Macroeconomics

Week 6

Ricardo Gouveia-Mendes
ricardo.mendes@iscte-iul.pt

Undergraduate in Economics
1st Semester 2023-24

The Central Bank Balance Sheet

How does the Central Bank set \(i\)?

• Last week: \(r=\overline{r} + \lambda \pi\)

• But we skipped the technicalities beyond the economic motivations
• The CB sets \(i\) by changing the financing costs of commercial banks
• Understanding these operations requires some understanding of the Central Bank Balance Sheet

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 Comercial Banks	15.0
Loans	32.5	Other liabilities	19.6
Other assets	10.5	Equity	21.0
Total assets	100.0	Total liabilities	100.0

Components of the CB Balance Sheet

• Assets
  • Securities: financial assets with a fixed return
  • Loans: money lent to commercial banks
• Liabilities
  • Currency: amount of money in circulation outside the banking system
  • Reserves: amount of money held by commercial banks

Financing operations with the CB

The Federal Reserve Bank of New York purchases $1B in U.S. Treasury bonds from a commercial bank.

Central Bank Balance Sheet

Assets	$B	Liabilities	$B
Securities	+1	Reserves	+1
Total	+1	Total	+1

Banking System’s Balance Sheet

Assets	$B	Liabilities	$B
Reserves	+1
Securities	-1
Total	0	Total	0

Example from the page 459 of the Text Book.

Financing operations with the CB

U.S. Treasury instructs the Federal Reserve to buy $1B worth of bonds denominated in euros.

Central Bank Balance Sheet

Assets	$B	Liabilities	$B
Foreign exchange reserves	+1	Reserves	+1
Total	+1	Total	+1

Banking System’s Balance Sheet

Assets	$B	Liabilities	$B
Reserves	+1
Securities	-1
Total	0	Total	0

Example from the page 459 of the Text Book.

Financing operations with the CB

Commercial banks borrow $100B from the Fed, through the “discount” window, providing collateral.

Central Bank Balance Sheet

Assets	$B	Liabilities	$B
Discount loans	+100	Reserves	+100
Total	+100	Total	+100

Banking System’s Balance Sheet

Assets	$B	Liabilities	$B
Reserves	+100	Discount loans	+100
Total	+100	Total	+100

Example from the page 461 of the Text Book.

Financing operations with the CB

Jane withdraws $100 from her checking account.

Central Bank Balance Sheet

Assets	$	Liabilities	$
		Currency	+100
		Reserves	-100
Total	0	Total	0

Jane’s Balance Sheet

Assets	$	Liabilities	$
Currency	+100
Deposits	-100
Total	0	Total	0

Jane’s Bank Balance Sheet

Assets	$	Liabilities	$
Reserves	-100	Deposits	-100
Total	-100	Total	-100

Example from the page 462 of the Text Book.

Financing operations with the CB

Summary

Operation	Initiator	Example	Impact
Open market operation	Central Bank	Purchase of Treasury Bonds	Reserves \(\uparrow\), Securities \(\uparrow\) MB \(\uparrow\), Assets \(\uparrow\)
Foreign exch. intervention	Central Bank	Purchase of foreign government Bonds	Reserves \(\uparrow\), Foreign Exch. Reserves \(\uparrow\) MB \(\uparrow\), Assets \(\uparrow\)
Discount loans	Commercial Banks	Extension of loan	Reserves \(\uparrow\), Loans \(\uparrow\) MB \(\uparrow\), Assets \(\uparrow\)
Cash withdrawal	Nonbank agent	Usage of the MB	Reserves \(\downarrow\), Currency \(\uparrow\) MB \(\uparrow \downarrow\)

The Monetary Base and the Money Supply

MB, M2 & the Multiplier

• The Monetary Base (\(MB\)) is the total amount of money issued by the Central Bank \[ MB = \text{Currency} + \text{Reserves} \]

• But the total amount of money supplied to the economy is much greater than the MB, due to the Credit Market

• This aggregate is called the Money Supply (M2 in the US)
• What links the two aggregates is the Money Multiplier

The Money Multiplier

The Money Multiplier¹ (\(\kappa\)) establishes the following relationship: \[ M_2 = \kappa \times MB \] where \[ \boxed{\kappa \equiv \dfrac{\beta +1}{\beta + rr}},\qquad \beta = \frac{\text{Currency}}{\text{Total Deposits}},\quad rr = \frac{\text{Reserves}}{\text{Total Deposits}} \]

1. Though beyond the scope of this course, you can check the derivation of the Money Multiplier in appendix A.

M2 and the Monetary Base

• In good times: stable relationship between the MB and M2
• In bad times: no stable relationship between the MB and M2

M2 and the Monetary Base

• The Money Multiplier suffered a big drop during the Financial Crisis of 2008
• After the crisis it became more volatile

Monetary Policy Tools

Defining the Monetary Policy

• Controlling M2 through the MB is extremely difficult
• What if instead of controlling quantity, the CB tries to control directly the interest rate? How?

