AEB 6184 – Simulation and Estimation of the Primal Elluminate - 6.

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Presentation transcript:

AEB 6184 – Simulation and Estimation of the Primal Elluminate - 6

Cobb-Douglas Parameters

Fuel Use (Field Operations)Fertilizer Dry Spread0.15Nitrogen91.80 Disk-Chisel1.70Phosphorous36.58 Field Cultivate0.70Potash23.50 Planting0.40 Spraying0.10 Combine1.45 Total Diesel4.50 Diesel Price2.64 Total Fuel11.88Total Fertilizer Field Data for Corn

Total Costs and RevenuesParameters Total Fuel11.88α Total Fertilizer151.88β Total Labor33.06γ Total Variable Cost196.82Diesel (gal.)4.50 Corn Yield135.0Fertilizer (tons) Corn Price4.50Labor (hours)4.15 Total Revenue Profit per Acre Revenues

Prices Corn Price (FL) Corn Price (GA) Fertilizer Price Fuel Price (Diesel) Labor Price

Cobb-Douglas Function

 We need to think about three four prices  Corn Price  Diesel Price  Fertilizer Price  Labor Price  We could assume normality  How to choose Ω?  Possible negative prices? Drawing Prices

 We could choose a uniform distribution.  For our purpose here, let’s assume that the standard deviation is 1/3 of the value of each price.  In addition, let’s assume that the input prices have a correlation coefficient of 0.35 and the output price is uncorrelated.  The variance matrix then becomes

 In the univariate form, given a mean of  and a standard deviation of  we would create the random sample by drawing a z from a standard normal distribution  In the multivariate world, we use the Cholesky decomposition of the variance matrix and use the vector of the means Drawing Random Samples

CornFuelFertilizerLabor Price Draws

Production Levels

FuelFertilizerLaborOutput Input Demands and Output Levels

 First stage estimation – Ordinary Least Squares  Second stage – System Ordinary Least Squares using the first-order conditions.  From the first-order conditions Estimation

 Each of the observations in the system can then be expressed as Estimation (Continued)

 Imposing the cross equation restrictions Estimation (Continued)

 First estimation (without heteroscedasticity) Estimation (Continued)

 With heteroscedasticity Estimation (Continued)

Parameter123True Alpha Alpha Alpha Alpha Kappa Kappa Results