Nominal and Real Interest Rates and Inflation

Nominal versus Real Interest Rates

• Basic Definitions and Core Principles:

  • Interest Rate: The cost of borrowing funds, expressed as a percentage of the amount borrowed.

  • Nominal Interest Rate: The stated interest rate on a loan.

  • Real Interest Rate: Corrects the nominal interest rate for the effect of inflation on purchasing power, measuring the percentage change in purchasing power resulting from lending or borrowing.

• Mathematical Relationship and Detailed Example:

  • Consider a loan of $1,000$ extended for one year at a nominal interest rate of $4\%$. At the end of the year, the borrower pays back $1,040$, which is $4\%$ more than the principal lent.

  • Assume the only product purchased in the economy is movie streams, priced at $10$ per movie at the beginning of the year:

    • Initial purchasing power of $1,000$ is $\frac{1000}{10} = 100\,\text{movies}$.

    • If the annual inflation rate is $2\%$, the price to stream a movie rises to $10.20$ by the end of the year ($10 \times 1.02 = 10.20$).

    • The repaid $1,040$ can purchase $\frac{1040}{10.20} \approx 101.96078\,\text{movies}$.

    • The lender can purchase almost $2\%$ more movies, making the actual real interest rate received $1.96\%$.

  • Approximation Formula:         $\text{Real interest rate} = \text{Nominal interest rate} - \text{Inflation rate}$

  • Applying the approximation formula to the example:         $2\% = 4\% - 2\%$         This approximation is close to the actual value of $1.96\%$.

  • If annual inflation were $3\%$ during the year:         $1\% = 4\% - 3\%$

• Effects of Inflation on Lenders and Borrowers:

  • Holding the nominal interest rate constant, a higher inflation rate results in a lower real interest rate.

  • If the inflation rate turns out to be higher than expected, borrowers pay and lenders receive a lower real interest rate than expected:

    • If both lender and borrower expect an inflation rate of $2\%$, both expect the real interest rate to be $2\%$ on a $4\%$ nominal rate loan.

    • If the actual inflation rate turns out to be $3\%$, the real interest rate falls to $1\%$.

    • This outcome hurts the lender (receives lower real return) and benefits the borrower (pays lower real borrowing cost).

Macroeconomic Measurement of Interest Rates and Inflation

• Standard Macroeconomic Benchmarks:

  • Aggregate Nominal Interest Rate: Measured using the interest rate on three-month U.S. Treasury bills.

  • U.S. Treasury Bills: Short-term loans made by investors to the federal government, representing the most important security in world financial markets.

  • Aggregate Inflation Rate: Measured by the percentage change in the Consumer Price Index (CPI) relative to the same quarter in the previous year.

• Historical Trends and Gap Analysis (1972–2023):

  • Low Inflation Eras: During periods of low inflation (such as most years from the early $1990\text{s}$ through $2020$), the gap between nominal and real interest rates is small.

  • High Inflation or Near-Zero Rate Eras: During high inflation periods (such as the mid- to late $1970\text{s}$) or when nominal rates are near zero (such as $2008$ through $2021$), the gap between nominal and real interest rates becomes large.

• Evaluating Nominal Rates Across Eras:

  • A single nominal interest rate can be associated with vastly different real interest rates across different time periods.

  • Late $1975$: The nominal interest rate was approximately $5.5\%$, but because inflation was $7\%$, the real interest rate was $-1.5\%$:         $-1.5\% = 5.5\% - 7\%$

  • Early $1987$: The nominal interest rate was also $5.5\%$, but because inflation was only $2\%$, the real interest rate was $3.5\%$:         $3.5\% = 5.5\% - 2\%$

  • Implication: It is impossible to judge whether a nominal interest rate is "high" or "low" without knowing the prevailing inflation rate.

  • Business Investment: When firms decide whether to borrow funds for investment goods (such as a new factory), they evaluate the real interest rate because it measures the true cost of borrowing.

• Deflation and Interest Rate Conditions:

  • The nominal interest rate can be less than the real interest rate only when the inflation rate is negative.

  • Deflation: A negative inflation rate that occurs on rare occasions when the overall price level falls.

Inflation, Incomes, and Purchasing Power Dynamics

• The Relationship Between Inflation and Average Incomes:

  • Hypothetical Scenario: Imagine waking up to find every price doubled (food, gasoline, clothing, laptops, houses, haircuts) while all wages and salaries also doubled overnight.

    • A Big Mac price rises from $5$ to $10$.

