August 15, 2007
Federal Reserve Bank of Cleveland
Peak Oil by Joseph G. Haubrich and Brent Meyer
Is the world running out of oil? when the actual numbers are exam- Though almost no one expects the ined: in 1950, years of supply stood at black stuff to literally stop coming out 22. In 1972, the supply was of course When will the world’s produc- of the ground anytime soon, some sug- not zero, and it had increased to 35 tion of oil peak, and what will the gest that oil production, having trended years; now in 2007, reserves stand at economic consequences be? Cal- upwards for the past century, will soon 40 years. (BP Statistical Review, 2007.) culating when turns out not to be reach a year of maximum produc- The problem comes in thinking of these so straightforward as it seems, but tion—a peak—and then decline. The proven reserves as a measure of the oil predicting the likely economic con- notion of a peak denotes a discern- left in the earth. Rather, as one expert sequences is—and they’re not as able change in the trend; as an alterna- puts it: “reserves are defi ned as the bleak as many fear. tive, some people argue a “plateau” of known amounts of a mineral that can roughly constant production is more be profi tably produced at current prices likely instead. In either case, given a using current technology.” (Fisher, fi nite amount of oil, production must 1981, p. 94) As exploration contin- terrestrial sources, this increase can’t decline sometime, and the question ues, technology advances, and prices go on forever, but what evidence is then becomes: When will world oil pro- increase, more oil becomes available. there that it might stop anytime soon? duction peak, and what will be the eco- Economically, reserves are more akin Those expecting an imminent peak in nomic consequences? to a store’s inventory than to some ulti- oil production employ a different type mate measure of resource availability. of trend line, a nonlinear sort. Most discussions of peak oil trace the While most people think of reserves concept back to the work of the geolo- increasing with new discoveries and Suppose instead of drawing a straight gist M. King Hubbert, who in the 1950s decreasing as oil is pumped out of the line through the production data we correctly predicted a peak in U.S. oil ground, reserves also increase when draw a curve, such as a logistic. Why production between the mid 1960s and new techniques make it cheaper to would we want to do this? For one, this early 1970s. Later, in a 1976 National pump more oil and decrease when the pattern has appeared before. Oil pro- Geographic article, Hubbert predicted price of oil falls. So, for example, fuel- duction in the United States, shown in a world oil peak for 1995, and though effi cient hybrid cars might decrease fi gure 2, did follow a nonlinear trend, this did not come about, the notion that oil reserves because they decrease the increasing, fl attening out, and then oil production would soon peak and demand for oil, driving down the price, decreasing. A logistic trend, also drawn start declining is now often referred to making some oil reserves no longer in fi gure 2, fi ts this pattern well for the “Hubbert’s peak.” economically feasible. U.S., so there is some reason to think that total world production may follow This approach to the problem of how Trends such a trend. Figure 3 shows what a much oil is available should not be con- Peak oil analysis looks not at reserves logistic trend could look like for world fused with another popular approach, but at production (extraction), the oil production. Using statistical meth- that of looking at proven oil reserves. yearly fl ow rather than the stock. The ods to choose the logistic curve that Most people don’t readily grasp exactly problem of reckoning future supply best fi ts the oil data yields 2014 as the whether say, 500 gigabarrels is a lit- then becomes discerning the trend in year of peak oil production. tle or a lot, so reserves are usually production. A look at total world pro- expressed in terms of how long they duction of crude oil (fi gure 1) does not Another reason for considering a logis- would last at current rates of usage. show any obvious signs of decreasing tic curve follows from a rather subtle For example, the Financial Times ran production. Since 1965, world produc- pattern in the data. Plotting yearly oil the headline “World still has 40 years tion has increased at an average of production (P) as a fraction of cumula- of oil, says BP.” (June 13, 2007.) This 2.4 percent per year. Indeed, fi tting a tive oil production (Q) against cumu- approach to determining our remaining simple trend and extrapolating from the lative oil production, as in fi gure 4, supply of oil becomes obviously fl awed past suggests that production will keep shows a declining trend. More impor- on increasing. Clearly, barring extra tantly, after about 1980, that trend ISSN 0428-1276 FIGURE 1 TOTAL ANNUAL WORLD PRODUCTION OF suggesting that dating the peak in oil CRUDE OIL production is an imprecise exercise. Billions of barrels Does Peak Oil Mean 35 $200 a Barrel? To some people, the notion of peak oil 30 sounds scary. What will the future bring as the world moves from a century of 25 increasing oil production to a period of decline? Despite the dramatic appeal 20 of Road Warrior scenarios, with bar- barians clashing over the few remain- 15 ing oil wells, reality should prove to be much more prosaic. The fi rst point 10 to realize is that the peak represents the point of maximum production, not the date that oil runs out. Furthermore, 5 the logistic curves all show a relatively 1965 1975 1985 1995 2005 fl at peak, with a pronounced “hang Source: BP Statistical Review 2006. time” near the peak. Production along the curve in fi gure 3 shows a much FIGURE 2 U.S. PEAK OIL smoother decline than in some recent Billions of barrels episodes. In the fi rst oil crisis, world production dropped from 21.4 billion 4 Peak: 1976, 3.3 gigabarrels barrels (bbls) in 1974 to 20.4 bbls in Annual production 1975. In the base peak oil scenario, it takes 10 years—from 2014 to 2024— 3 for a drop of that magnitude (0.7 bbls) to take place. A larger decline from 24.1 to 20.7 bbls took place from 1979 2 to 1983, but production (in our model) Logistic estimate doesn’t drop off 3.4 bbls until 2034, 20 years after the peak. 1 Of course, there are more uncertain- ties associated with these numbers than just those that arise from estimation 0 error. The trend between annual pro- 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 duction as a fraction of total produc- Source: Department of Energy, Energy Information Administration; and tion and cumulative production (P/Q authors’ calculations. and