14. Money, credit and banks - SWEETsweet.ua.pt/afreitas/aulas/notas apoio/money multiplier.pdf · 2018-10-28 · Politicas macroeconomicas, handout, Miguel Lebre de Freitas ([email protected])

Politicas macroeconomicas, handout, Miguel Lebre de Freitas ([email protected])

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28/10/2018 https://mlebredefreitas.wordpress.com/teaching-materials/

14. Money, credit and banks

Index:

14. Money, credit and banks ..........................................................................................1

14.1 Introduction........................................................................................2

14.2 Accountancy issues and definitions ...................................................2

14.2.1 The Central bank balance sheet .................................................................2

14.2.2 The balance sheet of other monetary institutions ......................................3

14.2.1 The consolidated monetary sector .............................................................4

14.2.2 The solvency ratio......................................................................................5

Box 2. Capital requirements ..................................................................................6

14.2.1 Reserves-deposits ratio ..............................................................................7

14.3 Monetary policy instruments .............................................................8

14.3.1 Intervention in the foreign exchange market .............................................8

14.3.2 Liquidity provision to (absorption from) commercial banks:....................8

14.3.3 Debt monetization....................................................................................10

14.3.4 Asset purchase programmes ....................................................................10

14.3.5 Sterilization ..............................................................................................11

14.4 The money multiplier.......................................................................12

14.4.1 The Money multiplier ..............................................................................12

14.4.2 Parameter instability ................................................................................13

Box.3 - The money multiplier during financial crises .........................................14

14.4.3 Capital constraints....................................................................................16

14.4.4 Demand and supply of credit ...................................................................17

14.4.5 Summing up .............................................................................................17

14.5 Conclusions......................................................................................17

Review questions and exercises...................................................................................19

Solved exercise ....................................................................................................19

Exercises ......................................................................................................22


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14.1 Introduction

So far, we have analysed the implications of monetary expansions, presuming that the

central bank has the power to decide the quantity of money in the economy. In practice,

however, central banks do not have full control over the money supply. The conduction of

monetary policy by central banks is mediated by banks, which carry most of the money held

by the public, in the form of deposits. The money supply is therefore determined by the triple

influence of the central bank, banks and the desire of the public for deposits rather than for

notes and coins.

In this note, we review the role of the banks in the process of money creation, and the

instruments the central bank can use to influence the money supply. In Section 2, we

introduce the main concepts and accounting identities. In Section 3 we briefly describe the

main tools of monetary policy available to central banks. In Section 4 we discuss how

changes in behaviour by the public or by banks may destabilize the relationship between the

money created by the central bank (monetary base), and the money supply in the economy. In

Section 5, we summarise the main ideas.

14.2 Accountancy issues and definitions

14.2.1 The Central bank balance sheet

The central bank is the government institution responsible for a country’ monetary

policy. The central bank holds the country’ foreign reserves and lends to the banking system

and to the government by creating a liability known as monetary base. The balancesheet of

the central bank obeys to the following identity (see Figure 1):

* B P GC C C C CeB L L D H , (1)

where, C denotes for the net worth of the central bank, *CeB for the domestic currency value

of (net) reserve assets, GCD for the net credit conceded by the central bank to the government,

BCL for loans to commercial banks, p

cL for loans to the private sector, and H for the Monetary

Base. The Monetary Base (H) is the most relevant liability of the central bank. It


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comprehends the Notes and Coins held by the Public ( ) and the Reserves held by

commercial banks (R):

H X R (2)

The reserves of commercial banks, R, may be held in the form of cash (in the vaults

of banks) or in the form of deposits held at the central, bank. This distinction is not however

relevant to the analysis that follows.

Figure 1: The Central Bank Balance sheet

C

*ceB

BCLPCL

GCD

H

Assets Liabilities

Equity

14.2.2 The balance sheet of other monetary institutions

Commercial banks are a special kind of financial institutions, because they are

authorised to issue deposits (D). The specific characteristic of bank deposits is that they are

so liquid that they can serve as means of payment. Because of this, bank deposits are part of

what we call “money”. The other component of money are the notes and coins held by the

public (X)1:

M=X+D (3)

1 In the real world, central banks monitor wider monetary aggregates, including short term securities held by the public (e.g, treasuries). For convenience, we ignore this complication.


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Banks are financial intermediaries, in the sense that they participate in the process of

transferring funds from lenders to borrowers at their own risk. Because banks have the power

to create money, they belong to the class of monetary institutions, together with the central

bank.

Banks obtain resources rising capital from shareholders or borrowing from other

agents. The bulk of banks liabilities are deposits, but banks also borrow from the central

bank2. With the funds raised, banks can hold reserves, extend credit to the private sector

(either in the form of loans or securities), and lend to the government. The balance sheet of

the banking sector obeys to the following identity (figure 2):

P G BB B B CR L D D L , (4)

where PCL denotes for banks’ loans to the private sector, G

CD for government securities, B

for the net worth of commercial banks, and the remaining variables are defined as before.

