Jeong, Seok-Oh
[UCL]
Simar, Léopold
[UCL]
This paper address the problem of estimating the monotone boundary of a nonconvex set in a full nonparametric and multivariate setup. This is particularly useful in the context of productivity analysis where the efficient frontier is the locus of optimal production scenarios. Then efficiency scores are defined by the distance of a firm from this efficient boundary. In this setup, the Free Disposal Hull (FDH) estimator has been extensively used due to its flexibilty and because it allows nonconvex attainable production sets. However the nonsmoothness and discontinuities of the FDH is a drawback for conducting inference in finite samples. In particular, it is shown that the bootstrap of the FDH has poor performances and so is not useful in practice. Our estimator, the LFDH, is a linearized version of the FDH, obtained by linear interpolation of appropriate FDH-efficient vertices. It offers a continuous, smooth version of the FDH. We provide an algorithm for computing the estimator, and we establish its asymptotic properties. We also provide an easy way to approximate its asymptotic sampling distribution. The latter could offer bias-corrected estimator and confidence intervals of the efficiency scores. In a Monte-Carlo study, we show that these approximations works well even in moderate sample sizes and that our LFDH estimator outperforms, both in bias and in MSE the original FDH estimator.
| Bibliographic reference |
Jeong, Seok-Oh ; Simar, Léopold. Linearly interpolated FDH efficiency score for nonconvex frontiers. STAT Discussion Papers ; 0501 (2005) 25 pages |
| Permanent URL |
http://hdl.handle.net/2078.1/122448 |
