Hotelling's theory, or Hotelling's rule, posits that owners of non-renewable resources will only produce a supply of their basic commodity if it can yield more than available financial instruments, specifically U. Treasury or other similar interest-bearing securities. This theory assumes that markets are efficient and that the owners of the non-renewable resources are motivated by profit. Hotelling's theory is used by economists to attempt to predict the price of oil and other nonrenewable resources , based on prevailing interest rates. Hotelling's rule was named after American statistician Harold Hotelling. Hotelling's theory addresses a fundamental decision for an owner of a non-renewable resource: keep the resource in the ground and hope for a better price the next year, or extract and sell it and invest the proceeds in an interest-bearing security.

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The prices of exhaustible resources—oil, natural gas, copper, coal, etc. Oil prices, for example, rose sharply in the s and then fell abruptly in with the onset of the Great Recession. Prices rose again with recovery, but are now trending down as new sources are tapped. How do such fluctuations affect inflation, and how should policy respond? More fundamentally, what makes prices of commodities like this fluctuate so much? The usual analysis with a simple supply-and-demand diagram is inadequate for answering this question.

What, after all, is the supply curve for a resource whose quantity is fixed and is brought to market simply by pulling it out of the ground? In , Harold Hotelling proposed an answer. We briefly discuss possible ways to resolve this failure, which we call the Hotelling puzzle. The owner can leave the oil in the ground indefinitely or extract and sell it right away and then purchase a financial asset with the proceeds. In other words, the owner can keep the oil as a physical asset or turn it into a financial asset.

By contrast, if the oil is left in the ground, the owner will get the price that is expected to prevail next year. Which action will yield the most profit? The answer, Hotelling would argue, lies in the current interest rate and the expected commodity price. Then, clearly, the owner will hold the oil underground until next year. The logic behind this simple and ingenious result is straightforward and draws from the profit-maximizing behavior of the owner described above extended to include many resource owners.

The Hotelling result is intuitive and well-known to economists. In addition, it has a clear and strong implication for prices of these resources over time. To examine this implication over a longer period and to understand if recent commodity price trends are simply an anomaly to the standard Hotelling-theory price trend, we examine data on the prices of 11 exhaustible resources for which we have a long historical record.

The accompanying table displays the average annual growth rates of the prices logged and adjusted for inflation of these exhaustible resources. The price of risk-free U. Treasury securities averaged 1. There are, of course, many other measures of the real interest rate, with higher-risk securities invariably generating higher average returns.

Large Image. The table shows that the prices of all our exhaustible resources have actually risen at a rate far lower than that on U. Prices on commodities for which we have the longest continuous data record lead, coal and gold rose at an annual average rate of 0. Not one of the 11 commodities examined rose at a rate comparable to U.

Treasury securities. Tin is the closest, at 0. What could be wrong with the theory? An immediate reaction might be that it should be modified to include fluctuations in demand. For example, many think that commodity prices rose in the s because of surging Chinese demand. Yet there seems to be no room for demand in the theory. If demand considerations cannot play a role, perhaps extraction costs could.

Indeed, Hotelling did include such costs in his analysis. Redoing the earlier analysis but this time including extraction costs, we find that the per-unit profit on resources should indeed rise at the real interest rate. This result from the more sophisticated version of the theory is sometimes referred to as the Hotelling principle. An even more refined version of this principle is that the value of the resources left in the ground must rise over time. The theory can then be reconciled with the observed lack of trend in prices if the per-unit extraction cost falls rapidly enough.

So, how rapidly must extraction costs fall for the theory to be consistent with the data? To simplify the analysis, we assume that the interest rate on risk-free securities is constant, and we consider two values for the interest rate, 1 percent and 4 percent per year. For ease of presentation, we give results for two commodity indexes rather than the 11 commodities individually. Our basic index is a weighted average of the individual prices where weights are computed using the average shares in overall production for the commodities during Then, to ensure that our results are not overly influenced by oil and coal, which account for 64 percent and 20 percent, respectively, of overall commodity production, our second index omits these two.

Both indexes indicate, again, that the data contradict the theory. The basic index displays no significant growth 0. The second index has a negative trend That is to say, commodity prices excluding oil and coal do not rise at all , let alone at the real interest rate.

Figure 2 displays our results under this assumption for the basic 11 commodity price index, without extraction costs, and with extraction costs and the two interest rates 1 percent and 4 percent. Our results for the price index excluding oil and coal not displayed are similar. For both interest rates and both indexes, this more sophisticated version of the theory implies that extraction costs fall so fast that they quickly turn negative!

Obviously, actual extraction costs cannot be negative. Therefore, it appears that even when we allow for extraction costs, we are still left with a Hotelling puzzle. His landmark theory is not consistent with actual data.

Further refinements of the analysis do no better. When we repeat the exercise using the simple theory excluding extraction costs with an expanded set of commodities—beyond the 11 for which we have long historical samples—we again find that average prices fall over time, at an annual rate of If we include extraction costs and use the expanded commodity set, the results are slightly different.

While the 1 percent interest rate results still require negative extraction costs, a 4 percent interest rate maintains positive extraction costs. Unfortunately, closer analysis of these results has found that they too are inconsistent with the Hotelling principle. Unfortunately, current theory fails in this regard. We refer to this failure as the Hotelling puzzle. We are exploring this idea in ongoing research.

The data were kindly provided to us by the authors. The prices in our table have been deflated by an aggregate price index in Harvey et al The 11 commodities used in our analysis are aluminum, coal, copper, gold, lead, nickel, oil, iron, silver, tin and zinc. Hotelling, Harold. The economics of exhaustible resources. Journal of Political Economy 39 2 , Harvey, David I.

Kellard, Jakob B. Madsen and Mark E. The Prebisch-Singer hypothesis: Four centuries of evidence. Review of Economics and Statistics 92 2 , Krautkraemer, Jeffrey A. Nonrenewable resource scarcity. Journal of Economic Literature 36 4 , The Optimal Extraction of Exhaustible Resources Conventional theory can't explain historic commodity price fluctuations, but modified models may provide better guidance. Chari Consultant.

Lawrence J. Christiano Consultant. The Optimal Extraction of Exhaustible Resources. Facebook LinkedIn Twitter. The papers are an occasional series for a general audience. The views expressed here are those of the authors, not necessarily those of others in the Federal Reserve System. More On. Related Content. Sign up for news and events Sign up for emails to get the latest news, research, and information from the Federal Reserve Bank of Minneapolis.


The Optimal Extraction of Exhaustible Resources

The prices of exhaustible resources—oil, natural gas, copper, coal, etc. Oil prices, for example, rose sharply in the s and then fell abruptly in with the onset of the Great Recession. Prices rose again with recovery, but are now trending down as new sources are tapped. How do such fluctuations affect inflation, and how should policy respond? More fundamentally, what makes prices of commodities like this fluctuate so much?


The Economics of Exhaustible Resources

Hotelling's rule defines the net price path as a function of time while maximizing economic rent in the time of fully extracting a non-renewable natural resource. The maximum rent is also known as Hotelling rent or scarcity rent and is the maximum rent that could be obtained while emptying the stock resource. In an efficient exploitation of a non-renewable and non-augmentable resource, the percentage change in net-price per unit of time should equal the discount rate in order to maximise the present value of the resource capital over the extraction period. This concept was the result of analysis of non-renewable resource management by Harold Hotelling , published in the Journal of Political Economy in Devarajan and Fisher note that a similar result was published by L.


Hotelling's Theory


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