Productivity, efficiency, and technical change of Tunisian schools: a bootstrapped Malmquist approach with quasi-fixed inputs

• The productivity of Tunisian high school is assessed using Malmquist indices.
• The Malmquist index takes into account quasi-fixed factors.
• The precision of the estimators is assessed using a smooth bootstrap procedure.
• The index and its components are highly sensitive to sample variations.
• There are virtually no significant productivity variation over the period studied.

In this study, we measure the productivity of high schools in Tunisia over the period 2000/2001–2003/2004 using a Malmquist productivity index that we decompose into technical efficiency, scale efficiency and technological change. This decomposition allows us to identify the source of productivity changes. We also adapt the definition of the Malmquist index to take into account quasi-fixed factors. The distance functions are then estimated using data envelopment analysis. To assess the statistical precision of the estimators, we implement a smooth homogenous bootstrap procedure that allows us to approximate the sampling distribution of the estimators, to correct their bias, and to construct confidence intervals for the various components of the Malmquist index. The application of our methodology to Tunisian high schools shows the high sensitivity to sample variations of the observed index changes and of its components. However, we are able to show that there is virtually no significant productivity variation over the period studied. This absence of productivity can be almost all attributed to technical regression and, to a lesser extent, to technical inefficiency.