Discounting the far future

In 2011 Andrew Haldane and Richard Davies of the Bank of England (HD) presented research showing that, when making investment decisions, investors applied discount rates much higher than the prevailing interest rates, and that this gap was increasing through time. One way of looking at their results was as an increase in short-termism; investors were increasingly reluctant to make investments with a long-term payoff. This reluctance clearly has many implications, including making dealing with climate change even more difficult. Their work has influenced our efforts to build an economic model of long-term storage, another area where the benefits accrue over a long period of time.

Now, Stefano Giglio of the Booth School and Matteo Maggiori and Johannes Stroebel of the Stern School (GMS) have a post entitled Discounting the very distant future announcing a paper entitled Very Long-Run Discount Rates. Their work, at first glance, seems to contradict HD. Below the fold, I look into this apparent disagreement.

GMS take advantage of particular aspects of the residential property markets of the UK and Singapore. In these markets some properties are freehold, and some are leasehold, with long terms:

Leaseholds are temporary, pre-paid, and tradable ownership contracts with maturities ranging from 99 to 999 years, while freeholds are perpetual ownership contracts. The price discount for very long-term leaseholds relative to prices for otherwise similar properties that are traded as freeholds is informative about the implied discount rates of agents trading these housing assets. This allows us to gather information on discount rates much beyond the usual horizon of 20-30 years spanned by bond markets.

By which GMS mean more than a century:

We use these estimated price discounts to back out the implied discount rate that households use to value cash flows to housing that arise more than 100 years from now. We find the discount rate for very long-run housing cash flows to be about 2.6% per year. Interestingly, we find similar implied discount rates in both the UK and in Singapore – two countries with very different institutional settings.

2.6%/yr is much lower than the discount rates HD found, which is good news for, among others, climate change policy:

In particular, our estimate of 2.6% provides some empirically-grounded guidance for choosing discount rates to evaluate long-term projects where the benefits arise hundreds of years from now. While the full implications of our findings for climate change policy depend on the precise modelling of the risks inherent to climate change and housing, our result of low long-run discount rates provides early evidence that agents are more willing than previously thought to invest today for the benefit of future generations, particularly if such benefits occur with certainty.

There are a number of important differences between the investment decisions underlying GMS and HD:

• GMS study decisions about housing, almost exclusively by individuals in their private capacity, where HD study decisions about investments, mostly by individuals in organizations acting in their professional capacity.
• The very long term of decisions in GMS is somewhat illusory. Almost no-one buying a house expects that they, or even their grandchildren, will be living in that house in a century. The short term of decisions in HD means that the investor expects, indeed demands, to get the return on their investment in the near future.
• The reason for the price reduction of leasehold property as the remaining term of the lease decreases is that the asset is actually depreciating. The stocks studied by HD are (hopefully) appreciating.

I believe that HD is closer to the kind of decisions taken for long-term storage than GMS:

• Storage media have relatively short economic lifetimes, so long-term storage requires a series of short-term investment decisions, not a single long-term decision. Here, for example, is Urs Hölzle, a senior vice president of technical infrastructure at Google in an interview with The Register:

  The things you focus most of your time on are nine months out, like this is your next generation that you're right now developing and then there's what we call n-plus-one, that's usually where you work concurrently on the thing after that

  He's referring to overall computing technology, not storage, which would have a somewhat longer timescale, but still a series of short-term decisions.
• Management in organizations needing long-term storage tends to think in IBGYBG (I'll Be Gone, You'll Be Gone) terms, which is the underlying motive for the short-termism identified by HD. Taking decisions whose payoff occurs after the manager has moved on is pointless. IBGYBG doesn't apply to the housing investments GMS study.
• Providing the Kryder rate stays greater than the real interest rate, the impact of successive decisions on the overall endowment needed decreases through time. So the important decision is the first one in the sequence. This is similar to the investment decisions HD study.

Our economic models actually use Treasury bond interest rates, which are currently well below GMS's 2.6% let alone HD's rates. We model HD's short-termism using a planning horizon, beyond which benefits are ignored. Besides being simpler to program, we believe this better represents IBGYBG. But we haven't yet studied the effects of changing the planning horizon or of different interest rate models in enough detail.