How much is our distant future worth?

In the first Superman movie, released in 1978, Lex Luthor, the supervillain played by Gene Hackman, buys up large swaths of real estate in the deserts of eastern California and Nevada. His plan is to hijack a nuclear missile and use it to cleave off coastal California into the Pacific Ocean, leaving him with newly valuable beach-front property. Well, maybe all Lex really needed was patience, not a nuclear device.

One new report estimates that – on the current path – perhaps $500 billion of U.S. coastal properties will be below sea level by 2100. (Of course, as Luthor would surely tell us, the disappearance of the current coastline would raise the value of property that is currently inland. But that’s beside the point.) We have plenty of other longer-run worries, too; like surviving a future asteroid hit (an event like the Tunguska blast of 1908 – perhaps 1,000 times more powerful than the Hiroshima bomb – probably occurs every 1,200 years) or managing radioactive waste (which can be toxic for tens of thousands or even millions of years).

How much should we care about such big threats that are potentially far off in time? How much ought we spend now to avoid a $1 worth of damage hundreds of years in the future? 

This is a complex and controversial question. The answer depends on a variety of factors, including the relative affluence of our descendants and the degree of uncertainty about the future. If our descendants, the future population of earth, will be far richer than we are, perhaps they should bear a larger part of the adjustment burden. However, postponing investments in public safety may not be desirable – or even possible – if the future threat is cataclysmic (think of the dinosaurs who disappeared 66 million years ago!). Campaigning for more spending on space exploration now, physicist Stephen Hawking has argued that human beings “won’t survive another 1,000 years without escaping our fragile planet.”

To simplify the question, imagine that the only thing we care about is the present value of the losses associated with a preventable future disaster. The chart below shows the present value of a $1 of loss occurring at time t at various discount rates. For example, at a discount rate of 2% (the blue line), $1 of loss in 100 years would be equivalent to a loss of $0.13 today. For comparison, if the discount rate were 4% (the black line), the present value of the loss would be less than $0.02. Or, if the discount rate were only 1% (the red line), the present value would be $0.37.

Present Value of $1 At Time t Using Selected Discount Rates

Clearly, the discount rate plays a central role in determining what we should do today about future threats. For threats that play out mostly beyond a few hundred years, the discount rate is critical. The rapid decline of the present value at discount rates of 2% or more helps explain why some economists are cautious about spending now to forestall very distant future losses (including some of those associated with climate change). It’s the magic of compound rates in reverse.

But what is the appropriate discount rate so far out? How can we measure it?

This is a very fraught question on which there has been quite a bit of debate. There are a number of ways to try to answer this question.  One common starting point is to look at what market information has to say. To do this, you might look at the real (inflation-adjusted) yields on very long-term bonds, but the sample of bonds with ultra-long maturities is small. There are still a few British consols (perpetual coupon bonds that never pay principal) in circulation. As of July 29, the 2.5% coupon consolidated stock (some of which were originally issued in 1751) offered a nominal yield of 4.1%. But much of that appears to be compensation for inflation. The expected real yield would be 2.1% if we adjust for the current U.K. breakeven inflation rate – which is consistent with the Bank of England’s 2% inflation target – on the longest-dated U.K. nominal and inflation-adjusted bonds.

Economists have tried several (more sophisticated) ways to measure very long-term discount rates based on observed asset prices. One inventive paper examined the discount rates implicit in housing transactions in the United Kingdom and Singapore. In these two markets, property buyers can acquire either a “freehold” that is unlimited in time or a fixed-term “leasehold” that can last up to 999 years! By comparing properties that are leased for hundreds of years with similar properties that are purchased without a time limit, the authors estimate the very long-term discount rate that investors implicitly use at less than 2.6%. Another approach involves constructing a theoretical model that links the ultra-long-term discount rate to the evolution of relatively short-term interest rates for which data are available. Using this method, one recent analysis put the U.S. long-term discount rate at about 2.1%.  (A thorough analysis of social discounting for public policy is available here.)

Importantly, the policy disagreements among serious analysts of climate change are closely related to the discount rates that they assume. One well-known report, which applied a relatively low discount rate of 1.4%, called for rapid, large reductions in carbon emissions to limit future losses associated with climate change. A different analysis based on a relatively high 4.3% discount rate called for a carbon tax only about one-tenth the level implied by the low-discount rate analysis. Why? The low discount rate puts a great deal more weight on losses that are predicted to occur hundreds of years in the future.

Of course, it’s not just about discount rates. It’s about the scale of future losses, too. If policy actions today can prevent a calamity that threatens life on earth, then most people (including us) might judge the appropriate discount rate to be quite low because we would not weight the value of future lives any lower than their own. And there’s at least one powerful reason to suspect that, like Superman’s nemesis Lex Luthor, today’s governments don’t weight those future lives sufficiently: our distant descendants don’t vote.