An Analysis of Ill‐Posed Production Problems Using Maximum Entropy

Abstract

Production economics problems are often ill-posed. This means that the number of parameters to be estimated is greater than the number of observations. In this article we show how to recover flexible cost functions from very limited data sets using a maximum entropy approach. We also argue that there exists a continuum of analysis between mathematical programming and traditional econometric techniques which is based solely upon the available information. The limiting case of a multi-output cost function recovered using only a single observation of a farmer's allocation decisions can be easily extended to handle more than one observation. Copyright 1998, Oxford University Press.

Positive Mathematical Programming for Farm Planning: Review

“…The two types of optimum conditions derived from the models are combined to derive linear equations for the calibration; however, the derived equations are indefinite because the number of parameters to be calibrated surpasses the number of equations. As a result, various methods have been proposed to solve this so-called ill-posed problem 32 . The objective of the present paper is to briefly survey the PMP studies that have been published.…”

“…Parameter c is specified on the basis of farm management data (see Nakashima 29 for the procedure), and once specified, it is denoted as ĉ. Given that the optimum dual variables associated with resource constraints coincide both in the QP model (1)- (3) and the LP model (4)- (7) The problem is that, without additional information, equation (8) does not have a unique solution in d and Q because there are fewer equations than unknowns to be calibrated (i.e., n < n + 0.5n (n + 1)), which is why this type of calibration is referred to as an ill-posed problem 32 . To solve the ill-posed problem, the following assumption has frequently been imposed: Assumption 1: Matrix Q is diagonal; that is, q ij = 0 if i ≠ j, where q ij (i = 1,2,…, n; j = 1,2,…, n) are the elements of Q. Assumptions 2.1 and 2.2 reduce the number of equations to match the number of parameters to be calibrated; therefore, respective unique solutions can be derived from equation (9) as…”

An ex-ante impact assessment of the Common Agricultural Policy reform in the North-Western Romania

“…The standard PMP (STPMP) means: (1) to specify a linear programming model bound by the calibration constraints, in order to find the shadow prices for the activities practiced in the base year; (2) to estimate a quadratic variable cost function that incorporates all the farming conditions not explicitly modelled elsewhere (C v ) Original Paper Agric.Econ.-Czech, 61, 2015 (2) Several critics were pointed out to the standard PMP (STPMP): (1) The marginal costs parameters (λ) do not permit to find all the cost function parameters (d and Q); (2) only the observed activities in the base year are incorporated into the final model; (3) there is a different treatment between the marginal activities (λ i = 0) and the others ). Some solutions were proposed to these critics: to use either the maximum entropy econometrics (Paris and Howitt 1998;Heckelei and Wolf 2003) or some a priori supply elasticity coefficients (Helming 2005), such as to recover all the data for an appropriate specification of the cost function; to introduce other a priori data about the activities that can be farmed in a specific region but not yet activated by the farmer (Arfini et al 2001).…”

Economics of Agricultural Water Conservation: Empirical Analysis and Policy Implications

“…Many authors since then have developed various refinements of PMP (e.g. Paris and Howitt, 1998;Preckel et al, 2002;Rohm and Dabbert, 2003;Heckelei and Wolff, 2003;Cai and Wang, 2006;Paris, 2001;Iglesias and Blanco, 2008;Cortignani and Severini, 2009). In our implementation of PMP, the first- order conditions for profit maximization are used to specify and estimate two parameters of a crop yield function that shows declining yields in the face of an expanded scale of land and water use.…”