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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.

M0=L0=R0/a

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.

Mt=Lt+Lt-1-Lt-1=Lt

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.

MV=YP

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

Pt=vMt/Y=vRt/(aY)

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.

M0=R0/a

P0=vR0/(aY)

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.

Recessions

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.

The Value of a Dollar

March 7, 2014 22 comments

Okay, yesterday I set out to explain how the value of a dollar  is determined and monetary policy functions under my collateral-backing theory.  I typed for two hours and felt like I didn’t get half way there (much of it is just rehashing what everyone else already believes).  So I am going to try to slice off a smaller piece again.  This time I won’t promise to fit everything else into the next post (reflecting on the fact that Sumner has been trying to explain that nominal rates are not a good indicator of the stance of monetary policy for five years…).  I will just take it one bite at a time and see what, if anything, people want to argue with and go from there.

So in this installment I basically want to deal with this criticism by J.P. Koning.

2) What anchors the price level? Why does $1 buy one apple and not $10 apples? Does a Canadian dollar by 0.98 US dollars because there are less debts to settle in Canada?

Frankly, I am a bit perplexed by this question because this is exactly the problem that I think his theory (and essentially every other theory I am aware of) has and which, in my mind, my theory solves quite nicely.  So in a sense, I feel like that’s what I’ve been explaining.  Somehow, I haven’t gotten my point across (maybe because I haven’t explained it well enough or maybe because there is a flaw that I don’t see), but I’m not exactly sure where the disconnect is so once I start trying to explain I tend to want to try to come at it from every possible direction and cover everything under the sun related to money.  I will try to resist that temptation here by avoiding a detailed discussion of how monetary policy functions.

So let me start by attempting to more clearly explain what I am trying (and not trying) to do here.  First of all, I don’t think I am overturning everything everyone ever thought about money and monetary policy and macroeconomics.  I think that monetary policy functions in essentially the same way that most economists do.  I just think that, on a basic level when you get to questions like “why is money valuable in the first place?” the explanations typically given are not the whole story.  In fact, I think they miss the most important piece of the story.

Once you fill in this piece of the puzzle, I do think that you can see some things that are a bit fuzzy without it more clearly and I do think that there are a few implications (or at least possible implications) that arise from this view which are missed by other simpler models of money creation though it takes a lot of analysis to get to them.  But this doesn’t mean, for instance, that I don’t think the CB can affect the value of the currency by buying and selling assets.

Now the answer to “what determines the price level at any given time,” on some level, has got to be the same for any theory.  It is determined by supply and demand.  At any given time, there is a certain number of dollars in circulation and a certain quantity of goods and services (or potential goods and services) and the dollars circulate at some velocity which is based on peoples’ willingness to hold them relative to other assets and this determines a “price level.”  This basically has got to be the case regardless of why you think the money has value.

The real question underlying this, which I have tried to answer is “why are people willing to hold money at all?”  Whatever the answer to this question, it will determine some willingness to hold money (which is to say a “demand form money” which depends on the cost of doing so) so people will hold money until the marginal benefit (from liquidity preference) is equal to the marginal cost (foregone return on other investments).  The higher the velocity, the higher the marginal liquidity preference will be (or vise-versa) and there will be some equilibrium price level.

Now, any theory about the demand for money also has to acknowledge that the willingness of people to hold money today depends on their beliefs about the value of that money in the future.  This is what makes everything complicated.  We know people must believe it will be valuable or else they wouldn’t hold it at all (and probably that it won’t be dramatically less valuable or nominal interest rates would be really high).  The question is: why do they believe this and, probably more importantly, is it reasonable to believe it?  Another (more rigorous) way of putting this is to ask whether the equilibrium is based on beliefs that are rational off the equilibrium path (is it a subgame perfect NE)?

For instance, if peoples’ willingness to hold dollars is based entirely on the belief that others will be willing to hold them in the future, and the value of them (either now or in the future) is not anchored to any real goods in any way, then if people started to question that belief, for whatever reason, you could see the willingness to hold them drop dramatically, possibly substituting other goods for use in exchange (essentially allowing P to decouple from M, V, and Y), and the price level could shoot off to infinity and the dollars become basically worthless in a Weimar/Zimbabwe-style hyperinflation.  This seems to be what most people who think the dollar is backed by nothing fear, and that fear would be reasonable if it were actually backed by nothing .

Similarly, if you think that the dollar is “backed” by the expectation that the CB would be willing to trade real goods for dollars to prevent the real value of the dollar from falling, then one must wonder whether they have enough such assets to do this if people “lost confidence” in a manner similar to that described above.  It is hard to see how this theory can explain a total value of the dollars which is much beyond the value of the real goods that the central bank has available to trade for them (accounting for a liquidity premium) without relying on the same type of logic, i.e. people know the CB couldn’t cash out all the dollars for gold at the current price of gold but they just hope that, for some reason, people will keep being willing to take the dollars at the current elevated value and so the CB will never have to do this.

