Posts Tagged ‘interest rates’

The Fisher Paradox

November 24, 2014 2 comments

There is a bit of a paradox underlying much of monetary economics. If real rates are independent of monetary factors, then a reduction in the nominal rate should be accompanied by a reduction in the expected rate of inflation (or vice-versa). Yet we typically observe, at least in the short run, that if the central bank lowers its interest rate target, it causes a higher rate of inflation. Of course, both old monetarists and market monetarists reconcile this by saying “never reason from a price change” (always good advice) and instead, reason from a change in the money supply (and expected future money supply), assuming sticky prices in the short run and then separate the effects on interest rates into the well-known liquidity, income and Fisher effects which allows for the real rate to change in the short run and for the nominal rate to go either way.

That’s all perfectly reasonable but lately there has been a school of thought emerging known as “neo Fisherites” who are bringing this issue back into the discussion. Nick Rowe (for one) has recently been taking them to task(here, here and here).

Now let me say for starters that I suspect everything Nick says about these papers is correct, and I’m not trying to defend them. I agree that denying that lowering rates raises inflation is contrary to all observations, and I suspect (though I haven’t read them yet) that his analysis of the specific papers as lacking in economic intuition and relying on strange assumptions to “rig” the results in favor of their prior beliefs is most likely spot on. That is how I feel about most modern economic papers I read, sadly. However, I think beneath the snow job and the tiny pebble of wrongness, there is actually a kernel of insight (or at least the pebble started out as a kernel before it got all mangled and turned to the dark side) and it is closely related to the stuff I have been trying to say. So I will try to flesh it out a little bit in a way that does not contradict everything we know about how monetary policy actually works.

Note that this actually began as a discussion of monetary and “fiscal” policy, which I intend to get to but I will put that off for a future post since just dealing with this Fisher paradox will be enough to fill a lengthy post by itself, but keep in mind that adding that piece in will be important for making this model look like the real world. (And also keep in mind that I don’t mean what other people mean when I say “fiscal policy.” Frankly, it’s almost tongue-in-cheek. All macro is monetary.) Read more…


Is it Dedication to High or Low Inflation Which Leads to Communism?

July 31, 2014 3 comments

Nick Rowe has a post about the line between fiscal and monetary policy which largely reflects my sense of the matter which essentially is that the line is not very clear.  However, this part was the opposite of how I see it (sort of).

Too dedicated a pursuit of low inflation and the optimum quantity of money leads to communism, with government ownership of everything.

Also Scott Sumner echoed the same sentiment.  Since both of those guys are “at least as smart” as I am and have been at this a bit longer, this has got my wheels turning trying to reconcile their conclusion with my own and I think it raises several important points about the way I am thinking about this thing relative to them (and probably nearly everyone else).

First, I apparently don’t know what Sumner (and probably nearly everyone else) actually means when they say “fiscal policy” since I recently said something to the effect of: clearly a helicopter drop is monetary policy, but then in the comments, Sumner says this.

I’m strongly opposed to helicopter drops. I favor monetary stimulus when NGDP is too low. There is never any need for fiscal stimulus, even at the zero bound, and a helicopter drop is fiscal stimulus. It is wasteful and inefficient.

So I’m not sure where Scott’s line is.  To me, if the central bank printed money and dropped it from a helicopter, it would increase the supply of base money and this would be monetary policy.  Perhaps Scott is thinking that the government “borrows” from the central bank and then drops the money (or whatever they do with it), and so this increases the deficit and this makes it fiscal policy which may or may not then be offset by some monetary policy.  If that is the case, it is just a matter of who we are imagining doing the “dropping.”  To me this is splitting hairs, and not that important (which is basically the point of Nick’s post).   This post also deals with helicopter drops.

On a side note, I am not sure why Sumner objects on the grounds of inefficiency.  It can’t be a matter of changing the income distribution since he is such a bloody utilitarian after all.  This got me very puzzled so I went on his blog and looked for posts about helicopter drops and found this one which raises two possibilities for inefficiency.  One is based on the expectation that the government will someday raise taxes to pay off the money it dropped.  This also explains why it counts a fiscal policy.  The other is that it may cause peoples’ expectations about inflation to become unhinged and cause hyperinflation.

But that’s not really what I am interested in.  I’m not arguing for helicopter drops.  I’m trying to get at why we are at the ZLB in the first place and how monetary policy relates to the central bank ultimately owning stuff.  And I think this helps bring things into focus.

But if the Fed did accompany the drop with an explicit price level target, then the optimal helicopter drop would be less than zero.  Indeed if the Fed committed to say 4% inflation, the public would not want to hold even the current $2 trillion in base money (unless they were paid to do so with an interest on reserve program.)

That makes perfect sense.  If you hold the money supply constant, and increase expected inflation, people will want to hold fewer dollars at the current price level and so they will try to get rid of them by spending them which will drive up the price level.   Or at least this is how you would see it if you take the money supply as exogenous.

