Archive for March, 2014

More on Reserve Requirements

March 28, 2014 Leave a comment

Will be busy this weekend but wanted to quickly respond to a comment by J.P. Koning on my previous post on reserve requirements indicating that Canada does not have such requirements.

I previously argued that a reserve requirement replaces a gold standard as a constraint on credit creation.  I believe this is correct but I don’t mean to imply that it is the only way credit creation can be prevented from going to infinity.  I realize I sort of said that but I was thinking in terms of a simplified model.  The important assumption was that people hold no currency and that all base money takes the form of bank reserves.  This of course is not the case in reality, it just made the model simpler.

Even when this is the case, it is possible for a reserve requirement to be non-binding.  This was the case in my characterization of a “liquidity trap.”  The only potentially problematic implication of this simplified model is that, when the reserve constraint is not binding, the expansion of credit is demand constrained in the sense that the interest rate will be driven down to zero (or the rate of IOR) and credit would expand only to the level that would be supported by the willingness to hold loans at that rate.

In reality, discount rates in Canada have not been zero since they dropped their reserve requirement, though they have been low (maximum of 4.25%) and reserve ratios have been low (usually around 3 or 4%) but not infinitesimal.  But this can be explained by relaxing the (false) assumption that all base money must be reserves and imagining that banks face some risk of becoming illiquid.  If they are concerned about this, they will demand some level of reserves which will most likely be inversely related to the interest rate since the more reserves they hold, the bigger the buffer against illiquidity but the higher the interest rate, the more revenue they must give up on the margin for additional protection.

This is another way of saying, they will have an upward sloping supply of loans.  And for the record, I acknowledged this in the comments of my original market-for-loans post when I said:

A more accurate supply curve would be a monotonically increasing curve above and to the left of the one I drew which is very flat and close to the level of IOR for low quantities and approaches infinity as the quantity approaches the maximum possible quantity but gets pretty close to that quantity for moderately high interest rates. It doesn’t change the essential point I am trying to make.

So I assumed a supply curve that looks like this.

loans market normal

A more realistic supply curve with a reserve requirement would be this.

Loanable goods market IV

And with no reserve requirement, it would look like this.

Loanable goods market V

So I suspect that, when the reserve requirement is (nearly) binding, removing it would lower interest rates and reserve ratios but everything should still work.  Of course, modeling this would require a different supply function from the one I assumed previously.  But the main implications should be basically the same.  This does put “liquidity traps in a slightly different light since we can’t just say that it’s because demand hits zero (or IOR) before you hit the reserve requirement.  But the nature of it is not much different since the rising supply is due to the liquidity risk, it should be a function of reserve ratios (holding other things equal) so when the base increases, it should stretch this curve to the right making supply higher for any given interest rate and so it is easy to imagine it being very close to zero/IOR for a long way out and this causing reserve ratios to be relatively high and rates to be close to zero/IOR.

So my approach is probably the result of good old-fashioned American myopia, I will try to broaden my horizons.  But I think the basic framework I am working with holds up in light of this wrinkle.  I do wonder what the reasoning for Canada dropping the requirement was though.  It would seem to me that this would make monetary policy a bit less precise since they would have to estimate the slope of the supply curve out at the end (they probably don’t think about it this way but somehow or another, there is an extra degree of freedom if reserve ratios are fluctuating with monetary policy).  But monetary policy is one area where it’s difficult to criticize our neighbors to the north since they have had somewhat less difficulty with it than we have lately.




Distinctions with a Very Slight Difference

March 25, 2014 14 comments

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).


Selgin Follow-Up

March 17, 2014 23 comments

In my last post I was pretty critical of an interview by George Selgin in which he argues that (price) deflation is good when productivity is increasing but bad when aggregate demand is decreasing.  In fairness to Selgin, this type of interview is always a very crude attempts at skimming a few key conclusions off of the surface of a much deeper body of reasoning.  I admit I do not fully understand the reasoning behind the claims in this case and I am partly arguing with other people who I have heard make similar claims.  So my method of argument was to sort of try to head off every method of reasoning which I can think of which could possibly lead to them.  Many of these can probably be answered pretty well but I don’t think that all of them can be answered simultaneously in a way that results in the basic idea that comes across in the interview.  However, I have put a bit more thought into it and I want to now take a different approach and instead of imagining a bunch of possible defects in the reasoning, try to put it in the best possible light and say how I think it could be said to be correct (and how I think it is not).

So admitting that I don’t completely understand what Selgin means, here is what I think he could mean that would be basically correct:  If we had a completely different monetary regime, in which people expected the price level to fall when productivity increased and rise when productivity decreased, then when that happened, it would not be bad.  I agree with this and I don’t think it is very far outside of the “mainstream.”  Here is what I mean.

