Whither goest the price of oil?
What Went Wrong?
Farther down on this page, we present a model for the price of oil. That model was constructed about a third of the way through 2008. The price we projected for the end of 2008 was about $148/bbl. The actual price, as of the end of 2008, was about $50/bbl. We were off by almost a factor of three. What went wrong?
In a sense the answer is obvious: The housing market in the United States crashed, and the repercussions rolled like thunder through the banking industry, and the world economy tanked as a result. But that begs the question -- in terms of the model presented here, what changed which caused the price to be so far off?
One might at first guess that the magnitude of the elasticity of the price of oil increased radically. This seems plausible; during a recession people become more price-sensitive. So, elasticity increases, and that (somehow!) results in a price drop.
It's plausible but it's wrong. If elasticity increases, people become more sensitive to price changes. But the price of oil plummeted. If elasticity had increased, and nothing else changed, surely that would have resulted in increased consumption -- but in fact consumption plummeted, and OPEC has cut production in an effort to avoid even steeper price declines.
In fact the answer seems to be far simpler: Demand dropped, pure and simple. The year-on-year demand growth, instead of being small and positive, was large and negative. The model turns out to be extremely sensitive to a change in baseline demand: If we plug in a value of -2.5% for baseline growth in demand, in place of the default value of 1.79%, with no other change, the model's projected price drops to $50/bbl.
So what does this all mean, anyway?
In short, it means that the price of oil is very sensitive to world economic conditions. But more than that, it means that, if we dig into the new production and consumption figures (something I haven't done as yet), we'll very probably find that the actual rate of oil consumption hasn't changed all that much. A small drop in consumption can have a large impact on the price. But if consumption hasn't dropped all that much, then the longer term effects of peak oil -- and the consequences on the climate which stem from burning fossil fuels -- are not likely to have changed much, either.
One other thing deserves mention. Both baseline demand and long-term elasticity can change, and over the past couple years we've been seeing signs that they were changing even before the crash. While the worldwide recession has chopped the price of oil, the fact that, for a while, the price went over $100/bbl and the price of gasoline at the pump in the United States shot to several dollars a gallon had a major effect on behavior. Prices have come down since, but past experience indicates that the changes in behavior are likely to persist. We're seeing electric cars coming to market, we're seeing more interest in alternative energy supplies -- in general people are switching to a less petroleum oriented operating mode. That, also, is not accounted for in the trivial model on this page, and it may have a major long term moderating effect on oil prices.
For the time being, I'm not making any changes to the model, nor to the default assumptions. I'm leaving them as they are; it will be interesting to see if prices eventually rebound to anything like what the model predicted for the end of last year.
And now, here's the model.
today's world that's a fascinating question. There's a huge
amount of misinformation, disinformation, and just plain confusion on
the subject, which prompted me to try to come up with an answer on my
The problem the world is facing is that demand for oil is
continuing to rise, while supply is limited by the available
extractable oil. According to what is now conventional wisdom,
the "peak" in oil production should be occurring ... now
As you can find on some websites, the scenario which one then
imagines is that demand, continuing to increase, "tears away" from
supply; they no longer match, and prices head for the moon.
assuming we really are at "peak oil", what actually should happen to
prices? What happens when the "natural" demand for an item is
above the maximum which can be supplied? The answer depends in
the price elasticity of demand
. Demand (for most goods)
depends on the price; there really is no single "natural" level of
demand. The elasticity is the percentage by which demand changes,
for a given percentage increase in the price. Elasticity is
normally negative -- if the price rises, demand drops.
if we know the elasticity of demand, and we postulate a change in the
amount of a good for sale, we can determine what price people will be
willing to pay for exactly that amount of the good. That's the
price at which the market "clears" and there's no unsatisfied demand,
and no unsold supply. The trivial
model on this page uses that principle to determine the price of oil a
year from now:
- We have an idea what the growth in demand for
oil "naturally" would be, if the price were flat.
- We can
hypothesize that, because we're at "peak oil", the supply will not
rise to meet the demand, but will remain static.
- We have an
idea what the price
elasticity of demand for crude oil is.
- And from that we can
determine what the price should be a year from now.
now present the model (which is, indeed, trivial; the computation it
does consists of one line of PHP code). Later on the page we'll
present the formulas used, discuss the default values in the form
(which are my best guesses), and discuss vagaries which
may affect the actual price of oil.
The Formulas Used in the Model
to refer to total demand for oil (in barrels per day) and
to refer to the price per barrel.
