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Central limit theorems for conditional efficiency measures and tests of the ‘separability’ condition in non‐parametric, two‐stage models of production


  • Cinzia Daraio
  • Léopold Simar
  • Paul W. Wilson


In this paper, we demonstrate that standard central limit theorem (CLT) results do not hold for means of non‐parametric, conditional efficiency estimators, and we provide new CLTs that permit applied researchers to make valid inference about mean conditional efficiency or to compare mean efficiency across groups of producers. The new CLTs are used to develop a test of the restrictive ‘separability’ condition that is necessary for second‐stage regressions of efficiency estimates on environmental variables. We show that if this condition is violated, not only are second‐stage regressions difficult to interpret and perhaps meaningless, but also first‐stage, unconditional efficiency estimates are misleading. As such, the test developed here is of fundamental importance to applied researchers using non‐parametric methods for efficiency estimation. The test is shown to be consistent and its local power is examined. Our simulation results indicate that our tests perform well both in terms of size and power. We provide a real‐world empirical example by re‐examining the paper by Aly et al. (1990, Review of Economics and Statistics 72, 211–18) and rejecting the separability assumption implicitly assumed by Aly et al., calling into question results that appear in hundreds of papers that have been published in recent years.

Suggested Citation

  • Cinzia Daraio & Léopold Simar & Paul W. Wilson, 2018. "Central limit theorems for conditional efficiency measures and tests of the ‘separability’ condition in non‐parametric, two‐stage models of production," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 170-191, June.
  • Handle: RePEc:wly:emjrnl:v:21:y:2018:i:2:p:170-191

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    1. repec:eee:ejores:v:277:y:2019:i:2:p:756-769 is not listed on IDEAS
    2. Cinzia Daraio & Léopold Simar & Paul W. Wilson, 2019. "Quality and its Impact on Efficiency," DIAG Technical Reports 2019-01, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    3. repec:eee:enepol:v:129:y:2019:i:c:p:985-996 is not listed on IDEAS
    4. repec:eee:anture:v:76:y:2019:i:c:p:266-277 is not listed on IDEAS
    5. repec:eee:ejores:v:277:y:2019:i:2:p:784-797 is not listed on IDEAS
    6. repec:kap:jproda:v:50:y:2018:i:1:d:10.1007_s11123-018-0532-z is not listed on IDEAS
    7. Kounetas, Konstantinos & Polemis, Michael & Tzeremes, Nickolaos, 2019. "An alternative probabilistic frontier analysis to the measurement of eco-efficiency," MPRA Paper 93686, University Library of Munich, Germany.
    8. Anders Rønn-Nielsen & Dorte Kronborg & Mette Asmild, 2019. "Exact tests on returns to scale and comparisons of production frontiers in nonparametric models," IFRO Working Paper 2019/04, University of Copenhagen, Department of Food and Resource Economics.
    9. Bădin, Luiza & Daraio, Cinzia & Simar, Léopold, 2019. "A bootstrap approach for bandwidth selection in estimating conditional efficiency measures," European Journal of Operational Research, Elsevier, vol. 277(2), pages 784-797.
    10. repec:eee:ejores:v:276:y:2019:i:3:p:1104-1118 is not listed on IDEAS

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