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”)

 

 

The Money multiplier trilogy (Part II: Resurrection)

After being killed, it is worthwhile to wonder if the Money multiplier deserves a second chance.

I think it does.

So gather round the Dragon Balls because the Money Multiplier is going to be resurrected.

First things first. Why did the multiplier died, again?

Banks don’t need Reserves to make Loans! Loans create Deposits!

Oh..ok.

So, do Central Banks supply whatever the amount of reserves Commercial Banks need (to comply with legal requirements, to settle payments or to face cash withdraws) ?

Yes and no.

Yes, in the short run they do. They normally establish a interest rate target, so if they don’t comply with quantity demanded of reserves by Commercial Banks, it would lead to financial havoc as interest rates diverge from their targets.

No, Central Banks have a goal for inflation (or NGDP or …) so they must adjust their intermediate target for interest rates in a way they can achieve their ultimate goal.

So, it’s true to say both Reserves and Interest Rates are endogenous, a trustworthy central bank will only set its ultimate goal as exogenous.

Even though a Commercial Bank is not (usually) reserve constrained, as it can look for reserves in the inter-bank market, or can go to the Central Bank (either by discount or overdraft), it faces uncertainty towards the future.

Uncertainty about the “loyalness” of its depositors, uncertainty about the demand for cash, uncertainty about the demand for non-bank assets. A bank must face the uncertainty of its “usual business” liability side (Deposits) with both the “unconventional” liability side  (Central Bank lending) and the liquidity of its Asset side of the balance sheet.

Banks face restrictions. They don’t possess a widow’s cruse.

The Central Bank creates some of those restrictions. The competition among financial assets create some of those restrictions. The Economy creates some of those restrictions.

My goal is to combine the three theories of banking in a unified one (credit creation theory, Money multiplier, financial intermediary). I believe they must be all the same.

Those 3 theories can be matched with the 3 restrictions stated above. The 3 theories are all different angles of the same reality.

Banks create Money through credit. Yes.

The Central Bank influences the credit creation by supplying Reserves. Yes.

Banks are in the end of the day, just financial intermediaries. Yes.

My next post will try to create a comprehensive model which puts together the 3 theories, which in my view (with some assumptions) will grant a simplified but general view of how Banking and Central Banking works.

Let´s try to give the multiplier, Immortality.

(and create another multiplier during the process)

The Money Multiplier trilogy (Part I: Death)

The Money Multiplier is one real beauty when you start to learn Monetary Economics (most probably from Mishkin textbook). It makes you feel wise, you DO understand how Central Banks influence the Money Supply and Bankers are only pawns in this magnificent Game of Thrones of the Economy in which the Central Bank reigns supreme.

But “they” are trying to kill it!

Everyone, from Monetarists to Keynesians.

Even though in a way or another, most economists still believe in some version of the Money multiplier it’s uncool to express it that way, and you will soon find yourself ridiculed by someone who really understands banking.

Ok.

I must confess my sins. I too believe the multiplier is dead.

Just look at this graph:

money-multiplier.png

Bernanke killed the Money multiplier!! Quantitative Easing exposed the “truth”!

What are the problems/wrong assumptions of the Money multiplier?

  1. Normally, central banks just “follow along” the demand for reserves, so instead of a “monetary policy driven injection of reserves” Money multiplier, it really is kind of a “Money divisor” as banks look for reserves after they create loans (and deposits). And Central Banks must accommodate the banking system expansion if it wants to ensure financial stability.
  2. A straw man version of the MM assumes Banks lend reserves. This is not true. (as it may be explained later)

So, the Money multiplier has been disproved by Central Banks operations during the crisis as by some “endogenous demand driven vision of the economy”.

But still, I still believe in its beauty and we should not mourn its death, because I know it will rise again, and stronger than ever.

Nick Rowe is not alone in this fight.

Let me do my best to try to defend (my version) of the Money multiplier.

The real real interest rate

Economics is all about price determination.

At least since the Great Knut (Wicksell) we started to see the Interest Rate as the Price.

It was the most important price in the economy, its determination would set the course of economic development, both in the short as in the long run.

We still live in a Wicksellian world. Ask any Central Banker. Better yet, ask Michael Woodford, one of the leading macroeconomists.

But this post is not really just about interest rates.

It’s really about Real interest rates.

