demand systems with nonstationary prices relative prices are nonstationary and standard root t inference is invalid for demand systems but demand systems are nonlinear functions of relative prices and standard methods for dealing with nonstationarity in linear models cannot be used demand system residuals are also frequently found to be highly persistent further complicating estimation and inference we propose a variant of the translog demand system the ntlog and an associated estimator that can be applied in the presence of nonstationary prices with possibly nonstationary errors the errors in the ntlog can be interpreted as random utility parameters the estimates have classical root t limiting distributions we also propose an explanation for the observed nonstationarity of aggregate demand errors based on aggregation of consumers with heterogeneous preferences in a slowly changing population estimates using u s data are provided

life cycle consumption and hyperbolic discount functions abstract studies of animal and human behavior suggest that discount functions are approximately hyperbolic ainslie picoeconomics 1992 hyperbolic models explain a wide range of empirical anomalies including 1 missing precautionary savings effects 2 incongruence between the elasticity of intertemporal substitution and the inverse of the coefficient of relative risk aversion 3 consumption discontinuities at retirement 4 variation in patience over the life cycle 5 consumer self reports of undersaving 6 disproportionate retirement accumulation in illiquid assets 7 asset specific marginal propensities to consume and 8 declining national savings rates in developed countries hyperbolic models also provide a new framework for analyzing the welfare gains that come from pro saving policies like social security and tax deferred retirement accounts

comments on credit ratings and the bis capital adequacy reform agenda the new basel capital accord basel committee on banking supervision 1999 has the objective of making capital requirements appropriately sensitive to the degree of risk in bank activities this is important because the original capital accord 1998 has been widely criticized for the lack of risk sensitivity of the capital charges assessed against various types of loans many observers believe this has resulted in regulatory arbitrage on the part of banks to the detriment of the quality of the assets banks hold on their books the basel committee has proposed a standardized approach for determining risk based capital using external ratings and two other approaches based on internal models for dealing with credit risk 1 altman et al 2002 examines in detail whether the goal of appropriate risk sensitivity is met by the proposed risk weights of the standardized approach the main conclusion of the altman et al paper and the underlying issues can be seen in fig 1 which plots the proposed risk weights and the historical corporate bond losses by rating as the authors note ratings aaa through a have experienced virtually no defaults but are assigned weights of 20 aaa and aa and 50 a percent more problematic the proposed risk weights for baa and ba rated loans are both 100 even though the loss experience for ba is 10 times higher than for baa finally the b and below rated loans have risk weights only half again as large as baa rated loans while the historical loss experience has been 55 times greater thus the basel proposal fails to capture the relative risks of the various ratings altman et al journal of banking finance 26 2002 923 928

measuring discounting without measuring utility we introduce a new method to measure the temporal discounting of money unlike preceding methods our method requires neither knowledge nor measurement of utility it is easier to implement clearer to subjects and requires fewer measurements than existing methods

the hyperbolic consumption model calibration simulation and empirical evaluation ur preferences for the long run tend to conflict with our short run behavior when planning for the long run we intend to meet our deadlines exercise regularly and eat healthfully but in the short run we have little interest in revising manuscripts jogging on the stairmaster and skipping the chocolate souffleala mode delay of gratification is a nice long term goal but instant gratification is disconcertingly tempting this gap between long run intentions and short run actions is apparent across a wide range of behaviors including saving choices a 1997 survey found that 76 percent of respondents believe they should be saving more for retirement looking only at respondents who believed they were at an age where you should be seriously saving already the survey found that 55 percent reported being behind in their savings and only 6 percent reported being ahead farkas and johnson 1997 the report on the survey concluded t he gaps between people s atti tudes intentions and behavior are troubling and threaten increased insecurity and dissatisfaction for people when they retire americans are simply not doing what logic and their own reasoning suggests they should be doing a 1993 luntz webber merrill lynch survey found similar answers when baby boomers were asked what percentage of your annual household income do you think you should save for retirement and what percentage of your annual

subjective discounting in an exchange economy this paper describes the equilibrium of a discrete time exchange economy in which consumers with arbitrary subjective discount factors and homothetic period utility functions follow linear markov consumption and portfolio strategies explicit expressions are given for state prices and consumption wealth ratios we provide an analytically convenient continuous time approximation and show how subjective rates of time preference affect risk free rates but not instantaneous risk return trade offs hyperbolic discount factors can be a source of return volatility but they cannot be used to address asset pricing puzzles related to high frequency sharpe ratios

