Money Multiplier in a fixed exchange regime framework

Even though it seems I had lost interest on my blog, it was my master’s dissertation fault…which you can find here, with the abstract below:

“This study provides a new empirical approach about the money multiplier process, using monthly monetary data from Angola since January 2012 until June 2018. The use of an ARDL model allows to test the long run relationship of both the money multiplier and the reserve to deposit ratio and consider the short-term adjustments from monetary shocks. The analysis focuses mainly on the level of concentration of the banking system, the degree of liquidity of banks’ liabilities and the interest rate as determinants of the long-term ratios. Other country specific factors such as the foreign exchange rate spread and the non-performing loans ratio have been included to the analysis, to consider Angola’s macroeconomic challenges. It was concluded that according to monetary theory, both the interest rate and the level of concentration of the banking system affect the long-term ratios. However, the non-statistical significance of banks’ liabilities liquidity opens a policy recommendation for Angola’s monetary policy.”



Wicksellian Exchange Rate

Remember Wicksell?

What about Frankel?

Let’s combine both of them, shall we?

Two countries, Russia and Angola are petro-dependent. While Russia has flexible exchange rates, Angola had a fixed (but adjustable) peg, until December 2017.

That meant that as Russian ruble was depreciating almost pairwise with oil, Angolan kwanza was slow to adjust to its “equilibrium value”.

What now?

Well, since the semi-administered floating starting in 2018, it lost more than 20% against the US Dollar, being now in counter cycle with oil prices, as can be seen below comparing the total variation against the US dollar since January 2014, of the Ruble, the Kwanza and Brent.

angola brent

So, imagine that Angola had Pegged to its Export Price, like Frankel said, its official exchange rate would be close to equilibrium (as it would move with oil prices).

But, as the gap between the official and the equilibrium rate started to widen, bigger desiquilibriums appeared, which would widen still further the equilibrium exchange rate gap. Just like a Wicksellian process when the market rate is set above equilibrium rate.

How can we know that? Well, the black market rate is still enormous (the informal rate stands today at USDAOA 415, when the official is USDAOA 213) which means we are still a long way from equilibrium.

But is that equilibrium about?

That’s the topic for the next  two posts..

In the long run we are all DUMB

Economics textbooks are chewed economic theory.

We can learn from them, but we shouldn’t learn from them.

Because they give us a stupid sense of superiority. They usually belittle the great minds of the past.

Ricardo believed the value of things resided in labor. How stupid he was…

Say said supply created its own demand. How naive he was…

Keynes said that in the long run we are dead. How inconsiderate he was..

Friedman wanted to target the money aggregates. Really??


If we read through the original ones, usually we will get a much sharper description of their reality that the one that is portrayed in textbooks.

But my point is not to belittle textbook and textbook writers, my point is concerns Keynes’ long run.

How much ink has been spilled denigrating the man, for saying that in the long run we are all dead.

You can read DeLong post and be shocked!

We all know why “they” offended Keynes, because he was a Keynesian, duh!

But Keynes wasn’t a Keynesian, at least in his Tract (the book where we can find the cursed sentence). Keynes “became a Keynesian” in 1936 with the publication of his General Theory, up until then he was a Monetarist. And a pretty damn good one.

So…what about the sentence?

The sentence is about the Quantity Theory of Money (although Keynes formulates it in another way). Here is what Lord Keynes says:


What Lord Keynes is saying is: If we put a whole lotta money in the economy, prices won’t respond accordingly. The parameters may shift (Brad deLong considers it a foreshadowing of Lucas Critique).

(This time what changed was r – the reserve ratio)

Who would say that Keynes was just forecasting the ridicule statements of all the hyperinflationists almost ninety years after. Oh! And the ones that were slamming for being childless..and gay.

History sometimes has this twists.

Except that this isn’t a twist.. just a bunch of uneducated people..

The Art of Central Banking

This is not about a book I wish I could have..

This one is a risky one.

I will question “everything”.

I will question the fundamental “fundamental propostition of monetary theory”, first stated by Keynes then by Friedman and afterwards greatly explained by Leland Yeager.

I will also question Nick Rowe, who is the champion of monetary disequilibrium analysis nowadays (and probably my favourite blogger).

Hell… I will even attack one of my favorites Classical Economists, Claude-Frédéric Bastiat.