Since the Great Irving (Fisher) we learned to differentiate between the real and the nominal interest rate, so to avoid the Money Illusion.

The real interest rate is (roughly, only for small numbers) the nominal interest rate minus the ex post inflation rate. (Remember that, when we compare current interest rates with inflation this is not correct. Current interest reflects the gain we shall have in the future, current inflation reflects the loss of purchasing power in the past).

Simple example:

Savings Deposit offering 10% interest rate. Inflation rate (future) would be 20%.

Although we are 10% richer (in nominal terms) next year, we would buy less 10%of goods (to be correct is less 8,33%).

So I guess, we can say, the lower the real interest rate the higher is the incentive to avoid saving (consume). Because, and this is the main point: TO SAVE IS TO DELAY CONSUMPTION.

But at the opposite side of the coin, we have Investment.

And if we follow the same logic, the lower is the real interest rate, the higher is the incentive to Invest.

But we would be wrong (at least partially). The goal of investing is to achieve the highest possible return.

And the evolution of returns does not follow the inflation rate. That’s the main difference.

Another example.

Imagine you borrowed at 10%.

Inflation would be 20%.

Therefore we shall have a -8.33% real interest rate and therefore an incentive to invest. Right? Wrong.

Why is it wrong this time? Because nobody invests in CPI baskets.

Imagine you invested in iron, which had a 30% increase in prices. You should use iron inflation to deflate the nominal interest rate. This would lead to high incentive to invest.

Imagine you invested in oil, which had a 30% decrease in prices. You should use oil inflation to deflate the nominal interest rate. This would lead to low incentive to invest.

(Things could get really tricky, but I dont want to go that way)

Imagine you borrowed at 5% to buy something that increased its price at 10% and your income increased 5%.

Well, what really matters is nominal income growth then? Hurray for the Market Monetarists and most particularly to Geoge Selgin? (future post).

Maybe.

All that really matters is that we really should know what a real interest rate really is.

Enough for today.

Two residuals multiplied become an illusion

You are a Monetarist.

You think Y=C+I+G+NX is just an identity, it doesn’t tell you much.

You believe fiscal policy is ineffective.

You believe the Keynesian multiplier is Zero.

You believe in the Sumner Critique.

Hence, the multiplier is nothing more than an ILLUSION, the shadow of Central Bank incompetence.

 

You are a Keynesian.

You believe fiscal policy is effective.

You believe monetary policy is effective (except in the Zero Lower Bound).

Monetary Policy is conducted through variations in the Monetary Base (which may affect interest rates).

You think M=mB is just an identity, it doesn’t tell you much.

Hence, the Money Multiplier is just a RESIDUAL.

You think MV=PY is just an identity, it doesn’t tell you much.

Therefore, the Money Velocity is just a RESIDUAL.

 

Let’s all be friends again?

Imagine two things:

You have a lot of unemployed resources in the economy, so an expansionary policy will only move Y (P is fixed).

You shall use a Helicopter Money. A Money Financed Deficit. Monetization. Whatever you want to call it.

Basically the Government spends newly-printed (or newly electronically  created) Monetary Base.

What will happen???

Hyperinflation!!! Zimbabwe! Weimar!

Nope.

Let’s build an example.

So, we have have dG= 1000 and dMB =1000.

The increase in Government Spending somehow (magic?) increases Output (Y) in 3000.

So… the Keynesian multiplier (dY/dG) of the increased spending would be 3.

Shall we continue? Of course.

We  know mBV=PY. We know P is constant (assumption), we know the Monetary Base increased 1000, and Real Output increased 3000 (multiplier effect).

So..By definition, we must have that the effect of the Money multiplier and Money velocity should lead to an increase in Output of 3000, given the increase of 1000 in the Monetary Base.

Basically the expansionary effect will be the result of the Money multiplier and the Money velocity, which must “multiply” the increase in Monetary Base by….3.

Some caveats:

  1. We can’t (in this model) disentangle which (V or m) “multiplies” the Monetary Base into Real Output, we must assume it’s a combination of both the indicators
  2. The Keynesian multiplier is about a flow, (an increase in GDP), the Money multiplier and velocity are about a Stock (the Money stock), so in this example both the multiplier and velocity represent variations of the Base (flow)

But in the end of the day, we can say this:

(Using flows, using deficit monetization and assuming fixed prices)

The Keynesian Multiplier is equal to the Money Velocity times the Money Multiplier

Or as I said in the tittle

Two residuals multiplied become an illusion

Are you a Socialist or a Communist??