The willingness of the CB to buy and sell a little on the margin does not seem to rectify this problem, if the promise to go all the way is not credible (due to insufficient real assets).  A classic Ponzi-scheme works for a while because the person perpetuating it stands ready to cash out people who demand their money but once it becomes clear that they do not have enough money to cash out everyone, it collapses.

I think what I have done is provide an explanation for why it makes sense for people to expect the dollar to continue to be in demand that does not rely on any kind of belief that could suddenly evaporate at any moment but instead is based on real exchange rates between dollars and real goods that are fixed in long-lasting, legally binding contracts.  In order to explain this further, let me start by defining what I mean by “money.”

Going forward, when I say “money” or “dollars” I mean anything that can be directly (without being converted to another form) used to repay debt from a bank.  I think the line may be a bit blurry in some cases but for the most part this includes, essentially cash and bank deposits (checking and savings).  I don’t count stocks or bonds because these must be sold at a market price for money before debt can be repaid.  Some things like money market funds or certificates of deposit are a bit tricky but I don’t want to get too distracted by this issue for now.

The important thing to notice is that I am coming at the “money supply” from the opposite direction of people who begin their reckoning from the money base.  This is only significant because they often talk about the willingness to hold money as the willingness to hold currency (cash) whereas I am talking about the willingness to hold dollars in any form.  Since currency and deposits can be converted into one another at any time at par, the composition of peoples’ “money holdings” between the two will be determined by the different liquidity of each.  While this willingness to hold cash has an important mechanical function in determining the amount of total “money” which will be created from a given quantity of base money at a given nominal interest rate, and is therefore important for modeling the effect of CB policy, this is not what I am after and so this distinction between cash and deposits is not of particular interest for my purpose.

So let us acknowledge that the CB has tools that can alter the quantity of money which is created at any given time and put the discussion of what those are and how they work aside for now.  It is true that people are willing to trade real goods for dollars and hold some quantity of those dollars.  This means that they must believe the dollars will be sufficiently valuable in the future (given their other options for holding wealth).  The question is why does this belief make sense?

The reason for the reliance on “network effects” to explain this, I think, stems from the Macro 101 view of the role of money in the economy.  This is essentially that money circulates through the economy like a perpetual, circular river and the CB simply determines how much water it wants and pours it into the system.  It can add water or take it out but it essentially has no purpose but to circulate and is not directly connected to the value of any real goods except by the seemingly arbitrary rate at which people choose to push it perpetually through the system.

I think this does serve as a reasonable approximation of how money functions but that the fundamental nature of this money is somewhat different.  I am saying that money does flow through the economy in this way and the quantity is determined by CB policy but that the meaning of those dollars is in fact anchored to specific real goods because of the way the dollars are created.

The CB does not just print dollars “out of thin air” and dump them into the economy.  Dollars are created when someone borrows.  CB policy does limit the extent to which this process can go on but that is what I’m trying not to get into here.  So I see the fundamental economic function of the banks as manufacturing liquidity.  Under a gold standard, if you don’t want to lug your gold around, weigh it for every transaction, slice it into pieces etc. you can take it to the bank and convert it into a more liquid form (bank notes) which are easier to use for transactions.

But this is not the only–or even the most significant–form of transaction cost that banks help people overcome.  For instance, if you are a shoemaker and you want to trade half the shoes you will make over the next twenty years for a house, you can offer this to the owner of the house but they will likely be reluctant to take it for several reasons.  For one, they don’t know you and don’t know if it is credible of you to promise this.  For another, they don’t want that many shoes and would have to be constantly re-trading them for the stuff they did want.

But you can overcome this by going to the bank.  The bank will verify your income, asses the value of the house and offer to lend you the money (or part of it) to purchase the house in return for a promise to repay some amount of money in the future or else lose the house.  You then trade this newly created money for the house.  The seller of the house now has an account representing the value of the house he just gave up which he can use to purchase other goods (including other investments) in whatever form or quantity and at whatever point in time he wishes.  You, on the other hand, are obligated to work (presumably producing shoes) for the next twenty years to get those dollars back to pay off your loan and keep your house.