The definition of the
elasticity is the percent change in demand, divided by the percent
change in price:
change is the total change
divided by the value, times 100. Since we're dividing one
percentage by another, the "times 100" factors cancel out. In
fact, unless E is constant, this definition of elasticity is only
really correct in the limit for very small changes in the price and
demand. For an infinitesimal
change we can rewrite the
formula in terms of derivatives, as:
Rearranging, we can separate P
Now, by making the entirely unjustified (but none
the less standard) assumption that E
is independent of the
price, we can easily integrate both sides:
This formula describes a situation in which the
price changes continuously from P1
and demand changes smoothly along with it, with the elasticity
remaining constant every step of the way. Alternatively, it
describes a situation in which supply
changes from Q1
, and price
follows along smoothly, which is
the situation we're interested in. Either way, it's not
completely realistic but it's close enough to be useful.
now solve for P2
To apply this to oil prices, we must make some
We first assume that the rate of oil consumption is
allowed to rise in line with rising demand for a year, while prices
remain fixed. Of course, this won't happen, but we pretend it
does, as it simplifies things for us. (In fact, since (5) is a
pure exponential, and Q1
exponential in the time which passes (they compound), we get the same
final result this way as we would by having prices rise smoothly
throughout the year.)
At the end of the year, the rate of oil
consumption is reduced
(or increased) to match the actual available supply of oil. We
assume the elasticity remains constant while the supply is reduced; in
consequence, the price
changes when that happens, and the new
price will be given by formula (5). We also assume the demand at
the beginning of the year is for 100 units (this value is arbitrary).
the values we plug into formula (5) to find the new price are:
The Starting Price
The default starting
price is currently set to the price of a 30 day oil future contract in
January 2008, which was around $95. That leads to a final price
almost $150/bbl, which is what we might expect to see in January 2009.
we set the starting price to what we were seeing early in April, 2008,
which was about $110/bbl, we find that the projected price for April,
2009 is about $170/bbl.
In January 2007, the price was around
$60/bbl. If we plug that value in, we get a projected price for
January 2008 of about $93/bbl -- which is very close to the actual
value! It would be interesting to see how the world oil
consumption rate changed from January 2007 to January 2008, but
unfortunately I don't yet have those numbers.
of Demand for Oil
The biggest unknown here is the price elasticity.
If one searches the Internet for anything having to do with
elasticity of oil prices, one finds several things.
elasticity of demand for gasoline was, historically, around
-0.2. However, I ran across a paper claiming that, in recent
years, its magnitude has dropped to a value roughly 1/10 that
size. This suggests that historical data may not always be very
useful in making projections about petroleum use! It also
suggests that something strange and rather disturbing is going on --
people are becoming less sensitive to the price of gasoline,
perhaps due to increasing prosperity.
- The elasticity of demand
for crude oil depends on the grade. Demand for light,
sweet crude is less elastic than demand for sour crude, perhaps because
many refineries require the better stuff and can't function without
- Overall, the demand for crude oil is far less elastic
than the demand for gasoline: Values I found ran from -0.01 to
-0.04. These are incredibly small magnitudes; they imply that
when the supply changes, the price moves between 25 and 100 times more
than the degree to which the supply changed.
and short-run elasticity of oil demand are very different.
We've been talking about the short-run elasticity.
In the short run, it's very hard to reduce oil use; there is no product
which can be substituted for it without substantial changes to many
systems. However, over the longer term it is practical to move
away from oil use for many things, and the long-term elasticity
reflects this: Its magnitude is believed to be far larger than
the short-run elasticity. Long-run elasticity may
be close to -1.
Unfortunately I didn't find a good definition
of the "short" versus "long" run, and the distinction seems a little
vague at best. In any case this suggests that using the short-run
elasticity to project oil prices probably won't work well for periods
of time longer than a few months or a year. For longer periods,
one should use a larger magnitude for elasticity.
isn't constant in any case. As prices rise, the magnitude of the
elasticity also usually rises.
The classic example of a "totally
inelastic" good is a heart. If you need a heart transplant,
you'll pay any price for the new heart. On the other hand, if you
don't, then you won't pay anything for a new heart. Consequently
the demand is claimed to be completely independent of the price.
But ... it's really not.
If the price of a new heart rises to $20,000,000, the demand will
drop off -- almost nobody will be able to afford one. So, if the
price rises high enough, the magnitude of the elasticity also rises to
some nonzero value. The same is true of food -- at high enough
prices, many people cannot afford the food, and starve; at very high
prices the elasticity is nonzero, even for necessities.
if the price of oil rises high enough, consumption will drop
off radically. In projecting a year or more out, we're
considering price changes which may be on the order of a factor of 2 or
more. That may very well be a large enough change to affect the
elasticity of demand, so our assumption of constant E may not be valid.
If so, that would suggest that prices may not go as high as
predicted by the model.
The value I chose for the default,
-0.04, is the high end of the magnitudes I found mentioned on the Web
for crude oil. My primary reason for picking this value rather
than, say, -0.02 (the middle of the range) or -0.01 (the bottom of the
range) is my gut reaction to values that small: I just can't
believe it's really that
inelastic! I also had another,
more rational reason, which is that we're considering prices in the
course of a full year, not just a few months. This is a long
enough period that we could very well be seeing the effect of the
long-run elasticity of demand for oil creep in. Since the
long-run elasticity has much larger magnitude than the short-run
elasticity, that would have the effect of raising the magnitude of the
effective elasticity. Thus it might be that we should actually be
using an even larger value for elasticity here, which would in turn
result in a lower final price.
