Hotellings Theory

Key Takeaways

• Hotelling's theory suggests that resource owners will only extract resources if the yield exceeds that of financial securities like U.S. Treasury bonds.
• The theory predicts changes in resource prices should reflect changes in real interest rates.
• The "Hotelling r-percent growth rule" states price changes of nonrenewable resources should match interest rates, assuming no extraction costs.
• In practice, studies suggest real-world commodity prices often deviate from Hotelling's theoretical predictions due to extraction costs.
• Harold Hotelling also contributed to statistics with theories like Hotelling's law and Hotelling's T-square distribution.

What Is Hotelling's Theory?

Hotelling's Theory, also known as Hotelling's Rule, is an economic principle that suggests owners of nonrenewable resources like oil or minerals will exploit these resources only if they can achieve a return greater than that of financial instruments such as U.S. Treasury bonds. This theory helps predict how resource prices fluctuate based on interest rates, providing insights into why resource owners might choose to delay or accelerate extraction. Hotelling's rule was named after American statistician Harold Hotelling.

We'll explain the application of Hotelling's Theory, its implications in real-world economics, and its historical development. By understanding this theory, you can better grasp how nonrenewable resource markets function and anticipate price changes.

How Hotelling's Theory Influences Resource Extraction Decisions

Hotelling's theory addresses a fundamental decision for an owner of a nonrenewable 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.

Consider an owner of iron ore deposits. If this miner expects a 10% appreciation of iron ore over the next 12 months, and the prevailing real interest rate (nominal rate less inflation) at which he can invest is only 5% per year, he will choose not to extract the iron ore. Extraction costs are ignored in his theory. If the numbers were switched, with a price appreciation expectation of 5% and an interest rate of 10%, the owner would mine the iron ore, sell it, and invest the sales proceeds at a 10% yield. The miner will be indifferent at 5% and 5%.

Applying Hotelling's Theory in Real Markets

The difference between the marginal extraction costs of natural resources and their price is called the Hotelling rent. It follows that the rate of change in the price of a depletable resource must equal the interest rate that a miner or extractor uses to discount the future; this is known as the Hotelling r-percent growth rule. Whenever marginal extraction costs are zero, the price of the resource in stock and that of the unmined resource are equivalent and the Hotelling rule applies equally to both. If, however, extraction costs increase over time, the price of the resource should rise at a rate that is lower than the discount interest.

Thus, all else being equal, an increase in the discount rate implies a higher price for the unextracted resource and would incentivize a faster rate of extraction. In theory, then, the price increase rates of nonrenewable resources like oil, copper, coal, iron ore, zinc, nickel, etc. should track the pace of real interest rate increases.

In practice, the Federal Reserve Bank of Minneapolis concluded in a 2014 study that Hotelling's theory fails. The price appreciation rates of all the basic commodities examined by authors fell short—some far short—of the annual average rate of U.S. Treasury securities. The authors suspected that extraction costs explained the difference.

Harold Hotelling: His Contributions to Economics

Harold Hotelling (1895 - 1973) was an American statistician and economist affiliated with Stanford University and Columbia University in his early and mid-career years, and later with the University of North Carolina-Chapel Hill until his retirement. Aside from the eponymous theory on prices of nonrenewable resources, he is known for Hotelling's T-square distribution, Hotelling's law, and Hotelling's lemma.

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