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lecture6-2k

# lecture6-2k - AEB 6182 Lecture VI Professor Charles Moss...

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AEB 6182 Lecture VI Professor Charles Moss 1 Farm Portfolio Problem: Part II Lecture VI I. 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. A. This article is the basis for the application of MOTAD (Minimize Total Absolute Deviation) in agriculture. 1. Hazell’s approach is two fold. He first sets out to develop review expected value/variance as a good methodology under certain assumptions. 2. Then he raises two difficulties. a. The first difficulty is the availability of code to solve the quadratic programming problem implied by EV. b. The second problem is the estimation problem. Specifically, the data required for EV are the mean and the variance matrix. However, the variance matrix is an artifact of the assumption of normality. B. The crux of the estimation problem is that the covariance terms in the EV formulation are estimated by: x x s c g c g j k hj j hk k h s k n j n 1 1 1 1 1 - - - = = = ( )( ) where x j is the level of activity j in the portfolio, c hj is the observed return on asset j at time h, g j is the expected return on asset j, s is the number of observations, and n is the number of assets. This equality can be reformulated as: s 2 1 1 2 1 1 1 = - - = = = s c x g x j j n j j j n h s . Hazell suggests replacing this objective function with the mean absolute deviation ( 29 A s c g x j j j n h s = - = = 1 1 1 . 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 j j j n h h j j j n = - - = - = + - = 1 1 where y h is the deviation from average. This deviation can be divided into positive deviations from the average, y h + , and negative deviations from the average, y h - . The

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lecture6-2k - AEB 6182 Lecture VI Professor Charles Moss...

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