Central Bank Money and Commercial Bank Money

Two Kinds of Money in One System

A person may keep some spending money as notes and coins and the rest in a checking account. Both can be used to make payments, but they are not the same kind of claim. The currency is issued by the central bank, while the deposit is a liability of the commercial bank that holds the account. This issuer distinction explains how central bank money and commercial bank money coexist.

The distinction matters when classifying monetary quantities. A bank’s reserve balance is central bank money, but it is not a deposit held by a household or business. Conversely, a customer’s account balance is commercial bank money, not a reserve balance. A sound calculation identifies the holder and issuer of each item before adding it to an aggregate. This topic is aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus.

Definition: In the conventional system used here, central bank money consists of currency held by the public, currency held in commercial banks’ vaults, and eligible institutions’ balances in accounts at the central bank. Commercial bank money consists principally of deposit claims that customers hold against commercial banks. Currency is a liability of the central bank; a customer deposit is a liability of the commercial bank that records the account.

The exact institutions eligible to hold central bank accounts, and the precise instruments included in official monetary statistics, vary across systems and measures. The definitions here provide a consistent framework for classifying the standard forms. They do not imply that every country uses identical monetary aggregates.

Components and Notation

Let $C$ denote currency held by the public. Let $R$ denote reserves held by commercial banks, defined here to include both their vault currency and their balances at the central bank. The monetary base in this simplified framework is the sum of public currency and reserves:

R = \text{vault currency} + \text{central bank balances}

$$ B = C + R $$

The components in $B$ are all central bank money. The definition of $R$ is important: vault currency is included in reserves for this calculation, even though it is physically held at a commercial bank. It remains currency issued by the central bank. By contrast, let $D$ represent deposits held by the nonbank public at commercial banks. Those deposits are commercial bank money, not part of $B$.

A simplified monetary aggregate might be defined as $M=C+D$, counting currency held by the public and selected customer deposits. This is an illustrative definition, not a universal formula for every country’s money stock. The relevant aggregate depends on its stated operational definition. In particular, bank reserves are not included in this $M$ because they are held by banks, not by the nonbank public.

Worked Example: Classifying the System’s Money

A hypothetical banking system has $460 of currency held by the public, $35 of currency in bank vaults, $105 of commercial-bank balances at the central bank, and $1,200 of customer deposits. For this question, define the monetary base as $B=C+R$ and the simplified public money measure as $M=C+D$. Find $R$, $B$, and $M$, and explain which items are commercial bank money.

Method. First group items by holder and issuer. The public currency is $C=460$. Reserves include vault currency and central bank balances, so:

$$ R = 35 + 105 = 140 $$

The monetary base is:

$$ B = C + R = 460 + 140 = 600 $$

The customer deposits are $D=1{,}200$. Under the specified definition:

$$ M = C + D = 460 + 1{,}200 = 1{,}660 $$

The $1,200 in customer deposits is commercial bank money. The $600 monetary base consists of $460 public currency and $140 in reserves; it is central bank money. The $35 of vault currency is included in $R$, not added a second time after $R$ has been calculated. Check: $R$ reconciles to $35+105=140$, and $M$ includes only public currency and customer deposits. The common mistake is to add the $35 of vault cash to $B$ again after calculating $R$, which would incorrectly give $635.

Why the Two Forms Are Different Claims

A deposit balance may be readily usable for payments, but its immediate usability does not change who owes it. The customer’s deposit is a claim on the commercial bank. The bank, in turn, may hold central bank balances and vault currency as part of its reserves. These reserves are claims on, or currency issued by, the central bank. The two forms of money therefore have different issuers and holders, even though they coexist in the same system.

The classification can be justified by sorting non-overlapping categories rather than by treating every payment-capable item as the same kind of money. Under the conventions above, the central bank money held across the public and commercial banks consists of public currency, vault currency, and central bank account balances. The latter two items form $R$, so grouping the categories gives $B=C+R$. A customer deposit is not in any of those three categories; it is a separate commercial-bank liability. If the chosen public money measure includes those deposits, they enter as $D$ alongside $C$, not as part of $R$.

\underbrace{C+\text{vault currency}+\text{central bank balances}}_{\text{central bank money }B} \qquad \underbrace{D}_{\text{commercial bank money}}

This distinction also clarifies why the two totals need not move together. A change in customers’ deposit balances does not, by itself, tell us the amount of central bank money. Likewise, a change in how much currency banks hold in their vaults can alter the composition of reserves without changing the total monetary base. The circumstances causing a particular change depend on the transaction; classification alone is not a complete account of bank operations.

Worked Example: A Customer Withdraws Cash

In a hypothetical system, the public holds $640 of currency. Banks hold $260 in vault currency and $90 in central bank balances. Customer deposits are $1,750. A customer withdraws $180 from an account, and assume the bank pays the full amount from its vault. Find the before-and-after monetary base and simplified public money measure $M=C+D$. Assume no other quantities change.

Method. A withdrawal transfers currency from the bank’s vault to the public and reduces the customer’s deposit by the same amount. Before the withdrawal:

R_{\text{before}}=260+90=350

B_{\text{before}}=640+350=990

M_{\text{before}}=640+1{,}750=2{,}390

After the withdrawal, public currency increases by $180, so $C=640+180=820$. Vault currency decreases by $180, so it is $260-180=80$. The central bank balance remains $90. Therefore:

R_{\text{after}}=80+90=170

B_{\text{after}}=820+170=990

Deposits fall to $1{,}750-180=1{,}570$, giving:

M_{\text{after}}=820+1{,}570=2{,}390

The monetary base and the specified public money measure are unchanged, but their components have shifted. Public currency is up $180, vault currency is down $180, and deposits are down $180. Check: the bank has enough vault currency to pay the withdrawal because $260 exceeds $180, leaving $80. A common mistake is to increase public currency while leaving vault currency unchanged; that would count the same $180 of notes and coins in two places.

