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

Abstract

In this paper, we propose a different way of using the Malmquist index that allows us to further analyze the relative performance divergences between two groups of decision-making units (DMUs) over time when only a pseudo-panel database is available. To do this, we extend the Camanho and Dyson ( 2006) one-period Malmquist-type index (CDMI) for a pseudo-panel database with a new pseudo-panel Malmquist index (PPMI). To illustrate the methodology, we apply it to examine how the performance gap between public and private government-dependent secondary schools in the Basque Country (Spain) performed across three PISA waves (2006, 2009 and 2012). The results suggest that performance is persistently and significantly higher for private government-dependent schools than for public schools.

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

“…However, there are two aspects that must be necessarily improved in the approach introduced by Aparicio et al (2017) for endowing the PPMI approach with greater usefulness among practitioners. First, the PPMI is the ratio of two CDMIs and measures the relative performance gap change between two groups of DMUs within periods t and t+1.…”

“…However, this is only true under some conditions. In particular, a factor baptized as a divergence component (DC), which is difficult to interpret, needs to be equal to one (Proposition 1 in 3 Aparicio et al 2017), something that does not always happen. Indeed, in the empirical application used by Aparicio et al (2017) for showing how PPMI works, the two DCs were different from one (specifically, 0.9138 and 0.9304).…”

“…The CDMI has been recently extended by Aparicio et al (2017) in the context where a panel data or a pseudo-panel data is available and the objective is to determine how the measured performance gap changes over time. A panel implies that the same group of DMUs is observed across all analyzed periods.…”

“…The production units contained in each wave vary from one period to another and are usually anonymous for researchers. This organization of the information is referred to as a pseudopanel database and, in this case, the approach introduced in Aparicio et al (2017) can be used to compare the performance of these representative groups of DMUs over time using a pseudo panel…”

“…With the aim of analyzing the evolution of the performance gap between groups A and B over two time periods, t and 1 t  , Aparicio et al (2017) proposed making the ratio of two CDMIs calculated for the two considered periods. The application of this strategy allows the evolution of the different groups of DMUs over time to be checked, thus providing policy makers with valuable information.…”