Measuring Resource Scarcity in Non-Renewable Resources with Inequality Constrained Estimation.

This paper uses annual Canadian exploration data to estimate a multiple-output translog exploration cost function. A new definition of depletion is introduced, and its estimated coefficient is found to be statistically significant. Monte Carlo integration ensures the estimated cost function satisfies concavity and monotonicity. The fitted cost function parameters are used to obtain estimates of marginal costs of exploration for oil and gas. Our estimated marginal exploration costs are smaller than previous studies because we allow for technical progress which offsets the depletion effects. We find evidence of a 10% per year increase in scarcity along the trend. For natural gas, the number is 1.8%.