Hyperbolic Discounting: praxeological reasoning and the nature of hyperbolic discounting as inherent to the axiom of action

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wegreenall Posted: Sun, Jan 6 2013 10:52 AM

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A friend an I, he an economics graduate, were recently discussing the phenomenon of hyperbolic discounting. At first it seemed so bizarre to me this idea, but something in the back of my mind made me feel as though it was actually perfectly consistent with praxeological reasoning and in fact that hyperbolic discounting is, as is time preference, inherent to the axiom of action.

After a while of thinking about it and having searched a few times for "hyperbolic discounting austrian" etc. on the internet I found no explanations of this phenomenon - the only thing i found was a blog on here of Don Lloyd saying that it was the reader's "homework" to find out the connection between action(in his terms, the subjective theory of value, which I don't currently see as a necessary qualification) and hyperbolic discounting.

As far as my reading has gone at least on Mises' and Rothbard's analyses of time preference, in almost all cases any practical references to time preference have referred only to a pair fo points in time, such as the example of Mises' when he refers to time preference of an acting man(/woman) preferring 104 dollars in a year rather than 100 dollars now, with the implication being that he/she would prefer 100 dollars now rather then 103 dollars in a year. This example is perfectly understood and a very clear exegesis (love those Greek words!) of time preference. Hyperbolic discounting of course is conceivable only in the context of 3 or more different values. If you were to look at a curve of the discounting factor of someone who exhibits hyperbolic discounting, you could see this phenomenon, but the curve that joins only two points cannot be ascertained at all - it could even be a linear curve, but nobody has claimed that we actually exhibit linear discounting.

In light of this then, I applied my thought to it and read the sections on time preference in Human Action and my (first) volume of Man Economy and State (I know, to a certain extent the same thing, but sadly my library isn't large enough to do any really extensive reading, and i don't have  Boehm-Bawerk's book) as well as Mises' analysis of Bawerk's view in his appendix in Human Action.

Unfortunately none of my friends have the relevant experience in praxeological reasoning to really test my ideas against, and so i turn to you all in order to try and settle this question.

So, first of all, when we act, we necessarily conduct action via the dimension of time, if you will. We cannot but act in time, and time is always passing us by. It is however something that needs to be economised. It is natural that the economisation of resources in our actions that take place via time, and the analyses of this, have not taken into account temporal flow (as it were, i'm sure there is a more proper terminology) as separate from action because in no conceivable world would the economisation of time be separate from that of resources. The choice to put the first horse to work on the most important need inherently contains the concept of "first" in a temporal sense. In a sense man is economising both time and resources at one and the same time. The fact that neither of these things can ever be separated in the realm of actual action is the reason no one has referred to the "simultaneous" but separate economisation of time AND resources.

References to these phenomena (Rothbard) have stated that a man for whom time was scarce would cease to be able to act because time preference would fall to zero. This however is, in my opinion, the result of a lack of separation conceptually between the economisation of time relative to the economisation of other resources.

As in all metaphors or examples, we have to suspend some specific factors to make the model believable. It is clear that here the theory is most likely to err, and so I shall try to be very careful in my wording, but this is the part I need some help on. Consider a man for whom time was not a scarce resource. He would live forever and his health would in no circumstance deteriorate. This of course would affect the judgments he would make as to his values, (such as questions of nutrition) but the ends themselves are not currently relevant. Despite his time being infinite, in a sense, he would still necessarily act in a certain temporal order. His resources would still have a diminishing marginal utility. Time's infinite nature to him would not allow him to act twice simultaneously. His needs are dealt with in order of their importance to him.

The obverse of the same is the question of a man with "infinite" resources, but limited time. In such a case he would still tend to his most important ends FIRST. Notice that the action itself has not changed, but in each case he is economizing each resource separately. In each case, the finite resource is being economised, whereas the infinite resource cannot be, it does not need to be. Once we see this, then, time can be considered the same as any other resource. It is the fact that it constantly passes us that confuses us in this judgment, but this does not change the nature of its role as a resource.

Another way of looking at it becomes a little more abstract. Consider a man who was outside time, but had time as any other resource. In order to conduct an action, he would take means x, y and z, and put them together to produce his end. Now imagine any of these resources as being time. It is of no importance which one it is, but this conception could be used to more clearly view time as a resource just like any other.

If the previous reasoning is consistent and correct (that's your job, to help me analyse it!) then time also has a diminishing marginal utility. Constant marginal utility would be shown by "exponential" discounting, that is a constant rate of discount between time points x, y and z. A diminishing marginal utility (which we understand as the nature of any good) is reflected (as the mathematicians put it) as a hyperbolic discount rate, that is, an increasing discount rate over time. Therefore, the action axiom contains within it the assumption of hyperbolic discounting.

I appreciate the length of this post is not conducive to casual reading, but I greatly appreciate the time of those who sit to read all of it, because I think it could be useful, and also it's a nice way of testing my own reasoning against others who have more of an understanding of praxeological reasoning. I don't mind if this all gets blown to bits by more consistent logic, I'm just curious as to whether it could be useful as an exposition of hyperbolic discounting.

tl,dr: hyperbolic discounting is inherent in the action axiom, because time is a resource like any other. It just doesn't look like it.

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Neodoxy replied on Sun, Jan 6 2013 11:10 AM

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So I think I'm missing something here: What exactly is hyperbolic discounting?