Figure 2: The Balance sheet of Commercial banks

C

RBCLP

BL

GBD

D

Assets Liabilities

Equity

14.2.1 The consolidated monetary sector

2 For simplicity, we are ignoring funds raised by banks through the capital market, such as long-term liabilities. Note that individual banks also rely on lending from each other as a source of finance, but when we consider the banking system as a whole, these inter-bank loans cancel out


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Taking together the central bank and the commercial banks’ balance sheets, we obtain

the consolidated balance sheet of the monetary sector:

DXLLDDeB pc

pb

gb

gccbc

* .

Using (3):

Bcc LeBM * , (5)

where pc

pb

gb

gc LLDDL is total domestic credit.

Equation (5) reveals that the counterparts of an economy’ money supply are the total

domestic credit (including the government and the private sector) and net credit to non-

residents (reserve assets).

14.2.2 The solvency ratio

The banking business is about leveraging. Banks make profits by borrowing funds at a

given interest rate and lending these funds at a higher interest rate, and the more funds they

borrow and lend, the higher the potential profits. The main problem with leveraging is that

banks are highly exposed to the risk of insolvency. Insolvency happens when a bank doesn’t

have enough assets to meet its debt obligations.

A key indicator of the risk of insolvency is given by the percentage of “risky assets”

that is backed by equity capital:

BPB

kL

(6)

In bad times, the bank may find that some of the risky loans previously conceded

became impossible to recover. In that case, the bank is forced to assume losses, and these

losses erode the bank capital. In the limit, the bank may find itself insolvent ( 0B ). As for

the public, fears of insolvency may tilt a bank run, whereby the public withdraws deposits,

and lenders refuse to rollover the bank’ debt, turning the fears of a solvency crisis into a

liquidity crisis.

To protect banks from these risks, bank regulators establish that banks must have

capital enough to ensure that deposits are fully repaid. In particular, authorities require banks


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to preserve a minimum proportion of capital relative to the amount of “risky assets”. This is

called the capital adequacy ratio, k :

kk (7)

In reality, the denominator of the relevant “capital adequacy ratio” is not exactly equal

to the credit to the private sector PBL : the amount of capital required depends on the

composition of the bank assets in terms of risk characteristics (see Box 2 for details). In what

follows, however, we treat all the credit extended to the private sector as being the “risky

asset”, and the loans to the government as being “non-risky”.

Capital adequacy ratios are set by the banking authorities to prevent highly leveraged

banks from engaging in further leverage. Whenever the constraint (7) is binding, a leveraged

bank can still expand its credit activity, but it must raise more equity from shareholders.

Box 2. Capital requirements

The international regulatory framework for banks (the Basel Accord) establishes that

banks shall hold as capital at least 8% of their “risk-weighted assets”.

The “risk-weighted-assets” are computed as the sum of different categories of credits,

with the different weights reflecting the perception of different credit risks. The weights may

differ according to local regulations, so there is no general rule in this respect. In the so-called

“standardized approach” (proposed under Basel II), claims on international institutions such

as the BIS, the IMF, and the main central banks have a zero weight (so, in practice, they are

out of the ratio). As for claims on sovereigns, financial institutions and corporations, banks

are required to use ratings from External Credit Rating Agencies to quantify the required

capital. For instance, claims on sovereigns may weight from 0% to 150%, depending on the

rating (from AAA to below B-). Similar, but more demanding rules (starting in 20%) apply to

financial institutions and rated corporations. The standardized approach also includes rules

for retail credit, requiring for instance 35% on claims secured by residential property and

100% on claims secured by commercial real estate. This means that a bank that is lending to

a safe government will need proportionally less capital than a bank lending to risky

entrepreneurs.


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Regulations also allow the numerator in (6) to include both “equity” and long-term

“subordinated” liabilities. These are liabilities that, in case of insolvency, are paid after all the

other bank debts are honoured, and immediately before finding out what is left to

shareholders. These liabilities are very close to equity for solvency purposes.

14.2.1 Reserves-deposits ratio

As part of the general principle of prudential management, banks must make sure that

they remain liquid, having cash enough to face the day-to-day payment obligations, including

deposit outflows. This is particularly important in the banking industry, because banks

borrow in short maturities (deposits) to buy illiquid assets (credit). When the bank doesn’t

have enough liquid assets to meet its immediate debt obligations, it is said to be illiquid.

When a bank finds itself illiquid, it may be forced to sell illiquid assets at discount, or to

request an emergency loan from the central bank, which may reveal costly.

