Week 15 Ch. 13: The Federal Reserve System

Determining Reserve Deficiency

Introduction

• Concept of determining whether a bank is reserve deficient, meaning it holds reserves below the level mandated by the central bank.

• Importance of required reserves in this determination, which are a fraction of specific deposit liabilities that commercial banks must hold as vault cash or deposits at the central bank. This is crucial for maintaining the stability of the banking system and controlling the money supply.

Required Reserves

• Formula: $\text{Required Reserves} (RR) = r \times \text{Checkable Deposits}$
  Where:

  • r: The required reserve ratio, a percentage set by the central bank (e.g., the Federal Reserve in the U.S.). This ratio dictates what portion of a bank's checkable deposits must be held in reserve and cannot be loaned out.

  • Checkable Deposits: Total deposits that are immediately available for withdrawal by customers, such as demand deposits and checking accounts, which are subject to reserve requirements.

Example Calculation

• If $r = 10\%$ (or $\frac{1}{10}$)

  • Checkable Deposits = $10,000,000$

  • Required Reserves = $0.10 \times 10,000,000 = 1,000,000$

  • Interpretation: The bank must hold $1,000,000$ in vault cash or at the central bank to meet its reserve requirement for the given deposit level.

• Different Scenario:

  • If $r = 8\%$ and Checkable Deposits are $9,000,000$

  • Required Reserves = $0.08 \times 9,000,000 = 720,000$

  • Interpretation: A lower reserve ratio or deposit level results in lower required reserves.

• Another Scenario:

  • If $r = 11\%$ and Checkable Deposits are $20,000,000$

  • Required Reserves = $0.11 \times 20,000,000 = 2,200,000$

  • Interpretation: A higher reserve ratio or deposit level increases the amount of required reserves.

Example Scenario

• Checkable Deposits = $40,000,000$, $r = 10\%$

• Required Reserves = $0.10 \times 40,000,000 = 4,000,000$

• If the bank holds reserves of $4,000,000$, its excess reserves =

  • Excess Reserves = $\text{Reserves} - \text{Required Reserves} = 4,000,000 - 4,000,000 = 0$

  • The bank is not reserve deficient; it holds precisely the amount of reserves required by regulation. Excess reserves are the reserves held by a bank over and above the legal requirement.

Impact of Withdrawals

• Assuming a withdrawal of $3,000,000$ decreases Checkable Deposits from $40,000,000$ to $37,000,000$. This withdrawal directly reduces both the bank's total deposits and its actual reserves by the same amount.

• Required Reserves post-withdrawal:

  • Required Reserves = $0.10 \times 37,000,000 = 3,700,000$. The required amount of reserves changes because the base (checkable deposits) has decreased.

• How much reserves does the bank have after the withdrawal?

  • Previous reserves were $4,000,000$, but the $3,000,000$ withdrawal paid out from the bank's reserves (either vault cash or its account at the central bank). So, actual reserves now equal $4,000,000 - 3,000,000 = 1,000,000$.

• Question: Is the bank reserve deficient?

  • The bank requires $3,700,000$ in reserves but it only holds $1,000,000$. Therefore, the bank is reserve deficient by $2,700,000$ ($3,700,000 - 1,000,000$). Being reserve deficient requires the bank to take action, such as borrowing from other banks (in the federal funds market), borrowing from the central bank (through the discount window), or selling some of its assets to acquire the necessary reserves.

Another Calculation Example

• If $r = 10\%$ and Checkable Deposits = $50,000,000$, Required Reserves = $0.10 \times 50,000,000 = 5,000,000$.

• Bank holding $10,000,000$ in reserves indicates it is compliant because it holds $5,000,000$ in excess reserves ($10,000,000 - 5,000,000$). This excess can be loaned out.

• New Withdrawal: $5,000,000$, decreasing Checkable Deposits to $45,000,000$. (Original checkable deposits were $50,000,000$. After withdrawal, they are $45,000,000$).

• Required Reserves for the new deposit level: $0.10 \times 45,000,000 = 4,500,000$.

• Remaining Reserves after withdrawal: The bank's actual reserves decrease by the withdrawal amount. Previously $10,000,000$, now $10,000,000 - 5,000,000 = 5,000,000$. Comparing actual reserves ($5,000,000$) to required reserves ($4,500,000$), the bank still has $500,000$ in excess reserves, showing it is not reserve deficient.

Open Market Operations

Open Market Operations (OMOs) are the primary tool used by central banks to implement monetary policy, influencing the money supply and interest rates by buying or selling government securities.

Types of Open Market Operations

• Open Market Purchase

  • The central bank (e.g., the Fed) purchases government securities (like Treasury bonds) from banks or the public. When the Fed buys securities from a bank, it pays for them by crediting the bank's reserve account at the Fed.

  • Example: Fed buys $10,000,000$ in securities from Bank X.

  • Effect: Increases the reserves of the bank that sold the securities. This injects new reserves into the banking system, increasing the monetary base and potentially expanding the money supply through lending.

• Open Market Sale

  • The central bank sells government securities to banks or the public. When a bank buys securities from the Fed, it pays for them by having its reserve account at the Fed debited.

  • Example: Bank Y pays $10,000,000$ to acquire securities from the Fed.

  • Effect: Decreases the reserves of the bank that buys the securities. This drains reserves from the banking system, reducing the monetary base and potentially contracting the money supply.

