Money and bank multiplier formula. Banking multiplier: formula and impact on the stability of the monetary system

As stated in previous chapters, the definition of money and its components money supply do not have clear boundaries and clear justifications. This will create considerable difficulties in assessing the supply of money and monitoring its dynamics. Cash - banknotes and coins - are issued in modern conditions exclusively by the country's central bank. But this is only a small part of the assets that can function as highly liquid funds. Various types of bank deposits are added to cash. Then they come into action financial intermediaries, offering quasi-monetary substitutes that can compete with full-fledged money. And the list of participants monetary process is not closed! Since competition in financial sector for liquid resources is high, we can expect the emergence of more and more new, increasingly sophisticated financial products circulating alongside or even instead of traditional money.

But let's consider everything in order. What happens to the money supply after central bank printed a new batch of banknotes or coins?

The mechanism of formation of the money supply includes two theories that are in some ways competing, and in some ways complementary to each other:

• 1) the theory of the credit multiplier;
• 2) the theory of market equilibrium.

Credit multiplier theory

In any country there are simply banks and there is a central bank. Banks are simply private commercial entities in which we can store money and which can provide us with loans. The central bank is owned by the state. We cannot store money there, and the central bank does not give loans to the population. The central bank deals only with other banks.

The Central Bank has a monopoly on the issue of coins and banknotes. There was a time when commercial banks could issue their own banknotes. But then it turned out that it would be more correct to transfer money printing to the state. Unlike ordinary private bikes, the state is a more reliable partner. And although today no one exchanges banknotes for gold and silver, the power of the state continues to create and maintain the reputation of the national currency.

Coins and banknotes constitute the monetary base of the economy. The monetary base is measured at a specific date. Since coins and banknotes can be on this date both in the hands of people and in bank reserves, when determining the monetary base, its composition is often specified: cash in circulation, outside the banking system and bank reserves.

The monetary base is the "raw material" for the production of money, the very first and simplest supply of money.

How monetary base gets to people if the central bank does not directly deal with the population and does not scatter coins from the air?

The role of the banking system

After the central bank has released coins and banknotes into circulation, it is the turn of the banking system. The monetary base initially goes to commercial banks. Banks buy cash from central bank, exchanging the monetary base for securities the Central Bank itself or the government that they have. In addition, banks accept deposits from the public. Cash purchased from the central bank and deposits from the public allow banks to issue loans. Deposit and lending operations give banks the ability to create money.

People open bank accounts for enough long terms. If a person has deposited any amount on a deposit (bank account), then, on the one hand, the bank can dispose of this amount at its discretion. On the other hand, there is a certain probability that the next day this person will want to withdraw all his money from the bank. Therefore, the bank must have available money at any time, which will be issued to deposit holders if necessary. Cash in the bank is kept in the form of reserves. Since banks are not always prudent in allocating reserves, it is beneficial for banks to more money issue in the form of loans from which they receive their income ( bank interest), – the central bank legislates the mandatory reserve requirement.

Question to think about

In the US, banks are required to keep 3% of their deposits as reserves. In Japan this value is 1.3%. The Bank of Russia has set the mandatory reserve requirement at 5%. But in Canada and the UK there is no mandatory reserve requirement. How can we explain such different policies among central banks?

Passive and active operations of banks have great value for the economy as a whole. As a result of these operations, the supply of money in the country changes.

Let's see how banks create money.

Let, for example, there be three banks operating in the economy. The Central Bank issued 100 rubles. into circulation. This amount was paid to the employees, who deposited it in the first bank. With a mandatory reserve requirement of, say, 5%, the bank is obliged to allocate reserves of 5 rubles. The remaining amount is 95 rubles. will be issued in the form of loans to firms and the population. After the loan is used, for example, for the production of goods, the proceeds from the sale of goods are again deposited, now, for example, in a second bank. Let's assume that the amount of revenue is equal to the amount of the loan - 95 rubles.

When 95 rub. end up in the second bank, 4 rubles. 75 kop. (5% of 95 rubles) will remain as a mandatory reserve, and 90 rubles. 25 kopecks will be issued on credit again. If then the amount is 90 rubles. 25 kopecks goes to the third bank as a deposit, 4 rubles. 50 kopecks will go to the reserve, and 85 rubles. 75 kop. - into a new loan. Thus, deposits of firms and households are converted through banks into loans, and loans again into deposits (Fig. 5.5).

This process will continue until the loan amount is reduced to zero.

Rice. 5.5.