Classifying Amounts Without Double-Counting

When several monetary figures appear together, first ask who holds the item? Then ask who issued it? The holder helps distinguish public currency and customer deposits from bank reserves; the issuer distinguishes central bank liabilities from commercial bank liabilities. Only after those questions are answered should the items be placed into a specified measure.

Identify the holder.
Separate currency held by households and businesses from currency held in bank vaults. Identify any central bank account balances held by eligible institutions.

Identify the issuer.
Currency and qualifying central bank balances are central bank money. A customer’s deposit account is a claim on a commercial bank.

Apply the stated aggregate definition.
For $B=C+R$, combine public currency with reserves, where reserves include vault currency and central bank balances. Add customer deposits only if the specified measure calls for them.

This procedure prevents a frequent double-counting error. If a problem supplies a total for $R$, do not add its vault-currency component again. If it supplies separate amounts for vault currency and central bank balances, first add those to obtain $R$. Similarly, do not count a bank’s reserve balance as though it were a household deposit merely because both are recorded as account balances.

Worked Example: Separating Public Money From Bank Reserves

A hypothetical system has public currency of $200. Bank A has $450 of customer deposits and Bank B has $350 of customer deposits. Across the banking system, vault currency is $20 and balances at the central bank are $80. Calculate the monetary base $B=C+R$ and the simplified public money measure $M=C+D$, where $D$ includes both banks’ customer deposits. How much larger is $M$ than $B$?

Method. Combine customer deposits because both are held by the nonbank public:

$$ D=450+350=800 $$

Calculate reserves from their two specified components:

$$ R=20+80=100 $$

Then the monetary base is:

$$ B=C+R=200+100=300 $$

The specified public money measure is:

$$ M=C+D=200+800=1{,}000 $$

The difference is $1{,}000-300=700$. This difference is not the deposits total of $800 because public currency of $200 appears in both measures, while the base also includes $100 of reserves. Equivalently, $M-B=(C+D)-(C+R)=D-R=800-100=700$. Check: both ways of calculating the difference give $700. The common mistake is to add all deposits, vault cash, and central bank balances to public currency, then call the result either $B$ or $M$; that mixes the definitions and counts items not included in either specified measure.

Common Mistakes and Why the Distinction Matters

Leaving vault currency out of central bank money. In this framework, vault currency is included in $R$, along with banks’ central bank balances. It is central bank-issued currency held by a bank.
Treating customer deposits as central bank liabilities. A deposit is a claim on the commercial bank that holds the account. It is not a central bank reserve balance.
Counting reserves as public deposits. Reserves are held by banks or other eligible institutions, while $D$ in the examples denotes customer deposits held by the nonbank public.
Assuming every money measure is defined identically. Always use the operational definition supplied. A measure may include some deposits and exclude others; the labels alone do not determine its components.
Adding a component twice. If vault currency is already included in a stated reserve total, it must not be added again when calculating $B$.

The distinction is useful because it separates the central bank’s money from the deposit claims commercial banks provide to their customers. Both can be used within a monetary system, but they are not interchangeable entries in every calculation: their issuers, holders, and treatment in a monetary aggregate differ. Being precise about those categories is the foundation for understanding later questions about banking and monetary policy.

Key takeaway: In the framework used here, central bank money includes public currency and reserves, with reserves comprising vault currency plus central bank balances. Commercial bank deposits are a separate form of money issued by commercial banks. Classify by issuer and holder, then apply the stated aggregate definition.

Check Your Understanding

For each problem, use the definitions given in its statement and keep public currency, reserves, and customer deposits distinct.

A system has public currency of $520, vault currency of $30, central bank balances of $150, and customer deposits of $980. Find $R$, $B=C+R$, and $M=C+D$. (Answer: $R=\$180$, $B=\$700$, and $M=\$1{,}500$.)
Initially, public currency is $640, vault currency is $260, central bank balances are $90, and customer deposits are $1,750. A customer withdraws $180 in cash directly from a bank’s vault. Find $B$ and $M=C+D$ after the withdrawal, assuming nothing else changes. (Answer: $B=\$990$ and $M=\$2{,}390$.)
Public currency is $360, vault currency is $15, central bank balances are $125, and customer deposits are $840. Find $B$, $M=C+D$, and the amount by which $M$ exceeds $B$. (Answer: $B=\$500$, $M=\$1{,}200$, and $M-B=\$700$.)
A customer deposits $60 of cash into a commercial bank account. Assume the bank retains all $60 as vault currency and no other amount changes. If public currency was $500, vault currency $40, central bank balances $110, and customer deposits $900 before the transaction, find $B$ and $M=C+D$ before and after. (Answer: $B=\$650$ both before and after; $M=\$1{,}400$ both before and after.)
A system reports $C=\$250$, vault currency of $45, central bank balances of $155, and customer deposits of $1,050. A student calculates the base as $450 by adding public currency, vault currency, and central bank balances, then separately adds customer deposits to obtain $M$. Identify the error and calculate the correct $B$ and $M=C+D$. (Answer: The stated base calculation is correct, but deposits must not be added to the base; $B=\$450$ and $M=\$1{,}300$.)

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