Imagine the Fed instituted a Sumner-style NGDP targeting regime in which the target for NGDP were rather low, let’s say 2%.  In this case, the predictive power of the “entrepreneur” would be set to work predicting things like productivity, and when they predicted output to rise more than 2%, they would predict the price level (most likely) would fall, and the markets would be employed in aggregating these predictions which would be incorporated into debt contracts.  In this case, if the forecast was wrong in one direction or the other, those contracts would end up favoring one side or the other but this would be the normal function of markets.  People would only take on the risk that they were willing to bear.  This would not necessarily cause systemic problems when prices fell.

However, I don’t think this is what most people come away from this type of interview thinking.  If you get the impression that what he is saying is that the price level could fall tomorrow due to increasing productivity without causing any problems, then I think you are drastically mistaken.  This is because under the current monetary regime, market participants are not taking NGDP for granted and using this as the starting point for their calculations, they are taking the inflation rate for granted (at least to some extent) because they expect the Fed to do whatever is necessary to produce a certain level of inflation regardless of changes in productivity.  This means that if the Fed suddenly fails to do this (perhaps they become convinced by Selgin’s argument) then the markets will be in the position of having made a systematic error across the board which is not the result of a defect in reasoning but of a misplaced belief about the behavior of the CB.  In this case, there will be all of the problems that I have been trying to describe in credit markets as the burden of debt becomes unexpectedly great.

Now I suspect that a New Keynesian like Paul Krugman would say that deflation would still be bad because wages/prices (particularly wages) don’t adjust downward efficiently, only upward and this is probably the fundamental disagreement between Selgin and the “mainstream.”  I suspect a market monetarist like Sumner would say that the first regime would be better than what we have but not quite as good as an NGDP targeting regime with a slightly higher target because of the same argument but also that it would be disruptive to move to this regime from where we are now because of the adjustment to the lower target and mainly for that reason, they would advocate a higher target.  (That adjustment would be problematic because of all the debt which was built up in expectations of a higher rate of inflation although I don’t know that market monetarists would cast it in that light.)

So basically, my gripe is with the impression that I think this argument creates.  This may or may not be exactly the impression that Selgin intends to create (and maybe it isn’t even the one that he does create, I may be the only one who sees it that way, but I don’t think so).


Categories: Macro/Monetary Theory

Selgin on Good and Bad Deflation

March 16, 2014 33 comments

George Selgin recently did an interview with RT  (about half way through the clip) in which he discusses deflation and why, in his view, sometimes it is good and sometimes it is bad.  I have several issues with this treatment of deflation.

Cause and effect

Selgin’s claim is that deflation is good when it is due to an increase in productivity but bad when it is due to a decrease in demand.  There are a few problems with this.  The first is that this seems to confuse the causes of inflation with the effect of inflation.

If we assume a simple free-market economy, then when productivity increases and the quantity of money stays the same, then one would expect the price level to fall in order to bring the economy into equilibrium.  In this case, the falling prices are a sign of increasing productivity which is good.  Similarly, one could argue that, given the increased quantity of goods and services and lower relative quantity of money, the fall in prices is itself good because it brings markets into equilibrium.

However, what is causing the fall in “demand” in Selgin’s mind?  I admit I don’t know but let’s imagine the converse of what I described above, namely that production remains constant and the quantity of money falls for some reason.  In this case, again the price level must fall in order to bring markets into equilibrium.  Is this bad now?

Aggregate Demand

The natural question which arises from this theory is what would cause a shortfall in aggregate demand?  Presumably Selgin believes in some form of Say’s law (supply begets its own demand in aggregate).  So how is it that there can be a reduction in “demand” which is caused by some real phenomenon not related to productivity that drives an undesirable deflation?  Is this some kind of “animal spirits” argument?  That doesn’t seem like Selgin’s M.O. though I am only casually familiar with him.

The reality is that “aggregate demand” is an inherently monetary concept.  In a money-neutral economy, there would be no such thing as aggregate demand and prices would adjust up and down to bring the market into equilibrium and this would always be good (at least it would always be Pareto optimal).  If there is such a thing as an aggregate demand shortfall it is a purely monetary phenomenon.  This is true whether productivity is rising or falling.  So why would it be bad in one case and good in the other?

Knock-on Effects

The reason “mainstream” economists think deflation is bad is not that falling prices themselves are inherently bad but that falling prices cause some kind “knock-on” effects in the real economy that rising prices do not cause.  Most of them explain these in terms of sticky prices or wages, I explain them with debt contracts but either way, there is something bad that happens if prices fall short of what people were expecting.