If you take nominal rates as exogenous, then an increase in inflation expectations, holding the nominal rate constant, will lower the real interest rate which will cause people to borrow more in order to buy stuff (both investment and consumption).  This drives up the price level and increases the money supply.  However, the interest rate regime can mimic the outcome in the money supply regime by raising the nominal rate to the point that the money supply doesn’t change.  Similarly, the money supply regime could expand the money supply until the nominal rate remained unchanged (or either of them could do something in between….or not in between for that matter).  That is not the important difference.

Either way you want to think about it, you have a tradeoff between the size of the money supply that is required to maintain a given price level and the expected rate of inflation.   If you are trying to hit a certain price level in the very short run, you can get there with a smaller money supply if people expect higher inflation in the longer run.  This seems to be the tradeoff between tight money and socialism that Nick and Scott have in mind and it is perfectly valid at any given point in time.  This instantaneous effect can be seen in my model as well (I’m pretty sure, although I can’t verify it right now due to technical difficulties…)

So essentially I have no argument with the way monetary policy functions in the short run.  My issue is about whether there is a stable long-run equilibrium.  This is where the relationship between money and debt becomes important.  If you think that money just floats around and has value solely because everyone believes that everyone else will always be willing to trade for it, then you imagine a demand for real money balances which depends only on the interest rate and output.  So if you can raise inflation, you can raise interest rates along with it and this will put you on a path where the desired money holdings will be smaller relative to the nominal value of output at all times.  Or in other words, the money supply will be higher but prices will be more higher and so the size of the central bank’s balance sheet in real terms will be smaller.

The point I am trying to make is that there is a sort of financial position that the economy gets into vis-a-vis the central bank when the central bank expands the money supply by expanding credit.  When they do this, they are essentially increasing the money supply by convincing people to lever up.  This can be done by either offering a lower nominal rate or convincing them that prices will be higher in the future.  Either one lowers the real rate of interest and makes it more attractive to go deeper into debt.  But this is not just more money floating around, it is more money and more debt which means that the public’s claim on the total money supply actually diminishes.

As an individual borrower, this works out fine as long as the central bank produces the anticipated inflation (0r more).  Then your income increases enough to repay the loans as expected and everybody wins.  But if everybody tried to repay their debts, the money supply would shrink which would mean that prices wouldn’t go up as anticipated.  So the central bank has to keep this from happening.  This means that they get into a pattern of perpetually lowering interest rates to further increase the money supply by increasing leverage and eroding the financial position of the overall economy.

Then one day they fail to produce the expected inflation, maybe because they hit the ZLB or maybe because they made a mistake, or maybe because people saw the ZLB coming and acted preemptively, or whatever and everything falls apart.  The reason it falls apart is because of the financial position of the economy.  It isn’t just that everyone suddenly thinks prices will only rise 1% instead of 2% so they start “hoarding” cash balances because the extra liquidity becames attractive at the lower inflation rate and this creates a death spiral (which is only “deathy” because prices can’t adjust fast enough to keep people from being laid off and output from falling).

It is that they think prices will only rise 1% instead of 2% and they took on a bunch of debt in anticipation of their income rising 2% which they now become concerned that they won’t be able to repay.  They start “hoarding cash” to repay the debts.  If they don’t, they will go bankrupt and lose real goods.  Since everyone else is in the same situation, everyone tries to grab the existing cash and pay off debts which causes the money supply to contract and prices to fall further until some combination of things restores the financial position of the economy to a point from which it can continue onward.

These things include:

1. Defaults.  This destroys debt without “destroying” money, which increases the ratio of money to debt.

2.  “Fiscal policy.”  This keeps the debt growing but it puts it on the government, so it can be done coercively (it doesn’t have to be individually rational).  This puts more money in circulation without increasing private debt.

3.  “Unconventional” monetary policy.  For instance a “monetary helicopter drop” by which I mean the central bank dropping money into the economy (a “fiscal helicopter drop” would then be when the government borrows money and drops it, in which case see number 2 above).  Or the central bank buying junk off of banks’ books for more than it is worth (this has some element of number 1 involved) or “adding zeroes” to their accounts, or buying up goods and services (rather than debt).  All of this will inject more money into the economy without increasing debt.  (We can throw dividends paid by the central bank into this category.)

So my point is that you can’t have what I would call a “long-run expansionary monetary policy” based purely on expanding credit.  You will need some combination of the above three things to keep the financial position of the economy on a sustainable path or to bring it back to such a path if it drifts away (as it is bound to do if you try to avoid those things for any extended period).

