When matching based on the Mahalanobis distance (MD), are there guidelines for selecting the caliper. For example, if the propensity score is used as the distance metric, literature supports starting with 0.2 standard deviations of the logit. Does something similar exist for the MD?
As with all matching, pick the caliper that yields the best balance after matching. Also consider the number and range of the remaining treated units. The correct caliper will depend on the characteristics of your data set. I know this doesn't really answer your question, but you should know that the ubiquitous 0.2 standard deviations of the logit of the propensity score is arbitrary.
Despite Gary King pointing out the issues with Propensity score matching a few years ago, propensity score matching seems to still be the most commonly used distance metric for matching, and all calipers I have been able to find is based on it.
This paper was the closest thing I could find to answering your question:
If you have found a better answer to your own question in the meanwhile, please do inform me about it.