Economics of Interest Rate Determination: Bond Market and Money Market Models

Overview of Interest Rate Determination

Primary Objective: Chapter four explores the mechanisms through which interest rates are determined in the economy.
Two Primary Models: - The Bond Market Model: Analyzes how factors affecting the supply and demand for bonds impact interest rates. This is often referred to as the Bond Market Theory. - The Money Market Model (Loanable Funds Approach): Views "loanable funds" or dollars as the good being traded. It focuses on how the supply and demand for money affect interest rates.

The Bond Market Framework

Graphical Representation: - Vertical Axis: Price of bonds ( $P$ ). - Horizontal Axis: Quantity of bonds ( $Q$ ). - Demand Curve: Downward-sloping, representing the inverse relationship between price and quantity demanded by investors. - Supply Curve: Upward-sloping, representing the direct relationship between price and the quantity of bonds issued by corporations or the government.
Market Equilibrium: - Equilibrium occurs where the supply curve and demand curve intersect. - Example Scenario: - Equilibrium Price ( $P^<em>$ ): $\$960$ . - Equilibrium Quantity ( $Q^</em>$ ): $\$500,000,000,000$ worth of bonds. - Equilibrium Interest Rate ( $i$ ): $4.2\%$ .
Calculation of Interest Rates (Yield): - The interest rate is derived from the bond's price relative to its face value ( $FV$ ). - Formula: $i = \frac{FV - P}{P} \times 100$ - Example Calculation: For a bond with a $\$1,000$ face value and a price of $\$960$ : - $i = \frac{1,000 - 960}{960} \times 100 = 4.166…\%$ (rounded to $4.2\%$ \text{ in the lecture}).
Market Disequilibrium: - Surplus (Excess Supply): Occurs if the price is above equilibrium (e.g., at $\$980$ ). - If quantity demanded is $\$400,000,000,000$ but quantity supplied is $\$600,000,000,000$ , a surplus exists. - The surplus causes the bond price to fall. As the price falls, interest rates rise (at $\$980$ , the rate is approximately $2\%$ \text{, which increases toward } $4.2\%$ \text{ as the price drops to } $\$960$ ). - Shortage (Excess Demand): Occurs if the price is below equilibrium (e.g., at $\$940$ ). - If quantity supplied is $\$350,000,000,000$ but quantity demanded is $\$650,000,000,000$ , there is excess demand. - Interest Rate at $\$940$ : $i = \frac{1,000 - 940}{940} \times 100 = 6.3\%$ - Excess demand pushes bond prices up. As prices rise, interest rates decline from $6.3\%$ \text{ toward the equilibrium of } $4.2\%$ \text{.}

Factors Shifting the Demand for Bonds

1. Wealth: - Definition: Wealth is the difference between an individual's assets and liabilities. - Impact: An increase in wealth leads to an increase in the demand for bonds ( $D$ shifts right), raising the equilibrium price and increasing funds allocated to bonds.
2. Expected Return on Bonds: - Impact: If the expected return on bonds increases relative to other assets, the demand for bonds increases because holding them becomes more attractive.
3. Expected Inflation: - Impact: Increased expected inflation leads to a decrease in demand for bonds. - Mechanics: Investors expect nominal interest rates to rise (Fisher Effect), which means bond prices will decline. Holding an asset expected to fall in value is unattractive.
4. Expected Returns on Other Assets: - Impact: If the returns on alternative assets (e.g., stocks) rise, the demand for bonds decreases as they become relatively less attractive.
5. Riskiness: - Impact: If bonds become riskier relative to other assets, demand decreases.
6. Liquidity: - Impact: If bonds become more liquid (easier to convert to cash without loss of value), the demand for bonds increases.

Factors Shifting the Supply of Bonds

1. Expected Profitability of Investment Opportunities: - Impact: When firms expect higher profits, they increase the supply of bonds to finance expansions. - Example: Tesla (Elon Musk) anticipating a surge in electric vehicle (EV) demand by 2030 ( $30\%$ \text{ to } $40\%$ \text{ of sales}). To build lithium battery plants in Nevada and reduce reliance on Chinese imports, Tesla issues bonds to finance the billions in capital expenditure.
2. Business Taxes and Tax Credits: - Corporate Taxes: An increase in taxes reduces the profitability of investments, decreasing the supply of bonds. - Tax Credits: Tax incentives (like those given to Samsung for its semiconductor factory in Taylor, Texas) reduce costs and increase profitability, thereby increasing the supply of bonds.
3. Government Borrowing (Budget Deficits): - Impact: When the government runs a budget deficit (e.g., current deficits reaching $\$1,000,000,000,000$ ), it must finance it by issuing bonds. - Result: An increase in government borrowing shifts the supply curve to the right, lowering bond prices and raising interest rates.

Economic Implications: Crowding Out and Business Cycles

The Crowding Out Effect: - As the government issues more bonds to finance deficits, the increased supply drives bond prices down and interest rates up. - Higher interest rates increase the borrowing costs for private firms (e.g., Tesla). - If borrowing costs rise too high, firms may cancel investment projects (like battery plants), leading to a loss of potential jobs and economic growth. This is the government "crowding out" private investment.
Interest Rates and the Business Cycle: - Interest rates generally move in tandem with the business cycle (rising during expansions, falling during recessions). - In an Economic Downturn (Recession): - Demand Side: Household wealth declines, shifting bond demand to the left. - Supply Side: Business profitability expectations fall, shifting bond supply to the left. - Net Result: Usually, the shift in supply is significant enough that bond prices rise and interest rates decline during a recession.

The Fisher Effect in the Bond Market

Fisher Equation: $i = r + \pi^e$ (where $i$ is the nominal rate, $r$ is the real rate, and $\pi^e$ is the expected inflation rate).
Classical Dichotomy: In the long run, nominal variables (inflation) and real variables (real interest rate) do not impact one another.
Market Shifts due to Expected Inflation: - Supply Shift: An increase in expected inflation increases the supply of bonds because the real cost of borrowing ( $r = i - \pi^e$ ) falls. - Demand Shift: An increase in expected inflation decreases the demand for bonds because the real return falls. - Combined Result: Both shifts work together to drive bond prices down and nominal interest rates ( $i$ ) up.

Case Study: Why Interest Rates Remained Low (2007–2020)

Historical Context: Before the 2007–2009 financial crisis, interest rates for 10-year Treasury notes were approximately $5\%$ \text{, and 3-month T-bills were } $4.6\%$ \text{.}
Post-Crisis Trends: Despite massive federal deficits under Presidents Bush, Obama, Trump, and Biden, interest rates stayed low.
Forces at Play: - Supply Expansion: Deficits increased the supply of bonds. Bush spent on wars (Iraq/Afghanistan) and Medicare Part D while lowering taxes. Obama used fiscal stimulus to stabilize the economy. Trump lowered taxes and spent on the pandemic ( $\$6,000,000,000,000$ stimulus). Biden continued these programs. - Demand Surge: The demand for bonds increased even more aggressively than supply due to: - Safety: Investors moved money into "safe assets" like government bonds after the 2007 crash. - Quantitative Easing (QE): The Federal Reserve and other central banks deliberately purchased massive amounts of Treasury bills and mortgage-backed securities to lower long-term interest rates.
Conclusion: Because the demand shift (Federal Reserve and investor safety) outweighed the supply shift (government deficits), bond prices rose and interest rates remained historically low for over a decade.