axiomatization and measurement of quasi hyperbolic discounting this article provides an axiomatic characterization of quasi hyperbolic discounting and a more general class of semi hyperbolic preferences we impose consistency restrictions directly on the intertemporal trade offs by relying on what we call annuity compensations our axiomatization leads naturally to an experimental design that disentangles discounting from the elasticity of intertemporal substitution in a pilot experiment we use the partial identification approach to estimate bounds for the distributions of discount factors in the subject pool consistent with previous studies we find evidence for both present and future bias jel codes c10 c99 d03 d90

hypothetical intertemporal consumption choices the paper extends and replicates part of the analysis by barsky juster kimball and shapiro 1997 which exploits hypothetical choices among different consumption streams to infer intertemporal substitution elasticities and rates of time preference we use a new and much larger dataset than barsky et al furthermore we estimate structural models of intertemporal choice while parameterizing the parameters of interest as a function of relevant individual characteristics we also consider lobehaviorallc extensions like habit formation models with habit formation appear to be superior to models with intertemporally additive preferences

time tradeoff sequences for analyzing discounting and time inconsistency this paper introduces time tradeoff tto sequences as a general tool to analyze intertemporal choice we give several applications for empirical purposes we can measure discount functions without requiring any measurement of or assumption about utility we can quantitatively measure time inconsistencies and simplify their qualitative tests tto sequences can be administered and analyzed very easily using only pencil and paper for theoretical purposes we use tto sequences to axiomatize quasi hyperbolic discount functions we demonstrate the feasibility of measuring tto sequences in an experiment in which we tested the axiomatizations our findings suggest rejections of several currently popular discount functions and call for the development of new ones it is especially desirable that such discount functions can accommodate increasing impatience

non hyperbolic time inconsistency the commonly used hyperbolic and quasi hyperbolic discount functions have been developed to accommodate decreasing impatience which is the prevailing empirical finding in intertemporal choice in particular for aggregate behavior however these discount functions do not have the flexibility to accommodate increasing impatience or strongly decreasing impatience this lack of flexibility is particularly disconcerting for fitting data at the individual level where various patterns of increasing impatience and strongly decreasing impatience will occur for a significant fraction of subjects this paper presents discount functions with constant absolute cadi or constant relative crdi decreasing impatience that can accommodate any degree of decreasing or increasing impatience in particular they are sufficiently flexible for analyses at the individual level the cadi and crdi discount functions are the analogs of the well known cara and crra utility functions for decision under risk

a comparison of the discounted utility model and hyperbolic discounting models in the case of social and private intertemporal preferences for health whilst there is substantial evidence that hyperbolic discounting models describe intertemporal preferences for monetary outcomes better than the discounted utility du model there is only very limited evidence in the context of health outcomes this study elicits private and social intertemporal preferences for non fatal changes in health specific functional forms of the du model and three hyperbolic models are fitted the results show that the stationarity axiom is violated and that the hyperbolic models fit the data better than the du model intertemporal preferences for private and social decisions are found to be very similar

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

the fragility of time time insensitivity and valuation of the near and far future we propose that the temporal dimension is fragile in that choices are insufficiently sensitive to it and second such sensitivity as exists is exceptionally malleable unlike other dimensions such as money which are attended by default to test this we axiomatize a constant sensitivity discount function and in four studies we show that the degree of time sensitivity is inadequate relative to the compound discounting norm and strongly susceptible to manipulation time sensitivity is increased by a comparative within subject presentation experiment 1 direct instruction experiment 3 and provision of a visual cue for time duration experiment 4 time sensitivity is decreased using a time pressure manipulation experiment 2 in each study the sensitivity manipulation has an opposite effect on near future and far future valuations increased sensitivity decreases discounting in the near future and increases discounting in the far future in contrast such sensitivity manipulations have little effect on the money dimension

uncertainty and hyperbolic discounting we propose an evolutionary explanation for the pattern of intertemporal preference reversals often ascribed to hyperbolic discounting we take the view that preferences manifested for example in urges cravings and inclinations are the outcome of evolutionary forces and so will induce animals or humans to make survival maximizing choices in typical decision problems we show that if the typical problem involves payoffs whose realization times are uncertain then optimal preferences give rise to relatively patient behavior when the time horizon is long but induce a switch to impatience when the horizon grows short such reversals do not entail dynamic inconsistency in typical decision problems behavior there is optimal however if a decision maker is confronted with a choice for which the realization time uncertainty falls outside the evolutionary norm her preferences may well prompt her to behave inconsistently we argue that if such a choice problem recurs her evolutionarily endowed aability to learn will lead her to make self commitments against these urges this abstract was borrowed from another version of this item

