Assessment of Competitive Position of a Firm Using a Multi-dimensional Herfindahl–Hirschman Index and Linear Additive Directional Distance Function

Abstract

Herfindahl–Hirschman has been one of the renowned techniques for the measurement of market concentration. This article proposes an assessment of concentration with the aid of a matrix termed as a multi-dimensional Herfindahl–Hirschman index for a set of outputs which are possibly categorised under line items. The extant research is aimed to achieve the sole objective of investigating and obtaining a direction vector for augmenting the market share of a firm in a specified manner to strengthen the competitive position. The first eigenvector computed from the normalised non-centred covariance matrix of output set is found to be carrying high degree of explanation of the market concentration. Directional distance additive model (DDAM) is applied to detect the peer firm while replacing the input–output vector of a firm with its vector of market share due to these inputs and outputs. The first eigenvector of the above stated covariance matrix is proved to be a legitimate direction vector which is inherited by the DDAM itself. Benefits of this model is illustrated finally with the aid of an example.