Lecture13-2004 - Farm Portfolio Problem: Part II Lecture...

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Farm Portfolio Problem: Part II Lecture XIII
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Fall 2004 Farm Portfolio Problem II 2 MOTAD Hazell, P.B.R. “A Linear Alternative to Quadratic and Semivariance Programming for Farm Planning Under Uncertainty.” American Journal of Agricultural Economics 53(1971):53-62.
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Fall 2004 Farm Portfolio Problem II 3 Hazell’s approach is two fold. He first sets out to develop review expected value/variance as a good methodology under certain assumptions. Then he raises two difficulties. The first difficulty is the availability of code to solve the quadratic programming problem implied by EV. The second problem is the estimation problem. Specifically, the data required for EV are the mean and the variance matrix.
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Fall 2004 Farm Portfolio Problem II 4 The variance of a particular farming plan can be expressed as x x s c g c g j k hj j hk k h s k n j n 1 1 1 1 1 - - - = = = ( )( ) σ 2 1 1 2 1 1 1 = - - = = = s c x g x hj j j n j j j n h s
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Fall 2004 Farm Portfolio Problem II 5 Hazell suggests replacing this objective function with the mean absolute deviation ( 29 A s c g x hj j j j n h s = - = = 1 1 1
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Fall 2004 Farm Portfolio Problem II 6 Thus, instead of minimizing the variance of the farm plan subject to an income constraint, you can minimize the absolute deviation subject to an income constraint. Another formulation for this objective function is to let each observation h be represented by a single row ( 29 ( 29 y c g x y y c g x h hj j j j n h h hj j j j n = - - = - = + - = 1 1
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Fall 2004 Farm Portfolio Problem II
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Lecture13-2004 - Farm Portfolio Problem: Part II Lecture...

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