So the question then is, why is the seller able to take those dollars and trade them to third parties for other goods?  The answer is that they know that somewhere out there is a guy who is obligated to produce shoes and trade them for those dollars in the future (as well as a bunch of other people producing other goods).  In this way, money is created by converting other real goods into a more liquid form.  This more liquid form of wealth then circulates in the economy in the way commonly understood and the willingness of people to hold it determines a velocity and a price level.  But that willingness to hold money, based on the belief that someone else will be willing to trade real goods for it in the future is “anchored” by all the people willing to trade “shoes” to get dollars and the rate at which they are willing to trade shoes is “anchored” to the rate at which they are contractually able/obligated to trade those dollars for their houses.  This rate, again, is nominally denominated and fixed (doesn’t fluctuate with market conditions or “confidence” in the dollar or anything like that).

So at any point in time there is some quantity of dollars circulating and there are people trying to get the dollars and “retire” them by paying off debt and there are people creating new dollars by securitizing new real assets and this determines the change in the quantity in circulation.  The CB can “steer” this quantity by altering the constraints on the creation of new credit (changing the money base for instance) or potentially by doing other things which I don’t want to get into.

Naturally, when someone enters into a long-term debt contract, they do so with some beliefs about market conditions in the future which will affect the price of the goods they intend to produce.  This depends largely on the rate of growth in the money supply relative to output and this depends on some belief about CB policy going forward.  Just how to model this becomes a complicated question which I will leave for another time but the central point remains that the real value of the dollar is inextricably “anchored” to real goods by these contracts.

This, I believe, is why we don’t see sudden losses of confidence leading to dramatic declines in the value of the dollar.  On the contrary, at times of financial panic (to put it dramatically) we tend to see the opposite.  People try to liquidate other assets and hold dollars, leverage dries up and we see defaults.  I suspect that if we drilled down, we would find that there are actually not enough dollars to pay off all the debt but doing so is not as easy as I first thought.

Finally, it should become clear how exchange rates are well defined here.  There are some quantity of US dollars circulating in the US which are “backed” by real goods in the US and represent claims on those goods and indirectly on the goods and services provided by the people holding the debt contracts on those goods.  This quantity along with the liquidity premium and associated velocity defines a price level in terms of US dollars in the US and the same process is going on in Canada with Canadian dollars.

When someone in Canada wants to buy shoes from the shoemaker in the US, they have to trade Canadian dollars for US dollars and vise-versa.  The flows of trade between the two countries, along with people speculating about future flows of trade and credit conditions in the two countries make a market for the currencies and the relative price is determined by supply and demand in that market in the way commonly believed.  But both currencies are “anchored” to real goods by debt contracts denominated nominally in their respective currencies and securitized by real goods.

Is Fiat Money an IOU?

February 27, 2014 34 comments

J.P. Koning has a post (make that two posts) about the IOU nature of bank notes.  While I agree that bank notes (fiat money) are not a Samuelsonian bubble asset, I think he still comes up short of the full explanation of why these are valuable.  Of course I think that I have that explanation but first let me explain why I think his is not fully satisfactory.

The meat of his argument is this.

So in the case of the two central banks that I’m most familiar with, banknotes are ultimately claims on whatever stuff the central bank happens to have in its vaults. This means that on the occasion of the winding down of the Fed or the BoC, note holders are entitled to receive real assets, in the same way that a bond holder or stock holder would have a claim on a company’s property, plant, & other assets upon the dissolution of that company. Banknote holders have an added bonus of being senior to other claimants, since notes provide a “first claim” in the case of the BoC, and a “first and paramount lien” in the case of the Fed.

But this does not fully address the problem.  This is because the process of unwinding a central bank, along with a currency, is fundamentally different from unwinding another type of entity.  Consider an individual bank that issues dollar-denominated bonds and uses the money to buy assets including some “real assets” (land, buildings, gold bars etc.) and some financial assets (loans) and imagine that the default rate on the loans is unexpectedly high and this causes the bank to become insolvent and need to be unwound.

The bonds, in this case represent a senior claim on the remaining assets of the bank.  The question is how much of those assets are the bondholders entitled to?  The answer in this case is straightforward because the bonds are denominated in dollars and the value of a dollar is determined independently from the state of this individual bank.  In other words, you can just liquidate all of the assets (convert them into dollar terms) and then assign that value to the various claimants in the order of seniority relative to the size of their claims in dollars.

If you are unwinding the central bank, you are unwinding the dollar itself.  So let’s imagine that the CB has some amount of gold in its vaults and it has some amount of notes outstanding which are denominated in dollars.  Those dollars are said to be a senior claim on the assets of the bank (the gold) and let us assume that there are some other claims (these may be dollar denominated debt or undenominated equity).  But the notes do not entitle the bearers to a specific quantity of gold.  So how much of those assets are they entitled to?

In this case the assets cannot be converted into dollar terms and divvied up in the same way as with an individual bank because the value of a dollar is not clear.  The whole market for dollars which forms the basis for the valuation of the assets relative to the various claims in the former case is the very thing being unwound in the latter case.  So how much of the gold goes to note holders versus other claimants?  The answer is not at all clear.  So it is hard to see how this claim serves as any kind of foundation for determining the value of a dollar.