(I can get off my high horse right now, I will not dispute anyone, just try to add something – except for Bastiat)

I do believe money is special. Money is the medium of exchange. The fundamental proposition of monetary theory is true. The supply of money (unlike other “goods”) determines its demand and therefore its stock. (this sentence doesn’t contradict the “endogenous money” theory, but that is for another day)

But I do believe Central Banks somehow have a higher level of “specialness” than money.  (Well, if I am trying to be “against” so many great economists, this one will also go against George Selgin and the Free Banking School also).

So, how would I do that?

I will tell a story of course!

Imagine a society. Workers, producers, capitalists, everything normal.

The medium of exchange is fiat money, created by the Central Bank at its own discretion.

We have full reserve backing, therefore banks are not “creators of money”.

The Central Bank has a mandate to keep prices stable, it issues money when deflation is expected. It destroys money when inflation is coming. Assume no productivity shocks.

But this Central Bank has a peculiar way to conduct monetary policy. It buys/sells art. Yes, the Chairman is a very sophisticated guy.

Paintings are generally produced and traded amongst citizens, but every once in a while Mr. Chairman buys a new panting and prints new money. (We can assume that paintings’ value will increase as time goes by, so it’s a type of seigniorage that increases CB’s capital).

Somehow, one day there was a change in “animal spirits”, increasing the general demand for money. As the money stock remained constant, Walras Law states that the excess demand for money will be reflected in an excessive supply of goods, a recession.

For simplicity, we will assume that poor old Joe the Window Maker, was the only one affected by this glut. To stop the Keynesian multiplier on its beginning, I assume that the general increase in money demand “only eats up” the desired saving of Mr. Joe, by allowing him to work only enough to keep his consumption stable.

Therefore we have an increase in unemployment. It’s not a big increase (only less hours worked for Mr. Joe, I could complicate the story but I won’t).

Up high in Valhalla, Thor was being annoyed by Claude Bastiat. He was continuously stating that Norse Gods worship was a waste of his time and therefore THEFT!

Thor just to annoy Bastiat released a thunderstorm that destroyed the big and beautiful Vitrail of the Central Bank.

Mr. Chairman despaired and as the Vitrail was essential for the Central Bank credibility, hired Mr. Joe to repair it.

As it charged 100 units, Mr. Joe was confronted by an embarrassed Chairman saying the rolling press was temporarily malfunctioning (talk about credibility) and therefore it would have to pay him with one of his paintings. He showed him how nice was the painting, but Mr. Joe was suspicious.

Mr. Joe was a simple man, but not stupid. He called his friend Vincent, the Art dealer, which told him that the painting was worth 200 units, but he had just told Mr. Chairman that it was only worth 100. Mr. Chairman truly was beloved among the citizens…

Mr. Joe gladly accepted it! Not because he wanted to hold it but because it could easily trade it for money, with profit!

He accepted art as a medium of exchange not because he wanted to hold it, but because he could sell it for profit. The Central Bank, unlike a private institution, can operate with loss  after loss, so it could “afford” to be mislead.

Oh well, enough with this dumb story…

What just happened?

There was an excessive money demand that should had led to a deflationary rot (not so big..) unless the Central Bank created more money. But the central bank unwillingly did not increase the money supply. Nevertheless it increased the money velocity, as the art dealer decreased its money demand by 200 (which indirectly paid for the extra demand). But in the end, all was paid by a big loss in the Central Bank capital position…

So, what’s the fuss all about? Three points.

  1. Bastiat’s Broken Window Fallacy does not apply when we have an excessive demand for money and the destruction is directed to a (non-convertible money issuing) Central Bank
  2. A Central Bank is not profit oriented so it can afford to have a loss. Therefore in a way, its loss was an non-injecting money helicopter drop.
  3. When we have a general depression, an increase in velocity (as seen) will do the job as well as an increase in the supply of money (so stupid CB actions like this one or smart Government Deficits could do the trick)

Attention attention! I am not advocating acts of destruction against money issuing Institutions.

As Keynes said, we can bury a bunch of notes and make people look for them.

But aren’t there more productive ways to do it?

You just got Sumnered

Sometimes one forgets how great an economist Scott Sumner is.

One may disagree with the feasibility of some of his NGDP targets proposals.

One may disagree with some of his “the banking sector is not essential”.

But one can’t deny he is (probably) one of the best monetary economists of our generation.

The following post on currency manipulation would speak higher than any other compliment I can make:


(And yes, David Glasner is probably even higher in my top favorite monetary economists)



Unwinding QE

The New York Fed blog wrote a great post yesterday, explaining the process of How should the Quantitative Easing revert.

I think it was a great lesson on monetary policy and mainly on Central Bank Balance Sheet monetary operations.

But… I think it could be better.

