relative’s money compared to for their own money in an
intertemporal choice experiment?
Oscar Knoeff University of Amsterdam
Master thesis
Abstract
42 subjects have performed an intertemporal choice experiment in which they needed to decide on their own payoffs and on their relative’s payoffs, to investigate differences in time preferences. Several statistical specifications are used, with those containing a
quasi-hyperbolic form, implementation of risk averseness and background consumption
considered most pioneering. The quasi-hyperbolic form relies on a theoretical framework that involves a trade-off between long-run optimization and short-run temptation. To evaluate the outcomes a regression and Wilcoxon signed rank tests are used. These tests show that participants have significantly more time preferences, and therefore act less rational, when they choose for themselves. This points to the need of involving third parties in intertemporal (investment) decisions on household level. A pre-made assumption implies that this difference is caused by an absence of short-term temptation and less utility
function curvature when a person makes choices for another. However, this study’s outcomes do not indicate that this is the case. Correcting for risk aversion seems to be valuable as its implementation increases the predictability of the regressions.
2
Introduction
There is research on one’s risk attitudes toward other people’s money. Chakravarty and Harrison (2011) conclude that people tend to be less risk averse in the case of dealing with someone else’s money. This finding is important for economics, because money
investments with consequences of others are an everyday life phenomenon. Therefore, this present study aims to investigate the effect on time preference in an intertemporal choice experiment, when someone decides on another person’s payoffs.
Fredericks et al. (2002) and Berns et al. (2007) emphasize the economic importance of time preferences. Berns et al. (2007) document that time discount rates have proven to be a key parameter in policy debate about global warming, and Fredericks et al. (2002) state the following:
Intertemporal choices decisions involving trade-offs among costs and benefits occurring at different times are important and ubiquitous. Such decisions not only affect one’s health, wealth and happiness, but, may also, as Adam Smith first recognized, determine the economic prosperity of nations.
Common examples of such intertemporal choices are consumers that decide how much to invest in for example savings, education, real estate, life insurance and how much to invest to diet, exercise and smoke, and whether to marry and when to have children. Furthermore, a large body of prior work suggests that individuals have different preferences over
analogous choices for others than for themselves (Shapiro 2010).
For the above mentioned reasons and because no study has been performed on this subject as of yet, it is interesting to investigate time preferences for other people’s money. An example of such a situation is when a person forces a relative to choose for a type of mobile phone contract or a washing machine, having to take into account the purchase price versus the energy costs. To evaluate its effect, these time preferences are compared with the time preferences when the subjects choose for themselves.
Several statistical specifications that are based on utility functions of participants are used to investigate differences in intertemporal decision-making behaviour. Some of these utility functions include parameters for risk averseness (since people exhibit concave utility behaviour) and background consumption, and others do not. In addition, there is a distinction between two functional forms over all statistical specifications, of which the exponential utility function contains a linear form to observe differences in decision behaviour and the other a quasi-hyperbolic form to investigate whether a theoretical framework can explain these differences. This theoretical framework, that is integrated in the quasi-hyperbolic discount function, involves a trade-off between long-run optimization and short-run temptation, as is supported by studies of Anderson et al. (2008), Fudenberg and Levine (2006), Andreoni and Sprenger (2012a) and Fredericks et al. (2002). The degree of time preferences is measured in discount rates.
3
Participants of this study elicit risk and time preferences for both themselves and their partner, using controlled experiments where two relatives separately perform all tests on the same location at the same time. The experimental design is presented in section 2, where risk aversion measurements builds on the experiments of Eckel et al. (2010) and time discount rate measurements on the experiments of Coller and Williams (1999). Wilcoxon signed rank tests and a regression are used to evaluate the statistical specifications. Using an exponential utility function model at 5% significance level, a Wilcoxon signed rank test shows that participants significantly have more time preferences, and therefore act less rational, when they choose for themselves. A pre-made assumption implies that this
difference is caused by an absence of short-term temptation and less utility function curvature when a person makes choices for another person. There is, however, no indication of a difference in short-term temptation, and the subjects’ own degree of risk aversion is actually higher than when they choose for their partners. The latter both contradicts Chakravarty and Harrison’s (2011) findings and the pre-made assumption regarding utility function curvature.
Although correcting for risk aversion allows for the possibility of creating negative discount rates, it also seems to increase the predictability of discount rates. Using statistical
specifications that control for risk averseness, regressions show that people that spent more than their partner show significantly more differences in discount rates over the two
treatments (own time preferences minus time preferences for relative), while subjects that have an economic background show significantly less differences in discount rates in most datasets. In one dataset, people with a higher income show less difference in discount rates. The results point to the need of involving third parties in intertemporal (investment)
decisions. This finding contributes to studies of Masclet et al. (2013), Shapiro (2010), Abdellaoui et al. (2013), Carlsson et al. (2012), Kono et al. (2011), who conducted similar experiments with different types of third parties that show similar results. All these studies explain the existence of institutions such as investment professionals, ROSCA1 and
companies that deduct pension from salary. Literature
To briefly introduce time preferences; imagine the proposition of choosing between 5 euro now and 6 euro tomorrow. Although it is not rational to choose for the first option (unless the daily interest rate is above 20 percent), there are people who exhibit a preference for the first option. The higher this preference for gaining in the present, the more time preference or higher time discount rate that person has.
Much research has been done on intertemporal choice. After Adam Smith noted its importance, the Scottish economist John Rae (1834) examined the sociological and
1
4
psychological determinants of such intertemporal choices. Rae wrote that immediate consumption is favoured by the uncertainty of human life and the prospect of immediate consumption (and the discomfort of deferring such available gratifications). Factors that favour future consumption are the bequest motive and the propensity to exercise self-restraint.
These factors reflect two fundamentally different views at that time that share the idea that intertemporal trade-offs depend on immediate feelings and the immediate discomfort of self-denial. Frederick et al. (2002) describe both these views in their paper. They first mention the anticipatory-utility perspective. “Variations in discount rates among people are due to differences in people’s abilities to imagine the future and to differences in situations that promote or inhibit such mental images.” The other is referred to as the abstinence perspective. Here individual variations are explained by individual and situational differences in the psychological discomfort associated with self-denial. Later, Eugen von Böhm-Bawerk (1889) proposed another factor that explains immediate consumption, stating that “Humans suffer from a systematic tendency to underestimate future wants.” In 1930, Fisher developed von Böhm-Bawerk’s model to the two-goods indifference diagram. A major change occurred in 1937 when Paul Samuelson introduced the discounted utility (DU) model. All the psychological factors discussed over the 19th and early 20th century were compressed into a single parameter, namely the discount rate.
Equation 1
, … , = ∗ = +
Here represents the individual’s discount function, which has an exponential form in this equation, and represents the individual’s discount rate. A higher causes a higher immediate utility ( !" ) relative to future utility ( #!" $ %). Samuelson never designed this model for a normative nor realistic descriptive approach, but rather to make a simple generalized model that was applicable to multiple time periods. However, its simplicity and elegance gave this model dominance in the field of economics until today.
