Comparing school ownership performance using a pseudo-panel database: A Malmquist-type index approach

The Malmquist Index methodology is widely used in production economics for measuring the productivity changes of a set of decision making units (DMUs) within different time periods. Moreover, it is quite usual in the management literature to compare public and private DMU performance operating under the same economic sector. However, the standard Malmquist index needs a panel database to be implemented, i.e. it focuses on analyzing the evolution of the same DMUs over time. In this paper, we propose a different way of using the Malmquist index that allows us to further analyze the performance divergences between public and private DMUs when only a pseudo-panel database is available. The paper extends Camanho and Dyson’s oneperiod Malmquist-type index (Camanho and Dyson, 2006) when a pseudo-panel database is available. We apply this methodology to examine the differences in public high school and private government-dependent high school productivity for three Spanish Regions -Catalonia, Castile-Leon and Basque Countrywhich entered representative samples in PISA 2003, 2006 and 2009. Finally, in order to obtain a measure of the significance of results, we use and adapt the bootstrap methodology proposed by Simar and Wilson (1999) to obtain the confidence intervals for the Malmquist-type indices and their components. The results suggest a persistent and significant higher performance of private government-dependent schools over public institutions in all three Spanish regions. Moreover, this difference persists over time.