The Central Bank and Monetary Policy Tools

Week 06

Vivaldo Mendes

vivaldo.mendes@iscte-iul.pt

Instituto Universitário de Lisboa (ISCTE-IUL)

March 17, 2025

1. The Central Bank Balance Sheet

Can the Central Bank Set $i$ By Law?

Last week, we saw the central bank will change the real interest rate $(r)$ as a response to changes in inflation $(\pi)$ or in the natural real interest rate $(\bar{r})$. \[r=\overline{r}+\lambda \pi \tag{MP curve}\]
And the Fisher equation says that the Fed must implement a change in the Fed Funds rate $(i)$ such that $r$ will change, given that $\pi$ is constant in the short-term: \[i = r+\pi \tag{Fisher equation}\]

Can the Central Bank Set $i$ By Law?

Can the central bank “set” by law the level of market short term interest rate $(i)$?
NO!
Does the central bank have some power to force the short-term interest rate $(i)$ to move to some target range/value?
YES!
To understand the logic behind this apparent contradiction we need to understand two issues:
- The balance sheet of the central bank.
- The main monetary policy tools available by law to the central bank.

The Central Bank Balance Sheet

European Central Bank Balance Sheet: 31 December 2000

Assets	%	Liabilities	%
Foreign exchange reserves	46.9	Currency	44.4
Securities	10.1	Reserves of Commercial Banks	15.0
Loans	32.5	Other liabilities	19.6
Other assets	32.5	Equity	21.0
Total assets	100.0	Total liabilities	100.0

Foreign exchange reserves: foreign currency + gold
Securities: financial assets with a fixed return
Currency: amount of money in circulation outside the banking system
Reserves: amount of money held by commercial banks
Loans: money lent to banks /// Equity: shareholders’ stake in the bank

2. Changes in the Central Bank Balance Sheet

Fed Buys US Treasury Bonds

The Federal Reserve Bank of New York purchases $1 billion in U.S. Treasury bonds from a commercial bank (page 459)

**Federal Reserve Balance Sheet**
Assets	$ Billions	Liabilities	$ Billions
Securities	$+1$	Reserves	$+1$
Total assets	$+1$	Total liabilities	$+1$

**Banking System’s Balance Sheet**
Assets	$ Billions	Liabilities	$ Billions
Reserves	$+1$
Securities	$-1$
Total assets	$0$	Total liabilities	$0$

Liabilities change $+1$ billion
Monetary Base changes $+1$ billion

Fed Buys Bonds Denominated in Euros

The U.S. Treasury instructs the Federal Reserve to buy $1 billion worth of bonds denominated in euros (page 459)

**Federal Reserve Balance Sheet**
Assets	$ Billions	Liabilities	$ Billions
Foreign Exchange Reserves	$+1$	Reserves	$+1$
Total assets	$+1$	Total liabilities	$+1$

**Banking System’s Balance Sheet**
Assets	$ Billions	Liabilities	$ Billions
Reserves	$+1$
Foreign Exchange Reserves	$-1$
Total assets	$0$	Total liabilities	$0$

Liabilities change $+1$ billion
Monetary Base changes $+1$ billion

Discount Loans to Commercial Banks

Commercial banks borrow $100$ million dollars from the Fed, through the “discount window”, providing collateral.¹ (page 461)

**Federal Reserve Balance Sheet**
Assets	$ Millions	Liabilities	$ Millions
Discount loans	$+100$	Reserves	$+100$
Total assets	$+100$	Total liabilities	$+100$

**Banking System’s Balance Sheet**
Assets	$ Millions	Liabilities	$ Millions
Reserves	$+100$	Discount loans	$+100$
Total assets	$+100$	Total liabilities	$+100$

Liabilities change $+100$ millions
Monetary Base changes $+100$ millions

Jane Takes Cash Out of Her Bank Account

Jane withdraws $100 from her checking account (page 462)

**Jane’s Balance Sheet**
Assets	$ Millions	Liabilities	$ Millions
Currency	$+100$
Deposits	$-100$
Total assets	$0$	Total liabilities	$0$

Jane changes money she had in Deposits into Currency

What changes will appear in the Fed’s balance sheet?
What changes will appear in the Banking System’s balance sheet?

