Unpacking experimental discount rates: Impatience, uncertainty, and credit constraints
*
Marco Casari Purdue University
September 2006
Keywords: experiments, time preferences, discounting, risk attitude. JEL:.C91, D90, D81
*
Correspondence address: Marco Casari, Krannert School of Management, Purdue University, 403 West State Street, West Lafayette, IN 47907, USA, tel +765-4943598, fax +765-4961567, email:
[email protected]. This study was initiated when visiting the Universitat Autònoma de Barcelona, Spain. Thanks for their comments to Colin Camerer, Jordi Brandts, Charlie Plott, Pierre Courtois, and of participants at seminars at the International workshop on behavioral game theory and experiments, Capua, Italy. All the remaining errors are mine. Thank you to Henrik Nordin for providing critical assistance in programming. Aurora Gallego and Nikos Georgantis kindly agreed to let me use the LEE (Laboratori d’Economia Experimental) of the Universidad Jaume I of Castellon, Spain, and Juan Gómez Pérez provided technical help. The financial support from an EU Marie Curie Fellowship and from the Russell Sage Foundation (grant #: 98-04-05) is gratefully acknowledged. Any opinions, findings, and conclusions or recommendations in this material are those of the author and do not necessarily reflect the views of the European Commission or of the Russel Sage Foundation.
1 INTRODUCTION Intertemporal decisions have recently received considerable attention from behavioral economists (for a review, Frederick et al., 2002). Even the most basic task of estimating individual levels of impatience through choices turned out to be difficult because of several confounding factors (Sozou, 1998, Fernandez-Villaverde and Mukherji, 2000, Rubinstein, 2003, Chapman, 2003). This paper focuses the attention on three of them. First, the ability of the person to fully understand the terms of the problem and the future consequences of her choices. Warner and Pleeter (2001) show that military personnel with lower cognitive abilities exhibit higher discount rates. A second factor is the possible presence of credit constraints. When an agent can borrow at market rates, she will be willing to wait for a later option that offers a higher-than-market interest rate (Harrison et al., 2005, Pender, 1996). The third confounding factor is that the future is uncertain, hence the trade off between a sooner and a later option reveals a discount rate, which is in general higher than the actual impatience level of the decision maker (Dasgupta and Maskin, 2002, Benzion et al., 1989, Azfar, 1999, Halevy, 2005). In a new experiment we measure discount rates while controlling for the above three confounding factors. To elicit discount rates we ask a series of simple question such as “would you prefer $100 in two days or $110 in two months?”. The experiment is not hypothetical but involves cash payments; moreover, the various options offered are paid with an actual time delay. Two novel aspects of this study is the way we control for individual differences in skills and the simultaneous collection of risk perception, risk attitude, and discount rate data for the same subject. The strongest empirical impact that we find for our student sample is for credit constraints. Subjects with self-reported difficulties to access the credit market exhibit significantly shorter waiting time for the larger reward. The direction of this finding is what one would expect. The presence of credit constraints may actually help in eliciting the degree of individual impatience because otherwise current market interest rates would censor the choices of the more impatient subjects. The perceived implicit risk in waiting for the later reward seems to matter for the actual choices. The magnitude of the self-reported perceived risk is considerable and makes it a factor that cannot be ignored in future empirical analysis. Although the regression analysis fails to
1
detect a significant impact, other statistics suggest that the reason may because of the way in which risk perceptions were elicited. Finally, subjects show differentiated ability to compute exponential discounting but these differences seem to be not significantly correlated with the discount rate. The next section outlines the experimental design employed. Sections 3 and 4 presents the results, where one section puts forward the findings with respect to the possible confounding factors and the other section integrates them into an explanation of discount rates.
