Advances on axiomatic nonparametric approaches to productivity and efficiency analysis

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School of Business | Doctoral thesis (article-based) | Defence date: 2014-05-23
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Aalto University publication series DOCTORAL DISSERTATIONS, 57/2014
This dissertation contains several important methodological results on nonparametric productivity and efficiency analysis. It spans both theoretically motivated and practically challenging topics in the planning, implementation, and interpretation of efficiency analysis. The dissertation consists of five articles, all of which contribute to the subject from closely related perspectives. Firstly, we study the connection between nonparametric nonconvex efficiency analysis and isotonic regression, and propose a mathematical programming approach for estimating multivariate isotonic regression. We also examine the estimation of non-convex frontier technologies in the presence and absence of stochastic noise. Secondly, we propose an enumeration technique for estimating the nonparametric nonconvex efficient frontiers under different returns to scale assumptions. Furthermore, we present an application of efficiency analysis to explore the changes in value added for a sample of Portuguese secondary schools over a four-year time period. A modified Malmquist index is proposed to measure how the value added evolves over time. We also study the linear relationship between the inputs and outputs of a nonparametric efficiency problem. We consider transformations that can be applied to inputs and outputs without disrupting the efficiency results. We use the concept of dominating cones to analyze the transformed problems. We focus on the selection of variables, and explain how this can impact the dominating cone. A discussion on using linear transformation for dealing with the curse of dimensionality is provided in the dissertation. Lastly, we build a transformation based on the Fourier-Motzkin elimination method, which permits the derivation of a single variable optimization problem from which efficiency scores could be estimated. We build the connection between the constraints of the transformed problem and the supporting hyperplanes of the production possibility set, and show that this transformation generates all the efficient and weakly supporting hyperplanes. Moreover, we show that the proposed transformation does not generate redundant constraints. Extensive numerical comparisons are done to show the performance of the proposed algorithm. 
Julkaistu vain painettuna, saatavuus katso Bibid. Published only in printed form, availability see Bibid
Supervising professor
Kuosmanen, Timo, Professor, Aalto University, Department of Information and Service Economy, Finland
Korhonen, Pekka, Professor Emeritus, Aalto University, Department of Information and Service Economy, Finland
productivity, efficiency, nonparametric, axioms, nonconvex
Other note
  • Keshvari, Abolfazl; Kuosmanen, Timo. 2013. Stochastic non-convex envelopment of data: Applying isotonic regression to frontier estimation. European Journal of Operational Research, 231, 481-491.
    DOI: 10.1016/j.ejor.2013.06.005 View at publisher
  • Keshvari, Abolfazl; Dehghan Hardoroudi, Nasim. 2008. An extended numeration method for solving free disposal hull models in DEA. Asia-Pacific Journal of Operational Research, 25, 5, 689-696.
    DOI: 10.1142/S021759590800195X View at publisher
  • Portela, Maria Conceição A. Silva; Camanho, Ana S.; Keshvari, Abolfazl. 2013. Assessing the evolution of school performance and value added: trends over four years. Journal of Productivity Analysis, 39, 1-14.
    DOI: 10.1007/s11123-012-0263-5 View at publisher
  • Keshvari, Abolfazl; Korhonen, Pekka. 2013. On the use of a non-singular linear transformation of variables in data envelopment analysis. Aalto University publication series BUSINESS+ECONOMY, 5/2013, 1–21.
  • Keshvari, Abolfazl. 2014. An enhanced Fourier-Motzkin method for data envelopment analysis. Aalto University School of Business. Unpublished. 1-20.