Is Denmark Part of the Faros?

The faro islands are still part of Denmark, but there is a substantial body of opinion on the islands that wishes they weren't. The island nation's economy is hugely dependent on fishing and in the 19 nineties when global fishing went into crisis, the faros economy tanked massively. So would the faros be better off if they were just fully independent? I mean, or does the relationship run the other way? Is it denmark kind of deriving some material or imperial kind of advantages from having control over the faro islands?"