After the introduction of the DU model scientists came up with more factors that may influence one’s time discount rate. Thaler and Loewenstein (1989) and Loewenstein (1987) mention dread: rationally, people should want to consume gains as soon as possible and postpone losses as long as possible. However, sometimes they are willing to consume in earlier stages to avoid unpleasant prospects (in the case of receiving an electrical shock for example). The other way around can also apply, because according to Thaler and
Loewenstein (1989) subjects prefer to delay a kiss from a movie star to savor its
anticipation. Another situation where future outcomes are favoured is when people prefer increasing utility over time. To illustrate, Hsee et al. (1991) found that employees equally
5
preferred an increasing salary sequence to a decreasing sequence that conferred much more money.
Anomalies
As is stated further on in this study, results of researchers who tried to estimate time discount rates are very ambiguous. However, over the past decades, three important features are discovered that apply to most researches. First, gains are discounted more than losses (Thaler & Loewenstein, 1989; Fredericks et al., 2002). This is often documented as the sign effect. Next, the magnitude effect implies that small outcomes are discounted more than large ones (Fredericks et al., 2002; Thaler & Loewenstein, 1989; Loewenstein, 1987).
Figure 1 – S and B are monetary amounts of which B > S and where S can be received earlier than B. Source: Ainslie 1975 And last, discount rates decline sharply the longer a person has to wait. In 2002, Fredericks et al. document in their influential (cited 2827 times) and comprehensive article that the most important modification of the DU model is its evolvement from the exponential discounting model into the hyperbolic discounting model. Equation 1 (p. 4) implies that the discount rate does not change over time. However, there are researchers (Thaler & Loewenstein, 1989; Fredericks et al., 2002; Ainslie, 1975; Fudenberg & Levine, 2006) who found a declining discount rate over time. Figure 1 helps to understand this reasoning. According to Ainslie (1975) people prefer amount B over amount S at t=0. However, when t=t* people like to switch to the earlier amount S because of increased short-term
temptation. Similar reasoning applies when someone wakes up in the morning and plans not to go out at night, but changes his mind when it becomes evening. Fudenberg and Levine (2006) explain this, closely in line with the old abstinence perspective, by stating the following. “The costliness of exercising self-control determines the trade-off between lifetime wealth maximization and short-term temptation, so final decisions tend to reflect neither pure short-term temptation nor pure lifetime wealth maximization.” According to Berns (2007), the bulk of evidence of time preference studies related to animals (primarily from rats and pigeons) suggest that they also discount the future in a non-exponential
6
manner. This theory makes the shape of the discount function depart from flat. In the older literature, a hyperbolic functional form (figure 2) was introduced to fit the data better and was described as can be seen in equation 2.
Equation 2
, … , = ∗ = & + '
More recently, Prelec (2004) came up with a more modern but similar hyperbolic specification (view equation 3). This equation is hyperbolic when parameter 0< β <1 and exponential when β=1.
Equation 3
, … , = ∗ = ∗ (
In the last decades, however, studies have proven that discount rates stop declining after a certain amount of time2 and therefore the hyperbolic specifications of equations 2 and 3 became outdated. These new (reputable) studies introduced a different hyperbolic functional form which is quasi-hyperbolic. In these studies the emphasis lies on the
importance of a term called present bias, which has already been documented frequently in intertemporal choice studies (Fredericks et al. 2002).
Present bias implies, closely in line with the old hyperbolic discounting, a high discount rate due to short-run temptation. The difference between the two is that people with present bias behave ‘rationally’ when subjects face delayed rewards but exhibit time preference when an immediate or (very) short-run reward is available. In other words, present bias assumes a declining discount rate between now and the next period, but a constant one thereafter. In the case of hyperbolic discounting this process of diminishing discount rates occurs more gradually. Nowadays, the theory of present bias seems leading and its quasi-hyperbolic form is mostly described with the following mathematic equation.
Equation 4
, … , = + ( ∗ = & + '
where ( represents present bias
The exponential-, hyperbolic- and quasi-hyperbolic discount functions are plotted in figure 2.
2
7
Figure 2 – Source: Berns (2007)
Regarding today’s leading studies, Frederick et al. (2002), O’donoghue and Rabin (1999) and Andreoni and Sprenger (2012b) support the theory of present bias. Andreoni and Sprenger (2012a) did not find evidence for hyperbolic discounting nor did they find evidence present bias. Benhabib et al. (2005) only proved the existence of present bias: “Our estimation provides clear experimental evidence against exponential discounting in that it exhibits a present bias.” Anderson et al. (2008) only mention the different discount functions but do not favour one. They used one month as their earliest pay-out date to exclude the influence of present bias, and analysed their data using both exponential- and hyperbolic discounting. The obtained discount rates were similar.
Andreoni and Sprenger (2012b) propose another explanation for present bias than short-term temptation. They argue that present bias is caused by uncertainty related to future earnings, while the present is certain and therefore preferred. Their findings are consistent with the intuition of the Allais Paradox (Allais, 1953). Accordingly to Andreoni and Sprenger (2012a), their explanation of finding no present bias lies in the unique (and sophisticated) steps they took to equate the costs and risks associated with sooner and later payments, in contrast to other studies.
Frederick et al. (2002, figure 2, p. 380) listed all researches (field and experimental researches) that tried to capture individual discount-rates and show that these rates are very ambiguous. In addition, the interval of the estimates does not shrink over time.
Frederick et al. (2002) provide possible explanations for these observations. They emphasize the wide variety of procedures that has been used to estimate discount rates. These
different procedures are vulnerable to all kinds of biases. Frederick et al. (2002) discuss many confounding factors that, apart from the functional form, can mispredict the discount
8
rates, namely intertemporal arbitrage, uncertainty, inflation, expectations of changing utility, habit formation, measuring procedures and concave utility.
To explain the latter it is important to keep in mind that economists have recently paid more attention to the (generally accepted) concavity of individual’s utility functions (Andreoni & Sprenger, 2012a; Andreoni & Sprenger, 2012b; Andersen et al., 2008). This means that the utility of 100 euro is more than half of the utility of 200 euro. If an experimenter asks a subject whether he wants 100 euro now or 200 euro in 26 weeks, the discount rate is driven upwards by this bias.
Fredericks et al. (2002, table 1, p. 379) also show annual discount rates in combination with time ranges of past studies. Disregarding aforementioned confounding factors, the anomaly that implies that discount rates decline with the waiting time seems to have a lot of
influence. For example, Kirby and Markovic (1995) use 3 to 29 days and have annual
discount rates from 3678 percent to ∞ and Benzion et al (1989) use 6 months to 4 years and have annual discount rates from 9 percent to 60 percent. Although Fredericks et al. (2002, figure 1a and 1b, p. 362) illustrate this effect in their paper they strangely do not emphasize on this in their conclusion as being the leading factor for the high variation. The variation of discount rates between studies will probably shrink over time when a certain standard over new studies is set concerning time ranges. The fact that studies compare elicited discount rates measured by different functional forms between studies with different time ranges seems problematic for the meaningfulness of these studies’ results.
The magnitude effect anomaly (small outcomes are discounted more than large ones) may have a significant influence on differences in elicited discount rates as well. Often,
experiments with a shorter time range use lower monetary rewards. Because of this plausible correlation between a shorter time range and lower rewards, part of the
explanatory power of the time range on the difference in discount rates might be accounted to the reward level.