Selgin, on the other hand, seems to believe that there are knock-on effects of falling prices when productivity is not rising but not when it is.  I have heard many people make this kind of argument but I have yet to hear one of them explain how this is possible.

Profit Inflation

Selgin argues that, for some reason, when productivity is increasing, inflation causes the prices of end products to increase without causing the prices of inputs to increase causing (real) profits to increase.  Again, this makes no sense to me and I don’t know how he comes to this conclusion.  To me it looks like he is applying the concept of inflation selectively here.  It is hard to see how an increase in the money supply would not lift the prices of inputs along with outputs.

Debt Contracts

Selgin touches on debt contracts but he does so in an inconsistent way.  He says that when deflation is because of increases in productivity both parties benefit but when you have the bad kind of inflation he says this.

“If you’re a lender, you get back dollars that are worth more, even at times when productivity hasn’t reduced prices so your gain comes at the expense of your creditors.”

That is a contradiction.  If there is deflation (you are getting back dollars that are worth more) by definition prices are reduced.  It makes no difference to you or your creditor why they are reduced.  The important thing is whether the deflation was anticipated.  If both sides anticipated it, then both benefit from the exchange.  If the deflation is unanticipated, then the debtor may be made worse off.  This does not depend on the reason for the deflation.

Of course, an unexpected inflation has the opposite effect (benefitting creditors and harming debtors) and this could simply be chalked up to a risk that both parties willingly undertake but what Selgin (and seemingly everyone else) fails to notice is that debt contracts are not just a thing that exists between two private parties in a free economy, they are the very thing which create the money which drives the inflation/deflation.  This means that the economy as a whole is always in the position of net debtors vis a vis the banking system.  This is why I argue that deflation is bad.

Of course, if deflation is caused by a productivity increase, it is possible that everyone ends up better off because there is more stuff to go around, but this tells us nothing about deflation, it only tells us about productivity increases.

It’s monetary systems that matters

Selgin explains that there have been times in history when deflation was good and times when it was bad.  I agree.  But the difference between those times was not that in the good times productivity was increasing and the bad times demand was decreasing (though that is the case).  The difference is that the monetary systems in place were different.

In the times when deflation was accompanied by increasing productivity, there were commodity standards.  This means that the price level is just the price of gold or silver or what have you in relation to other goods.  So naturally, if you have the productivity of other goods relative to gold or silver increase, you see the price level falling and it is a sign of something good (the productivity increase).

But in more modern cases (like in the thirties) the quantity of money, and therefore the price level, has been detached from the price of any commodity like gold (although only partially in the thirties).  In these cases “aggregate demand” and the price level as well as expectations of the same, are determined by central bank policy.  This is the case regardless of what is happening to productivity.

In this system, what we have in the cases of bad deflation is a shortfall in “demand” caused by tighter than expected monetary conditions.  But if we had increasing productivity and this caused deflation, it would be the result of the same thing and it would have similarly negative effects.  There is no way to conceive of a demand shortfall that is not a monetary phenomenon. 

The logic behind this view of the price level seems to be based on some notion that there is a “natural” or proper rate of change in the price level and that that rate of change is related to the value of something like gold even though the value of money is no longer linked to anything like that.  So people like Selgin think that when productivity increases, prices should decrease (and vise versa) because that is what would happen if we were on a gold standard and for some reason that is what people expect to happen so when something else happens it is disruptive.

But the monetary system is not based on the price (and therefore the relative supply) of a real good, it is based on credit.  The demand for credit is based on expectations about the price level in the future.  Those expectations are based on expectations about the future stance of monetary policy.  Monetary policy is determined by the central bank and the central bank tells us that it is trying to cause a certain amount of inflation.  So people, for better or worse, expect prices to rise when productivity increases and rise when productivity falls.  When this doesn’t happen, it is disruptive and the disruption is not balanced in the sense that some people gain and some lose.  Because people are net creditors, when inflation comes in below expectations, people are net losers.

Categories: Uncategorized

A Monetary Policy Base Model

March 13, 2014 22 comments

In this post I will (finally) lay out a mathematical model describing roughly how I see monetary policy functioning in view of the relationship between money and debt.  This model will look a lot like other simple macro models but it will highlight a bit more, the role that debt plays in the process.  I will then use it to tell some stories about depressions and liquidity traps.  I am going for the simplest formulation possible which still makes my point here so I will use a lot of assumptions, many of which could be relaxed to get a model with more complexity.

The most important aspect of such a model is the treatment of credit markets and their role in money creation.  I will assume that the following takes place simultaneously.

1. The central bank determines the quantity of reserves and the reserve requirement.  I assume that all reserves are held by banks and that the reserve requirement is constant (changes in the requirement and the quantity of reserves are functionally equivalent).

