Distinctions with a Very Slight Difference

Nick Rowe and Scott Sumner both have posts up arguing with a paper from the Bank of England.  Both are excellent and I agree entirely with them (except a couple small, mostly semantic gripes with Sumner) so I won’t reproduce all of the arguments but I think this serves as a nice illustration of how hard it is to understand economics models–so hard, it seems, that even the people in charge of setting monetary policy don’t really understand them.

I think at least half of the arguments that go on in the blogosphere regarding monetary policy are completely superfluous and are just bickering about different ways to describe the same thing.  If you are making a model, the way you describe things matters because it affects the way the model works but often times, there are multiple ways to do it that don’t make it work any differently (at least not materially different).  But for some reason people get all caught up in arguing about which is the “right” way to describe it.

The two main examples of this that come out of the BOE paper are whether or not banks “lend out reserves” and whether central banks set interest rates or the supply of money.  I already addressed the first one here (and Sumner does a pretty good job of burying it), so I won’t bother with that.   They also both (especially Rowe) do a very good job of dismantling the second but just for fun, I will wade into it a bit.

As Rowe points out, the intro textbook theory has the CB choosing the quantity of money and then the demand for money determines the interest rate.  An equivalent way of saying the same thing is that the CB targets an interest rate and then chooses the quantity of money which will “cause” that rate given the demand for money.  It is relatively easy to see that there is no difference between these two descriptions when one is looking at a snapshot in time, holding demand constant.

The argument seems to arise when considering how the CB responds to changes in demand.  If they kept the money supply constant and demand increased, interest rates would increase.  If they target an interest rate, then when demand increases, the money supply must increase.  That is a meaningful distinction.  But all that means is that the CB determines the supply of money not just the quantity supplied.  Of course a supply function is just a collection of quantities which they intend to supply under different circumstances.  The meaning of this depends on what circumstances you are wondering about.

There are basically two different versions of “supply” going on here and the difference is entirely a matter of communication.  First, there is a “long run” version of the supply of money.  In this version, the CB is facing some unknown profile of “snapshot” demand functions at various points of time in the future and it has the ability to adjust the quantity of money in keeping with its long-term policy objective (for instance an inflation target).

So we can think about the CB, at any given time, looking at the demand for money and choosing the quantity which is necessary to meet that objective.  Similarly, we can imagine the CB looking at the demand at any point in time and determining the interest rate that will produce the quantity of money that is consistent with the long-run policy objective.  There is no difference.

Note that the CB can’t set a long-run inflation target and an independent long-run interest rate target, it is the inflation target (along with the demand for money) that determines the path of both the quantity of money supplied and the interest rate.  So when the CB says it will target a certain inflation rate, it is telling you a certain supply of money that it intends to follow as a function of prices and interest rates, namely a supply function which is perfectly elastic at the targeted price level.  But this means that interest rates will need to fluctuate to bring markets into equilibrium in the short run.

If the CB knew all market conditions at all points in time exactly, they could state this same price level target as an interest rate target at all points in time, or a quantity of money target at all points in time.  But since, they don’t know all of this, it becomes a “supply curve” in the sense that it tells you which things they will allow to adjust and which they will not (at least allegedly).  In the example of an inflation target, they will theoretically allow both interest rates and the quantity of money to shift to keep inflation on target.  Because the interest rate and the quantity of money are linked, it makes no difference which one you imagine is endogenous or exogenous at any point in time.  The thing that is actually exogenous is the supply “curve” of money (the policy rule) and the real shocks to demand.

Now the debate about whether the CB chooses the quantity of money or the interest rate revolves around the short run and in my mind it stems entirely from this distinction: The CB does not set policy continuously.  In fact, it sets policy at regular intervals (usually once per month) and at those times, it has to set the policy for the entire interval.  This means that they have to determine a supply curve that they will stick to for that interval and they have to communicate it.

Because of this, in the minds of the bankers, there is a distinct difference between setting the quantity of money and setting an interest rate but in either case they are setting the supply of money, they are just two different supply curves.  If the CB came out and said “we are increasing the quantity of base money to X,” they would be indicating a perfectly inelastic supply of base money between now and the next policy meeting.  Alternatively, if they said “we are lowering interest rates to X,” they are indicating a perfectly elastic (in interest rates) supply until the next policy meeting.  There are two things to point out about this.  One is that if policy were made (and communicated) continuously, there would, again, be no distinction between an interest rate target and a quantity of money target.  Second, if the CB could perfectly communicate a complex supply function for the short run (with some combination of interest rate and quantity of money moves prescribed for every possible demand scenario), then they would most likely not use either of these short-run “targets” but something more complex that would be exactly in line with their long-run target at every point in time.

But because this would be too complicated, they set a simple short-run supply curve and they adjust it up and down (if it is a rate target) or left and right (if it is a quantity target) at certain intervals to approximate the long-run supply curve that is consistent with their policy objective.  So a rate target or a money quantity target are just communication devices in the short run, the way that something like an inflation target or NGDP level target is in the long run.

Since central bankers put a lot of effort into determining exactly how to communicate short-run policy, this distinction between rate targeting and money quantity targeting probably seems very important to them.  But to most economists it is pointless nit-picking because economists mostly think about long-run policy regimes and are mainly concerned with short-run policy tools only to the extent that they fit into a long-term model.  So most economic models do not depend in an important way on unexpected shocks to demand in between short-run policy changes.  You could make one but it would probably only tell you that they each err in a slightly different way and that the shorter the interval in policy adjustments, the less it matters.

So in reality, when the CB “lowers interest rates” what they are really trying to do is say “we are getting looser.”  What they mean by “getting looser” is expanding the money supply.  It’s just that if you asked “how much are you expanding the money supply,” instead of saying “we are increasing it to X” they are saying “however much it takes to make short-term interest rates equal X until the next meeting.”  Of course, they are doing this because they are hoping that this quantity will be enough to raise prices in the future in line with their long-run mandate and this upward pressure on prices may cause them in the future to have to increase the short-run interest rate to prevent the quantity of money from increasing too much.

Thus you get the “low rates don’t mean loose money” non-paradox.  The confusion about low rates and loose money would likely not exist if people thought about the CB setting the quantity of money rather than interest rates because they would not be confusing the short run, where a decrease in the rate signals more expansionary policy (an increase in the quantity of money) and the long run, where more contractionary policy (a lower quantity of money) causes low inflation and lower inflation causes lower interest rates.  [For more on that, here is Sumner.]

 

P.S. I think Sumner might accuse me of having a “banking theory disguised as monetary theory.”  But I sort of think it is the other way around.  Won’t go into that here though.

P.P.S Nick Rowe’s follow-up presents a model which is very similar to mine (that’s actually what sucked me into this topic but then I got distracted).