Transitive Multilateral Comparisons of Agricultural Output, Input, and Productivity: A Nonparametric Approach

Abstract

EKS Index number methods are examined for multilateral comparisons of input, output, and productivity. The EKS index number procedure was introduced by Caves, Christensen, and Diewert (1982a) Caves, Christensen, and Diewert (1982b) and is now routinely applied in multilateral comparisons. The EKS method is currently used by Ball et al. (1999) Ball et al. (2000) in the construction of transitive multilateral output and input index numbers. These numbers, in turn, are used in measuring TFP growth in different states. One of the problems associated with using the EKS index is that it considers all binary comparisons to be equally reliable. However, in the context of interstate comparisons, some binary comparisons are intrinsically more reliable than others. The reliability issue arises because of the different output and input structures in different states. This study explores the use of Minimum Spanning Trees (MST) introduced by Hill (1999) in constructing output and productivity comparisons, and also describes a method for generalizing EKS indices. This approach, first proposed by Rao and Timmer (2000), assigns weights to different binary comparisons. The empirical part of this chapter focuses on the implementation of these two methods using inter-state data. The chapter also highlights the problems associated with the application of the MST approach. Empirical results reported and analytical arguments suggest that the weighted EKS method is likely to provide an improved method for constructing transitive multilateral index numbers of output and productivity.