Previous literature has focused on one’s individual discount rate. Current study’s purpose is, however, to conduct research on discount rates for relatives. There are also other studies where the decision-maker is not the only one who bears consequences in an intertemporal choice experiment. Most of these studies focus on collective decision-making (Masclet et al., 2013; Shapiro, 2010), of which some primarily on the collective decision making of couples and spouses. (Abdellaoui et al., 2013; Carlsson et al., 2012; Kono et al., 2011). After all, intertemporal decision making of couples and spouses also is an everyday life phenomenon. The most prevalent finding of these studies, is that groups and couples exhibit more
patience and therefore have lower discount rates than individuals.
Only the study of Shapiro (2010) contains one treatment condition that is similar to the research of this study. In Shapiro’s study the decision-maker is matched to a randomly selected partner and communication between them is prohibited. This is different from the
9
design of this study in that the partners in this study are close relatives. Shapiro (2010) found that deciding for another person results in a lower discount rate compared to when the decision-maker himself bears the consequences. In the same study, the elicited discount rate for deciding for a third person is comparable to the discount rate of a couple.
As neuro-economics is gaining importance in the field of economics, McClure et al. (2004) tried to determine the neural underpinnings of intertemporal decisions. They found that “prefrontal regions are involved in all intertemporal choices (relative to rest) but that the mesolimbic dopamine system and associated regions are involved only in choices with an immediate outcome.Moreover, when immediate payment is one of the options, the relative activation of the two regions (prefrontal or dopamine) is a significant predictor of choice.” This research supports the theory that (quasi-)hyperbolic discounting results from the interaction of two systems with different perspectives toward the future. Here the prefrontal cortex has an important role in implementing more patient preferences. If individuals discount the payoffs of others differently than they do their own, they might make better choices for others than they do for themselves, in the sense of making decisions that are not influenced by short-run impatience. It is conceivable that the mesolimbic dopamine system would not activate when the immediate reward does not accrue to the decision-maker (Shapiro 2010).
Andersen et al. (2008) document that one’s utility function is concave due to the aversion of the risk one has. When this is related to the findings of Chakravarty and Harrison (2011) (people are less risk averse when investing with other people’s money), a subjects’ utility function should be less concave in the (Partner-)treatment condition.
Because of this less utility curvature and because it is conceivable that the decision-maker is not influenced by short-run impatience, this study’s hypothesis is that people have a lower time-discount rate when they invest with other people’s money in an intertemporal choice experiment.
DMPL and CTB
Andersen et al. (2008) correct for utility function concavity by using their double multiple price list (DMPL) approach and Andreoni and Sprenger (2012b) use their Convex Time Budget (CTB) mechanism. All researchers found lower discount rates than the average discount rate in figure 4. DMPL and CTB are the two most pioneering elicitation techniques for estimating discounting and curvature parameters. The most important difference between these methods is the way risk measurement is implemented. The DMPL first estimates risk aversion with a Holt and Laury (2002) experiment and then separately uses the experiments of Coller and Williams (1999) to measure the discount rate. Both obtain data with pricelists, which explains the term DMPL.
10
CTB is a single instrument that jointly captures time discounting and concavity of utility. Continuous experimental budgets are its key feature. Subjects can allocate between X [0 – 100] tokens into the early reward and 100-X tokens into the later reward. This makes it econometrically possible to estimate utility curvature, present bias and discount rate. One common finding from standard multiple price list experiments is that between 10 percent and 50 percent of subjects switch more than once (Holt and Laury, 2002; Meier and Sprenger, 2010; Jacobson and Petrie, 2009). This can be seen as an extreme form of non-monotonic demand. Concerning CTB, Andreoni and Sprenger (2012a) found that 37 percent of their participants has no interior choices in all 45 convex budgets, consistent with linear utility preferences. For the remaining subjects, an average of approximately 50 percent of decisions is found at corners (0 or 100 tokens allocated to early reward). This is not in line with earlier findings that imply that more people exhibit risk aversion and therefore do not have linear preferences. Apparently, DMPL and CTB have their disadvantages.
Two other important features that are covered both by DMPL and CTB are consumption smoothing and background consumption. Most researchers do not focus on these factors whereas it is important to take these into account. Experimental payoffs do not need to represent actual consumption for that period and can be smoothed over other periods. Therefore, these factors can mislead the discount rate. As with regard to background consumption, most analyses of discounting models assume the formula,
) ∗ *" = ) + ∗ *" $ while this should actually be,
) ∗ + ω + *" + ) + ∗ + ω = ) ∗ U ω + ) + ∗ + ω + *"
where ω is background consumption.
Andersen et al. (2008) use the per capita consumption of private nondurable goods on an average daily basis as ω. Andreoni and Sprenger (2012a) both estimate discount rates with a Stone-Geary parameter ω and with the use of average typical daily expenditures obtained from administered questionnaires.
A pressing question is to what extent the results of DMPL and CTB differ. Andersen et al. (2008) find a discount rate of 0,101 and Andreoni and Sprenger (2012a) a discount rate of 0,300 while estimating ω, and 0,246 while using average typical daily expenditures for ω. Is this lower discount rate of DMPL caused by the elicitation techniques, by the population, different time ranges, the use of a front end delay (no present bias) by Anderson et al. (2008), by the payment methods or caused by other factors? Luckily, an important part of this question can be answered because Andreoni and Sprenger (2012b) additionally
performed a DMPL test on the same subjects. DMPL yields a higher discount rate of 033 and more utility function curvature than CTB estimates. Present bias is found to be similar. Table 1 shows the first payment dates and the delay between the payment dates of the two
11
studies. It is plausible that the elicited discount rates by Anderson et al. (2008) differ due to (again) different time ranges and the use of a front end delay in all pricelists.
Study First payment date Delay between payment dates
Andreoni and Sprenger (2012)
0, 7 or 35 days 35, 70 or 98 days
Anderson et al.(2008) Always 1 month 1 month, 4 months, 6 months, 12 months,
18 months or 24 months
Table 1
2. Research method
For this study, relatives (such as friends, family, neighbours and colleagues) are asked to participate in an experiment. It is important that this experiment is conducted with at least two persons at the same time in their accommodation or at university. These two persons know each other (they are either roommates, a (married) couple or friends) and they have to decide on each other´s payoffs. They do this separately without knowing the purpose of the experiment and the task of the partner, to avoid alignment. The instructions are given on paper once they are separated.
During the first two phases of the experiment, the subjects perform the intertemporal choice experiment. To correct for order effects, 50 percent of the subjects first decide on their own payoffs (self-treatment) and subsequently decide on their partner’s payoffs (partner-treatment) and vice versa. It is important for the internal validation of this research that the monetary outcome in the partner-treatment does not directly affect the utility of the decision-maker. In other words, the money the partner can earn must be spent by that partner for his own consumption. Therefore, subjects can earn 5 to 20 euros. Lower rewards could cause a lack of motivation and higher rewards may lead to division between partners. To enable to investigate differences in present bias, immediate rewards and front-end delays are used for both conditions.
As one can see in Appendix C, participants face 12 different multiple price lists of which 6 contain outcomes that affect the decision-maker’s own earnings and 6 identical price lists that affect the outcomes of his partner. Every pricelist contains 16 intertemporal choices. Half of all price lists have t = 0 days as the first payment date and the other half t =14 days. The future payment delays are 7, 14 or 28 days.
