Performance measurement using linear additive directional distance function and PCA based directions

Abstract

In this paper, the performance of a firm vis-à-vis its rivals is measured with a reoriented form of the Linear Directional Distance Function and setting the Directions obtained from the Principal Component Analysis of non-central covariance matrices. Eigenvectors thus obtained will have a connection with the variance explained and Competitive Intensity. In this context, two types of covariance matrices are analysed within two alternative models prescribed here. The former one investigates the position of a firm in comparison to others and prescribes a path of effective utilization of resources to generate outputs using the extant technology by the firms. The second approach is centred on comparing the weighted sum of input-output vectors of all rivals with the concerned Decision-Making Unit. This matrix is akin to the Multi-Dimensional Herfindahl Hirschman Indices (input and output-based) to symbolise the market concentration when the current firm (as if) is assumed to be a new entrant. The paper finds the Second approach superior to the former one for two major reasons. Firstly, a typical non-central covariance matrix obtained from the former may fail to provide a legitimate direction vector. Secondly, even if one is found then also it may not be pointing towards the direction of the highest variation to clarify the large extent of competitive intensity. However, the later method overcomes all these issues.