Journal of Productivity Analysis, 15, 79–94, 2001 c  2001 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands. A Parametric Distance Function Approach for Malmquist Productivity Index Estimation HUGO J. FUENTES hfuentes@campus.ccm.ites.mx Tecnol´ ogico de Monterrey, Campus Ciudad de M´ exico EMILI GRIFELL-TATJ ´ E emili.grifell@uab.es Departament d’Economia de l’Empresa, Universitat Aut` onoma de Barcelona SERGIO PERELMAN * sergio.perelman@ulg.ac.be CREPP, Universit´ e de Li` ege Abstract Malmquist indexes of productivity are generally estimated using index number techniques or non-parametric frontier approaches. The aim of this paper is to show that Malmquist indexes can be estimated in a similar way using parametric-deterministic or parametric-stochastic frontier approaches. To allow a multi-output multi-input technology and for technical change in production, we adopt an output distance function which is specified in a translog form. We then show that using the estimated parameters, several radial distance functions can be calculated and combined in order to estimate and decompose the productivity index. Finally, this approach is applied to a panel of Spanish insurance companies. The main results confirm those generally obtained for financial services: very low rates of growth and technical change in spite of a rapid deregulation process and expansion of activity. JEL classification: D24, C43, G22 Keywords: distance functions, Malmquist index, parametric frontier, Spanish insurance 1. Introduction Caves, Christensen and Diewert (1982) introduced the Malmquist (1953) index for the first time in productivity analysis and showed that it corresponds to the ratio of two distance functions. 1 As these functions were assumed to be parametric and specific for each firm and period, they could not be directly estimated. Therefore, Caves, Christensen and Diewert proposed an index number approach which, based on usual perfect competition assumptions, * The authors wish to thank Bert Balk, Tim Coelli, Rolf F¨ are, Shawna Grosskopf and the anonymous referees for their valuable comments. Financial support from: Communaut´ e Fran¸ caise de Belgique (PAC 98/03-221), Ministerio de Educaci´ on y Cultura (SEC99-0843-C02-01) and Generalitat de Catalunya (1998SGR 00073) are also acknowledged. Any errors which remain are our own. Address any correspondence to Sergio Perelman, CREPP - Universit´ e de Li` ege, Bd. du Rectorat 7 (B31), B-4000 Li` ege - BELGIUM, Phone: 32 4 3663098/32 4 3663108, Fax: 32 4 3663106