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Estimating heterogeneous capacity and capacity utilization in a multi-species fishery

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Abstract

We use a stochastic production frontier model to investigate the presence of heterogeneous production and its impact on fleet capacity and capacity utilization in a multi-species fishery. We propose a new fleet capacity estimate that incorporates complete information on the stochastic differences between vessel-specific technical efficiency distributions. Results indicate that ignoring heterogeneity in production technologies within a multi-species fishery as well as the complete distribution of a vessel’s technical efficiency score, may lead to erroneous fleet-wide production profiles and estimates of capacity. Our new estimate of capacity enables out-of-sample production predictions which may be useful to policy makers.

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Notes

  1. Ad hoc approaches such as the “peak to peak” method have been used in the past, which prompted many authors to discuss their limitations and suggest more rigorous methodologies.

  2. This is an oversimplification of the current state of the literature, but our purpose is not to discuss the relative merits of DEA and SPF models.

  3. This is true if we assume that fishermen do not alter their technological choice or targeting strategies for output, measured as the assemblage of species caught within the fishery. Changes in regulatory measures will have many implications on people’s choice sets for inputs and outputs, which will not only reflect technological production possibilities, but also other factors not captured by the production function.

  4. A vessel’s age is recorded but vessels are often refurbished and using their build dates to indicate the vintage of their technology is often times erroneous.

  5. A random coefficients stochastic frontier model has been developed by Greene (2005).

  6. In the sequel we augment the production function with a random error term, independent of efficiency.

  7. This may not be true if a vessel is very inefficient and expending a lot of effort for their size. In this case the capacity utilization score could be high, and \( Y_{it|j}^{MAX} \) could be less than \( Y_{it|j}^{TE} . \)

  8. These capacity estimates do not allow vessels to increase the number of weeks they fish each year, only the number of days they fish within the weeks observed. Therefore, our estimates of capacity may be biased downward. However, the relative comparisons of the different capacity estimates, including the new estimator we propose, will not be compromised by this assumption.

  9. There are a number of issues that must be addressed when defining capacity measures. For a more detailed discussion of these issues see Kirkley et al. (2002).

  10. Alternatively, we could estimate capacity utilization \( Y_{it|j}^{TE} / Y_{it|j}^{TE,MAX} \) as proposed by Fare et al. (1998) which is ‘unbiased’ because it is not directly influenced by technical inefficiency.

  11. In addition, these vessels catch a fair amount of Pacific cod and pollock. These species compose about 8% and 6% of the total retained catch, respectively. However, we exclude them from the analysis since they are considered bycatch.

  12. We focus on retained catch in our analysis instead of total catch, since we believe it more closely reflects the targeting practices of the fleet. In the case that the retained amount of yellowfin sole was zero we substituted in a value of 0.0001 metric tons to facilitate the log-transformation of the production variables.

  13. We also investigated using each vessel’s horsepower but due to multicollinearity concerns it was eliminated.

  14. Given that both Duration and Days are definitions of time, it is important to note that the linear correlation is only 0.75, which is not as high as one may hypothesize. This is because duration is a time input relating to product quality, the captain’s ability to locate fish, and the processing technology used on board the vessel. Days, on the other hand, is a temporal input determine how long the vessel stays at sea and is influenced by the vessels hold capacity, freezing capacity and how fast the holds are filled.

  15. A referee pointed out that the latent variable model assumes that vessels remain in their classes, so any vessel switching across production classes may call into question the validity the analysis.

  16. Dummy variables within this framework can be problematic, for it is possible for a given dummy variable to be unvarying within a given segment.

  17. Initial investigations used S t , but it was statistically insignificant and highly collinear with the constant term due its relative stability throughout the period studied.

  18. Our criterion for this selection was a collinearity estimate of 0.9 or greater.

  19. Restrictions on the coefficients were not implemented a priori, curvature restrictions were tested following estimation.

  20. Estimation results assuming J = 2 are available upon request from the author(s).

  21. The crAIC is −2ln(L) + G*(2 + (2*(G + 1)*(G + 2))/(N − G−2)) and the BIC is −2ln(L) + G(ln(N)), where G is the number of parameters estimated in the model and N is the number of vessels in the fishing fleet.

  22. Another commonly used measure is the conditional expectation of exp{− u i|j }, but this is simply a monotonic transformation of the conditional mean used here. Therefore, they are essentially the same for the purposes of comparative analysis and policy evaluation.

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Authors and Affiliations

  1. Alaska Fisheries Science Center, US Marine Fisheries Service, 7600 Sand Point Way NE, Seattle, WA, 98115, USA

    Ronald G. Felthoven

  2. Center for Policy Research, Department of Economics, Syracuse University, 426 Eggers Hall, Syracuse, NY, 13244, USA

    William C. Horrace

  3. Department of Economics, Andrew Young School of Policy Studies, Georgia State University, 14 Marietta Street NW, Suite 436, Atlanta, GA, 30303, USA

    Kurt E. Schnier

Authors
  1. Ronald G. Felthoven
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  2. William C. Horrace
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  3. Kurt E. Schnier
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Correspondence to William C. Horrace.

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Felthoven, R.G., Horrace, W.C. & Schnier, K.E. Estimating heterogeneous capacity and capacity utilization in a multi-species fishery. J Prod Anal 32, 173–189 (2009). https://doi.org/10.1007/s11123-009-0139-5

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