Discount your kids? (!)
From the Economist’s Green.View - How to Value a Grandchild:
When economists do a cost-benefit analysis, they try to place a present-day value on benefits assumed to be enjoyed in the future. To do this they discount the future value by an annual percentage rate, a discount rate, which is typically set at around 3-5%.
But such calculations are typically done for benefits expected to come in 20, 30 or, at most, 50 years’ time. Climate-change economics requires a time horizon of centuries. A typical discount rate would assign almost no current value to benefits accruing in, say, the 23rd century. So why spend money today on something with no apparent value today?
Sir Nicholas argues that, in this case, we are wrong to use a typical discount rate. How can we say that our great-great-great-grandchildren are worth less than we are worth ourselves? He argues for a discount rate of 0.1%. That places a much higher present-day value on benefits accruing centuries into the future, and thus makes a stronger case for spending money now.
Now I’m a huge believer in the value of discount rates. I spent most of my career (as a fixed income trader) eating, sleeping and breathing discount rates. Net present value is the prism through which I look at pretty much every economic outcome… and yet. And yet, the notion that there is no (net present) value (NPV) in future generations - which to be fair is the logical reductionist conclusion one would come to by mechanically applying a conventional discount rate to the economic value a century or two forward - is so obviously wrong. Probably a doctoral thesis in economics in there somewhere to explore and articulate why and when the concept of NPV breaks down. Some sort of generational phase transition? Akin to classical physics giving way to quantum physics past a certain threshold?
But whether or not there is a Nobel prize up for grabs in working the details out, I think most of us will be able to get along with no more than the idea that, in the long run, if we’re all dead, everything else is well…moot.
I’d love somebody to articulate it better (I like to think I could but I’m lazy…) because I remain staunch in my belief that understanding and harnessing the power of NPV is the key to financial success and security in our world. (And if understanding this concept was made a requirement of gaining a high school diploma, that there would be a much smaller pensions crisis and fewer millionaires on Wall Street or in the City…) But refuse to subscribe to the dismal dogma that says I should apply this thinking with just as much zeal to value my future descendents. If that’s being hypocritical, well then so be it. But I’m certain it’s not… proof welcome!
(btw ever hear of Hugg? does the world need a ‘green’ Digg?)
February 21st, 2007 at 7:33 pm
You wrote this post on Dec 7, 2006 and the NYT has a piece on Feb 21, 2007 concerning the issue of discount rate used in global warming:
http://www.nytimes.com/2007/02/21/business/21leonhardt.html
-JD
February 22nd, 2007 at 4:59 pm
Thanks for the pointer. It’s good to see the mainstream press picking up on these issues with an intelligent and clear articulation of the debate.
When I read the article, I stumbled over the ‘dinner-out-today’ vs. ’saving-for -future’ argument: at first reading it seemed reasonably logical but felt wrong - like one of Escher’s drawings…and because of this I went back and pondered it a bit more. The author writes:
Indeed this misses the entire point of looking at value through an NPV prism. Firstly $1000 in 100 years time is exactly equivalent (in NPV terms) to $50 dollars today assuming a discount rate (ie nominal investment returns) of around 3% - ie unless the price of health care, education or a supercomputer falls dramatically in real terms (which of course is possible,) the great-grandchild is only going to get ‘$50 dollars worth’. The whole idea behind using NPV is to bring everything into a common and unique frame of reference. Equivalence is equivalence (at least mathematically.)
Secondly, is the question of utility; here the author didn’t need to jump 3 generations (mucking up the NPV concept and introducing extra complications) to make his point. Imagine the argument transformed to one lifetime. Dinner today or dinner 20 years from now, when we really don’t feel like cooking…the math remains very simple. Our $50 today will be worth some given amount in 20 years time as a function of the average investment returns (or losses); the key question is what hurdle rate should one set (and what probability to give that our investment choices will beat said hurdle rate) to judge whether not going out to dinner tonight will be worth it.
In the (selfish) continuum of one life, the hurdle rate actually needs to be set a bit higher that the ‘risk-free’ 20 year rate, especially as one gets older/lives a riskier lifestyle…utility of the forward consumption drops to zero upon death. (The old ‘you-can’t-take-it-with-you’ or ‘a-bird-in-hand’ paradigm…) Getting this balance right is at the heart of maximizing the value of one’s earnings and savings. I think most people would understand this intuitively but get tripped up in the mental arithmetic and escheresque properties of NPV and so are unable to implement an optimal balance between investment and consumption over time (to the great great financial benefit of the few that do I might add…) Indeed that is why I picked up on this point so extensively here: embedded in an otherwise intelligent, well-written, authoratative article, most people would have accepted the logic as presented above as given.
As for the complications engendered by jumping generations, this is actually - and unintentionally - a more interesting question and what I was trying to discuss in my original post. My point / question is that it is a much thornier - and philosophical not mathematical - problem to put a value on competing claims between generations. Indeed the point of agreement on the climate change debate as reported in the article - that the potential (even if reasonably remote or manageable) for catastrophic/unknowable consequences is reason enough to act - is in my view a special (more easily understood or digested) case of the more general inter-generational discount case. Ie If the future outcomes are described by a probability surface of future value/utility, we can agree (ethically) to try to avoid any zero-value future outcomes. (Ie don’t blow up the planet, at least not without a watertight plan B!) It’s a starting point…