The History of Studies on Intertemporal Choices
The Early Psychological Arguments of Choice over Time
Intertemporal choices are far from being a new research topic in economics as attentions paid to this subject started at the very beginning of the discipline. Rae (1834) notably expressed an ex-plicit interest in this topic as a research investigation on its own (Loewenstein and Elster, 1992). He generated an in-depth discussion on the psychological motives underlying intertemporal choices. The difference in wealth across nations is, according to him, partly attributable to the “effective de-sire of accumulation”. This psychological factor is a joint product of four determinants that either limit or promote the preference for the future.
The first two motives that promotes the preference for the future are self-restraint,1 and be-quest.2 The self-restraint motive is what economists would call foresight and is often handled as the precautionary motive for saving. Rae saw culture as a critical determinant of the effective de-sire of accumulation in more primitive societies and lower orders of society, where intellectual powers, habits of reflection, and prudence were less developed. On the other hand, the bequest motive can be understood as the manifestation of individuals’ desire for immortality to transcend their own ends, and leads individuals to seek survival through their significant ones and ultimately broadens the decision-makers horizon beyond their own existence.
The two other motives that limits the effective desire of accumulation is the uncertainty of human life, and the excitement/passion of immediate consumption. The uncertainty of human life limits the desire of accumulation as unhealthy and hazardous places suffering from war and famine for instance tends to reduce the likelihood of benefiting from the accumulation of their provisions for the years to come (Rae, 1834, p. 57). The pleasure provided by the immediate pres-ence of an object of desire also limits the preference for the future. In particular, the real presence of the immediate object of desire leads to a very living conception of enjoyment which it offers to their instant possession. John Rae himself mentioned that there is probably no man who would not see any difference between the enjoyment of a good today and the enjoyment of the same good but in a very distant future, even if that enjoyment was certain in both cases (Rae, 1834, p. 120). Although Rae’s first intention was not to study individual behavior per se, but rather the determi-nants of a nation’s collective desire to explain differences in capital accumulation, his work laid the first psychological foundations of the research on intertemporal choices.
Following Rae’s work, one can distinguish two emerging opposite views that intend to summa-rize these determinants —those of Jevons and Senior— of the underlying psychological emotions driving intertemporal choices. While both support the normative view of equal treatment between the present and the future, they explain individual’s deviations from that prescription using two different emotional explanations.
According to Jevons (1905), individuals are only concerned by their immediate utility: precau-tionary behaviors only stems from the ability to derive utility from the present anticipation of fu-ture consumption rather than the future consumption itself. Hence, a decision maker who defers a consumption does not defer a pleasure but substitutes a pleasure now with the pleasure derived from the anticipation of a future pleasure. The variation in intertemporal choices hence arises from the individual’s variation of the imperfect transcription of future events into present utility.
For his part, Senior (1836) explained the inability to view equal treatment between the present and the future as resulting from the pain of refraining from immediate consumption3 which he viewed as “the most painful exertions of the human will” (Senior, 1836, p. 60). Contrary to Jevons, Senior analyzes individuals’ differences in intertemporal choices as being caused by the difference in the inherent difficulty to delay immediate gratifications.
Although these two views differed in the underlying psychological mechanism driving the pref-erence for the future, both share the idea that the immediately experienced emotions limits the horizon of the decision maker, either because of the immediate pleasure of anticipation or be-cause of the immediate suffering of abstinence.
Bohm-Bawerk et al. (1890) provided one alternative theory of intertemporal choices that is based on a cognitive perspective: while he recognized that future utility weight less than current utility, he did not believe, unlike Jevons, that the decision maker is solely oriented toward her immediate utility: “It can be hardly maintained, as some of our older economists and psychologists used to be fond of assuming, that we possess a gift of literally feeling in advance the emotion we shall experience in the future” (Bohm-Bawerk et al., 1890, p. 60). Instead, the decision maker Böhm-Bawerk depicts makes the trade-off between pain and pleasures that are comparable on the same cognitive dimension even though they occur at different points in time.
According to him, people discount the future as they have a systematic tendency to underesti-mate their future needs due to the ability (or lack, thereof ) of imagination and abstraction of the future especially in the distant future. It is based on a sophisticated cognitive psychology simi-lar to the modern of concept of availability of Tversky and Kahneman (1973): “we accord to goods which are intended to serve future ends a value which falls short of the true intensity of their future marginal utility » (Bohm-Bawerk et al., 1890, p.268 – p. 269).
In addition, Böhm-Bawerk adds an emotional component that refrain the decision maker to achieve her goals. He acknowledges the fact that when people choose between a present and a future pain or pleasure, they can decide to favour the present pain or pleasure although they know perfectly that the future disadvantage of making this choice is greater and that their total life’s well-being would be smaller. Thus, in introducing this additional component that refers to a lack of self-control, Böhm-Bawerk endorses an emotional perspective of intertemporal choices that deviates from a purely rational utility maximization.