A measure of the bank position regarding the liquidity risk is given by the so-called

reserves-deposits ratio:

Rrr

D . (8)

This indicator gives the percentage of bank deposits D that are backed by reserves, R.

In most banking systems, central banks impose a minimum level for the reserves-

ratio (the “minimum reserve requirements”)3. However, this legal constraint is not always

binding: in many circumstances, banks decide to hold more reserves than the minimum

requirements, to reduce the risks of finding themselves in a position of insufficient liquidity.

The policy of reserve requirements only imposes a floor on the reserves ratio, (8).

3 In the euro area, for instance, banks are required to have a minimum amount of reserves corresponding to 1% of their deposits with agreed maturity lower than 2 years. For agreed maturities over 2 years, the minimum reserve requirement is zero.


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14.3 Monetary policy instruments

The principle of double-entry book keeping implies that the total value of assets in a

balance sheet shall be equal to the total value of liabilities plus equity. Having this in mind,

one can discuss the different operations through which a central bank can influence the

monetary base.

14.3.1 Intervention in the foreign exchange market

When the CB buys assets denominated in foreign currency or gold, the monetary base

expands:

*cBeH (9)

This is the case, for instance, when the central bank buys dollars to avoid the

appreciation of the domestic currency.

14.3.2 Liquidity provision to (absorption from) commercial banks:

When the central bank provides liquidity to commercial banks, the counterpart of the

increase in the monetary base are loans to banks:

RLH bc . (10)

Liquidity provision to commercial banks can occur at the central bank initiative (open

market operations) or at the initiative of the commercial bank (standing facilities).

In open market operations, the central bank decides the instrument and terms and

conditions of the financing (absorption) operation. The most common types of open market

funding are “repurchase agreements” and “collateralised loans”. Typically, open market


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operations consist in short-term lending (one week, three months). However, in exceptional

circumstances, long-term lending is also possible4.

Standing facilities are available on a permanent basis and may be used on the

initiative of commercial banks. These are mainly aimed to provide and absorb overnight

liquidity. The interest rates on these facilities are set by the central bank, but the central bank

does not control the amounts banks borrow or lend through these facilities.

By setting the interest rates on standing facilities and in open market operations

(intervention rates), central banks play a key role in influencing the money market interest

rates. On one hand, the overnight standing facilities define a corridor for the interest rate at

which commercial banks provide loans to each other with the maturity of one day5. On the

other hand, open market operations, by creating and absorbing liquidity at different

maturities, influence the terms structure of interest rates at which commercial banks lend to

each other6.

Note however that the relevant opportunity cost for investment and durable

consumption is the long-term interest rate, not the money market interest rate. Hence, when

the central bank targets a given money market interest rate, its influence in the long-term

interest rate is mediated by the term structure of interest rates, whereby the long-term interest

rate corresponds to the average of the future expected short-term interest rates. This means

4 During the European Debt Crisis, in 2011, the ECB launched the Long-Term Refinancing Operations (LTRO), whereby liquidity to banks was conceded with a maturity of 3-years. In 2014, these operations were replaced by Targeted Long Term Refinancing Operations (TLTRO), which required that banks used the liquidity thereby generated to extend credit to the private sector.

5 In the ECB framework, the permanent discount window applies to overnight loans, and is labelled Marginal Lending Facility. Banks can also deposit funds overnight at the ECB at their own discretion, using the so-called Deposit Facility. These two rates define the corridor for EONIA, the Euro Overnight Index Average, which is the rate at which commercial banks provide overnight loans to each other.

6 In the Euro Area, the average short-term money market interest rate for un-collateralized loans is called Euribor (Euro Interbank Offered Rate).


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that expectations regarding the future stance of monetary policy matter for its effectiveness

today7.

14.3.3 Debt monetization

When governments find it difficult to finance the budget deficits, they may be

tempted to borrow directly from the central bank in the primary market. In this case, the

monetary base expands because the central bank buys government bonds:

gb

gc DRDH (11)

Purchases of government debt by the central bank are labelled “government debt

monetization”. Because continuing debt monetization is the main cause of high inflation, this

possibility has been banished in most developed nations. Yet in many other countries, central

bankers are often instructed by the Minister of Finance to buy government bonds. When this

is so, the central bank is said to be under “fiscal dominance”8.

14.3.4 Asset purchase programmes

In exceptional circumstances, central banks engage in purchases of financial assets

from commercial banks and other financial institutions. These assets may include government

bonds, asset backed securities, covered bonds, equities, and commercial paper. In this case,

the central bank buys securities (bonds) in the secondary market and holds them until

7 During the recent financial crisis, both the FED and the ECB announced that the policy of keeping low money market rates today would be extended for a long period of time. The intention was to help keep all the term structure of interest rates down, and thereby influence on the downside the interest rates on long-term contracts.

