Least Squares Regression Estimates of the Schaefer Production Model: Some Monte Carlo Simulation Results

Abstract

Both analytical methods and Monte Carlo experiments are used to determine the amount of bias in the regression estimates of the Schaefer model when it is estimated with catch and effort data. It is shown that the use of the catch–effort ratio and effort as regressors leads to the classical errors in variables problem which produces asymptotically biased parameter estimates. Since the seriousness of the bias, and even its direction in the case of certain formulations of the model, cannot be determined by analytical methods, Monte Carlo simulation experiments were used. Four variations of the Schaefer model were investigated; two of which come from a discrete formulation of the model and two of which come from a continuous formulation. The least squares regression estimates of all formulations result in substantial bias although one formulation is considerably better than the others.Bias in the optimal levels of the population size, the harvest rate, and fishing effort are also calculated. It is found that under likely conditions regarding the model equation errors that the optimal population size and harvest rate may be as much as 40–50% in error depending on the model used. In general, however, the bias in these quantities is much smaller than the bias in the parameter estimates themselves.Key words: Schaefer model, Monte Carlo, optimal fishery management, errors in variables, biased estimates