A production function in the red grouper fishery, Mexico

Transcription

1 A production function in the red grouper fishery, Mexico Alvaro Hernández-Flores Carmen Monroy-García Manuel Rodríguez International Institute of Fisheries Economists and Trade IIFET Conference 216 Aberdeen, Scotland, July 14, 216 Universidad Marista

2 Production Function Relationship between the quantities of inputs (productive factors) and the amount of product obtained. QQ = ff(ll, CC, NN) Short run yield production function in fisheries: Y = q XE (Schaefer, 1957) Where Y - catch, q - catchability coefficient, X - stock size and E - effort. Assumptions: linear model, does not obey the Law of diminishing marginal productivity or returns (Marshall, 1938). In the long run, the production function has been described as: Y Short Run X = constant Y E Long Run Y = a E + be 2 The quadratic model is determined by the PEC or the level of biomass at equilibrium for a particular effort. (Anderson and Seijo, 21) PEC B E E

3 Research questions: What is the relationship between the productive factors of a fishery and the amount produced in the short run? How can an empirical short run production function be developed? How can the short run production function be interpreted?

4 The Red gouper fishery in Yucatan Epinephelus morio (Valenciennes, 1828) Characteristics of the Species: Max length: 122 cm TL Max Weight: 25. kg Age: 29 years Reef-associated; oceanodromous; depth range 1-9 m Adults - Caves Juveniles - seagrass beds Diet - fish, crabs, and other crustaceans and mollusks Solitary, diurnal and may form schools for reproduction IUCN: Near Threatened

5 522 vessels Multispecific fishery: 52 Red grouper and other finfish Types A and B vessels. 385 Octopus 28 Lobster Yucatan Fleet Multispecies Type "A" Type A or mother ships - 12 vessels, each with 7 to 12 small boats, and a crew of 7 to 16, each fisher using individual lines with 1 to 15 hooks Type "A" N = 12 Vessel characteristics Mean Std. Dev. Min. Max. Size Length 16.2 m Size of engine 2 HP Type "B" Effort Days at sea (per trip) Crew Output Total catch (kg trip -1 ) 2,16 1, ,445 Type B or Mechanical winch, 382 vessels with long-line, 3 hooks; and from 3 to 4 crew members

6 Effort Days at sea per trip Number of fishers per trip Effort = Days at sea crew

7 Catch (kg) Catch (kg) Catch and effort data (year 215) 8, 7, 8, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, Effort (DAS Crew) Effort (DAS Crew) Effort data were grouped and sorted in fixed intervals Effort Ranged between 5 and 33 days-crew Interval width for effort (E ) was: w = 2 days crew Average catch (Y) was computed per each effort (E) interval per year, from 1984 to 215* Catch (kg) Effort (DAS Crew) * No data analyzed for 211 and 213

8 LL = 1 MP = 1.5 HL = 2 LL = 21 MP = 3.5 HL = 4 Year: 1988 N: 2,448 trips E (D*C) Catch (Kg) , , 21 1, , 21 1, ,8 24 1, 24 1, , 24 2, ,5 27 1, 27 1,6 27 2, ,2 3 1, ,8 3 1,9 3 9 Catch (kg) Numerical Procedure Effort (D*C) Interval MP Avg. Catch (Kg) , , , , , , , ,19 8 Days at sea Crew N 2,448

9 Production function Catch (Y) and effort (E) regression models Linear model: Reciprocal model: Quadratic model: YY = ββ 11 + ββ 22 EE + UU YY = ββ 11 + ββ EE + UU YY = ββ 11 EE + ββ 22 EE 22 + UU Where Y is the catch, β 1 and β 2 are the coefficients of the models; E is the effort (days at sea crew) and U is the error term. The model with the highest goodness of fit for the entire period was analyzed to detect any structural changes over time.

10 Catch (kg) YY = ββ 11 + ββ 22 EE + UU E Results Model: Linear Dependent Variable: Production 1988 Method: Least Squares Variable Coefficient Std. Error t-statistic Prob. Catch Effort R-squared.8634 Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarts criterion Log Likelihood F-statistic Durbin-Watson stat Prob (F-statistic).111 Catch (kg) 1988 YY = ββ 11 + ββ EE + UU E Model: Reciprocal Dependent Variable: Production 1988 Method: Least Squares Variable Coefficient Std. Error t-statistic Prob. Catch Effort R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarts criterion Log Likelihood F-statistic Durbin-Watson stat Prob (F-statistic).73 Catch (kg) YY = ββ 11 EE + ββ 22 EE 22 + UU E Model: Quadratic Dependent Variable: Production 1988 Method: Least Squares Variable Coefficient Std. Error t-statistic Prob. Catch Effort Quad_ R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarts criterion Log Likelihood F-statistic Durbin-Watson stat Prob (F-statistic).97

11 Coefficients of the quadratic models for years: 1984 to 215* * No data analyzed for 211 and 213 Results Year β 1 β 2 R 2 N , , , , , ,