Or do you just want to see the world burn?

 

(This post builds on ad absurdum arguments, if you are not able think “theoretically”, this one is not for you)

Imagine the mother of all crisis!

This is not the Great Recession! This is not the Japan Crash! Not even the Great Depression!!!

All people stop consuming in large scale, all companies start investing! Unemployment reach maximum peaks! Why? Oh..forget why.. Let’s call it…the animal spirits, a decrease in confidence, whatever…that’s not the point.

Well.

At least we have a Central Bank, some will shout!

At least we have a Fiscal Authority, others will scream!

Let’s start with the first ones: What would the Central Bank do? It would start buying Short Term Treasury Securities (or define a short term interest rate), but then suddenly the interest rate reaches the Zero Lower Bound (or another bound..) and they decide to buy longer term bonds, until the interest rate reaches zero too! Then it will go to corporate bonds! Stocks! Houses? What else??

The Central Bank just bought everything…and still no resurgence in private spending to acceptable levels.

Did the Central just buy everything? And the Central Bank is part of the Government, right? So if the Government owns all the assets in an Economy…

Those who shouted for Monetary Policy ended up as Communists! (Friedman would not be happy about this – neither would Sumner)

What about the ones who called for the Fiscal Authority?

Well…Let’s say, first of all, the Ministry of Finance cuts taxes all the way to zero… Still..no resurgence in private spending to acceptable levels.

What else? Well..Government Spending it is!

The Government will just Deficit Spending all the way to prosperity, choosing the sector in which to spend/invest as it would seem fit. It would choose the direction of the economy!!

What? Those who shout for Fiscal Policy ended up as Socialists! (I guess both Keynes and Krugman wouldn’t mind…)

So..in the end,  are we all just Socialists or Communists?

No..You could just shout (as Mises): “YOU’RE ALL A BUNCH OF SOCIALISTS” and watch the world burn.

 

P.S: I know, I know.. I maybe distorted a little the meaning of socialism and communism, but if the great Nick Rowe can (but much better), so can I, right? (Wrong)

Scott Sumner, semantics and bias

Scott Sumner is referred by some as “the economist that saved the economy”.

He is kind of an hero to me, because he rose from the blogosphere and became one of the most influential economists nowadys.

In a recent entry in his blog, he refutes Old Keynesianism based on Japan.

I don’t think he is completely right, and maybe his “libertarian” bias is leading him to the kind of semantics error that he so hard tries to fight (regarding monetary policy).

Let me explain.

(My apologies in advance if you don´t agree with what I think you believe, Scott)

A macroeconomic policy is the set of policies that are taken by the Government (and/or Central Bank) to achieve some macroeconomic targets (employment, inflation, NGDP,…).

Scott thinks the best target is Nominal Gross Domestic Product (or some proxy). I agree.

Scott thinks monetary policy is the best policy to achieve that target. I agree, most of the times.

Scott thinks that although fiscal policy may have some macroeconomic effects, it is highly ineffective and subject to various kinds of political incentives, that should reduce its use to bare minimum. It should reduce its use to microeconomics purposes and not to stabilization. I do agree, most of the times.

So, Scott doesn’t think of fiscal policy as a macroeconomic policy. But Keynesians do.

And when he tries to play the “Keynesian game” and tries to refute them, he falls to same type of fallacy Keynesians fall in terms of monetary policy.

“it’s one of the most expansionary fiscal policies in all of history coinciding with the worst performance of aggregate demand ever observed in a major economy”

If you replace “fiscal” with “monetary”, Scott would roll over his eyes (probably).

As Scott would deem monetary policy in Japan since the 1990s highly contractionary (by the bad performance of the economy), despite low interest rates, it’s legitimate that Keynesians see fiscal policy as highly contractionary, despite high fiscal deficits. Just ask Richard Koo.

Maybe fiscal policy is Japan is being highly ineffective, but maybe because it’s not being applied the right way.

Maybe Quantitative Easing (the first round) in Japan was highly ineffective, but maybe because it’s not being applied the right way.

I guess this is all for today. But I will publish more on this topic during the week.

A simple IS/LM type of model but regarding fiscal policy.