You can’t look at economic and translation risk separately, there is an interaction between the two, assuming a firm is exposed to both.
So what the minimum variance hedge ratio tries to do is solve for the hedge ratio that reduces the variance in exchange rate fluctuation given the relationship between translation and economic risks.
Say you’re a Japanese firm that exports to the US, but you purchase inputs from the US. If the USD strengthens, your inputs will increase, but so will your sales since the JPY is weaker. So the two effects naturally hedge each other, although it may not be perfect. Thus, you would want to enter a derivatives contract in order to hedge the residual piece.