If you believe that the IS curve slopes up, then what the Bank of Canada says about "monetary policy accommodation" makes sense. If you believe the IS curve slopes down, like in the textbooks, then it doesn't make sense.

This is supposed to be a simple teaching post. My own mind is pretty simple anyway.

The IS equation is D(Y,r)=Y, where D is output demanded (desired expenditure), which depends positively on actual output (=income) Y, and negatively on the real interest rate r.

If we take the total derivative of the IS equation D_{y}dY+D_{r}dr=dY, and rearrange, we get the slope of the IS curve as dr/dY= (1-D_{y})/D_{r}. The textbook assumes that 0 < D_{y} < 1, so the IS curve has a negative slope, because D_{r} < 0. If instead we assume D_{y} > 1, we get a positive slope. And if firms don't want to invest when output is low and there is lots of spare capacity, this assumption that D_{y} > 1, and so the IS curve has a positive slope, may be plausible.

Define the natural rate of interest r* as the solution to D(Y*,r*)=*Y***, where Y* is "potential output" -- the level of output consistent with inflation staying at the 2% target.

If there is a recession, so Y < Y**, *then the Bank of Canada will need to set r below r* just to prevent Y falling even further below Y*, and set r even lower still to get Y to grow back to Y*. The Bank of Canada calls this "monetary policy accommodation".

Here's a picture:

It's more complicated than this of course. It always is. Expectations of future interest rates, output, inflation, and exchange rates, matter too. And it may take time for output and expectations to adjust. The natural rate of interest moves around over time, and a loss of "business confidence" (firms fear demand won't be there to justify investment) may take time to recover. And the IS curve might not slope up everywhere -- it might slope down at very low levels of Y, when gross investment is already zero and can't fall any further. But I think that's the gist of it.

And yes, if the Bank of Canada just sets an interest rate and holds it constant regardless of what happens to output and inflation (so the LM curve is horizontal forever) this is an unstable system (so resist the temptation to say that an upward-sloping IS curve means that if the Bank of Canada cuts the rate of interest this will cause a recession). But the Bank of Canada doesn't do that.

We have r* set to normal but the economy is recessing. Hence, I suspect r* is a measurement of past activity and setting r down a notch implies rates were too high in the past, as Uncle Milt says.

It is not unstable, it is asymptotically stable, the member banks always move toward r*, taking the shortest path but never really reaching it.

The unstable case you imply is the one where member banks are uneconomic, and the BoC wants to be unstable by taking on a measurable market making risk, the key term is measurable. The BoC actually has to act as a depositor and fund uneconomic loans. The risk should appear on its balance sheet, or be measurable risk on government.

Posted by: Matthew Young | January 19, 2018 at 05:42 PM

Matthew: "We have r* set to normal but the economy is recessing. Hence, I suspect r* is a measurement of past activity and setting r down a notch implies rates were too high in the past, as Uncle Milt says."

Yep. The reason the economy got into recession, according to this perspective, is either: the CB raised r above r*; or r* fell below r. (Both the same really.)

Posted by: Nick Rowe | January 20, 2018 at 07:56 AM

"the CB raised r above r*; or r* fell below r. (Both the same really.)"

Not the same. Seems latter is the case at the moment and that CBers are trying out why to assess whether this is a secular reduction in r*.

Unclear if tech driven (price deflation or, rather, lack of "normal" price inflation during period of expansion because of digital production, which lowers marginal costs to near zero); or if demand driven (lack of "normal" consumption boost in recovery period - possibly because of sluggish wage growth)

Posted by: Armine Yalnizyan | January 21, 2018 at 09:53 AM

Armine: Fair point. Both make (r-r*) > 0 and so create a recession, but two different histories and different futures. Yes, the recent recession seems to be (mostly/wholly?) a story of r* falling and central banks failing to cut r quickly enough in response. And maybe the 82 recession is closer to an example of the former (though maybe not exactly).

Posted by: Nick Rowe | January 21, 2018 at 03:21 PM

Excuse me if I dare ask, but - with a non-negative aggregate demand for Y=0, which is sensible to assume, as negative demand does not make sense - does an equilibrium level of output exist when Dy > 1 ?????

Posted by: GF | January 27, 2018 at 01:31 PM

GF: If D(Y,r) is a linear function, then that is correct. But as I mentioned in the post "And the IS curve might not slope up everywhere -- it might slope down at very low levels of Y, when gross investment is already zero and can't fall any further." it's probably non-linear.

But we shouldn't a priori rule out the possibility that a monetary exchange economy could collapse, and people revert to barter, under the "right" (i.e. wrong) circumstances.

Posted by: Nick Rowe | January 27, 2018 at 02:13 PM