Jane’s Impact on the Banking System

Recall that Jane changed money in her deposit account (Deposits) into money in her pockets (Currency)

**Federal Reserve Balance Sheet**
Assets	$ Millions	Liabilities	$ Millions
		Currency	$+100$
		Reserves	$-100$
Total assets	$0$	Total liabilities	$0$

**Banking System’s Balance Sheet**
Assets	$ Millions	Liabilities	$ Millions
Reserves	$-100$	Deposits	$-100$
Total assets	$-100$	Total liabilities	$-100$

Liabilities change $0$ dollars
Monetary Base changes $0$ dollars

3. The Monetary Base and the Money Supply

MB, M2, and the Money Multiplier

We saw that whenever the central bank buys/sells assets or lends money to banks, the Monetary Base changes.
The Monetary Base (MB) is the total amount of money printed by the central bank that is outside of the central bank (its liabilities). \[ MB=\text { Currency }+ \text { Reserves } \]
The Money Supply (M2) is the total quantity of money supplied to the economy by the banking sector (central bank + commercial banks) and is given by: \[M2 = \text { Currency }+ \text { Deposits }\]
M2 is much greater than MB and the link between the two aggregates is the Money Multiplier.

The Money Multiplier

The derivation of the money multiplier is not required in this course.¹
The money multiplier gives the following relationship: \[ M 2=\kappa \times M B \] where $\kappa$ is called the money multiplier and \[ \kappa=\frac{\beta+1}{\beta+r r} \]
$\beta=Currency/Deposits$
$rr=Reserves/Deposits$

Monetary Base (MB) and M2

The total amount of money supplied by the banking system (M2) is much greater than the Monetary Base (MB)

The Money Multiplier: Terribly Unstable

The money multiplier $(\kappa)$ is extremely unstable.

So, even if the central bank has a large control over the MB, it ends up with no control over the M2 because $\kappa$ is terribly unstable.

4. Monetary Policy Tools

Four Monetary Policy Tools

Controlling M2 is extremely difficult for the Fed, because the money multiplier is extremely unstable, as we saw in the previous figure.
The other option is trying to control (target), not the quantity of money, but its price: the short-term interest rate (Fed Funds Rate).
The fed has 4 policy tools (instruments) to do that:
- Target Federal Funds Rate Range
- Interest Rate on Excess Reserves (IOER Rate)
- Discount Rate
- Reserve Requirement

Monetary Policy Tools: Summary

How Are the Tools Combined?

The Fed sets the quantity of reserves supplied $(R^s)$

For a given level of the demand for reserves $(R^d)$
The equilibrium between $R^d$ and $R^s$ will deliver the interest rate the Fed wants (Target rate)

Extreme Situations: the Case of 2008-2015

The Fed implemented huge increases in $R^s$, a policy known as Quantitative Easing (QE).

The Fed’s goal was to keep interest rates as low as possible
For as long as desired
The equilibrium moved from point A to C.

An Increase in the IOER

In 2016 the Fed decided to increase the IOER.

The Fed’s goal was to get an increase in interest rates
The equilibrium moved from point C to D.

Fed’s Perfect Control of the Fed Funds Rate

The Fed navigates with the tools close to perfection.

Monetary Policy in the ECB

The ECB has a similar monetary policy structure. The names change a little bit, but the essence is the same.

Unconventional Policy Tools (Not covered in this course)

Fed’s Unconventional Tools

When the Fed Funds Rate comes down to zero, and the economy still needs some support from monetary policy, the Fed has two options:

Force short-term interest rates (Fed Funds Rate) to go below zero, as many European central banks did from 2010 to 2021.
Keep rates at zero and use some “unconventional policy tools”.