So in my model, it is not just about the willingness to hold cash balances, it is about the willingness to hold cash (or I would say “money” to include all balances denominated in dollars, or whatever) balances and the willingness to hold debt.  So to me the tradeoff between expansionary monetary policy and “socialism” is not just about how big the central bank’s balance sheet will have to be relative to the nominal value of output in a stable long-run equilibrium.  It is about how much of number 2 and 3 you would need relative to the value of output in a stable long-run equilibrium.  And I suspect that the more “expansionary” (the higher the intended rate of inflation), the more of this you will need in order to keep it from crashing.

Unfortunately, because of the previously mentioned technical difficulties, I  can’t show this in the context of the model at the moment.  But notice that there would be no such “socialism” necessary if there were no central bank in the first place and the money supply consisted of an exogenously determined quantity of some commodity like gold or silver.  In that case, there would almost certainly be some amount of deflation as the quantity of that commodity would most likely grow more slowly than output. (Or a better way of putting it: the rate of return on holding that commodity would have to be equal to the real rate of interest minus the liquidity premium and this would most likely be positive.  The selection of commodities which increase in quantity relatively slowly compared to output as money would happen endogenously.)

In this case, the private (excluding the central bank but not necessarily the government) claim on the money supply would always remain at 100%.  It is the adoption of a central bank which promises to create inflation by growing the money supply (by increasing credit/debt) which creates the gap between the money supply and the monetary wealth in the economy which has to be filled by some kind of non-credit injection of money or else closed by a wave of defaults.

Similarly, if the central bank just kept the rate of inflation (deflation) and the nominal interest rate equal to what they would be if it didn’t exist, it would do nothing, credit would not expand, the financial situation of the economy would not be eroded in any way and no “socialism” would be necessary.  It becomes necessary when they endeavor to expand the money supply by expanding credit.  The more inflation they want to create, the more they will have to do this and the more they will erode the financial condition of the economy in the absence of the three things mentioned above.  Or in other words, the more they will have to do those things to keep it going.  Or in still other words,  too dedicated a pursuit of high inflation and the optimal quantity of money leads to communism with the government owning everything.

Some Graphs

July 18, 2014 1 comment

In my last post, I put forth a model which leads to the crackpot conclusion that central banks, doing what they do, necessarily lead us into a “liquidity” trap unless there is some significant, and ever-increasing, leakage of money which is not backed by debt back into the economy (in other words “fiscal policy”).  I didn’t say very much about fiscal policy, there is a lot of work left to do which I intend to be doing for a while.  But at this point, just in case you are thinking that this theory is nutty, here are some graphs.

Quick history for the uninitiated.  The U.S. went off the (international) gold standard in 1971.  Then there was a decade of “stagflation” where inflation was high and, to put it (overly) simply, the Fed’s policy goals were not all that clear and people were still trying to figure out what was going on and what it meant in the long-run.  Then Paul Volcker was appointed chair of the Fed and vowed to rein in inflation which he did.  Since then, it has been supposed by many that the Fed has essentially been following a de facto inflation target.  The following graphs go from August 1979 (when Volcker was appointed) until the present.  We all know basically what output and the price level have done, so let’s cut to the chase.

Fed Funds Rate

fed funds rate

Ten-Year Yield

ten year yield

Now total debt is a little tricky.  Here is loans and leases in bank credit; all commercial banks, and the M2 money stock.

Loans and leases in bank credit, all commercial banks



Notice that the ratio of M2 to total bank credit is about 1.74 in Nov. 1980 (this is as far back as the M2 series goes) and about 1.10 in Nov 2007.  Obviously, we know what happened next, and bank credit fell bringing the ratio back down to about 1.47 currently.  But of course, we also know what else happened….

“Fiscal Policy”

Federal debt held by fed banks

Endogenous or Exogenous Money

June 15, 2014 27 comments

There are quite a few arguments in economics which are entirely superfluous.  One of them is over whether central banks determine the money supply or whether it is determined by the banking sector.  I have dealt with this previously (following along on the coat tails of Rowe and Sumner) but as I work through Keen’s lectures on “endogenous money” (see primarily 06 part 2 and 07 part 1) I can’t help but notice that this issue seems to be central to much of his criticisms of mainstream economics.  So in pursuit of my ultimate goal of rescuing the theory of money and debt from the Marxists–er, I mean “post Keynesians”–and folding it somehow neatly into regular old-fashioned economics, let me first address this whole endogenous/exogenous ball of wax.

The first problem with this debate is that it usually begins with a misunderstanding of the significance of those terms.  Endogenous and exogenous only have meaning in the context of a model.  A model can be designed in such a way that it treats something as exogenous, meaning that the determination of it is not explained in the model but taken for granted, or it can be designed in such a way that that thing is endogenous or determined in the model.  Neither one of these is right or wrong.  In the real world, everything is endogenous (except the laws of nature and some set of initial conditions).  Of course, if we are trying to demonstrate how or why a thing is what it is, we have to make a model in which it is endogenous or we are just saying what it is without adding any additional layers of logic to justify it.