2 EXPERIMENTAL DESIGN AND PROCEDURES A total of 120 subjects were recruited from the undergraduate population of Jaume I University of Castellon, Spain. Six sessions were run with 20 subjects in each session. Recruitment was done through announcements in class and by people stopping by at the laboratory to sign-up. Exactly 50% of the subjects were women and about 88% of them were economics or business major. The overwhelming majority of the subjects had participated to other, unrelated economic experiments in the same laboratory. An experimental session included the measurement of risk attitude and of individual discount rates. A questionnaire was completed at the end of the session.1 Individual risk attitude was measured through ten binary choices about lotteries. The purpose of these choices was to elicit individual risk attitude. A subject chose between a “safe” Option A and a “risky” Option B. The potential payoffs for Option A (2.00€ or 1.60€) were less variable than the potential payoffs for Option B (3.85€ or 0.10€). In the first decision, the probability of the high payoff for both options was 1/10. In subsequent decisions, the probability of the high payoff outcome increased by 1/10. A risk neutral person would choose A in lotteries one through four and then switch to B in lottery five. The incentive structure was identical to that in Holt and Laury (2002). Discount rates were measured using choices between pairs of delayed monetary rewards, A1 and A2. Option A1 was a sooner-smaller reward of 100€ that was paid in two days, or A1=(SS, t2)=(100, 2). Option A2 was a later-larger reward of 110€ that was paid at time t3 > 2, or A2=(LL, t3)=(110, t3). In the first decision, A2 paid in 9 days (t3 =9). In each of the following 1
After the measurement of the discount rate and before completing the questionnaire, subjects performed additional tasks that are beyond the scope of the present article. Complete instructions are available online at http://www.mgmt.purdue.edu/faculty/casari/timex.htm. Including instruction readings, a session lasted between 2 and 2.5 hours.
2
decisions t3 was progressively increased by at least one day and at most 21 days. Particular care was taken to avoid calendar effects.2 As soon as the subject chose A1 over A2, Task 2 was interrupted. At that decision, we set ∆*= t3. Any subject with a positive discount rate will eventually switch. A switch had to be confirmed in a follow-up choice where t3= ∆* + 2, otherwise the procedure would continue.3 Moreover, if the switch did not occur for t3 < 228 days (January 10, 2005), the elicitation of the discount rate was interrupted. At this point, a list of all decisions was presented and the subject had a chance to modify them. Using the delay t3 of the switching decision, together with the delay t3 of the previous decision, one can elicit individual discount rates. Everyone received a show up fee of 3€.4 In addition, one random decision from Table … was paid, where the random device was a bag containing ten tokens. Answers in the questionnaire were not rewarded with the exception of 50 cents for each correct answer on the understanding of exponential discounting. An average 5.61€ ($6.68) per person was given immediately after the session (conversion rate at the time, 1€ = $1.19). The largest component was a payments based on decisions in the discount rate elicitation procedure. The actual payment was carried out at a later date, but the selection was done immediately at the end of the session by a subject randomly drawing a number out of a bag. That provided a true moment of suspense. One person per session was selected and given a signed letter with university letterhead promising a later payment of 100€ or 110€. The specific decision paid out was determined with a second random draw. The time and amount of the actual payment reflected the subject’s choice during the experiment in that decision.5
2
If delays of payment t3 or t2 fell on Saturday, Sunday, or an official holiday, the delay was automatically adjusted either backward or forward to make it easy for subjects to cash the reward. The summer period was also excluded. Difficult periods were the Christmas vacations (December 22-January 6) and several other national or local festive days (for example October 9 and 12, November 1, December 6 and 8, February 27, March 19, May 1, June 29). Classes ran up to May 28, and then there were exams up to June 30. The summer period excluded was July 25September 5. The university was closed in August. One should consider that about 90% of the subjects’ families lived in the university town or in the region (Valencia province). 3 At this point one or two additional decisions may be prompted in order to bracket the exact willingness to wait in days into a narrower interval. The difference in wait t3 between the “A1” and “A2” choices was split in two, and eventually the relevant half interval divided in two again if the half interval was more then eight days long. 4 The participation fee was 2€ in the first two sessions. 5 All post-session handling of payments was done by the personnel affiliated with LEE, the Jaume I University laboratory of experimental economics. They are professors in the departments of economics. They are also involved in paying subjects for other experiments not related to the present one. Subjects had participated in other experiments of other types before and were familiar with paid economic experiments. These circumstances made it credible that the experimenter was going to honor the promise to pay in the future. Participants were periodically