    • An individual's salary rises from $45,000\,\text{per year}$ to $90,000\,\text{per year}$.

    • Purchasing power remains unchanged, and affordability of goods remains identical.

  • Economic Identity: Nominal incomes generally increase alongside inflation.

    • A $5$ price for a Big Mac represents both the product's value and the total income generated in producing it.

    • When the price rises to $10$, the extra $5$ ends up as income distributed to McDonald's workers, suppliers, or stockholders.

  • Common Misconception: The primary issue with inflation is not that consumers can no longer afford goods and services as prices rise.

  • An expected inflation rate of $10\%$ raises average prices by $10\%$, but also raises average incomes by $10\%$, keeping goods and services as affordable to an average consumer as under zero inflation.

Income Distribution and Costs of Anticipated Inflation

• Why Inflation Causes Harm Across the Economy:

  • Average vs. Individual Impact: Average income tracking inflation applies to the average person, but not to every single individual.

  • Paper Money Depreciation:

    • Firms and consumers must hold paper money to facilitate transactions.

    • Paper money loses purchasing power each year at the rate of inflation.

    • Economic agents try to minimize cash holdings, but cannot eliminate them entirely.

  • Divergent Income Growth:

    • Individuals whose incomes rise faster than inflation gain purchasing power.

    • Individuals whose incomes grow slower than inflation (or not at all) experience falling purchasing power.

  • Fixed Income Earners:

    • Retired workers receiving a fixed pension (e.g., $3,000\,\text{per month}$) suffer reduced purchasing power over time.

    • Inflation changes the distribution of income in ways widely perceived as unfair.

• Costs of Perfectly Anticipated Inflation:

  • Even if an inflation rate of $10\%$ per year over $10$ years is fully anticipated:

    • Workers demand wage increases of at least $10\%$ per year, which businesses grant because product prices increase.

    • Lenders charge higher interest rates to compensate for depreciating dollars, and borrowers pay them knowing repayment occurs in depreciated currency.

  • Residual Costs:

    1. Income Redistribution: Some individuals' incomes inevitably lag behind expected inflation.

    2. Menu Costs: Retailers and supermarkets marking physical prices on packages or store shelves must incur operational costs to update price tags.

Inflation Impacts Across Income Tiers

• Recessions versus Inflation Across Income Tiers:

  • Recessions: Unemployment increases during recessions are typically larger for lower-income individuals because they hold lower-skilled jobs. Firms expect to easily re-hire low-skilled labor post-recession, whereas high-skilled workers are harder to replace and thus retained.

  • Inflation Criteria: For inflation to affect low-income people more severely, they must purchase a significantly different mix of goods and services whose prices rise faster during high inflation.

• Empirical Research by the Bureau of Labor Statistics (BLS):

  • Research by Joshua Klick and Anya Stockburger at the BLS constructed separate CPI measures for low-income and high-income households.

  • 2005–2021 Period: Prices of goods and services purchased by low-income households increased somewhat faster than those purchased by high-income households.

• Covid-19 Pandemic Era Findings (March 2020 – April 2023):

  • Wage growth for workers in the lowest wage quartile grew faster than wage growth for higher-wage workers or all workers overall.

  • Driver: Severe labor shortages in service industries (e.g., restaurants, hotels) compelled employers to rapidly raise nominal wages to attract staff.

  • Real Wage Outcomes:

    • Low-income workers: Wages grew faster than CPI prices, causing real wages to rise.

    • High-income and average-income workers: Real wages fell.

    • Conclusion: During this period, lower-income workers were hurt less by inflation than higher-income workers.

• Methodological Differences in Wage Growth Calculations:

  • Researchers at the Federal Reserve Bank of Atlanta (Atlanta Fed) compute wage growth as a $12\text{-month}$ moving average.

  • This differs from standard CPI inflation calculations, which measure percentage changes relative to the exact same month in the prior year.

Consumer Price Index (CPI) Measurement and Structure

• Calculation of the Consumer Price Index (CPI):

  • The CPI measures the average price paid by urban consumers for a fixed market basket of goods and services relative to a designated base year.

  • Formula:       $\text{CPI}_t = \left( \frac{\text{Cost of Market Basket in Year } t}{\text{Cost of Market Basket in Base Year}} \right) \times 100$

• What the CPI Measures:

  • Evaluates the overall change in the cost of living for urban households over time.

  • Serves as the primary indicator for tracking consumer price inflation and adjusting cost-of-living allowances (COLAs), tax brackets, and social safety net benefits.