Now keen characterizes the debate as over money being exogenous to “the economy.”  However, I think most staunch “exogenous money” types would still agree that the behavior of the central bank depends to some extent on conditions in the economy.  So, in some sense, as I said, everything is endogenous.  But let’s be honest, that is dancing around the issue.  The real question is what is the best way to model monetary policy.  It is hard to make a model where everything is endogenous.  And monetary policy, at least in theory, could be conducted independently of other conditions in the economy.  And furthermore, a large part of what we are usually trying to determine/demonstrate is the effect of monetary policy.  So it makes sense to treat this, somehow defined, as exogenous.  The question then becomes how to define it.

At this point, we arrive at the real crux of the matter.  The exogies claim that the central bank determines the quantity of base money and then the market determines the rate of interest.  The endogeroos insist that it is the other way around and the central bank merely determines the rate of interest and then the economy determines how much base money is needed and the central bank supplies it.  Now we have a report from the bank of England which tells us that what banks really do is the latter.  But the problem with Keen’s exposition on the subject is that he seems to act as though the rate of interest set by the central bank has no effect on the quantity of money which is thusly “endogenously” determined.

Essentially, this boils down to a common “paradox” in principles classes.  Does the monopolist take price for granted and choose a quantity or take quantity for granted and choose a price?  Answer: No.  The monopolist takes the demand curve for granted and chooses a price/quantity pair along that demand curve.  And so it is with the monetary authority, at least in the short run.  In the long run, there is a sort of supply and demand for money, though it is difficult to characterize them precisely.  The supply takes the form of some kind of reaction function by the central bank specifying either the quantity of money they will provide (if you are an exogie) or the short-term interest rate they will charge (if you are an endogeroo) under all possible economic scenarios.  The demand can be thought of as the quantity of money “the economy” will “demand” at any given interest rate (if you are an endogeroo) or the short-term interest rate that they will bid up to for any given quantity of money (if you are an exogie) under any given set of economic circumstances.  These two then interact in a very complicated way to determine the interest rate and the quantity at any given moment and market expectations of them at all points in the future which are represented by prices (including various interest rates).

Now, is the quantity or the price (interest rate) endogenous?  Answer: yes.  Better answer: they both are, of course, that’s supply and demand 101, can we get some harder questions in here?

So for most practical purposes, this distinction doesn’t matter.  It becomes the horizontal/vertical supply curve debate which Keen alluded to but I didn’t see him address (maybe he did it earlier).  That might make a difference for some minor reasons like the effect of misestimating demand or of changes in demand in the ultra-short run (faster than the CB can adjust policy) but as far as the big picture is concerned, this is a smokescreen.

But Keen seems to take it a step further than just arguing about what I would consider a bit of meaningless minutia.  He seems to be implying that monetary policy in general is not exogenous.  Which, in this context, since we know that the CB has the ability to determine monetary policy independently of what is happening in the economy, amounts to the statement: monetary policy is meaningless.  Here is the argument “in a nutshell.”  For the record, Keen is quoting Basil Moore.  By the end, the astute observer, thoroughly trained in sound “neoclassical” economics should see the flaw in this reasoning leaping off the page (or screen, as the case may be).

“Changes in wage and employment largely determine the demand for bank loans which, in turn determine the rate of growth of the money stock.

Central banks have no alternative but to accept this course of events, their only option being to vary the short-term rate of interest at which they supply liquidity to the banking system on demand.

Commercial banks are now in a position to supply whatever volume of credit to the economy that their borrowers demand.” (Moore 1:3-4)

In a nutshell

-The supply of money and credit is determined by the demand for money and credit.  There is no independent supply curve as in standard micro theory.

-All the state can do is affect the price of credit (the interest rate).

Did you spot it?  Here’s a hint: a monopolist doesn’t have a supply curve.  Does that mean the monopolist’s quantity is determined only by the demand curve?  No, because the monopolist can control the price.  But wait! says the smart kid in the front of the class.  If he doesn’t have a supply curve, and he is facing a given demand, and he controls the price, then isn’t he effectively choosing a quantity?  Like, couldn’t we just as easily say that he controls the quantity and the price is determined by the demand curve given that quantity?

Yes! Bonus points for the smart kid who doesn’t need them anyway!  Now all of the other people in the class hate your guts even more, congratulations!  A demand curve can’t determine a quantity all by itself.  There has to be something else determining which point along the demand curve we are at.  You can say that the central bank sets the price and then the demand curve, along with that price determine the quantity.  If you say that the CB sets the quantity and the demand curve, along with that quantity, determines the price, it’s not really different (assuming the demand curve is fixed and the CB knows what it is.  No doubt, Keen would say “well those assumptions aren’t true so your whole theory is garbage” but those are at best second order concerns).

