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.