Daniel Santín

Measuring educational efficiency at student level with parametric stochastic distance functions: an application to Spanish PISA results

The aim of the present paper is to examine the observed differences in Students’ test performance across public and private‐voucher schools in Spain. For this purpose, we explicitly consider that education is a multi‐input multi‐output production process subject to inefficient behaviors, which can be identified at student level using a parametric stochastic distance function approach. The empirical application of this model, based on Spanish data from the Programme for International Student Assessment implemented by the Organization for Economic Co‐operation and Development in 2003, allows us to identify different aspects of the underlying educational technology. Among other things, the results provide insights into how student background, peer group, school characteristics and personal circumstances interact with educational outputs. Moreover, our findings suggest that, once educational inputs and potential bias due to school choice endogeneity are taken into account, no further unexplained difference remains between students’ efficiency levels across public and private‐voucher schools.

The measurement of technical efficiency: a neural network approach

The main purpose of this paper is to provide an introduction to artificial neural networks (ANNs) and to review their applications in efficiency analysis. Finally, a comparison of efficiency techniques in a non-linear production function is carried out. The results suggest that ANNs are a promising alternative to traditional approaches, econometric models and non-parametric methods such as data envelopment analysis, to fit production functions and measure efficiency under non-linear contexts.

Alternative approaches to include exogenous variables in DEA measures: A comparison using Monte Carlo

The theory for measuring efficiency of producers has developed alternative approaches to correct for the effect of non-discretionary variables in the analysis. A review of different options in the specific literature of Data envelopment analysis (DEA) allows us to identify three main approaches: one-stage, two-stage and multi-stage models. Recently, some of these models have been improved through the development of bootstrap methods making it possible to make inference and to avoid bias in the estimation of efficiency scores. The aim of this paper is to test the performance of these recent models and to compare among them using simulated data from a Monte Carlo experimental design.

How to generate regularly behaved production data? A Monte Carlo experimentation on DEA scale efficiency measurement

Monte Carlo experimentation is a well-known approach used to test the performance of alternative methodologies under different hypotheses. In the frontier analysis framework, whatever the parametric or non-parametric methods tested, experiments to date have been developed assuming single output multi-input production functions. The data generated have mostly assumed a Cobb-Douglas technology. Among other drawbacks, this simple framework does not allow the evaluation of DEA performance on scale efficiency measurement. The aim of this paper is twofold. On the one hand, we show how reliable two-output two-input production data can be generated using a parametric output distance function approach. A variable returns to scale translog technology satisfying regularity conditions is used for this purpose. On the other hand, we evaluate the accuracy of DEA technical and scale efficiency measurement when sample size and output ratios vary. Our Monte Carlo experiment shows that the correlation between true and estimated scale efficiency is dramatically low when DEA analysis is performed with small samples and wide output ratio variations.

On the approximation of production functions: a comparison of artificial neural networks frontiers and efficiency techniques

The aim of this article is to show how Artificial Neural Networks (ANN) is a valid semi-parametric alternative for fitting empirical production functions and measuring technical efficiency. To do this a Monte-Carlo experiment is carried out on a simulated smooth production technology for assessing efficiency results of ANN compared with Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA). As ANNs provides average production function estimations this article proposes a so-called thick frontier strategy for transform average estimations into a productive frontier. Main advantages of ANN are in contexts where the production function is smooth, completely unknown, contains nonlinear relationships among variables and the quantity of noise and efficiency in data is moderate. Under this scenario, the results display that an ANNs algorithm can detect, better than traditional tools, the underlying shape of the production function from observed data.

Testing the accuracy of DEA estimates under endogeneity through a Monte Carlo simulation

Endogeneity, and the distortions on the estimation of economic models that it causes, is a usual problem in the econometrics literature. Although non-parametric methods like Data Envelopment Analysis (DEA) are among the most used techniques for measuring technical efficiency, the effects of such problem on efficiency estimates have received little attention. The aim of this paper is to alert DEA practitioners about the accuracy of their estimates under the presence of endogeneity. For this, first we illustrate the endogeneity problem and its causes in production processes and its implications for the efficiency measurement from a conceptual perspective. Second, using synthetic data generated in a Monte Carlo experiment we evaluate how different levels of positive and negative endogeneity can impair DEA estimations. We conclude that, although DEA is robust to negative endogeneity, a high positive endogeneity level, i.e., the existence of a high positive correlation between one input and the true efficiency level, might bias severely DEA estimates.

Assessing European primary school performance through a conditional nonparametric model

This paper uses a fully nonparametric framework to assess the efficiency of primary schools using data about schools in 16 European countries participating in PIRLS 2011. This study represents an original enterprise since most of the empirical research in the field is restricted to evaluations at regional or national level and focused on secondary education. For our purpose, we adapt the metafrontier framework to compare and decompose the technical efficiency of primary schools operating in heterogeneous contexts, which in our case is represented by different educational systems or countries. Similarly, we use an extension of the conditional nonparametric robust approach to test the potential influence of a mixed set of environmental school factors and variables representing cultural values of each country. Our results indicate that the intergenerational transmission of non-cognitive skills such as responsibility or perseverance are significantly related to school efficiency, whereas most school factors do not seem to have a significant influence on school performance.

Measuring the technical efficiency of football legends: who were Real Madrid's all-time most efficient players?

Many football players contribute to aggregate results throughout a football clubs history. However, no scientific research has pinpointed the most technically efficient players in a football clubs history considering their position on the field. The aim of this paper is to propose an output-oriented nonincreasing returns to scale super-efficiency data envelopment analysis (DEA) model in order to measure football players’ performance. The model is applied empirically to Real Madrids best players (white legends) from the signing of Luis Molowny to Raul Gonzalezs departure. Results are also calculated and compared with the standard DEA in order to form the most efficient and super-efficient historical squad of Real Madrid footballers.

Imposing monotonicity on outputs in parametric distance function estimations

The technology set involved in the estimation of a multi-output production frontier theoretically implies monotonicity on outputs. This is because an efficient firm cannot reduce the vector of outputs holding the vector of inputs fixed while it still belongs to the frontier. In empirical studies dealing with the estimation of parametric distance functions, this hypothesis is often violated by observations with far from average characteristics. To overcome this limitation, we propose a new approach for allowing the easy imposition of monotonicity on outputs in this context. This methodology is tested in the educational sector using Spanish student level data from the Programme for International Student Assessment (PISA) database. The results indicate that a nonnegligible 8.33% of the production units break the monotonicity assumption. Furthermore, although there is no statistically significant difference in efficiency distribution by school ownership, our methodology helps to detect a slight worse mathematical performance for students attending public schools.

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

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.