Does Hyperbolic Discounting Really Exist?

by gwern 8y3rd Dec 201112 comments


“Beware of WEIRD psychological samples” because results derived from them may reflect the specific sample more than any kind of generalized truth. And LessWrong has generalized hyperbolic discounting out the wazoo. (See the tags akrasia and discounting.) Hyperbolic discounting is bad, of course, because among other things it leaves on vulnerable to preference reversals and inconsistencies and hence money-pumping.

But isn’t it odd that for a fundamental fact of human psychology, a huge bias we have spent a ton of collective time discussing and fighting, that it doesn’t seem to lead to much actual money-pumping? The obvious examples like the dieting or gambling industries are pretty small, all things considered. And online services like BeeMinder specifically devised on a hyperbolic discounting/picoeconomics basis are, as far as I know, useful but no dramatic breakthrough or silver bullet; again, not quite what one would expect. Like many other heuristics and biases, perhaps hyperbolic discounting isn’t so bad after all, in practice.

Ainslie mentions in Breakdown of Will somewhere that financial incentives can cause people to begin discounting exponentially. What if… hyperbolic discounting doesn’t really exist, in practice? If it may reflect a failure of self-control, a kind of teenager trait, one we find in younger (but not older) populations - like university students?

The following quotes are extracted from the paper “Discounting Behavior: A Reconsideration” (102 pages) by Steffen Andersen, Glenn W. Harrison, Morten Lau & E. Elisabet Rutström, January 2011:

The implied econometrics calls for structural estimation of the theoretical models, allowing for joint estimation of utility functions and discounting functions. Using data collected from a representative sample of 413 adult Danes in 2009, we draw striking conclusions. Assuming an exponential discounting model we estimate discount rates to be 5.6% on average: this is significantly lower than all previous estimates using controlled experiments. We also find no evidence to support quasi-hyperbolic discounting or “fixed cost” discounting, and only modest evidence to support other specifications of non-constant discounting. Furthermore, the evidence for non-constant discounting, while statistically significant, is not economically significant in terms of the size of the estimated discount rates. We undertake extensive robustness checks on these findings, including a detailed review of the previous, comparable literature.

…We do find evidence in favor of flexible Hyperbolic specifications and other nonstandard specifications, but with very modest variations in discount rates compared to those often assumed. We find that a significant portion of the Danish population uses Exponential discounting, even if it is not the single model that best explains observed behavior.

Given the contrary nature of our findings, in terms of the received empirical wisdom, section 6 contains a systematic cataloguing of the samples, experimental procedures, and econometric procedures of the alleged evidence for Quasi-Hyperbolic and non-constant discounting. We conclude that the evidence needed reconsideration. The one clear pattern to emerge from the received literature is that non-constant discounting occurs for some university student samples.

One major robustness check is therefore to see if the disappointing showing for the Quasi- Hyperbolic model is attributable to our population being the entire adult Danish population, rather than university students. Although it is apparent that the wider population is typically of greater interest, virtually all prior experimental evidence that we give credence to comes from convenience samples of university students. We find that there is indeed a difference in the elicited discount rates with (Danish) university students, and that they exhibit statistically significant evidence of declining discount rates. On the other hand, the size of the discount rates for shorter time horizons is much smaller than the received wisdom suggests.

…Coller and Williams [1999] were the first to demonstrate the effect of a front end delay; their estimates show a drop in elicited discount rates over money of just over 30 percentage points from an average 71% with no front end delay.11 Using the same experimental and econometric methods, and with all choices having a front end delay, Harrison, Lau and Williams [2002] estimated average discount rates over money of 28.1% for the adult Danish population. Andersen, Harrison, Lau and Rutström [2008a] were the first to demonstrate the effect of correcting for non-linear utility; their estimates show a drop in elicited discount rates of 15.1 percentage points from a discount rate over money of 25.2%. These results would lead us to expect discount rates around 10% with a front end delay, with a significantly higher rate when there is no front end delay.

