Positive Mathematical Programming

Abstract

Positive Mathematical Programming (PMP) is an approach to empirical analysis that uses all the available information, no matter how scarce. It uses sample and user-supplied information in the form of expert opinion. This approach is especially useful in situations where only short time series are available as, for example, in sectoral analyses of developing countries and environmental economics analyses. PMP is a policy-oriented approach. By this characterization we mean that, although the structure of the PMP specification assumes the form of a mathematical programming model, the ultimate objective of the analysis is to formulate policy recommendations. In this regard, PMP is not different from a traditional econometric analysis. PMP grew out of two distinct dissatisfactions with current methodologies: first, the inability of standard econometrics to deal with limited and incomplete information and, second, the inability of linear programming (LP) to approximate, even roughly, realized farm production plans and, therefore, to become a useful methodology for policy analysis. The original work on PMP is due to Howitt. After the 1960s, a strange idea spread like a virus among empirical economists: only traditional econometric techniques were considered to be legitimate tools for economic analysis. In contrast, mathematical programming techniques, represented mainly by LP (which had flourished alongside traditional econometrics in the previous decade), were regarded as inadequate tools for interpreting economic behavior and for policy analysis. In reality, the emphasis on linear programming applications during the 1950s and 1960s provided ammunitions to the critics of mathematical programming who could not see the analytical potential of quadratic and, in general, nonlinear programming.