The total amount of money in the economy will be equal to the sum of all bank deposits:

Deposits constitute the money supply of an economy because buyers and sellers—individuals and firms—can use bank accounts as a means of payment and a store of value, which characterizes the main functions of money.

Compared to the monetary base of 100 rubles. aggregate supply money as a result of the activities of banks increased in our example by 20 times.

Monetary multiplier

The rate of increase in the supply of money relative to the monetary base is called monetary multiplier, since it shows the magnitude of the multiplicative effect of the multiplication of money when it enters the banking system through the processes of lending and depositing.

The multiplicative growth of the money supply is limited by two factors. The mandatory reserve requirement does not allow banks to lend out the entire amount of deposits. Some very cautious banks also prefer to hold a little more in reserves than is prescribed by the central bank. They have excess reserves, which also reduce the multiplier. In addition to reserves, part of the monetary base remains in the form of cash in the hands of the population and thereby also flows away from the multiplicative process of banks.

Given these restrictions, the value of the monetary multiplier μ is calculated as follows:

where is the value With shows the population’s tendency to keep money in cash (at home) rather than in the bank:

Where Si – cash outside the banking system; DD- the total amount of checkable deposits of the banking system, R – Bank reserves (obligatory and excess):

Question to think about

Can the monetary multiplier be less than one?

Factors influencing s are:

• institutional factors (method of remuneration - in the form of cash or deposits);
• tax rates for deposits;
• prevalence plastic cards and checkbooks in economics;
• interest rate on demand deposits;
• size of the shadow economy;
• degree of public confidence in the banking system.

The more common transfers are in the economy wages on deposits in a bank (for example, through the issuance of salary bank cards), the less the population is inclined to use cash, the larger the average amount will be stored within the banking system, the smaller the value will be With and the higher the multiplier value will be.

When the government introduces or increases tax rates on deposit income, the population tends to withdraw money from banks. Magnitude With shrinks, the multiplier decreases. But the abolition of taxes on deposits and growth interest rates on deposits, especially on demand deposits, leads to a decrease With and increasing the multiplier.

The more common payments are using plastic cards or check books, the less cash is required, the more willing the population is to keep money in the bank, the smaller the amount will be With and larger – the magnitude of the multiplier.

The presence of a shadow economy stimulates the circulation of money outside the banking system, since bank transactions easy to track, and shady companies do not like control. Therefore, the more the shadow sector is represented in the economy, the higher the demand for cash will be, the less the need for bank deposits, greater value With and a smaller multiplier.

The greater the confidence of households and firms in their banking system, the more willing economic agents put funds in banks and leave them there for long periods, the lower the value will be With and more an animator.

Problem illustrating the theory

Let the required reserve ratio in a given banking system be set at 20%. Currently the bank does not have excess reserves. Now suppose that Mrs. Ilyinskaya deposits 100 rubles. to your current account with this bank.

A. Without resorting to mathematical formulas, explain why this action (placing money in a bank) can lead to an increase in the money supply by more than 100 rubles.

Answer

The supply of money includes not only cash, but also deposits poste restante. That is, the money in Mrs. Ilyinskaya’s account (100 rubles) will also be taken into account in the supply of money, since she can use it in the same way as if she had it in the form of cash. But, besides this, having received Ms. Ilyinskaya’s contribution at her disposal and setting aside 20 rubles. Of these, the bank will issue the remaining 80 rubles to the required reserve. as a loan to another person or company. These 80 rubles. will be taken into account in calculating the supply of money either as cash (if this individual decides to make his feasible contribution to the shadow economy or decides to keep banknotes in his wallet) or will be taken into account further down the chain as a deposit of a second citizen in next bank etc.

B. Discuss two limitations of this process.

Answer

First, a decrease in the nominal interest rate reduces profitability and increases the liquidity of money. This may discourage individuals from using bank deposits, the banking system as a whole will become less efficient.

Secondly, a general economic downturn may prompt banks to create excess reserves beyond the required 20%. This will also cause the process to stop much earlier than theoretically intended. *1*1

However, banks offer customers not only current deposits, which function as good substitutes for cash, but also time deposits, which to a lesser extent can perform the functions of money. The more time deposits are represented in the banking system, the smaller the magnitude of the multiplier effect.

To account for the additional impact time deposits on the process of money creation, you can use another, more complex, formula for the monetary multiplier:

where c is the ratio of cash to deposits; t – ratio of time deposits to current deposits; R.R. – mandatory reservation norm; ER – the rate of excess reserves of banks.