Table 2 gives an example of a price list used in this experiment. For this study’s purpose, subjects need to switch from A to B down the list. The point where a subject changes preference from A to B is referred to as the switching point3. The average of the last chosen
3
When a subject has two switching points, the one with the highest sequence of preferred payment-options B in the subsequent situations is used for the analysis. A subject’s data is omitted for analysis when he has more than two switching points in a particular pricelist or when he prefers 5 euro over 20 when there are two switching points.
12
A and the first chosen B will be considered as switching point value. The utility of this switching point value at later payment date B equals the utility of 5 euro in the early payment date A.Using table 2 as an example, it can be said that if a subject prefers 5 euro over 7 euro, but chooses 8 euro over 5 euro, the switching point value will be . /0 = 7,5. It is assumed that the utility of receiving 5 euros now equals the utility of receiving 7,5 euros in a week.
Situation
Payment option A Payment option B Choice
Corresponding exponential daily discount rate w=0 r=0
Now In 7 days
Situation 1 5 euro 5 euro A / B 0,00%
Situation 2 5 euro 5,1 euro A / B 0,28%
Situation 3 5 euro 5,25 euro A / B 0,70%
Situation 4 5 euro 5,5 euro A / B 1,37%
Situation 5 5 euro 6 euro A / B 2,64%
Situation 6 5 euro 6,5 euro A / B 3,82%
Situation 7 5 euro 7 euro A / B 4,92%
Situation 8 5 euro 8 euro A / B 6,94%
Situation 9 5 euro 9 euro A / B 8,76%
Situation 10 5 euro 10 euro A / B 10,41%
Situation 11 5 euro 11 euro A / B 11,92%
Situation 12 5 euro 12 euro A / B 13,32%
Situation 13 5 euro 14 euro A / B 15,85%
Situation 14 5 euro 16 euro A / B 18,08%
Situation 15 5 euro 18 euro A / B 20,08%
Situation 16 5 euro 20 euro A / B 21,90%
Table 2 - example of a price list. The right column represents the corresponding exponential discount rate.
As shown in table 1 and the paper of Fredericks et al. (2002, table 1, p. 379), the time ranges used in previous studies are very divergent. Table 3 shows the time ranges used in the studies where the decision-maker also influences payoffs of others. The delays of these studies are much smaller. This may be partly the result of the fact that these studies compare different discount rates within the study itself instead of between studies. The height of the discount rates is of less importance as long as the research question can be answered.
Considering that the current study’s research also compares two treatments and that the earning range in this research was set to 5-20 euros, it was believed to be most appropriate to keep the payment options between immediate and 1,5 months in order to have switching points in all price lists.
13
Study First payment date Delay between payment dates
Shapiro (2010) Unclear, certainly 0 days and
1 week
1 and 4 weeks
Kono et al.(2012) 0, 21 days 3 days
Abdellaouiet al. (2013)
1 week 1 month, 3 months, 6 months, 1 year
and 2 years
Carlsson et al 0,4 days 0,4 days
Masclet et al. 2013 1 day 4 weeks
Table 3
In the last two phases, the subjects have to perform a risk experiment. Because it is proven that many individuals performing a Holt and Laury (2002) experiment switch more than once, the experiment of Eckel et al. (2010) is chosen to measure risk averseness. In addition, this experiment is more convenient in use. An example of the Eckel et al. (2010) risk
experiment is presented in table 4. Every participant has to perform this risk experiment for their own payoff and for their partner’s payoff. To correct for order effects, 50 percent of the subjects first performs the risk experiment that affects their own payoff and the other 50 percent first does the experiment that affects their partner’s payoff.
For every option a range of risk aversion is constructed by comparing the gamble to its neighbours and calculating the value that generates the same utility level for the payoffs associated with each adjacent gamble, using constant relative risk aversion (CRRA, + * =37 8456). The mean of every range is used for the degree of risk aversion4. Subjects are instructed that one of their decisions will be randomly selected for possible payoff after the experiment. Subjects are then paid out with a 5,6 percent possibility. This is determined by rolling two dice; the first must show a 1 or a 2 and the second a 6. When the experimenter has to pay out, the subject first has to pick a card [1,2,3,4] of which each number corresponds to the part of the subject’s experiment. The 1 and 2 always contain an intertemporal choice condition and 3 and 4 always contain a risk condition. Subsequently, when a 1 or 2 is picked, the participant has to pick a card [1-6] to determine the two reward dates. After that, the subject picks a card [1-16] that determines the payoff of the later reward date. In case of the risk condition, a fair coin is flipped and the upper surface of the coin corresponds with the subject’s choice.
4
For gambles 1 and 6, the same difference between them and their neighbor is taken as the difference between their neighbor and that neighbor’s other neighbor.
Option If the coin indicates 1 Head Tail 2 Head Tail 3 Head Tail 4 Head Tail 5 Head Tail 6 Head Tail
Table 4 – Example of Eckel et al.’s (2010) risk experiment. Corresponding degree of risk aversion is presented in the right column
Many studies, among which those by (2012a), discuss the influence of uncertainty rates. In this field within economics
sooner and later payments. In this experiment, immediate rewards are paid out in cash and future rewards are immediately execute
receipt is set. With this procedure
and therefore it is conceivable that the uncertainty of future earnings i immediate rewards cash is chosen over internet banking payment because, transfer does not need to be immediate
tempting when they are tangible present bias.
14
If the coin indicates You earn in Euros Your choice
7 O 7 9 O 6 11 O 5 13 O 4 15 O 3 17 O 0
et al.’s (2010) risk experiment. Corresponding degree of risk aversion is presented in the right
among which those by Fredericks et al. (2002) and Andreoni and Sprenger (2012a), discuss the influence of uncertainty related to future earnings on elicited discount
. In this field within economics, it appears to be difficult to equate risks associated with In this experiment, immediate rewards are paid out in cash and future rewards are immediately executed by ABN AMRO internet banking whereby
procedure the participant witnesses the actual payment execution and therefore it is conceivable that the uncertainty of future earnings is minor. For
en over internet banking payment because, firstly
transfer does not need to be immediate and secondly, immediate rewards may be more tempting when they are tangible and therefore create realistic circumstances to incentivize
Degree of risk aversion 3,69 2,31 0,93 0,60 0,17 -0,25
et al.’s (2010) risk experiment. Corresponding degree of risk aversion is presented in the right
Fredericks et al. (2002) and Andreoni and Sprenger on elicited discount it appears to be difficult to equate risks associated with In this experiment, immediate rewards are paid out in cash and
whereby a date of actual payment execution
minor. For firstly, a bank immediate rewards may be more
15
At the end of the experiment a questionnaire is handed out to obtain information about gender, profession, income, spending behaviour, age, education and the type of relationship with the partner.
Because of the functional form of the intertemporal choice experiment, background consumption and risk behaviour are implemented in some statistical specifications. Consumption smoothing has been left out, because it is assumed that the experimental rewards are that low that they will not be spread over days, and because the difficulties of the implementation of consumption smoothing.
The model
The utility for person i when he decides on his own payoffs is described by the following formula.
, = ω + − + + ω + −
The utility for person i when he decides on the payoffs of partner j is described by the following formula.
# : , : % = : ω + −: + : + ω + :−
Where ) = discount function for person i, ; ) discount function for person i to person j´s payoffs, *{ ,;}" = experimental payoff at time t of person i or j. ω= background consumption, r = degree of risk aversion, t=date of first reward, t+k= date of last rewards and k = delay between rewards.