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z1235 replied on Sun, Jan 6 2013 1:00 PM

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Interesting, but I don't think diminishing marginal utility could be applied to time as a resource/means. One important distinguishing characteristic of time against all other resources/means is that it is essential and necessary for action (almost by definition). You may choose between a banana and an apple as means towards the end if extinguishing your hunger but you have no choice about using (the resource/means) of time. No end could be met without the means/resource of time. 

As for hyperbolic discounting or any time-inconsistent model of discounting, I think the best explanation is the one from risk and uncertainty (Explanations => Uncertain Risks towards the end of the wiki link). In the example of hyperbolic discounting at the beginning of the wiki link, an agent prefers $1 today (t = n) to $3 tomorrow (t = n+1) but prefers $3 one year + one day in the future (t = n+366) to $1 one year later (t = n+365). This makes perfect sense to me as the increase in risk/uncertainty between 365 and 366 days in the future is insignificant compared to the increase in the reward (3x), whereas the increase in risk/uncertainty between 0 and 1 day in the future is much larger and may warant taking the certain $1 today vs. waiting for $3 tomorrow. 

In short, discounting is time-inconsistent because risk/uncertainty increases exponentially with time. 

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wegreenall replied on Sun, Jan 6 2013 1:50 PM

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I suppose you're saying then that the power by which the exponential factor (i don't like talking in these terms but it seems frustratingly necessary considering the phenomenon we're trying to describe) increases tends towards zero the lower the amount of risk there is. But what about in the ERE? Discounting, ie the effect of time preference would still occur - for the same reason interest would exist in the ERE. Would the hyperbolic tendency move towards an exponential tendency? (awful phrasing, I know)

As to your first point, the choice of using a supply of a good to satiate a need or not is separate from the praxeological notion that  you necessarily satiate the most important need first. Whilst you don't have a choice, your use of time is still put towards the most important needs necessarily, again by definition. It's a strange idea to think of time as a resource because it doesn't act like a resource - I suppose i was trying to deal with this question by considering the (admittedly non-existent, bizarre) conditions in which it would act JUST like a resource of another kind, and show that the criteria by which we describe it as not a separate resource aren't so valid as those which would suggest it IS treated like a resource.

There is one other argument which is rather poor but i suppose it might be useful; why are labour saving devices important if not for a varying "utility" of time? Why does time need to be economised? How would the hyperbolic discounter act in choosing an output after time x compared with a similar output relative to time y. How would he value one over the other? Shorter processes compared to longer processes are beneficial when the returns are the same. What about process of similar returns between two periods in which the returns are similar relative to the changes in output? how would one decide between the two? Perhaps in the same vein as the praxeological category of time preference it is possible to say that man would choose the shorter period over the longer period EVEN THOUGH the returns are relatively the same because of hyperbolic discounting - this question needs some heavy reasoning applied to it. I need to read the Pure Theory again... but these are just some questions.

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z1235 replied on Sun, Jan 6 2013 2:58 PM

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wegreenall:

I suppose you're saying then that the power by which the exponential factor (i don't like talking in these terms but it seems frustratingly necessary considering the phenomenon we're trying to describe) increases tends towards zero the lower the amount of risk there is. But what about in the ERE? Discounting, ie the effect of time preference would still occur - for the same reason interest would exist in the ERE. Would the hyperbolic tendency move towards an exponential tendency? (awful phrasing, I know)

Yes, discounting would still occur in ERE but would be time-consistent (i.e. exponential) as all risk/uncertainty about the future has been eliminated. I believe that the ERE yield curve (the interest rate term-structure; the yield vs. maturity graph) would be a horizontal line at the level of the originary interest -- as opposed to the upward sloping one that typically exists in reality (which reflects risk/uncertainty about the future). 

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wegreenall replied on Sun, Jan 6 2013 4:55 PM

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Hmm. The example in the wiki article however refers to the uncertainty of receiving the later payment, but in all the examples of asking someone, you would receive answers that would reproduce the effects of hyperbolic discounting, even though the payment is (in the hypothetical question) guaranteed. I appreciate it's getting a little slippery here because we not only have to differentiate between two types of risk to the decision-maker (ie, risk of the need for the good in some intermediate emergency circumstance, and risk of the actual payment coming through), and also consider the difference between what people say they do, and what they actually do.

Firstly, discounting of course is not to do with the actual thing they will receive (of course, people can often be incorrect in terms of their discount factor, or a risk factor, which is in effect a function of the difference between the hyperbolic and exponential discounting) in the future but the expected result, and the question of "demonstrated preference" or demonstrated action has not been a criticism of the classic examples used to explain interest or discounting in the first place. The second problem, regarding the risk of being paid as a risk that needs to be factored in, is dealt with within the question (ie the hypothetical construct guarantees the payment, and hyperbolic discounting is still exhibited). The third question then regards the case of general uncertainty. The commodity often used is money, whose (by definition) usefulness is based on its exchangeability. What if the commodity used was a different one? A commodity that could be considered desirable but was not money and so the questions of its usefulness in "risky periods" between now and the future point in time could be ignored? Perhaps this would go some way in removing the question of risk... yet none of these things seems to suggest that the decision maker would necessarily exhibit an exponential form of discounting...? There is certainly no reason why an entirely different discounting function should apply to a monetary commodity rather than any other.