An Alternative to Discounting
by Benjamin on June 16, 2009
In a comment to the previous post, Brandt W noted that there are many humanistic factors which we can never fully appreciate or work into cost-benefit analysis. I would expect the standard reply by policy economists to be that cost-benefit is the best tool we have, and regardless of the factors we need a valuation which will allow us to guide policy. [Afavourite example is: If you could build a roadside barrier which would save 1 life per year on average (a tenuous method for approaching the costing side, which I will look at in a later post) and the barrier cost $1 would you do it? - ok... What if it costs one billion dollars? Would you still do it? If the answer is yes and no, then somewhere in the middle you must have placed a value on a 'life', and then the marginalist approach is to find that 'tipping point' and set the maximum cost of the project... and so we have cost-benefit]
Lets accept that argument for the moment, but then I think we need to consider the issue of discounting within the cost-benefit framework. Sticking with the barrier example, the modeler would then apply a discount rate to the value of life over time, and work out the ‘total’ benefit of the barrier.
I am not convinced discounting is the way forward here. I see the rationale behind discounting an asset over time at some given interest rate or depreciation, but surely a ‘life’ is not worth less in the future than it is now? From our current perspective dying tomorrow is preferable to dying today, but the loss and externalities will be the same when the even occurs, they will not have depreciated like some outdated computer, whose loss you might mourn as you nostalgically recall the happy days of playing pacman. The new computer will let you play the latest games and (hopefully) run Vista, it is inherently more valuable than the old machine. A new child is certainly a treasury, but no more so than the one who was killed in the accident. Let’s not even try to calculate the externalities associated with the death.
That ranting aside, at The History of Recent Economics conference I attendend this weekend, one presentation reviewed an alternative idea which is to avoid discounting. This was in the context that Ramsey (of the growth model fame) himself had been staunchly against discounting in macroeconomics.
The example given was for inputs, renewables like trees. If we apply a discount factor to the value of trees over time, and use cost benefit to decide when to chop them down, we will, regardless of how small the discount factor, predict a point in the future when all the trees are worth zero and chop them down before that point in order to maximize x.
x = (1, … , 1), (0, … ,0)
x = (0, … ,0) , (1, … , 1), (0, … , 0)
But if we do not discount the stream of wood taken out of the forests, we can still maximize x, but our consumption would be very different. We would consume the amount required to maximize the average inputs harvested per year, (or technically, you maximize the output in the limit).
x = (1/5, …, 1/5, … ,1/5)
Over time you avoid the (0, … ,0) period when there are no trees, which under discounting is irrelevant as the value of those inputs today is zero. Trust me, when we run out of rainforest, I get the feeling we will be rather dissatisified with that discount factor.
Tags: Cost-Benefit Analysis, Discounting, Growth, input, Ressources, Sustainable Development
Fair enough, I think the whole thing got a bit buried under text there. My (admittedly un-original) alternative was simply to not discount the input side of things.
So instead of looking to maximize the total benefit to us, as seen from today with a discount factor and expected returns (on some infinite or finite time horizon), the alternative is to apply no discount factor and maximize the total benefit over an infinite time-horizon.
That way you have to focus on creating the highest average output each time period, as this will maximize the benefit, and this means aiming for sustainable output. If ever we deplete a resource in this scheme it will give less benefit than even an infinitesimally small return each period. Of course a higher output is better than less, so we would be aiming to get the highest sustainable output.
A counter point might be to say that non-renewable resources should then be taken out all at once as they will yield the same benefit regardless of the infinite time as they have only a finite output. This is fair, but that is the conclusion under discounting anyway…
What do you reckon?
Is this the same method that Edward Prescott and Finn Kydland won the nobel for?
It’s not really the same, although they have these big simulated computational models, the consumers in their model do calculate their utility over an infinite time-span, but they discount that utility with respect to time.
Kydland in his Nobel lecture outlines a simple model where the utility function maximizes utility over an infinite horizon with a discount factor ‘Beta’ “The parameter ‘Beta’ is a number slightly less than 1 and can be calibrated from knowledge of the long-run real interest. It simply describes the degree of people’s impatience” noted Kydland (2005: 343).
They seems to have gotten the nobel for big (monte carlo type?) simulations with a lot of agents and a lot of firms responding to policy decisions which are built into the model. At least that’s how I am reading Kydland’s acceptance speech and lecture.
Kydland, Finn. 2005. “Quantitative Aggregate Theory.” Nobel Prize Lecture 8 December 2004: Web: http://nobelprize.org/nobel_prizes/economics/laureates/2004/kydland-lecture.pdf