Federal Reserve, Monetary Policy, and Banking: Q&A Study Guide

Federal Reserve and Discount Loans

Bank Loans from the Federal Reserve

Bank loans from the Federal Reserve are called discount loans and represent a source of funds for banks. These loans are part of the Fed's monetary policy toolkit and affect bank liquidity and interest rates.

• Discount loans: Short-term loans from the Federal Reserve to commercial banks, usually at the discount rate.

• Federal funds: Interbank overnight loans, not loans from the Fed.

• Cash reserves: Increase when banks borrow from the Fed; liability rises for the bank.

• WatchOuts: Do not confuse the discount rate (Fed to banks) with the federal funds rate (bank-to-bank).

Bank Balance Sheets and Reserves

Assets and Liabilities

Banks report reserves (vault cash + deposits at the Fed) as assets on their balance sheets. Borrowings and savings deposits are liabilities; bank capital is owners' equity.

• Reserves: Asset to the bank, liability to the Fed.

• Bank capital: Equity, absorbs losses.

• WatchOuts: Reserves are an asset to the bank but a liability of the Fed.

Required Reserves and Deposit Outflow

Banks must hold a fraction of checkable deposits as required reserves. If reserves fall below the required level, banks may need to borrow or reduce lending.

• Required reserve ratio: The percentage of deposits banks must hold as reserves.

• Formula: $\text{Required reserves} = r \times \text{Deposits}$

• Example: If $r = 0.20$ and deposits = $400,000$, required reserves = $80,000$.

Bank Capital and Solvency

Bank Capital

Bank capital (equity) is the loss-absorbing buffer for banks. Higher capital means greater solvency and ability to withstand losses.

• Solvency: Ability to absorb losses and remain solvent.

• WatchOuts: Capital addresses solvency, not short-term liquidity or income.

Interest Rates and Mortgages

Adjustable Rate Mortgages (ARMs)

ARMs have interest rates that adjust periodically based on a market index. They typically start with lower initial rates than fixed-rate mortgages but shift interest rate risk to the borrower.

• ARM: Interest rate based on an index + margin; payments vary as rates change.

• WatchOuts: ARMs shift interest rate risk to the borrower; do not protect against rising rates.

Derivatives and Financial Instruments

Derivatives

Derivatives (futures, options, swaps) are designed to transfer or hedge rate risk. Debt/credit cards are payment instruments, not hedges.

• Derivatives: Financial contracts whose value depends on underlying assets.

• WatchOuts: Debt/credit cards are not hedges; junk bonds are high-yield debt.

Regulatory Arbitrage and Loopholes

Regulatory Arbitrage

Regulatory arbitrage involves exploiting loopholes in financial regulations to avoid restrictions. This can include shifting transactions or using ambiguous language.

• Example: Loophole mining to get around rules.

• WatchOuts: Exploits permissive rule language; not necessarily illegal concealment.

Federal Reserve System Structure

Federal Reserve Banks

The Federal Reserve System includes 12 regional banks. The Open Market Trading Desk (Markets Group) is at the Federal Reserve Bank of New York.

• Federal Reserve Banks: Significant roles, but Desk is at NY Fed.

Monetary Base and Money Supply

Monetary Base (MB)

The monetary base is the sum of currency in circulation and bank reserves. It is a key measure of the money supply controlled by the central bank.

• Formula: $\text{MB} = C + R$

• Components: Currency (C) and reserves (R).

• WatchOuts: Currency and reserves are components; M1/M2 are broader money supply measures.

Borrowed and Nonborrowed Base

The monetary base can be divided into borrowed and nonborrowed components, reflecting sources of funds.

• Formula: $\text{MB} = C + R = MB = C + R$

• WatchOuts: Duplicates of Q10; watch the identity vs source distinction.

Federal Reserve Actions and Deposit Creation

Discount Loans and Monetary Base

When the Federal Reserve calls in a discount loan from a bank, the monetary base and reserves decrease.

• Immediate effect: Reserves and MB decrease; M1 may remain unchanged initially.