3
The procedure aimed to keep transactions costs low and constant across all possible options. Choosing the early options would not save the extra trip of coming back to the lab to retrieve the money. The large rewards were never paid immediately after the session, and were paid with at least a two-day delay. Moreover, the transaction cost of returning was paid only by the person selected for payment. Payments were made in cash, hence no trip to a bank was necessary. After signing up, all the students were informed about the payment procedures. More precisely, it was explained that everyone would receive a small payment for participating and one out of ten would be randomly chosen to receive a large payment of 100/110€, which could be delayed days or months. This had no obvious effect on recruiting, and none of the subjects explicitly canceled his or her participation because of this warning. No senior student was allowed to sign up. Subjects were seated at computer terminals that were separated by partitions. Instructions were read aloud and questions answered. First, instructions for risk-elicitation lotteries were read and the corresponding decisions taken with pen and paper. Then, the instructions for the other parts were read and the corresponding decisions taken via a Visual Basic PC application. Finally, a questionnaire was distributed and completed with pen and paper. No communication among subjects was allowed. All subjects received a hard copy of the instructions.6
3 RESULTS ON SKILLS, CREDIT CONSTRAINTS AND UNCERTAINTY From the questionnaire data we can draw conclusions on the extent of the three confusing factors mentioned in the introduction, skill level, credit constraints, and perceived risk of default. The next section will use these values as possible explanations for the individual waiting time. Were the subjects confused? As illustrated in Figure 1 participants faced simple binary choices and several informational aides were provided.7 We employ two distinct ways to control for possible misunderstanding, a measure of general skills from a standardized admission test and a score based on ability to solve specific time discounting problems. The test is required for applicants seeking college admission in this region of Spain (Catalonia) and the score can range informed by email about how the experiment was proceeding and could also send emails to a dedicated account to inquire about the experimental procedures. 6 Sessions were run between April 26 and April 28, 2004. The maximum wait ∆* was 276 days. 7 Information includes the delay difference in days, the calendar date for each option, including the day of the week, the amount difference in euros, the annual discount rate, and a graphical representation of the wait in the form of line of asterisks proportional to the length of the delay.
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from 0 through 10. Our statistics are based on self-reported scores and yield an average score of 6.22 with a variance of 0.71. In addition we employed three targeted questions to measure understanding of exponential discounting. Subjects were paid 50 cents for every correct answer. In the questionnaire we explained that “the interest is compounded and computed in the same way banks usually do” and provided an example.8 For each question, there was a list of six possible answers: S) If your initial capital was 1,000 euros, what is your final capital after 6 year at 5% interest rate? (N=120)
(€1005, €1405, €1300, €1600, €1340 correct, €1683)
T) If your final capital in 10 years will be 10,000 euros with 8% interest rate, what is your initial capital?
(€4630 correct, €9080, €5550, €9260, €8000, €9920)
U) If your initial capital was 500 euros and your final capital after 5 years is 1,000 euros, what is the interest rate?
(5%, 11%, 8%, 15% correct, 10%, 20%)
A hand calculator was provided. In an early study, Wagenaar and Sagaria (1975) reports a poor understanding of exponential functions. In our sample, the fractions of correct answers were 50.0%, 35.8%, and 40%, respectively. We had a good level of variation within the subject pool with only 29.2% giving “all correct answers” and 45.8% giving all wrong answers. The existence of credit constraints was measured using non-paid answers from the following question: L) If you were to go to a bank to apply for a loan or credit card, what do you think your chances would be of being approved for at least one of the two? (N=119) (Possible answers)
(No. subjects
Classification)
At least 90%
(32
No credit constraint)
At least 75%
(18
Credit constraint)
At least 50%
(27
Credit constraint)
8
The following example with an interest rate of 10% may help you. (Deposit one year from now = deposit today x 1,10) i.e. if you deposit today 200 euros, you have 220 in one year. (Deposit two years from now = (deposit today x 1,10)x 1,10) i.e. if you deposit today 200 euros you have 242 in two years.
