Measurement of Technical Efficiency in Public Education: A Stochastic and Nonstochastic Production Function Approach

Abstract

1. Introduction Efficiency in the public education system is a significant issue in the United States. Nationwide, real expenditure per student in public education increased more than 3% per year between 1960 and 1998, but output as generally measured by standardized test scores has not increased and in some cases (e.g., the verbal SAT score) has declined.' One explanation is that resources are not being utilized efficiently. There may be productive or technical inefficiency and/or allocative or price inefficiency (i.e., given the relative prices of inputs, the cost minimizing input combination is not used). This paper focuses on the former by evaluating technical inefficiency in public education using data from Utah school districts. The pioneering work by Farrell in 1957 provided the definition and conceptual framework for both technical and allocative efficiency. Although technical efficiency refers to failure to operate on the production frontier, allocative efficiency generally refers to the failure to meet the marginal conditions for profit maximization. Considerable effort has been made in refining the measurement of technical efficiency. The literature is broadly divided into deterministic and stochastic frontier methodologies.2 The deterministic nonparametric approach that developed out of mathematical programming is commonly known as data envelopment analysis (DEA), and the parametric approach that estimates technical efficiency within a stochastic production, cost, or profit function model is called the stochastic frontier method. Both approaches have advantages and disadvantages, as discussed in Forsund, Lovell, and Schmidt (1980). DEA has been used extensively in measuring efficiency in the public sector, including education, where market prices for output generally are not available. For example, Levin (1974), Bessent and Bessent (1980), Bessent et al. (1982), and Fare, Grosskopf, and Weber (1989) used this method to estimate efficiency in public education. The stochastic frontier methodology was used by Barrow (1991) to estimate a stochastic cost frontier using data from schools in England. Wyckoff and Lavinge (1991) and Cooper and Cohn (1997) estimated technical efficiency using school district data from New York and South Carolina, respectively. Grosskopf et al. (1991) used the parametric approach to estimate allocative and technical efficiency in Texas school districts. The recent literature has seen a convergence of the two approaches and their complementarity is being recognized.3 However, there is a lack of empirical evidence in the literature about the proximity of these two approaches in measuring technical efficiency. Policy formulations based on only one of these efficiency estimates may not be accurate because of the inherent limitations of each. Before any correctional measures are taken, the stability of the technical efficiency estimates obtained from a parametric method should be evaluated by comparing them against those found when using the nonparametric method. In this study, the technical efficiency estimates for each school district using the stochastic frontier method and Tobit residuals from the two-stage DEA model are compared. In the twostage DEA model, technical efficiency scores obtained from DEA using controllable inputs are regressed on student socioeconomic status and other environmental factors. The residuals of this regression measure pure technical efficiency after accounting for fixed socioeconomic and environmental factors. The empirical analysis uses data from the 40 school districts in Utah for the academic year 1992-1993. The standardized test score for 11 th-grade students is used as a measure of school output, and two classes of inputs are included. The first class is considered to be subject to control by school administrators and includes the student-teacher ratio, the percentage of teachers having an advanced degree, and the percentage of teachers with more than 15 years of experience. …