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

individual and collective time consistency this paper reconsiders the strotz pollak problem of consistent planning and argues that a solution to this problem requires a refinement of subgame perfectness such a refinement is offered through an analysis based on greenberg s theory of social situations the properties of this refinement are investigated and illustrated a unifying framework is presented whereby consistent one person planning as a problem of individual time consistency and renegotiation proofness as a problem of collective time consistency are captured through the same general concept

decision making over time and under uncertainty a common approach this paper considers a number of parallels between risky and intertemporal choice we begin by demonstrating a one to one correspondence between the behavioral violations of the respective normative theories for the two domains i e expected utility and discounted utility models we argue that such violations or preference reversals are broadly consistent with three propositions about the weight that an attribute receives in both types of multiattribute choice specifically it appears that 1 if we add a constant to all values of an attribute then that attribute becomes less important 2 if we proportionately increase all values of an attribute or if we change the sign of an attribute from positive to negative then that attribute becomes more important the generality of these propositions as well as the constraints they would impose on separable representations of multiattribute preferences is discussed

value functions for infinite period planning cost benefit and risk analysis studies that model tradeoffs between the present and the distant future by means of present value discounting have been criticized for according the future and thus future generations far too little importance this paper presents an alternative means of modeling tradeoffs between different periods that accords the future far more importance than present value discounting and that is no more difficult to apply the paper also presents a means of modeling the preference issue of concern for equity or stability between different periods

testing the mechanisms of structural models the case of the mickey mantle effect the article assesses the ability of structural econometric models to reasonably predict economic behavior a lack of consideration of inherent variables in most structural models is found there is no current means of recording how parental wealth transfers to children affect the child s college attendance choices although it is recognized as an obvious factor research into free health insurance has found it does not lead to riskier behavior by consumers contrary to the traditional moral hazard model health insurance is examined for what the authors call the mickey mantle effect mantle died prematurely due to alcohol abuse and once observed he d have taken better care of himself had he known he d live as long as he did that comments represents how thee subjective thoughts of consumers affect economic models an analysis of data on medical patients life expectancy finds a strong correlation between shorter expectations and smoking while results linking heavy drinking and high body mass index were mixed

strotz meets allais diminishing impatience and the certainty effect abstract decision makers tend to exhibit a higher degree of impatience when considering a delay to an immediate reward than when contemplating an identical delay to an equal future reward this work argues that diminishing impatience originates from the distinction between the certain present and the risky future a simple functional representation of preferences exhibiting time inconsistency when the future is uncertain is derived experimental evidence which is inconsistent with other formulations that account for diminishing impatience supports the proposed approach the new theory uncovers a tight relation between diminishing impatience and well known behavioral regularities in choice under risk and uncertainty jel d12 d81

procrastination and obedience in this lecture i shall focus on situations involving repeated decisions with time inconsistent behavior although each choice may be close to maximizing and therefore result in only small losses the cumulative effect of a series of repeated errors may be quite large thus in my examples decision makers are quite close to the intelligent well informed individuals usually assumed in economic analysis but cumulatively they make seriously wrong decisions that do not occur in standard textbook economics this lecture discusses and illustrates several pathological modes of individual and group behavior procrastination in decision making undue obedience to authority membership of seemingly normal individuals in deviant cult groups and escalation of commitment to courses of action that are clearly unwise in each case individuals choose a series of current actions without fully appreciating how those actions will affect future perceptions and behavior the standard assumption of rational forwardlooking utility maximizing is violated the nonindependence of errors in decision making in the series of decisions can be explained with the concept from cognitive psychology of undue salience or vividness for example present benefits and costs may have undue salience relative to future costs