Böhm-Bawerk’s characterization of intertemporal choices consists in the allocation of con-sumption among time periods, Fisher (1930) formalized this perspective in a theoretical frame-work whereby intertemporal choices between current and future consumption could be conceived as a choice of consumption’s allocations between two different goods: Fisher plotted the intertem-poral consumption decision on a two-goods indifference diagram with current consumption on the x-axis and future consumption on the y-axis. By treating the allocation of consumption over time as the atemporal allocation of consumption between two different goods, Fisher assumed that the marginal rate of substitution between current and future consumption depends on both time preference and diminishing marginal utility.
In his contribution, Fisher encapsulated all the previous psychological determinants of the intertemporal choices proposed by all the predecessors into a single parameter. The time prefer-ence parameter includes the inverse of Böhm-Bawerk systematic tendency to underestimate fu-ture wants and the four determinants mentionned by Rae. Fisher also added the fashion motive as a novel determinant of intertemporal choices corresponding to the influence of the peers or a community in the way individuals behave. This new determinant of time preference is of great importance as it allows to understand time preferences as the result of situational factors present in the society in which the individual belongs. Fisher illustrated this new determinant by the En-glish poor people who developed the habit of saving when postal savings banks were introduced (Fisher, 1930). Thus, his analytical framework describes time preference as the amalgamation of all the motives mentioned above.
Thus, the genesis of intertemporal choices as a field of study in economics is deeply embedded in a psychological approach. Interestingly, each of these early perspective adopts the same nor-mative statement: they all viewed equal treatment between the present and the future as an ideal and time discounting is construed as an explanation of the deviation from that norm. Fisher’s representation of intertemporal choice had a great impact on the economic discipline. Despite an extensive discussion of the psychological and situational origins of such a parameter, the in-tertemporal analysis he proposed is not dependent on the value of the psychological insights: in-tertemporal choice in such a model can be seen as a generic atemporal problem of consumption between two goods. This mathematical representation of intertemporal choices thus paves the way for the emergence of economic models avoiding a discussion on the psychological origins of time preferences.
The Clean Slate of Psychological Fondations in Modern Economics
The rise of economic modeling, which gradually reached centre stage for legitimacy purposes, has resulted in a new representation of the decision-maker. Economic models propose an abstract and coherent formalism that attempts to produce theoretical objects that are extricated from their psychological and subjective connotations: the individual is reduced to an Homo Oeconomicus agent who makes rational decisions to maximize her utility with respect to a set of constraints given initial endowments. Within this framework, the individual’s true preferences are given: their determination are not denied but has been relegated to a black box at the expense of all previous developments on the origins of such preferences and their roles in intertemporal choices. This epistemological turning point has lead to the emergence of hypothetico-deductive models whose aim is not necessarily to reflect reality but to imitate how it works in particular applications (Mas-son, 2000). The main advantage of these models lies in their heuristic power. They make possible the assessment of the consequences produced by alternative policies, the exploration of other en-vironments —imaginary or real— or the attribution of the gap between predictions and reality to certain phenomena temporarily omitted by the formalization. Hence, time preferences had be-come a neutral concept with respect to physiology, anthropology, and psychology, by sacrificing some important aspects that are relevant to study real-world behaviours
The Discounted Utility Model
Samuelson (1937) proposed in his article “A Note on Measurement of Utility » a general model of intertemporal choices that could be applied over infinite horizons, unlike Fisher’s model which could only represent two periods. The intertemporal analysis is a maximization of the sum of dis-counted instantaneous utilities, in which the utility function is separable and additive. Similarly to Fisher’s representation of time preference, the discounting parameter of instantaneous utilities potentially encapsulated all of the previous psychological motives into one single and unique parameter for the sake of parsimony. The model specifies the preferences of a decision maker over a sequence of consumption levels (c0 . . . cT ) weighted by the discounting function D(.). Such prefer-ences can be represented by the following utility function: Ut (c0 . . . cT ) =D(k)u(ct +k ) (I.1) k=0 where the discounting function D(.) ∈ [0; 1] is monotonically decreasing with respect to time: δ is a subjective and idiosyncratic parameter called the exponential discount factor. It cor-responds to the weights attributed to future utilities. The closer from unity δ is, the longer the decision-making horizon. ρ refers to the pure rate of time preferences whose role is to reflect all the psychological considerations that have been previously mentioned. Its content is subjective and can be thought as the propensity of the agent to magnify forthcoming pleasures and pains relative to very distant ones. u(ct ) is a concave4 instantaneous utility function of consumption at date t .
The advantage of such a simple specification lies on the tractability of the behavioural model: such a formulation provides a simple and elegant framework to analyse an individual’s consump-tion profile over time.
Koopmans (1960) showed that this model could be derived from a set of axioms that make the discounted utility compatible with the ordinal approach. In particular, Samuelson’s model repre-sents time preferences only if it satisfies five axioms. While the first three axioms of completeness,5 monotony,6 and continuity7 are usual in decision theory, the two last axioms of impatience and stationarity are specific to time preferences and are the most important features of the exponen-tial discounting function.
