In this article I’m going to propose a visual interpretation with Python of the so-called deposits multiplier. The latter is a macroeconomics indicator which describes how an initial deposit leads to a greater final increase in the total money supply.

To fully understand how it works, we have to consider three actors in the market: Central Bank, Commercial Banks and Households. The idea is that there is a so-called monetary base, which is formed by either currency or reserves held from commercial banks, which represent their assets, while from the Central Bank’s point of view those are liabilities.

On the other hand, commercial banks give loans to households, whose balance-sheet look like so:

As you can see, from a consumer’s point of view, deposits are an asset (something remunerative, which guarantees a positive rate).

Since commercial banks are nothing but societies, and as such they aim at getting a profit at the end of the year which could either remunerate shareholders or being reinvested in the society itself, they can’t simply keep the liquidity deriving from the deposit in their moneybox.

On the contrary, the aim is reinvesting this liquidity into more profitable assets: indeed, they rely on the fact that, once deposited a certain amount of money, the client will not use the entire amount immediately, hence banks will be free to invest this liquidity, with the only constraint of keeping an ’emergency fund’. The latter is determined by the reserve ratio, which is the portion of reservable liabilities that commercial banks must hold onto, rather than lend out or invest. This is a requirement determined by the country’s central bank, and in this article we will assume it to be equal to 20%.

Now imagine the following scenario with two banks A and B. Bank A has 100 deposits, 20 of which secured in its reserve. The remaining 80 is given as a loan to bank B. From bank B’s point of view, that loan is a deposit, hence a liability. As such, B will be forced to secure 16 in its moneybox, while for the remaining 64 it decides to give a loan to a third bank, let’s say bank C. The process could keep going for many banks, and at the end we will have a total amount of deposits which is far greater than the real monetary base, which did not change at all from the initial 100.

To give you an idea, this is what happens in commercial banks’ balance-sheet after a loan:

While central banks’ balance-sheet remains the same:

Of course, in the reality of market, commercial banks do not transfer all the 80% of their deposit solely to other commercial banks: they also perform loans to households, which is pivotal for guaranteeing demand for goods and services. However, that money which we spend everyday via our credit cards do not always have a ‘physical’ counterpart: they might simply arises from the deposits multiplier.

Let’s now consider 11 banks in a scenario where each bank of the list will lend the available 80% of its deposit to the successor of the list:

import numpy as np
deposits.clear()
deposits=[]
deposits.append(100)
for i in range(1,11):
    deposits.append(0.8*deposits[i-1])

loans=deposits[1:12]
reserves=np.asarray(deposits[0:10])-np.asarray(loans)
reserves=reserves.tolist()
loans.append('-')
reserves.append('-')
banks=['A','B','C','D','E','F','G','H','I','J','K']
data_tuples = list(zip(banks,deposits,loans,reserves))
df=pd.DataFrame(data_tuples, columns=['Bank','Deposits','Lent Out','Reserves'])

df.set_index('Bank', inplace=True)

df

As you can see, each bank is lending 80% of the deposits received from the previous bank, securing only 20% of it. As a result, the money supply increases more and more, without a real counterpart, which is the monetary base and it is still at the 100 initial level. Let’s visualize it:

import matplotlib.pyplot as plt



x = np.arange(len(banks))  # the label locations
width = 0.35

fig, ax = plt.subplots()
rects1 = ax.bar(x - width/2, monetary_base, width, label='Monetary Base')
rects2 = ax.bar(x + width/2, increasing_deposits, width, label='Deposits')

ax.set_ylabel('Euros')
ax.set_title('Deposit Multiplier')
ax.set_xticks(x)
ax.legend()

plt.show()

Now let’s see what happens in the balance-sheets of the first three banks after a loan. To simplify, imagine that bank A starts from an initial situation of 100 deposits (let’s see, from the central bank), and it has already secured 20 of them as reserve. The other banks exhibit an empty balance-sheet until they receive deposits from the previous bank (namely, bank B will have only the deposits received from bank A):

Again, keep in mind that the real, consistent amount of money is still 100, even though the amount of deposits is higher.

As anticipated, the monetary multiplier guarantees a virtuous cycle in the economics, since allows households to get loans in order to make purchases, hence it keeps the demand high. Nevertheless, the other side of the coin is the possibility that banks will receive, simultaneously and for great amount, the request of withdrawing deposits, which is perfectly legit since there is full availability for the client in a deposit contract. Well, in that case, since banks have kept only the 20% of those deposits, they won’t be able to repay all the deposits, with the result of spreading negative feelings about banks and letting even more people decide to withdraw.

This phenomenon is called ‘bank run’ and, in the history of financial markets, there was more than one episode like that (just think about the 1929 financial crisis). That’s why there is plenty of debates and innovations concerning the robustness of banks’ balance-sheet, ranging from the amount of legal reserve to the kind of assets in which deposits should be invested.

Published by valentinaalto

I'm a 22-years-old student based in Milan, passionate about everything related to Statistics, Data Science and Machine Learning. I'm eager to learn new concepts and techniques as well as share them with whoever is interested in the topic.

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