Abstract
The purpose of this paper is to combine the estimation of output price risk and positive mathematical programming (PMP). It reconciles the risk programming presented by Freund with a consistent estimate of the constant absolute risk aversion (CARA) coefficient. It extends the PMP approach to calibration of realized production outputs and observed input prices. The results of this specification include 1) uniqueness of the calibrating solution, 2) elimination of the tautological calibration constraints typical of the original PMP procedure, 3) equivalence between a phase I calibrating solution and a solution obtained by combining phase I and phase II of the traditional PMP procedure. In this extended PMP framework, the cost function specification involves output quantities and input prices—contrary to the myopic cost function of the traditional PMP approach. This extension allows for a phase III calibrating model that replaces the usual linear technology with relations corresponding to Shephard lemma (in the primal constraints) and the marginal cost function (in the dual constraints). An empirical example with a sample of farms producing four crops illustrates the novel procedure.
Highlights
The treatment of risk in a mathematical programming setting has interested researchers for several decades
The purpose of this paper is to combine the estimation of output price risk and positive mathematical programming (PMP)
It extends the PMP approach to calibration of realized production outputs and observed input prices. The results of this specification include 1) uniqueness of the calibrating solution, 2) elimination of the tautological calibration constraints typical of the original PMP procedure, 3) equivalence between a phase I calibrating solution and a solution obtained by combining phase I and phase II of the traditional PMP procedure
Summary
The treatment of risk in a mathematical programming setting has interested researchers for several decades. It all began with Markowitz [1] who presented the problem of portfolio selection in a mean-variance framework. Freund [2] discussed a quadratic programming approach to deal with output price risk in a mean-variance specification of revenue. Pratt [4] proposed a general way to characterize absolute risk aversion—known as the Arrow-Pratt measure of risk—which is defined as the negative ratio of the second derivative to the first derivative of a utility function of wealth. The objective of this paper, is twofold: 1) to estimate the CARA parameter in an empirical way that is consistent with the available sample information; 2) to combine the CARA risk analysis with a positive mathematical programming (PMP) approach that uses all the available information
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