2. People take out a certain amount of dollar-denominated loans from the banks and use it to buy stuff.  This is where all of the “money” comes from.

3. People withdraw “money” from the economy (by selling goods or liquidating money “savings”) to pay off the debts which were accumulated in the previous period.

4.  Any interest payments to the bank from the debt in the previous period is remitted back into the economy through dividend payments and/or operating expenses.

So the money supply in each period will be the quantity of money which remains in the economy after all of this and is carried over to the next period.  I will assume that the economy starts with zero money so that in period 0, the quantity of money is equal to the amount of loans and I will assume that in this period, the banks are reserve constrained (the reserves ratio is at the minimum allowable level).  This means that, given the initial supply of reserves (R) and reserve ratio (a), the initial “money supply” (M) and new loans (L) will be the following.


In the following period, this same quantity will need to be paid back plus interest, but the interest will flow back into the economy along with the quantity of money created by new loans so at any time t, the quantity of money will be given by the following.


In other words, the quantity of money in circulation is equal to the quantity of debt.  Now we must model the market for debt.

Let the willingness to hold debt (demand for new loans) be a function of the real interest rate r and the value of real goods in the economy PY.  (Y can be thought of as either real output or real wealth.)  For the sake of exposition let this be the following.

Lt=PtY(1-rt)=Y(1-ite)   for it> πe

Lt=PtY                                 for it< πe

For our purposes let us assume that Y is constant and determined by “real” factors.  So by assumption, money is neutral.  A more specific treatment of the business cycle would have to relax this assumption of course but I’m not going to do that here.  Similarly let us assume that expected inflation is constant.  For instance, assume that the central bank has an inflation target which everyone believes they will (and can) hit, at least on average.  The exact specification of this function is chosen for its simplicity not its realism but the important points are that it is downward sloping in the real interest rate and that it cannot be greater than the total value of real goods.  The maximum amount of loans possible does not have to be exactly equal to the total stock of real goods, it is likely to be somewhat less (I suspect an argument could be made for it somehow being more but this would be a bit more complicated to justify) but the important thing is that there is some maximum (the demand for loans does not go off to infinity as real rates (or alternatively, nominal rates) approach zero.

By assuming that inflation expectations are fixed, I am assuming that nominal rates move one-for-one with real rates.  This is a simplifying assumption of course.  Much of the complexities that arise in modeling monetary policy are related to the way in which these expectations are modeled but I don’t want to deal with that extensively here, though I will add some discussion of this issue at the end.

The supply of new loans as a function of the nominal rate will look like I describe in this post.  Namely, it will be horizontal (perfectly elastic) at i=0 (or alternately at the rate of interest on reserves) up to the maximum quantity which is possible to create from the given quantity of reserves and the reserve requirement.  At that point it will be vertical (perfectly inelastic).  So in “normal times” (when nominal rates are above zero) the equilibrium quantity of loans in this market (and thus the money supply) will be equal to the maximum allowable quantity and the nominal interest rate will be given by the point at which this quantity intersects the demand curve.

Mt=Rt/a=Lt= PtY (1-ite)

it=1-Rt/(a PtY)+ πe

Finally, let the price level in each period be determined by the equation of exchange.


And let velocity be fixed at v so that the price level in any period is given by the following.


The assumption of a fixed velocity is another drastic simplification.  This, along with inflation expectations, represent the main points of this model which deserve more careful analysis, expecially because the theory I am working from is one which holds that money demand is essentially liquidity demand and that demand aught to be related to velocity in an important way.  In other words, people find high velocity inconvenient and so they are willing to pay a price to acquire more money which lowers velocity (but likely increases prices).  But digging into this would greatly complicate things and at this point would distract from my main point.  So essentially, I am assuming that any increase in money goes entirely to prices.  One could imagine however, that some of the increase is soaked up by a decrease in velocity.

This describes a complete model of the money supply and the economy.  The path of the money supply, price level and interest rates, then depends entirely on the quantity of reserves provided by the central bank.  So let us imagine that the central bank tries to hit its inflation target every period.

Assuming some initial condition for the quantity of reserves R0, the initial quantity of money, price level, and interest rate will be the following.



i0=1-R0/(aP0Y)+ πe=1-1/v+ πe

In the next period, the central bank will try to make P grow by a factor of (1+ πe).

P1=P0(1+ πe)

This will require a proportionate increase in the money supply which requires a proportionate increase in the quantity of reserves.

