TITLE:
Estimation of CARA Preferences and Positive Mathematical Programming
AUTHORS:
Quirino Paris
KEYWORDS:
CARA Coefficient, Chance-Constrained Approach, Positive Mathematical Programming, Solution Uniqueness, Calibrating Model
JOURNAL NAME:
Open Journal of Statistics,
Vol.8 No.1,
January
26,
2018
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.