AEB 6184

1
AEB 6184 Mitscherlich-Baule Production Function
and McFadden Cost Function

• Elluminate - 13

2
Mitscherlich-Baule Production Function

• Starting with the simulated cost surface for
  production
• I generated 200 minimum cost solutions using
  numerical optimization for a vector of randomly
  drawn prices.
• I also added a correlated error term.

3
Normalized Quadratic Cost Function

• Following our discussion from the class, I
  estimated the normalized quadratic cost function

4
Normalized Quadratic Results
Coefficient Estimate Std. Dev. t-ratio
A0 10.1091 0.0019 5386.0690
A1 25.2884 0.0302 838.1074
A2 20.6540 0.0303 681.2309
A11 -40.9602 0.0301 -1360.3379
A12 11.7768 0.0261 450.4070
A22 -30.8339 0.0303 -1018.9975
B1 0.0355 0.0001 -438.4198
B11 0.0001 0.0000 49.3547
G1 0.0513 0.0002 273.4090
G2 0.0443 0.0002 208.2206
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Eigenvalues of A

• The eigenvalues of A indicate that the cost
  function is concave in input prices.
• In addition, the negative sign on the squared y
  indicates that the surface is convex in output
  levels.

6
McFadden Cost Function

• Diewert, W.E. and T.J. Wales. 1987. Flexible
  Forms and Global Curvature Conditions
  Econometrica 55(1), 43-68.

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Shephards Lemma

• Taking the derivatives Two cases
• i1
• i 2,

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Hessian Matrix

• The Hessian matrix is then determined by the
  quadratic term
• Concavity can be imposed by Laus method

9
McFadden Estimates
Parameter Estimate Std. Dev. T-Ratio
c11 -0.0117 0.0045 -2.5800
c12 0.0029 0.0021 1.3648
c22 -0.0038 0.0016 -2.4328
b11 0.0262 0.0072 3.6396
b22 0.0428 0.0110 3.8931
b33 0.0441 0.0188 2.3492
b1 -2.2196 2.0865 -1.0638
b2 47.2642 20.0597 2.3562
b3 4.8732 1.5026 3.2431
byy -3.0245 1.0477 -2.8867
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Concavity