The actual explanation for the value of fiat currency, which I have been trying to argue, (also here) I think is actually fairly simple but seems to be absent from all discussion of the topic.  One dollar is precisely what is required to extinguish one dollar worth of debt.  When money is created, there is always a corresponding debt created.  The central bank creates base money by buying government debt or MBS or lending to banks.  Banks then “multiply” this money (create additional money) by making loans to businesses and consumers.  But these loans eventually need to be paid back.

When a person takes out a mortgage the money supply (some measure of the money supply at least) increases.  But this also sets in motion a 30-year process by which that person must grab money back out of the economy and pay back the loan.  If they don’t do this, they will lose their house.  In this way the increase in money is accompanied by a built-in increase in demand for money in the future.  And in this sense money is “backed” by real assets.  In this case the borrower is able to “convert” dollars into his house at a specific rate.  It is just that this rate, and the convertible asset, varies from person to person rather than applying uniformly to everyone.

This demand for money to repay loans is fundamentally different and separate from the demand for liquidity (though demand for liquidity also factors into the value of a dollar).  It is also not based on any kind of “greater fool” or “bubble” mentality.  It is (at least to some degree) stable in the sense that it does not depend on mysterious, arbitrary feelings about the value of a dollar.  The amount of debt owed is a real number that is denominated in dollars.  It is the product of actions that have taken place over a long period of time and it doesn’t suddenly change drastically or disappear because people “lost confidence” in the dollar.

This in fact explains why people don’t lose confidence in the dollar.  If the value of the dollar were based only on the expectation that someone in the future would accept the dollar at a given rate in exchange for goods and services and that belief were suddenly called into question for some reason, the “bubble theory” leads us to believe that everyone would start trying to get rid of the dollars and the value would plummet.  But if this happened, we would find that many (most) people would actually try to take advantage of the newly weak dollar by exchanging newly valuable (in dollar terms) goods and services to get the dollars to pay off their debt.  In this sense, that demand is backstopping the real value of the dollar and because of this, that scenario never occurs (at least in major “developed” economies).

This also solves the unwinding issue.  Imagine that we wanted to abandon the entire system of central banking we currently have and replace it with nothing, no new fiat currency, just whatever the market wanted to use.  We stop creating new dollars and set a date by which all current debt obligations have to be settled using the current supply of dollars.  These dollars would not become worthless, people would be trying to get them before that date to pay off their debts and keep their homes, cars, boats, businesses, etc.  This would mean that there would still be a market for them in terms of other (real) goods.  You might have to refinance your mortgage in some other terms (gold, silver, Yen, whatever) but this would be better than defaulting and losing it all together.  The quantity of dollars would not exactly match the quantity of debt (I suspect it would actually be much less but haven’t been able to quite figure out the right way to observe this) so there would probably need to be some method of settling the excess dollars/repossessed property, and the whole thing would admittedly be pretty messy, especially the issue of how to treat government debt which is not collateralized and makes up the bulk of CB balance sheets, but when you look at it this way, I think you can see that dollar denominated debt (and the collateral backing it) is the main factor guaranteeing the value of the dollar.

In this way a dollar can be said to represent an IOU but I see it as exactly the opposite.  Rather than an IOU from the bank, it is a means of extinguishing an IOU to the bank.  It can be seen either way because the two look the same on the bank’s balance sheet.  If the bank takes in gold and hands you an IOU redeemable in gold the gold goes on its balance sheet as an asset and the IOU as a liability.  If you take out a loan, you are essentially writing an IOU to the bank for a quantity of dollars and the bank hands you the dollars.  In this case, the loan goes on as an asset (account receivable) and the dollars go on as a liability to balance out the new asset.  The gold IOU in the first case is a liability because it can be brought back and redeemed for the asset (gold).  In the second case, the dollar is a liability because it can be brought back and redeemed for the asset (debt).  In both cases the rate at which this redemption occurs is fixed and not subject to market fluctuations.  The accounting is the same but the meaning is somewhat different and this seems to me to be why people have difficulty seeing dollars as an IOU.

Banks and Credit

October 19, 2013 4 comments

Here is the next installment dealing with credit and banking.  The next installment will go into the expansion of credit by banks in more detail.

A primitive credit model

Credit is a fundamentally different economic phenomenon from money, though they are often confused or conflated.  The two, of course, are intimately related but in theory, there is no reason that either one could not exist without the other.  Indeed there is some debate over which developed first.  The answer to this question is of no importance to the issues discussed here.  I have already laid out a story to explain the emergence of money from a barter economy without credit.  To understand credit, I will first develop the institution of credit in a barter economy with no money.  Then I will put money and credit together.

