Lecture 05-2005

# Lecture 05-2005 - Estimation of the Primal Production...

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1 Estimation of the Primal Production Function Lecture V I. Ordinary Least Squares A. The most straightforward concept in the estimation of production function is the application of ordinary least squares. 1. Taking the quadratic production function as a starting point 2 0 1 1 2 2 3 3 11 1 12 1 2 13 1 3 22 22 2 23 2 3 33 3 ya a x a x A x x x Ax Axx Ax ε =+ + + + + + + ++ + a. Note that we have already applied symmetry on the quadratic. From an estimation perspective, since 12 21 x xx x = any other approach would not work. b. Using data from Indiana and Illinois, we apply ordinary least squares to this specification to estimate Table 1. Estimates of the Quadratic Production Function. Parameter Estimate α 0 100.28194 (6.81173) a α 1 -0.00535 (0.07911) α 2 0.23445 ** (0.10630) α 3 0.05900 (0.07947) A 11 0.00014 (0.00030) A 12 -0.00089 (0.00082) A 13 0.00073 (0.00047) A 22 0.00019 (0.00038) A 23 -0.00087 * (0.00049) A 33 -0.00007 (0.00031) ** Denotes statistical significance at the .05 confidence level. * Denotes statistical significance at the .10 confidence level. a Numbers in parenthesis denote standard deviations.

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AEB 6184 Production Economics Lecture V Professor Charles B. Moss Fall 2005 2 c. Do these estimates make any sense? What is wrong? 2. Turning to the Cobb-Douglas form ( ) ( ) ( ) ( ) ( ) 123 1 2 3 ln ln ln ln ln yA x x x y A x x x αβγ =⇒ = + + + a. One alternative is then to run the regression ( ) ( ) ( ) ( ) 01 1 2 2 3 3 ln ln ln ln yx x x α αα ε =+ + + + b. What are some of the problems with this specification? (1) First, the one problem is that there may be zero input levels. What is the production theoretic problem with zero input levels? What is the econometric problem with zero input levels?
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Lecture 05-2005 - Estimation of the Primal Production...

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