four score and seven years from now the date delay effect in temporal discounting we describe a new anomaly in intertemporal choice the date delay effect discount rates that are imputed when time is described using calendar dates e g on october 17 are markedly lower than those revealed when future outcomes are described in terms of the corresponding delay e g in six months date descriptions not only reduce discount rates but also affect the implied shape of the discount function when inferred from intertemporal choices between options referenced by calendar dates the discount function appears markedly less hyperbolic we discuss potential psychological bases of the date delay effect its implications and other modes of temporal reference

healthy food unhealthy food and obesity abstract we examine whether the latent behavioral mechanisms embedded in two price effects explanations of the obesity problem are operative our findings lend support to the hypothesis that falling food price is one likely cause of the obesity epidemic

the revealed preference theory of changing tastes we analyse preferences over finite decision problems in order to model decision makers with changing tastes we provide conditions on these preferences that identify the strotz model of consistent planning building on an example given by peleg and yaari 1973 we show that for problems with infinitely many choices strotz s representation of preferences may not be well defined for that case we propose a well defined approximation which is empirically indistinguishable from the strotz preference that is being approximated

consumption savings decisions with quasi geometric discounting we study the consumption savings problem of an infinitely lived rational consumer who has time inconsistent preferences in the form of quasi geometric discounting the consumer operates a weakly concave production function and must simply divide current resources into current consumption and savings there is no uncertainty a solution to the consumer s problem is a subgame perfect equilibrium of a dynamic game between the consumer s successive selves we show that this game has a continuum of equilibria in stationary markov strategies not only is the stationary point of the consumer s asset holdings indeterminate but each stationary point has a continuum of dynamic paths converging to it the savings policy rules underlying these dynamic paths are step functions

choice and procrastination author s o donoghue ted rabin matthew abstract recent models of procrastination due to self control problems assume that a procrastinator considers just one option and is unaware of her self control problems we develop a model where a person chooses from a menu of options and is partially aware of her self control problems this menu model replicates earlier results and generates new ones a person might forego completing an attractive option because she plans to complete a more attractive but never to be completed option hence providing a non procrastinator additional options can induce procrastination and a person may procrastinate worse pursuing important goals than unimportant ones

habits and the anomalies in intertemporal choice this paper analyzes a model of discounted utility under habit formation habit formation means that utility in each period is determined by the difference between the received outcome and the customary outcome at that point in time preferences are rational in the sense that the decision maker correctly anticipates the habit formation process and behaves in a dynamically consistent manner i e plans are truly carried out the purpose is to demonstrate that this generalization of the discounted utility model accounts jointly and in a meaningful way for the most striking anomalies with respect to classical discounted utility theory the common difference effect is explained first this effect also called decreasing impatience effect has usually been viewed as evidence against exponential discounting then the frequently observed preference for increasing sequences of outcomes is examined such preference under the traditional discounted utility model would be regarded as a paradoxical case of negative discounting a discussion of the descriptive prescriptive and normative values of the model is included

an analysis and critique of the bis proposal on capital adequacy and ratings abstract this paper examines two specific aspects of stage 1 of the bank for international settlement s bis s proposed reforms to the 8 risk based capital ratio we argue that relying on traditional agency ratings could produce cyclically lagging rather leading capital requirements resulting in an enhanced rather than reduced degree of instability in the banking and financial system despite this possible shortcoming we believe that sensible risk based weighting of capital requirements is a step in the right direction the current risk based bucketing proposal which is tied to external agency ratings or possibly to internal bank ratings however lacks a sufficient degree of granularity in particular lumping a and bbb investment grade corporate borrowers together with bb and b below investment grade borrowers severely misprices risk within that bucket and calls at a minimum for that bucket to be split into two we examine the default loss experience on corporate bonds for the period 1981 1999 and propose a revised weighting system which more closely resembles the actual loss experience on credit assets

hyperbolic discounting and the standard model eliciting discount functions abstract experiments on static intertemporal choice find evidence of particularly extreme impatience toward immediate rewards while this is often taken as support for hyperbolic discounting it could also arise because the most likely participants in experiments may be those with the most immediate need for money we conduct a calibration exercise and find that the extreme impatience observed in experiments can be accommodated by a standard exponential discounting model with no discounting and expectation of a small increase in the base consumption level the calibration uses existing estimates of curvature of utility

