Empirical testing of a risk-adjusted Hotelling model

Abstract

The Hotelling model of the optimal depletion of an exhaustible resource specifies that in a world without risk, equilibrium rates of return on nonrenewable resource assets and on alternative assets will be equalized. In applied work, where the rate of return on the resource asset is typically measured as the rate of increase of marginal profits while the return on the alternative asset is measured by a market rate of interest, the Hotelling model has not, in general, held up well to empirical scrutiny. In the recent literature, the Hotelling model has been reconsidered in the context of a world where risk is present. In such a context, the expected rates of return on an exhaustible resource and on other assets will not necessarily be equalized in equilibrium. In fact, unless agents are risk neutral, the relative riskiness of the resource asset will play a crucial role in a ‘risk-adjusted’ Hotelling rule. Specifically, with competitive firms, the expected rate of return on an exhaustible resource will differ from the expected rate of return on alternative assets by the risk premium associated with the resource asset. In this paper we investigate how well this ‘risk-adjusted’ Hotelling model withstands empirical scrutiny. Given the role of expectations in this modified Hotelling rule and in the Euler equations that yield this rule, we use Generalized Method of Moments (GMM) estimation in our empirical analysis. Our application, which is based on three different utility specifications, examines returns for various resource industries (lead, zinc, copper, silver), utilizing aggregate annual Canadian price, extraction cost, and interest rate data since 1950.