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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).
Laxton1.gif


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).
Laxton2.gif


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).
Laxton3.gif


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).
Laxton4.gif


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.



James D. Hamilton has been a professor in the Economics Department at the University of California at San Diego since 1992, where he also served as department chair from 1999-2002. He had previously taught at the University of Virginia and received a Ph.D. in economics from the University of California at Berkeley in 1983.

Professor Hamilton has published articles on a wide range of topics including econometrics, business cycles, monetary policy, and energy markets. His graduate textbook on time series analysis has over 10,000 scholarly citations and has been translated into Chinese, Japanese, and Italian. Academic honors include election as a Fellow of the Econometric Society and Research Associate with the National Bureau of Economic Research. He has been a visiting scholar at the Federal Reserve Board in Washington, DC, as well as the Federal Reserve Banks of Atlanta, Boston, New York, Richmond, and San Francisco. He has also been a consultant for the National Academy of Sciences, Commodity Futures Trading Commission and the European Central Bank and has testified before the United States Congress.

Editorial Notes: Also posted at Consumer Energy Report. -BA

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