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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.

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  • $\begingroup$ 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. $\endgroup$
    – user18214
    May 24, 2022 at 16:49

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