New School Economic Review

Don’t get a Bachelors if you discount by 6-7%

by Benjamin on August 8, 2009

I have today discovered that my discount factor of future income is less than 6-7%, because I would tell my kids to do their homework and stay in school… If I was to discount future income by more than 6.56% I would not send my daughter to do a B.A., but rather would put her into the maximum allowable full-time work under New York State labour laws from the day she starts school, and let her fail after 9th grade. Her discounted income from the two activities equal out at the 6.56% discount rate. Similarly, due to gender differences in U.S. median wages, my son shouldn’t try to get an undergrad degree if my discount rate is more than 7.95%. While a Masters degree increases the discount rates, a Ph.D. is not at all desirable for the boys out there (anything above 7.2% rate equalises the return with dropping out at 9th grade), while a masters degree or Ph.D. is almost the same for girls (7.1% and 7.08% respectively).

If my child is lazy – the genetics factor works against me here – and therefore wont work full-time during their school years, my discount of the future would have to be considerably higher for allowing them to fail school. In fact they will be encouraged to get some form of education, as the BA requires a whopping 14.86% discount of the future for boys, and 13.61% for girls to give the same return as dropping out. If my discount rate was a bit lower, say 10.66% (boys) or 11.1% (girls), I’d discourage the Ph.D., but still go for the Masters…

This is either a fun example of why discounting isn’t such a great idea for long term projects; or it’s an example of the governments belief in the rational behaviour when they instituted 12 years of compulsory schooling – although the NY legislative forgot about it when they set up the child labor laws of the State.  Below is the full table of discount rates which would equal out a degree holders gross 2004 median income and years in school.

I could play with the data to get net rates of pay, change my assumption of retiring at 64, get regional specifics etc, but I just wanted to make this point, and happily share my excel calculations, sources and data-set here, so you can play with it. Beware the Long-term discounter…

Ramsey didn’t discount over time

by Benjamin on July 1, 2009

Frank Ramsey (1928) condemned the use of a discount factor to the utility of future generations. However, for postwar growth economists, who consider Ramsey to be one of their patron saints, the discount factor, applied either to individual‘s or to social planner‘s decision making, is a technical requirement of dynamic general equilibrium models.

That is part of the story told by Pedro G. Duarte (University of São Paulo, Economics Dept) at this weekends History of Economics Society conference, and it is a particularly poignant argument, seeing the discounting debates currently taking place in areas as diverse as ressource economics and microeconomics.

Ramsey “assumed that we do not discount later enjoyments in comparison to earlier ones, a practice which is ethically indefensible and arises merely from weakness of the imagination” (Ramsey 1928, 543). But he was still able to solve the micro model mathematically, through a method forgotten perhaps by todays modellers who find the discount factor essential… More details in the paper below.

Duarte, Pedro G. 2009. “A Path Through the Wilderness: Time Discounting in Growth Models.” Presented at History of Economics Society Annual Conference 2009: Denver, CO: http://hes-conference2009.com/papers/SAT1E-Duarte.pdf

Ramsey, F. P. 1928. A Mathematical Theory of Saving. Economic Journal 38.152:543-59.

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.