A note on measuring group performance over time with pseudo-panels

Aparicio et al. (2017) recently extended the Camanho and Dyson (2006) Malmquist-type index (CDMI) for determining group performance in cross-sectional studies to panel or pseudo-panel databases. In that paper, it was shown that the pseudo-panel Malmquist index (PPMI) can be easily interpreted as the ratio of aggregated productivity changes in two groups of decision making units over time if and only if a new -difficult to interpret- term, the so called ‘divergence component’ (DC), is equal to one. The aim of this paper is twofold. First, based upon considering a baseline group technology we define a new base-group base-period PPMI where the DC always vanished. Second, when more than two groups are analyzed we show that under this framework the new base-group base-period PPMI, the new base-group CDMI and the components of both indexes satisfy the circular relation. As a consequence, the complicated ‘adjusted index’ defined in Camanho and Dyson (2006) for measuring the technology gap to satisfy the circular relation also vanishes. Both results will make it easier for practitioners applying the two indexes in different economic sectors regardless of how many groups are being compared.