Scale properties in data envelopment analysis

Recently there has been some discussion in the literature concerning the nature of scale properties in the Data Envelopment Model (DEA). It has been argued that DEA may not be able to provide reliable estimates of the optimal scale size. We argue in this paper that DEA is well suited to estimate optimal scale size, if DEA is augmented with two additional maintained hypotheses which imply that the DEA-frontier is consistent with smooth curves along rays in input and in output space that obey the Regular Ultra Passum (RUP) law (Frisch 1965). A necessary condition for a smooth curve passing through all vertices to obey the RUP-law is presented. If this condition is satisfied then upper and lower bounds for the marginal product at each vertex are presented. It is shown that any set of feasible marginal products will correspond to a smooth curve passing through all points with a monotonic decreasing scale elasticity. The proof is constructive in the sense that an estimator of the curve is provided with the desired properties. A typical DEA based return to scale analysis simply reports whether or not a DMU is at the optimal scale based on point estimates of scale efficiency. A contribution of this paper is that we provide a method which allows us to determine in what interval optimal scale is located.DEA; efficiency

Nonparametric production technologies with multiple component processes

We develop a nonparametric methodology for assessing the efficiency of decision making units operating in a production technology with several component processes. The latter is modeled by the new multiple hybrid returns-to-scale (MHRS) technology, formally derived from an explicitly stated set of production axioms. In contrast with the existing models of data envelopment analysis (DEA), the MHRS technology allows the incorporation of component-specific and shared inputs and outputs that represent several proportional (scalable) component production processes, as well as nonproportional inputs and outputs. Our approach does not require information about the allocation of shared inputs and outputs to component processes or any assumptions about this allocation. We demonstrate the usefulness of the suggested approach in an application in the context of secondary education, and also in a Monte Carlo study based on a simulated data generating process

Greenland surface mass-balance observations from the ice-sheet ablation area and local glaciers

Glacier surface mass-balance measurements on Greenland started more than a century ago, but no compilation exists of the observations from the ablation area of the ice sheet and local glaciers. Such data could be used in the evaluation of modelled surface mass balance, or to document changes in glacier melt independently from model output. Here, we present a comprehensive database of Greenland glacier surface mass-balance observations from the ablation area of the ice sheet and local glaciers. The database spans the 123 a from 1892 to 2015, contains a total of similar to 3000 measurements from 46 sites, and is openly accessible through the PROMICE web portal (http://www.promice.dk). For each measurement we provide X, Y and Z coordinates, starting and ending dates as well as quality flags. We give sources for each entry and for all metadata. Two thirds of the data were collected from grey literature and unpublished archive documents. Roughly 60% of the measurements were performed by the Geological Survey of Denmark and Greenland (GEUS, previously GGU). The data cover all regions of Greenland except for the southernmost part of the east coast, but also emphasize the importance of long-term time series of which there are only two exceeding 20 a. We use the data to analyse uncertainties in point measurements of surface mass balance, as well as to estimate surface mass-balance profiles for most regions of Greenland

Efficiency analysis with ratio measures

In applications of data envelopment analysis (DEA) data about some inputs and outputs is often available only in the form of ratios such as averages and percentages. In this paper we provide a positive answer to the long-standing debate as to whether such data could be used in DEA. The problem arises from the fact that ratio measures generally do not satisfy the standard production assumptions, e.g., that the technology is a convex set. Our approach is based on the formulation of new production assumptions that explicitly account for ratio measures. This leads to the estimation of production technologies under variable and constant returns-to-scale assumptions in which both volume and ratio measures are native types of data. The resulting DEA models allow the use of ratio measures “as is”, without any transformation or use of the underlying volume measures. This provides theoretical foundations for the use of DEA in applications where important data is reported in the form of ratios

The structure of production technologies with ratio inputs and outputs

Applications of efficiency and productivity analysis in which some inputs and outputs are given in the form of percentages, averages and other types of ratio measures are sufficiently common in the literature. In two recent papers, the authors developed the variable and constant returns-to-scale technologies with both volume and ratio types of inputs and outputs, referred to as the R-VRS and R-CRS technologies. These technologies are generally nonconvex and have a complex structure. In this paper we explore this in detail. We show that the R-VRS technology can be stated as the union of a finite number of specially constructed standard VRS technologies. Similarly, the R-CRS technology in which all ratio inputs and outputs are of the fixed type, which are typically used to represent environmental and quality factors, can be stated as the union of a finite number of partial polyhedral cones. We show that these results have important theoretical, including conceptual, implications