…The Exponential discounting model indicates a discount rate of only 5.6%, where all discount rates will be presented on an annualized basis. The 95% confidence interval for this estimate is between 4.1% and 7.0%, so this indicates even lower discount rates than the 10.1% reported by Andersen, Harrison, Lau and Rutström [2008a] for the same population in 2003.25 For comparison, the Exponential discounting model assuming a linear utility function implies an 18.3% discount rate, with a 95% confidence interval between 15.5% and 21.2%, so this is also lower than the estimate for 2003 (25.2%, with a 95% confidence interval between 22.8% and 27.6%). We again conclude that correcting for the non-linearity of the utility function makes a significant quantitative difference to estimated discount rates.

The most striking finding from Table 1, for us, is that there is no Quasi-Hyperbolic discounting. The key parameter, $, is not statistically or economically significantly different from 1, and the parameter * is virtually identical to the estimate from the Exponential discounting model. The p-value on a test of the hypothesis that $=1 has value 0.55, although the 95% confidence interval for $ is enough to see that it is not significantly different from 1.

…The Weibull discounting model in panel F allows a very different pattern of non-constant discounting. Indeed, these parameter estimates do imply discount rates that vary slightly, from 6.7% for a 1 day horizon, to 6.0% for a 2 week horizon, and then down to 5.1% for a one year horizon. But the 95% confidence intervals on all of these is at least between 3% and 7%, and one cannot reject the Exponential discounting model hypothesis that s=1 (p-value of 0.73).

…The only demographic covariate to have any statistically significant impact on elicited discount rates is whether the individual is a female. Women have discount rates that are 6.6 percentage points lower than men, and the p-value on this estimated effect of 0.092. In turn, this derives from women being more risk averse: their RRA is 0.294 higher than men, with a p-value on this estimated effect of 0.026. Hence they have a more concave utility function and, by Jensen’s inequality applied to (0), have a lower implied discount rate. Looking at total effects instead of marginal effects, men on average have discount rates of 7.4% and women have discount rates of 3.6%, and the difference is statistically significant (p-value = 0.004).

…Our results were a surprise to us, and the robustness checks reported above did not lead us to qualify that reaction. We fully expected to see much more “hyperbolicky” behavior when we removed the front end delay, and particularly when that was interacted with not providing the implied interest rates of each choice. We were not wedded to one hyperbolicky specification or the other, and did not expect the exponential model to be completely overwhelmed by the alternatives, but we did expect to see much more non-constant discounting. We therefore examined the literature, and tried to draw some inferences about what might explain the apparent differences in results.

…[Literature survey] We ignored all hypothetical survey studies, on the grounds that the evidence is overwhelming that there can be huge and systematic hypothetical biases, and it is simply inefficient to repeat those arguments and waste time taking such evidence seriously. [Like prisoners doing a long sentence, and knowing the jokes and arguments of cellmates by heart, we would rather just point to surveys and evaluations of the evidence in Harrison [2006] and Harrison and Rutström [2008b].] We also focused on experiments, rather than econometric inferences from naturally occurring data, because those data are easier to interpret and have generated the conventional wisdom.36 We excluded studies that did not lend themselves to inferring a discount function.37 Finally, we excluded any study that used procedures that were patently not incentive- compatible or that involved deception.38

…One conclusion that we draw is that virtually all previous evidence of non-constant discounting comes from studies undertaken with students. We therefore conducted a conventional laboratory experiment, described below, using the same procedures as in our (artefactual) field experiment but with students recruited in Copenhagen…In order to determine if the evidence for non-constant discounting, such as it is, derives from the general focus on students samples, we replicated our field experiments with a student sample in Copenhagen recruited using standard methods.39 The experimental tasks were identical, to ensure comparability. Table 7 lists estimates from the student responses of the basic models in Table 1. The background risk attitudes of this sample were virtually identical to those of the adult Danish population.40 The results are clear: we obtain no evidence of quasi-hyperbolic discounting, no evidence of fixed-cost discounting, and no evidence of simple hyperbolic discounting. We do observe some non-constancy of some discount rates with the Weibull discounting specification, although the overall effect of the student sample is not statistically significant, as shown by the p- value of 0.18 on the null hypothesis that the specification is actually Exponential.41