Let me try to give my humble contribution.

In the post there is an implicit assumption that the Treasury General Account interacts directly with the Reserves Account (both liabilities of the Federal Reserve) only in one way.

When the Treasury Bonds are issued there is a drain of reserves and an increase in the TGA.

When the Bonds mature, the Treasury pays its due, depleting the TGA and increasing Bank Reserves.


I think we should add another interaction between both accounts.

How is it possible for the Treasury to pay its debts? By having a (temporary) surplus. Therefore the Treasury must drain more Reserves (by taxes) than it injects (by Government Spending). This “destruction” of Monetary Base (Fed´s liability) is accompanied by a decrease in its assets (Treasury bonds).

If, the Treasury issues bonds, it must be to “finance” its deficit (Sorry Mrs. Kelton). This operation (deficit) injects more Reserves (Gov. spending) than it drains (taxes). If the Fed wants to keep its Balance Sheet constant, it must buy some of the new bonds (increase in its assets) by injecting Bank Reserves (liabilities).

This was general proceeding of Monetary/Treasury operations up until 2008 (as we can see in the chart below). Afterwards we live in a strange world where the Treasury issues bonds to help the Fed and not only to fund themselves.


Sem Título

Stop “employing” unemployment

Economists waste too much time “employing” the unemployment rate concept.

Oh boy..

The unemployment rate.

Do we really have to go all over this again?

Why are people continuing discussing about Full Employment? The natural rate of unemployment? NAIRU?!!?

Economists sound like those annoying children yelling during the trip (the economic recovery):

– Are we there yet? Are we there yet?

No. We are not.

Forget about the theory that says if the unemployment rate is below the “natural rate” we must have inflation. It´s not incorrect, it’s only half true. The NAIRU story is incomplete.

The NAIRU story states that if inflation isn’t rapidly increasing, the unemployment rate must be above the natural unemployment rate.

However, I believe the United States most probably has the unemployment rate below its “natural” ratio, the one that pushes wages up. When workers increase their bargaining power. Yes, the Phillips curve story, Marx’s reservation army, …

Just look at the data, we are seeing one of the lowest unemployment rates recorded (since the hippies).

United States Unemployment Rate

But…that does not mean, we are already there.

Just look at the data, the US has suffered a big decrease in employment since the Crisis and its still a great deal behind the curve.

United States Employment Rate

The Labor Force Participation is still recovering.

United States Labor Force Participation Rate

Of course, some part of the decrease in participation is due to demographics…

But, in my opinion, we must probably watch this sequence of events in the proceeding recovery, a convergence to the natural rate of unemployment combined with low inflation from (drums…) BELOW:

  1. As the economy expands and the unemployment rate contracts, more people that were out of the Labor Force will return as they perceive an increase in the demand for labor
  2. The rise in the participation rate will lead mathematically to an increase in unemployment and/or employment
  3. As long as the ratio of the increase in unemployment to the increase in participation is lower than the official unemployment rate, the Unemployment rate will continue to decrease (just do the math)
  4. But eventually it will come a time when the increase in participation will not totally be reflected in new employment and the inflection time will initiate
  5. The unemployment rate will start to increase (but the employment rate is also increasing (remember?), as the participation rate is increasing)
  6. Eventually we will reach a ratio of employment which will cause pressure on wages
  7. We will start to see the “white in the eyes” of inflation
  8. Finally the Federal Reserve will definitively remove the “punch bowl” by pursuing a contractionary policy
  9. Will we have a recession next?
  10. Are we there yet?

The lazy theory of Monetary Disequilibrium    

Don’t worry, I am not going to “Yeager” you a long lesson on Monetary Disequilibrium Theory.

Just a quick one.

Laziness reigns supreme in a monetary world. Laziness is the “ugly” counterpart of specialization.

You don’t just specialize in the things you like (or have an advantage). You also de-specialize in things you don’t (or that you are too lazy to perform).

Therefore laziness allows specialization. It allows innovations. It allows productivity. It allows the Wealth of Nations.

Let’s imagine now, we live in a world of Monetary Disequilibrium.

There is an excess of Money Demand or an excess of Money Supply.

If there is excessive money demand, by definition there will be a lack of aggregate demand for output. We will have a general depression. We shall have unemployment all around.

If there is excessive money supply, by definition there will be an excessive aggregate demand for output. We will have an (unsustainable) expansion. We shall have inflation all around.

Unemployment and Inflation are not bad things per se (despite what your casual economist would say).

Unemployment in a sector of activity may be a sign of a shift in consumer preferences.

