The Many Decompositions of Total Factor Productivity Change

Total factor productivity change, here defined as output quantity change di- vided by input quantity change, is the combined result of (technical) efficiency change, technological change, a scale effect, and input and output mix ef- fects. Sometimes allocative efficiency change is supposed to also play a role. Given a certain functional form for the productivity index, the problem is how to decompose such an index into factors corresponding to these five or six components. A basic insight offered in the present paper is that mean- ingful decompositions of productivity indices can only be obtained for indices which are transitive in the main variables. Using a unified approach, we ob- tain decompositions for Malmquist, Moorsteen-Bjurek, price-weighted, and share-weighted productivity indices. A unique feature of this paper is that all the decompositions are applied to the same dataset of a real-life panel of decision-making units so that the extent of the differences between the various decompositions can be judged

Economic Cross-Efficiency

This paper is concerned with introducing a series of new concepts under the name of Economic Cross-Efficiency, which is rendered operational through Data Envelopment Analysis (DEA) techniques. To achieve this goal, from a theoretical perspective, we connect two key topics in the efficiency literature that have been unrelated until now: economic efficiency and cross-efficiency. In particular, it is shown that, under input (output) homotheticity, the traditional bilateral notion of input (output) cross-efficiency for unit l, when the weights of an alternative counterpart k are used in the evaluation, coincides with the well-known Farrell notion of cost (revenue) efficiency for evaluated unit l when the weights of k are used as market prices. This motivates the introduction of the concept of Farrell Cross-Efficiency (FCE) based upon Farrell’s notion of cost efficiency. One advantage of the FCE is that it is well defined under Variable Returns to Scale (VRS), yielding scores between zero and one in a natural way, and thereby improving upon its standard cross-efficiency counterpart. To complete the analysis we extend the FCE to the notion of Nerlovian cross-inefficiency (NCI), based on the dual relationship between profit inefficiency and the directional distance function. Finally, we illustrate the new models with a recently compiled dataset of European warehouses

New Definitions of Economic Cross-Efficiency

Overall efficiency measures were introduced in the literature for evaluating the economic performance of firms when reference prices are available. These references are usually observed market prices. Recently, Aparicio and Zofío (2019) have shown that the result of applying cross-efficiency methods (Sexton et al., 1986), yielding an aggregate multilateral index that compares the technical performance of firms using the shadow prices of competitors, can be precisely reinterpreted as a measure of economic efficiency. They termed the new approach ‘economic cross-efficiency’. However, these authors restrict their analysis to the basic definitions corresponding to the Farrell (1957) and Nerlove (1965) approaches, i.e., based on the duality between the cost function and the input distance function and between the profit function and the directional distance function, respectively. Here we complete their proposal by introducing new economic cross-efficiency measures related to other popular approaches for measuring economic performance. Specifically those based on the duality between the profitability (maximum revenue to cost) and the generalized (hyperbolic) distance function, and between the profit function and either the weighted additive or the Hölder distance function. Additionally, we introduce panel data extensions related to the so-called cost Malmquist index and the profit Luenberger indicator. Finally, we illustrate the models resorting to Data Envelopment Analysis techniques--from which shadow prices are obtained, and considering a banking industry dataset previously used in the cross-efficiency literature

An Evaluation of Cross-Efficiency Methods, Applied to Measuring Warehouse Performance

In this paper method and practice of cross-efficiency calculation is discussed. The main methods proposed in the literature are tested not on a set of artificial data but on a realistic sample of input-output data of European ware- houses. The empirical results show the limited role which increasing automation investment and larger warehouse size have in increasing productive performance. The reason is the existence of decreasing returns to scale in the industry, resulting in sub-optimal scales and inefficiencies, regardless of the operational performance of the facilities. From the methodological perspective, and based on a multidimensional metric which considers the capability of the various methods to rank warehouses, their ease of implementation, and their robustness to sensitivity analyses, we conclude to the superiority of the classic Sexton et al. (1986) method over recently proposed, more sophisticated methods

A Total Factor Productivity Toolbox for MATLAB

Total Factor Productivity Toolbox is a new package for MATLAB that includes functions to calculate the main Total Factor Productivity (TFP) indices and their decompositions, based on Shephard’s distance functions and using Data Envelopment Analysis (DEA) programming techniques. The package includes code for the standard Malmquist, Moorsteen-Bjurek, price-weighted and share-weighted TFP indices, allowing for the choice of orientation (input or output), reference period (base, comparison, geometric mean), re- turns to scale (variable or constant), and specific decompositions (aggregate or identifying scale effects as well as input and output mix effects). Classic definitions of TFP corresponding to the Laspeyres, Paasche, Fisher, or Törnqvist formulas can also be calculated as particular cases. This paper describes the methodology and implementation of the functions and reports numerical results so as to ease the comparison between indices and illustrate their use