The question was about "in this regard" which you use when you refer to a specific aspect, probably mentioned in the previous sentence. What you suggested will always need some clarifying afterwards:
In reference to sth, concerning sth, etc.
However:
Several aspects should be considered, especially the economy. In this regard, blah. or Respecting this, blah.
With your suggestions, even when use is appropriate, the entire structure need be changed, as in "Concerning the economy, blah" which should probably be left for one of the next paragraphs where you discuss many possible aspects, otherwise, it could be repetitive and/or redundant, as it needs reference to the original subject, whereas "in this regard" doesn't. To me it's not a matter of right and wrong, but of style, if you will.