Central banks actually will lend (or take deposits) at their rate. So in that sense it's not made-up.

Does it matter? Central banks are creating money, so of course they can pay the interest rates they made up from whole cloth.

My point was, if you can act on the number quoted, then market forces will eventually move it back into line with reality.

And history teaches that there is eventually an end to governments' ability to print unrealistic amounts of money. See Zimbabwe, the Weimar Republic, etc.

In this case the market forces act only when the projections are too unrealistic compared to the size of the economy. Small variations in rates of less than a percentage point will not doom an economy in the medium term, but certainly can make a huge fortune for people involved in the manipulation. This is the case in all western economies.

I'm not sure what you're talking about now. There are no market forces acting on projections: that's my point.

EDIT: and LIBOR isn't much of a projection, it is "I believe I could borrow at this rate, today, if I needed to"

I am talking about projections of growth and their relationship to interest rates. Interest rates have to be paid based on future earnings, but projections for future earnings have always a big variance. Therefore, small changes in interest rate have little meaning in terms of capacity of repayment, but have great meaning in term of money made by banks (or in terms of policy, by central banks). That's why it is so easy to manipulate interest rates within certain limits, contrary to what you said about resulting inflation.