At the beginning of this thesis we discuss DEA methods, which measure efficiency of Decision Making Units by comparing weighted inputs and outputs. First we describe basic DEA models without random inputs and outputs then stochastic DEA models which are derived from the deterministic ones. We describe more approaches to stochastic DEA models, for example using scenario approach or chance constrained programming problems. Another approach for measuring efficiency employs stochastic dominance. Stochastic dominance is a relation that allows to compare two random variables. We describe the first and second order stochastic dominance. First we consider pairwise stochastic efficiency, then we discuss the first and second order stochastic dominance portfolio efficiency. We describe different tests to measure this type of efficiency. At the end of this thesis we study efficiency of US stock portfolios using real historical data and we compare results obtained when using stochastic DEA models and stochastic dominance. Powered by TCPDF (www.tcpdf.org)

The outcome of a production process might not only deviate from a theoretical maximum due to inefficiency, but also because of non-controllable influences. This raises the issue of reliability of Data Envelopment Analysis in noisy environments. I propose to assume an i.i.d. data generating process with bounded noise component, so that the following approach is feasible: Use DEA to estimate a pseudo frontier first (nonparametric shape estimation). Next apply a ML-technique to the DEA-estimated efficiencies, to estimate the scalar value by which this pseudo-frontier must be shifted downward to get the true production frontier (location estimation). I prove, that this approach yields consistent estimates of the true frontier. (author's abstract) / Series: Department of Economics Working Paper Series

This paper surveys four distinct approaches to frontier estimation of multi-output (and simultaneously multi-input) technologies, when nothing but noisy quantity data are available. Parametrized distributions for inefficiency and noise are necessary for identification of inefficiency, when only cross-sectional data are available. In other respects suitable techniques may differ widely, as is shown. A final technique presented rigorously exploits the possibilities from panel-data by dropping parametrization of distributions as well as functional forms. It is illustrated how this last technique can be coupled with the others to provide a state-of-the-art estimation procedure for this setting. (author's abstract) / Series: Department of Economics Working Paper Series

No / Regular Network Data Envelopment Analysis (NDEA) models deal with evaluating the performance of a set of decision-making units (DMUs) with a two-stage construction in the context of a deterministic data set. In the real world, however, observations may display a stochastic behavior. To the best of our knowledge, despite the existing research done with different data types, studies on two-stage processes with stochastic data are still very limited. This paper proposes a two-stage network DEA model with stochastic data. The stochastic two-stage network DEA model is formulated based on the satisficing DEA models of chance-constrained programming and the leader-follower concepts. According to the probability distribution properties and under the assumption of the single random factor of the data, the probabilistic form of the model is transformed into its equivalent deterministic linear programming model. In addition, the relationship between the two stages as the leader and the follower, respectively, at different confidence levels and under different aspiration levels, is discussed. The proposed model is further applied to a real case concerning 16 commercial banks in China in order to confirm the applicability of the proposed approach at different confidence levels and under different aspiration levels.

This paper provides simulation evidence concerning some statistical properties of two different approaches to technical efficiency estimation for multiple-output production under noisy conditions: The Ray Frontier Approach (RFA) from Löthgren (1997) DEA+ proposed in Gstach (1996). RFA, unlike earlier approaches in the realm of stochastic frontier analysis, is capable of efficiency estimation in the case of multiple outputs as well and lends itself for comparison with DEA+. Several settings with varying sample sizes, noise to signal ratios and mean inefficiencies are investigated. (author's abstract) / Series: Department of Economics Working Paper Series