Emili Grifell-Tatjé

A note on the Malmquist productivity index

In recent years the Malmquist index has gained in popularity as a measure of productivity change. We demonstrate that, in the presence of non-constant returns to scale, the Malmquist productivity index does not accurately measure productivity change. The bias is systematic, and depends on the magnitude of scale economies.

Deregulation and productivity decline: the case of Spanish savings banks

Abstract During the 1980s many regulatory constraints limiting competition in Spanish banking were relaxed or removed, although deregulation came later to savings banks than to the rest of the banking sector. Two consequences of partial deregulation of savings banks have been a rapid growth in branching activity, much of it geographically dispersed, and a burst of merger activity. In this paper we investigate productive efficiency, and total factor productivity change, in Spanish savings banks over the 1986–1991 post-deregulation period. Neither branching nor mergers provide an adequate explanation for the magnitude or the nature of the productivity decline we observe over the period.

The sources of productivity change in Spanish banking

Abstract In this paper we examine the pattern of productivity change in Spanish banking over the period 1986–1993. Two sectors dominate Spanish banking, commercial banks and the faster-growing savings banks. We begin by examining productivity change separately within each sector. However since the two sectors are gradually becoming more competitive, we continue by merging the two sectors, and by examining productivity change in the industry. The merging procedure follows a methodology originally proposed by Charnes, Cooper and Rhodes (1981), in which intra-sectoral managerial inefficiency is eliminated prior to merging. This procedure allows us to distinguish differences in managerial efficiency within each sector from differences in the institutional efficiency of the two sectors. It also enables us to decompose potential productivity change into institutional efficiency change, technical change, and the impact of scale economies. We find the commercial banks to have had a slightly lower rate of productivity growth, but a slightly higher rate of potential productivity growth. We attribute this phenomenon to differences in both managerial efficiency and institutional efficiency, to differences in the rate of technical progress, and to the adverse impact of diseconomies of scale in the commercial banking sector.

A Parametric Distance Function Approach for Malmquist Productivity Index Estimation

Malmquistindexes of productivity are generally estimated using index numbertechniques or non-parametric frontier approaches. The aim ofthis paper is to show that Malmquist indexes can be estimatedin a similar way using parametric-deterministic or parametric-stochasticfrontier approaches. To allow a multi-output multi-input technologyand for technical change in production, we adopt an output distancefunction which is specified in a translog form. We then showthat using the estimated parameters, several radial distancefunctions can be calculated and combined in order to estimateand decompose the productivity index. Finally, this approachis applied to a panel of Spanish insurance companies. The mainresults confirm those generally obtained for financial services:very low rates of growth and technical change in spite of a rapidderegulation process and expansion of activity.

Sensitivity analysis of efficiency and Malmquist productivity indices : An application to Spanish savings banks

Hypothesis testing and statistical precision in the context of nonparametric efficiency and productivity measurement have been investigated since the early 1990s. Recent contributions focus on this matter through the use of resampling methods?i.e., bootstrapping techniques. However, empirical evidence is still practically non-existent. This gap is more noticeable in the case of banking efficiency studies, where the literature is immense. In this paper, we explore productivity growth and productive efficiency for Spanish savings banks over the (initial) post-deregulation period 1992?1998 using Data Envelopment Analysis (DEA) and bootstrapping techniques. Results show that productivity growth has occurred, mainly due to improvement in production possibilities, and that mean efficiency has remained fairly constant over time. The bootstrap analysis yields further evidence, as for many firms productivity growth, or decline, is not statistically significant. With regard to efficiency measurement, the bootstrap reveals that the disparities in the original efficiency scores of some firms are lessened to a great extent. Desde principios de los anos noventa ha habido avances notables en el contraste de hipotesis dentro del contexto de la medicion de la eficiencia y la productividad mediante tecnicas parametricas. Las contribuciones mas recientes han enfocado el tema a traves de metodos de remuestreo -conocidos en la literatura como tecnicas bootstrap-. Sin embargo, practicamente no ha habido aplicaciones, algo tambien patente en el estudio de la eficiencia de la empresa bancaria. En este articulo, analizamos la eficiencia productiva y el crecimiento de la productividad de las cajas de ahorro espanolas durante el periodo 1992-1998 a traves de tecnicas no parametricas (DEA) y de tecnicas bootstrap, con el fin de poder realizar inferencia estadistica. Los resultados indican que la productividad ha aumentado, principalmente debido a una mejora en las posibilidades de produccion, mientras que la eficiencia promedio no ha variado sustancialmente. El analisis bootstrap revela que, en el caso de la productividad, para muchas empresas su aumento o disminucion no es estadisticamente significativo. En cuanto a la eficiencia, muestra que las diferencias entre empresas individuales se reducen de manera notable cuando consideramos intervalos de confianza.