M1=(1+ πe) R0/a= R1/a

R1=(1+ πe) R0

Because the demand for loans is proportionate to the nominal value of output, this demand increases proportionately with the price level and so the nominal interest rate will be constant across time as well as the proportion of debt to nominal output.

i1=1-R1/(aP1Y)+ πe=1-(1+ πe) R0/(a(1+ πe)P0 Y)+ πe=i0=1-1/v+ πe

The same thing will have to repeat in all following periods, so that at any time t, the state of the economy is described by the following dynamic equations.

Rt=(1+ πe)t R0

Mt=(1+ πe)t R0/a

Pt=P0(1+ πe)t

it=1-1/v+ πe

This constitutes a “base scenario” in which, in order to hit its inflation target in every period, the central bank has to increase the supply of reserves exponentially which increases the supply of “money” by the same factor and also increases prices by the same factor.  The nominal rate, real rate, and inflation rate are all constant.

Now some interesting points about this model.


As I said, this does not explicitly model recessions but we can imagine how one would occur and what it would look like by imagining a sort of “off the equilibrium path” scenario.  Consider what would happen if at some period, the money supply failed to hit the expected quantity.  This may happen because the central bank fails to inject enough reserves or it could be because demand for new loans drops unexpectedly (which amounts to the same thing since the CB would have to fail to account for the drop).

If this happens, then prices will not rise as much as people had expected when they initiated their old loans.  Since people borrow in anticipation of paying the loans back with income generated from the sale of goods and services in the future, their income will be less than they expected in nominal terms and so will their ability to repay those loans.  But because they have real goods backing those loans, they will be competing more fiercely over the smaller-than-expected quantity of money left out in circulation.  This is what causes prices to fall.

This condition of falling prices will be accompanied by some people (more than usual) being unable to repay their previous loans.  This will cause houses to be foreclosed, businesses to close down etc.  If people expect prices to continue to fall, they will be even more reluctant to undertake further debt (inflation expectations decrease which shifts loan demand to the left and lowers interest rates) and the process may be self-reinforcing to some degree.

This process of “deleveraging” will continue until enough people have defaulted, wiping away their debt without retiring the requisite quantity of money and therefore causing the ratio of debt to real goods to drop, (or until the government/central bank intervenes in some other way to increase the money supply) that the economy reaches a new equilibrium path.

This process of default can be avoided (at least in normal times) by central bank easing (increasing reserves) which allows interest rates to fall and more money to be created (monetary policy).  Alternatively, if the CB refuses to do this for some reason, the government, because it has the ability to borrow with no collateral constraints, can add to the demand for new loans by borrowing and spending (fiscal policy).  Either one of these should work equally well, at least if not in a liquidity trap (more on that below).

In this explanation, debt essentially plays the role that “sticky prices/wages” play in most other models (though they are not at all mutually exclusive).  In my opinion, this is a far better explanation because debt is literally fixed nominally by the contract over very long time periods.  The quantity of debt in the system is huge and it is directly linked to the quantity of money by the process of money creation.  You don’t have to make any strained arguments about “labor’s” unwillingness to work for less even though it is in their interest, or businesses being unable to change their menu prices for years on end or anything like that.

“Nominal rates are not a good indicator of the stance of monetary policy.” 

I put this in quotes as a nod to Sumner (and indirectly Friedman).  There are two ways of interpreting this in the context of this model.

1.  In a model with more realistic modeling of inflation expectations, the demand for loans would shift around with those expectations.  So if the CB did something that increased the money base in the current period but also increased inflation expectations for the future, you would have loan demand shifting to the right along with the supply and you could see rates either rise or fall.  So if we allow inflation expectations to change we can easily represent this phenomenon.  (A similar thing could be done if Y were a measure of expected future wealth which depended on expectations).

2.  Even without letting these things shift about, different specifications of this model could result in credit conditions (interest rates, and leverage ratio) that are not constant over time (more on this to come).  If this were the case (and I suspect it is) then it may be the case that the interest rate associated with “neutral” monetary policy (producing the targeted inflation rate) is different in different periods.  Specifically, I think a case can be made that this will tend to get lower, the longer this system goes on.  If this is the case, one may mistakenly interpret low rates in one period as “looser” policy (more inflationary) than higher rates were in previous periods when in fact they may actually be “tighter” (less inflationary).  This type of case will be left for a later post however.

Liquidity traps

In this model a “liquidity trap” occurs if the central bank finds that it cannot increase the quantity of loans (and hence the money supply) by increasing the quantity of reserves.  In other words, it means banks have excess reserves and the supply/demand in the market for loans is such that demand crosses supply along the elastic section of the demand curve (at i=0 or the level of interest on reserves).

