It's the investment accelerator. Monetary tightening means lower expected NGDP; real interest rates can go either way. Think of this as a teaching post, to explain the intuition. Or look at Miles Kimball's great post.

Here's a thought-experiment. **Do not take this thought-experiment literally.** It's just my weird way of doing the math, where I start with the answer and work back to the question it answers. Sometimes it's easier this way. Like trying to figure out the relationship between policy X and outcome Y when you know that Y/2=X but you are really bad at algebra so you can't solve for Y=2X.

Imagine that expectations are totally non-rational. Expectations are just exogenous, and do not adjust to match what is actually happening. And one day everyone wakes up expecting a permanent recession. When they went to bed they expected that output would remain at 100 forever, and nothing would ever change. Now they expect that output will be 90 forever. A permanent 10% drop in output.

But the central banker is an New Keynesian macroeconomist who years ago made a bet with his grad skool classmates that expectations are rational. He has since learned that expectations are totally non-rational and exogenous, but he doesn't want to lose his bet. So he has to figure out a way to make the world adjust to match the expectations people hold, since the expectations people hold do not adjust to match the world.

**So what does the central banker need to do to the real interest rate to make those non-rational expectations of a permanent recession look like a rational expectations equilibrium?** (Remember, I'm just solving for the New Keynesian equilibrium in a weird way, to make the math easier.)

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