Keen’s (and I guess Moore’s) mistake is to ignore the effect of controlling the price of money (interest rate) on the quantity demanded.  He acts as if this is a meaningless novelty.  But if the demand curve is downward sloping, this is everything.

Furthermore, the Keen/Moore theory has a gaping hole in the middle of it.  He claims that the money supply doesn’t “cause” price increases but that price increases cause an increase in the money supply.  But that leaves us with no way of determining a price level (or a change therein).  By the way, this is why it’s hard to make a model where everything is endogenous.  What determines all of them in that case?  Each exogenous variable you want to make endogenous requires another equation to identify it.  This presents problems if you are trying to have all of your equations make sense for some reason.  On the other hand, if you are just assigning arbitrary relationships between variables and calibrating them to fit the data, then no problem.

Finally, Keen begins with an empirical analysis by Kydland and Prescott which apparently finds evidence that changes in the money base lag the business cycle while changes in credit money (M1-M0) lead the cycle.  This is not surprising to me and fits with my view of the role of credit and monetary policy in the business cycle (which, for the record, I think has a lot of overlap with Keen’s view) but this does not prove that one causes the other.  The flaw is in Keen’s notion that if X follows Y, X couldn’t have caused Y (and therefore by implication, Y must have caused X).  Though he does make some equivocations for this, I think it shows what happens when you try to strip the “agent” out of economics, which seems to be Keen’s overarching mission.  You treat relationships between variables like the sterile cause/effect relationships that underlie most of the hard sciences.  The rate of acceleration due to gravity (near the earth’s surface) just is what it is and it is just a matter of measuring it.

In economics, things are seldom that straightforward.  Because you are modeling the behavior of thinking people, they have the ability to anticipate things that will happen in the future and this affects their actions today and in turn affects what happens in the future, just like those movies in the eighties with Michael J. Fox, it becomes a whole confusing mess with paradox on top of paradox that is difficult to sort out.  Or, to put it in the words of Scott Sumner quoting Paul Krugman: “it’s a simultaneous system.”

Does Tighter Monetary Policy Increase Investment?

April 14, 2014 Leave a comment

I came across a short piece recently citing a former New York Fed economist entitled Tighter Fed Policy Will Boost Economy.  I was pretty taken aback by this and I’ve been trying to wrap my mind around it.  I couldn’t find he actual report (it may be an internal UBS document or a clients-only sort of thing) and the press release I am going on is pretty brief so I have to guess a little bit as to what Matus has in mind.  It’s also worth noting that he is not quoted in the body using the word “tightening” so it’s possible the headline writer is more confused than Matus.  But whatever his reasoning, it provides a pretext for an attempt to explain why looking at monetary policy through an interest-rate lens is potentially misleading.

There are two issues here.  One is the question: what is tightening?  The other is: do low rates cause more or less investment?  To answer the first, we have to consider the second and see that it is not really a coherent question.

On the surface, conventional wisdom tells us that low rates lead to more investment.  This is the story behind the Keynesian IS-LM model taught in intermediate macro classes.  The CB increases the money supply which causes interest rates to fall (shifting the LM curve to the right) and the lower rates increase investment which increases output (moving along the IS curve).  In the context of that model, this is what we would call monetary “easing.”  Note that whether you look at this as an increase in the money supply or a decrease in interest rates is purely semantic as I try to explain here.

Yet, here is an economist claiming that higher rates will lead to more investment.  How is that possible?  The short answer is that this is “reasoning from a price change” which is a cardinal sin of economics but which is nearly impossible to avoid if you are thinking about policy in terms of interest rates.

Interest Rates and Investment

It makes no sense to try to determine the effect of a change in the price of coffee on the quantity of coffee beans exchanged.  But we constantly talk about changes in the interest rate “causing” changes in investment or consumption etc.  This is a sort of conundrum created by the central bank saying that they are fixing the interest rate exogenously as a matter of policy.  They can do this because they can control the quantity of money and the nominal rate is the price of money (in a sense at least).  But even if you take the nominal rate to be exogenous, you still don’t know the cost of investment because the cost of investment is the real rate which is the nominal rate minus the expected rate of inflation.

If you are deciding whether to invest in a new factory, your decision depends on whether or not the (net) present value of the produce of the factory in the future will be more than the cost of building it.  The lower the nominal rate, the more these future values will have to be discounted, or to say it another way, the more interest you will have to pay on the loan (or forego on the money) that it takes to build it.  But the higher the expected rate of inflation, the higher those future values will be.  So if the nominal rate changes, the effect depends on why it changes.

The simplest way to get to the Keynesian result above, is to imagine that expected inflation is fixed and doesn’t change when the CB “lowers the interest rate.”  In this case, the real rate will also fall and investments that were not appealing before will become viable.  Alternatively, if inflation expectations suddenly increase and the CB does not allow nominal rates to increase as much, you also have the real rate decreasing which should also increase investment.

