Peter Dorman brings up an interesting point:
... models of the macroeconomy incorporate monetary policy as just another component of “the economy”, along with the behavior of households and firms. [They] include the reaction functions of monetary authorities as determinate behavioral foundations of how the economy works; there is no corresponding behavioral rule on this fiscal side.
Back in the days of IS-LM with a fixed money supply (fixed for some unmentioned reason by an almighty central bank), the model consisted of behavioral responses in the money and goods markets, leading to a predicted outcome, equilibrium levels of national income and interest rates.
... you plugged in a policy choice and it told you how the economy was supposed to respond.
Now it’s different, at least on the monetary side. In the new versions of IS-LM and AS-AD, as well as the more elaborate models in the professional literature, monetary policy is inside the model. The choices of central bankers are built in. You may have interest rate targeting, inflation targeting or some version of a Taylor Rule, but in all of them the monetary choices themselves are predetermined.
This is effectively the choice between a "floating" information destination and a "constant" information destination (in the market P:NGDP→MB) in the information transfer framework (see here or here). "Floating" means the Fed uses some target or rule, effectively looking to the market like any other business building widgets. "Constant" means it just builds its widgets at some fixed rate. In the former case, the Fed's behavior may be "constrained" (as Dorman says) but it's the kind of constraint that follows from there being lots of dollars (basically, the law of large numbers) and has little to do with volition on the part of the Fed. We don't say an ideal gas is "constrained" from doing what it wants by the ideal gas law. The physical system follows the ideal gas law. These Fed reaction functions are more like Maxwell distributions; Maxwell distributions don't constrain the movements of atoms (which can have any speed) -- they are the result of gazillions of atoms following the laws of physics. These Fed reaction functions don't constrain how the Fed increases the monetary base, they are the result of billions of dollars interacting with the market. The information transfer model with a floating information destination makes minimal assumptions about these functions and just assumes at a fundamental level information in is equal to the information out, or one level up, supply and demand is at work.
In the case of a constant information destination, where the Fed just sets an interest rate or targets a monetary aggregate, the aggregate demand (NDGP) is the only thing doing the reacting. This case generally leads to accelerating inflation.
Why isn't there a government reaction function (asks Dorman)? My best answer in this framework: Because the government (G) is only a piece of aggregate demand NGDP = C + I + G + (X-M). If G were a floating information source then it would just mix in with C, I, X and M as floating information sources leading to NGDP being a floating information source. If G were a constant information source (basically how it is treated), we'd still have C, I, X and M as floating sources that would still allow NGDP to adjust to the monetary base MB.