Consider a very small town where everyone knows everyone else and assume that they all generally trust each other to keep to their word.  In this town there is a butcher, a baker and a candlestick maker.  The butcher regularly buys bread from the baker and the baker regularly buys meat from the butcher.  One way that they could conduct this trade is to trade bread and meat directly.  The drawbacks to this method are well understood, most important is the fact that they would have to continuously trade quantities of equal value.

As an alternative to barter, they could each hold some amount of some other good such as gold or silver and trade this for bread and meat.  In this way if there were a trade surplus between them, it would be reflected in a balance of payments in gold or silver from one to the other.  If, for instance, the baker wanted to purchase meat of greater value than the bread that the butcher wanted to purchase, he could pay the excess in silver coins.  The butcher could then use those coins to buy other things from other people.  Meanwhile the baker would have to get the extra coins by selling bread to other people.

In this way some quantity of money can circulate in an economy and act as a store of value and a medium of exchange.  People accumulate money as a result of delivering more goods than they collect from others.  Money such as precious metals works well for this purpose because it holds its value well.  This is mainly due to its durable nature and the fact that the supply in the long run is limited by nature (highly inelastic).

It is possible though to carry on trade without this type of “hard” money.  Imagine the same butcher and baker but with no gold or silver nor any other good suitable to use as a store of value and medium of exchange.  When the baker wants to buy meat, he can simply promise to deliver some number of loaves of bread at some point in the future that the butcher may find suitable.  He may write ten notes that say “I, the baker, owe you, the butcher, one loaf of bread to be delivered at any time upon presenting this note” and bearing his signature.  These notes would then represent a contract which could be enforced by the courts. Read more…

Real Interest Rates, Hoarding, and the Zero Lower Bound

December 29, 2012 Leave a comment

A line at the end of a recent post by David Andolfatto got me thinking.

I want to stress, however, that while getting inflation and inflation
expectations back to target (and firmly anchored to target) may be a solution to
one problem, it is unlikely to be a solution to every problem currently facing
the U.S. economy. To put it another way, suppose that the current real interest
rate of -1% is too high relative to the current “natural” rate of -x%. Somehow
driving the real return on bonds to -x% may then help things a bit, but it does
nothing to address the more pressing question of why the “natural” rate is so
low to begin with.

I believe the theory I have tried (somewhat crudely) to lay out on this blog explains why real rates are below zero.  However, rather than try to give a complicated theoretical explanation for this phenomenon here, I will simply discuss some of the implications of this.  The difference being that interest rates, which are prices, are “caused” by more than one force (supply and demand), and are therefore complicated and elusive, especially when these forces are derived from expectations of variables at various points in the future.  Nonetheless we can look at investment supply in isolation and identify some things which must be true if the market rate is below zero, and I think noticing these things will help put this phenomenon into perspective.

Negative Real Interest Rates

If credit markets are in equilibrium, then the real interest rate must be equal to lenders’ marginal rate of substitution between consumption now and consumption in the future.  In other words, lenders must be willing to give up 1 unit of consumption today for 1+r (where r is the real interest rate) of consumption in the future.  There is pretty much no getting around this fact.  However, since utility functions are subjective, theory cannot tell us what they “should” look like, it can only assert certain shapes for them and see what those assertions imply.  Usually, they imply a positive real interest rate.

One way to imply a positive real interest rate is to assume a positive discount factor.  For many macro models, this is assumed to be constant, and therefore, implies a fixed (by assumption) real interest rate.  In a more realistic model, marginal utility is decreasing in consumption each period but agents are assumed to prefer consumption today over consumption tomorrow at a given rate (the discount factor).  This means that if consumption is constant over time, the real interest rate will be equal to this discount factor, but the real rate can be higher if people are expecting to be richer in the future since higher consumption then will mean lower marginal utility relative to today.  If they are expecting to be poorer in the future, they will be willing to transfer consumption to the future at a premium, since lower consumption implies higher marginal utility of consumption.

There is no economic reasoning which proves that people prefer consumption today to consumption in the future.  There is however a long history of observation to justify this assertion.  This observation being positive real interest rates in the face of rising consumption.  Similarly, there is no economic reasoning for assuming that people prefer consumption in the future to consumption today and since there is no significant history of observation that implies this there are few, if any, models which assume this.

So if people don’t arbitrarily prefer consumption in the future to consumption today, there is only one explanation for a negative real interest rate: people expect to be poorer in the future than they are today.  When this is the case, their marginal utility of consumption in the future (relative to today) will be higher because expected future consumption is lower.  Therefore, people will be willing to pay a premium to transfer some real wealth from today to some point in the future.  The negative real rate is implying that the market for investment reaches equilibrium before consumption is perfectly smoothed out between periods (with a positive discount rate, this could be the case even at a positive real rate, so long as it is below that discount factor).  In other words, this amounts to a market prediction of a recession.