5
Less than 50%
(42
Severe credit constraint)
About 73.3% stated that their chances of getting either a bank loan or a credit card were less than 90% (“credit constraint”). About 35% stated that their chances were less than 50% (“severe credit constraint”). Discounting of future rewards may be partly due to the implicit default risk contained in the promise of a later reward. For instance when the earlier option is certain while the later option has a default risk of at least 0.091, a risk-neutral agent always prefers the earlier option. More generally, consider an agent comparing alternative consumption profiles, c =( co, c1,…, cT) that spread consumption among discrete time intervals between today (t=0) and period T under the budget constraint K=Σt=0,..,T (1+r)t ct, where r is the interest rate of the available saving technology. The immediate utility of consumption is given by u(ct), which is increasing in consumption, u’>0. The present utility U0 of consumption profile c is: U0(c) = Σt=0,..,T λ(t) s(t) u(ct)
(1)
Time discounting is the product of two components - the level of impatience embedded into the time preferences, λ(t), and the survival uncertainty, s(t), which may relate either to the credibility of a promise of a future reward, to the survival of the decision maker itself, or to both. When the time horizon is relatively short, the most relevant issue is not the survival of the decision maker but the implicit default risk in delivering the promised reward (Benzion et al., 89). For example, suppose you paid in full for five years of electric energy supplied by Enron and the company went bankrupt in the meanwhile. In this study we are interested in the discount function, which measures time preferences of the agent: 0≤ λ(t) ≤1, i.e. it indicates today’s utility value of one unit of utility delayed t periods (impatience). The survival function specifies the probability that the reward can be realized after a delay of t periods. The exponential discounting model is a special case of (1) where λ(t) = δt and the future consumption level is achieved with certainty, s(t) = 1. In the exponential model, δ is the discount factor is 0 ≤ δ ≤1 while the discount rate r = (1- δ) / δ. A descriptive model in this
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category which is widely used in the psychological literature is hyperbolic discounting, λ(t) = 1/(1 + k t). In both models, future consumption levels are achieved with certainty, s(t) = 1.9 An entirely different explanation for choice reversal is based on the survival probability. Sozou (1998) presents a model where the agent is infinitely patient, λ(t) =1, and the only component of time discounting is the risk of mortality, s(t). The risk that a reward which is still available after a delay of t is lost between t and t+1 is the hazard rate, h(t) = [s(t)-s(t+1)]/s(t). When considering marginal rates of intertemporal substitutions, his model can be observationally indistinguishable from either the exponential or the hyperbolic models. In particular, the exponential model is equivalent to a situation where the hazard rate h(t) has a constant value. We study empirically (1) by assessing the overall level of uncertainty of future rewards, s(0)s(T) and by measuring subject risk attitude. The higher the level of uncertainty the more risk attitude influences the discount rate. Assuming that s(t) and risk aversion are independently distributed, risk averse agents should exhibit a higher discount rate than risk neutral agents. Subjects were asked to state their perceived risk associated to a reward in two days and in one month: R) Suppose you have been selected for a 100 or 110 euro payment. If the date of payment is two days from today (“one month” in question Q) what are the chances to cash that? Include the possibility that you forget, that you cannot came to the laboratory that day, and the possibility that we are not going to pay you (N= 120). (Possible answers)
(2 days, no. subjects)
(1 month, no. subjects)
99% or more
(63
44)
Below 99% and above 95%
(38
31)
Below 95% and above 85%
(12
26)
Below 85% and above 60%
(7
15)
Below 60%
(0
4)
For 96% of the subjects the perceived risk for the later reward is equal or higher than for sooner reward. The impact of perceived risk on discounting is mediated by the risk attitude of the 9
Economists have mostly used a simplified version of this, quasi-hyperbolic discounting, which was originally proposed by Phelps and Pollak (1968), λ(t) = βδt if t > 0 and λ(t) = 1 if t = 0, 0>β>1. An axiomatic approach for non-exponential time preferences is presented in Ok and Masatlioglu (2003).
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subject. The results on risk attitude are summarized in Figure 2. The wide majority of the subjects are risk averse, with some being highly risk averse. In the next section we evaluate the role of these individual characteristics in explaining the discount rate.
