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Estimation of Catfish Production Function Using Cross-Sectional Survey Data

Aloyce R. Kaliba Southern University and A&M College, Baton Rouge, LA 70809

David BourasLincoln University, Jefferson City, MI 65102

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Presentation Format

• Introduction• Rationale & Significance• Literature Review• Source of Data • Data Analyses• Results and Discussion • Summary

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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.

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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.

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Introduction: Production Function

• Commonly used production Function

• Cobb-Douglas production function

• Polynomial production function

• Constant elasticity of substitution (CES) production function

• Translog production function.

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Introduction: Translog Production Function

1, , , , , ,

1

ln( ) 0.5 ln( ) ln( )ln( ) ln( )ln( )N

jj

N K

i t j ij t ij t ij t j ij t i tkij j k

y x x x x x

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.

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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.

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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.

1,

1

ln( ) 0.5 ln( ) ln( )ln( ) ln( )ln( )N

jj

N K

i j ij ij ij j ij t ikij j k

y x x x x x

ln( ) ln( )ij j j

K

ij j ijkij k

S x x

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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:

1 2 3

2 2 3

3 2 3

j j j i j i

j j j i j i

j j j i j i

SIZE EC

SIZE EC

SIZE EC

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.

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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

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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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THANK YOU FOR YOUR ATTENTION

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04/19/23