Lecture05-2011

# Lecture05-2011 - Estimation of the Primal Production...

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Estimation of the Primal Production Function: Lecture V Charles B. Moss September 6, 2011 Charles B. Moss () September 6, 2011 1 / 19

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Outline 1 Ordinary Least Squares Empirical Estimates of the Quadratic The Cobb-Douglas Production Function Empirical Estimates of the Cobb-Douglas Transcendental Production Function Empirical Results for the Transcendental 2 Nonparametric Production Functions Two Nonparametric Approaches Nonparametric Regression Kernel Production Frontier Contour Plot Marginal Physical Product of Nitrogen Charles B. Moss () September 6, 2011 2 / 19
Ordinary Least Squares Ordinary Least Squares The most straightforward concept in the estimation of production function is the application of ordinary least squares. y = a 0 + a 1 x 1 + a 2 x 2 + a 3 x 3 + A 11 x 2 1 + A 12 x 1 x 2 + A 13 x 1 x 3 + A 22 x 2 2 + A 23 x 2 x 3 + A 33 x 2 3 + ± (1) Note that we have already applied symmetry on the quadratic. From an estimation perspective since x 1 x 2 = x 2 x 1 any other approach would not work. Using data from Indiana and Illinois, we apply ordinary least squares to this speciﬁcation. Charles B. Moss () September 6, 2011 3 / 19

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Ordinary Least Squares Empirical Estimates of the Quadratic Empirical Estimates of the Quadratic Parameter Estimate Parameter Estimate α 0 100.2819 A 12 -0.00089 (6.8117) (0.00030) α 1 -0.0054 A 13 0.00073 (0.0791) (0.00047) α 2 0.2344 A 22 0.00019 (0.1063) (0.00038) α 3 0.0590 A 23 -0.00087 (0.0795) (0.00049) A 11 0.000138 A 33 -0.00007 (0.00030) (0.00031) Do these estimates make any sense? What is wrong? Charles B. Moss () September 6, 2011 4 / 19
Ordinary Least Squares The Cobb-Douglas Production Function The Cobb-Douglas Production Function Turning to the Cobb-Douglas form y = Ax α 1 x β 2 x γ 3 ln ( y ) = ln ( A ) + α ln ( x 1 ) + β ln ( x 2 ) + γ ln ( x 3 ) ln ( y ) = ln ( A ) + α ln ( x 1 ) + β ln ( x 2 ) + γ ln ( x 3 ) + ± (2) What are some of the problems with this speciﬁcation?

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Lecture05-2011 - Estimation of the Primal Production...

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