Q) changed between the 1960s and the 1980s, and quite possibly could change again. Estimates for P and Q becomes linear, showing a roughly the range of uncertainty is even larger, are not certain, and for strategic reasons constant rate of decline in production because these are statistical estimates, not all countries freely share their oil as a fraction of cumulative production. subject to error. One advantage of sta- data. Furthermore, market disruptions In fractions, this linear trend translates tistical techniques, however, is that they such as OPEC cartels and technology to a logistic trend in production levels give us estimates of how big the errors changes or major new discoveries may (Deffeyes 2005 provides some intuition are expected to be, and thus give some shift demand and supply enough to dra- for this mathematical fact, or for the notion of how confi dent we should be matically change the peak in oil pro- hard stuff, check your favorite differen- in the predictions. In fact, it’s a useful duction. tial equations textbook). exercise to look at the estimation error of the coeffi cients and see what bounds Pumping Economically In fact, this provides another approach those put on peak oil. The concept of peak oil originated with to estimating the year of peak oil: fi t petroleum geologists and engineers, the linear trend, and translate that into For the nonlinear logistic case (2014), but oil production is not exclusively a logistic curve for production. The the 95 percent confi dence bounds are determined by geology: it results from answer this method yields depends a 1989 and 2040. For the linear case the equilibrium of demand and supply. bit on when you start the series, but our (2007), the estimates put peak oil There are economic reasons that sug- calculations show a peak in oil produc- between 2004 and 2010. Looking at gest that a “peak oil” scenario might be tion in 2007. both estimates together puts peak oil plausible, but these reasons also con- somewhere in a 50-year band (though, siderably lessen the scare factor in such The two different approaches give two obviously, 1989 was not a peak), again a scenario. different answers (2014 and 2007), but FIGURE 3 WORLD PEAK OIL be indifferent about when we pump? The fi rst guess would be when the Billions of barrels royalty is equal in both periods. This 35 is not quite right, because of the time Peak: 2014, 28.7 gigabarrels value of money—a dollar today is not 30 the same as a dollar next year, because Annual production you can put the dollar today in a bank, 25 earn interest, and get more than a dol- lar tomorrow. Thus, tomorrow’s royalty Logistic estimate 20 should be larger than today’s by the rate of interest. Roughly speaking, you have 15 two choices—pump the oil today and sell it, putting the money in the bank, or 10 pump the oil next year, and sell it then. The payoff should be the same.
5 In the simplest case of applying this 1965 1985 2005 2025 2045 2065 2085 2105 logic, with a known, fi xed supply of Source: BP Statistical Review 2006; and authors’ calculations. oil and with zero extraction costs, we get what economists call Hotelling’s FIGURE 4 ANNUAL PRODUCTION AS A FRACTION OF rule: the price should rise at the rate TOTAL of interest. With a fi xed supply of oil, P/Q this means that in each period, less and 0.08 less oil is produced (thus increasing the 1974 price). In this case, optimal oil deple- tion looks like the down side of the 0.06 Hubbert curve. That has a lesson: With 1980 a known, fi nite amount of a resource, gradually extracting less over time is 0.04 1990 the best thing to do, balancing off cur- 2000 rent returns against future benefi ts. The gradually increasing price serves to 0.02 conserve oil and also provides incen- tives for increased exploration and pro- duction. 0.00 0 200 400 600 800 1000 1200 Would peak oil ever look optimal? The Q (gigabarrels) analysis so far has ignored explora- tion. In fact, the world did not start out Source: BP Statistical Review 2006; and authors’ calculations. with a “known, fi xed supply of oil.” At one time no one knew there was oil in Texas, much less the Middle East, The standard economic story argues it means the price of oil is often quite and Cleveland was the oil capital of that production takes place until price higher than the cost of pumping it out the world! equals the marginal production cost— of the ground—which is exactly as it that is, the point at which the cost of should be because it is a resource in With exploration, the price of oil ini- producing one more unit is just offset fi xed supply. tially drops as the large oil fi elds get by the price for which you can sell that discovered and world supply increases. Finding the best pattern of oil produc- unit. Just like any other good, higher Eventually, it becomes harder and tion thus comes down to specifying prices will call forth more oil (drilling harder to fi nd more oil (think drilling the path of the royalty over time. This in colder areas, moving further out on further and further out into the conti- should make sense because the net the continental shelf, and so forth) and nental shelf), and the increasing roy- social gain from pumping oil today is also reduce demand, as people sub- alty drives the price up. This pattern of the price less the production cost, that stitute away from oil by driving less, a falling then rising price is refl ected in is, the royalty. Consider the choice turning down the heat, and buying a the quantity produced, which increases between pumping the oil now or next solar heater for their pool. In the case and then decreases—the pattern pre- year. If we are depleting oil at the of oil, it’s a little trickier because there dicted by peak oil. Rather than indicat- optimal rate, we should be indifferent is an added cost—pumping oil today ing a failure or fl aw in the oil market, between the choices. For example, if means you can’t use that oil tomor- though, it represents the solution to the oil is more valuable in the future, we row. This adds what economists call problem of balancing demand, produc- should forego pumping it today and an “opportunity cost” or a “rent” to the tion costs, and the value of conserving leave it in the ground for next year, marginal cost. Oilmen would often call oil for the future. it a premium or royalty. In either case, when it is worth more. When will we PRSRT STD Federal Reserve Bank of Cleveland U.S. Postage Paid Research Department Cleveland, OH P.O. Box 6387 Permit No. 385 Cleveland, OH 44101
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Uncertain, not Necessarily Recommended Reading BP Statisical Review of World Energy. Gloomy Future Joseph G. Haubrich is a consultant and June 2007.