Estimation of Catfish Production Function Using Cross-Sectional Survey Data

1. Estimation of Catfish Production Function Using Cross-Sectional Survey Data Aloyce R. Kaliba Southern University and A&M College, Baton Rouge, LA 70809 David Bouras Lincoln University, Jefferson City, MI 65102

2. Presentation Format • Introduction • Rationale & Significance • Literature Review • Source of Data • Data Analyses • Results and Discussion • Summary

3. Introduction: Production Function • A production function describes a mapping from quantities of inputs to quantities of outputs as generated by a production process. • The production function presupposes technical efficiency and states the maximum output obtainable from every input combination.

4. Introduction: Production Function • Yit = f(Xn,it: B)+uit • Y =output • i = farm • t = time • X = input • n = number of inputs • B = parameter • U =random noise Therefore f(.) is average output of the farm given the technology.

5. Introduction: Production Function • Commonly used production Function • Cobb-Douglas production function • Polynomial production function • Constant elasticity of substitution (CES) production function • Translog production function.

6. Introduction: Translog Production Function Where, y is the gross output, x is real input, α is the intercept or the constant term, βj are first derivatives, θj are own second derivatives, and γj are cross second derivatives. The translog functional form imposes no a priori restrictions on the substitution possibilities between the factor inputs by relaxing the assumption of strong separability of input.

7. Rationale and Significance • Catfish production is an important segment of the Aquaculture Industry • Competitiveness of the industry depends on productive efficiency. • Marginal productivity analyses identify the most efficient and inefficient input; therefore area of improvement. • Discuss any other means of evaluation. Input Elasticity shows the most limiting input; therefore focus for research and extension efforts.

8. Literature Review • Generic translog Production function • Under perfect competition assumption, output elasticity with respect to input equals to cost share of that input. We can get a system of cost share equations by differentiating the translog production function with respect to each factor input. • Where βj represents the average cost share of inputs j, θj represent input j own constant share elasticity, and γj represent input j constant share elasticity with respect to other input k.

9. Literature Review: Multilevel Generic translog Production function • The parameters βj (average cost share of inputs j) , θj (own constant share elasticity), and γj and cross-constant-share elasticity) depend on farm size and extension contacts. We can add the system:

10. Estimation of Marginal Product of Inputs • The marginal product of a factor can be computed as the product of the factor’s elasticity times its average product. • Therefore marginal productivities can be computed at any point of the production function. • It is convenient, however, to present the discussion in terms of the “average farm”, i.e., at the geometric means of output and inputs.

11. SOURCE OF DATA • Farm Survey of 41 catfish producer (input and outputs) • Complete data for 34 farms. • Outputs: Live catfish • Inputs: feed, lab, fuel and gas, electricity, other expenditures • Created Pseudo Sample of 1000 farms using Cholesky Decomposition Method

15. Summary and Conclusion • Farm size and Extension Contact Matters • Small Farms needs more research and extension efforts to optimize all input use. • Apart from large farm, feeding is a limiting factor for all other farm sizes.

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