A subject’s daily average expenditure is used as ω, as is acquired with the questionnaire. The discount rates are elicited in the following manner.
Exponential functional form
+ #*{ ,;}", *{ ,;}" $% = &1 + '1 "∗ ω + *{ ,;}"1 − ? 7 8 + &1 + '1 " $∗ ω + *{ ,;}" $1 − ? 7 8 If *{ ,;}" $ equals the switching point value the following formula holds.
&1 + '1 " ∗ ω + *{ ,;}"1 − ? 7 8 = &1 + '1 " $∗ ω + *{ ,;}" $1 − ? 7 8
{ ,:}= @ A +A + { ,:}
16
Quasi-hyperbolic functional form
+ #*{ ,;}", *{ ,;}" $% = C D E D F G ω + *{ ,;}" 7 8 1 − ? + H &1 + '1 " $ ω + * { ,;}" $ 7 8 1 − ? IJ ) = 0 H &1 + '1 " ω + *1 − ?{ ,;}" 7 8 + H &1 + '1 " $ ω + *1 − ?{ ,;}" $ 7 8 IJ ) > 0
M D N D O G
If *{ ,;}" $ equals the switching point value the following formula holds. ω + *{ ,;}" 7 8
1 − ? = H &1 + '1
" $ ω + *{ ,;}" $ 7 8
1 − ? IJ ) = 0
H &1 + '1 " ω + *{ ,;}"1 − ? 7 8 = H &1 + '1 " $ ω + *{ ,;}" $1 − ? 7 8 IJ ) > 0
{ ,:} = C D E D F G @( A +A + { ,:} { ,:} B P − Q = @ A +A + { ,:} { ,:} B − Q > 0 MD N D O G
For the analysis, present bias (β) is estimated by comparing two price lists with the same delay k. In this case, a β is computed (at t=0) that leads to the same discount rate when t = 14 days. This is done in two ways, of which the formulas are presented below.
( Estimation 1:
=
R SA P ∗ A { ,:} 5{ ,:} P 5
( Estimation 2:
=
R S P ∗ { ,:}{ ,:} P
where Sis the discount rate of t=14 with equal delay
In the first formula β is computed after correcting for background consumption and risk averseness and in the second formula β is computed before correcting for background consumption and risk averseness.
Several tests are conducted to compare T and T;. To find out whether subjects make different choices for their own outcomes and the payoffs of others, T and T; are compared by using an exponential discount function while ω and r are 0. Next, the same test is done with the exception that and ; is represented by quasi-hyperbolic discount functions and ? ≠ 0. The difference between T and T; is hypothesized to be 0, while 0<β<1 is expected for and a β=1 for ;, because these quasi-hyperbolic functions correct for utility curvature
17
and present bias. If the obtained discount rates of the quasi-hyperbolic forms are similar, this would suggest that the underpinnings of time preferences are understood. All statistical specifications test H0: − ; = 0 versus H1: − ; > 0 and are summarized in the table 5.
Test 1 = ;= exponential, ω = 0 , ? = 0 Test 2 = ;= quasi-hyperbolic, ω = 0 , ? = 0 Test 3 = ;= exponential, ω ≠ 0 , ? ≠ 0
Test 4 = ;= quasi-hyperbolic, ω ≠ 0 , ? ≠ 0, β = estimation 1 Test 5 = ;= quasi-hyperbolic, ω = 0 , ? ≠ 0, β = estimation 1 Test 6 = ;= quasi-hyperbolic, ω ≠ 0 , ? ≠ 0, β = estimation 2 Test 7 = ;= quasi-hyperbolic, ω = 0 , ? ≠ 0, β = estimation 2 Table 5
Data description
42 subjects participated in the experiment. Only one subject has two switching points in a certain price list. The bold numbers indicate the chosen future rewards of this price list. 5 - 5.1 - 5.25 - 5.5 - 6 - 6.5 - 7 - 8 - 9 - 10 - 11 - 12 -14 - 16 - 18 – 20. According to the protocol, 8 is allocated as the switching value. Some subjects have no switching point in some price lists because they only choose the latest payment option; a discount rate of 0 percent is
allocated to those lists. A switching point of 25,51 is used for the four subjects that have no switching point in at least one price list because they only choose the first payment options. This 25,51 corresponds with a daily discount rate of 6 percent when an exponential form is used with ω=0 and r=0.
3. Results
Since annually discount rates would result in exorbitantly high percentages (due to the used time ranges), elicited discount rates are calculated on daily basis.
As a pricelist with a switching point generates a discount rate, the average discount rate of all 6 pricelists is used to measure a subject’s overall discount rate. The results of all tests are presented in the Appendix A. For example, the average exponential (ω=0 and r=0) discount rate is 3,13 percent when subjects decide on their own earnings and 2,64 percent when they decide on their partner’s earnings. The corresponding p-value of a Wilcoxon signed rank test is 0,0315 (Z value -1,859), which implies that H0 is rejected at a 5 percent significance level.
18
The subjects’ own average degree of risk aversion is 0,705 and 0,975 when deciding for their partners. This contradicts the findings of Chakravarty and Harrison (2011), who state that people are less risk averse with other people’s money. A Wilcoxon signed rank test reveals that these degrees of risk aversion are not different at 5 percent significance level (p-value of 0,08).
Present bias
Figures 3 and 4 show comparisons between exponential discount rates of payment dates with equal delays. According to the literature, the difference in time preferences between the treatment and Partner-treatment is strongly affected by present bias in the Self-treatment. Therefore, the dark blue bars should transcend the light blue ones in figure 3 and equalize in figure 4. A Wilcoxon signed rank test proves that not one of the bars differ significantly5.
Another way to measure present bias is by deriving betas in the quasi-hyperbolic model. The results of these measurements are presented in figure 5. A Wilcoxon signed rank test is conducted, as a Shapiro-Wilk test proves that the betas are not normally distributed6. Appendix B figures B1 to B6 also provide insights into derived betas per delay. The Wilcoxon signed rank tests show that betas are not significantly different from 1.
5
P values of H0: p (0 days) – p (14 days) = 0 vs H1: p (0 days) - p (14 days) > 0 are respectively 0,294, 0,387, 0,813, 0,626, 0,914 and 0,355.
6
P-values of the Shapiro-Wilk tests are respectively: 0,039, 0,002, 0,000, 0,000, 0,001, 0,000.
Figure 4 – Exponential daily discount rates Partner treatment (r=0 w=0), where t represents first payment dates and k the delay between the two reward dates
Figure 3 – Exponential daily discount rates Self treatment (r=0 w=0), where t represents first payment dates and k the delay between the two reward dates.
19
Figure 5, Beta values – the numbers in the brackets indicate the corresponding P-values of a Wilcoxon signed rank test (H0: β=1 vs H1:β≠1)
Best model
Table 6 presents the average discount rates and P-values of all tests.
