Is the money market model based on assumption of no interest rate targeting on the part of the central bank?
I remember making myself the same question when studying those models in Mankiw's book. The answer I arrived is that from the point of view of the model, the Central Bank's policy is reflected in the money supply variable, and the interest rate variable is an abstraction that represents the main interests rates in an economy that are given by the equilibrium.
Think about this, in the model when there's an increase in money supply, what happens with the equilibrium interest rate ceteris paribus? It goes down. And the opposite is also true. But, who controls the money supply variable? The Central Bank.
So if you look at what happens in reality is somehow like that, the Central Bank cuts rates so the money supply decreases. Obviously the mechanism by which this happens in reality is different compared to the model, even they're like the 'opposite', but remember that models simplify reality in order for it to be more understandable, and in this case the CB intervention is modeled this way.