مدل ابزار با تخفیف و ترجیحات اجتماعی :: برخی از فرمولاسیون های جایگزین به تنزیل معمولی

Abstract This paper considers four patterns of intertemporal choice. First, the time effect, an inverse relation between time preference (TP) and the time implied in the choice. Secondly, the magnitude effect, an inverse relation between TP and the amount implied in the choice. Thirdly, delay/speed-up asymmetry, that is to say, a change in the preferences in function of the framing of the choices. Fourthly, the domain effect, where TPs differ as between health and money. The novel aspect of the paper is the finding that such patterns are present when individuals face intertemporal social choices with respect to money and health which, therefore, could be interpreted as fundamental properties of intertemporal choice. Furthermore, given the time effect, consideration is given to the quantitative form of the discount function. It is found that hyperbolic discounting models provide a better description of the stated preferences than the conventional discounted utility model or the quasi-hyperbolic discounting model. The results provide evidence in support of the hyperbolic social discounting models.

. Introduction The Samuelson (1937) discounted utility (DU) model, together with its axiomatic derivations, defines individual behaviour with respect to time in normative terms. However, the attitude of individuals in intertemporal choices contradicts the properties of this model. Such an incompatibility between normative hypotheses and observed behaviour is described in the economic literature as an anomaly ( Loewenstein & Prelec, 1992). A significant number of anomalies arise when individuals exchange private products over time. Furthermore, there is an extensive theoretical literature (see, for example, Marglin, 1963; Sen, 1960, Sen, 1961 and Sen, 1967; Warr & Wright, 1981) which argues that individual decisions motivated by private or egoistic preferences differ from those that rest on altruistic or social preferences. In this paper we use data obtained from a survey in order to consider whether such anomalies are present when individuals make intertemporal social choices, or if they are confined solely to private choices. One of these properties consists of time preference (TP) rates falling as the time horizon implied in the choice increases. If we accept this evidence against the conventional discounting model, it becomes necessary to search for models that better describe individual social behaviour. In this paper, applying the methodology which is typical of analyses carried out by behaviourists – for example, Kirby and Marakovic (1995) and Kirby (1997) – we study whether other forms of the discount function provide a better description of individual social behaviour with respect to both monetary and health exchanges. With these two objectives in mind, the rest of the paper is organised as follows. In Section 2 we briefly describe the normative properties of the DU model, together with the anomalies that come to light in hypothetical situations of intertemporal choice. The method applied to estimate the TPs and the results of this estimation are considered in Section 3. Section 4 is dedicated to an analysis of the alternative discount formulations. Section 5 closes the paper with a review of the main conclusions.

. Conclusions The present study has moved from a focus on private individuals' time preferences to one of social individuals' exchanges. As a consequence, several novel issues have been addressed. First, the behaviour of time preferences with respect to intertemporal exchanges of social health and money has been analysed for different time horizons, magnitudes and frames. Furthermore, individuals' TPs for health and money have been compared for all the time horizons and in both the delay and speed-up frames. On the basis of our results, we can conclude that the stated preferences when individuals are placed in the role of a decision maker do not appear to agree with the behaviour predicted by the axioms of the DU model. In this regard, our results contribute to the existing theoretical literature and complement it by incorporating the social dimension. In this way, we provide support for the assumption that the time effect, the magnitude effect and the delay/speed-up asymmetry are fundamental properties of intertemporal choice. This aspect is particularly worthy of note. It seems to be indicating that similar choice mechanisms apply whatever the intertemporal choice faced by individuals, whether private or social, and for both monetary and health choices. Although different preference maps, mental schemes or motivations could arise in every case, leading, for example, to higher TP rates for health than for money, these do not seem to contaminate the effects that have been reported earlier in the literature. An interesting topic for further research could be to identify the psychological processes underlying the relationship between time and domain that generate the same patterns of intertemporal choice, in the case of the former, and different TPs for health and money, in the case of the latter. A second issue to which attention should be drawn is that we have been able to compare different discounting functions (conventional, hyperbolic and quasi-hyperbolic) under social choice with respect to different magnitudes, frames and domains. Our results clearly favour hyperbolic functions as a description of the behaviour with respect to time exhibited by the individuals in the sample. Moreover, the quasi-hyperbolic model, despite its successful use to characterise real individual decisions with intertemporal consequences, shows the poorest goodness of fit of all the models analysed. This comparison between different discounting functions gives rise to two findings that deserve further consideration. First, the use of a quasi-hyperbolic model makes it possible to discover differences between individuals' real and hypothetical decisions. The gap identified could have two alternative explanations, with each of these carrying different implications. In our study the choices made by each individual are social in nature, whereas in real decisions these choices are private. This could account for the poor performance of the quasi-hyperbolic model, and could provide a basis for additional research to compare both non-constant discounting models when exchanges are merely private. Similarly, it is possible that contextual or other kinds of factors differ as between real and hypothetical choices, causing one or the other model to dominate. Again, further research is needed into contextual factors in hypothetical, as opposed to real, intertemporal choices. Secondly, the fact that the same hyperbolic model has not always shown itself to offer a better fit in every scenario could imply that such models are scenario specific. This suggests it is unlikely that we will be able to find a unique functional form that could be seen as a substitute for the well-established constant discounting model in economic theory. On the basis of all the above it is clear that, by contrast to the conventional discounting model, non-constant discounting models assign a lower weight to consequences that are closer in time. However, as the time horizon increases, this tendency is inverted, and hence these models give a higher present value to the monetary amounts and the future lives saved than does the constant discount model. This makes hyperbolic models more attractive for three reasons. First, because they are more in accord with the TPs of individuals, whether private or social. Secondly, by making it possible to give a higher consideration to future costs and benefits, such models are of undoubted interest in the economic evaluation of public policies that have inter-generational effects (e.g. energy and natural resources). Thirdly, if we combine these first two reasons, it may be possible to give a higher weight to future social costs and benefits, at the same time as considering individual social TPs. For this reason, the results offered by hyperbolic discounting are of special interest not only from a psychological point of view, but also from those of other social scientists, mainly philosophers (Sagoff, 1994) and environmentalists (Crowards, 1997; Howarth & Norgaard, 1993; Lumby & Saville, 1996). In closing, we can say that whilst the DU model, and the constant discount rate upon which it is built, remain unequalled as normative theory, economists must be aware of their limitations. If such limitations are ignored then, as Knetsch (1995, p. 75) has observed, this would be “(…) at odds with the large number of reports of such evidence that have appeared in leading professionals journals, the significant social costs that are likely to result from continued disregard to the possibilities for improvement; and the frequency of claims of policy analysts that better analyses can lead to more rational and reasonable policy responses”. Fortunately, papers such as those of Ahlbrecht and Weber (1995); Azfar (1999); Cairns and van der Pol (2000); and Henderson and Langford (1998) have pointed us in the right direction, and we hope that our contribution follows in this line.