In the model presented here, this would occur if the real rate fell to zero or below.  In this case all of the real property would essentially be mortgaged and so the CB could print more reserves and this would have no effect on the quantity of loans and therefore the quantity of money. Alternately, it could occur without all property being mortgaged if demand for loans hits the horizontal axis (or IOR) before this happens.  If this is the case, the CB may be unable to create the quantity of money which is required to create the expected inflation and this could lead to a recession as described above which cannot be easily cured by “traditional” monetary policy.

Market For Loans

loans market zlb2

This may happen because, for some reason, demand for loans drops (inflation expectations drop, government deficits drop, a real shock to output occurs, appetite for debt declines, etc.) or it may be that the economy approaches such a state in a systematic, deterministic way.  Whatever the reason, a wave of defaults and deleveraging will occur unless additional methods of increasing the supply of money are found.

One such method, as already described, is to have the government do additional borrowing and spending.  Alternatively, the central bank can do a similar thing by printing money and buying other stuff (“quantitative easing”).  Quantitative easing as we currently know it seems to be a method of increasing demand for loans by pushing down the longer end of the yield curve.  Similarly, the CB can try to increase this demand through “forward guidance,” promising to be “looser” for longer.  If this increases inflation expectations, it will increase demand for loans.

Of course, if just pushing down the long end of the yield curve is not sufficient to get out of the liquidity trap, the CB, in theory, could just print a bunch of money and use it to buy all kinds of stuff, pushing up prices and increasing the quantity of money in circulation without increasing debt.  Of course, whether this would count as monetary or fiscal policy is debatable.

This should answer questions like “how does monetary policy work” or “how is inflation created” in the context of a credit-based theory of money.  I have some ideas about why an economy may deviate from this scenario in a systematic way but I will try to present them as variations to this base model.  Stay tuned for that.

Reserve Requirements and Monetary Policy

March 12, 2014 4 comments

I have been trying to describe in detail the way money is linked to debt.  (If you are jus joining us start here, then go here and here.)  This leads naturally into a discussion of monetary policy which I will now begin to undertake.  I will provide a simple model of the way I look at monetary policy but first some discussion about what determines the aggregate supply of money is required.  I will begin with a gold standard in order to further highlight the similarity and difference between that system and a fiat money regime.

As I have been arguing so far, “money” as we know it is really credit created by banks.  Under a gold standard, you can take your gold to the bank and convert it into “money” (for instance bank notes or a checking account).  You can also convert other real assets into money like a house or a car or a business, this money just happens to be denominated in units of gold.  The quantity of money in circulation can expand far beyond the quantity of gold but this requires other assets to be put up for collateral. (Note that these assets may not always be as obvious as a house, they could be something like the produce of labor in the future.)

So if we want to deal with broader macroeconomic questions, we have to ask what determines the extent to which this process of money creation will be carried out.  Under a “free gold standard,” by which I mean a system free from any government restrictions other than the enforcement of the convertibility of the money into gold at the stated conversion rate, the extent to which money will be able to be created is limited by the willingness of the public to hold that money.  This is a matter of liquidity preference.

The price of gold (both the spot price and the rate of change) will be determined (at least primarily) by “real” factors in the gold market (quantity of gold, expected future production, expected future demand, etc.) and the value of money will be anchored to the value of gold.  (I say “primarily” because the evolution of the value of gold over time depends partly on it usefulness as a medium of exchange/store of value and money acts as a substitute in these regards so the extent of credit creation likely has some effect on the gold price but put that aside for now.  (For more on this topic see this post and this one and this one.  Note however that my thinking on these things is evolving fairly rapidly and some things like the definition of money may not be entirely consistent throughout.)

In this system, people are able to convert gold into money (and vise-versa) at par but the banks will find that they can issue additional money backed by other assets and charge some rate of interest.  The reason they are able to do this is that there is excess demand for liquidity when the price of liquidity is zero.  So essentially, when someone mortgages their house, they are converting the house into a different asset (money) which has liquidity characteristics more closely resembling those of gold.  It is more easily transported, divided, recognized, etc.  For this service they are willing to pay some positive nominal interest rate.

But the bank can only make a profit on the quantity of money it is able to float above the quantity of gold it has.  This money floats because of the willingness of people to hold their wealth in that form as opposed to others and this willingness will depend on the interest rate.  The higher the rate, the less money people will be willing to hold.  This may mean any of the following: they take out fewer loans, they pay off existing loans, they redeem money for gold.  Which one it means for any individual obviously depends on the financial condition they find themselves in at the time.

