FINANCIAL HEALTH OF THE SPANISH EDUCATIONAL PRIVATE INSTITUTIONS
Education is of vital importance for the competitiveness and growth of any country, but as any sector is affected by the amount of public and private investment, in particular, by governments and the economic leverage of citizens to pay tuitions. The financial crisis, originated in 2008, had some degree of impact in the European education system, which has not been completely understood. Spain is one of the countries that has suffered most from its impact, as reflected in the report of the Organization for Economic Cooperation and Development (OECD) of 2016. While in most countries public spending on education has remained stable at 11%, in Spain public spending on education has fallen from 9 to 8% from 2008 to 2013. The expenditure per student was below the OECD average in all stages, from primary to university. But usually data are known for the public sector and the impact of the private sector is neglected. However, a considerable percentage of students in Spain received education in private institutions, turning it a good case-study for studying the impact of economy in education.
Our work examines the efficiency of more than 4.000 Spanish private institutions divided into four educational levels: pre-primary, primary, secondary and higher education, in the period 2006-2016. We study their evolution at three distinct stages: efficiency levels; efficiency patterns; and efficiency determinants. Our results clarify which are the profile of institutions that are most efficient and which are not, giving some insight about the improvements which could be applied to raise their effectiveness. To this end, we take as a starting point the financial statements of each institution, considering variables that allow us to interpret measures of leverage, liquidity, profitability, management and evaluation of the institution. Its efficiency and corresponding financial situation is analysed. Then, the obtained information is related with students enrolment and performance.
The main mathematical tool used is a nonparametric deterministic method for measuring efficiency, the Multidirectional Efficiency Analysis (MEA) of (Bogetoft 1999), in combination with other techniques. In contrast with the standard DEA, MEA also allows to investigate changes in efficiency patterns. Since the selection of relevant variables is of major importance, a combination of techniques to choose the most meaningful ones is used, namely, through Principal Component Analysis and to avoid loss of information (under-fitting) or the adding random noise (over-fitting), the RV coefficient is computed, see Robert and (Escoufier 1976). Comparisons between groups with different levels of efficiency are made by calculating a coefficient that measures the overlapping of two Gaussian distribution functions (Inman 1989).
 P. Bogetoft and J. L. Hougaard, Efficiency evaluations based on potential (non-proportional) improvements, J. Productivity Analysis, 12(3), 233-247, 1999.
 Inman, H.F. and Bradley, Jr E.L., The overlapping coefficient as a measure of agreement between probability distributions and point estimation of the overlap of two normal densities, Comm. in Stat, Theory and Methods, 18(10), 3851--3874, 1989.
 Report: Panorama de la Educacion, Indicadores de la OCDE, Inst Nacional de Evaluacion Educativa, Madrid, 1--77, 2016.
 Robert P. and Escoufier Y, A unifying tool for linear multivariate statistical methods: the RV coefficient, Appl Stat, 25, 257--265, 1976.