One of the main problems in efficiency analysis is to determinate the environmental variables that have an impact on the production process. This paper shows that applying bootstrap to data envelopment analysis (DEA) before performing classification and regression trees (CART) increase the quality of the results. In particular, employing data on the Italian Health System, the paper highlights that bias corrected DEA allows to individuate variables affecting health efficiency which would remain undiscovered when the traditional DEA model is applied.
Many models have been developed to find an optimal solution to the problem to improve healthcare efficiency. In this paper, the concept of efficiency, measured by data envelopment analysis (DEA), is implemented together to classification and regression trees (CART) analysis to provide a set of rules that permit to identify on which environmental variables the governments should operate to improve healthcare efficiency. DEA is a well know non-parametric method developed by Charnes, Cooper, and Rhodes (1978) that identifies a production frontier and determines the efficiency scores of a set of decision making units (DMU), with the common set of inputs and outputs (Heidari and Mohammadi, 2012 and Lin et al., 2009). In the other hand, one of the significant limits on applying this non-parametric technology is that the efficiency scores are an estimate of the true (and unknown) production frontier, conditional on observed data resulting from an underlying Data Generating Process (DGP) (Simar and Wilson, 1998 and Simar and Wilson, 2000). As a consequence, DEA efficiencies are biased by construction and are sensitive to the sampling variations of the obtained frontier. In order to overcome this problem, Simar and Wilson (1998) proposed a bootstrap procedure to approximate the sampling distribution of the efficiency scores and to make inference. See Halkos and Tzeremes, 2012, Curi et al., 2011 and Gitto and Mancuso, 2012 for recent applications of bootstrap-DEA methodology.
The CART methodology (Breiman, Friedman, Olshen, & Stone, 1984) which allows to identify some rules with the aim to classify a sample into two or more groups, has been applied in different fields (D’uva and De Siano, 2007, Li et al., 2010 and Sohn and Tae, 2004). Nowadays, to the best of our knowledge, it is never applied to support policy intervention in the health system.
In this paper, bootstrapped DEA and CART analysis are implemented in order to define policy intervention aimed to improve health efficiency. Moreover, this study discusses the importance to use DEA in an inferential setting by employing the bootstrap technique.
1.1. Research objectives
The main objectives of this study are:
1. To demonstrate the applicability of the CART methodology in the health sector.
2.To stress the importance of the bootstrap in DEA analysis.
DEA has had wide applications in measuring the relative efficiency scores of a sample of DMUs. But, especially in health sector, the performance is often affected by environmental variables on which government and managers hardly operate. This paper has employed a bootstrap-DEA methodology with CART analysis as the tool for uncover the predictive structure of health efficiency. The paper pointed out that, the percentage of hospital beds directly managed by the regional government, used as proxy of the way in which the region performs its role of “third party player/purchaser” in the health direction, results to be the environmental variable with the most influential role in determining health efficiency. This imply that the regional governments, promoting a significant form of competition inside their healthcare system, can increase their health efficiency. In addition, the analysis demonstrate that future policy intervention, aimed to increase the health efficiency, should also consider patient mobility. Finally, under a methodological perspective, the paper underlines that the use of bias corrected efficiency scores, improve the quality of the CART analysis.