Lower Bounds

It is widely recognized that there is a zero lower bound for nominal interest rates.  This is because negative nominal interest rates always open the door to arbitrage.  If the nominal interest rate is -1%, then (if possible) I could take out a trillion dollar loan, put 990 billion dollars under the mattress (metaphorically speaking) to pay it back in a year and go spend the extra 10 billion on whatever I wanted.  In other words, demand for loanable funds would be infinite.  It’s not so much that interest rates couldn’t be made negative but the market could not function in such a case, it would require an entirely different system of rationing.  There is no such lower bound with real interest rates, because they don’t allow for such arbitrage.  But there is a considerable amount of inertia around the zero level.  To see why, we must examine why the potential for arbitrage doesn’t exist as it would for negative nominal rates.

If the rate of inflation were uniform across all goods, then there would be potential for arbitrage with zero real rates.  Imagine that inflation were expected to be 5% and the nominal rate is only 3%, implying that the real rate is -2%.  If inflation is uniform across goods, then you could make a profit by taking out a loan at 3% and buying a durable good like gold and holding it for a period, then selling it after its price increased 5% and repaying your loan.  The reason this doesn’t work is that everyone enough people recognize this potential that they drive the price of gold up today and down in the future to the point where this arbitrage is no longer possible.  This point will be when the real return on gold is equal to the real return on other investments which is -2%.  If the price of consumption goods is rising at 5%, then the price of gold will have to rise at only 3% (the nominal interest rate).  This will be the case no matter how high inflation rates are expected to be.  If inflation is expected to be 100% and nominal rates are 3%, then gold will have to find a price where the expected increase is still 3% (assuming the real rate is still -2%).  Thus gold cannot be used to cash in on expected inflation.

Of course, if one happens to be holding gold when inflation expectations increase, the price will rise sharply.  But this rise should not be interpreted as a sign that it will continue to rise rapidly, even in the face of high expected inflation.  On the contrary, it should be seen as a sign that the price will rise more slowly.  Listen up all you Austrians, libertarians, and other gold-jockeys.

The effect of this is that a fixed quantity of gold will become more valuable in both nominal and real terms and therefore, it will take up a larger portion of peoples’ portfolios.  This reduces the quantity demanded of other financial assets which imposes some inertia on real interest rates.  Or to put it another way, people will take money out of bonds and other financial assets and put it into gold which will put upward pressure on the rates of those assets and tend to raise real interest rates.

But gold is not the only durable asset.  In a world of negative real interest rates, if you can buy consumer goods today and save them, you benefit.  If the price of canned food is expected to increase 5% and nominal rates are only 3%, then you are better off to buy the food today and store it than to invest the money and buy it in the future.  This of course, imposes additional costs such as taking up space and rotating stock that gold does not because canned food is bulkier and less durable than gold.  Nonetheless, this type of “hoarding” is a perfectly rational response to negative real interest rates.  The lower the rate, the more effort people will be willing to devote to this type of activity.  The result will be increased demand for canned food today and decreased demand tomorrow which means higher prices today and lower tomorrow.  Although the rate of increase will probably be greater than gold, it will be less than the rate for haircuts.

Goods which are not durable like haircuts, vacations, and nights on the town, cannot be stored so there is no way of mitigating inflationary effects on them.  The price of these will rise the most.

Summary

1.  Negative real interest rates imply that people expect to be poorer in the future than they are today (assuming no negative discount rate).

2.  Inflation is not uniform, it will be more severe the less durable/storable a good is.

3. “Hoarding” is a predictable economic response to negative real interest rates.

4.  The ability to convert wealth holdings into real assets that can be stored, exerts considerable inertia on real rates once they fall below zero.  The greater the ability to do this, the more inelastic the demand for other financial assets will become and the stronger the inertia will be.

Deflation Part II

November 17, 2012 Leave a comment

[Note: For some reason, the columns don’t line up in the finished product the same way that they do when I’m typing them.  I tried to fix it but it’s not perfect.  Should be decipherable though.]

In the last post (quite a while ago, I know) I said this:

What I have not done here is show that this is bad on a macro level.  Some may argue that, this is bad for Bob, but his loss is offset by a real gain to his creditor, so this is still nothing to fear on an economy-wide scale.  Again, this would be the case with free money, but it is not the case with our system.  However, I will leave that discussion for another post.

This is that post.