Deposit Creation Process

When the Fed supplies the banking system with extra reserves, deposits increase by more than the dollar amount supplied—a process called multiple deposit creation.

• Fractional reserves: Repeated rounds of lending/ depositing expand deposits by a multiple.

• Formula: $\Delta D = (1/r) \times \Delta R$ (upper bound)

• WatchOuts: Leakages (currency holdings, excess reserves) reduce the real-world multiplier.

Deposit Multiplier and Reserve Ratio

Simple Deposit Multiplier

The simple deposit multiplier is the reciprocal of the required reserve ratio.

• Formula: $m = 1/r$

• Example: If $r = 0.10$, $m = 1/0.10 = 10$.

• WatchOuts: Higher reserve ratio means a smaller multiplier.

Deposit Outflow and Excess Reserves

Deposit outflows can exceed initial excess reserves because required reserves fall with deposits.

• Example: If excess reserves = $7,000$, deposits = $100,000$, required reserve ratio = 10%, required reserves = $10,000$, actual reserves = $17,000$.

Money Multiplier and Currency Drain

Money Multiplier with Leakages

The money multiplier is affected by the currency-to-deposit ratio and excess reserves. Lower currency/deposit ratio means less currency drain and a larger multiplier.

• Formula: $m = (1 + c)/(r + e + c)$

• Variables: $c$ = currency/deposit ratio, $e$ = excess reserve ratio, $r$ = required reserve ratio.

• WatchOuts: With $M1$ constant, $M = m \times MB$ rises when $m$ rises.

Federal Reserve Mandate and Policy Regimes

Dual Mandate

The Federal Reserve's mandate is dual: price stability and maximum employment.

• Hierarchical mandates: Some central banks (e.g., ECB) prioritize price stability first.

Monetary Policy Regimes

From the 1980s to 2006, the Fed followed a regime with an implicit nominal anchor, not an explicit inflation target.

• Policy: Volcker/Greenspan Fed did not adopt explicit inflation targeting; pursued price stability with an implicit anchor.

• WatchOuts: Inflation target (2%) came later; monetary targeting was brief.

Taylor Principle and Taylor Rule

Taylor Principle

According to the Taylor Principle, when inflation rises, the nominal interest rate should be increased by more than the inflation increase to raise the real rate and stabilize inflation.

• Formula: $i = r^* + \pi^* + 0.5(\pi - \pi^*) + 0.5(\text{output gap})$

• Example: If $r^* = 2.0\%$, $\pi^* = 2.0\%$, $\pi = 1.8\%$, output gap = 0.06%, $i = 1.96\%$.

• WatchOuts: Keep unit consistency (percent vs decimals).

Glossary and Rapid Review

Key Terms and Concepts

• Discount loans: Short-term loans from the Fed to banks; rate = discount rate.

• Federal funds: Overnight interbank loans; rate = federal funds rate.

• Reserves: Asset to banks, liability to Fed.

• Bank capital: Equity; absorbs losses.

• ARMs: Adjustable rate mortgages; interest rates vary.

• Derivatives: Contracts to hedge interest rate risk.

• Regulatory arbitrage: Exploiting rules to avoid restrictions.

• Monetary base (MB): Currency + reserves.

• Money multiplier: $m = (1 + c)/(r + e + c)$; lower $c$ or $e$ = higher $m$.

• Taylor rule: $i = r^* + \pi^* + 0.5(\pi - \pi^*) + 0.5(\text{output gap})$.

Table: Key Monetary Base Identities

Identity	Formula	Description
Monetary Base (MB)	$MB = C + R$	Currency in circulation plus bank reserves
Simple Deposit Multiplier	$m = 1/r$	Reciprocal of required reserve ratio
Money Multiplier (with leakages)	$m = (1 + c)/(r + e + c)$	Accounts for currency and excess reserves
Taylor Rule	$i = r^* + \pi^* + 0.5(\pi - \pi^*) + 0.5(\text{output gap})$	Sets nominal interest rate based on inflation and output gap