Comparing Firm Performance Using Transitive Productivity Index Numbers in a Meta-frontier Framework

The meta-frontier framework has been used extensively for evaluating the technical efficiency of heterogeneous production units that can be classified into different groups. This paper shows how the framework can also be used to make total factor productivity (TFP) comparisons within and across groups. The paper develops a new measure of the distance between a group frontier and the meta-frontier (the so-called ‘technology gap’). It then shows how a spatially- and temporally-transitive TFP index can be decomposed into measures of global technical change (measuring movements in the metafrontier), local technical change (measuring movements in the group frontiers) and efficiency change (measuring movements towards or around the group frontiers). To illustrate the methodology, the paper examines the productive performance of road authorities responsible for maintaining interstate highways in the US state of Virginia.

Measuring and analysing productivity change in a metafrontier framework

We consider the problem of measuring and analysing productivity change when firms have access to multiple technologies (i.e., techniques for transforming inputs into outputs). We measure productivity change using an index that satisfies a set of basic axioms from index theory (e.g., identity, proportionality, transitivity). We show how indices of this type can be exhaustively decomposed into various measures of environmental change, technical change and efficiency change. We are particularly interested in the relationship between productivity and technical efficiency. In theory, if firms have access to multiple technologies, then measures of technical efficiency can be decomposed into metatechnology ratios (measures of how well firm managers choose technologies) and measures of residual technical efficiency (measures of how well chosen technologies are used). We explain how data envelopment analysis (DEA) can be used to estimate these components. To illustrate, we use DEA to estimate the productivity gains and losses associated with using different highway maintenance technologies in Virginia

Dynamic Analysis of Production

A parable of economic life is that some factors can adjust rapidly while others adjust slowly in a given time scale. Focusing on production analysis in the dynamic setting leads us to emphasize the technology specification that permits the theoretical construction that can be translated and amenable to empirical implementation. A historical perspective of the framing the dynamic decision-making is reviewed. The adjustment cost model of the investment is the key conceptual feature as it can be incorporated into the formal structure of a production technology, which offers the opportunity to exploit primal-dual theory in both analysis and empirical implementation. An overview of empirical formulations in both econometric (parametric) and nonparametric settings is discussed. Dynamic production decision environment allows explicitly for the evolution of assets implying firms may not be in long-run equilibrium at a given point in time. The dynamic generalizations of modern production theory concepts measuring economic performance are reviewed given the need to properly account and value the factors that are out of equilibrium. Empirical nonparametric and parametric approaches are addressed at length. While these cases can be addressed relatively easily within a nonparametric, dynamic data envelopment analysis setting, econometric formulations are a greater challenge