Test nr. Average discount rate Self Average discount rate Partner
Wilcoxon test P value H0 Rejected at 5%? N=42 Test 1 3,13%, 2,64%. 0,0315 Yes Test 2 3,22% 2,79% 0,108 No Test 3 0,35% 0,07% 0,074 No Test 4 0,36% 0,00% 0,007 Yes Test 5 1,34% 0,29% 0,018 Yes Test 6 0,45% 0,21% 0,327 No Test 7 1,34% 0,48% 0,232 No Table 6
Table 7 shows that, by using Wilcoxon signed rank tests, there are four tests that accept the H0 hypothesis. As test 1 and test 2 concerns, deviating from exponential to quasi-hyperbolic
0,990307 1,022706 0,98445 1,00234 1,035803 1,022797 0,95 0,96 0,97 0,98 0,99 1 1,01 1,02 1,03 1,04 Test 5 Partner (1,000) Test 5 Self (0,399) Test 4 Partner (0,807) Test 4 Self (0,480) Tests 2, 6 & 7 Partner (0,326) Tests 2, 6 & 7 Self (0,302)
20
lowers the P-value in a manner that the average self-treatment discount rate is not significantly higher anymore than the average partner-treatment discount rate. Beta estimation 2 leads to results that are more in line with the hypothesis than beta estimation 1. Next to that, correcting for background consumption and risk averseness both lowers the average discount rates.
Other factors that affect the differences in discount rates
All data obtained from the questionnaire are put in a regression. Since every participant generates 6 discount rates in every treatment, while these pricelists in both treatments are identical, it is possible to conduct a regression with panel data. Every subject generates
− ; for every type of pricelist. This leads to 252 observations. The regression is presented below. The variance inflation factors7 (VIF), an approximation to detect multicollinearity, of all regressors in all tests are below 10 which imply that there is no correlation between the explanatory variables.
V V: = W + X YZ [ Q \ ] ^\ [ + X_`]^[^a ] bZ] c ^ [d
+ Xef \\ g [d \ + XS ^ g [d \
+ Xhi c []^a + Xjf^ []^a + Xkl [d + Xmnc
+ XoY ] p \ + X Y ] p \ _ + X Y ] p \ e + X _Y ] p \ S + X eY ] p \ h + q
The results of the regressions are presented in table B78. The regressions control for random effects to eliminate individual specific effects. Hausman tests show that all predictive
variables are uncorrelated with the subjects. This is not surprising, since r7 to r. are price list invariant and the price list dummies are the same for all participants. The H0 hypothesis of the following F-statistic s : Xo= X = X = X _ = X e = uv s : X:≠
, Z p Z\ ^[ :, : = o, … , e is accepted for tests 3, 4, 5 and 7, at a 5 percent significance level. Therefore, rw to r7x are left out of those tests’ regressions.
As becomes clear, significance of predictive variables and the model’s predictability itself changes when risk averseness is implemented in the utility functions. Regarding tests 1 and 2, only rw (10 percent significance test 1) and r70 (1 percent significance tests 1 and 2) have significant positive coefficients. Their (overall) R2’s are respectively 0,1060 and 0,1085. In tests 3, 4, 5, 6 and 7, the regressors r0, and ry turn significant. ‘Economic background’ lowers (1 percent significance) and ‘More expenditures’ (5 percent significance) increases the difference in discount rates. In tests 4, 5, 6 and 7, the regressor r7 increases the
7
VIF8}~8}••€8 =7 • 7 6‚ƒ6‚„„…6
† , when regressed on other explanatory varables. VIF values are respectively: 1,22, 1,26, 1,32, 1,59, 1,65, 1,90, 1,43, 1,22, 1,67, 1,67, 1,67, 1,67, 1,67.
8
Because participants had the possibility to fill in ‘unkown’ to the questions if they spend more and if they have a higher income than their partner both dummies for More & Less expenditures and Higher & Lower income are included
21
difference in discount rates at 10 percent significance level. Price list 4 has a positive coefficient (5 percent significance) in test 6. R2’s of tests 3, 4, 5, 6 and 7 are respectively 0,3186, 0,3189, 0,2843, 0,3329, 0,2847.
It is remarkable that the r7 (‘Partner first chosen’) coefficient turns positive at 10 percent significance level when risk measurement is implemented. Similar regressions on the treatments’ single discount rates (instead of their difference) of tests 3 to 7 show that the r7 coefficient is negative at 10 percent significance level in the partner-treatments and insignificant in the self-treatments (Table B8 and B9). If ; reduces, the dependent
variable − ; goes up. As tests 1 and 2 concern, the r7 coefficients are insignificant in both treatments. This points to the fact that the sequence of the parts of the intertemporal choice experiment does not influence a subject’s discount rates, but that the sequence of the parts of the risk experiment do, which is problematic. To solve this, the same Wilcoxon tests and regressions are conducted for tests 3 to 7 with subjects that first choose for their partner in the risk experiment for the following reason: As people are more likely to behave in their self-interest when financial incentives apply to them, it does not matter whether the self-treatments are conducted in the first and third or second and fourth part. This may not apply for the partner-treatments. When the partner-treatments are carried out after the self-treatments during the experiment, the subject has a reference point and may be affected in a way that the subject chooses more rational for his partner than he does for himself. Similar to tests 1 and 2, there is no need to also revise the Betas, since participants’ present bias is derived from the data of the first two parts of the experiment.
The results of the Wilcoxon tests are presented in table 7.
Test nr. Average discount rate Self Average discount rate Partner Wilcoxon test P value H0 Rejected at 5%? Regression’s R2 N=21 Test 3 0,22% -0,29% 0,112 No 0,5077 Test 4 0,23% -0,36% 0,020 Yes 0,5122 Test 5 0,97% -0,81% 0,066 No 0,4418 Test 6 0,31% -0,15% 0,327 No 0,5039 Test 7 0,97% -0,62% 0,332 No 0,4402
Table 7 – Discount rates of subjects that first choose for their partner and subsequently for themselves
Compared to the Wilcoxon signed rank tests of table 7, the only difference relates to test 5 since its H0 hypothesis is now accepted. A similar regression as before is conducted with the
22
only exception that the ‘Partner first chosen’ parameter is dropped. Again, ‘Economic background’ lowers and ‘More expenditures’ increases the difference in discount rates in tests 3 to 7 (Table B10).
Implementation of risk averseness in the dataset of table 8 leads to, on average, negative discount rates for the partner-treatment. A negative discount rate occurs when a subject has a degree of risk averseness that is higher than one, which happens when one of the first two options in the risk experiment is chosen. These options are considered most rational and may explain the significant coefficient of r7in the regression with 252 observations. However, it is not conceivable that people have negative discount rates in reality. Therefore, two additional tests are conducted in which one drops all observations of the 10 people who do not have an r<1 in both treatments and where the other test sets a 0,00 percent discount rate as lower bound. Because all subjects are allocated with an r=0 in tests 1 and 2, only tests 3 to 7 are conducted. The results of the Wilcoxon signed rank tests are presented in tables 8 and 9. Their corresponding regressions can be found in tables B11 and B12.
