Lecture 06-2005 - Simultaneity and Other Simple Problems...

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1 Simultaneity and Other “Simple” Problems Lecture VI I. Simultaneity and Estimation of the Production Function A. The above discussion (and estimates) makes the experimental plot design assumption regarding the data. 1. Specifically, I essentially assumed that the data are being generated from some sort of experimental design so that the errors are truly random. 2. If the data are actually the result of farm level decisions, the data are endogenous. B. The simultaneity literature starts with: Hock, Irving. “Simultaneous Equation Bias in the Context of the Cobb-Douglas Production Function.” Econometrica 26(4)(Oct 1958): 566-78. 1. The basic firm-level model is that we have an empirical model under the assumption of: a. A Cobb-Douglas production function, and b. Competition. 2. In Hoch’s notation the production function becomes 00 1 q Q a q q X KX = = a. where 0 X is the level of output, b. q X is a level of physical input, c. q a is the elasticity of output with respect to an input, and d. 0 K is a constant. 3. Assuming profit maximization, an output price of 0 P , and input prices of q P , we have the profit maximization conditions qq XX PP a P  = =   Dividing through by q P 0 1 q XP Y aa Y = = where 0 Y is the total value of output and q Y is the total value of each input. a. Klein demonstrates that the best linear unbiased estimate of q a is 1 1 0 ˆ I I qi q i i Y a Y = =
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AEB 6184 – Production Economics Lecture VI Professor Charles B. Moss Fall 2005 2 b.
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Lecture 06-2005 - Simultaneity and Other Simple Problems...

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