# Gini coefficients - Accounting for firm exits

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:

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