Has the Real Price of Oil Followed Hotelling's Rule? WTI Crude, 1947-2025, an Endpoint Identity, Cost-Adjusted Growth Bounds, and Why 78 Years Cannot Settle the Question

Hotelling's rule says that the net price of an exhaustible resource rises at the rate of interest. I test the rule on the real spot price of West Texas Intermediate crude, deflated by the US consumer price index, using annual averages from 1947 to 2025. I prove three results. First, the mean of annual log price growth equals the log change between the end years divided by the number of years, so the test depends only on the two end points. Second, with a constant real extraction cost the market price grows at the interest rate times one minus the cost share, so it grows more slowly than the interest rate and approaches it from below. Third, under a random walk the standard error of mean growth is the annual standard deviation divided by the square root of the number of years, which fixes the smallest gap any test can detect. The real oil price rose by a factor of 2.49, or 1.17% a year, while the ex post real three-month Treasury bill rate averaged 0.45%. The gap of 0.72 points has a standard error of 2.67 (Newey-West 2.53), so the data neither reject the rule nor support it. Annual real price growth has a standard deviation of 22.6 points, so 78 years can detect only a gap of 7.2 points or more with 80% power, and detecting a one point gap would need about 4,000 years. Mean growth to 2025 ranges from minus 1.77% to 3.11% a year as the start year moves between 1947 and 2000.