8 In countries were the central bank is prohibited from buying government debt directly, central banks still have the possibility of buying government bonds indirectly, in the secondary market. When this possibility materializes, a question may arise as to whether the central bank is in fact monetizing the government debt. To avoid the “label”, the policy must be justified very carefully. For instance, under quantitative easing, government bonds have been purchased with the aim to expand money supply and avoid the risk of deflation, not to finance government deficits. Thus, central banks in principle stand ready to revert the policy (by selling the government bonds back into the market) in case the risks of inflation materializes.


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maturity. Since in this case the ownership of the security moves from the commercial bank to

the central bank, this operation not only provides liquidity to banks, it also induces the de-

leveraging of commercial banks.

When the central bank buys government bonds, the impacted accounts are shown in

(11). When the central bank buys private securities, the impacts are:

pb

pc LRLH (12)

The purchase of private and public securities in secondary markets by the central bank

is not a conventional tool of monetary policy. It has been used however by many central

banks around the World since the global financial crisis of 2007-2008, under the general

umbrella of Quantitative Easing9. The main goal of Quantitative Easing (QE) is to raise the

market price of financial assets, lowering their yields, when standard monetary policy tools

become ineffective. When the money market interest rate reaches the zero-lower-bound, the

central bank can no longer rely on open market operations to achieve further reductions in

long-term interest rates. Buying long-term bonds in the secondary market, the central bank

recovers its ability to drive down the bond yields, even if its money market policy becomes

impotent. Note that QE is also an effective policy to contain a credit crunch when banks are

capital-constrained.

14.3.5 Sterilization

Sometimes, central banks try to offset the monetary impact of their purchases of

domestic or foreign securities, by conducting symmetric operations involving other assets.

When the central bank buys or sells financial assets to offset the impact of other asset sales or

9 Quantitative easing was first launched by the Bank of Japan in 2001. During the global financial crisis, quantitative easing was swiftly implemented by the United States (2008) and the United Kingdom (2009). In 2010-2011 and 2014, the Eurosystem launched two Covered Bonds Purchase Programmes (buying euro-denominated covered bonds), but the amounts involved were too small for these operations to be labelled as “quantitative easing”. Only in 2015, the ECB engaged in a large-scale purchase of assets, under the label of APP (for “Expanded Asset Purchase Programme”).


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purchases ad keep the monetary base unchanged, is said to be conducing a “sterilized

intervention”.

The most popular form of sterilization happens when the central bank offsets the

effects of foreign exchange market interventions:

0* cc LBeH (14)

In this case, the central bank uses the open market to completely offset the

intervention in foreign exchange market, so that the money base does not expand at all.

Sterilization may also be used to change the composition of domestic credit. For

instance, a loan to the government can be sterilized with an offsetting open market

operation10:

0gc cH D L (15)

14.4 The money multiplier

14.4.1 The Money multiplier

The fact that the central bank controls the monetary base (H) does not imply that the

central bank has control over the money supply. The impact of the monetary base on the

money supply is mediated by the so-called “money multiplier”, defined as the ratio between

the money supply and the monetary base:

10 In Europe, during the European sovereign debt crisis of 2011-2012, the ECB engaged in a program of acquisitions of sovereign bonds (the so-called Securities Market Program), with the aim to stabilize the financial markets, which became “dysfunctional”. In order for this not to be interpreted as debt monetization, the central bank committed with the full sterilization of these purchases, drawing the liquidity thereby generated from commercial banks, through open market operations. By committing with sterilized intervention, the ECB wanted to signal that price stability was not at stake. The same principle holds for the SMP successor, the OMT mechanism (Outright Monetary Transactions).


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H

M (16)

Using (2) and (3) and dividing both members by D, we get:

1,

X DxDrr x

X R x rrD

, (16a)

where

Xx

D (17)

is the ratio of currency in circulation to deposits, and rr R D is the ratio of reserves-to-

deposits. The money multiplier is labelled as such because it is greater than 1: one unit of

monetary base translates into 1 units of money, on average. Because the monetary base

has a multiplied effect on the total money supply, it is often labelled “high-powered money”.

14.4.2 Parameter instability

The fact that equation (16) suggests a proportionality between H and M, does not

mean that a given increase in H will deliver an increase in M by the same proportion.

Because the desired bank’ reserves (rr) and liquidity preference by the public (x) are

behavioural parameters that change over time, one should not trust too much the stability of

the money multiplier.

The currency-deposits ratio (x) depends for instance on the interest rate on time

deposits relative to other assets, and it may be decrease over time because of financial

innovation. More important, this parameter may be seriously destabilized during a financial

crisis, if the public confidence in the banking system becomes at stake.