Inflation in a sector of activity may be a sign of scarcity of the “good” exchanged.

They symbolize what the “market” wants and what the “world” provides.

But if we experience General Unemployment (excessive demand of money), we as workers will spend too much time trying to find a Job. Time we could, should and would be producing whatever the market demanded.

But if we experience a General Inflation (excessive supply of money), we as consumers will spend too much time trying to find a Reserve of Value (to “protect” us from inflation). Time we could, should and would be producing whatever the market demanded.

We shouldn’t be forced to desperately look for Jobs and Reserves of Value.

We should specialize in supplying whatever the market demands (and we are good at) and demanding whatever our distorted minds may want.

Don’t force us to do extra, unproductive work.

Give us Monetary Equilibrium.

Comparative Advantage and Socialism

If you are a free market advocate, if you are opposed to excessive Government or you just are a Punk Anarchist which doesn’t support any form of authority, you must knowingly or unknowingly worship Adam Smith, and let’s Say… David Ricardo.

Anyone that studied International Economics, knows that each country must specialize in something.

Adam Smith said: Do what you do better!

But Ricardo replied: Even though you may the Best in some deed, maybe there’s some other quest you must pursue

After that, the Invisible Hand would do its magic and through international trade, Earth’s welfare would increase.

Let’s now narrow our vision, let’s focus on intranational trade, our everyday lives.

Just a simple example.

In country A, there are two professions: Fisher and Builder.

Let’s say John is a “10” fisher, but a “8” builder.

Adam is a “8” fisher, but only a “3” builder.

Both wannabe employees, Adam and John will first apply to be a Fisher, because they know they are good at it, so they may end up earning a higher wage.

And the captain of the ship, will obviously choose John, which is the better Fisher.

Therefore sadly, Adam will end up being a lousy builder.

So…the free market society, through its invisible hand will end up with total welfare (measured as production in this simple example assuming we can compare fishes with buildings) of 13!

The free society will exploit naturally the absolute advantages, trying first to employ the ones with the “best” absolute advantage, disregarding the possible job misallocations that that may lead to.

“A socialist society, through the visible hand of its benevolent dictator” would allocate the employees not to their decision (based on absolute advantages) but to society’s “greater good”, taking into account comparative advantages, achieving in this example a total welfare of 16!!

This is all great, but honestly my head could not feel peaceful with this socialist victory through efficiency. It was a true puzzle, which even asking some die-hard libertarians, I couldn’t get a better answer than: “Stop talkin about Unicorns, dumb ass”

But eventually I came up with a solution to this socialist victory puzzle.

Socialism wins clearly the (short-term) battle.

But Capitalism wins the war.


Imagine you know that you may excel at something, but eventually some crazy Government bureaucrat will tell you that you are more useful to society picking thrash off the streets.

Can you feel the frustration? Yap..

Who will try their best to excel at something ever again?

Hurray for Liberty and free markets (in this simple example).

Capitalism won by inter-temporal efficiency knock-out.

I guess David Ricardo can stop now rolling in his grave.


The Money multiplier trilogy (Part III: Immortality)

After the Death and Resurrection came Immortality.

So I will try my best to reach a general theory of the multiplier.

Some initial points:

  1. Christmas. For simplification (bear with this please) I will assume that only in the 25th of December do Central Banks inject new Reserves in Banks Balance Sheets, taking into account the Central Bank goal for next year.The Banks had received during the year a bunch of loan applications and now they can finally proceed with lending. (I am not assuming banks need reserves to lend money, but if you assume the deposits a credit creates “fly away” and banks are already fully “loaned up”, banks will eventually need that High Powered Money)
  2. Banks, unlike the traditional money multiplier story (“The textbook story implicitly assumes that each bank is small relative to the whole banking system, and is looking for the Nash equilibrium.”) are not small, they have market share. Therefore, some of the deposits they create do not “fly away” they remain in the same bank.
  3. Banks create money by creating an asset (credit) alongside with a liability (deposit).
  4. Deposits are redeemable with Central Bank currency.
  5. Other assets provided by other financial intermediaries compete with deposits.
  6. Banks are obliged to have a percentage of its deposits (liability) as an asset (reserves). They may want to keep a little more than required to face uncertainty about flow of funds in the economy.
  7. Central Banks inject monetary base (reserves) through Open Mark Operations (they just swap assets in a Bank balance sheet, a bond by reserves)
  8. Banks have a market share of deposits comparing to the banking system and are expected to maintain that share.

