Federal Reserve Balance Sheet and Money Multiplier Study Notes

The Three Determining Groups: There are three primary groups that collectively determine the money supply ( $MS$ ): * The Federal Reserve (The Fed): The central authority responsible for controlling the money supply and regulating the financial system. * The Banking System: Instrumental in creating checking accounts, which represent a major component of $M1$ . * The Non-banking Public: Their role is to decide the form in which they hold their money, specifically choosing between currency or checking accounts.

Definition of Monetary Base ( $MB$ ): The process of money creation starts with the monetary base. It is defined as the sum of currency in circulation and reserves. * Formula: $MB = ext{Currency in Circulation} + ext{Reserves}$
The Money Multiplier Connection: The money multiplier ( $m$ ) serves as the link between the monetary base and the overall money supply.
Stability and Control: When the money multiplier is stable, the Federal Reserve can effectively control the money supply by manipulating the monetary base. The fundamental relationship is expressed as: * Formula: $ext{Monetary Base} imes ext{Money Multiplier} = ext{Money Supply}$ * In this interaction, the Federal Reserve determines the monetary base, while the money multiplier is influenced by the Fed, the banking system, and the public.

Currency in Circulation: This refers specifically to paper money circulating outside the Federal Reserve.
Vault Cash: This is the physical currency held by banks. It represents the banking sector's involvement in the currency component.
Relationship to $M1$ : $M1$ currency is defined as the currency held by the non-banking public. It can be calculated as: * Formula: $M1 ext{ (currency component)} = ext{Dollars in Circulation} - ext{Vault Cash}$
Bank Reserves: These consist of bank deposits held at the Federal Reserve plus the vault cash held within the banks themselves.

The relationship between the monetary base and the Fed is defined by its balance sheet, which lists assets and liabilities.

Primary Assets: * Government Securities: Primarily government bonds (U.S. Treasuries). * Discount Loans: Loans made by the Federal Reserve to member banks.
Primary Liabilities: * Currency in Circulation: Essentially $M1$ (currency outstanding minus vault cash). * Reserves: The bank deposits held at the Fed plus vault cash.
Monetary Base as Liabilities: The monetary base is the sum of the Fed’s two major liabilities: currency in circulation and reserves.
Reserves as Assets and Liabilities: Reserve deposits are simultaneously liabilities for the Fed and assets for the commercial banks because banks can request repayment of these deposits on demand using Federal Reserve notes (the cash in hand).

Total Bank Reserves: This is a broad category encompassing several components: * Required Reserves ( $RR$ ): The amount of reserves the Fed mandates banks to hold against demand deposits and other NOW accounts. * Excess Reserves ( $ER$ ): Any reserves held by banks above the level required by the Fed.
Required Reserve Ratio ( $rrr$ ): The specific percentage of checkable deposits that the Fed dictates banks must hold as reserves. This ratio is a critical variable in the money multiplier calculation.

Transmission Mechanism: Changes in the monetary base lead to changes in the money supply, which ultimately impact the macroeconomy.
Method of Change: The Fed changes the monetary base by altering the levels of its assets (government securities and discount loans) through two main methods: * Buying or selling government securities. * Issuing discount loans to banks.

Definition: Open Market Operations involve the purchase and sale of securities, typically US Treasuries, in financial markets.
Open Market Purchase: The Fed buys securities. This translates to converting bonds into dollars, increasing the money supply as the Fed injects liquidity into the system.
Open Market Sale: The Fed sells securities to take currency out of circulation, thereby decreasing the money supply with the goal of increasing interest rates.
Execution: These operations are conducted electronically by primary dealers at the Federal Reserve's trading desk located at the New York Fed, following directives from the Federal Open Market Committee (FOMC).

Discount Operations: Like OMOs, discount loans change the monetary base, though the Fed has less direct control over these than OMOs.
The Discount Rate: The interest rate the Federal Reserve charges banks on discount loans. This rate is set administratively by the Fed rather than being determined by the supply and demand of loanable funds in a market.
Components of the Base (Alternative View): Some economists split the monetary base into two components: * Non-borrowed Monetary Base ( $B_{nonborrowed}$ ): The portion the Fed controls directly via OMOs. * Borrowed Reserves ( $BR$ ): The portion resulting from discount loans (also referred to as discount loans). * Formula: $MB = B_{nonborrowed} + ext{Borrowed Reserves}$

The Process of Multiple Expansion: 1. The Fed conducts an open market purchase. 2. This increases a bank's excess reserves ( $ER$ ). 3. The bank lends these excess reserves to a borrower (e.g., "Peter"). 4. The borrower uses the funds to buy goods/services. 5. The payment is deposited back into the banking system. 6. The receiving bank holds a fraction ( $rrr$ ) and lends out the remainder. 7. This process continues until it diminishes to cents.
Simple Money Multiplier Formula: * Formula: $m = rac{1}{rrr}$

Theoretical Assumptions: The simple multiplier assumes that banks hold zero excess reserves and the non-banking public makes no changes to their currency holdings.
Non-bank Public Influence: Funds deposited in checking accounts undergo multiple expansion, while funds held as physical currency do not. * If the public increases their currency holdings relative to deposits (e.g., keeping cash under a mattress), the multiplier becomes lower.
Banking System Influence: If banks choose to hold more excess reserves relative to their deposits instead of lending them out, the money multiplier will be smaller.
Conclusion: Because of these real-world behaviors, the money multiplier formula serves as an estimation or best approximation rather than a perfectly accurate representation.