Testing for Unit Roots in Market Shares

A unique characteristic of marketing data sets is the logical consistency requirement in market share models that market shares are bounded by 0 and 1, and they sum to unity. To take account of this logical consistency requirement, we propose to test for unit roots in individual market share series within the context of a market share attraction (MCI) framework. Our paper offers new contributions in testing for unit roots in market shares. First, a novel feature of our paper is that we propose a new unit root testing methodology designed to deal with the logical consistency requirement in market share models within the context of a market share attraction (MCI) framework. A second novel component of our paper is that we demonstrate how one could use the Johansen (1995) test to identify unit roots. This is implemented using Eviews software. The Johansen test is a system-based test rather than a single equation test; it is more appropriate given the dependencies in the market share relationships. Finally, we demonstrate using simulations that our procedure works well and improves substantially on the univariate Dickey-Fuller procedure. Accordingly, our procedure leads to better unit root inference than the univariate Dickey-Fuller method; the latter is not that reliable when dealing with market shares. We conclude the paper with suggestions for future research.