It is important to not here that, assuming financial markets are perfectly competitive, the marginal liquidity preference of money will have to be the same for everyone and equal to the cost of holding the money which is the interest rate.  To see why this is important notice that borrowing and lending can take place outside of banks as well.  So if one person is accumulating a lot of money to the point where their demand for liquidity is low, they can either turn it in for gold and hold gold, or they can lend it in the financial markets to someone else who’s demand for liquidity is higher.  This process of non-bank borrowing and lending does not create additional money, it only distributes the existing money in such a way that the people with highest demand for liquidity end up holding it.

But if at the current market rate of interest, the quantity of money in circulation is greater than that which can be held by the public at large when their marginal liquidity preference of money is equal to that rate, then some holders of that money will not be able to find borrowers at that rate and they will bid the rate down.  This lower rate will cause some people who were holding debt at the higher rate to “refinance” with debt from non-bank lenders and retire the money by paying off debts from the bank until the money supply and interest rates fall to a point where the marginal conditions are met for everyone.  Similar arguments can be made for other disequilibrium scenarios.  So the interest rate is linked to the quantity of money in circulation relative to the demand for liquidity.

Note that there is no need for people to redeem their money for gold unless they become concerned that the bank is or may become insolvent due to people failing to repay their loans and the value of the assets backing those loans (in terms of gold) being insufficient.  If nobody ever became concerned about this, the gold that the banks had on hand relative to the money outstanding would be inconsequential.  However, because people sometimes do fail to repay their loans, and the value of collateral is subject to market fluctuations, there is some danger of this.  The holdings of gold which the bank stands ready to redeem for their notes acts as a kind of buffer against this problem.

In theory, if a bank had a bunch of bad loans, it could go into some form of bankruptcy, liquidate all the assets it had, including good loans and collateral seized from bad loans for gold (or “money” attached to other sound banks) and distribute this to the people holding accounts at the bank or notes from the bank.  This means that some risk of loss from the loans of the bank would be born by the holders of the bank’s “money.”  The willingness to convert that money into gold at par acts as an indication of the solvency of the bank.  So in essence the willingness of people to hold money rather than gold comes down to a balancing between the liquidity premium and the risk premium here described.  These things may fluctuate over time and the bank may need to balance them by redeeming gold for money or vise-versa.

The more gold reserves a bank has on hand relative to its money outstanding (given the soundness of its loans) the lower the risk premium which will be associated with that money.  The less concerned people are about this risk, the more willing they will be to hold money at any given interest rate and the more banks will be able to expand the money supply for a given quantity of gold reserves without it coming back and being redeemed for gold.

In this way, banks allow for the conversion of less liquid assets into a more liquid form and the extent to which this goes on is determined by some balance between the demand for liquidity and the associated risk involved in that conversion.  The exact extent also depends on the structure of the banking market.  For instance, if banking is perfectly competitive, we could expect the money supply to be expanded to the point where the resulting nominal interest rate provides banks with zero economic profit.  If it is a monopoly, we can imagine the bank choosing the quantity of money and associated nominal rate in order to maximize their profit.  For more on this see this post.

As far as I know this form of pure free-market banking has never actually existed.  I suspect something similar has at some point somewhere and that this essentially describes the genesis of fractional reserve banking but if it has, it was a long time ago and I can’t point to a specific example.  An alternate way of constraining the extent of credit creation is through a statutory reserve requirement.  This can exist along with a gold standard.  In this case, there are two constraints on credit creation: the quantity that the market will bear based on the arguments laid out above and the quantity which it is legally possible to create from the quantity of reserves available to the banking system.  At any given time only one of these will be binding (except for the special case where they are both the same).

In other words, the reserve requirement may be meaningless (at least in the aggregate) because it may require a level of reserves which is less than what would naturally occur in an entirely free market or it may arrest the process of credit creation at some level lower than that.  In the latter case, the quantity of available reserves, along with the reserve requirement determine the quantity of total credit (money) which will be created by the banking system.

A pure free banking system would not be possible without a gold standard (or at leas some sort of similar standard) because it would create an enormous moral hazard for the banks.  Banks are able to float money because people are willing to hold it.  People are willing to hold it because they believe it will hold its value.  The reason it is possible for banks to expand the supply of credit in the way described without it losing value is that ever dollar they create creates a corresponding future liability.  This means that the supply of money created in this way is systematically anchored to the quantity of real goods backing those claims.  Over time the liabilities grow because of the positive interest rate but the money does not and the differential represents the bank’s profit.  But this is only possible with some regulating force like a gold standard.  To see why, consider two things that could occur without it.

1.  Banks could create a lot of money and use it to simply buy stuff.  This would create no corresponding liability.  Without that liability acting as a counterweight to pull money out of the system should the demand for that money decline, the only mechanism left to bring the market into equilibrium will be the price level.  So the more money they print, the more prices will rise.  But because of this, and the fact that there is no limit to what they can print, there will be no reason to believe that the value of a dollar from that bank will have a certain value in the future, and the willingness to hold it will likely collapse to zero and the money will become worthless.

