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You need a way to weed out solutions like: promise to implement severe austerity 50 years from now, with G(t) dropping to zero and staying there forever. The model will tell you that works fine as a way of eliminating output shortfalls. The immortal representative agent gratefully revise consumption plans in the light of the lower future tax burden and C(t) rises. There's a reason why those clever NK economists don't spend much time on policy rules of that sort.

Kevin: I think it's the other way around.

If we set it up as a Type 2 problem, we should be able to find *all* the policy rules (for Gdot(t) and r(t) in this case) that let us hit the target. We can then pick the one(s) we like best, and that don't lead to bad outcomes 50 years from now. In this case it would be something like: "cut Gdot when the ZLB is a binding constraint, and raise Gdot when it isn't".

If we set it up as a Type 1 problem, we are only looking at that narrow class of policy rules the modeller happened to try out and figured would be easy to find solutions for.

In fact, any halfway competent math economist (i.e. anyone but me) could solve for the policy rules for G(t) and r(t) that maximise the present value of the SWF subject to the constraints that r(t) = n(t) - alphaGdot(t) and r(t) > the ZLB.

They couldn't do that with the Type 1 method.

"Type 2. Assume full-employment Y=200. Solve for G that gets us to full employment Y. . . .
"But what policymakers really want is the solution to Type 2 problems."

Would it were so!

Min: Touche! (But that's not our department.)

In macro, solving type 2 problems is known as calibration! Specify the equilibrium equations and outcomes, then find the parameters that make it happen.

Dave: Hmmm. I think calibration is something different again. Because you are solving for the parameters, not the policy variables. Related, but different.

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