The desired ratio of reserves by banks ( rr ) depends in general on the money market

interest rate, on the time structure of banks’ liabilities, on the cost of borrowing from the

Central Bank and - when binding - on minimum reserve requirements. During episodes of

financial crisis, banks may become more cautious, increasing significantly their reserves, to

stand ready to respond to frightened depositors.


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Dramatic declines in the money multiplier were observed during the Great Depression

and during the Great Recession. In both episodes, the total demand for monetary base

increased, reflecting a higher demand for currency rather than deposits by the public, and a

higher demand for reserves rather than loans by banks (see box 3).

Box.3 - The money multiplier during financial crises

Figures 2 and 4 describe the time paths of money supply and of monetary base in the

US, during the Great Depression and during the Great Recession.

Figure 3 – Money supply and monetary base, US 1929-1933

Figure 4 – Money supply and Monetary Base in the US, 2007-2009


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Source: Miskhin, 2009.

In the United states, the money supply contracted 28% between august 1929 and

march 1933. This fall could not be explained by a decrease in the monetary base, because the

later actually expanded by 18% in the period. The fall in the money supply was basically

driven by the decrease in the money multiplier. The fall in the money multiplier during the

Great Depression was initially caused by in increase in the liquidity preference by the public,

x. The reason is that there was a series of bank failures, that eroded the public confidence in

the banking system. As people withdrew their deposits, banks faced a drain on reserves and

responded increasing the desired reserves-deposit ratio. Together, these changes caused a

large fall in the money multiplier.

In the case of the Great Recession, the fall in multiplier was mostly driven by the

increase in banks’ reserves: in an environment were risk was perceived to be unusually high,

highly leveraged banks preferred to hold cash or deposits at the central bank, rather than to

lend to each other or to the public. Note that in the case of the Great Recession (figure 4), the

Federal Reserve managed to increase the money base the enough to prevent the money


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supply from falling, despite the fall in the money multiplier. During the Great Depression

(figure 3), that was not the case11.

14.4.3 Capital constraints

Rising liquidity among banks may be an effective measure to achieve a monetary

expansion when banks are constrained on liquidity. However, this is not a sufficient

condition. One reason why liquidity provision may fail in expanding the money supply is that

banks may lack the capital to engage in further credit expansion. When capital ratios are close

to the capital adequacy limit, banks will be unable to expand further the credit to the private

sector, unless they manage to raise more capital from shareholders.

The existence of capital constraints may induce a pro-cyclical behaviour in the money

supply. During episodes of booms, banks are more likely to make profits, in which case it

will be easy for them to attract new capital. Then, with more equity, banks will be able to

lend again. During downturns, on the contrary, the increase in non-performing loans causes

banks to have losses, eroding the existing capital and making more difficult for banks to

attract new capital. Whenever banks do not comply with the capital adequacy ratio, they will

tend to reduce credit to the private sector and eventually to change the composition of asset

holdings towards government debt, which does not “consume” capital (see box 2). An

implication of this “flight-to-quality” is that it drives down the interest rates on government

bonds and other safe assets, at the same time that credit becomes scarcer to the public in

general.

During the Great Recession, many banks in the United States and in Europe found

themselves with too little capital, after incurring in significant losses. Since banks found it

difficult to raise new capital among the shareholders, they reduced lending, to repair their

11 In their “monetary history of the United States, 1867-1960”, Milton Friedman and Anna Schwartz, Friedman contended that the Great Depression was significantly aggravated by a fall in money supply that the Federal Reserve could have prevented.


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balancesheet. In order to avoid bank failures, and to help bring the lending activity back to

normal, governments stepped in, using public funds to recapitalize banks.

14.4.4 Demand and supply of credit

Even if banks have liquidity and capital enough to lend, lending may not increase

because there is no demand for credit and banks prefer not to lend. During periods of

financial stress, investment opportunities in the real sector are less abundant, driving down

the demand for credit. On the other hand, banks may become more cautious in loan

concession, rationing the credit. With less demand and less supply of credit, the credit market

may become frozen, turning it difficult more a central bank to expand the money supply.

14.4.5 Summing up

In sum, although theoretically an increase in monetary base may lead to an increase in

money supply, changes are not necessarily proportional. To asses the impact of a given

liquidity provision in the money supply, what matters is not the average relationship between

money base H and money supply M, but rather the marginal impact ( HM ). Sometimes,

the marginal impact is significantly smaller than the average, and eventually nil.

14.5 Conclusions

The money multiplier is not a constant parameter: it depends on behavioural

parameters that are out of control of monetary authorities. In normal times, expanding the

monetary base will imply more money, bank deposits and loans in the economy. Capital

constrained banks will have an incentive to raise more capital or otherwise they will be

forced to reallocate their holdings towards less risky assets, such as government bonds.

