Comparison of proxies for fish stock. A Monte Carlo analysis
Introduction
It is common in fisheries research to include a measure of fish stock as an argument in fishing production functions. The idea is that the more fish in the sea, the higher the catch will be, so it seems logical to include an estimate of stock in the production function (Pascoe and Herrero, 2004; Solís et al., 2015). Given that this information is not available in many cases, researchers must resort to the use of stock proxies. This approach raises some interesting modelling issues, since the use of proxy variables can lead to biased and inconsistent parameter estimates due to measurement error (Gordon, 2015).
The most commonly-used proxy of fish stock is ‘catch per unit effort’ (CPUE), a concept that has a long tradition in fisheries (Schaefer, 1954). While CPUE can be calculated in various ways, a common procedure is to estimate the stock in a given period as the average catch of all (or some) boats in that period. Since measures of stock biomass are not available in many cases, CPUE has been widely used in empirical fisheries work as an index of stock abundance, especially in fish population assessments for fisheries management (Myers and Worm, 2003).
Even though some papers in the fishing literature have been critical of the use of CPUE as a measure of stock abundance (Richards and Schnute, 1986; Wallace et al., 1998; Maunder et al., 2006), this variable continues to be frequently used in the empirical estimation of fishing production functions (e.g., Duy and Flaaten, 2016; Chavez Estrada et al., 2018). Hence, while many papers have shown concerns about the precision of CPUE as an estimate of abundance, we are interested in the performance of CPUE as a proxy of fish stock in the context of estimating fishing production functions.1
We compare CPUE with an alternative proxy for fish stock that uses time dummy variables to account for the temporal variation in the stock. The rational for this approach to proxying the unknown stock is that, in many fisheries, fish stock can be considered common to all boats but varying over time. For this reason, using time dummies to model the effect of an unobservable variable that only has time variation seems appropriate.2 This approach has also been frequently used in the empirical literature (e.g., Campbell and Hand, 1998; Fousekis and Klonaris, 2003). In any case, it should be noted that time dummies will represent not only fish stock but also the effect of all unobserved effects which are common to all boats, such as the state of the environment.
The main contribution of the paper, therefore, is to analyze the statistical properties of both approaches to proxying fish stock: CPUE and time dummies. We do this in the framework of a model where there is a single catch (an aggregate of all species or just a single species without considering age-size classes), and stock is considered common to all boats. The individual vessel-level production function is linear with just two inputs (effort and stock), no individual boat effects and no technical change. We compare the performance of both proxies in this model using Monte Carlo simulation.3 The main finding of the paper is that the proxy that estimates stock based on average catch is shown to impose strong parametric restrictions. In particular, the estimated coefficient of CPUE is always equal to 1, a result that holds true under different scenarios. On the other hand, the time dummies allow for unbiased estimation of the production function parameters.
The paper is organized as follows. Section 2 discusses the general role of stock in a production function. The two different proxies for fish stock are presented in Section 3. Section 4 performs Monte Carlo simulations, which allow us to check the results of the theoretical section. Section 5 contains a discussion of the implications of the paper for empirical analysis, and Section 6 presents some conclusions.
Section snippets
The role of stock in fishing production functions
The analytical framework is based on a simple production model where fishing output of boat i at time t (yit) is a function of one variable input (Zit) and fish stock (St), which is assumed to be common to all boats. Additionally, catches depend on luck and other stochastic effects (uit). Therefore, the fishing production function can be written as:
If the model is linear, we have:4
Proxies for fish stock
The issue at hand is how to control for the effect of biomass stock when data for this are not available. As stated in the Introduction, two main proxies for fish stock have been used in empirical work. One is average catches in a given period, which is known as ‘catch per unit of effort’ (CPUE), while the other proxy uses time dummies to account for variations in the stock over time.
Monte Carlo simulation
In this section, we will show the empirical implications of the theoretical results obtained above. However, the exact results of Section 3 will be difficult to reproduce in most data sets due to problems caused by multicollinearity between inputs and the stock proxy, as well as to the presence of noise. For this reason, we have decided to use a simulated data set.9
Results
The production function is first estimated without correlation between effort and stock. We then allow for different degrees of correlation between these two variables. The estimation was conducted using Limdep V10.
Discussion
The size of the stock elasticity is of great interest to fisheries scientists because of its important implications for policy recommendations. The previous sections contribute to showing that CPUE is not a good proxy of the effect of fish stock when included in a linear fishing production function. In fact, the finding that CPUE - computed as the average catch of all vessels - always results in an estimated stock parameter equal to 1, regardless of the species, must be of some concern to
Conclusions
This paper compares two alternative proxies for fish stock in the framework of the estimation of a fishing production function. The theoretical analysis shows the estimated coefficient of CPUE is always equal to 1 in the case of a linear production function, while time dummy variables are a better proxy for stock. In the empirical section we use Monte Carlo simulations to show that the predictions of the theoretical model are correct. Concretely, the result that the estimated coefficient of
Declaration of Competing Interest
None.
Acknowledgements
The author is grateful for comments received from Carlos Arias, William Greene, Peter Schmidt, David Roibas and Alan Wall. Very useful suggestions were also made by two anonymous reviewers. The editor, Andre Punt, was also very helpful during the review process.
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