4
RESULTS ON DISCOUNT RATES
Subject choices on time discounting are summarized in Figure 3. Two major patterns emerge. First, there is wide individual diversity in the level of time discounting, with some subjects willing to wait as much as 40 times longer than others. Second, in general, subjects discount future rewards quite heavily. Given a choice between 100 over 110 euros, the median subject is willing to wait at least 13 days but at most 17 days for the latter. When using annual capitalization, this median wait corresponds to discount rates between 215% and 281%.10 Coller and Williams (1999) and Harrison et al. (2002) obtained lower discount rates. Eckel et al. (2004, Table 5) reports comparable levels of individual discount rates elicited through a field experiment. Frederick et al. (2002, Table 1) presents estimates taken from the psychological and economic experimental literature, some of which are higher and some lower than the figures reported here. The willingness to wait in days for 110 euros over receiving 100 euros in two days is the dependent variable of the OLS regression shown in Table 1. The purpose of the regression is to assess the relevance of the three common confounding factors already described in this paper. Although not included in Table 1, the general skill level measured through the admission score was not significant in explaining waiting time. When controlling for other factors, also “all correct answers” was not significant in explaining waiting time. These findings suggest that subjects understood the task and that variations in ability within the subject pool did not interfere significantly with the elicitation of time preferences. The discount rate implied in subject choices is rather high in comparison with the credit market conditions faced by our participants. A one-year car loan granted from the campus branch of a major bank was offered to students at a 7.5% interest rate. Using such a rate in the experimental design leads to a wait of at least 481 days. If access to credit is precluded, this market rate may be irrelevant. According to a bank teller interviewed, car loans were uncommon among students.
10
Among the assumptions necessary to interpret this calculation as a measure of subjects’ impatience are instant utility at the moment of receiving the monetary reward and linear utility function in money.
8
More generally, Spanish undergraduates have limited access to credit cards and bank credit lines. The most frequent credit line was a loan of few hundred dollars in order to pay for tuition that was granted at a 5.5% rate. The money would be given after a 3-4 day period and had to be repaid within 11 months. Credits of about 200-400 euros could be obtained to attend language classes at a 6.75% rate. Students qualified for credit cards only if they had a monthly deposit in the account or a guarantee from one of their parents, but in practice credit cards were issued mostly to exchange students that went abroad.11 When asked directly, experiment participants shared this perception of difficult access to the credit market to such an extent that we classify three-quarters of them as credit constrained. In Table 1, participants with credit constraints showed less willingness to wait than the others and that impact is significant at a 5% level. Harrison et al (2002) reported a similar effect of credit constraints using a sample of the Danish population. When using just the six most significant regressors, having a loan is also a significant variable (Table 1, col. (2)). We interpret this result as a further support for the impact of credit constraints, because having a loan may simply signal the absence of credit constraints. The third confounding factor is the perceived risk of default for the future reward. About 35% of the subjects expected to cash a reward with at least 99% probability in both two days and one month (“very low or no risk”). When restricted to this sub-sample, yearly interest rates for the median subject range from 109% to 140%.12 Although substantially lower than the risk unadjusted rates, these figures are still a far cry from market interest rates.13 In Table 2 subjects are classified into four categories according to the differential level of uncertainty for future rewards, s(two days) − s(one month). The fraction of subjects immediately grabbing the immediate reward, i.e. choosing the minimal wait, increases monotonically as the additional risk perceived for the future reward grows. There is also an interesting, although puzzling, inverse relation between higher levels of additional risk and the percentage of correct answers to the discounting questions. Surprisingly, when controlling for other factors, perceived risk is not significantly
11
The interest is compounded once a year. Personal communication from a bank teller of Caixa Catalunya, UAB campus branch, Bellaterra, Spain, May 12, 2003. 12 The discount rate calculation assumes that in both options no risk is involved. The median willingness to wait ranged from 26 to 33.5 days. 13 The difference may not be too troublesome. It may simply come from a magnitude effect, i.e. small amounts are discounted more then large amounts (Thaler, 1981, Green, Myerson, and McFadden, 1997). Impatience levels should not be computed on money amounts but on the utility of money. Ok and Masatlioglu (2003) show that the magnitude effect is compatible with the exponential discounting model, given an appropriately concave utility function.
