Keith M. Marzilli Ericson, John Myles White, and Jonathan D. Cohen,
“Money Earlier or Later? Simple Heuristics Explain Intertemporal Choices
Better than Delay Discounting.” NBER Working Paper No. w20948, February 2015.
• A series of “Money Earlier or Later” (MEL) choice problems are given to 1000 participants on Amazon’s Mechanical Turk service. Each MEL problem asks a person to choose between a Small-Early option (x1, t1), where x1 is the amount of money to be received t1 time periods from now, and a Large Late option (x2, t2); the names of the options recognize that x1<x2, and t1<t2. So, are you willing to wait until time t2 (instead of t1) to receive a larger payment of x2 (instead of the smaller but earlier payment of x1)?
• Problems with existing models of discount rates are what motivate this experiment. We have already seen why exponential discounting is inconsistent with common choice behavior. But even hyperbolic or quasi-hyperbolic discounting, though they can generate a present bias, cannot explain the magnitude effect, where multiplying up the dollar amounts by a common factor leads to lower revealed discount rates: a person who will take $10 today instead of $13 a week from now (often) will not take $1000 today instead of $1300 one week from now.
• The authors propose that in MEL problems, people employ rules of thumb, heuristics, so they call their model the ITCH model, for Intertemporal Choice Heuristics. In the ITCH models, the four factors that people employ to make their decision are the absolute (x2-x1) and relative ((x2-x1)/(x1+x2)/2) differences in monetary amounts and, the absolute (t2-t1) and relative ((t2-t1)/(t1+t2)/2) time delays. These four factors are combined via a weighted sum, which turns out to be fairly stable across individuals and “frames” for the MEL problems. The use of average time and delay in determining relative changes provides a sort of reference point interpretation to the heuristic.
• ITCH explains decreasing impatience (with time) and the absolute magnitude effect: If both the early and late options are delayed by a week, the relative time delay falls, so the use of a lower discount rate results. Alternatively, increasing the stakes proportionally increases the absolute payoff, and again, a lower discount rate will be chosen by the heuristics.
• Calibration of the model on a subset of the data shows that relative money is a much larger factor than absolute money, whereas relative and absolute time have similar weights. (But the time periods were rather paltry, and were presented always in absolute form, so a different approach could raise the decision weight of the relative time component.)
• In predicting the out-of-sample data, the ITCH model out-performs all the tested alternatives such as exponential discounting or quasi-hyperbolic discounting.
• So, perhaps people do not have “a” discount rate, but rather, use some rules of thumb to make intertemporal trade-offs.
Tuesday, June 30, 2015
People are Not Exponential Discounters, and That’s OK
Some Notions Drawn, as I Recall, from Rabin (2002) and Frederick, Loewenstein, and O'Donoghue (2002)
• Would you rather have $20 now or $21 one week from now? If you choose the immediate $20 – a perfectly reasonable choice – then you discount monetary rewards by at least 5 percent per week. Would you rather have $20 now, or $250 one year from now? If you are an exponential discounter, and you preferred the immediate $20 in the initial situation, then you must prefer the immediate $20 to $250 one year hence, as 1.05 to the 52nd power is more than 12.6. If the question concerned two years from now, you would turn down $3100 in two years’ time for an immediate $20.
• Would you rather have $20 now or $22 one week from now? If you chose the immediate $20, then you discount by at least 10 percent per week. Would you rather have $20 now, or $2800 one year from now? If you are an exponential discounter, you must still want the $20, as 1.10 to the 52nd power is more than 140. In two years’ time, you’d turn down $400,000 (1.1 to the 104th power is more than 20,000) for an immediate $20.
• Rabin showed that the sort of risk aversion over small-stakes gambles that most people display is inconsistent with expected utility theory, because such behavior would necessitate crazy choices for higher stakes gambles. What is demonstrated above is rather analogous, that the sort of time preference that people display for small stakes, short time-frame situations is not consistent with exponential discounting, because it would necessitate crazy choices for longer time-frame choices.
• Would you rather have $20 now or $21 one week from now? If you choose the immediate $20 – a perfectly reasonable choice – then you discount monetary rewards by at least 5 percent per week. Would you rather have $20 now, or $250 one year from now? If you are an exponential discounter, and you preferred the immediate $20 in the initial situation, then you must prefer the immediate $20 to $250 one year hence, as 1.05 to the 52nd power is more than 12.6. If the question concerned two years from now, you would turn down $3100 in two years’ time for an immediate $20.
• Would you rather have $20 now or $22 one week from now? If you chose the immediate $20, then you discount by at least 10 percent per week. Would you rather have $20 now, or $2800 one year from now? If you are an exponential discounter, you must still want the $20, as 1.10 to the 52nd power is more than 140. In two years’ time, you’d turn down $400,000 (1.1 to the 104th power is more than 20,000) for an immediate $20.
