With the Old Keyensian IS curve, the natural rate of interest is a positive function of the level of government expenditure. High G means high r*.
With the New Keynesian IS curve, the natural rate of interest is a negative function of the rate of change of government expenditure over time. High Gdot means low r*.
That's because:
In the Old Keynesian IS curve, the levels of desired C and I are negative functions of the level of r.
In the New Keynesian IS curve, the rates of change of desired C and I are positive functions of the level of r.
Please don't make me do the math. I'm not very good at math.
I have a very strong hunch that this is at the root of the disagreement between Paul Krugman and John Taylor.
I did a post on this, about a year or so back. Somewhere.
If you are a dyed-in-the-wool New Keynesian, and you want an expansionary Aggregate Demand policy, to get the economy up off the ZLB, and if you don't agree with Scott Sumner and other "monetary policy optimists", and so you want to use fiscal policy, you will want to increase the natural rate of interest, and you do that by ensuring that G will be expected to be falling over time from now on. And there are two ways to do that: either raise current G holding expected future G constant; or else cut expected future G holding current G constant. Probably: Paul Krugman wants to do the first; John Taylor wants to do the second.
John Taylor: "In contrast, in our Wall Street Journal article and our research on
fiscal consolidation we consider the effect of permanent changes [presumably reductions NR] in government
spending which are phased in over time to bring the budget deficit down."
Whether the New Keynesian or Old Keynesian IS curve is right, is another question.
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