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correlated with waiting time, although the coefficient has the correct sign (Table 1). We do think that perceived risk is important but we most likely employed a too coarse of a measure for perceived risk. Finally, subjects’ risk attitude has little predictive power. The regression coefficients show correct signs for risk averse and risk neural subjects, but neither coefficient is significant. Moreover, other proxies for risk attitude and impatience, such as smoking or fastening seat belts, are also insignificant.
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REFERENCES Azfar, Omar (1999) “Rationalizing Hyperbolic Discounting,” Journal of Economic Behavior & Organization, 38, 245-252. Benartzi, Shlomo and Richard H. Thaler (2004) “Save More Tomorrow: Using Behavioral Economics to Increase Employee Saving,” Journal of Political Economy CXII, S164-S187. Benzion, Uri, Amnon Rapoport, and Joseph Yagil (1989) “Discount rates inferred from decisions: An experimental study.” Management Science, 35, 270-84. Chapman, Gretchen B. (2003) “Time discounting of health outcomes.” In Lowenstein, G., Read, D. and Baumeister, R.F. (eds.) Time and Decision: Economic and psyuchological perspectives on intertemporal choice, New York, Russel Sage Foundation. Coller, Maribeth, and Williams, Melonie B..1999. “Eliciting Individual Discount Rates,” Experimental Economics, 2, 107-127. Dasgupta, Partha and Maskin, Eric. 2005. Uncertainty and Hyperbolic Discounting, American Economic Review, 95, 4, 1290-99 Fernandez-Villaverde, Jesus and Arijit Mukherji (2000) “Can we really observe hyperbolic discounting? “, University of Minnesota, mimeo Frederick, Shane, George Loewenstein, and Ted O’Donoghue (2002) “Time Discounting and Time Preference: A Critical Review”, Journal of Economic Literature, XL, 351–401 Green, L., Myerson, J., & McFadden, E. (1997). Rate of temporal discounting decreases with amount of reward, Memory & Cognition, 25, 715–723. Halevy, Yoram (2005) “Diminishing Impatience: Disentangling Time Preference from Uncertain Lifetime,” Mimeo, Department of Economics, University of British Columbia, Canada. Harrison, Glenn W., Morten I. Lau, and Melonie B. Williams (2002) “Estimating individual discount rates in Denmark: a field experiment”, American Economic Review, forthcoming Holt, C. and S. Laury (2002) “Risk Aversion and Incentive Effects in Lottery Choices”, American Economic Review, December, 92, 5, 1644-1655. Kirby, K. N. and R.J. Herrnstein (1995) “Preference reversals due to myopic discounting of delayed reward,” Psychological Science, 6, 2, 83-89. Laibson, David (1997) “Golden eggs and hyperbolic discounting.” Quarterly Journal of Economics, 112, 443-77. Leland, J.W. (2002) “Similarity judgments and anomalies in intertemporal choice”, Economic Inquiry, 40, 4, 574581 Loewenstein, George (1987) “Anticipation and the Valuation of Delayed Consumption.” Economic Journal, 97, 666- 84. Mazur, J.E. (1987) “An adjusting procedure for studying delayed reinforcement,” In M.L. Commons, J.E. Mazur, J.A. Nevin, and H. Rachlin (Eds.), Quantitative analyses of behavior, Vol.5, The effect of delay and of intervening events on reinforcement value, 55-73, Hillsdale, NJ, Erlbaum. McClure, Samuel M., David I. Laibson, George Loewenstein, Jonathan D. Cohen (2004) “Separate Neural Systems Value Immediate and Delayed Monetary Rewards,” Science, 306, 15 October 2004, 503-507. Ok, Efe A. and Yusufcan Masatlioglu (2003) “A General Theory of Time Preferences,” Mimeo. Pender, John L. (1996) “Discount Rates and Credit Markets: Theory and Evidence from Rural India,” Journal of Development Economics, 50, 257-296. Phelps, E.S. and Robert Pollak. 1968. “On Second-Best National Saving and Game-Equilibrium Growth.” Review of Economic Studies, 35, 185-199. Warner, John T.and Pleeter, Saul. 2001.The Personal Discount Rate: Evidence from Military Downsizing Programs, American Economic Review, 91, 1, 33-53 Rubinstein, Ariel (2003) “‘Economics and Psychology’?: The Case of Hyperbolic Discounting,” International Economic Review, 44, 4, 1207-1216. Sozou, Peter D. (1998) “On Hyperbolic Discounting and Uncertain Hazard Rates,” Proceedings of the Royal Society of London: Biological Sciences (Series B), 265 (1409), 2015-2020. Wagenaar, William A., and Sagaria, Sabato D. (1975) “Misperception of Exponential Growth,” Perception and Psychophysics, 18(6), pp. 416-422.
