Dithering with the Discount Rate

Dithering with the Discount Rate 

Recall that the discount rate is often taken as being large if the economy is expected to grow rapidly, or if we behave as if we don’t like giving money to future generations because they will be so much richer than we are, or if we prefer things now rather than later (so, essentially, we behave as if we are more important than future generations). The last of these is often the starting point for ethical critiques of such modeling and will come up again in Module 12. We won’t say too much here about our willingness to transfer money to wealthier people in future generations; but, that willingness won’t matter if future generations aren’t wealthier than we are. So, let’s take a look at the assumption of continuing economic growth.

Economists are surely correct—if you take a sufficiently broad and long view, the economy always has grown, as we have become better and better at providing goods and services for each other. Local reversals occurred, but the broadest trend has been upward.

The mere existence of this trend does not prove it will continue—when Dr. Alley was 20, he had been getting stronger and faster his whole life, and merely extrapolating those trends to today would make him a world-record holder in numerous athletic events, which did NOT occur.

But, economists not only see the trend, but they understand how new scientific discoveries and commercial innovations make economic progress possible as we invent and build, and pass on to future generations the roads and buildings, and the knowledge. Think of a smartphone, which is nothing but a little sand, a little oil, and a few appropriate rocks, plus an immense amount of accumulated know-how. Even with the recent shortage of rare-earth elements, there is little doubt that the world can produce far more smartphones than have been made to date, with more apps, contributing to economic growth in many ways.

However, some parts of the economy, such as fishing and forestry and farming and fossil fuels, are supported by much larger parts of the Earth. We have already seen that our energy system is grossly unsustainable—if we keep doing what we’ve been doing, the highly concentrated fuels that yield more energy than needed to extract them will run out as practical resources, possibly in decades, almost certainly before many centuries pass. Economists will rightly point out that resources don’t really run out; as prices rise, substitutes are found. But, an energy system that looks a lot like our current one is almost guaranteed to become impractical within a time frame that is short compared to the written history of humanity.

Many other human activities are unsustainable as well. We rely heavily on phosphorus for fertilizer (as well as nitrate; see below). The Earth has huge amounts of phosphorus, but almost all of it is very widely scattered and not even vaguely commercial at modern prices. We are using the concentrated deposits very rapidly. With enough energy, we could re-concentrate phosphorus we have scattered, or that nature has scattered, but that takes us back to the unsustainable energy system.

Many scholars have attempted to calculate the “ecological footprint” of our lifestyle—how much land and ocean is required to grow the food we use or the fish we catch, process our wastes and provide the other things we rely on. Typically, these estimates find that with our current practices and technologies, the Earth cannot support the population already here with the lifestyle we are living. And, with expectations of improved lifestyle, and the population growing, many people expect this imbalance to increase.

Video: Rabbits - Exponential Growth (2:50)

Technology is surely improving, as it always has, helping us deal with such challenges. But, as we bumped up against limits in the past, we used improved technologies, but we also used unoccupied space. Thus, when a shortage of natural sodium nitrate made fertilizing crops difficult, Fritz Haber figured out a new technology, using energy to convert the nitrogen from the air into nitrogen fertilizer. But, when the Yankee whalers could no longer find right whales in the Atlantic, the fleet moved to the Pacific and then into the Arctic. And for whales, when the whole ocean was utilized, that option was no longer available. True, we might have some huge breakthrough and start mining asteroids, or we might get nuclear fusion working to provide power. But without major jumps in technology, we are increasingly finding that wherever we go, someone is already there and using the resources.

Suppose we ask the question “Are there practical limits to growth, that will cause economic expansion to slow down, soon enough to affect the present value of events considered in the integrated assessment models?” You could probably find well-respected scholars making convincing but conflicting arguments that would give different answers to this question. The correct answer might be “No, there aren’t”, or “Yes, there are very strong limits that cannot be breached and that will be reached soon.” Or, the correct answer may be somewhere in-between, with the limits making growth more difficult in some areas.

Economists are well aware of these issues, and many informative discussions are available. You may be interested in the essay by R.M. Solow, 1991, Sustainability: An Economist’s Perspective, presented as the Eighteenth J. Seward Johnson Lecture to the Marine Policy Center, Woods Hole Oceanographic Institution, and available at many libraries and at sites on the web when we checked. Also see Nordhaus, W.D., 1994, Reflections on the Concept of Sustainable Economic Growth, in Economic Growth and the Structure of Long-Term Development, L.L. Pasinetti and R.M. Solow, eds., Oxford University Press, p. 309-325.

Some integrated assessment models, such as the DICE Model mentioned earlier (which you will work with in the summative assessment for this module), do consider the influence of limits to growth on economic expansion.  Indeed, the version of the DICE model we will use has the global GDP growing at increasingly slower rates as we move through the next century. Uncertainty about how GDP will grow means that such models may overestimate or underestimate the present value of future damages from emitting CO₂. However, other models have worked with the assumption that there are no practical limits to growth that will affect us soon enough to be included, using a constant discount rate over a century, for example. If we do hit limits to growth before then, such studies are underestimating the optimal effort to reduce warming now.

An extreme application of discounting can lead to absurd results. For example, with a constant discount rate, you could show that investing a penny now to stop the destruction of civilization 10,000 years from now would not be economically efficient. Such apparent silliness again is recognized in the research community, and motivates interesting scholarship, including the work by R.G. Newell and W.A. Pizer, 2003, Discounting the distant future: how much do uncertain rates increase valuations, Journal of Environmental Economics and Management 46, 52-71. They found that uncertainty about future discount rates translates into a lower discount rate over longer times. Importantly, this in turn almost doubles the estimated value of taking actions now to reduce global warming from fossil-fuel CO₂. See the Enrichment linked below.