developments in non expected utility theory the hunt for a descriptive theory of choice under risk this article reviews recent developments in the economic theory of individual decision making under risk since the 1950s it has been known that individual choices violate the standard model of expected utility in predictable ways considerable research effort has now been devoted to the project of developing a superior descriptive model following an overview of non expected utility theories which distinguishes between conventional and non conventional approaches the paper seeks to assess these alternative models in terms of empirical success using laboratory and field data and theoretical usefulness the closing sections reflect on some new directions emerging in this literature

decreasing impatience a criterion for non stationary time preference and hyperbolic discounting despite recent interest in hyperbolic discounting there has been little discussion of exactly what property of time preferences is instantiated by hyperbolic or quasi hyperbolic functional forms the paper revives an earlier proposal in prelec 1989 that the key property is prattarrow convexity of the log of the discount function which corresponds to decreasing impatience di at the level of preferences di provides a natural criterion for assessing the severity of departure from stationarity in that greater di is equivalent to more choices of dominated options in two stage decision problems as well as greater convexity of the log of the discount function inefficient choices may arise as intentional precommitments or as unintended reversals of preference by naive agents

discounting by intervals a generalized model of intertemporal choice according to most models of intertemporal choice an agent s discount rate is a function of how far the outcomes are removed from the present and nothing else this view has been challenged by recent studies which show that discount rates tend to be higher the closer the outcomes are to one another subadditive discounting and that this can give rise to intransitive intertemporal choice we develop and test a generalized model of intertemporal choice the discounting by intervals dbi model according to which the discount rate is a function of both how far outcomes are removed from the present and how far the outcomes are removed from one another the model addresses past challenges to other models most of which it includes as special cases as well as the new challenges presented in this paper our studies show that when the interval between outcomes is very short discount rate tends to increase with interval length superadditive discounting in the discussion we place our model and evidence in a broader theoretical context

credit risk in private debt portfolios default loss severity and average loss rates for a large sample of privately placed bonds are presented and compared with loss experience for publicly issued bonds the chance of very large portfolio losses is estimated and some determinants of such losses are analyzed results show ex ante riskier classes of private debt perform better on average than public debt both diversification and the riskiness of individual portfolio assets influence the bad tail of the portfolio loss distribution private placements are similar to corporate loans in that both are monitored private debt the results are thus relevant to management and securitization of private debt portfolios generally more than half of nonfinancial corporate debt finance is iss ued privately and decisions of the financial intermediaries that invest in such debt depend importantly on its credit risk regulators of such institutions are similarly attentive to portfolio credit risk and it is an important consideration in the design of securitizations of pools of private debt in spite of its importance little is known empirically about private debt credit risk especially ex ante risk as a function of portfolio characteristics many studies have examined the loan portfolio performance of banks thrifts and insurance companies but the ex ante risk characteristics of the portfo

ramsey meets laibson in the neoclassical growth model the neoclassical growth model is modified to include a variable rate of time preference with no commitment ability and log utility the equilibrium features a constant effective rate of time preference and is observationally equivalent to the standard model the extended framework yields testable linkages between the extent of commitment ability and the rates of saving and growth the model also has welfare implications including the optimal design of institutions that facilitate household commitments steady state results are obtained for general concave utility functions and some properties of the transitional dynamics are characterized for isoelastic utility

credit ratings and the bis capital adequacy reform agenda abstract in this paper we have revised and updated our earlier study in order to analyze the most recent second draft of the bis s proposed reforms of bank capital requirements we conduct monte carlo experiments using data on defaults and severity rates on publicly traded us corporate bonds over the 1981 1999 period analyzing the whole period and various sub periods it is clear that the most recent draft of the bis proposed reforms seriously overestimates the relative riskiness of high quality debt relative to low quality debt in the so called standardized model as a result the most recent proposal still contains inherent risk shifting taking incentives for banks

anticipation and the valuation of delayed consumption this paper presents a model of intertemporal choice that incorporates savoring and dread i e utility from anticipat ion of delayed consumption the model explains why an individual with positive time preference may delay desirable outcomes or get unpleas ant outcomes over with quickly contrary to the prediction of convent ional formulations of intertemporal choice implications of savoring and dread for savings behavior empirical estimation of discount rate s and public policy efforts to combat myopic behavior are explored the model provides an explanation for common violations of the indepe ndence axiom as applied to intertemporal choice copyright 1987 by royal economic society