• The FED has 3 policy tools/instruments to determine a range for the Fed Funds Rate:
  • Interest Rate on Reserve Balances (IORB)
    (formerly Interest Rate on Excess Reserves (IOER))
  • Discount Rate
  • Reserve Requirement (more or less discontinued)

Monetary Policy Tools’ Definitions

• IOER Rate — Rate paid by the FED on the reserve balances of commercial banks¹
• Discount Rate — Rate charged by the FED on loans to commercial banks²
• Reserve Requirement — Fraction of the deposits that commercial banks need to keep (at the FED or in their vaults)

1. The equivalent rate at the ECB is called Rate on the Deposit Facility.

2. The equivalent rate at the ECB is called Rate on the Marginal Lending Facility.

Banks refinancing operations

• The deposited reserves at the CB yield an interest (at the IORB) to the commercial banks
• On the other hand, commercial banks pay interests (at the Discount Rate) on the loans taken from the CB itself

• But they can also lend and borrow reserves from each other

The Monetary Tools in action

• In that case they will do it at an interest rate between the previous two
• By controlling the limits of the range and reserves’ supply, the CB is implicitly defining a Target Federal Funds Rate¹

1. The equivalent rate at the ECB is called Rate on the Main Refinancing Operations.

The Fed Funds Rate in the USA

• The FED navigates with the tools close to perfection
• The ECB does it as well

Readings

Main reference

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

Chapter 17

“The Central Bank’s Balance Sheet” (pp. 453–457). The subsection “The Importance of Disclosure” is not required reading.

“Changing the Size and Composition of the Balance Sheet” (pp. 457–463).

“The Monetary Base and the Money Supply” (pp. 468–473). Please skip the (abundant) details about the money multiplier.

Chapter 18

“The Federal Reserve’s Conventional Policy Toolbox” (pp. 485–494). Pay special attention to Table 18.1 and to figures 18.2 to 18.4.

“Unconventional Policy Tools” (pp. 506–513). The subsection “Making an Effective Exit” is not required reading.

Appendix

(not required reading)

Appendix A: Deriving the Money Multiplier

Remember that: \[ MB \equiv C + R \qquad M_2 \equiv C + TD \] where \(C\) is Currency, \(TD\) is Total Deposits and \(R\) is Reserves.

Define:

• \(rr \equiv R/TD\) as the reserves requirement rate set by the CB
• \(\beta \equiv C/TD\)

Appendix A: Deriving the Money Multiplier

Then:

\[ \begin{gathered} \frac{M_2}{MB}=\frac{C+TD}{C+R} \Leftrightarrow \frac{M_2}{MB}=\frac{C+TD}{C+R} \color{red}{\frac{TD}{TD}} \\ \Leftrightarrow \frac{M_2}{MB}=\frac{\beta+1}{\beta+rr} \Leftrightarrow \boxed{M_2=\underbrace{\frac{\beta+1}{\beta+rr}}_{\equiv \kappa} MB} \end{gathered} \]

Appendix B: Unconventional MP

• What happens when the Fed Funds Rate comes down to zero? Zero is the lower-bound for nominal interest rates
• Since no further decreases in the interest rate are allowed, the CB needs to use other tools to control liquidity in the economy and stabilize inflation and economic activity
• Some of the unconventional tools used in the last two decades are: quantitative easing, forward guidance and targeted asset purchases

Appendix B: Unconventional MP

Quantitative easing

• The CB buys vast quantities of bonds, expanding its balance sheet by a magnitude of 3 or 4 in a few years
• Bonds bought under QE:
  • are long term maturity bonds (in opposition to short term maturity)
  • have considerable risk
  • belong to classes of bonds that were not eligible for conventional policy

Appendix B: Unconventional MP

Forward guidance

• CB tries to influence private agents expectations
• At the ZLB there is a risk of deflation
• The BC must make clear that it “will do whatever it takes” to avoid deflation, even if that means allowing inflation to “overshoot” the 2% target for a significant time

Appendix B: Unconventional MP

Targeted asset purchases

• The CB changes the composition of the balance sheet to boost the price of certain assets, reducing their yields, and stimulate economic activity
• A recent example — in “Operation Twist” the Fed:
  • bought longer-term Treasuries and Mortgage-Backed Securities
  • sold some of the short-term assets
  • which brought down long-term interest rates

Appendix B: Unconventional MP

How unconventional can the Fed be?

• The Fed applied QE largely since 2008
• In 2008: \(MB\) was 0.8 trillion dollars
• in 2021: \(MB\) was 6 trillion dollars