A Stochastic Equilibrium Model of the World Crude Oil Market
Crude oil is the world's predominant energy source and by far the most internationally traded commodity, both physically and on paper markets. Despite the high attention it receives, the crude oil market has been a perennially challenging subject for economic analysis due to the many elusive aspects of its underlying dynamics. To be convinced, one needs only to look at major energy information sources' year-on-year revisions on their price and supply projections. Economic models have generally failed to predict the oil market's future evolution. Ours is yet another such long-term dynamic modeling attempt, not aimed specifically at producing market "forecasts" but at offering an alternative mathematical programming framework for understanding the market's behavior and explaining its possible future evolution. We develop a stochastic differential gaming model of oligopoly competition in the world crude oil market. The Organization of Petroleum Exporting Countries (OPEC) is considered as a collusive cartel while the big non-OPEC fringe is comprised of many independently acting identical firms. We also consider the recently-emerging oil sands industry as a second fringe in order to investigate its market potential. The producers pursue to maximize their individual discounted sum of future profits as quantity setters a la Cournot. As a first in the literature to our knowledge, the market price of oil is modeled as a mean-reverting stochastic process whose "long-term mean" is a function of total quantity supplied. As an improvement over existing long-term oil market models, production capacity is treated separately from supply and modeled endogenously via a dynamics including an exponential decline term, in order to account for this crucial phenomenon in the oil industry. We seek a Nash equilibrium solution of producers' Markovian supply and capacity expansion strategies. The generalized Hamilton-Jacobi-Bellman (HJB) equations characterizing the equilibrium solution are approximated by a finite difference (FD) scheme on the time, price, and capacity states and solved via a dynamic programming approach. The model is carefully calibrated to the oil market. The numerical solution is used in a Monte Carlo simulation for obtaining 20-year projections of the price, production capacity, and supply paths for different cost scenarios. The results are also compared and contrasted to the recent long-term projections of major energy information authorities. Simulation results generally indicate that oil prices can be expected to rise gradually in the next decade or so if the market continues to do "business as usual". Total world supply also increases gradually, where the largest share of this increase comes from OPEC depending on relative levels of costs. The supply projections for non-OPEC are a plateau around current levels or a mild growth or decline depending on the relative cost levels, consistent with many a claim that non-OPEC production has recently or is about to peak/plateau. The projections for oil sands indicate a significant relative growth of their supply but still an insignificant fraction in total world supply. Besides indicating a strategic OPEC supply and capacity expansion behavior, the results also predict an OPEC spare capacity, thereby making the model the first one of its kind, to our knowledge, to explain this historical phenomenon by a completely endogenous specification.
Preckel, Purdue University.
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