Int. J. Production Economics 76 (2002) 177–188 Bias in Malmquist index and cost function productivity measurement in banking Ana Lozano-Vivas a, *, David B. Humphrey b a Department of Economics, University of Malaga, Plza. El Ejido, 29013 Malaga, Spain b Department of Finance, Florida State University, Tallahassee, FL, USA Received 30 August 2000; accepted 26 March 2001 Abstract This paper illustrates how many prior studies of productivity growth in the banking industry have been overstated. This occurs with both DEA (Malmquist index) and parametric (stochastic cost frontier) productivity measurement approaches. The problem is not due to the technique used but in how it is applied. It is easiest to see in the banking industry due the nature of the data available. The bias is eliminated when all outputs and inputs are included in the analysis, ensuring that the balance sheet restriction is met. Although simple in concept, this problem and its solution have so far been neglected in the literature. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Productivity; Malmquist index; Frontier cost; Banking industry 1. Introduction Productivity measurement has a long history, ranging from changes in output per unit of labor input to more complex, but more complete, measures of total factor productivity (TFP). In this transition, growth accounting measures of TFP have given way to nonparametric (linear programming) Malmquist index and parametric (regression-based) stochastic frontier cost function TFP estimates. However, many published studies using the Malmquist index in the banking area appear to have significantly overstated estimates of productivity growth. The bias is not due to the technique used but rather in how it is applied. This problem in recent productivity studies is most easily seen in applications of the Malmquist index to banking industry data but exists in stochastic frontier cost function applications as well (including our own work). Fortunately, the bias is simple to correct and it can be measured, reduced, or eliminated in future productivity studies. The problem is not new but has been consistently overlooked in published work. Our guess is that it has persisted because no one has shown how large it can be. While other productiv- ity measurement difficulties remain, the one we identify is amenable to correction. In what follows, we explain how the bias arises in Section 2. Its importance is illustrated by showing that in many studies, it is the source of the main part of measured productivity growth. Due to the special nature of banking data and the Malmquist index itself, it is relatively simple to *Corresponding author. Tel.: +34-952-131256; fax: +34- 952-131299. E-mail addresses: avivas@uma.es (A. Lozano-Vivas), dhumphr@garnet.acns.fsu.edu (D.B. Humphrey). 0925-5273/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII:S0925-5273(01)00162-1