2.  The other side of the coin: When someone takes out a loan, they do so with some expectation about the value of the money they will have to obtain in the future to repay the loan.  The value of the money in the future, of course, depends on the quantity of that money which is available in the future and that is at the discretion of the bank.  So a potential borrower has to try to imagine how much money lending the bank will be doing in the future.  Since loans carry a positive interest rate, there is never enough money to pay them all back without additional credit creation.  This raises the possibility that at some point, the bank could decide to stop creating more such credit and essentially pull the rug out from under its current debtors in order to make it difficult for them to repay and thus be able to repossess their collateral.  Borrowers, of course would have to anticipate this and this may lead to nobody being willing to borrow.

In either case, people on one side of the market (holders of money) or the other (holders of debt) are at the mercy of the bank who is unrestrained in their ability to expand or contract the money supply.  But a gold standard makes it impossible to alter the value of money much above or below that of gold.  If they tried, people would simply start swapping one for the other (either redeeming money for gold or using gold to repay loans).  This imposes a degree of discipline on an otherwise unconstrained issuer of credit.

A reserve requirement is an alternative mechanism for imposing some discipline on the process of credit creation.  This prevents banks from expanding credit beyond a certain amount determined by that requirement and the quantity of available reserves.  (The second problem is solved by having a competitive market for creation of interchangeable money so one bank cannot unilaterally restrict it.)  As I said, this can (and did) exist along with a gold standard but when it does, the two are to some degree redundant.  Once you have a legal reserve requirement, the gold standard is no longer necessary for the system to function.

So once you remove the gold standard, the value of money will not fall to zero because the gold was only a small part of the assets that were actually backing that gold.  But now that value will no longer be anchored to the value of gold.  It will instead be determined by the degree of credit expansion which is allowed to go on at any given time (and expectations of the same).  This, in turn, will depend (at least in “normal” times) on the quantity of available reserves and the reserve requirement which are determined by some central authority (the central bank).

So in essence, the reserves (base money) which the central bank issues are simply a license to create credit (liquidity).  Because the creation of credit is limited by the amount of reserves and the reserve requirement, and in “normal times” (more on this later) that total quantity that can be created is less than the quantity which would be demanded if the price of liquidity were zero, the price of liquidity will be positive and therefore banks will be able to make profits by creating credit and therefore, they will compete to get the reserves which allow them to do this.  This will be reflected in a positive rate on deposits (when you transfer your “money” from one bank account to another, a corresponding quantity of reserves must be transferred along with it), as well as a positive discount rate (the rate at which banks borrow and lend reserves to each other).  The price banks receive for creating liquidity is then represented by the difference between this (let’s imagine that the two previously mentioned rates are equal) rate and the rate at which they are able to lend.

In this case, the willingness to hold money, and the corresponding willingness to hold debt, will be determined by expectations about the future stance of “monetary policy” (most importantly the size of the money base and the level of reserve requirements) along with the state of the credit markets (demand for money, demand for currency relative to bank accounts, supply of goods etc.).  This willingness to hold money and debt, combined with the current supply of money/debt will then determine the state of the current credit markets (interest rates, price level, etc.).

Next (tomorrow unless fate conspires against me) I will present a simply dynamic model of this which I think provides a good explanation of liquidity traps.


Why Austrian Economics is Devastating to Libertarians

March 9, 2014 56 comments

Since it’s the weekend, I’m going to take a break from my attempts to reinvent (essentially) the existing macroeconomic paradigm from the ground up using debt (and collateral) as the backing for money and do something much easier–bash Austrians.  This is from a recent post on The Money Illusion.

I constantly hear conservatives complain that elderly savers can’t earn positive interest rates because of the Fed’s “easy money” policy.  Is there any time limit on how long you will make this argument, before throwing in the towel and admitting rates are low because of the slowest NGDP growth since Herbert Hoover was President?  Or is your model of the economy one where decades of excessively easy money leads to very low inflation and NGDP growth?

In other words, is there some sort of model of monetary policy and nominal interest rates that you have in your mind, or do you see easy money everywhere and tight money nowhere?  What would tight money look like?  What sort of nominal interest rates would it produce?

If you have spent any time at all reading econ blogs you should know exactly what answer you will get to this without bothering to check the comments section.  But in this case, you don’t have to wade too deep into the 266 (and counting) responses before you get it.  On the second comment Old Reliable, Major_Freedom, supplies it for us.  (I bet when people see “Free Radical” they expect me to be like that guy but it’s partly tongue-in-cheek!) Read more…