Lecture 07-2005

# Lecture 07-2005 - The Stochastic Nature of Production...

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1 The Stochastic Nature of Production Lecture VII I. Stochastic Production Functions Just, Richard E. and Rulan D. Pope. “Stochastic Specification of Production Functions and Economic Implications.” Journal of Econometrics 7(1)(Feb 1978): 67–86. A. Our development of the random characteristics of the production function was largely one of convenience. 1. We started with a production function that we wanted to estimate ( ) () 12 0 22 1 2 0 1 1 2 2 11 1 12 1 2 22 2 , ,2 fxx xx gxx a ax ax Ax Axx Ax αα α = =+ + + + + 2. In order to estimate each function, we multiplied or added a random term to each specification ( ) ( ) ( ) ( ) 0 0 1 1 2 2 1 2 0 1 1 2 2 11 1 12 1 2 22 2 ,l n , l n l n u xxe x x u Axx Ax v =⇒ = + + + + + + 3. Just and Pope discuss three different specifications of the stochastic production function ( ) ( ) ( ) () () () 1 2 3 0 1 0 yFX fXe E yFX fX E E ε εε == = = + = B. Each of these specifications has “problematic” implications. For example, the Cobb-Douglas specification implies that all inputs increase the risk of production: ( ) 2 2 0 0 1 , ,0 Vfxx E E xxe x ∂   = >  Note that this expectation is complicated by the fact the expectation of the exponential. Specifically, under log-normal distributions 2 1 2 Ee e µ σ + = C. Just and Pope propose 8 propositions that “seem reasonable and, perhaps, necessary to reflect stochastic, technical input-output relationships.” 1. Postulate 1: Positive production expectations [ ] 0 Ey > 2. Postulate 2: Positive marginal product expectations 0 i X > 3. Postulate 3: Diminishing marginal product expectations ( ) 2 2 0 i X < 4.

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## This note was uploaded on 07/15/2011 for the course AEB 6184 taught by Professor Staff during the Fall '09 term at University of Florida.

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Lecture 07-2005 - The Stochastic Nature of Production...

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