The total increase in the money supply after the central bank increased the monetary base will be

where Δ M S – change in money supply; Δ Μ 0 – change in the monetary base; μ – multiplier value.

Thanks to the action of the multiplier, the influence of the central bank on the supply of money - both upward and downward - is significant. The central bank only needs to slightly change the initial amount of cash - and the result will be significant. This multiplicative dependence forces the central bank to take a responsible and serious approach to monetary regulation of the economy.

• The geometric progression formula is used here.

Given the existence of two levels of the banking system, the emission mechanism operates on the basis of the money multiplier. Money multiplier is the process of increasing (multiplying) money in the accounts of commercial banks during the period of their movement from one commercial bank to another.

The money multiplier mechanism can only exist in conditions of two-level (or more) banking systems, with the first level - the central bank managing the mechanism, the second level - commercial bank forces him to act. In order to reveal the mechanism of action of the money multiplier, it is necessary to find out how banks create money.

Suppose that in a conditional country A an entrepreneur has 1000 rubles. cash that is temporarily available. He decides to deposit them in one of the commercial banks where he has an account (let's call it Bank 1).

This operation will be reflected in the balance sheet of Bank 1 as follows:

Money is not stored in a bank like in a safe. He needs them to provide loans to those who need them. The bank does not store money, but provides accounting for it. The main function of the bank is to provide loans to industry. Based on your commercial interests Bank 1 will strive to use the money received - to issue a loan to another borrower based on its capabilities. However, he can only use part of the money received, since he is obliged to transfer a certain amount to reserve fund the country's central bank. Let's assume that in our example there is only one type of deposit, for which the reserve rate is 20%. This means that, having received 1000 rubles. cash, the bank is obliged 200 rubles. transfer to the reserve fund, and 800 rubles. can be issued in the form of a loan to someone who currently needs funds.

Balance Can 1 after these operations it will look like:

Thus, as a result of this operation, Bank 1 created an additional 800 rubles, which will be added to the original amount of cash - 1000 rubles, and the total money supply in the economic system is now (1000 + 800) rubles.

Borrower received money Can 1 put it in his commercial bank, let's call it - Bank 2. Similar transactions on reserves and loans in the balance sheet of Bank 2 will be reflected as follows:

So, an additional 640 rubles have been created. and the money supply in the system will be: (1000 + 800 + 640) rub. If a loan of 640 rubles issued Bank 2, is invested in the next bank, which gives 20% to the reserve, and 80% again lends out, then the amount of money in the economy will increase by another 512 rubles. Ultimately, deposits can theoretically increase by 1/y times compared to the amount of cash initially entering the banking system:

Where r– the norm of bank reserves.

Coefficient 1/ r received the name in the theory of monetary circulation money multiplier, and the amount of cash initially entering the banking system is base money or monetary base.

Money multiplier (T) – a coefficient that serves as a measure of the increase in the money supply as a result of non-cash issue (bank issue). It shows how many times the money supply is greater than the amount of cash in the banking system.

Monetary base (H) – an independent component of the money supply that characterizes the amount cash entered into the system of commercial banks.

Offer money in modern world determined, as a rule, by the amount of non-cash issue. The size of this issue depends not only on the size of the monetary base, but also on the level of development and operating conditions of commercial banks, i.e. on the ability of the banking system to expand the funds entering it. An indicator characterizing this ability of the banking system is the money multiplier. Statistical study of this indicator, i.e. calculating the level, identifying the factors of its change and determining the degree of their influence is the most important task of monetary circulation statistics.

Money multiplier shows how many times the total number of deposits in the banking system is greater than the amount of base money initially received into the system, and is equal to:

,

where m is the money multiplier;

M – money supply;

N – monetary base.

At the same time, in accordance with economic theory, the multiplier is the reciprocal of the reserve rate:

,

those. it can be determined based on the value of the reservation norm.

Depending on the method of calculating the money supply, the monetary base and the reserve ratio, there are several approaches to calculating the value of the money multiplier, each of which reflects different aspects of the multiplier effect and makes it possible to study the factors influencing its dynamics.

If we take aggregate M2 as the value of the money supply, then

.

We obtain the actual value of the multiplier, which characterizes the general operating conditions monetary system: the development of the banking and credit systems, reserve conditions established by the central bank and the system for monitoring their implementation, the structure of the money supply and, above all, the share of cash and its circulation system.

Another approach to calculating the multiplier, based on the fact that it is the reciprocal of the reserve rate, allows us to calculate the upper limit of its change.

