Measuring productivity in the open economy: Törnqvist perspectives

In this paper, we use a simple model of the production sector of an open economy to derive several Törnqvist measures of technological change, each one describing the same phenomenon, but from a different perspective. We argue that each one is legitimate in its own right, but that it is important to be aware of their differences in order to be able to reconcile them. While Törnqvist indices are superlative indices, they do not satisfy the factor reversal test. This can be viewed as a minor flaw, but it nevertheless is somewhat unsatisfactory for our work since it requires the making of arbitrary choices. We therefore propose a symmetric version of the Törnqvist index that satisfies the test, and which enables us to reduce the number of truly distinct perspectives. We furthermore show how these indices of technological change relate to average labour productivity measures, most of which also reflect changes in input and/or output mixes over time. We argue that in principle average labour productivity is a useful concept, but most of these ratios are inadequate as measures of technological change since their numerators and denominators are typically inconsistent with one another.