In the latter case, you would see nominal rates rising along with investment.  And if you only judged the stance of monetary policy by the nominal interest rate, you might conclude that “tightening” was causing an increase in investment.  However, this is not a good way to think about monetary policy because the higher rates would be the result of a more expansionary monetary policy.  I can’t think of a possible explanation for thinking that “tighter” monetary policy would cause increased investment unless all that one means by “tighter monetary policy” is higher nominal rates.  In which case, as Scott Sumner likes to remind us, Weimar Germany had incredibly tight monetary policy.

The most confusing thing in the article was this statement.

‘The expectation for rising rates may prove helpful,” said Matus. “Low rates not only lower the cost of delaying investment decisions but also encourage other behavior that can be detrimental to business investment.’

In periods of low rates, equity investors usually favor companies that buy back shares and pay dividends, said Matus. That encourages chief executive officers to use cash in those ways, rather than invest in new plants or machinery.

The first part about “lowering the cost of delaying investment decisions” makes no sense to me.  Low nominal rates (holding inflation expectations constant) means lower cost of investment.  There is a cost and a benefit to investment and we expect businesses to invest when they think the benefit is greater than the cost.  Are executives sitting in boardrooms saying “we want to delay some investment but we’re not sure how long to delay it, what are the costs and benefits?”  Even if they were, wouldn’t the cost of delaying it be lower with higher nominal rates?  You would make more on your “cash” reserves (which I believe is typically not technically cash) in the meantime (or pay less on loans).  This seems like pure carelessness to me but seemingly this guy is getting paid to figure this stuff out and I can’t say the same, so maybe I am missing something.

But putting that aside, is it true that investors favor companies that buy back shares and pay dividends when interest rates are low?  That doesn’t seem like what we have been observing lately.  In fact, we have seen a plethora of “growth” stocks with little to no earnings skyrocket in price relative to broader market averages over the last couple years.  It’s true that may larger-cap stocks have increased dividends and buybacks, and some others, like Apple, have been under pressure to do so from activist investors.  But is this really a sign that investors are demanding less investment?  I don’t think so.  Here is an alternative story.

Companies each have access to some set of investment opportunities and some amount of cash/credit, the cost of which is the nominal interest rate.  The nominal return on their investment opportunities is given by the real rate of return plus the expected inflation rate.  Companies invest until the marginal real rate of return on investment is equal to the real interest rate.  When the real rate is lower, it makes more investments look profitable.

Now assume that the low real rates are accompanied by an influx of cash into the economy.  But because different companies have access to different investment opportunities, the ones who accumulate this cash may not be the ones with the optimal investment opportunities.  For instance, imagine that one company, let’s call it “Tesla,” happens to have the ability to invest a large amount of money and return 2% in real terms, while the real interest rate is 0%.  And let’s say that there is another company, call it “Apple,” that is accumulating a lot of cash on its balance sheet but is already investing in all the projects available to it with a positive real rate of return.

Now if you are an investor sitting on a big pile of cash, and just to make things a little cleaner, let’s assume that you have access to a secondary offering of each company at book value, which one do you want to invest in?  The answer should be clear, you want the one which will earn a higher return on the money you invest.  This means that the companies with the best investment opportunities will attract more capital.  Conversely, if you own Apple, and they are sitting on a pile of “cash” which is earning no interest and which they have no productive use for, you will want them to give you that cash so that you can divert it to a company with better investment opportunities.

Another way of coming at the same idea is to say that, if both companies are trading at the same premium to book value, people will want to “rotate” into the high-growth companies which will cause them to trade at a higher premium.  The companies with a lot of cash, in the face of this rotation away from them, may start throwing off that cash in the form of dividends and buybacks to increase their dividend yields and prop up their stock prices.

The same logic can be applied to mergers and acquisitions.  If Apple has a lot of cash and no good investments and Tesla has good investments but not cash, instead of returning cash to shareholders and letting them invest it in Tesla, Apple can just cut out the middle man and buy Tesla itself.  But none of this is evidence that low interest rates are causing companies to invest less in aggregate.  It is just evidence that cash has to move around to find the best investments.  That, after all, is basically the whole point of equity markets.

Interest Rates and the Stance of Monetary Policy

Hopefully we can agree that the lower nominal rates, all other things (including inflation) equal, the more incentive to invest there is.  Similarly, the higher expected inflation is, all other things (including nominal rates) equal, the more incentive to invest there is.

This is not that difficult to understand, but the problem comes in when you insist on seeing rising interest rates as “tightening” (or for that matter, on seeing “tightening” as rising interest rates).  But when you step outside of that mindset, things get a little complicated.  This is because, nominal rates and inflation are both components of monetary policy and they are not independent.  In order to generate more inflation, the CB has to increase the money supply.  And if you see monetary policy as just setting an interest rate, the only way to increase the money supply is by lowering the rate.  So you find yourself having to say that they are trying to raise interest rates by lowering interest rates.  Is that easing or tightening?

