What a great question! And because anything that involves food is close to my heart I can answer with authority having done the experiments :-)
There's a simple answer, a more complex answer and even an unexpected answer! The simple answer is that if you just want to boil off water you should leave the lid off. If you try the experiment of putting a known mass of water in the pan on a steady heat and periodically measuring it, you quickly show water is lost more rapidly with the lid off.
The complex answer is that the temperature of the saucepan is roughly constant (at 100C), so the energy going in is mainly used to boil water. With a bit of effort you could even estimate the power input from the rate of water loss and the latent heat of vaporisation. Anyhow, with the lid off or on the water is turned to steam at roughly the same rate. However the lid acts as a cooler and the steam condenses on it's underside and drips back into the pan. That's why the water loss is slower when the lid is on. Without the lid the steam escapes from the pan.
The unexpected answer is that you are not necessarily thickening a bolognese sauce by removing the water. All meat contains some connective tissue, which at 100C is slowly hydrolysed by water into gelatin like molecules, and this thickens the sauce. In particular it gives it that rich texture you associate with meals like osso buco. It takes one to two hours to hydrolyse connective tissue, so if you cook the sauce for an hour or two with the lid on you should still find it thickens up. How much it thickens depends on the meat used. Paradoxically the cheaper forms of meat can be better for this as they contain more connective tissue.