12 Trend of the Production Function Catch (kg) 3, , 2,5 2, 1,5 1, , ,5 3, 2,5 2, 1,5 1, , , 2,5 2, 1,5 1, , , 2,5 2, 1,5 1, ,5 24 3, 2,5 2, 1,5 1, ,5 29 3, 2,5 2, 1,5 1, , , , 3, 2,5 2,5 2, 2, 1,5 1,5 1, 1, , , , 3, 2,5 2, 1,5 1, , , 2,5 2, 1,5 1, ,5 2 3, 2,5 2, 1,5 1, ,5 25 3, 2,5 2, 1,5 1, ,5 21 3, 2,5 2, 1,5 1, ,5 2, 1,5 1, , , 2,5 2, 1,5 1, ,5 21 3, 2,5 2, 1,5 1, ,5 26 3, 2,5 2, 1,5 1, , , 2,5 2, 1,5 1, Fishing Effort (crew*fihsing days) 3, , 2,5 2, 1,5 1, , , 2,5 2, 1,5 1, , , 2,5 2, 1,5 1, ,5 27 3, 2,5 2, 1,5 1, , , 2,5 2, 1,5 1, , ,5 3, 2,5 2, 1,5 1, , , 2,5 2, 1,5 1, , , 2,5 2, 1,5 1, ,5 23 3, 2,5 2, 1,5 1, ,5 28 3, 2,5 2, 1,5 1, , , 2,5 2, 1,5 1,

13 Economic Efficiency of the Fleet (catch-cost) Catch (kg) 3, , 2,5 2, Catch-Costs* 1,5 1, , ,5 3, 2,5 2, 1,5 1, , , 2,5 2, 1,5 1, , , 2,5 2, 1,5 1, ,5 24 3, 2,5 2, 1,5 1, ,5 29 3, 2,5 2, 1,5 1, , , , , 3, 3, 2,5 2,5 2,5 2, 2, 2, 1,5 1,5 1,5 1, 1, 1, , , , , 3, 3, 2,5 2,5 2,5 2, 2, 2, 1,5 1,5 1,5 1, 1, 1, , , , , 3, 3, 2,5 2,5 2,5 2, 2, 2, 1,5 1,5 1,5 1, 1, 1, ,5 2 3, , 3, 3 2,5 2,5 25 2, 2, 2 1,5 1,5 15 1, 1, ,5 25 3,5 26 3,5 27 3, 3, 3, 2,5 2,5 2,5 2, 2, 2, 1,5 1,5 1,5 1, 1, 1, ,5 21 3, , , 3, 3, 2,5 2,5 2,5 2, 2, 2, 1,5 1,5 1,5 1, 1, 1, Fishing Effort (crew*fihsing days) 4, ,5 3, 2,5 2, 1,5 1, , , 2,5 2, 1,5 1, , , 2,5 2, 1,5 1, ,5 23 3, 2,5 2, 1,5 1, ,5 28 3, 2,5 2, 1,5 1, , , 2,5 2, 1,5 1, *Costs and prices of 212

14 Economic performance of the fleet (Quasi profits ) Total Fleet Vessels Vessel Fleet Size Total fleet Quasi-profits of the variable costs for the fleet ( mother ships ) Quasi-profits of the variable Type A :"Mother costs ship" Type B : Mechanical Winch" per trip

15 Quadratic Production Function in the short run Catch (kg) 3, 2,5 2, 1,5 1, Diminishing Returns Fishing ground depletion (local depletion) Limit or maximum area covered by the vessel Distance Friction Crew Fatigue Transfer Costs Effort (Days at sea Crew) YY = ββ 11 EE + ββ 22 EE 22 + UU

16 Remarks Analysis of the production function of this study is partial and does not include bycatch with the market value In addition to the bycatch, vessels can change fishing gears to target other species with higher economic value, such as lobster or octopus. The transition from the fleet of mother ships to longlines shot with a mechanical winch, can be an strategy to reduce variable costs and increase the catch per trip. It is necessary to extend the study to the entire fleet as this is part of the multi-gear and multi-specific fishery, using the same procedure.

17 Preliminary Conclusions 1. The procedure of aggregating the effort, significantly reduced the raw data variability and was useful for measuring the production function in the short run 2. The short run production function for the red grouper fishery provided not to be linear or monotonically increasing, but a quadratic function showing that in the short term applies the law of diminishing returns 3. The change in the shape of the production function (in the coefficients) over the time is the result of a reduction in the biomass 4. The change in values of the coefficients of the production function over time indicates that Catchability is not constant and is dependent on the level of biomass and fishing technology 5. Changes in the production function indicates that the effort per vessel has increased steadily over time to maintain its revenues, which could be an indicator of over- capitalization 6. The multi-gear and multi-specific nature of the fishery could be threatening the sustainability of the red grouper

18 THANK YOU Alvaro Hernández: Carmen Monroy García : c.monroygarcia@gmail.com Manuel Rodriguez: mrodriguez@marista.edu.mx Marist University of Merida