An application and test of Hotelling's rule: The case of old-growth forest
The Hotelling rule, which states that the shadow price of an exhaustible resource must grow at a rate equal to the interest rate, has been recognized as the fundamental principle of the economics of exhaustible resources. Recently, many economists began to focus attention on testing whether the data support the Hotelling rule. These tests, however, have provided only limited empirical support for the Hotelling rule. This thesis derives a modified version of the Hotelling rule for the case of the "exhaustible" resource of old-growth forest and tests its empirical validity using data from old-growth timber sales in the U.S. Pacific Northwest. Since the choice of old-growth timber obviates many of the problems faced by previous researchers working with minerals in measuring shadow price, the Hotelling rule of old-growth is tested directly using the data. Three models of old-growth harvest are set up corresponding to the three types of harvesting cost functions. For the basic case in which the unit harvesting costs are assumed to be constant, the modified Hotelling rule for old-growth forestry reveals that the shadow price of standing old-growth timber must increase at a rate equal to the interest rate plus a term reflecting the opportunity cost of capital adjusted for the carrying cost of holding a unit of old-growth stands. When the harvesting cost function is either generalized to be nonlinear or to allow for stock effects the derivation of the modified Hotelling rule is made more complex. Despite the complexities, a relatively simple Hotelling rule for each case has also been obtained. Each one predicts the determinants of the time path of the stumpage price for the optimal harvest of old-growth in its corresponding case. Empirical models are constructed to test the modified Hotelling rule directly. In addition, two variations of alternative empirical models are developed to incorporate a stock-based model and an inflation-based model with the purpose of providing further interpretation and corroboration for the findings from the direct models. The empirical result demonstrates that the set of the Hotelling hypotheses is not rejected as an empirically valid description of the harvest path for the old-growth forests. The predictive success of the Hotelling rule of old-growth significantly improves the empirical performance of Hotelling's theory, which is a major contribution to the literature in natural resource economics. It is also shown to be useful to identify and direct appropriate resource conservation and management practices for the old-growth forestry.