• Rabin showed that the sort of risk aversion over small-stakes gambles that most people display is inconsistent with expected utility theory, because such behavior would necessitate crazy choices for higher stakes gambles. What is demonstrated above is rather analogous, that the sort of time preference that people display for small stakes, short time-frame situations is not consistent with exponential discounting, because it would necessitate crazy choices for longer time-frame choices.
Hardisty, Appelt, and Weber (2013), on Magnitude Effects in Intertemporal Choice
David J. Hardisty, Kirstin C. Appelt, and Elke U. Weber, “Good or Bad, We Want it Now: Fixed-cost Present Bias for Gains and Losses Explains Magnitude Asymmetries in Intertemporal Choice.” Journal of Behavioral Decision Making 26: 348–361, 2013.
• A positive discount rate means that you want to capture gains immediately, and postpone losses as long as possible. Why would people have a positive discount rate? (1) opportunity cost; (2) uncertainty (for instance, you might not actually have to pay that cost if it is postponed); (3) resource slack, the belief that your budget won’t be as tight in the future; and (4) preferences themselves display present bias, or impatience.
• The magnitude effect: people discount future small gains much more highly than they discount substantial sums. This will be the case, for instance, if preferences have a sort of fixed cost present bias. People might be willing to pay $4, for instance, to achieve an immediate reward rather than wait for a larger, later reward. This fixed cost will induce people to move to take small gains immediately, but for larger amounts (which involve larger future gains, too), they are willing to wait.
• In the loss domain, there is evidence for small or even reverse magnitude effects: small losses are discounted less than large losses. A fixed cost present bias explains observed magnitude effects for gains, but does not predict asymmetric magnitude effects. People with a fixed cost present bias would still want to postpone losses, contrary to some empirical evidence.
• Hardisty, Appelt, and Weber argue that people want to resolve uncertainty right away, now. Such resolution is not their only concern, but all else equal, it means that gains are taken right away and that losses are realized right away. Further, this resolution bias is insensitive to magnitude, while the other factors, such as uncertainty and opportunity costs, tend to scale with magnitude. As a result, the resolution bias yields greater discount rates for gains and smaller ones for losses. Further, small losses will involve negative discounting. In the experiments, zero and negative discount rates are common in the small loss condition.
• A positive discount rate means that you want to capture gains immediately, and postpone losses as long as possible. Why would people have a positive discount rate? (1) opportunity cost; (2) uncertainty (for instance, you might not actually have to pay that cost if it is postponed); (3) resource slack, the belief that your budget won’t be as tight in the future; and (4) preferences themselves display present bias, or impatience.
• The magnitude effect: people discount future small gains much more highly than they discount substantial sums. This will be the case, for instance, if preferences have a sort of fixed cost present bias. People might be willing to pay $4, for instance, to achieve an immediate reward rather than wait for a larger, later reward. This fixed cost will induce people to move to take small gains immediately, but for larger amounts (which involve larger future gains, too), they are willing to wait.
• In the loss domain, there is evidence for small or even reverse magnitude effects: small losses are discounted less than large losses. A fixed cost present bias explains observed magnitude effects for gains, but does not predict asymmetric magnitude effects. People with a fixed cost present bias would still want to postpone losses, contrary to some empirical evidence.
• Hardisty, Appelt, and Weber argue that people want to resolve uncertainty right away, now. Such resolution is not their only concern, but all else equal, it means that gains are taken right away and that losses are realized right away. Further, this resolution bias is insensitive to magnitude, while the other factors, such as uncertainty and opportunity costs, tend to scale with magnitude. As a result, the resolution bias yields greater discount rates for gains and smaller ones for losses. Further, small losses will involve negative discounting. In the experiments, zero and negative discount rates are common in the small loss condition.
Ifcher and Zarghamee (2011) on Positive Affect and Time Preference
John Ifcher and Homa Zarghamee, “Happiness and Time Preference: The Effect of Positive Affect in a Random-Assignment Experiment.” American
Economic Review 101: 3109–3129, December 2011.
• Mild positive affect has many beneficial correlates, including increased self-control. But does happiness cause low discounting of the future or does low discounting cause happiness?
• This article describes an experiment that tries to get at the causality question. The experiment allows discount rates to be measured fairly well, but instead of examining happiness directly, only positive affect is tested.
• The experiment revealed that indeed, people with an induced positive affect discount at a lower rate, they display more self-control, or less present bias.
• One of the hurdles that the experiment works hard to overcome is to be able to compare present and future payments where the transaction costs and hassle of receiving the payments are similar in both cases.