Consider two different banking systems.  In the first system, base money is some commodity (like gold) and people lend this to banks in return for bank credit.  In addition to this, banks also issue credit to other borrowers in excess of the amount of base money they have in reserves.  This is, in fact, the way most people think of the banking system.  Let us begin by imagining that depositors deposit 1000 oz. of gold in the bank and the bank issues them notes redeemable for the same.  Assume that the interest rate on deposits is zero for now (interest plays a key role but not in the point I am trying to make here).   The balance sheets of depositors and banks will then look like this.

Depositors                                                     Banks

Assets                             Liabilities                  Assets                                      Liabilities

Notes     1000                                                     Gold               1000               Notes    1000

Banks then make an additional loan in the form of bank notes redeemable for gold in the amount of 2000 oz. to entrepreneurs, again at a zero interest rate.  The entrepreneurs then spend these notes on productive assets.  The balance sheets of the banks and the entrepreneurs will then look like this.

Banks                                                                   Entrepreneurs

Assets                              Liabilities                      Assets                           Liabilities

Gold        1000              Notes        3000             Notes       2000           Loans         2000

Loans      2000

Now imagine that entrepreneurs produce “goods” and the value of a “good” in terms of gold is initially 1 oz./good.  Also, assume that entrepreneurs believe the price level will remain at this level in the near future.  Furthermore, their productive investments of 2000 goods (the amount they can purchase with their loans at the above price) will yield 3000 goods in the future.  At the expected future price of 1 oz. of gold per good, this will easily allow them to repay their loans and leave them with a profit of 1000 goods (or oz. of gold depending on how you wish to account for it).

But now, instead of the price remaining at 1 oz. per good suppose that the price level falls to 1/2 oz. per good.  If this happens, entrepreneurs will be unable to repay their loans as their goods will only be worth 1500 oz. of gold.  They will go bankrupt and the bank will repossess their goods.  The bank’s balance sheet will now look like this.

Bank

Assets                                    Liabilities

Gold             1000                 Notes              3000

Goods          1500

Notice that the notes, which the entrepreneurs took out on loan and then spent, are still out there but the loan which offset them has been wiped off the books and replaced with a real asset which at the current price level is worth less than the face value of the notes.  In other words, the bank is now insolvent.  At this point, let us assume that the contract governing this bank’s agreement with its depositors was along the lines of that which I have previously suggested would prevail in a free market for banking and this caused the bank to suspend convertibility, liquidate all assets and distribute the remaining gold to the holders of notes at whatever rate were then possible.

This would mean the bank would sell the goods for gold which would give them 2500 oz. of gold to offset 3000 oz. worth of notes.  The conversion rate would then be 5/6 of face value.  So depositors would receive 833.33 oz. instead of the 1000 that they deposited.  So are they worse off or better off than they would have been if the price level stayed the same?

With the 833.33 oz. of gold that depositors receive, they can now buy 1666.67 goods at the new price level of 1/2 whereas they could only buy 1000 at the old price level with their full 1000 oz. of gold.  So in real terms, (in terms of goods), depositors became richer from the deflation even though they lost some gold.  In addition, the people who sold the original goods to the entrepreneurs for bank notes, will be in the same position being able to redeem those notes at only 83.33% of par but being able to buy twice as much with the gold they receive.  They will be able to buy 3,333 goods instead of 2000.

So even though the entrepreneurs lost all of their profit (1000 goods), this loss was more than offset by the gains to the holders of notes (2000).  It is worth noting here that the failure the losses to exactly offset the gains is due to the fact that our actors are holding an initial endowment of gold which becomes capable of purchasing an additional 1000 goods from somewhere outside our model.   A model in which prices were neutral in the sense that the gains were exactly equal to the losses would have to be bigger and more complicated.  Specifically, it would have to say something about why the price level changed.  For instance increasing the amount of goods or decreasing the amount of gold would add a source of real gain or monetary loss which would allow one to account for all of the net gains and losses as being from some non-monetary cause.  The goal here, is simply to show that deflation itself would not cause a dramatic fall in real wealth in that type of system even if it were unexpected, it would only shift real wealth from debtors (entrepreneurs) to creditors (depositors).

Banks, in this model are essentially just a vehicle for facilitating the use of credit for exchange and function as an intermediary between borrowers and lenders.  Since their assets and liabilities are both nominally delineated, a fall in the price level would not harm the bank if their debtors still paid their loans.  It is the defaults caused by the deflation which hit the banks’ balance sheets and then ultimately hit the depositors in a nominal sense.  But the nominal hit is more than offset in a real sense by the increased purchasing power of their money.

Now consider a different case.  Instead of base money being a commodity like gold whose quantity is fixed by circumstances of nature, base money is dollars which are printed by the central bank and loaned to the banks.  Again, assume that all interest rates are zero for the sake of simplicity and assume that banks borrow $1000 from the central bank which it prints up and delivers to them to be held as reserves.  Then firms borrow $2000 to invest in capital and the households who would have been depositors before, having no ability to print their own base money, now become borrowers and borrow $1000 from the bank to purchase durable consumer goods like houses, cars, boats, etc.

