Theoretical papers show that there could be a welfare gain from switching to tax regulation if managers are more uncertain about key parameters of a fishery than fishermen. We estimate the size of the welfare gain that would result if a manager of the Danish cod fishery in the Kattegat switched from the current individual transferable quota system to tax regulation. We find that this would generate a small welfare gain of 0.023% of the industry profit and variations in parameter values (+/- 20 %) at most result in a gain of 0.029%