# Can the Mahalanobis distance measure ( as defined by Bloom, Schankerman, Reenen Econometrica 2013) between a firm and itself be greater than 1?

I am currently working on estimating a Knowledge Proximity measures for firms and wanted to replicate the Mahalanobis distance measure discussed in Appendix C.2 of Bloom, Schankerman, and Van Reenen (2013).

I developed a Python program to compute the Mahalanobis distance but am puzzled to find that the Mahalanobis distance between a firm and itself is not 1 for all firms.

• Is the range of the Mahalanobis distance (as defined in BSV (2013)) 0-1?
• Can the distance between a firm and itself not equal 1 and vary across firms?
• Can the Mahalanobis distance between a firm with other firms be higher than within the firm itself?

My intuition about the Mahalanobian distance is that the measure should lie between 0 and 1, should be equal 1 on the diagonal (distance between a firm and itself) and the similarity between firms cannot be higher than the similarity of a firm with itself.

• Don't know about your specific case. But in general Mahalonobis distance is really just a generalization of measuring absolute distance between 2 datapoints in terms of standard deviations to $\mathbb{R}^n$. Obviously this is not between zero and 1 in the scalar case. May 24, 2022 at 16:49