Abstract
In the previous chapter, standard DEA models analyzing the performance of DMUs producing multiple outputs using multiple inputs were presented. These models provide a useful starting point for analyzing educational and other public sector production processes. One of the key distinguishing features of public sector publication is the presence of non-discretionary environmental factors of production that introduces heterogeneity among decision making units. It is well known, for example, that socioeconomic factors such as income, poverty, parental education etc. play a large role in the production of output. In fire services, the material of the houses (brick vs. wood) determines how successful firefighters will be in putting out fires. In health care, preexisting conditions and age of the patients could determine the success of a particular treatment.
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Notes
- 1.
Estelle, Johnson, and Ruggiero (2010) compare and contrast using OLS, tobit, fractional logit and nonparametric regression in the second stage. The results provide similar results.
- 2.
In the multiple stage model presented later in the chapter, the assumption of a monotonically increasing relationship between output and the environmental factors is dropped.
- 3.
For programming purposes, we refer to the nondiscretionary input as z 1. In Sect. 3.5 we consider the multiple stage model when there are multiple nondiscretionary variables.
- 4.
The environmental scale measures can be defined using either a VRS or CRS technology. We follow Ruggiero (2000) and only consider VRS measures.
- 5.
Alternatively, we could remove scale inefficiency from this measure by using the constant returns to scale projections.
- 6.
The output results are modified for formatting purposes.
- 7.
We could define an index of environmental harshness based on the ratio of minimum costs
- 8.
This variable is labeled C1 in the SAS code that follows.
- 9.
Other regression procedures have been considered. For example, McCarty and Yaisawarng (1993) used Tobit. Banker and Natarajan (2008) provided the conditions under which OLS provided consistent parameter estimates. McDonald (2009) argued that Tobit is inappropriate and recommend either OLS or fractional logit. Estelle et al. (2010) provided a Monte Carlo analysis using OLS, Tobit, fractional logit and nonparametric regression. The models provided nearly identical results. In this chapter, we only consider OLS.
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Blackburn, V., Brennan, S., Ruggiero, J. (2014). DEA in the Public Sector. In: Nonparametric Estimation of Educational Production and Costs using Data Envelopment Analysis. International Series in Operations Research & Management Science, vol 214. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7469-3_3
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