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What is the appropriate way to measure the Gini coefficient over time in an industry where a large number of firms are exiting? Should the Gini coefficient be calculated using the initial number of firms, or the number of remaining firms at any point in time?

This question arises from reading reports about a controversial fisheries policy instrument--individual fishing quotas (IFQs). The implementation of IFQs is commonly associated with a significant drop in the number of fishing vessels. Yet, when many researchers calculate changes in the Gini coefficient on vessel revenue before and after IFQ implementation they do so using revenue per active vessel only. In my view this method ignores the drop in revenue (to zero) for vessels that become inactive as a result of the IFQ program.

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An example from the Gulf of Mexico Red Snapper fishery:

Number of active vessels: before = 482, after =360

Gini coefficient among active vessels: before = 0.81, after = 0.79

Average revenue per active vessel: before = 28,960 after = 58,630

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Is there a way to use this information to calculate the Gini coefficient for the total number of vessels (active and inactive) before and after IFQ implementation?

Any comment or insight would be greatly appreciated.

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The specific paper I'm think about is Performance of federally managed catch share fisheries in the United States by Ayeisha A. Brinson abd Eric M (2016), but similar methods are used for many other US IFQ programs. Thunberg. https://www.sciencedirect.com/science/article/pii/S0165783616300649

The specific Gini coefficient forumula used:

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where i = 1 to n; i is the vessel’s rank order in ascending order; x is the annual revenue for vessel i; n is the number of active vessels; u is the mean revenue

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I think the best way to show the effect of the loss of vessels is not to calculate the Gini by revenue/initial vessels but to the show the change of Gini index from revenue/active share owner or shares/active share owner since the loss of vessels is mainly due to the increase in rents. The increase in rents lead to a consolidation of shares which is not apparent when just looking at individual vessels. Also just looking at revenue/vessel doesn't take into account the increase of costs. I wouldn't include firms that have left the market as that's not an accurate way to describe the change in the Gini index for that market.

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  • $\begingroup$ I'm not sure I understand how the increase in rents would directly lead to a consolidation of shares. If quota shares are separable from vessel ownership (as they are in most IFQ programs), then consolidation in the number of vessels (due to rents) could occur without any consolidation in shares. $\endgroup$ – Jack Cramer Apr 12 '18 at 18:13
  • $\begingroup$ I agree that revenue/active share owner or shares/active share owner would provide useful information. However, those metrics are not commonly available and they would overlook the impacts of consolidation on fishery participants other than share owners (captains, crew). $\endgroup$ – Jack Cramer Apr 12 '18 at 18:17
  • $\begingroup$ What came to mind when I was writing was how the medallion system works with NYC cabs. The cab drivers usually lease/rent medallions from a company as it is more profitable that way. The same concept would apply to Catch Share programs where the shares would rise in price to the point where they are not actually owned by fisherman but leased from a larger firm unless there are share caps and regulations in place to prevent that from happening. So yes it would depend on how the shares were traded and who could actually own them. $\endgroup$ – Tom V. Apr 12 '18 at 19:45
  • $\begingroup$ I think you could extrapolate share distribution by having the assumption that most vessels will reach their share quota 100% and then use the per vessel revenue to predict share ownership/vessel but that's not really different than revenue/vessel... $\endgroup$ – Tom V. Apr 12 '18 at 19:47

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