A confidence crisis may translate into higher liquidity preference by the public and

higher desired reserves by banks. In this case, the money multiplier falls sharply. If the

central bank doesn’t act, there will be a contraction of money supply and of domestic credit.

In the case of a liquidity crisis, the central bank – as the lender of last resource - may provide

extraordinary liquidity to the banking system. This will avoid the contraction of domestic

credit. The policy will not be inflationary as long as the extra liquidity provided is just the


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enough to prevent the money supply from falling. In that case, the central bank is just

responding to an increasing demand for monetary base with an increasing in supply of

monetary base.

During financial crisis, asset values erode, impacting negatively on the banking

system’ net worth. When losses are large enough to make the capital adequacy constraint

binding, capital constrained banks (that is, banks finding difficult to raise capital in the

markets) will reduce their exposure to the private sector, reallocating as much as possible

towards government bonds or other safe assets, which consume less capital. In the worst case,

banks will accumulate excess reserves (deposits in the central bank). If nothing is done, the

credit to the private sector will contract sharply.

When banks are capital constrained, rising liquidity in the inter-bank money market

will not work. With a programme of asset purchases, the central bank could, at least in

theory, purchase the excess assets of leveraged banks, avoiding the contraction of credit by

capital constrained banks. In that case, the total credit to the economy would not decrease; it

would only change hands away from capital constrained banks to the central bank, which is

not subject to capital requirements. This would require, however, the central bank to buy

securities with some risk, like corporate bonds. Note however that the main goal of QE is not

to help deleverage banks. The main goal of quantitative easing is to drive down the long-term

interest rate when money market operations fail to do so.


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Review questions and exercises

Solved exercise

14.1. Consider the following initial situation in a given banking system: D=200; X=40; R=10; 50* CeB , 0 g

cbc

pc DLL , 10g

bD , 0c and 20b . Along the exercise,

assume that the capital adequacy ratio, k , is 8%.

(Accountancy) How much are the money supply, the monetary base, and domestic credit granted by commercial banks?

From the definition of money: M=X+D=240.

The monetary base is H=X+R=50.

The domestic credit granted by banks can be obtained using the banks’ balance sheet

identity, that is: 21010200200 RLDDL bbc

gb

pb . Since banking

credit to the government is equal to 20, the banking credit to the private sector

equals 200210 gb

pb DL .

(Capital adequacy) Assume that banks in this economy are required to hold a minimum capital ratio of 8%. Does the banking sector in this numerical example satisfy the capital adequacy condition?

The capital ratio is equal to %1020020 pbb Lk , so banks are in shape with the

capital adequacy ratio.

a) (Money multiplier) Find out the reserves ratio, the liquidity preference coefficient and the money multiplier.

The money multiplier is equal to 8.450/240 HM

The reserves ratio is 10 / 200 5%rr R D

The liquidity preference coefficient is %20200/40 DXx

We can check with the formula for the money multiplier 1 1, 2

4.80.25

x

x rr

b) (Monetary expansion – unchanged multiplier): Assuming that the ratio of desired reserves and the liquidity preference parameter were constant, what would be the impact on money supply of an open market operation increasing the central bank liabilities by 12.5? Will the banking system as a whole still meet the capital ratio?

The policy consists in 5.12 bcLH

With the reserve ratio and the liquidity preference constant, the money multiplier will be constant, so 605.12*8.4 HM . The new money supply will be M=300.

[Note that this presumes that there is demand for credit and that banks are willing to increase its exposure to the private sector].


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In the new equilibrium, we have: D=250; X=50; R=12.5.

The total credit granted by banks will be

2705.12205.12250 RLDDL bbc

gb

pb . If the credit to the

government sector remained constant, credit to the private sector would be

260270 gb

pb DL . In this case, the bank would not be satisfying the capital

adequacy ratio: %69.726020 pbb Lk .

In order to meet the capital ratio, some of the credit expansion has to be achieved through

purchases of “safe” assets. For instance, if 20gbD , then 250270 g

bpb DL , in

which case %825020 pbb Lk .

[Note that expanding the credit to the government may imply an increased competition for government bonds, driving down the respective yields; in alternative, the bank may buy foreign governments bonds].

c) (Liquidity crisis) Returning to the initial situation, assume that, due to a bank scare, the coefficient of liquidity preference increased to x=0.25. Also assume that, in face of a collapse in the inter-bank money market, banks decided to increase the ratio of desired reserves to rr=0.15.

(c1) If the central bank did not intervene, what would happen to domestic credit?

With the new behavioral parameters, the money multiplier becomes 1 1.25

3.1250.4

x

x rr

Hence, if the money base remained unchanged, there would be a contraction of money supply to 25.15650*125.3 HM .

Accordingly, in the new equilibrium: D=125; X=31.25; R=18.75.

