On testing the dimensionality of regression coefficients

In this paper, the distribution of a statistic based on the likelihood ratio method for testing the dimensionality of regression coefficients has been derived. The method of integration over alternate variables has been used to derive the results.     

Supplier selection with rank reversal in public tenders

For supplier selection in the public sector, the Weighted Sum Model is often used in combination with relative scoring methods that allow rank reversal. With rank reversal we refer to a changed order in the ranking of bids leading to a new winner, after removing or adding a non-optimal bid that does not win the original tender. In practice, an important reason indicated by practitioners for using methods that allow rank reversal is that it would rarely occur in practice. Based on an analysis of 303 Dutch public tenders, this research shows this is not true. In about 1 out of 5 the tenders, rank reversal occurs after adding non-optimal fictional bids to tenders that do not have quality thresholds. After removing bids, the rate is about 1 out of 40 if a curved relative scoring method is used. In addition, the research shows that rank reversal rates increase when (i) there is no quality threshold, (ii) the number of bids increases, (iii) bid price variance increases, and (iv) price weights are not very low or high. We argue that relative scoring methods that allow rank reversal should not be used in public procurement, or otherwise only in exceptional cases, as it conflicts with public procurement principles and leads to reduced overall bid value.     

The reduced-rank beta in linear stochastic discount factor models

In a linear stochastic discount factor model, failure of the full-rank conditions affects the standard statistical inference of coefficients. We propose a novel risk measurement, the reduced-rank beta, which is the risk sensitivity to the effective part of factors for the full-rank covariance matrix. Our reduced-rank beta is a generalisation of the standard beta when the full-rank condition is not satisfied. By considering the Fama–French five-factor (FF5) model for the US equity market, the failure of the full-rank condition is found to affect beta estimates. We demonstrate the reduced-rank beta has important empirical implications for model reductions and anomaly explanations.