5 Bennet Indicator
Description: Bennet Indicator
Found in: State of the Ecosystem - Gulf of Maine & Georges Bank (2018, 2019, 2020, 2021), State of the Ecosystem - Mid-Atlantic (2018, 2019, 2020, 2021)
Indicator category: Database pull with analysis
Contributor(s): John Walden
Data steward:Kimberly Bastille, kimberly.bastille@noaa.gov
Point of contact: John Walden, john.walden@noaa.gov
Public availability statement: Derived CFDBS data are available for this analysis (see Comland).
5.1 Methods
5.1.1 Data sources
Data used in the Bennet Indicator were derived from the Comland data set; a processed subset of the Commercial Fisheries Database System (CFDBS). The derived Comland data set is available for download here.
5.1.2 Data extraction
For information regarding processing of CFDBS, please see Comland methods. The Comland dataset containing seafood landings data was subsetted to US landings after 1964 where revenue was \(\ge\) 0 for each Ecological Production Unit (i.e. Mid-Atlantic Bight, Georges Bank, and Gulf of Maine). Each EPU was run in an individual R script, and the code specific to Georges Bank is shown here.
5.1.3 Data analysis
Revenue earned by harvesting resources from a Large Marine Ecosystem (LME) at time t is a function of both the quantity landed of each species and the prices paid for landings. Changes in revenue between any two years depends on both prices and quantities in each year, and both may be changing simultaneously. For example, an increase in the harvest of higher priced species, such as scallops can lead to an overall increase in total revenue from an LME between time periods even if quantities landed of other species decline. Although measurement of revenue change is useful, the ability to see what drives revenue change, whether it is changing harvest levels, the mix of species landed, or price changes provides additional valuable information. Therefore, it is useful to decompose revenue change into two parts, one which is due to changing quantities (or volumes), and a second which is due to changing prices. In an LME, the quantity component will yield useful information about how the species mix of harvests are changing through time.
A Bennet indicator (BI) is used to examine revenue change between 1964 and 2015 for two major LME regions. It is composed of a volume indicator (VI), which measures changes in quantities, and a price indicator (PI) which measures changes in prices. The Bennet (1920) indicator (BI) was first used to show how a change in social welfare could be decomposed into a sum of a price and quantity change indicator (Cross and Färe 2009). It is called an indicator because it is based on differences in value between time periods, rather than ratios, which are referred to as indices. The BI is the indicator equivalent of the more popular Fisher index (Balk 2010), and has been used to examine revenue changes in Swedish pharmacies, productivity change in U.S. railroads (Lim and Lovell 2009), and dividend changes in banking operations (Grifell-Tatjé and Lovell 2004). An attractive feature of the BI is that the overall indicator is equal to the sum of its subcomponents (Balk 2010). This allows one to examine what component of overall revenue is responsible for change between time periods. This allows us to examine whether changing quantities or prices of separate species groups are driving revenue change in each EPU between 1964 and 2015.
Revenue in a given year for any species group is the product of quantity landed times price, and the sum of revenue from all groups is total revenue from the LME. In any year, both prices and quantities can change from prior years, leading to total revenue change. At time t, revenue (R) is defined as \[R^{t} = \sum_{j=1}^{J}p_{j}^{t}y_{j}^{t},\] where \(p_{j}\) is the price for species group \(j\), and \(y_{j}\) is the quantity landed of species group \(j\). Revenue change between any two time periods, say \(t+1\) and \(t\), is then \(R^{t+1}-R^{t}\), which can also be expressed as: \[\Delta R = \sum_{j=1}^{J}p_{j}^{t+1}y_{j}^{t+1}-\sum_{j=1}^{J}p_{j}^{t}y_{j}^{t}.\] This change can be decomposed further, yielding a VI and PI. The VI is calculated using the following formula (Georgianna, Lee, and Walden 2017):
\[VI = \frac{1}{2}(\sum_{j=1}^{J}p_{j}^{t+1}y_{j}^{t+1} - \sum_{j=1}^{J}p_{j}^{t+1}y_{j}^{t} + \sum_{j=1}^{J}p_{j}^{t}y_{j}^{t+1} - \sum_{j=1}^{J}p_{j}^{t}y_{j}^{t})\] The price indicator (PI) is calculated as follows: \[PI = \frac{1}{2}(\sum_{j=1}^{J}y_{j}^{t+1}p_{j}^{t+1} - \sum_{j=1}^{J}y_{j}^{t+1}p_{j}^{t} + \sum_{j=1}^{J}y_{j}^{t}p_{j}^{t+1} - \sum_{j=1}^{J}y_{j}^{t}p_{j}^{t})\] Total revenue change between time \(t\) and \(t+1\) is the sum of the VI and PI. Since revenue change is being driven by changes in the individual prices and quantities landed of each species group, changes at the species group level can be examined separately by taking advantage of the additive property of the indicator. For example, if there are five different species groups, the sum of the VI for each group will equal the overall VI, and the sum of the PI for each group will equal the overall PI.
5.1.4 Data processing
Bennet indicator time series were formatted for inclusion in the ecodata R package using the R code found here.
catalog link https://noaa-edab.github.io/catalog/bennet.html