The total credit granted by banks would be

25.12675.18200125 RLDDL bbc

gb

pb .

If the credit to the government sector remained constant, credit to the private sector would collapse to 25.11625.126 g

bpb DL .

e2) If the central bank, as a lender of last resort, decided to launch a large refinancing operation (eg. LTRO) amounting to 8.26b

cL , would this be enough to avoid the

contraction of domestic credit?

An expansion of the monetary base by 26.8 will produce a change in money supply amounting to 75,838.26*125.3 HM . Thus, the new money supply will be

2408.76*125.3 HM .

Accordingly, in the new equilibrium: D=192; X=48; R=28,8.

The total credit granted by banks would be

2108.28208.26192 RLDDL bbc

gb

pb .

If the credit to the government sector remained constant, the policy would have been successful in avoiding the collapse of the banking credit to the private sector. Note however that bank reserves increased dramatically: the central bank liquidity provision aimed precisely satisfy this extra demand for reserve money by commercial banks.


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d) (Capital constraints): Returning again to the initial situation, suppose that non-performing loans and erosion is asset prices forced banks to write off an amount of 10 in their credit bookings.

d1) With all else constant, describe the balance sheet of commercial banks immediately after the write off. Does the banking system in this case satisfy the capital adequacy constraint?

With the write off, credit to the private sector would become 19010200 pbL . Since

this comes at a loss, the banking sector capital would erode to 10b .

In this case, the capital adequacy ratio would decline to %26.519010 pbb Lk ,

thus not meeting the legal standard.

d2) If nothing was done how much would banks want to reallocate credit out of the private sector towards government bonds or reserves?

If nothing was done, credit to the private sector would have to decline to

12508.01008.0 bpbL .

Banks would try to buy 190-125=65 of government bonds, or otherwise they would have to hold the excess reserves.

d3) (Ineffective liquidity provision) Would in this case an open market operation avoid the contraction of credit to the private sector?

An open market operation in this case does not help credit to the private sector to recover, because banks are capital-constrained. The problem in this case is not of liquidity, but instead excess leverage.

e) (Asset purchases) Following (d), suppose the central bank bought assets from the banking system amounting to 65, with full sterilization. Would this operation avoid the contraction of domestic credit?

In this case, the policy consists in a monetary expansion 65 pb

pc LLH

followed by full sterilization 65 bcLH (that is, the central bank retains the

proceeds of this operation by selling securities to banks in the amount of 65).

Since the monetary base does not expand, total money in the economy will be 24050*8.4 HM , just like in this initial state. Accordingly, D=200; X=40;

R=10.


135101065200 RLDDL bbc

gb

pb . If credit to the government

sector remained constant, credit to the private sector would be 125135 gb

pb DL . In

this case, the bank would be exactly satisfying the capital adequacy ratio:

%812510 pbb Lk .

Note that, although commercial banks reduced domestic credit, this was replaced by central bank credit. Using the consolidated balance sheet of the monetary sector, we see

that 2401020050* Bcc LeBM , with

65125100 pc

pb

gb

gc LLDDL .


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f) (Asset purchases) Back from (d), suppose that the central bank bought assets from the banking system amounting to 90, but sterilizing only 85. Would total credit expand in this case?

In this case, the central bank buys more than needed for banks to meet the capital adequacy ratio. Moreover, the intervention is such as to increase the supply of monetary base, creating the conditions for credit to expand.

The net increase in the monetary base amounts to 5H . Thus – as long as there is demand for credit - the money supply will increase to 26455*8.4 HM . In the new equilibrium, D=220; X=44; R=11.


134111085220 RLDDL bbc

gb

pb . If the credit to the government

sector remained constant, credit to the private sector would be 124134 gb

pb DL .

In this case, the commercial bank would meet the mandatory capital

ratio: %06.812410 pbb Lk .

The consolidated balance sheet of the monetary sector, will show up as

2641022450* Bcc LeBM , with

90124100 pc

pb

gb

gc LLDDL .

Exercises

14.2. Consider the following initial situation in a given banking system: D=100; X=20;

R=10; 30* CeB , and the commercial banks’ equity is NW=10.

a) (Accountancy) How much will be the money supply, the monetary base, and domestic credit granted by commercial banks?

b) (Capital adequacy) Assume that banks in this economy are required to hold a ratio of equity to total credit equal to 8%, irrespectively of the risk weight in each particular loan. Does this banking system satisfy the capital adequacy condition?

c) (Money multiplier) Find out the reserves ratio, the liquidity preference coefficient and the money multiplier.

d) (Money expansion - normal times): Assuming that the ratio of desired reserves and the liquidity preference coefficient were constant at the levels estimated in (b), what would be the impact on money supply of an open market operation increasing the central bank liabilities by 8.4?

e) (Liquidity crisis) Returning to the initial situation, assume that, due to a bank scare, the liquidity preference coefficient increased to 0.25. Also assume that, in face of such change, banks decided to increase the ratio of desired reserves to 0.15.