do workers prefer increasing wage profiles we present survey data challenging the assumption implicit in analyses of labor supply that all else being equal workers prefer declining over increasing wage profiles we test several explanations for our results including that a there is something special about wages e g their association with productivity as opposed to other types of payments that induces the preference for increasing wages b utility depends not only on absolute levels of consumption but also on changes in consumption over time and c respondents who prefer increasing wage profiles are irrational and would change their behavior if the rationale for preferring declining wages were explained

incentives for procrastinators we examine how principals should design incentives to induce time inconsistent procrastinating agents to complete tasks efficiently delay is costly to the principal but the agent faces stochastic costs of completing the task and efficiency requires waiting when costs are high if the principal knows the task cost distribution she can always achieve first best efficiency if the agent has private information the principal can induce first best efficiency for time consistent agents but often cannot for procrastinators we show that second best optimal incentives for procrastinators typically involve an increasing punishment for delay as time passes

tying odysseus to the mast evidence from a commitment savings product in the philippines we designed a commitment savings product for a philippine bank and implemented it using a randomized control methodology the savings product was intended for individuals who want to commit now to restrict access to their savings and who were sophisticated enough to engage in such a mechanism we conducted a baseline survey on 1777 existing or former clients of a bank one month later we offered the commitment product to a randomly chosen subset of 710 clients 202 28 4 percent accepted the offer and opened the account in the baseline survey we asked hypothetical time discounting questions women who exhibited a lower discount rate for future relative to current trade offs and hence potentially have a preference for commitment were indeed significantly more likely to open the commitment savings account after twelve months average savings balances increased by 81 percentage points for those clients assigned to the treatment group relative to those assigned to the control group we conclude that the savings response represents a lasting change in savings and not merely a short term response to a new product

intertemporal tradeoffs for gains and losses an experimental measurement of discounted utility this article provides a parameter free measurement of utility in intertemporal choice and presents new and more robust evidence on the discounting of money outcomes intertemporal utility was concave for gains and convex for losses consistent with a hypothesis put forward by loewenstein and prelec 1992 discount rates declined over time but less so than previously observed under the assumption of linear utility for approximately 40 of our subjects constant discounting provided the best fit the remaining 60 were most consistent with harvey s 1986 power discounting our data provide little support for the popular quasi hyperbolic model which is widely used in economics today we observed an asymmetry in the discounting of gains and losses that unlike earlier findings cannot be explained by a framing effect

credit risk models and agricultural lending credit risk models are developed and used to estimate capital requirements for agricultural lenders under the new basel capital accord the study uses credit value at risk methods to calculate probability of default loss given default and expected and unexpected losses two applied models creditmetrics and moody s kmv are estimated using farm financial data the results show that the necessary capital for agricultural lenders under the new basel accord varies substantially depending on the riskiness and granularity of the portfolio

self confidence and personal motivation the maintenance and enhancement of self esteem has always been identified as a fundamental human impulse philosophers writers educators and of course psychologists have all emphasized the crucial role played by self image in motivation affect and social interactions the aim of this chapter is to bring these concerns into the realm of economic analysis and show that this has important implications for how agents process information and make decisions conversely the tools of economic modelling can help shed light on a number of apparently irrational behaviours documented by psychologists

uncertain lifetime and intertemporal choice risk aversion as a rationale for time discounting this article makes explicit the links between preferences over lotteries on length of life and intertemporal choice it shows that the approach used by traditional life cycle models to account for uncertain survival corresponds to a strong assumption of risk neutrality with respect to length of life relaxing such an assumption leads us to develop a more general formulation of lifetime utility in which time discounting is directly related to preferences over length of life exponential and hyperbolic discounting are found to result in a first approximation from constant and hyperbolic risk aversion with respect to length of life

on money pumps abstract the question of whether money pump arguments justify standard consistency assumptions about behavior has remained unresolved partly because of the absence of an appropriate analytical framework we present a new framework which fills this gap provide a formal definition of invulnerability to money pumps and formulate a requirement of maximal opportunism we show that behavior which satisfies none of the standard consistency assumptions can be both invulnerable and maximally opportunist we present two conditions which combined with maximal opportunism imply the existence of a choice function rationalized by an ordering and satisfying the sure thing principle journal of economic literature classification numbers b41 c73 d81