A monetary policy pop quiz

I freely admit that I don't understand monetary policy incredibly well. Sure, I solved some New Keynesian models in my field classes. I remember what happens in equilibrium. And I taught intro macroeconomics a few times, and learned all the standard kiddie models - money demand, loanable funds, AD-AS, long-run and short-run Phillips curves. I saw the "Friedman Rule" derived a couple times. But there is much about monetary policy I don't understand. First, I don't understand all of the particulars of how monetary policy is actually conducted. Second, I don't have much intuition for what happens far away from the equilibria in most models, especially if the equations that define the equilibrium are not linearized. Finally, I do not understand what would happen if this or that assumption of the models I know were dropped, or how plausible alternative, non-mainstream models are. All I know, really, are: A) the linearized equilibria of New Keynesian sticky-price models, similar models like Mankiw's "sticky information" models, B) some "New Classical" models like the Lucas Islands and RBC models, and C) some heuristics and hand-wavey ideas from the age of Milton Friedman and Paul Samuelson.

So I'm really not sure what to think when I read things like this pronouncement from two years ago by Narayana Kocherlakota:

[I]f the FOMC maintains the fed funds rate at its current level of 0-25 basis points for too long, both anticipated and actual inflation have to become negative. Why? It’s simple arithmetic. Let’s say that the real rate of return on safe investments is 1 percent and we need to add an amount of anticipated inflation that will result in a fed funds rate of 0.25 percent. The only way to get that is to add a negative number—in this case, –0.75 percent. 

To sum up, over the long run, a low fed funds rate must lead to consistent—but low—levels of deflation.

Is this right? Do permanently low interest rates eventually lead to permanent deflation? My instincts say that this cannot be true. My instincts say that printing more money cannot lead to deflation at long time scales - if you wait long enough, an increase in the supply of money will decrease money's value.

So what would happen if the Fed kept interest rates at zero forever? Would inflation rise to a new, higher average level and stay there, or would it keep accelerating until hyperinflation resulted and the real interest rate plunged to negative infinity? I'm not sure.

OK, so let's think about the opposite policy. What if the Fed tried to keep the nominal interest rate at, say, 50% forever? First of all, could it do that, or would it empty out its balance sheet and have to give up, like an emerging market trying to maintain a currency peg? And if a 50% real interest rate caused deflation - which seems like it would certainly happen - then the real interest rate would be above 50%. That would make govt. bonds a much more attractive proposition than the stock market or any other private asset, so it seems like everyone would abandon the real economy and stampede into govt. bonds. with the whole country earning >50% real rates of return, we'd all get rich really quick...this seems physically impossible to sustain for very long.

OK, so you see my problem. I just don't understand the extremes of monetary policy. So instead of making any pronouncements, I want to conduct a pop quiz. This quiz has two short-answer problems. Please answer in the comments, as concisely and succinctly as possible.

Problem 1

Suppose that the Fed targets only one interest rate, a short-term nominal interest rate, and that its only tool is Open Market Operations (it cannot provide any "forward guidance" or communicate with the public at all). Suppose that at date T, the Fed decides to keep the interest rate at zero in perpetuity, and remains unwaveringly committed to this decision for all time > T.

a) Describe the time path of the price level (or inflation/deflation), starting at time T, and going forward to infinity (or until the policy ends).

b) Describe the sequence of Open Market Operations that the Fed will conduct.


Problem 2


Suppose that the Fed targets only one interest rate, a short-term nominal interest rate, and that its only tool is Open Market Operations (it cannot provide any "forward guidance" or communicate with the public at all). Suppose that at date T, the Fed decides to keep the interest rate at 50% in perpetuity, and remains unwaveringly committed to this decision for all time > T.

a) Describe the time path of the price level (or inflation/deflation), starting at time T, and going forward to infinity (or until the policy ends).

b) Describe the sequence of Open Market Operations that the Fed will conduct.


I'm looking forward to reading your answers...


Update 1: Answers are coming in...keep em coming! Mark Thoma sends this video of George Evans explaining a New Keynesian model.