(e1) If the central bank did not intervene, what would happen to domestic credit?

(e2) If the central bank, as a lender of last resort, decided to extend an emergency credit line to the banking system (e.g, LTRO) amounting to 4.8CL , would this be enough to avoid the contraction of domestic credit?


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f) (Capital constraints): Returning again to the initial situation, suppose that non-performing loans in this economy amounted 5, forcing banks to assume the corresponding losses.

f1) All else constant, describe the balance sheet of commercial banks after the write off. Does the banking system in this case satisfy the capital adequacy constraint?

f2) If nothing was done how much would banks like to reallocate out of credit into excess reserves, so as to satisfy the capital adequacy ratio? Would an open market operation avoid the contraction of domestic credit in this case?

f3) (Asset purchases) Now suppose the central bank bought assets from the banking system amounting to 32.5. Would this operation avoid the contraction of domestic credit? What about the excess liquidity in the banking system?

14.3. Consider the following initial situation in a given banking system: D=480; X=36; R=24; 60b

cL 240gbD , and 24b . Further assume that banks in this economy are

required to hold a minimum amount of capital, corresponding to 8% of the credit granted to the private sector, p

bL . Liquidity preference stands at x=X/D=7.5% and the ratio of

desired reserves by banks is rr =R/D=5%.

a) (Accountancy) Find out the amount of credit to the private sector, pbL , total money

supply, M, and the money multiplier in the initial situation.

b) (Refinancing operation) Suppose that the central bank increased the amount credit granted to commercial banks by 16,444 to 444.76b

cL . Would this policy translate

into an expansion of credit to the private sector? Why?

c) (Liquidity crisis) Returning to e), suppose that, due to a confidence crisis, both the liquidity preference ratio and the desired reserves ratio increased to 8%. If the central bank did not intervene, what would happen to domestic credit? How should the central bank intervene in this case? Quantify.

d) (Solvency crisis): Returning again to e), suppose that, in the sequence of a sovereign debt crisis, banks were forced to assume losses amounting to 5% of their holdings of government debt (5%*240=12). (h1) with all else constant, describe the balance sheet of commercial banks immediately after the write off; (h2) If nothing was done, how much credit would banks need to reallocate credit away from the private sector? (h3) In order to prevent this contraction, how should the central bank intervene? Quantify.

14.4. Consider the following initial situation in a given banking system: D=100; X=20; R=10; 30* CeB , and 0 bc . Further assume that in this economy the money

demand is given by PYM , where Y=120 denotes for the (constant) output level and that PPP holds, with 1* Pe .

a) How much will be the money supply, the monetary base, and domestic credit granted by commercial banks?

b) Find out the reserves ratio, the liquidity preference coefficient and the money multiplier.


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c) Assuming that the ratio of desired reserves and the liquidity preference coefficient were constant, what would be the impact on money supply of an open market operation increasing the central bank liabilities by 40?

d) Returning to the initial situation, assume that, due to a bank scare, citizens in this economy wanted to hold 1/2 of their money in the form of cash. Also assume that, in face of such change, banks decided to increase the amount of desired reserves to 20.

(d1) If the central bank did not intervene, what would happen to domestic

credit?

(d2) If the central bank, as a lender of last resort, decided to extend an emergency credit line to the banking system amounting to 40CL , would this

be enough to avoid the contraction in the money supply? What about domestic credit? Compute the new parameters of the money multiplier and explain.

(d3) If the central bank’ aim was to keep domestic credit unchanged relative to (a) and at the same time avoid the monetary expansion, what should it do?

e) (Bailout) Returning again to the initial situation, suppose that non-performing loans in this economy amounted to one third of the credit granted by commercial banks. What would be the monetary implications of rescuing the banking system using central bank’ money?

14.5. Consider a banking system where initially: 100 RLH bc , 900p

bL , 160gbD ,

and 60b . In this economy, the liquidity preference is zero (x= 0%). Further assume

that the minimum capital requirement was 8% of the credit granted to the private sector, and that no more government bonds were available to banks.

Find out: (a1) the total money supply, M; (a2) the money multiplier. (a3) If nothing was done, what should happen to the domestic credit? Explain. (a5) How would you expect government bond yields to evolve in this case? (a6) Which policy could the central bank use to avoid this scenario? Explain and quantify.

Documents

14. Money, credit and banks - SWEETsweet.ua.pt/afreitas/aulas/notas apoio/money multiplier.pdf · 2018-10-28 · Politicas macroeconomicas, handout, Miguel Lebre de Freitas ([email protected])