missing hose on 1996 s40

[dpolden]

I have a 1996 s40 2.0 , bought s/h, have just noticed that above exhaust manifold there is a cover with a air hose outlet sticking up from it, on looking further have noticed a hose connection on airbox with no hose connected. should the 2 be linked with a hose. what does hose do , if fitted would it improve economy, Have been using car for 4 years without it. or can I forget about it. look forward to replies. many thanks.
David Polden