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

Aparicio, Crespo-Cebada, Pedraja-Chaparro, and Santin (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 vanishes. 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. Both results will make it easier for practitioners applying the two indexes in different economic sectors, regardless of how many groups are being compared.