The application of production frontier techniques to the metaproduction function: Estimating international agricultural productivity and efficiency

Total factor productivity, technical change, and technical efficiency change in international agriculture are measured and examined by three procedures. Agricultural production technologies are represented by a best-practice frontier, a theoretical construct that is considered in this study to be synonymous with a metaproduction function. The first two estimation procedures involve an econometric model and a linear programming technique applied to the same data set in constructing the best-practice frontier. The varying coefficients model where coefficients are now random, not fixed, estimates the best-practice frontier by the econometric estimation of a Cobb-Douglas functional form of the metaproduction function. A linear programming technique known as Data Envelopment Analysis (DEA) is used to construct this best-practice frontier. Distance functions derived from the DEA procedure are then used to calculate a Malmquist productivity index, an index which can be decomposed into a technical change component and an efficiency change component. The third estimation technique involves the derivation of distance functions from the varying coefficients procedure and substituting them into the formula for a Malmquist productivity index.; The data consist of an annual, cross-sectional, time series set of agricultural and educational variables from 92 selected countries between 1961 to 1990.; With one exception, no complete consensus exist on the results among the three estimation procedures. The one exception is that most countries in the data set exhibited an average negative productivity growth in agriculture. The varying coefficients model and the DEA-based Malmquist productivity index exhibited a high degree of correlation in tracking productivity growth rates but a divergence in their respective measures of technical change and efficiency change. The varying coefficients model and the Malmquist productivity index derived from it are similar in placing a greater weight on the efficiency change component and a lesser amount on technical change but have differing measures of productivity growth. Further and more extensive research is needed to determine whether or not alternative estimation techniques of productivity measures produce collaborative results.