orderalpha: Nonparametric order-α efficiency analysis for Stata
Despite its frequent use in applied work, nonparametric approaches to efficiency analysis, namely data envelopment analysis (DEA) and free disposal hull (FDH), have bad reputations among econometricians. This is mainly due to DEA and FDH representing deterministic approaches that are highly sensitive to outliers and measurement errors. However, recently, so-called partial frontier approaches—namely order-m (Cazals, Florens, and Simar, 2002, Journal of Econometrics 106:1–25) and order-a (Aragon, Dauia, and Thomas-Agnan, 2005, Economic Theory 21: 358– 389)—have been developed; they generalize FDH by allowing for super- efficient observations to be located beyond the estimated production- possibility frontier. Although these methods are purely nonparametric too, sensitivity to outliers is substantially reduced by partial frontier approaches enveloping just a subsample of observations. I present the new Stata command orderalpha that implements order-a efficiency analysis in Stata. The command allows for several options, such as statistical inference based on subsampling bootstrap. In addition, I present the accompanying Stata command oaoutlier, which is an explorative tool that employs orderalpha for detecting potential outliers in data meant for subsequent efficiency analysis using DEA.
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- Aragon, Y. & Daouia, A. & Thomas-Agnan, C., 2005. "Nonparametric Frontier Estimation: A Conditional Quantile-Based Approach," Econometric Theory, Cambridge University Press, vol. 21(02), pages 358-389, April.
- Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, vol. 106(1), pages 1-25, January.
- Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
- Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
- Choonjoo Lee, 2010. "An Efficient Data Envelopment Analysis with Large Data Set in Stata," BOS10 Stata Conference 3, Stata Users Group.
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