Advanced Robust and Nonparametric Methods in Efficiency by Cinzia Daraio

By Cinzia Daraio

Delivering a scientific and entire remedy of contemporary advancements in potency research, this e-book makes to be had an intuitive but rigorous presentation of complex nonparametric and powerful equipment, with functions for the research of economies of scale and scope, trade-offs in construction and repair actions, and reasons of potency differentials.

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The same is valid for the DEA case. If point A is an extreme point, outlying the cloud of other points, the estimated efficient frontier is strongly influenced by it. 5, the solid line is the frontier that envelops point A, while the dash-dotted line does not envelop point A. 5. Influence of outliers on the FDH estimation of the production set Ψ. We will come back on this problem in Chapter 4 where we propose robust nonparametric approaches based on various nonparametric measures less influenced by extreme values and outliers, which have also nice statistical properties.

For firm B, the estimates of its efficiency score, in output oriented framework, are: λF DH (x0 , y0 ) = |OB |/|OB| ≥ 1, λDEA (x0 , y0 ) = |OB |/|OB| ≥ 1. Practical computation of the FDH In practice, the FDH estimator is computed by a simple vector comparison procedure that amounts to a complete enumeration algorithm proposed in Tulkens (1993), which is now explained. 36 The measurement of efficiency Input Oriented Framework X2 B=(Xo,Yo) A . B’ C(y) . 3. FDH and DEA estimation of C(y) and ∂C(y).

12) with δ in (x, y) ≥ 1, ∀(x, y) ∈ Ψ. Similarly, the Shephard output distance function provides a normalized measure of Euclidean distance from a point (x, y) ∈ Rp+q + to the boundary of Ψ in a radial direction orthogonal to x: δ out (x, y) = inf{λ > 0|(x, λ−1 y) ∈ Ψ} ≡ (λ(x, y))−1 . 13) For all (x, y) ∈ Ψ, δ out (x, y) ≤ 1. If either δ in (x, y) = 1 or δ out (x, y) = 1 then (x, y) belongs to the frontier of Ψ and the firm is technically efficient. A taxonomy of efficient frontier models 25 As pointed out in Simar and Wilson (2001), no behavioral assumptions are necessary for measuring technical efficiency.

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