Four Essays on the Measurement of Productive Efficiency

Abstract

This collection of essays contains two kinds of contributions. All four essays include applications of the existing DEA (Data Envelopment Analysis) toolbox on real world datasets. But the main contribution is that they also offer new and useful tools for practitioners doing efficiency and productivity analysis.

Essay I is about benchmarking by means of applying the DEA model on electricity distributors. A sample of large electricity distribution utilities from Denmark, Finland, Norway, Sweden and the Netherlands for the year 1997 is studied by assuming a common production frontier for all countries. The peers supporting the benchmark frontier are from all countries. New indices describing cross-country connections at the level of individual peers and their inefficient units as well as between countries are developed, and novel applications of Malmquist productivity indices comparing units from different countries are performed.

The contribution of Essay II is to develop a method for classifying self-evaluators based on the additive DEA model into interior and exterior ones. The exterior self-evaluators are efficient “by default”; there is no firm evidence from observations for the classification. These units should therefore not been regarded as efficient, and should be removed from the observations of efficiency scores when performing a two-stage analysis of explaining the distribution of the scores. The application to municipal nursing- and home care services of Norway shows significant effects of removing exterior self-evaluators from the data when doing a two-stage analysis.

The robustness of the efficiency scores in DEA has been addressed in Essay III. It is of crucial importance for the practical use of efficiency scores. The purpose is to demonstrate the usefulness of a new way of getting an indication of the sensitivity of each of the efficiency scores to measurement error. The main idea is to investigate a DMU’s (Decision Making Unit) sensitivity to sequential removal of its most influential peer (with new peer identification as a part of each of the iterations). The Efficiency stepladder approach is shown to provide relevant and useful information when applied on a dataset of Nordic and Dutch electricity distribution utilities. Some of the empirical efficiency estimations are shown to be very sensitive to the validity and existence of one or a low number of other observations in the sample. The main competing method is Peeling, which consists of removing all the frontier units in each step. The new method has some strengths and some weaknesses in comparison. All in all, the Efficiency stepladder measure is simple and crude, but it is shown that it can provide useful information for practitioners about the robustness of the efficiency scores in DEA.

Essay IV is an attempt to perform an efficiency study of the construction industry at the micro level. In this essay information on multiple outputs is utilized by applying DEA on a cross section dataset of Norwegian construction firms. Bootstrapping is applied to select the scale specification of the model. Constant returns to scale was rejected. Furthermore, bootstrapping was used to estimate and correct for the sampling bias in the DEA efficiency scores. One important lesson that can be learned from this application is the danger of taking the efficiency scores from uncorrected DEA calculations at face value. A new contribution is to use the inverse of the standard errors (from the bias correction of the efficiency scores) as weights in a regression to explain the efficiency scores. Several of the hypotheses investigated concerning the latter are found to have statistically significant empirical relevance.