In the Republic of Belarus, a system of minimum required reserves was introduced with the formation of the National Bank. In accordance with this system, the National Bank of the Republic of Belarus establishes a certain minimum percentage of the deposit amount, which fixes the amount of funds required to be kept by each bank in the form of cash in the National Bank of the Republic of Belarus, i.e.

Reserves = r  Deposits.

If the reserve rate is 20%, this means that a commercial bank with current liabilities in the amount of 1 million rubles must have a reserve in the amount of 200 thousand rubles in the National Bank of the Republic of Belarus. If next month its current liabilities increase to 2 million rubles, then the commercial bank must increase its reserve to 400 thousand rubles.

In reality, there is no single reservation standard. The reserve ratio has different meanings for deposits that differ in terms of terms, volumes and types of funds raised. For example, the differences may be:

on demand accounts and term obligations of a commercial bank up to 30 days – 20%;

for term obligations over 30 days to 90 days – 14%;

for urgent obligations over 90 days – 10%;

for funds in accounts in foreign currency – 1.5%.

The reserve ratio can be calculated as the ratio of the amount of reserves of the National Bank of the Republic of Belarus to the amount of deposits of the banking system:

.

The value of the money multiplier, as identically equal to its inverse, is equal to:

.

In this case, the multiplier characterizes the actual capabilities of commercial banks to expand the volume of credit investments in the economy.

In addition to these differences, the value of the reserve norm for certain types of deposits may change during the period depending on the tasks being solved within the framework of the state’s monetary policy.

Thus, the National Bank of the Republic of Belarus, managing the money multiplier mechanism, expands or narrows the issuing capabilities of commercial banks, thereby fulfilling one of its functions - the function of monetary regulation.

A bank multiplier (from the Latin multiplicator - multiplying) is the process of increasing money in the deposit accounts of a commercial bank as it moves from one banking institution to another.
Banking animation is the process of multiple increase (decrease) of money as permanent deposits in commercial banks as a result of an increase (decrease) in bank reserves when carrying out operations within the banking system.
Both expansion and contraction of the money supply can be multiplicative. In the economic literature, more attention is paid to the processes of increasing money, since the stability of the monetary system and the level of inflation largely depend on this.

Money multiplier

The growth of the money supply is facilitated by the money multiplier that arises with the development of the credit system.

Money multiplier is a numerical coefficient showing how many times the money supply will increase or decrease as a result of an increase or decrease in deposits monetary system per one monetary unit.

The essence of the money multiplier is that the money supply in circulation increases as a result of the expansion of banks' lending operations by receiving funds from the Central Bank reserve, formed from mandatory contributions from banks.

The multiplication coefficient is calculated for a certain period of time, usually a year, and characterizes how much the money supply in circulation will increase over this period. By managing the money multiplier, the Central Bank implements monetary regulation in the country and expands or contracts the issuing capabilities of commercial banks.

Banking multiplier mechanism

The bank multiplier mechanism can be activated if bank loans, as well as when the central bank buys securities or currency from commercial banks. As a result of this, the resources of banks invested in active operations decrease and the free reserves of these banks used for credit operations. Thus, the banking animation mechanism is activated.

Similarly, if the Central Bank reduces the rate of deductions of required reserves. In this case, the free reserve of commercial banks also increases, which leads to an increase in lending and the inclusion of a bank multiplier.
Consequently, managing the banking multiplier mechanism is the task of the Central Bank. Commercial banks issue money. The issuing capabilities of commercial banks are regulated by the Central Bank by expanding or contracting these capabilities. This is how the Central Bank performs its monetary regulation function.

Deposit and credit multiplier

Based on the fact that banking animation is a combination of the processes of deposit and credit expansion, in the economic literature it is called deposit-credit.
Credit multiplier represents the ratio of the change in bank deposit liabilities caused by the expansion of credit to the initial increase in reserve assets
Deposit multiplier reflects the animation object, i.e. money in deposit accounts of commercial banks, which increase through the process of multiplication.
These processes cannot exist in isolation; they are connected by the common nature of money: Central Bank funds in the reserve account and CB funds in client deposit accounts. The money in the reserve account represents the liabilities of the Central Bank and at the same time the assets of the commercial bank.
Moreover, among all active operations Bank only credit investments create new deposits, thus performing the issuing function of the country's banking system. The greater the share of loans in assets, the greater the volume of issuing activity.

How does the bank multiplier work?

The banking animation mechanism can only work within the framework of a two-tier banking system: the central bank (first level) controls this mechanism, commercial banks (second level) force it to operate automatically, regardless of the wishes of the heads of individual banks.
One bank cannot multiply money; this requires a system of commercial banks. If the norm of mandatory minimum reserves of the central bank decreases, commercial banks' free reserves will increase, which will lead to an increase in lending volumes and the inclusion of a banking multiplication mechanism.