The unconventional monetary policy tools are basically three:

Quantitative easing
Forward guidance
Targeted asset purchases (TAP)

Quantitative Easing (QE)

QE consists basically of one decision by the central bank: buying vast quantities of bonds and expanding its balance sheet by a magnitude of 3 or 4 in a few years.

Why is it different from “conventional” monetary policy?

Because the bonds bought under QE are:

Long term maturity bonds (in opposition to short term maturity)
They have considerable risk attached to them (in opposition to risk free)
They belong to classes of bonds that were not eligible to be used by conventional policy.

Forward Guidance

Forward guidance is usually used by central banks when they communicate with private agents. If the central bank thinks that is convenient to signal a particular point to the private sector, they will do that.
But if short term interest rates are at zero (call this as the Zero Lower Bound), this guidance becomes vital.
At the ZLB there is a danger of deflation, and it is crucial if the private sector gets a clear commitment from the central bank that “we will do whatever it takes” to avoid the trap of a long deflationary period.
The central bank has to clarify that it will not increase interest rates if inflation surpasses the $2 \%$ target value by a significant amount: it will allow inflation to “overshoot” the $2 \%$ main goal for a significant time.

Targeted Asset Purchases

In contrast to QE, which increases the size of the central banks balance sheet by all sorts of bonds, targeted asset purchases (TAP) shift the composition of the balance sheet toward selected assets in order to boost their relative price, reducing their yields, and stimulate economic activity.
A recent example of this type of tool has become known as the “Operation Twist”. The Fed bought longer-term Treasuries and Mortgage-Backed Securities. It simultaneously sold some of the short-term assets it already held to ease the economy by bringing down long-term interest rates.

How Far Unconventional Can I Go?

In 2008: MB=0.8 trillion dollars; in 2021: MB = 6 trillion US dollars

:::

Appendix A: Derivation of the Money Multiplier (Not required studying)

Money Multiplier: Derivation

Money Supply (M2) and Monetary Base (MB) are defined as:

\[M 2=Cur+Dep \tag{1}\] \[M B=Cur+R \tag{2}\] where $Cur$ is “Currency”, $\ Dep$ is “Deposits”, $\ R$ is “Reserves”. From (1) and (2):

\[\frac{M 2}{M B}=\frac{Cur+Dep}{Cur+R} \tag{3}\]

Dividing the right hand side of eq. (3) by $Dep$:

\[\frac{M 2}{M B}=\frac{Cur / Dep+ Dep / Dep}{Cur / Dep+R / Dep} \tag{4}\]

Money Multiplier: Derivation (continuation)

In eq.(4) we have $Cur /Dep$, a ratio that is stable in the short-run: $Cur / Dep=\beta$
Moreover, the reserves requirement rate set by the central bank is given by: \[ R / Dep=rr \]
Therefore, eq. (4) can be simplified to: \[ \frac{M 2}{M B}=\frac{\beta+1}{\beta+r r} \]
Then: \[ M 2=\underbrace{\frac{\beta+1}{\beta+r r}}_{=\kappa} \times M B \]
$\kappa$ is the money multiplier.

5. Readings

Readings

For this topic, we recommend reading some parts of Chapters 17 & 18 of the following textbook:

Stephen G. Cecchetti and Kermit L. Schoenholtz (2017). Money, Banking, and Financial Markets, Fifth Edition, McGraw-Hill.

Chapter 17: “The Central Banks Balance Sheet” (pages 453-457). The subsection “The Importance of Disclosure” not required reading.

“Changing the Size and Composition of the Balance Sheet” (pages 457-463).

“The Monetary Base and the Money Supply” (468-473). It deals with the money multiplier in some detail. This part should be skipped. You have just to know what the money multiplier is supposed to do; nothing else.

Readings (continuation)

Chapter 18: “The Federal Reserves Conventional Policy Toolbox” (485-494). All pages are very important. Concentrate on Table 18.1 and on figures 18.2 a 18.4, as we do in the slides above.

“Unconventional Policy Tools” (pages 506-513). This part should be skipped; not covered in this course