The axiom of impatience says that it is always better to receive something later than sooner. More formally, if an outcome x is desirable, then the individual would prefer getting x sooner than later and zero is the time-neutral outcome: the individual is indifferent between getting zero sooner or later. This axiom hence holds the spirit of the impatience trait of Rae (1834) and Bohm-Bawerk et al. (1890).
The last axiom for the representation of time preference is stationarity. It asserts that if an individual is indifferent between getting x in t and getting y in t + τ, if the two times t and t + τ are advanced or deferred by the same amount s, then indifference will be preserved. Stated differently, the indifference between two time-dependent outcomes depends only on the delay between the periods (τ) but not the periods themselves. This axiom of time consistency is the most discussed feature of the exponential model because it has the most important implication in time-related decision making. The individual optimally plans in a time-consistent manner her consumption needs until the end of her life: she should neither revise his plans, nor experiencing regrets of her past choices.
These two last axioms for the representation of time preferences provide an ambiguous view on the interconnection between economics and psychology. While the first axiom shows that the rep-resentation of time preferences is necessarily grounded in the psychological realm, the second is more debatable from a psychological perspective and had lead plenty of researchers to document anomalies of the exponential discounting model.
Anomalies In the Discounted Utility Model
Despite the appealing tractability and elegance of the exponential discounting model, it fails to match several empirical regularities. Few decades after Samuelson’s article, behavioural sciences had evidenced several behavioural regularities which are incompatible with the exponential dis-counting model. For example, people prefer to get quickly unpleasant outcomes rather than defer them as predicted by the standard model (Loewenstein, 1987). Losses are generally discounted at a lower rate than gains (Thaler, 1981), People have asymmetric preferences for speeding-up vs. delaying of consumption whereas, according to the discounted utility model, these preferences should be symmetrical (Loewenstein, 1988). A full list of discounted utility anomalies is enumer-ated by Loewenstein and Prelec (1992), including their explanations and a variety of other phe-nomena.
One of the most documented anomalies of the exponential discounting model is time incon-sistency. Evidence is accumulating, both in the economic and psychological literature, that people do not have time consistent preferences and that their discount rates are declining over time. First, casual observations and introspection on people behaviours can provide great examples of time inconsistent choices. While people set goals by promising to stop smoking, to save more, and to finish their Ph.D dissertation, they often fail to meet their goals: they keep smoking, they spend money on things they often regret later on, and they fail to redact their thesis for the due date. Yet, the exponential discounting model fails to account for these choices we often regret and, in that sense, time inconsistency is in the same spirit as Bohm-Bawerk et al. (1890)’s lack of willpower. Experimental studies from both economics and psychology have also shown that people do not make time consistent choices. When participants are asked to choose between a sooner and smaller reward and a later and larger reward, the implicit discount rate over long horizons is gen-erally lower than the discount rate over short horizons. This generates a declining discount rate which is inconsistent with the exponential discounting model. For example, Thaler (1981) asked subjects to specify the amount they would like to receive in one month, one year, and ten years that would make them indifferent to receiving 15 dollars today. The median responses of 20, 50, and 100 dollars imply that the annual implied discount rate of such choices is 345%, 120% and 19%.
In addition, individual preferences between two future rewards can be reversed in favour of the most proximate reward as the time of both reward diminishes. For example, someone may prefer to receive 110 euros in one month and a day over 100 euros in one month, but also prefer 100 euros today over 110 euros tomorrow. Such preferences reversals have been observed both in human beings (Kirby and Herrnstein, 1995) and in pigeons (Ainslie, 1992).
Table of contents :
2 The History of Studies on Intertemporal Choices
3 Three Directions for Further Investigations
4 TheMethodologies of the Thesis
5 Outline of the Thesis
I Betting Against Yourself forWeight-Loss
2 Literature Review
3 Model of Commitment Choice
4 Experimental Design
I.A Proofs of theModel of Commitment Choice
I.C Correlations between Time Discounting and Temporal Perspective Scales
II Self-Control, Fatigue and BodyWeight
2 Fatigue & Self-Control: the StrengthModel
3 Data andMethods
II.A Tables and Figures
II.B Additional Results
III Measuring Identity Orientations for Understanding Preferences
2 Conceptual background
3 Validation of a French version of the AIQ: method
5 Identity and Preferences
III.A French Version of the AIQ-IV
III.B Main model (Model 2): technical details of the validation study
III.C Development of new items and model comparisons
IV Time Preferences and Relational Identity
3 Study 1: Is Self-continuity associated with Aspects of Identity?
4 Study 2: Priming the Salience of Aspects of Identity
5 Study 3: Instability of Identity Priming
6 Concluding Remarks
IV.C Multiple Hypothesis Testing
List of Tables
List of Figures