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By James Hamilton on Jun 14, 2012 with 4 responses

Modifying Hubbert’s Model of Peak Oil to Account for a Rise in Production Due to Higher Prices

Here I describe some interesting new research on modifying Hubbert’s model of peak oil to take into account the incentives for additional production that higher oil prices would be expected to bring.

A recent IMF Working paper by Jaromir Benes, Marcelle Chauvet, Ondra Kamenik, Michael Kumhof, Douglas Laxton, Susanna Mursula and Jack Selody begins by noting the trend in forecasts of oil production from the U.S. Energy Information Administration. In earlier years, these forecasts were primarily just extrapolations of trends in global demand, with the assumption that supply would grow as needed to meet demand. If EIA’s 2001 forecast had proven accurate, the world today would be producing about 100 million barrels of oil each day. The EIA forecast for 2012 has been revised downward in each successive year, and now stands just under 90.

EIA forecasts of total world oil production (in millions of barrels per day) for 2000-2020 as issued in consecutive years over 2001-2010. Source: Benes, et. al. (2012).

The IMF researchers note that although forecasts based on mechanical extrapolation of trend have done badly, so too have the pessimistic forecasts of geologist Colin Campbell, who expected his definition of conventional oil production to have fallen much more rapidly than has actually been observed.

Colin Campbell forecasts made in 2003, 2005, and 2010 of conventional oil production (in millions of barrels per day) as per his definition. Source: Benes, et. al. (2012).

Likewise, Kenneth Deffeyes’ (2005) widely cited adaptation of King Hubbert’s (1956), (1982) approach predicts a linear relation between total cumulative production (Q on the horizontal axis below) and the ratio of current to cumulative production (q/Q on the vertical axis). This too has proven too pessimistic, as production in recent years has been higher than such a relation would have predicted.

Actual and predicted values for the ratio of current to total cumulative oil production according to Deffeyes (2005) model. Source: Benes, et. al. (2012).

Another recent paper by University of Calgary Professor John Boyce documents a systematic track record of misses of the Hubbert-Deffeyes model, with the set-up ex post proving to have been too pessimistic when estimated for a variety of different data sets and sample periods. Boyce also notes that fitting analogous relations to agricultural production would lead to a prediction that production of each of 21 different crops is headed to eventual exhaustion, and notes that a variety of fully sustainable increasing production paths would appear to imply imminent resource exhaustion when confronted with the Hubbert-Deffeyes’ methodology.

The IMF team propose modifying the Hubbert-Deffeyes model to allow for a response of supply to the price of oil, where higher oil prices will (with a lead time of 4-6 years) stimulate higher production levels. They combine this with a traditional model in which demand for oil depends on growing GDP and the price of oil. The model strikes a compromise between the EIA and Hubbert-Deffeyes approaches, and has a better track record than either in simulated out-of-sample predictions over the last decade.

Forecasts of the Benes, et. al. model when estimated using data only up to a given date, as represented by different colors. Source: Benes, et. al. (2012).

The IMF model predicts that growth in demand will put continual upward pressure on price, with the inflation-adjusted price of oil headed for $180/barrel by the end of the decade. According to their estimates, those price increases would be sufficient to keep global production increasing at about the same reduced rate we have seen since 2004.

My view is that the IMF researchers’ approach is clearly better than the simple Hubbert-Deffeyes linearization, but may still be subject to some of the other problems documented by Boyce (2012), as well as the familiar challenges of statistically distinguishing supply and demand effects. Notwithstanding, the IMF research should help raise awareness of an issue that remains underappreciated by many economists, which is that we will eventually reach a point, and may have already, at which quite significant increases in price and improvements in technology can produce only modest increases in production, or may be insufficient to prevent outright declines in annual crude oil production levels. For those still in doubt about that possibility, I would again call attention to Pennsylvania, the place where the oil industry began in 1859. The price of oil today is 5 times as high in real terms as it was in 1891, and of course there have been tremendous technological advances in the century since then. But the state produced 8 times as much oil in 1891 as it does today.

Figure 3. Annual crude oil production (in thousands of barrels per year) from the states of Pennsylvania and New York combined. Source: Hamilton (2012).

We like to think that the reason we enjoy our high standards of living is because we have been so clever at figuring out how to use the world’s available resources. But we should not dismiss the possibility that there may also have been a nontrivial contribution of simply having been quite lucky to have found an incredibly valuable raw material that for a century and a half or so was relatively easy to obtain. Optimists may expect the next century and a half to look like the last. Benes and coauthors are suggesting that instead we should perhaps expect the next decade to look like the last.

This article originally appeared on Econbrowser.

  1. By Robert Rapier on June 14, 2012 at 3:41 pm

    For the record, I thoroughly debunked the standard model of the Hubbert Linearization in 2007: Does the Hubbert Linearization Ever Work? A lot of people were not too happy about it, as you can see in the comments, because I was challenging some of the peak oil darlings. But the ensuing 5 years has shown that I was absolutely correct about Saudi Arabia. There was no imminent plummet in production.


  2. By KLR on June 14, 2012 at 7:35 pm

    Mmm, calling Colin’s 2 year old forecast “inaccurate” is a bit silly/premature, no?  And his 2005 looks like it’s tracking just fine, albeit it’s Colin’s restrictive definition of crude, quoted in the paper:  ”based on EIA data but excludes heavy oil (<17.5 deg API), bitumen, oil shale, shale oil, deepwater oil and gas (> 500m), polar oil and gas, and NGL from gas plants.”  And biofuels too, I’m sure.  Interesting curve that results.  2009 and 2010 can be considered outliers so that’s 7 years his prediction’s held up; albeit we’re free to disregard it on the basis of being too restrictive, of course. 

  3. By David on June 14, 2012 at 10:15 pm

    It is interesting to me that these kinds of analysis are still not calculating in renewable energy.  Wind and solar costs have fallen dramatically, and continue to fall.  They are both similar to the cost of energy from oil (compare the per mile cost of a Nissan Leaf – with power coming from solar panels, or wind turbines – to a similar gas vehicle).  The costs on renewables will continue to drop – and battery technology will continue to improve.  Sooo – If oil prices rise significantly, the economic advantage will go to the alternatives – and the great switch to electrification will accellerate.  Surely this should be a standard piece of the energy analysis at this point, no?

    • By George Best on June 15, 2012 at 6:56 am

      It is interesting to me that these kinds of analysis are still not calculating in renewable energy. 

      Because these things are not oil. Nor is a lot of the stuff that is counted as oil nowadays like NGL’s etc.

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