Reconciling Tests of the Theory of Exhaustible Resources

Does the economic theory of exhaustible resources adequately explain producer behavior? Extant empirical tests show mixed support and are not encouraging in terms of usefulness of the theory in describing producer behavior. There are many differences in extant tests, including differences in resource(s) and market structure analyzed; aggregation over time and resources; whether and, if so, how the in situ resource price, which is not directly observable, is estimated; and the type of test employed. A natural question arises as to whether rejection of the theory is an artifact of these differences. This paper first develops a general theoretic model of an integrated firm that encompasses the existing tests in the literature as special cases. From this model, we use duality theory to derive the theoretical relationship between gross and final (refined) resource indirect cost functions and to develop alternative measures of the in situ resource price. This leads to four distinct tests of the theory, two of which are new to the literature. Using a single micro-level panel of data, we test the theory under each test category. We find the methodologies that directly test the resource stock transition equation do not result in support for the theory. However, the tests that employ the unrestricted and restricted indirect cost functions do not reject the theory. Since a single data set is used in the tests, the variation in results cannot be based on different resource, aggregation level, or market structure assumptions, explanations that have been suggested in the literature as potential reasons for negative results. We find that the alternative tests lead to opposite conclusions regarding the rejecting the theory or not. This suggests that the mixed results are potentially attributable to either a difference in power of the test statistic employed and/or the statistical differences between the formulations of the test (i.e., using a test based on the variation around the transition equation versus testing the variation around the indirect cost function). We conclude that the theory is indeed useful in explaining producer behavior for the natural gas resources we analyze.