Does
the World Bank overstate the cost of depleting resources?
Sometimes GDP stands for Grossly Distorted
Product. Suppose that Kazakhstan spends
$1 million to repair potholes in its highways.
Clearly, Kazakhstanis are not $1 million better off than they were last
year; the pothole remonti merely keep
the roads in the same shape as before.
In principle, we can correct GDP’s overstatement of
welfare by subtracting from it the $1 million.
This gives us net domestic product, or gross domestic product minus the
wear and tear of capital (“depreciation”).
Easier said than done. Measuring depreciation is a subtle business. My jalopy wears out a bit every
time that I can coax it out of the garage, so we might model its depreciation
as a simple function of time. But my
notebook computer worked perfectly for years until the day when I pressed the
Start button and the darn thing refused to wake up. Five years, zero depreciation; five years and
one day, 100% depreciation. This is
called the “one-hoss shay” model of depreciation, for reasons that won’t astonish
the Amish.
We’ve been talking about physical capital – things
that people make in order to make other things.
But Nature is an input into production, too. Kazakhstan lives on oil,
and it may lose a little of its livelihood every time it extracts another
barrel from the ground. Using up a
finite resource is also depreciation, so we should penalize GDP accordingly.
But how?
The most obvious way is to divide the value of the
oil remaining in the ground by the number of years of remaining use. If we have $20 million of oil in deposits
that we plan to exhaust in 10 years, then the annual depreciation of our oil
stock is $20 million divided by 10, or $2 million. We should subtract this amount from annual
GDP. Easier said….
One problem is to estimate the period of
exhaustion. Non-economists (some of whom
claim to be economists) divide the estimated amount of reserves by the amount
of annual extraction. If we have 30
million barrels of oil in the ground, and we extract one million barrels each
year, then the period of exhaustion is 30 years. This is the “static reserve index.”
Put
on your thinking cap
Looks good, but the index doesn’t always work. What do we mean by reserves? In its estimates of natural depreciation in the
World Development Indicators, the World Bank uses “proven reserves,” the
amount of oil that we can profitably extract.
But this depends on the price of oil and the cost of extracting it – two
factors that change over time. As a
resource becomes more scarce, its price rises, inducing discovery, innovation,
substitution and conservation, which increase the exhaustion time. (Indeed, the World Bank authors acknowledge this
point in their footnotes to the book that developed their methods of estimation, Changing the
wealth of nations.) The index ignores these price effects, so it
overstates the pace of depletion.
According to the index, we should have run out of
oil a century ago. Even today, the World
Bank adopts the 2005 static reserve index for oil, which is 16 years. But oil prices in the last 18 months have
halved -- hardly consistent with any perception among market players of utter exhaustion
by 2021.
In a way, the World Bank’s formula for depletion
cost – value of reserves divided by exhaustion time -- can give us good information. Given reserves if the exhaustion period is short, then the
estimate of depletion cost is high, which signals scarcity. But if exhaustion is centuries away, the
depletion cost is small, suggesting that we may have better things to worry
about. For example, the Bank’s static
reserve index for soft coal is more than four centuries. Maybe we should agonize more over oil than
coal.
So what does the Bank actually do? Does it calculate a depletion cost for each
resource based on its own period of exhaustion?
No. For every
resource and every country, the Bank caps the estimated period of exhaustion at
25 years. This virtually guarantees high
estimates of depletion costs for every nation, even those generating
electricity by burning their abundant supplies of soft coal. In fact, for coal, the Bank may overstate depletion
costs by a factor as large as 18. The World Bank has joined the Club of Rome,
which propounds Thomas Malthus’ theory that
natural resources are becoming scarce because the population using them is
growing more rapidly than they are.
I’m not arguing that coal is trouble-free. Burning coal emits particulates, sulfur
dioxide, oxides of nitrogen, and carbon dioxide. All are pollutants. But let’s not confuse the issue. The problem with coal is not that we are
about to run out of the stuff; quite the contrary. – Leon Taylor tayloralmaty@gmail.com
Notes
(1) Remonti is
Russian for “repairs.”
(2) The
World Development Indicators, one of the world’s most famous datasets of
national statistics, include estimates for mineral depletion and
energy depletion, which this post discusses.
The methods for computing these time series is in a 2011 World Bank book,
The changing wealth of nations: Measuring
sustainable development in the new millennium.
Appendix A discusses the
calculation of exhaustion time. The
authors explain that 25 years is “about” typical of the static reserve indexes
for most of the 14 resources considered (four in the energy depletion account,
10 in the mineral depletion account).
According to my calculations, the median value for the 14 exhaustion
times is 35, and the mean value is 69.
A more important point is
this: For an accurate
estimate of exhaustion time, why not compute a weighted average for
each nation, where the weight is the resource’s share of total value? For example, suppose that Country A had two
resources – soft coal (50% of total value remaining in the energy account;
exhaustion time 456 years); and oil (50% of total value; exhaustion time 16
years). Then the estimate of exhaustion
time in A’s energy account would be .5*456 + .5*16 = 236 years.
As this calculation suggests, a
problem with the 25-year cap is that it suppresses differences between nations
in depletion rates. We don’t get an
accurate sense of which nations face the worst depletion crises, measured as
the ratio of depletion costs to GDP, because nations with abundant reserves
have the same exhaustion time as nations with fairly scarce reserves. Wasn’t international comparison the whole
point of providing the World Development Indicators?
To justify its universal 25-year
limit, the World Bank argues that “under uncertainty, it is unlikely that
companies or governments will develop reserves to cover more than 25 years of
production.” It provides no evidence for this contention; one could hold as
easily that uncertainty makes at least some of these agents more likely to develop 25-year reserves, since they cannot count
on just-in-time inventories. A simple
example is the fund of resource rents that many nations (including Kazakhstan) develop
in order to compensate future generations for depleted resources, since they
cannot be sure that new technology will offset their losses. But suppose that the World Bank is correct: All governments and firms are myopic when
they are uncertain. Then wouldn’t we want to reduce their uncertainty by
supplying accurate estimates of depletion costs?
The next quote from The changing wealth of nations comes
closer, I suspect, to expressing the World Bank’s real reason for simplification: “From a purely pragmatic point of view, the
choice of a longer exhaustion time would require an increase in the time
horizon for the predictions of total rents.” In other words, the Bank wants to
avoid a lot of tiresome calculations.
But since it assumes a discount rate of 4%, the discount factor for year
26 is only (1.04)-26 = .36. In
any event, if the Bank is truly concerned that estimates of rents distant in
time may be inaccurate, then it should provide the estimates to the user with
its caveats and let her decide whether to discard the calculations. It should not pretend that the rents don’t
exist.
(3) In addition to oil, Central Asians may take
interest in the exhaustion times computed for gold (17 years) and silver (14
years). Since the statistics were calculated in 2005, they imply that we will run out of silver by 2019.
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