Capacity utilisation and profitability: A decomposition of short-run profit efficiency

The principal aim of this paper is to measure the amount by which the profit of a multi-input, multi-output firm deviates from maximum short-run profit, and then to decompose this profit gap into components that are of practical use to managers. In particular, our interest is in the measurement of the contribution of unused capacity, along with measures of technical inefficiency, and allocative inefficiency, in this profit gap. We survey existing definitions of capacity and, after discussing their shortcomings, we propose a new ray economic capacity measure that involves short-run profit maximisation, with the output mix held constant. We go on to describe how the gap between observed profit and maximum profit can be calculated and decomposed using linear programming methods. The paper concludes with an empirical illustration, involving data on 28 international airline companies. The empirical results indicate that these airline companies achieve profit levels which are on average US

A Generalized Malmquist Productivity Index

815m below potential levels, and that 70% of the gap may be attributed to unused capacity.

A Quasi-Malmquist Productivity Index

In 1953 Sten Malmquist, a Swedish economist and statistician, published inTrabajos de Estadística the foundations of a productivity index which now bears his name. In this paper we generalize the Malmquist productivity index. We show that (i) the generalized Malmquist productivity index can be expressed as the product of a Malmquist productivity index and a Malmquist scale index; (ii) the generalized Malmquist productivity index can also be expressed as the ratio of a Malmquist output quantity index to a Malmquist input quantity index; (iii) the geometric mean of a pair of Malmquist scale indexes is equal to the reciprocal of the Törnqvist scale index, which implies that (iv) the geometric mean of a pair of generalized Malmquist productivity indexes is equal to a Törnqvist productivity index.

Cost and productivity

The Malmquist productivity index is based on distance functions, which are reciprocals of radial Debreu-Farrell efficiency measures, and which have a number of desirable properties. Linear programming techniques are frequently employed to calculate the efficiency measures. However these techniques can leave slacks, which constitute a non-radial form of inefficiency which is not incorporated into the analysis. Thus a radial efficiency measure overstates true efficiency, the reciprocal distance function understates the distance to the relevant efficient subset, and the Malmquist productivity index is adversely affected, although in an analytically indeterminate direction. This has led us to consider a new definition of “one-sided” efficiency, and to develop a new nonradial efficiency measure which incorporates all slacks on the selected side. Replacing conventional radial efficiency measures with our new non-radial efficiency measures generates what we call a quasi-Malmquist productivity index. We illustrate our quasi-Malmquist productivity index with an application to productivity change in Spanish banking.

Bootstrapping profit change: An application to Spanish banks

This study develops an analytical model capable of decomposing both intertemporal and multilateral cost variation. It begins by attributing cost variation to a price effect and a quantity effect. Then the quantity effect is decomposed into a productivity effect and an activity effect. The productivity effect in turn decomposes into a cost efficiency effect and, in the intertemporal context, a technical change effect. This paper also shows how the intertemporal and multilateral cost decompositions can be implemented, using linear programming techniques. These techniques offer certain advantages over conventional econometric techniques whenever a substantial portion of cost variation is due to variation in cost efficiency. The two cost decompositions are illustrated with a pair of benchmarking exercises based on a panel of 93 US electric power generating companies, in which variation in cost efficiency does play a key role. Copyright