticity of the value function is bounded between zero and one. Nevertheless, all the remaining points in al-Nowaihi and Dhami (2006) remain valid

Evidential Equilibria: Heuristics and Biases in Static Games of Complete Information

Standard equilibrium concepts in game theory find it difficult to explain the empirical evidence from a large number of static games, including the prisoners’ dilemma game, the hawk-dove game, voting games, public goods games and oligopoly games. Under uncertainty about what others will do in one-shot games, evidence suggests that people often use evidential reasoning (ER), i.e., they assign diagnostic significance to their own actions in forming beliefs about the actions of other like-minded players. This is best viewed as a heuristic or bias relative to the standard approach. We provide a formal theoretical framework that incorporates ER into static games by proposing evidential games and the relevant solution concept: evidential equilibrium (EE). We derive the relation between a Nash equilibrium and an EE. We illustrate these concepts in the context of the prisoners’ dilemma game

A Note On The Loewenstein-Prelec Theory Of Intertemporal Choice

In one of the major contributions to behavioral economics, Loewenstein and Prelec (1992) set the foundations for the behavioral approach to decision making over time. We correct a number of errors in Loewenstein and Prelec (1992). Furthermore, we provide a correct, more direct and simpler derivation of their generalized hyperbolic discounting formula that has formed the basis of much recent work on temporal choice

Coordination Failures, Philanthropy, and Public Policy

We focus on an “equilibrium analysis” of coordination problems in giving that lead to multiple equilibria; the notion of strategic complements and substitutes turns out to be useful in this regard. Some societies can get stuck at a low level of giving while others might, by accident or policy, be able to coordinate on a higher level of giving. Ceteris-paribus, this furnishes one plausible reason for heterogeneity in philanthropy. We give conditions under which tax exemptions to private giving can have perverse effects by reducing equilibrium private giving. Direct government grants to charity, possibly temporary, can enable an economy stuck at an equilibrium with a low level of giving to attain an equilibrium with a high level of giving. Therefore, direct government grants can crowd-in private giving to charity. The paper contributes to the economics of philanthropy as well as to an understanding of the role of public policy in the face of private coordination failures

Inequality and size of the government when voters have other regarding preferences

The celebrated relation between inequality and redistribution is based on selfish voters who care solely about own-payouts. A growing empirical literature highlights the importance of other regarding preferences (ORP) in voting over redistribution. We reexamine the relation between inequality and redistribution, within a simple general equilibrium model, when voters have ORP. Our contribution is five-fold. First, we demonstrate the existence of a Condorcet winner. Second, poverty can lead to increased redistribution (which implies a countercyclical social spending to GDP ratio). Third, we show that disposable income 'strongly median-dominates' factor income. Fourth, we show that fair voters respond to an increase in 'strong median-dominance' by engaging in greater redistribution. Fifth, an illustrative em- pirical exercise using OECD data points to the importance of fairness in explaining redistribution

Non-Linearities, Large Forecasters And Evidential Reasoning Under Rational Expectations

Rational expectations is typically taken to mean that, conditional on the information set and the relevant economic theory, the expectation formed by an economic agent should be equal to its mathematical expectation. This is correct only when actual inflation is “linear” in the aggregate inflationary expectation or if it is non-linear then forecasters are “small” and use “causal reasoning”. We show that if actual inflation is non-linear in expected inflation and (1) there are “large” forecasters, or, (2) small/ large forecasters who use “evidential reasoning”, then the optimal forecast does not equal the mathematical expectation of the variable being forecast. We also show that when actual inflation is non-linear in aggregate inflation there might be no solution if one identifies rational expectations with equating the expectations to the mathematical average, while there is a solution using the “correct” forecasting rule under rational expectations. Furthermore, results suggest that published forecasts of inflation may be systematically different from the statistical averages of actual inflation and output, on average, need not equal the natural rate. The paper has fundamental implications for macroeconomic forecasting and policy, testing the assumptions and implications of market efficiency and for rational expectations in general

Hyperbolic Punishment Functions

All models in Law and Economics use punishment functions (hereafter, PF) that incorporate a trade-off between probability of detection, p, and punishment, F. Suppose society wishes to minimize the total costs of enforcement and damages from crime, T( p,F). For a given p, an optimal punishment function (OPF) determines an F that minimizes T( p,F). A popular and tractable PF is the hyperbolic punishment function (HPF). We show that the HPF is an OPF for a large class of total cost functions. Furthermore, the HPF is an upper (lower ) bound for an even larger class of punishment functions. If the HPF cannot (can) deter crime, then none (all ) of the PF’s for which the HPF is an upper (lower ) bound can deter crime. Thus, if one can demonstrate that a particular policy is ineffective (effective) under the HPF, there is no need to even compute the OPF. Our results should underpin an even greater use of the HPF. We give illustrations from mainstream and behavioral economics

A value function that explains the magnitude and sign effects

Two of the anomalies of the exponentially discounted utility model are the ‘mag- nitude effect’ (larger magnitudes are discounted less) and the ‘sign effect’ (a loss is discounted less than a gain of the same magnitude). The literature has followed Loewenstein and Prelec (1992) in attributing the magnitude effect to the increasing elasticity of the value function and the sign effect to a higher elasticity for losses as compared to gains. We provide a simple, tractable, functional form that has these two properties, which we call the simple increasing elasticity value function (SIE). These functional forms underpin the main explanation of the magnitude and sign effects and may aid applications and further theoretical development

Hang 'em with probability zero: Why does it not work?

A celebrated result in the economics of crime, which we call the Becker proposition (BP), states that it is optimal to impose the severest possible punishment (to maintain effective deterrence) at the lowest possible probability (to economize on enforcement costs). Several other applications, some unrelated to the economics of crime, arise when an economic agent faces punishments/ rewards with very low probabilities. For instance, insurance against low probability events, principal-agent contracts that impose punitive fines, seat belt usage and the usage of mobile phones among drivers etc. However, the BP, and the other applications mentioned above, are at variance with the evidence. The BP has largely been considered within an expected utility framework (EU). We re-examine the BP under rank dependent expected utility (RDU) and prospect theory (PT). We find that the BP always holds under RDU. However, under plausible scenarios within PT it does not hold, in line with the evidence