Boundary problems with the “Russell” graph measure of technical efficiency: a refinement
Tóm tắt
In an influential paper, Färe and Lovell (J Econ Theory 19:150–162, 1978) proposed an (input based) technical efficiency index designed to correct two fundamental inadequacies of the Debreu-Farrell index: its failure to satisfy (1) indication (the index is equal to 1 if and only if the input bundle is technically efficient) and (2) weak monotonicity (an increase in any one input quantity cannot increase the value of the index). Färe et al. (1985) extended the index to measure efficiency in the full space of input and output quantities. Unfortunately, this index fails to satisfy not only indication and monotonicity at the boundary (of output space), but also weak monotonicity. We show, however, that a simple modification of the index corrects these flaws. To demonstrate the tractability of our proposal, we apply it to baseball batting performance, in which zero outputs occur frequently.
Tài liệu tham khảo
citation_journal_title=Ann Oper Res; citation_title=A new measure of baseball batters using DEA; citation_author=T Anderson, GP Sharp; citation_volume=73; citation_publication_date=1997; citation_pages=141-155; citation_doi=10.1023/A:1018921026476; citation_id=CR1
citation_journal_title=J Prod Anal; citation_title=A graph type extension of Farrell technical efficiency; citation_author=W Briec; citation_volume=8; citation_publication_date=1997; citation_pages=95-110; citation_doi=10.1023/A:1007728515733; citation_id=CR2
citation_journal_title=Ann Oper Res; citation_title=A developmental study of data envelopment analysis in measuring the efficiency of maintenance units in the US air force; citation_author=A Charnes, CT Clark, WW Cooper, B Golany; citation_volume=2; citation_publication_date=1984; citation_pages=95-112; citation_doi=10.1007/BF01874734; citation_id=CR3
citation_journal_title=J Environ Manag; citation_title=Productivity and undesirable outputs: a directional distance function approach; citation_author=Y Chung, R Färe, S Grosskopf; citation_volume=51; citation_publication_date=1997; citation_pages=229-240; citation_doi=10.1006/jema.1997.0146; citation_id=CR4
citation_journal_title=J Prod Anal; citation_title=Some models and measures for evaluating performances with DEA: past accomplishments and future prospects; citation_author=WW Cooper, LM Seiford, K Tone, J Zhu; citation_volume=28; citation_publication_date=2007; citation_pages=151-164; citation_doi=10.1007/s11123-007-0056-4; citation_id=CR5
citation_journal_title=J Prod Anal; citation_title=Theory and application of directional distance functions; citation_author=R Färe, S Grosskopf; citation_volume=13; citation_publication_date=2000; citation_pages=93-103; citation_doi=10.1023/A:1007844628920; citation_id=CR6
citation_journal_title=J Econ Theory; citation_title=Measuring the technical efficiency of production; citation_author=R Färe, CAK Lovell; citation_volume=19; citation_publication_date=1978; citation_pages=150-162; citation_doi=10.1016/0022-0531(78)90060-1; citation_id=CR7
citation_title=The measurement of efficiency of production; citation_publication_date=1985; citation_id=CR8; citation_author=R Färe; citation_author=S Grosskopf; citation_author=CAK Lovell; citation_publisher=Kluwer-Nijhoff
citation_title=Production frontiers; citation_publication_date=1994; citation_id=CR9; citation_author=R Färe; citation_author=S Grosskopf; citation_author=CAK Lovell; citation_publisher=Cambridge University Press
citation_journal_title=J R Stat Soc Ser A Gen; citation_title=The measurement of productive efficiency; citation_author=MJ Farrell; citation_volume=120; citation_publication_date=1956; citation_pages=253-282; citation_doi=10.2307/2343100; citation_id=CR10
citation_title=Analysis of production as an efficient combination of activities; citation_inbook_title=Activity analysis of production and allocation; citation_publication_date=1951; citation_id=CR11; citation_author=TC Koopmans; citation_publisher=Physica-Verlag
citation_journal_title=J Optim Appl; citation_title=New optimality principles for economic efficiency and equilibrium; citation_author=DG Luenberger; citation_volume=75; citation_publication_date=1992; citation_pages=221-264; citation_doi=10.1007/BF00941466; citation_id=CR12
citation_title=Evaluating the relative efficiency of baseball players; citation_inbook_title=Data envelopment analysis: theory, methodology and applications; citation_publication_date=1995; citation_id=CR13; citation_author=MJ Mazur; citation_publisher=Kluwer
citation_journal_title=J Econ Theory; citation_title=Measures of technical efficiency; citation_author=RR Russell; citation_volume=35; citation_publication_date=1985; citation_pages=109-126; citation_doi=10.1016/0022-0531(85)90064-X; citation_id=CR14
citation_title=On the axiomatic approach to the measurement of technical efficiency; citation_inbook_title=Measurement in economics: theory and application of economic indices; citation_publication_date=1987; citation_id=CR15; citation_author=RR Russell; citation_publisher=Physica-Verlag
Russell RR, Schworm W (2011) Properties of inefficiency indexes on
$$\langle \hbox{input}, \hbox{output}\rangle$$
space. J Prod Anal (forthcoming)