• Three Largest Expenditure Weights in the U.S. CPI:

  1. Housing: Represents the largest category (roughly $40\%$ to $45\%$ of the basket), including shelter (rent and owners' equivalent rent), fuel, utilities, and household furnishings.

  2. Transportation: Accounts for approximately $15\%$ to $17\%$ of the basket, covering motor vehicles, gasoline, public transit, and airline fares.

  3. Food and Beverages: Comprises roughly $13\%$ to $15\%$ of the basket, including food consumed at home and food away from home.

• Behavior of the U.S. CPI and Inflation Rate in the 2020s:

  • 2020 (Pandemic Shock): Inflation remained low (below $1.5\%$) due to sudden contractions in economic activity and reduced consumer demand during initial COVID-19 lockdowns.

  • 2021–2022 (Surge to Peak): Inflation surged rapidly, reaching a 40-year peak of approximately $9.1\%$ in June 2022. Key drivers included severe global supply chain bottlenecks, massive fiscal stimulus, tight labor markets, and energy price shocks following geopolitical conflicts.

  • 2023–2024 (Disinflation Trend): Inflation gradually trended downward toward $2.5\%$ to $3.0\%$ as aggressive monetary policy tightening (interest rate hikes by the Federal Reserve) slowed aggregate demand and supply chain disruptions resolved.

Calculating Inflation and Economic Growth

• Inflation Rate Calculation:

  • Measures the annual percentage change in a aggregate price level (such as the CPI) from one period to another.

  • Formula:       $\text{Inflation Rate}_t = \left( \frac{\text{CPI}_t - \text{CPI}_{t-1}}{\text{CPI}_{t-1}} \right) \times 100$

• Economic Growth Calculation:

  • Measured by the percentage change in Real Gross Domestic Product (Real GDP), adjusting nominal output for price changes to reflect actual growth in physical output.

  • Formula:       $\text{Economic Growth Rate}_t = \left( \frac{\text{Real GDP}_t - \text{Real GDP}_{t-1}}{\text{Real GDP}_{t-1}} \right) \times 100$

Personal Consumption Expenditures (PCE) Price Index

• Definition of the PCE Price Index:

  • A measure of the prices that people in the United States pay for goods and services, compiled by the Bureau of Economic Analysis (BEA) as part of the National Income and Product Accounts (NIPA).

  • Measures price changes across all personal consumption expenditures included in GDP calculation.

• Key Differences Between PCE and CPI:

  • Substitution Effect: The PCE uses a chain-weighted index structure that dynamically adjusts for consumer substitution (e.g., consumers buying chicken when beef prices rise), whereas the CPI uses a fixed market basket updated less frequently.

  • Scope and Coverage: The CPI only includes out-of-pocket expenditures made directly by urban households. The PCE includes goods and services purchased on behalf of consumers by third parties (e.g., employer-provided health insurance, Medicare, and Medicaid).

  • Weighting: Expenditure weights in the PCE reflect total business sales data rather than consumer expenditure surveys.

• Importance to the Federal Reserve:

  • Preferred Policy Benchmark: The Federal Reserve specifically targets the PCE price index (specifically Core PCE, which excludes volatile food and energy prices) for its long-run inflation target of $2\%$.

  • Reasons for Preference:

    1. Accounts for Consumer Behavior: Dynamic weighting captures product substitution when relative prices change.

    2. Broader Coverage: Captures total healthcare and medical costs incurred on behalf of households by third-party payers.

    3. Data Quality: Derived from comprehensive business surveys rather than household sample surveys, reducing reporting biases.

  In the 2020s, the behavior of the U.S. CPI and its inflation rate followed three main phases: 1. **2020 (Pandemic Shock)**: Inflation remained low (below $1.5\%$) due to sudden contractions in economic activity and reduced consumer demand during initial COVID-19 lockdowns. 2. **2021–2022 (Surge to Peak)**: Inflation surged rapidly, reaching a 40-year peak of approximately $9.1\%$ in June 2022. Key drivers included severe global supply chain bottlenecks, massive fiscal stimulus, tight labor markets, and energy price shocks following geopolitical conflicts. 3. **2023–2024 (Disinflation Trend)**: Inflation gradually trended downward toward $2.5\%$ to $3.0\%$ as aggressive monetary policy tightening (interest rate hikes by the Federal Reserve) slowed aggregate demand and supply chain disruptions resolved.