Mechanics of Open Market Operations

1. Open Market Purchase

   • Bank sells securities to the Fed for $10,000,000$. This is reflected in the bank's balance sheet: Securities (asset) decrease, and Reserves (asset) increase by $10,000,000$.

   • Increase in reserves:

     • If a bank initially had deposits at the Fed (which count as reserves) of $40,000,000$, after selling securities, its deposits at the Fed increase to $50,000,000$. Assuming vault cash remains constant, this results in an increase in total reserves held by the bank.

2. Open Market Sale

   • Bank buys securities from the Fed, paying $10,000,000$. This means the bank uses its reserves to fund the purchase. On the bank's balance sheet: Securities (asset) increase, and Reserves (asset) decrease by $10,000,000$.

   • Decrease in reserves:

     • If a bank's deposits at the Fed were $40,000,000$, after buying securities, its deposits decrease to $30,000,000$. This reduces the total reserves available to the bank and potentially limits its lending capacity.

Changing the Money Supply

Open market operations are a powerful tool for the central bank to manage the economy by influencing the money supply.

Overview of Money Supply Calculation

• $M1 = \text{Currency held outside banks} + \text{Checkable Deposits} + \text{Traveler's Checks}$

  • Currency held outside banks: Physical paper money and coins in circulation with the public.

  • Checkable Deposits: Funds in checking accounts at commercial banks and other depository institutions that are readily available for transactions.

  • Traveler's Checks: Although a smaller component now, they represent funds that can be used for purchases like cash.

• Example of an M1 calculation and its components:

  • Currency = $10,000,000$

  • Checkable Deposits = $12,000,000$

  • Traveler's Checks = $1,000,000$

  • Therefore, $M1 = 10,000,000 + 12,000,000 + 1,000,000 = 23,000,000$.

Mechanisms of Increasing Money Supply

• Excess reserves are the key to money creation. When banks have excess reserves, they can use these funds to create new loans. These loans, when deposited into borrowers' accounts, become new checkable deposits, thus increasing the money supply (M1).

• Initial example with Bank A shows that with reserves of $10,000,000$ at the Fed and $2,000,000$ in vault cash, the total reserves equal $12,000,000$. These total reserves are the sum of vault cash and deposits held at the central bank.

• If Bank A has checkable deposits of $10,000,000$ and a required reserve ratio (r) of $10\%$, the Required Reserves formula provides insight into how reserves are utilized to calculate excess reserves, allowing for loan issuing:

  • Current example:

  • Required Reserves = $0.10 \times 10,000,000 = 1,000,000$

  • Excess Reserves = $\text{Total Reserves} - \text{Required Reserves} = 12,000,000 - 1,000,000 = 11,000,000$. This large amount of excess reserves means Bank A has significant capacity to make new loans.

Example of Open Market Operations Driven Increase

• When the Fed undertakes an open market purchase of $10,000$ from Bank A (e.g., buying a security):

• Adjusts Bank A's reserve account:

  • Assuming Bank A initially had $1,000,000$ in its reserve account at the Fed (part of its total reserves). The Fed's purchase increases this balance. New Balance = $1,000,000 + 10,000 = 1,010,000$. (Note: Assuming required reserves are still $1,000,000$ for simplicity of demonstrating the initial impact on excess reserves before any new lending, but in reality, checkable deposits may also have increased, changing RR slightly).

• Result:

  • New Excess Reserves (from this specific injection) = $1,010,000 - 1,000,000 = 10,000$. This newly added $10,000$ to excess reserves can now be loaned out.

• Bank A issues a loan of $10,000$. When this loan is made and deposited into a customer's account, it creates new checkable deposits.

• New money supply after loan:

  • If the initial M1 (from the previous M1 calculation) was $23,000,000$, the new loan directly adds to checkable deposits, thus M1. Money Supply = $23,000,000 + 10,000 = 23,010,000$. This is just the initial increase. The money multiplier effect will cause a much larger expansion.

Simple Deposit Multiplier Formula

• The simple deposit multiplier illustrates the maximum potential expansion of the money supply resulting from an initial injection of reserves into the banking system.

• Formula:

  $\text{Change in Money Supply} = \frac{1}{r} \times \text{Change in Reserves}$

  Where r is the required reserve ratio.

  • Assumptions: This formula assumes that banks lend out all of their excess reserves, and that all money loaned out is redeposited into the banking system (no cash drains to the public).

• Example with r = 10% (or 0.10)

  • The simple deposit multiplier = $\frac{1}{0.10} = 10$

  • If the initial injection of reserves is $10,000$ (from the Fed's open market purchase), the maximum potential change in the money supply (checkable deposits) is $10 \times 10,000 = 100,000$.

  • Conclusively, if the starting M1 was $23,000,000$, the new amount now potentially equals $23,000,000 + 100,000 = 23,100,000$. This demonstrates how a small initial change in reserves can lead to a much larger change in the overall money supply through the fractional reserve banking system.

Conclusion

• The process of an open market purchase injects reserves into the banking system, which then leads to an increase in the money supply through multi-tiered loan creation across various banks. Each loan creates new deposits, which become the basis for further loans, limited by the reserve requirement.

• Overall understanding built by examples, calculations, and definitions demonstrates the integral relationship between reserve requirements, banks' holdings of actual and excess reserves, central bank open market operations, and the quantitative changes in the broader money supply. This entire framework is central to monetary policy and its impact on economic activity.