The simplest way around this is to think in terms of the quantity of money instead.  Then you can just say that “easing” means expanding the money supply which lowers nominal rates (and increases investment) in the short run but increases inflation and has an ambiguous effect on long-term nominal rates.  Of course, if we all did that, then we would dramatically reduce the demand for confused debates about the effect of interest rates on stock prices and investment.  And nobody wants that.





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).


Banks Can Lend Out Excess Reserves

January 4, 2014 21 comments

In the comment section of a post by Scott Sumner on EconLog, a commenter made the claim that banks cannot lend out excess reserves and cited this paper.   While most of the details discussed in the paper are correct, the conclusion that banks can’t lend excess reserves is not.  I will try to explain the confusion.

First, the author makes the important point that “A key distinction to bear in mind (hinted at in the last previous paragraph) is between individual banks and banks in aggregate.”  But then he goes on to “prove” his claim that banks can’t lend out excess reserves by showing that they can’t change the quantity of aggregate reserves.  This is true but an individual bank can lend out excess reserves.

Consider the bank’s balance sheet as represented in the paper.

Reserves (R) + Loans (L) + Bond holdings (B) = Deposits (D) + Equity (E)

When a bank makes a loan, they create additional deposits and additional loans (initially keeping their reserves unchanged).  However, people don’t just take out loans to keep the money in a deposit account at the bank who gave them the loan.  Usually they spend these deposits.  When they do this, they become deposits in someone else’s account, possibly at another bank (some may become cash held by the public).  When this happens the other bank settles with the first bank and reserves are transferred.  This decreases reserves and deposits at the first bank, keeping the above equation intact.  It’s true that this doesn’t change the total quantity of reserves in the economy but it does change the quantity of reserves held by that individual bank.  They have been traded for loans (notice that this still keeps the above equation intact, it has just changed the composition of the left-hand side.

If a bank does this, it will increase the money multiplier because while the total reserves in the economy remain unchanged (they have just changed banks) the total amount of loans and deposits has increased (those deposits ending up on the balance sheet of the other bank which got the reserves which left the first bank).

Note that even if you assume that when a bank makes loans, it increases its own deposits only and does not decrease its reserves at all, the minimum reserve requirement will still be a constraint on lending because as it increases lending, L and D will increase but R will remain the same.  Obviously, at some point, this will cause the ratio L/R to hit the minimum.

Now the claim that banks are not constrained by reserve requirements in normal times is mystifying.  Again, this is a case of making an argument about aggregates and extrapolating (erroneously) to the behavior of individual banks.  Here is the claim.

The money multiplier view of the world envisages the central bank creating reserves and the reserves multiplying into new lending. That is, reserves constrain bank lending. That would seem compelling. If banks are subject to minimum reserve requirements (requiring them to hold reserves in a certain proportion to their deposits, and deposits are the balance-sheet counterpart to loans at the point of credit creation), then, by restricting the amount of reserves that the central bank supplies, it should be able to control the amount of credit.

But modern central banking doesn’t work this way. Central banks don’t constrain the amount of bank reserves they supply. Rather they supply whatever amount of reserves that the banking system demands given the reserve requirements and the amount of deposits that have been created.

This seems to indicate a deep confusion about what it means to be “constrained.”  It’s true (or at least I will accept the premise) that the central bank sets an interest rate target and provides whatever amount of reserves are necessary to hit that target.  This does not mean that banks are not constrained by reserves! 

This fact I think is indisputable: a legal minimum requirement for reserves exists.  This means that if a bank has a ratio of loans to reserves which is equal to that minimum level, they cannot make more loans.  When banks make loans in the way described above (which is the same way described in the paper), they increase aggregate loans and deposits without changing the aggregate quantity of reserves.  This means that for a given quantity of reserves, there is a maximum amount of loans and deposits that the banking system is capable of creating and this maximum is determined by the minimum reserve requirement.

The author seems to claim that this technical constraint is meaningless because if a bank runs into it, the Fed just creates more reserves.  This is not true for an individual bank.  A bank cannot hit the minimum level of reserves, want to keep making loans, and just call up the Fed and say “give me more reserves, I want to keep making loans.”  They have to trade some other asset for more reserves (this may include attracting deposits) or else they cannot make more loans.   This means that the reserve requirement is a binding constraint if the bank is in that situation.

Furthermore, and more importantly, this claim that Fed just supplies whatever reserves the banking sector “demands” given the reserve requirements and deposits being created is complete nonsense.  He is just saying that, instead of the Fed determining the amount of reserves (money base) and this leading to some amount of deposits which is determined by the reserve requirement (which is a constraint on the creation of deposits), there is some exogenously given quantity of deposits and the Fed just mindlessly fills in the reserves which this amount of deposits requires.  That’s completely upside down.  The amount of deposits depends on the amount of loans.  The amount of loans and interest rates are determined in the market.  Yes the Fed tries to target an interest rate but how do they do this?