This is a preliminary encyclopedic article on this topic. You can contribute to the development of the project by improving and expanding the text of the publication in accordance with the rules of the project. You can find the user manual

The effect of the banking multiplier consists in the automatic expansion of the emission process, which is carried out by multiple multiplication of new reserves formed in the banking system

Bank multiplier is the process of multiplying funds in deposit accounts of commercial banks during the period of their movement. from one bank to another

This mechanism can only exist in a two-tier banking system.

The value of the regulatory banking multiplier is determined by the formula:

where m is the bank multiplier;

N is the norm of mandatory reservation.

The bank multiplier (normative) shows the maximum number of new means of payment that each monetary unit of excess reserves can create for a given value of the required reserve ratio

The regulatory multiplier characterizes the maximum (theoretical) capabilities of the banking system to increase means of payment in circulation through credit expansion.

Since the animation process is continuous, the multiplication coefficient is calculated for a certain period (per year).

Let's consider the effect of the banking multiplier using a conditional example, with a reserve ratio of 10%.

In our example: t = 1\0.1=10 (times)

This means that each unit of excess reserves can create 10 units of new means of payment (credit money) for a given required reserve ratio (10%).

Maximum number of new means of payment that can be created banking system based on this amount of excess reserve is determined by the formula:

∆ M = m * E

where ∆ M - maximum amount new means of payment;

t - standard multiplier;

E is the amount of excess reserves received by the banking system.

This formula determines the multiplier effect in real monetary terms.

In our example: ∆M = 10x9 = 90.0 thousand UAH.

For clarity, let us present the mechanism of action of the bank multiplier in the form of Table 3.2.

Table 3.2

	Action	bank multiplier Thousand UAH
Banks	Reserves received (new deposits)	Mandatory (regulatory) reserve	Excess reserve	Newly created means of payment
Other banks together
Total for the banking system as a whole

The table shows that the excess reserves that an individual bank loses when making appropriate investments are not lost by the banking system as a whole. In addition, the banking system repeatedly (in our example, 10 times) increases deposit resources from 10 thousand hryvnia to 100 thousand hryvnia. Based on the 9 thousand hryvnia of excess reserves received by the banking system, the commercial banking system as a whole is able to provide a loan of 90 thousand hryvnia.

At the same time, there is an endless transfer of deposits from one bank to another, but each time the resource of individual banks is reduced.

The actual money multiplier is the ratio of the money supply (money supply) to the monetary base and reflects the practical implementation of the capabilities of the banking system to multiply expand the money supply

The actual value money multiplier determined by the formula:

m =Ms\(M1, M2, MZ)\B

where Ms is the supply of money, measured by aggregates M1, M2, MZ;

B is the monetary base.

Then, money offer can be reflected in the following form:

Ms = m" x B

The monetary base can be defined as the sum of the following components: where R - reserves (required + excess); MO - cash. The money supply can be defined as the sum of the following components:

Ms(M1) = MO +D,

where MO is cash; B - demand deposits.

Based on their presented dependencies, the value of the actual money multiplier can be determined by the formula:

m’= MO +D\ M0 + R

Divide the numerator and denominator of the equation term by term onABOUT:

where Kd is the deposit ratio, which is determined by the ratio of cash to deposits. The value of Kd is determined mainly by the behavior of physical and legal entities, deciding in what proportion MO and B will be located.

Kr is the coefficient (norm) of effective reservation, which is determined by the ratio of reserves to deposits. The value of the coefficient depends on the norm of required reserves established by the Central Bank and on the norm (value) of excess reserves that commercial banks create in excess of the required amount.

The money supply model is as follows:

Thus, the supply of money directly depends on the size of the monetary base and the monetary multiplier (monetary base multiplier), which shows how the supply of money will change when B increases by one.

An increase in the capital reserve ratio and the required reserve ratio reduces the money multiplier.

The process of ische-nii obsia money supply

I stage : initial modification of the monetary base by changing the obligations of the Central Bank to the banking system, individuals and legal entities (impact on the amount of reserves and the amount of cash)

II stage: subsequent change in the money supply through the multiplication process in the commercial banking system

The central bank can control the money supply primarily by influencing the monetary base. Changes in the monetary base, in turn, have a multiplier effect on the money supply.

Monetary policy instruments adjust the money supply (money supply), affecting either B or m'.