Historic Oil Consumption Growth
I located a table, here,
showing world oil consumption dating back to 1960. The annualized
compound growth rate for all years in the table is 3.08%.
However, the growth rate from 1995 to 2005 was smaller: it was
One might wonder if recent slower consumption rise rates
might be due to rising prices. Perhaps we're already looking at
the consequences of the nonzero elasticity in petroleum demand.
located table of historic oil prices here
and looked for periods when prices weren't rising. It turns
out that from 1988 through 2003, prices were fairly level (though they
jiggled up and down a bit). From 1991 through 2001,
inflation-adjusted prices were nearly level, and from 1992 to 1999
prices were relatively flat in nominal
From 1991 to
2001 demand grew at 1.42% per year. From 1988 to 2003 it grew at
1.36% per year. And from 1992 to 1999, it grew at 1.65% per year.
this, we might conclude that the "natural" -- constant-price -- demand
growth rate was about 1.5% or 1.6% during the 1990's. However,
since the data from 1995 to 2005 spans a more recent set of years than
that, and demand grew faster during that period than it did in the
earlier years despite increasing oil prices, it seems more realistic to
use the value from that period. So, that's what I've used for the
default demand growth rate.
Income Elasticity of Demand; China
and India: Wild Cards
The concept of elasticity can be
applied to more than just prices. In particular, one can consider
elasticity of demand. When income increases,
the capability to buy goods increases. When world income
increases, world oil demand increases as well. The ratio of the
percent increase in demand resulting from a particular percent increase
in income is the income elasticity of demand.
The income elasticity
of crude oil appears to be substantially higher than the price
elasticity. Consequently, when world income increases
significantly, demand for oil increases significantly as well. If
consumption is restricted by supply lagging the new demand, the result
is a large increase in prices.
This issue is particularly important
with regard to the developing world, and in particular it is
significant with regard to India and China. While demand for oil
in Europe and the Americas has been increasing at a relatively even
rate for many years, and may even have dropped slightly in the past
year, demand from India and China is moving in tandem with the rapidly
-- and recently -- increasing incomes in those countries. This
could push the constant-price increase in demand up well above the
"historic" rate of increase, which was dominated by demand from the
United States and Europe.
To put it simply, "new" demand from
China and India may result in world demand growing by a lot more than
the 1.79% I used for the default value.
As I mentioned earlier, it's widely believed that oil
production is "peaking". This was originally based on
sophisticated models of the petroleum industry, and I'm not in a
position to second-guess that modeling. However, we can simply
look at recent news to get an idea of whether this claim looks
- Saudi Arabia, Russia, and Mexico are having a
hard time maintaining their production levels.
- Saudi Arabia is
finally opening up their next-to-last large field, the Khurais field,
which will require water injection from day 1 to get the oil out.
This will require an enormous engineering effort on the part of
Aramco. They have put off tapping this field for quite a long
time. They are probably looking at declining output from their
existing fields, which is one major reason for bringing this field on
stream now; they are also looking for ways to meet world demand, which
continues to increase. Without opening up new oil fields, they
can't turn up the flow rate beyond where it currently is.
has just made a much-ballyhooed find: Perhaps 40 billion barrels
of oil have been discovered. But it's under a mile of seawater,
and it's not going to hit the market any time soon. Furthermore,
it's not going to be easy to get the oil out, and it's quite likely
that no more than half of it will actually be recoverable (and I've
read claims that as little as a third may ultimately be recovered).
So, we're looking at maybe 20 billion barrels of recoverable oil,
which won't be available for years (it takes a while to open up a deep
ocean field). World oil consumption is about 30 billion barrels
per year. So, the new field in Brazil could supply world oil
demand for about eight months ... and the last reported find of
that magnitude, anywhere on Earth, was decades ago.
of this is conclusive, of course, but it seems to fit with the claim
that oil production is at a peak, and it can only go down in the coming
years as the huge oil fields we've been drawing on gradually run down.
What Can We Do About It?
As a purely passive thing, I suppose you
should avoid making long-term investments in airlines or oil tanker
operators. The former will suffer if oil hits $170/bbl, as the
default values for the model suggest; the latter may find there's less
and less oil being shipped around the world if supplies are indeed
Something you can do which is more active, and
which also helps with global warming, is conserve. And the best
way for you as an individual to do that is to switch to a plant
. Raising animals for food consumes an enormous
fraction of the world's petroleum supply; see the FAO report, Livestock's
. It's a rather lengthy report, but there's a
short summary page on it here
Page created on 4/25/2008. Added "What Went Wrong?" box, 1/25/2009