Test nr. Average discount rate Self Average discount rate Partner Wilcoxon test P value H0 Rejected at 5%? Regression’s R2 N=42 Test 3 0,62% 0,40% 0,045 Yes 0,2475 Test 4 0,63% 0,36% 0,006 Yes 0,2508 Test 5 2,05% 1,37% 0,014 Yes 0,2655 Test 6 0,70% 0,53% 0,308 No 0,2471 Test 7 2,05% 1,52% 0,193 No 0,2527
23
Test nr. Average discount rate Self Average discount rate Partner Wilcoxon test P value H0 Rejected at 5%? Regression’s R2 N=32 Test 3 0,72% 0,49% 0,073 No 0,3417 Test 4 0,73% 0,43% 0,006 Yes 0,3515 Test 5 2,36% 1,68% 0,044 Yes 0,3624 Test 6 0,81% 0,64% 0,341 No 0,3439 Test 7 2,36% 1,87% 0,330 No 0,3491
Table 9 – Subjects with r<1 in both treatments
Both datasets have significant coefficients in ‘More expenditures’ and ‘Economic background’. In some tests pricelists 1 and 4 also have significant coefficients. A major difference between these two additional tests is that ‘Partner first chosen’ is only significant in the tests of the dataset that contains people who have r<1 in both treatments. Therefore another test is conducted with subjects that had an r<1 in both treatments and who first chose for their partner. The results of this test are presented in table 10.
Test nr. Average discount rate Self Average discount rate Partner Wilcoxon test P value H0 Rejected at 5%? Regression’s R2 N=15 Test 3 0,75% 0,41% 0,147 No 0,6466 Test 4 0,76% 0,35% 0,013 Yes 0,6395 Test 5 2,40% 1,47% 0,182 No 0,5296 Test 6 0,84% 0,56% 0,488 No 0,6434 Test 7 2,44% 1,66% 0,433 No 0,5406
Table 10 – subjects with r<1 in both treatments and who first chose for their partner
The corresponding regression shows that, in contrast to all earlier conducted regressions, ‘Economic background’ is insignificant and ‘Higher income’ is significant. ‘More
expenditures’ is still significant (Table B13). The R2’s of this dataset are higher than the R2’s of all other datasets.
24
4. Discussion & conclusion
This current study performed a comparison between time discount rates of an individual and time discount rates of the same individual making choices for a relative, in an
intertemporal choice setting. Using an exponential utility function model at 5% significance level, results show that the individuals’ own discount rates are higher than the discount rates for their partners. This implies that people make more rational choices for their partners than they do for themselves. The difference in discount rates was hypothesized to be caused by present bias in the individual (self-)treatment, and by less utility function curvature when a person chooses for the partner (partner-)treatment. However, there is no evidence of present bias’ existence in the treatments. In addition, the subjects’ own degree of risk aversion is actually higher than when choosing for their partners. This suggests that, regardless whether the earliest payment date is now or in the future, people always make less rational choices for themselves.
The results point to the need of involving third parties in intertemporal (investment) decisions. This contributes to studies of Masclet et al. (2013), Shapiro (2010), Abdellaoui et al. (2013), Carlsson et al. (2012) and Kono et al. (2011), who conducted similar experiments with different types of third parties that show similar results.
To evaluate the data, a basic linear utility model was first introduced to observe differences in the decision behavior of subjects. Next, a quasi-hyperbolic utility model was used to see if the elicited discount rates of the two treatments equalized. Psychological underpinnings in intertemporal decision-making are assumed to be captured and understood when this would occur. The theoretical framework behind the quasi-hyperbolic function was based on the studies of Anderson et al. (2008), Fudenberg and Levine (2006), Andreoni and Sprenger (2012a) and Fredericks et al. (2002) that involved a trade-off between long-run optimization and short-run temptation. Some of the statistical specifications also included parameters for risk averseness (since people exhibit concave utility behaviour) and background
consumption.
Compared to the exponential model, the quasi-hyperbolic model does diminish the
difference between the discount rates of the two treatments when concave utility and risk averseness are left out of the model. This resulted, in line with the hypothesis, in
significantly higher self-treatment discount rates than partner-treatment discount rates in the exponential model, while the discount rates of both treatments in the quasi-hyperbolic model did not differ significantly.
Two drawbacks of the implementation of risk averseness in the utility functions of current study lie in the possibility of creating negative discount rates and the partner-treatment’s correlation with the sequence of the risk experiment’s parts.
25
Negative discount rates lead to lower average discount rates. The existence of these rates is not conceivable and they occur when subjects choose one of the two safest (out of six) options in the experiment of Eckel et al. (2010), which corresponds with a CRRA higher than 1. The risk experiment of Holt and Laury (2002) generates CRRA’s that better suit the model and are therefore recommended for future research. Two additional tests were conducted; one dropped all observations of the 10 people who did not have an CRRA lower than 1 in both treatments; and the other set a 0,00 percent discount rate as lower bound. Despite this resulted in higher average discount rates of both treatments, the results were similar to the original dataset.
The correlation between a subject’s degree of risk aversion for the partner and the sequence of the risk experiment’s parts may have resulted in bias. Therefore, additional tests were conducted for datasets which regressions contained significant predictors for the sequence of the (risk) experiment’s parts. These additional tests consisted only of subjects, who first chose for their partner and subsequently for themselves, as people are always more likely to behave in their own interest when financial incentives apply to them. In contrast to that, subjects who first choose for themselves and subsequently for their partner may not as they may use their first decision on themselves as reference point for their subsequent decision on their partner. Further research should therefore not randomize the order of the treatments or conduct a between-subjects study instead of a within-subjects study. As the results of these additional tests concern, most imply that the discount rates between the two treatments do not differ.
It is not surprising that the implementation of background consumption converges the discount rates more towards 0, as the relative difference between the early and future reward diminishes. It could be more interesting for future purposes when background consumption is combined with consumption smoothing in the statistical specification. All regressions in this study contained the dependent variable own time preferences minus time preferences for the relative. Models that did not correct for risk averseness had insignificant regressors and low predictability (R2’s). Implementation of risk averseness, however, increased the predictability of the model as regressors turned significant and R2’s went up in all models and datasets. These regressions showed that people who spend more than their partner show significantly more difference in discount rates over the two
treatments, while subjects that have an economic background show significantly less differences in discount rates in most datasets. The latter finding supports the need of investment professionals. In one dataset people with higher incomes significantly lowered the dependent variable. This occurred in the dataset of people who have a CRRA <1 and first choose for their partner. The datasets that only contained subjects who first choose for their partner had higher predictabilities than the datasets that contained all subjects.
The estimation that derives the parameter for present bias, beta, before correcting for utility curvature and risk aversion leads to results that are more in line with the hypothesis
26
and vice versa. However, it does not lead to different results for the regressions. Further research should investigate which type of beta estimation is more appropriate.
An interesting question is what the motives are when one chooses for a partner’s payoffs. This study missed the opportunity of asking for these motives in the provided questionnaire. However, some subjects shared their underlying motives without asking after the
experiment. Although this is not documented, and therefore important for further research, subjects seemed to be driven by two incentives: Either they choose what they thought their partner would conceive as the most desirable outcome, or they choose what they thought was best for their partner. As neuro-economics is gaining importance, it could also be interesting for future research to capture the neural underpinnings of these altruistic incentives, which could lead to an important predictive variable when the outcome shows that one of these two incentives is the motivation for people to make their choices. There may be external factors that affected the outcomes. First, actual payments occurred when a participant first rolled a 1 or 2 and subsequently a 6 with two dice. This corresponds with a probability of 5,56 percent. Kahneman and Tversky’s prospect theory (1979) implies that people hope for a large gain when a low probability is at issue. Keeping the findings of Chakravarty and Harrison (2011) in mind, this may explain the difference in discount rates between the two treatments. Further research should make sure the probability of payment is 100 percent.