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Table 1: What can explain time discounting? Dependent variable: willingness to wait in days for
(1)
(2)
13.8828 (15.3513) -31.3502 (15.3630)** -14.2973 (13.5946) -23.6868 (18.2746) 16.5159 (13.5376) 15.6532 (17.5820) -15.0113 (18.7959) 0.0133 (13.7663) -0.8868 (18.4721) -11.7516
18.9746 (13.3431) -27.5008 (13.5024)**
110 euros over receiving 100 euros in two days All discount answers correct Credit constraints Not working No loans No or very low risk Risk neutral or risk seeking subject Risk averse subject Male Smoker, never tried to quit Never smoked
-33.2019 (15.7380)** 13.6165 (12.6841)
(14.0100) Wears seat belts in front and back seats Session 2 Session 3 Session 4 Session 5 Session 6 Constant
Observations R-squared
-2.0164 (14.2565) -26.8425 (23.0791) -43.0460 (22.7054)* -23.6455 (23.3089) -28.3012 (22.3267) 9.7528 (22.0798) 105.0070 (28.7751)***
82.0139 (19.5001)***
120 0.17
120 0.11
-26.1607 (16.3165) -13.3698 (16.3408)
Notes: OLS regression, Stata program, Standard errors in parentheses. A subject is classified as risk averse if she showed consistency in lottery choices and switched to option B in decision 8, 9, or 10. A subject is classified as risk
12
neutral/seeking if she showed consistency in lottery choices and switched to option B in decision 1,2,3,4, or 5. Smoking questions N and O; seat belts (questions P, always when in front, frequently or always when in the back seat). No loan (question I=4, not even from parents) Not working (question G, not even part time). * significant at 10%; ** significant at 5%; *** significant at 1%
Table 2: Time discounting and perceived risk Discounting Median wait (days)
Choices of
questions
minimal wait (%) (answers all
Number of subjects
correct) No risk or very low risk
26
4.8%
40.5%
42
Low risk
10
6.1%
30.3%
33
12.5
7.9%
18.7%
32
12
23.1%
15.4%
13
10.0%
29.1%
120
Medium risk High risk Overall
Note: Subject classification based on two questionnaire answers. The “no risk” subjects stated a likelihood of receiving the reward 99% or higher for both a two days and a month horizons. The “high risk” category either stated a likelihood of receiving the one month reward at below 60% or has a minimum risk differential between two days and one month of at least 9.1%. The threshold is a risk of s=0.091 on 110 euros because it makes an agent indifferent with 100 euros. Moreover, while a perfectly patient “medium risk” subject may want to take the two days over the one month reward, a perfectly patient “low risk” subject never does.
13
Figure 1: Input screen for intertemporal decision task (English version)
14
Figure 2: Individual risk attitude, fraction of subjects choosing the “risky” option
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3
Full sample, obs=120
0.2 Risk neutral decision-maker
0.1
0 ry 1 te lo t
ry 9 te lo t
ry 8 te lo t
ry 7 te lo t
ry 6 te lo t
ry 5 te lo t
ry 4 te lo t
ry 3 te lo t
ry 2 te lo t
lo t
te
ry 1
0
15
Figure 3: Individual time discounting: minimum willingness to wait for 110 euros versus 100 euros
Minimal (0-4 days)
10.00%
Up to a week (5-7 days)
18.30%
More than a week, up to two weeks (8-14)
26.70%
More than two weeks, up to a month (15-30) More than a month, up to two months (31-60) More than two months
16.70%
15.00%
13.30%
Note: Number of subjects: 120. The waiting time tabulated is a lower bound to the willingness to wait. For 90% of the subjects it is elicited with an approximation of 8 days or less.
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