I guess everything is settled now and abstracting from the Christmas assumption, I guess all the other points are straight forward and in accordance with Banking Theory.

Now for the model:

Grab a pencil and a paper.

ER is excessive reserves, DRR is the desired reserve ratio (legal requirement plus precautionary), c is the demand for currency by deposit created, a is the demand for other financial assets (outside the banking system – a la Tobin),  is the amount of deposits a Commercial Bank can create given ER, MS is the bank market share (the amount of deposits it has – and expects to have comparing to the system).

So, my goal is to determine what will be the amount of X we will have given ER.

Lets assume the Central Bank injects ER into a bank  by an OMO (which does not affect the liability side of the bank).

The bank will create a credit (asset) by the amount of X (and a deposit in the liability side of the same value).

The deposit will transform part of the ER into Desired Reserves (by DRR) – in the asset side.

Next as part of the deposits (liability) flow out of the Bank  depending on the bank’s market share:  (1-MS)*X, Reserves will flow out in the asset side: DRR*(1-MS)*X will represent the decrease in Desired Reserves, (ER-DRR*X) will represent the loss in Excess Reserves.

We must assume in the end that c*X*MS and a*X*MS is the proportion of the deposits that stayed in the bank that got transformed either in currency or in other financial assets. (deduction in the liability side of the balance sheet). In the asset side you must deduct: MS*DRR*X*c – MS*(1-DRR)*X*c + MS*DRR*X*a – MS*(1-DRR)*X*a.

I hope you have written everything. Now the fun starts. Let’s find how much X can a bank create for each ER it has received. By applying all the information above we have (left hand side: liabilities, right hand: assets):

(ER – DRR*X – MS*(1-DRR)*X*c – MS*(1-DRR)*X*a) – DRR*(1-MS)*X – MS*DRR*X*c – MS*DRR*X*a          =    – (1-MS)*X – MS*X*c- MS*X*a    «=» (getting rid of parenthesis)

– ER + DRR*X + MS*X*c – MS*DRR*X*c + MS*X*a – MS*DRR*X*a  – DRR*X +DRR*MS*X – MS*DRR*X*c – MS*DRR*X*a = – X + MS*X – MS*X*c- MS*X*a «=» (X to one side)

X + MS*X*c – MS*DRR*X*c + MS*X*a – MS*DRR*X*a + DRR*MS*X – MS*DRR*X*c -MS*DRR*X*a – MS*X +MS*X*c + MS*X*a = ER      «=» (X multiplied by the rest)

X * ( 1 + MS*c – MS*DRR*c +MS*a – MS*DRR*a + DRR*MS – MS*DRR*c – MS*DRR*a – MS +MS*c + MS*a) = ER     «=»

X * ( 1 + MS * (c – DRR*c +a – DRR*a + DRR – DRR*c – DRR*a – 1 + c + a) = ER «=»

X * ( 1 + MS * (2c + 2a -1 + DRR * (1 – 2c -2a) ) ) = ER

X = ER / ( 1 + MS * (2c + 2a -1 + DRR * (1 – 2c -2a) ) )

Wow…this was a long journey.

But let’s take some conclusions:

First of all, if you assume as in the textbook that each is infinitesimal comparing to the system (MS=0), its individual multiplier is 1! (like in the textbook) A bank can’t lend more than its Excess Reserves.  X = ER 

Let’s assume now that a bank is as big as the system (this is the textbook multiplier), so that MS=1 we have X = ER / ( 2c + 2a + DRR  -2DRRc  -2DRRa ) wich transforms into (as ER transform into required reserves)

X/ ER = 1/( 2c + 2a + DRR  -2DRRc  -2DRRa ) which is (kinda) like the textbook multiplier (added with the other assets).

In between (0<MS<1) banks can create more money than they have initially as Excessive reserves, but they have to take into account desired reserves, competition against other banks deposits, demand for currency and demand for other assets.

So, like I promised, in the end of the day:

  1. Banks create Money. Yes, they do. If they have the market share.
  2. Bank Reserves multiply into Bank Deposits. Yes they do, as banks seek to expand their credit, they “use up” Bank Reserves supplied by the Central Bank
  3. Banks are Financial Intermediaries. Yes, just like others (which they have to compete with), although their liabilities are Medium of Exchange (Money), they are constrained by the laws of the market and don’t have widow’s cruse.

This was a long and exhausting post. I hope I protected the fair Money Multiplier and its usefulness to understand Banking and Central Banking operations.

Nick, I gotchyour back!

(Yes, banks can “cheat” and just ask the Good Ol’ Central Bank for more “juice”)