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Estimating Rivalness: The Role of Choice Consistent Parameter Normalisation

By drawing on a nested logit model that unifies the conditional logit model and the Poisson regression, Brülhart and Schmidheiny (2015) have developed a method to estimate the degree of rivalness between options by a factor rho. This paper suggests that the Brülhart and Schmidheiny (2015) method involves a parameter normalisation of the nested logit model that is not choice consistent. Aside from being unsatisfactory from a theoretical point of view, this also implies that the estimated rivalness factor (rho) is time constant. A remedy for these caveats using the choice consistent normalisation of Herger and McCorriston (2013) is provided.