On the Generational Discount Rate (and Zero Lower Bounds)

Wikipedia defines the social discount rate as “a measure used to help guide choices about the value of diverting funds to social projects. It is defined as “the appropriate value of r to use in computing present discount value for social investments.” Determining this rate is not always easy and can be the subject of discrepancies in the true net benefit to certain projects, plans and policies.”

The social discount rate often stars in discussions about climate change. Take the forceful argument against a carbon tax, from Jim Manzi:

Nordhaus offers a thought experiment to demonstrate just how unrealistic [such a low discount rate] is: Imagine a scenario in which global warming would lead to zero costs between now and the year 2200, at which point global economic growth would be permanently reduced by 0.1 percent — in other words, that economic output starting in 2200 would be 99.9 percent of what it would have been had there been no global warming. Under this scenario, how much should we be willing to pay today as a lump sum to avoid this cost? Using the assumptions of the Stern Review, Nordhaus points out, we would pay about $30 trillion, which is more than half of the world’s entire annual economic output. Thanks, but no thanks.

As it happens, I find it hard to square my (relatively) utilitarian bias with anything but negative inverse (back in time) social discount rates. However, I disagree with Manzi’s argument for several reasons. Most obviously, it falls flat once we note that tax has to be collected somehow and each dollar from pollution is better than one from income (why Manzi, a conservative, ignores this is beyond me). Climate disaster also poses a tail risk that can’t easily be imported into a standard discounting model. I also happen to care about the wildlife and natural cost of a solvable problem.

Many liberals – and perhaps the “we’re burdening our children with debt” conservatives – will jump at the idea of a high social (or negative inverse) discount rate. That, after all, means we shouldn’t invest in schools or roads, that we shouldn’t fix our power grid and build libraries. But that’s not what I’m arguing at all. In fact, I’m not arguing anything that has direct relevance to policy itself. I think it’s first important to design a more lenient intellectual framework for this discussion.

I’ll call it the generational discount rate: that is, how do we discount one unit of utility for a discretely antecedent generation from our own. (). Defining “generation” is difficult, especially with the rich web of relationships and obligations in the modern world. However, I’m making what will become a historical argument, so we can take the long view. So note “generation” as: the discrete time step at which the last person alive today dies. The next generation would begin sometime around 2130 (incidentally when the really calamitous effects of global warming will begin to emerge).

Of course, you’ll note, the “generational sequence” is path dependent, which results in an almost infinite number of “paths” back in time to a previous generation. Where you “start” tracing time is crucial in the discrete breaks between one generation and the next. However, this friction is largely an inconvenience that doesn’t alter the point I’m about to make.

Important to note is that the social discount rate is usually concerned with the rather tangible measure of “consumption”, whereas the generational discounting pertains to the the more metaphysical idea of utility. Ultimately, the philosophical idea behind consumption and utility are not too different: to what extent will we defer happiness today for even greater happiness tomorrow, an introductory finance book might ask.

Indeed, the idea of social discounting is intimately connected with that of redistribution. By ordaining a high social discount rate, other things equal, we’re bringing future consumption into the present. Similarly, someone could quite naturally define a “kinship discount rate” which measures the extent to which someone will be willing to help a friend or family member based on “steps removed”. This framework also – at the broadest level – captures modern redistribution. Americans pay lots into social security to help their own, and a little into USAID to help Ugandan peanut farmers.

Discounting, in some abstract sense, is therefore the key to understanding means of redistribution. The word normally concerns space (tax dollars from Beverly Hills to the Bronx; from America to Africa), but is of equal relevance to distribution through time.

Indeed, inequality through time is far deeper than that across space. Of America’s total output – ever – imagine the disproportional accrual to those by total luck living between 1975 and 2025. The incredible utility from modern American medicine, transportation, communication, and entertainment: freely available to all? That is the reason for against a positive generational discount rate (which values equal utility in generation t more than generation t-1). A low generational discount rate then suggests that, ideally, we should take some percent of our current utility and send it back in time. Not just to the first American; but to the first man.

(As an example, the total economic income earned by someone between 1950 and 2050 is far less than what I will earn ipso facto between 1995 and 2095. It is then incumbent on me to tolerate higher taxes in the future to equalize our income to the extent possible. That 25% of America’s elderly fall below the poverty line is sign that we should be expanding benefits in any “reform”).

From standard utilitarian creed, in which I fall, it is of unimpeachable ethic that I should sacrifice just a little bit of my happiness to help those slave to a Malthusian world. Here it becomes very clear, for physical and not economical, reasons why backward redistribution of utility (though impossible) – and not income – is the lowest common denominator. Were we to redistribute income, denizens of history would invest more and we ourselves would be richer. This derives from basic principles of time travel and spacetime to which neoclassical economics is immune. Therefore, I prefer to mull within a framework of utility which is, after all, the charge of a utilitarian.

But the generation discount rate can’teven if it is welfare efficient, fall below zero! This is the most damning zero lower bound, of them all: liquidity traps pale in comparison to the almighty generational discount trap! But, unlike the European Central Bank, when market conditions dictate you bring rates below zero, you should at least bring it to zero. And our current policy does not reflect this thinking, at all. The whole “debt is hurting our children” argument is crap because:

  • It’s only hurting American children. Chinese kids will do great from American interest outflow, thank you very much.
  • Our kids our going to be richer than us anyway, because of technology we invented, because of economic growth, and because of a million other things. We should do as much as we can to borrow from them!

Of course, not everyone can think like this. We’re not actually borrowing from our kids. America just has a low generational discount rate whereas China’s is quite high: it all has to balance out (it would be genius if we could all figure out how to borrow from our kids, but this would break the global zero lower bound).

But I told you, I’m not arguing against investment in research, education, and infrastructure. After all, I wouldn’t want all the generations to be “equally poor”. However, the next time we hear on the TV that the social security retirees are taking everything away from our youth, remember we are rich as we are today because of that generation. They gave us Microsoft and Apple, Netscape and Mosaic. Economic growth is path dependent, and if the previous generation were a bunch of bozos, we the millennials would be the poorer for it.

The answer to the tension between redistributing utility forward in time (until the zero lower bound, at least) and the need for economic growth can be realized from both a low generational and social discount rate (remember, one is backward and the other is forward in time – so it’s really the opposite). Here the length of one “generation” matters a lot, but that’s why I like my Randian definition: it concerns “we the living”. A low social discount rate means we build the roads for our kids and even grandchildren, it means we give them the education they need to prosper.

But a low – even zero – generational discount rate means we want to do our best to redistribute utility back in time. (Remember, in this little philosophical game, that means our future kids give us utility as well). That means, social security and Medicare are not in fact unethical. It means consumption for this generation, is what the driving policy ought to be.

The normative tension arises primarily from the definition of “generation”. Mine is rather long, and hence not dangerous. Thomas Jefferson thought a “generation” was 19 years, and that would be disastrously myopic under this framework. This is a subjective question for moral philosophers. But I will personally no longer bemoan the principle of “borrowing from our kids”. At 18, I am sure I and my friends will be largely responsible for repaying any deficits incurred towards elderly entitlements, but that redistribution is one utilitarians shall be thrilled to commit.

Think not just space, but time.

P.S. It really doesn’t matter whether you think “forward” or “backward” in time. A forward generational discounting (like the normal social discount rate) would result in a “one upper bound”, if you will.

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