• The experiment involved questions such as: How much money would you need to be paid today to forgo the opportunity to receive m dollars t days from now? The questions involved m’s ranging from about $11 to about $51, and t's ranging from one day to 56 days.
• The experiment reproduces the usual finding that longer delays to receive a payment fixed in size are less valuable to someone in the here and now.
• Mild positive affect has many beneficial correlates, including increased self-control. But does happiness cause low discounting of the future or does low discounting cause happiness?
• This article describes an experiment that tries to get at the causality question. The experiment allows discount rates to be measured fairly well, but instead of examining happiness directly, only positive affect is tested.
• The experiment revealed that indeed, people with an induced positive affect discount at a lower rate, they display more self-control, or less present bias.
• One of the hurdles that the experiment works hard to overcome is to be able to compare present and future payments where the transaction costs and hassle of receiving the payments are similar in both cases.
• The experiment involved questions such as: How much money would you need to be paid today to forgo the opportunity to receive m dollars t days from now? The questions involved m’s ranging from about $11 to about $51, and t's ranging from one day to 56 days.
• The experiment reproduces the usual finding that longer delays to receive a payment fixed in size are less valuable to someone in the here and now.
Markle, Wu, White, and Sackett (2014) on Reference Points in Marathons
Alex Markle, George Wu, Rebecca J. White, and Aaron M. Sackett, “Goals as Reference Points in Marathon Running: A Novel Test of Reference Dependence.” Fordham University Schools of Business Research Paper No. 2523510, November 12, 2014 [subsequently updated].
• Marathoners are asked for a time goal prior to the race; the notion is that these goals serve as reference points through which prospect theory-style preferences pivot.
• Runners also are asked to indicate how happy they will be with meeting their time goal, or with beating it, or with not meeting it. Answers to these questions suggest that runners believe that their experience utility will display loss aversion, with the time goal as reference point.
• Actual satisfaction with marathon performance indeed tracks performance relative to the time goal with loss aversion and diminishing sensitivity. People overestimate their degree of loss aversion (or their benefit from success), but nevertheless they do experience some aversion (or benefit).
• Unlike the standard prospect theory gain-loss function, the satisfaction experienced by runners takes a jump discontinuity at the reference point.
• Runners who indicated that their time goal was particularly important seem to display larger loss aversion.
• The existence of additional reference points, such as past best time or most recent marathon time, also can mediate results.
• Note that reference-dependent preferences might be “rational” if, as here, actual experienced utility displays reference dependence.
• Marathoners are overly optimistic about their chances of meeting their time goal.
• Marathoners are asked for a time goal prior to the race; the notion is that these goals serve as reference points through which prospect theory-style preferences pivot.
• Runners also are asked to indicate how happy they will be with meeting their time goal, or with beating it, or with not meeting it. Answers to these questions suggest that runners believe that their experience utility will display loss aversion, with the time goal as reference point.
• Actual satisfaction with marathon performance indeed tracks performance relative to the time goal with loss aversion and diminishing sensitivity. People overestimate their degree of loss aversion (or their benefit from success), but nevertheless they do experience some aversion (or benefit).
• Unlike the standard prospect theory gain-loss function, the satisfaction experienced by runners takes a jump discontinuity at the reference point.
• Runners who indicated that their time goal was particularly important seem to display larger loss aversion.
• The existence of additional reference points, such as past best time or most recent marathon time, also can mediate results.
• Note that reference-dependent preferences might be “rational” if, as here, actual experienced utility displays reference dependence.
• Marathoners are overly optimistic about their chances of meeting their time goal.
Heffetz and List (2014) on Reference Points and Endowments
Heffetz, Ori and John A. List, “Is the Endowment Effect an Expectations Effect?” Journal of the European Economic Association 12(5): 1396-1422, October 2014.
• Three experiments are conducted to test the Koszegi and Rabin (2006) version of prospect theory, in which the reference point consists of recent expectations for future consumption. In part, Koszegi and Rabin were motivated by List’s evidence that endowment effects dissipate with market experience.
• A pared-down description of the experimental set-up: Subjects flip a coin to determine whether they are assigned a mug or a pen. After this assignment, in the Strong Expectations condition, they are told that there is a 99% chance that the good (mug or pen) that they were assigned by the coin flip is what they have to keep, but there is a 1% chance they will be allowed to trade for the other item. (That is, Strong Expectations means that you virtually own the good that was randomly assigned.) In the Weak Expectations condition, the probability is reversed, so the assignment is very unlikely to be binding. Then (eventually), subjects have to choose which good they want. Only after that do they learn whether their choice matters, or whether the realization of the randomization dictated that they had to stick with their assignment.