A bank has the ability to trade assets of one kind for assets of another kind at certain prices which are determined in the market.  Different assets have different rates of return.  Barring any other constraints on their behavior, they will choose the quantities of these assets (and the market prices will adjust) in such a way that the rate of return (net of risk premiums and other such considerations) is equal.  Reserves usually have a low or zero rate of return.  This is fixed by the rate of interest on reserves.

The rate of return on loans is determined by the supply and demand.  The demand is beyond the control of the banks.  The aggregate supply of loans is essentially flat (maybe not perfectly flat but at least pretty flat) at (or near) the rate of IOR (abstracting from risk premiums) for quantities up to the maximum quantity of loans which is possible for the given quantity of total reserves and the minimum reserve requirement.  At that point, it becomes perfectly inelastic (vertical) because there is no way that the banking system can make more loans without the Fed either increasing the total reserves or lowering the reserve requirement. (In other words it is constrained by these two things!)

In normal times, interest rates on loans are high enough that the return on them dominates the return on holding reserves so banks try to make more loans and they do this until they hit the reserve requirement constraint and the market interest rate is determined by where this quantity of loans hits the demand for loans.

Market For Loans

loans market normal

Here i* is the market interest rate R is total reserves and r is the minimum reserve requirement and I am assuming there is no currency held by the public just for simplicity. (I don’t know why it’s blurry I’m not very good at blogging…)  Now if the Fed were to increase the total amount of reserves in the economy, this supply curve would shift to the right which would lower interest rates (of course there could be some effect on demand from changing expectations about the stance of monetary policy but that isn’t important for our purposes).  The Fed can increase or decrease the quantity of total reserves to try to hit its interest rate target but this doesn’t mean that banks aren’t constrained by reserves.  On the contrary, it is because banks are constrained that this works.  By increasing the total quantity of reserves (money base) they are relaxing the constraint and this allows banks to make more loans until the constraint becomes binding again.

The quantity of reserves (money base) is a tool the Fed uses to manipulate interest rates to the supposed target.  The reason this works is that the expansion of credit is constrained by this quantity.  This means that the quantity of base money determines the quantity of credit created and the interest rate.  You can say that the quantity of reserves the Fed has to create is determined by the interest rate target and the demand for loans and the reserve requirement but this is not saying something different from the “fractional-reserve banking theory of credit creation,” it is just saying it in a different order.  It is still a fact that the Fed controls the size of the monetary base and that this puts a constraint on the total amount of loans and deposits banks can create.

“Zero” Lower Bound and Interest On Reserves

If for some reason the quantity of base money becomes high enough relative to the demand for loans that the demand hits the supply to the left of the maximum quantity of loans which can be created, then this constraint will cease to be binding and instead bank behavior (on an individual level) will be equating the marginal return on loans to the marginal return on reserves (recall that while banks as a whole cannot reduce their reserves, individual banks can).  The reserve-requirement constraint still exists but it is not binding.  When this happens banks could make additional loans but they are choosing not to because the rates at which they would have to make those loans are not worth it.  This is not a criticism of banks.  So while the imagery of reserves being parked at the Federal Reserve instead of being loaned out may seem misleading, this is only because if banks made more loans, the reserves in the aggregate would still be parked there.  This does not mean that the presence of those reserves, however they are described, does mean that banks have the ability to make more loans.

In this environment, increasing the money base does not relax the constraint on lending because it is not binding and therefore, it does not have the usual effect on interest rates and borrowing/lending.  (This is not to say it has no effect since it still affects inflation expectations which affect the demand).  On the other hand, lowering the IOR would lower the rate of return on reserves (obviously) which would make loans relatively more attractive.  In other words, it would shift supply downward, which would increase the quantity of loans and further reduce interest rates.

Market for Loans

loans market zlb2

Now if demand suddenly increased in this environment, banks would start making more loans and this could cause inflation if the Fed did nothing to restrain it.  However, I agree with the author that the Fed would have no difficulty reigning this in by reducing the base if such a thing occurred.  Indeed, I believe the Fed would love to have that problem instead of the current one.  However, just because the Fed can change the constraint by changing the total quantity of reserves does mean that it isn’t a constraint.

The claim that “banks can’t lend out reserves” seems to be purely a semantic argument.  He doesn’t want to call it “lending out reserves” but his reasoning for this–that an individual bank’s reserves don’t decrease when they lend more–is not correct since, even though they may trade deposits for loans, those deposits are usually quickly transferred, along with reserves, to other banks.  This means that individual banks can’t change the total quantity of reserves but they most certainly can change the quantity of their own reserves.