A possible explanation for the absence of present bias is Andreoni and Sprenger’s (2012b) theory, which implies that it is caused by equated costs and risks associated with sooner and later payments. Another (more likely) possibility lies in the sequence of price lists. Every participant had to fill in according to the following order: 0-7 days, 0-14 days, 0-28 days, 14-21 days, 14-28 days and 14-42 days. Since it is rational to exhibit higher switching points over the first three price lists, this may influence subjects not to choose a lower switching point in the fourth list than in the first list. As can be seen in appendix A (test 1),
corresponding average exponential discount rates are:
0-7 days 0-14 days 0-28 days 14-21 days 14-28 days 14-42 days
Self-treatment 4,15% 3,17% 1,97% 4,73% 2,80% 1,94%
Partner-treatment 3,32% 2,69% 1,76% 3,58% 2,67% 1,84%
Further research should randomize the pricelists for every subject to avoid order effects.
Finally, future research could use longer delays and higher rewards to see if the current study’s results hold in all (and more conventional) time ranges and to obtain neat annual discount rates. As a last note, the use of long time ranges in the empirical literature may partly be caused by the popularity of the old hyperbolic model, which validity is very
27
dependent on (long) time ranges. To illustrate; hyperbolic models would not fit in the current study because:
= ) + #*{ ,;}"% − )#*{ ,;}" $%#*{ ,;}" $% − #*{ ,;}"%
To obtain positive discount rates ) + #*{ ,;}"% > )#*{ ,;}" $% " $" >33{‡,ˆ}‰PŠ
{‡,ˆ}‰ . Imagine
that t=14, t+k=21, *{ ,;}"=5 and a subject switches between the later rewards 7 euro and 8 euro. In this case, 7,5 is assigned to *{ ,;}" $. The denominator equals zero which makes it impossible to calculate p. As the real switching point could also be 7,4 or 7,6, the
corresponding discount rate range would be between 171,43 percent and -185,71 percent. To make this model appropriate, the relative payment date must increase or the relative rewards must decrease. However, because almost all subjects have switching points, this would not make sense.
References
Abdellaoui, Mohammed, Olivier L’Haridon, and Corina Paraschiv. Do couples discount future consequences less than individuals. No. 201320. Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS, 2013. Ainslie, George. "Specious reward: a behavioral theory of impulsiveness and impulse control." Psychological bulletin 82.4 (1975): 463.
Allais, Maurice. "Le comportement de l'homme rationnel devant le risque: critique des postulats et axiomes de l'école américaine." Econometrica: Journal of the Econometric Society (1953): 503-546.
Andersen, Steffen; Harrison, Glenn W.; Lau, Morten I., and Rutström, E. Elisabet, “Eliciting Risk and Time Preferences,” Econometrica, 76(3), 2008a, 583-619
Andreoni, James, and Charles Sprenger. "Risk preferences are not time preferences." The American Economic Review 102.7 (2012): 3357-3376.
Andreoni, James, and Charles Sprenger. 2012a. “Estimating Time Preferences from Convex Budgets.” American Economic Review. 102 (7): 3333–56.
Baker, Ronald, Susan Laury, and Arlington Williams. "Comparing small-group and individual behavior in lottery-choice experiments." (2007).
Benhabib, Jess, Alberto Bisin, and Andrew Schotter. "Present-bias, quasi-hyperbolic discounting, and fixed costs." Games and Economic Behavior 69.2 (2010): 205-223.
28
Berns, Gregory S., David Laibson, and George Loewenstein. "Intertemporal choice–toward an integrative framework." Trends in cognitive sciences 11.11 (2007): 482-488.`
Böhm-Bawerk, E. von. "Kapital und Kapitalzins." Zweite Abteilung: Positive Theorie des Kapitales 3 (1889).
Carlsson, Fredrik, Haoran He, Peter Martinsson, Ping Qin, and Matthias Sutter. "Household decision making in rural China: Using experiments to estimate the influences of
spouses." Journal of Economic Behavior & Organization 84, no. 2 (2012): 525-536. Chakravarty, Sujoy, et al. "Are You Risk Averse over Other People's Money?."Southern Economic Journal 77.4 (2011): 901-913.
Dave, Chetan, et al. "Eliciting risk preferences: When is simple better?."Journal of Risk and Uncertainty 41.3 (2010): 219-243.
Fisher, Irving. The theory of interest. New York: Macmillan, 1930.
Frederick, Shane, George Loewenstein, and Ted O'donoghue. "Time discounting and time preference: A critical review." Journal of economic literature 40.2 (2002): 351-401.
Fudenberg, Drew, and David K. Levine. "A dual-self model of impulse control."The American Economic Review (2006): 1449-1476.
Holt, Charles A., and Laury, Susan K., “Risk Aversion and Incentive Effects,” American Economic Review, 92(5), December 2002, 1644-1655.
Hsee, Christopher K.; Robert P. Abelson and Peter Salovey. 1991. "The Relative Weighting of Position and Velocity in Satisfaction," Psych. Sci. 2:4, pp. 263-66.
Jacobson, Sarah, and Ragan Petrie. "Learning from mistakes: What do inconsistent choices over risk tell us?." Journal of Risk and Uncertainty 38.2 (2009): 143-158.
Kahneman, Daniel, and Amos Tversky. "Prospect theory: An analysis of decision under risk." Econometrica: Journal of the Econometric Society (1979): 263-291.
Kono, Hisaki, et al. "Does Marriage Work as a Savings Commitment Device?: Experimental Evidence from Vietnam." Unpublished Working Paper (2011).
Loewenstein, George, and Richard H. Thaler. "Anomalies: intertemporal choice." The journal of economic perspectives (1989): 181-193.
Loewenstein, George. "Anticipation and the valuation of delayed consumption."Economic Journal 97.387 (1987): 666-84.
29
Masclet, David, Nathalie Colombier, Laurent Denant-Boemont, and Youenn Loheac. "Group and individual risk preferences: A lottery-choice experiment with self-employed and salaried workers." Journal of Economic Behavior & Organization 70, no. 3 (2009): 470-484.
McClure, Samuel M., David I. Laibson, George Loewenstein, and Jonathan D. Cohen. "Separate neural systems value immediate and delayed monetary rewards." Science 306, no. 5695 (2004): 503-507.
Meier, Stephan, and Charles D. Sprenger. Discounting financial literacy: Time preferences and participation in financial education programs. No. 3507. IZA Discussion Papers, 2008. O'Donoghue, Ted, and Matthew Rabin. "Doing it now or later." American Economic Review (1999): 103-124.
Prelec, Drazen. "Decreasing Impatience: A Criterion for Non-stationary Time Preference and “Hyperbolic” Discounting." The Scandinavian Journal of Economics 106.3 (2004): 511-532. Rae, John. Statement of some new principles on the subject of political economy: exposing the fallacies of the system of free trade, and of some other doctrines maintained in the" Wealth of nations.". Hillard, Gray, 1834.
Samuelson, Paul A. "A note on measurement of utility." The Review of Economic Studies 4.2 (1937): 155-161.
Shapiro, Jeremy. Discounting for you, me, and we: Time preference in groups and pairs. Mimeo, 2010.
