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I was teaching the money multiplier the other day, and showing how lower interest rates tend to reduce the multiplier, and hence M1. A student asked for clarification—they’d been told that lower interest rates were expansionary. I knew how I was going to answer the question, but I sort of wondered how other (less heterodox) money and banking professors would respond to the question. (Let me know in the comments.) In any case here’s my answer. First let’s see why low rates are contractionary:

A fall in interest rates will increase the demand for base money (here I assume no IOR, or at least a fixed IOR.) As money demand increases the value (or purchasing power) of a dollar bill increases. Here I use the standard 1/price level as the value of money, although I actually prefer 1/NGDP.

So that’s the answer. But of course that’s not a sufficient answer for a student; you also need to explain to students why they had the false belief that low interest rates are expansionary. So I draw another graph, this time showing the case where lower interest rates are caused by a fall rise in the monetary base.

In this case the supply curve moves first. In the very short run we assume prices are sticky, so the interest rate must fall to equilibrate Ms and Md. In the long run expectations of higher future NGDP cause an increase in current AD. When all wages and prices have fully adjusted to the increased money supply, interest rates return to their original level, and the demand for money shifts back. The value of money falls to point C, which means prices have risen. So the myth that low interest rates are expansionary comes from the fact that in some cases low interest rates are caused by an increase in the base. In that case the base is the expansionary impulse, and the accompanying fall in interest rates actually delays the inflationary impact of the higher money supply (point b).

What would be an example of the first case? That’s easy. Between August 2007 and May 2008 there was no change in the monetary base, and yet interest rates fell sharply. Not surprisingly NGDP growth slowed and we tipped into recession.

Nick Rowe has a new post that argues the money supply is fully exogenous, even when the central bank is targeting interest rates. I’m not sure I fully understand the post, but I’ll attempt to translate his argument into Ms/Md graphs, and then see if he corrects me.

Most students are used to a Ms/Md graph with interest rates on the vertical axis, not 1/P. Suppose there was an increase in the demand for credit, Md shifted to the right on the interest rate graph, and the Fed had to raise the quantity of money (“money supply”) enough to keep interest rates from rising. That’s what most people think of as “endogenous money.” Here’s Nick:

P and Y will (eventually) adjust until the quantity of money demanded equals the quantity of money created by the supply (function) for money and the demand for loans. The supply (function) of money, and the demand for loans, together determine the quantity of money created, and that quantity created (eventually) determines the quantity of money demanded.

I believe Nick is saying that if the central bank increases the quantity of money to accommodate the loan demand (and hence keep interest rates from rising) that will boost AD, which will raise P and Y. If you use my graph above, he seems to be saying that just because Md shifts right on an interest rate graph, doesn’t mean it shifts right on a Ms/Md graph with 1/P (or 1/NGDP) on the vertical axis. Instead on that graph only the Ms line shifts right, causing you to slide down to the right on the stable Md curve (point C on my graph.) That’s what he means by more quantity of money demanded.

In other words, interest rate targeting creates a money supply function that causes quantity of money changes that are exogenous on a “1/P” graph, and hence the normal monetarist assumptions about money still hold. I think that’s a good way to think about the whole “endogenous money” issue (which has spawned more nonsense than almost another other topic in economics.)

PS. I’m never too sure what the MMTers are trying to say, but in comments to my blog they seem to claim that if for some weird reason the Fed were to do an exogenous increase in M, interest rates would fall, we’d go to point b, and just stay there.

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