Simple axioms for countably additive subjective probability

This paper refines Savage’s theory of subjective probability for the case of countably additive beliefs. First, I replace his continuity axioms P6 and P7 with a simple modification of Arrow’s (1970) Monotone Continuity. Second, I relax Savage’s primitives: in my framework, the class of events need not be a σ-algebra, and acts need not have finite or bounded range. By varying the domains of acts and events, I obtain a unique extension of preference that parallels Caratheodory’s unique extension of probability measures. Aside from subjective expected utility, I characterize exponential time discounting in a setting with continuous time and an arbitrary consumption set.     

Hyperbolic discounting and the standard model: Eliciting discount functions

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.     

Management of a capital stock by Strotz's naive planner

The capital management problem posed by R.H. Strotz is analyzed for the case of the ‘naive’ planner who fails to anticipate changes in his own preferences. By imposing progressively stronger restrictions on the primitives of the problem – namely, the discounting function, the utility index function, and the investment technology – the planner's behavior is characterized first as the solution to an ordinary differential equation and then via explicit formulae. Inasmuch as these characterizations leave the discounting function essentially unrestricted, the theory can accommodate, in particular, decision makers who discount time according to the hyperbolic and ‘quasi-hyperbolic’ curves used in applied work and said to be supported by psychological studies. Comparative statics of the model are discussed, as are extensions of the analysis to allow for credit constraints, limited foresight, and partial commitment.     

The Impact of Discounting Room Rates on In-House Restaurant Sales

This study investigates whether discounting hotel room rates during low seasons of demand influences in-house hotel restaurant sales in a positive way. A linear regression function was utilized to assess the relationship between discounting room rates and the hotel's in-house restaurant sales. The model summary provided results indicating that the discounting of room rates during the low season did not significantly influence in-house restaurant sales. The value of this study lies in the empirical results that may provide guidance to the revenue management practices of hotel managers.     

Models of Quality‐Adjusted Life Years when Health Varies Over Time: Survey and Analysis

Abstract.  Quality‐adjusted life year (QALY) models are widely used for economic evaluation in the health care sector. In the first part of the paper, we establish an overview of QALY models where health varies over time and provide a theoretical analysis of model identification and parameter estimation from time trade‐off (TTO) and standard gamble (SG) scores. We investigate deterministic and probabilistic models and consider five different families of discounting functions in all. The second part of the paper discusses four issues recurrently debated in the literature. This discussion includes questioning the SG method as the gold standard for estimation of the health state index, re‐examining the role of the constant‐proportional trade‐off condition, revisiting the problem of double discounting of QALYs, and suggesting that it is not a matter of choosing between TTO and SG procedures as the combination of these two can be used to disentangle risk aversion from discounting. We find that caution must be taken when drawing conclusions from models with chronic health states to situations where health varies over time. One notable difference is that in the former case, risk aversion may be indistinguishable from discounting.     

Folk Theorem For Bilateral Bargaining with Vector Endowments

We analyse a bargaining game of two players on the division of the sum of their vector endowments, with alternating proposals and discounting of single period utilities. The pair of endowments is not weakly Pareto‐efficient. Until they reach an agreement, each of the parties can withdraw from bargaining and keep their endowments. Any strictly individually rational division of the sum of endowments can emerge in some subgame perfect equilibrium if discount factors are close enough to one. Each subgame perfect equilibrium, in which the parties’ decisions do not depend on past rejected proposals, leads to a weakly Pareto‐efficient agreement in the first period.     

Improving the Delphi process: Lessons from social psychological research

The Delphi technique was largely developed to avoid the problems of freely interacting groups such as dominant individuals and pressure to conform to the majority view. Our review of the social psychological literature reveals some obstacles to Delphi achieving its full potential relative to other cheaper and easier methods of aggregating judgment. We identify residual normative and informational pressures towards consensus that potentially reduce process gain that might otherwise be achieved. For instance, panelist confidence may act as a signal of status rather than be a valid cue to expertise, whereas consensus appears to have a strong influence on the final outcome that can reduce its accuracy when there are valid minority opinions. We argue that process gain in Delphi must occur through those further from the "truth" changing their opinion more than those closer to the truth, with the general direction of opinion change being towards the truth. For such virtuous opinion change to occur we suggest the need to both facilitate opinion change and provide good cues as to where the truth lies. Research on Judge Advisor Systems shows that people usually do not change their opinion as much as they should, giving too much weight to their own opinion and too little to the views of others—this bias can be reduced by increasing involvement and motivation. In addition, we propose that the best way to provide good cues as to the direction of the truth is to elicit rich reasoning from panelists about the judgment or choice in question, then use this as feedback. We suggest practical ways of focusing and deepening panelists’ consideration and evaluation of such reasoning—such that all proffered opinions are well-evaluated. Additionally, we propose a model of opinion change in Delphi for use as a paradigm for future process-orientated research.     

Mathematical optimisation of drainage and economic land use for target water and salt yields*

Land managers in upper catchments are being asked to make expensive changes in land use, such as by planting trees, to attain environmental service targets, including reduced salt loads in rivers, to meet needs of downstream towns, farms and natural habitats. End‐of‐valley targets for salt loads have sometimes been set without a quantitative model of cause and effect regarding impacts on water yields, economic efficiency or distribution of costs and benefits among stakeholders. This paper presents a method for calculating a ‘menu’ of technically feasible options for changes from current to future mean water yields and salt loads from upstream catchments having local groundwater flow systems, and the land‐use changes to attain each of these options at minimum cost. It sets the economic stage for upstream landholders to negotiate with downstream parties future water‐yield and salt‐load targets, on the basis of what it will cost to supply these ecosystem services.     

Tools for Financial Innovation: Neoclassical versus Behavioral Finance

The behavioral finance revolution in academic finance in the last several decades is best described as a return to a more eclectic approach to financial modeling. The earlier neoclassical finance revolution that had swept the finance profession in the 1960s and 1970s represented the overly‐enthusiastic pursuit of only one model. Freed from the tyranny of just one model, financial research is now making faster progress, and that progress can be expected to show material benefits. An example of the application of both behavioral finance and neoclassical finance is discussed: the reform of Social Security and the introduction of personal accounts.     

Mortgage Choice as a Natural Field Experiment on Choice under Risk

Data on approximately 280,000 borrowers from the UK Survey of Mortgage Lenders are used to model choices between variable and fixed rate mortgages. The choice is assumed to depend on three factors: risk attitude, interest‐rate expectations, and individual discount rate. The ordered probit model is used for estimation, while taking account of a number of econometric issues including missing counterfactuals, selectivity, and endogeneity. A large number of strong effects are found, including: higher income borrowers are less risk averse and have a lower discount rate, and risk aversion rises with the amount borrowed, providing evidence of increasing relative risk aversion.