Catch, stock elasticity and an implicit index of fishing effort

Economists are interested in the relationship between fishing effort and stock size, and how these impacts catch levels. The interest lies in the stock elasticity where it is thought that for pelagic fish species it is close to zero and for demersal fish stocks closer to one. We statistically model and estimate the relationship between stock size and catch for two species, Northeast Arctic cod and saithe. In doing so we are able to recover estimates of stock elasticity but also estimates of catchability coefficients for different age classes and importantly an implicit index of fishing effort. Data on observed catch and a measure of biomass-at-age are available from the International Council for the Exploration of the Sea. The generated stock data are problematic and instrumental variables and bootstrapping are used in estimation. Time-series techniques applied to panel data are used to statistically motivate the estimation, which is carried out within a two-way panel framework