Then the balance sheets will look like this.

Banks     

Assets                                       Liabilities 

Reserves            $1000           Loans (from C.B.)       $1000

Loans                 $3000           Notes                             $3000

Firms

Assets                                        Liabilities

Capital                   $2000      Loans              $2000

Households

Assets                                        Liabilities

Con. Goods            $1000       Loans             $1000

Again, assume that firms can turn their capital into what would be $3000 worth of goods at the initial prices and assume that everyone expects the price level to remain constant.  Also, assume that households own the firms and expect to receive the profits from them ($1000) as income to pay off their loans.

Then, unexpectedly the price level falls by 1/2.  The output of firms is now only worth $1500 which is less than they owe so the bank repossesses their assets.  Households then receive no income and can’t pay their loans so the bank repossesses their assets.  The bank’s balance sheet then looks like this.

Bank

Assets                                                  Liabilities

Reserves                     $1000             Loans (from C.B.)               $1000

Goods                         $2000             Notes                                     $3000

The goods represent the output of the firms and the consumer goods revalued at the new price level of 1/2.  The bank is now insolvent.  The Central bank, which insured the bank’s notes, seizes the assets of the bank, and prints dollars to pay off the bank’s liabilities.  In this way the central bank sucks up all of the real assets.

The key difference here is that in the first system, every dollar borrowed was offset by a dollar loaned from someone in the private sector.  In the second system, the private sector is a net borrower with the surplus borrowing being loaned by the central bank.  So whereas a fall in the price level in the first system just shifts real wealth from private borrowers to private lenders, in the second it shifts real wealth from the private sector to the central bank.

There are two important issues not addressed here.  One is what the central bank does with those assets.  A favorable view of central banking might suppose that, having created money to redeem the debts of the bank, they then sell the goods back onto the market which would simply transfer the real wealth to the holders of that debt.  A less favorable view would be to imagine that the central bank distributes these assets to the member banks who control it in a way that is very favorable to them.  Regardless of what you think actually happens, as a libertarian, I’d prefer not to put a centralized authority in a position to wield this kind of power, but that’s just me.

The second question is “why would a sudden unexpected fall in prices occur in the first place?”  This is really the million dollar question.  And I will take this opportunity to remind the reader that you should never reason from a price change (shout out to Scott Sumner) since in a market economy, prices are inherently endogenous.  That this phenomenon is actually caused by central banking is what I intend to show eventually.

For now, let me point out that it is pretty difficult to imagine why this would happen in a system of free banking with a commodity monetary base.  This would require a sudden unexpected decrease in the quantity of money, increase in the quantity of all other goods, or decrease in velocity.  The production of individual goods are certainly subject to significant random shocks but it is hard to think of a shock which would unexpectedly increase the output of all goods significantly.  And the quantity of precious metals is determined by the amount in nature, which is fairly constant, relative to the expected total demand over all of time.  Neither of these things is prone to sharp fluctuations which would result in an unexpected fall in the price of precious metals, especially when the demand comes largely from use as money.  And this is no coincidence, it is precisely why these goods are selected by the market for use as money in the first place.

It is asserted by many that a fall in prices can have a significant negative effect on real wealth.   But this claim seems dubious to many because it is not clear how changes in prices actually destroy real goods.  Nonetheless, we seem to observe that the economy is subject to catastrophic downturns as a result of monetary causes.  The anti-central banking crowd has done little to square this reality with the notion that deflation should be harmless in a free market.  This is because they fail to fully appeciate  the difference between such an economy and the one we are observing.  Hopefully this will help to illuminate this difference.

The Argument Gary North Has Been Waiting For Since 1933

August 8, 2012 2 comments

The nice thing about patronizing a not-so-popular blog: you get a lot of individual attention.  “Anonymous” (a very popular name here in the blogosphere…) directed me to this post by Gary North so I thought I would address it.  Here is the heart of his argument:

. . . (I)t is not possible for depositors to take sufficient money in paper currency notes out of banks and keep these notes out, thereby reversing the fractional reserve process, thereby deflating the money supply. That was what happened in the USA from 1930 to 1933. If hoarders spend the notes, businesses will re-deposit them in their banks. Only if they deal exclusively with other hoarders can they keep money out of banks. But the vast majority of all money transactions are based on digital money, not paper currency.

Today, large depositors can pull digital money out of bank A, but only by transferring it to bank B. Digits must be in a bank account at all times. There can be no decrease in the money supply for as long as money is digital. Hence, there can be no decrease in prices unless it is FED policy to decrease prices. Read more…