• The Koszegi and Rabin model suggests that under Strong Expectations, the coin-flip assignment should affect preferences – but not under Weak Expectations. What Heffetz and List found, however, is that the assignment matters a lot, with no difference between the Expectation conditions.
• Experiments by Marzilli Ericson and Fuster, alternatively, found a big effect of strong v. weak expectations in a different experimental set-up. Heffetz and List run two experiments similar to those of Marzilli Ericson and Fuster, but do not replicate their results. Instead, Heffetz and List basically continue to find that the random assignment matters, and that the Expectations condition has no effect – contrary to Koszegi and Rabin and to Marzilli Ericson and Fuster.
• Three experiments are conducted to test the Koszegi and Rabin (2006) version of prospect theory, in which the reference point consists of recent expectations for future consumption. In part, Koszegi and Rabin were motivated by List’s evidence that endowment effects dissipate with market experience.
• A pared-down description of the experimental set-up: Subjects flip a coin to determine whether they are assigned a mug or a pen. After this assignment, in the Strong Expectations condition, they are told that there is a 99% chance that the good (mug or pen) that they were assigned by the coin flip is what they have to keep, but there is a 1% chance they will be allowed to trade for the other item. (That is, Strong Expectations means that you virtually own the good that was randomly assigned.) In the Weak Expectations condition, the probability is reversed, so the assignment is very unlikely to be binding. Then (eventually), subjects have to choose which good they want. Only after that do they learn whether their choice matters, or whether the realization of the randomization dictated that they had to stick with their assignment.
• The Koszegi and Rabin model suggests that under Strong Expectations, the coin-flip assignment should affect preferences – but not under Weak Expectations. What Heffetz and List found, however, is that the assignment matters a lot, with no difference between the Expectation conditions.
• Experiments by Marzilli Ericson and Fuster, alternatively, found a big effect of strong v. weak expectations in a different experimental set-up. Heffetz and List run two experiments similar to those of Marzilli Ericson and Fuster, but do not replicate their results. Instead, Heffetz and List basically continue to find that the random assignment matters, and that the Expectations condition has no effect – contrary to Koszegi and Rabin and to Marzilli Ericson and Fuster.
Abeler et al. (2011) on Reference Points and Effort Provision
Johannes Abeler, Armin Falk, Lorenz Goette, and David Huffman,
“Reference Points and Effort Provision.” American Economic Review 101: 470-492, April 2011.
• An experiment is conducted in which people engage in a tedious and pointless task, but one that requires some attention.
• The participants do not know with certainty how much they will be paid. They know that they will either receive a fixed fee (of which they are informed), or their accumulated, piece-rate earnings, each with equal probability.
• The experiment varied only the fixed fee, which is either low (3 euros) or high (7 euros). The relevant choice for the worker is how long to work.
• For an expected utility maximizer, the size of the fixed fee will not influence the decision about how long to work. (This claim requires the assumption that utility is separable in money and effort.) Even for a prospect theory decider, if the reference point is the status quo prior to the experiment, the size of the fixed fee will not influence the decision about how long to work.
• If the worker is a prospect theory decider whose reference point is determined by the fixed fee – perhaps by fixing expectations of earnings – then the fixed fee size will influence the amount of work, as losses relative to the fixed fee will be quite aversive.
• Sure enough, the participants worked longer when the fixed fee was higher. Further, the most common stopping point occurred when the accumulated earnings equaled the fixed fee, so the payment involved no uncertainty at all.
• Workers whose responses to a series of questions suggest that they are particularly loss averse are also relatively more likely to stop working at the no-risk point.
• An experiment is conducted in which people engage in a tedious and pointless task, but one that requires some attention.
• The participants do not know with certainty how much they will be paid. They know that they will either receive a fixed fee (of which they are informed), or their accumulated, piece-rate earnings, each with equal probability.
• The experiment varied only the fixed fee, which is either low (3 euros) or high (7 euros). The relevant choice for the worker is how long to work.
• For an expected utility maximizer, the size of the fixed fee will not influence the decision about how long to work. (This claim requires the assumption that utility is separable in money and effort.) Even for a prospect theory decider, if the reference point is the status quo prior to the experiment, the size of the fixed fee will not influence the decision about how long to work.
• If the worker is a prospect theory decider whose reference point is determined by the fixed fee – perhaps by fixing expectations of earnings – then the fixed fee size will influence the amount of work, as losses relative to the fixed fee will be quite aversive.
• Sure enough, the participants worked longer when the fixed fee was higher. Further, the most common stopping point occurred when the accumulated earnings equaled the fixed fee, so the payment involved no uncertainty at all.
• Workers whose responses to a series of questions suggest that they are particularly loss averse are also relatively more likely to stop working at the no-risk point.
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