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
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Presentation Format
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Introduction
Rationale & Significance
Literature Review
Source of Data
Data Analyses
Results and Discussion
Summary
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
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•
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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
N
N
K
j 1
j 1
j k
ln( yi ,t )      j ln( xij ,t )  0.5 j ln( xij ,t )ln( xij ,t )   j ln( xij ,t )ln( xki )  i ,t
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
N
N
K
j 1
j 1
j k
ln( yi )      j ln( xij )  0.5 j ln( xij )ln( xij )   j ln( xij ,t )ln( xki )  i
•
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.
K
Sij   j   j ln( xij )    j ln( xki )  ij
j k
•
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.
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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:
 j   1 j   2 j SIZE i   3 j EC i
 j   2 j   2 j SIZE i   3 j EC i
 j   3 j   2 j SIZE i   3 j EC i
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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
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• 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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