CPI vs GDP Deflator: Comprehensive Notes

The CPI and the GDP Deflator: Key Concepts

• CPI (Consumer Price Index) measures the overall cost of the goods and services bought by a typical consumer.
• The BLS (Bureau of Labor Statistics, part of the Department of Labor) computes and reports the CPI every month.
• GDP deflator is another broad-price measure, discussed in the preceding chapter, and equals the ratio of nominal GDP to real GDP.
• Economists and policymakers monitor both indices (and other indicators) to gauge how quickly prices are rising; they usually tell a similar story but can diverge for important reasons.

How the CPI is calculated (step-by-step)

• Step 1: Construct the basket of goods and services
  • Weights reflect what a typical consumer buys, based on surveys.
  • Example in the transcript: basket includes four hot dogs and two hamburgers; prices and quantities reflect relative importance.
• Step 2: Find the prices of each basket item over time
  • For several years, track the prices of hot dogs and hamburgers in the basket.
  • Only prices change when isolating price effects from quantity effects.
• Step 3: Compute the basket’s cost in each time period
  • Use prices to calculate the total cost of the fixed basket.
  • This isolates price changes from quantity changes.
• Step 4: Choose a base year and compute the index
  • The base year is arbitrary; the index is used to measure percentage changes in the cost of living.
  • CPI formula:
    \text{CPI}t = \frac{P{\text{basket},t}}{P_{\text{basket},\text{base}}} \times 100
  • In the example, 2022 is the base year and the basket costs $8.00, so CPI = 100 in 2022.
• Step 5: Compute the inflation rate
  • Inflation rate between year t and year t-1:
    \text{Inflation rate}{t} = \frac{\text{CPI}t - \text{CPI}{t-1}}{\text{CPI}{t-1}} \times 100
  • Example in the transcript: inflation is 75% in 2023 and 40.3% in 2024 (per the simplified two-good basket).

The CPI in practice

• The BLS collects and processes price data for thousands of goods and services every month.
• In addition to the overall CPI, CPI reports for narrow categories (food, clothing, energy) and core CPI (CPI excluding food and energy).
• Core CPI is often viewed as a better reflection of underlying inflation trends because food and energy prices are highly volatile.
• The BLS also computes the Producer Price Index (PPI), which measures prices received by domestic producers; formerly known as the Wholesale Price Index.
• Note: The CPI has several measurement challenges that can bias inflation estimates, as discussed below.

Problems in measuring the cost of living (three main issues)

• Substitution bias
  • When prices change, consumers substitute toward relatively cheaper goods.
  • A fixed basket understates substitution, causing an overstatement of the true rise in the cost of living.
  • Example: Apples become cheaper relative to pears; consumers buy more apples. If next year pears become cheaper, the fixed basket still assumes the old quantities, overstating the cost of living.
• Introduction of new goods
  • New goods increase consumer opportunities and make each dollar more valuable.
  • A fixed basket cannot reflect the increased value from new products (e.g., iPod, iPhone), so CPI can fail to capture improvements in well-being.
  • Basket updates eventually incorporate new goods, but the initial decrease in the cost of living from new goods may be missed.
• Unmeasured quality changes
  • If quality improves but price stays the same, the value of a dollar rises; if quality worsens, the value falls.
  • The BLS adjusts prices for quality changes when possible, but measuring quality is difficult and controversial.
• Magnitude of bias
  • Studies estimate upward bias in measured inflation of about
    0.5\% \text{ to } 1\% \text{per year}
  • These measurement issues have real policy implications because CPI is used to adjust Social Security, wages, and some tax parameters.

The GDP deflator vs the CPI: Two key differences

• What they measure
  • CPI: prices of all goods and services bought by consumers (includes imports; fixed basket).
  • GDP deflator: prices of all goods and services produced domestically (excludes imports; basket can change over time).
• What adjusts when prices change
  • CPI uses a fixed basket; only prices change.
  • GDP deflator uses a changing basket of currently produced goods and services; both prices and composition can change.
• Implications of the differences
  • If imports rise in price (e.g., oil price increases), CPI can rise more than the GDP deflator since CPI includes imported goods; oil-price spikes historically caused CPI to diverge upward relative to the GDP deflator.
  • When the relative prices of different goods change, the weighting differences between CPI and GDP deflator can cause divergence in measured inflation.
• Examples of divergence
  • 1979–1980: CPI inflation spiked due to large oil-price increases; GDP deflator rose less.
  • 2009 and 2015: CPI inflation fell below GDP deflator due to plunging oil prices.
• Practical note
  • Since 2008, rising U.S. oil production reduced import dependence, making oil-price-driven divergences less pronounced but not eliminated.
• How the indices are built over time
  • CPI: weighted by a fixed basket that changes only slowly via occasional updates.
  • GDP deflator: weights change automatically as the composition of GDP changes.

Using price indexes to compare dollars across time

• The goal: convert a past amount into today’s dollars to compare purchasing power.
• Core formula: \text{Amount in today’s dollars} = \text{Amount in year } t \text{ dollars} \times \frac{P{\text{today}}}{P{t}}
  • Where $P$ is the price level (a price index like CPI).
• Example: Babe Ruth’s 1931 salary of $80,000 into 2021 dollars
  • CPI in 1931: $CPI{1931} = 15.2$; CPI in 2021: $CPI{2021} = 271$.
  • Calculation:
    \text{Salary}_{2021} = 80{,}000 \times \frac{271}{15.2} \approx 1{,}426{,}316.
  • Interpretation: Ruth’s $80k in 1931 is worth about $1.43 million in 2021 dollars.
• Example: Hoover’s 1931 salary of $75,000
  • Using the same CPI values:
    75{,}000 \times \frac{271}{15.2} \approx 1{,}337{,}171.
• Practical note on interpretations
  • The result shows relative changes in price levels, not relative real purchasing power of all consumption or income categories.

Regional differences in cost of living

• The BEA uses CPI data to compute regional price parities (RPPs), which measure variations in cost of living across states.
• Example figures (2020):
  • Hawaii: about 112% of the U.S. typical cost of living (i.e., 12% higher than average).
  • Mississippi: about 87.8% of the U.S. typical cost of living (i.e., 12.2% lower than average).
• What accounts for regional differences?
  • Goods: prices of tradables (food and clothing) explain only a small part of regional differences because goods are tradable and prices tend to converge.
  • Services: larger differences, e.g., a haircut can cost more in one state than another; housing services are particularly important since housing is a large share of consumer budgets and is less mobile geographically.
  • Housing costs are persistent because land and housing stock are immobile; rents can differ widely (e.g., Hawaii vs Mississippi).
• Implications for job offers
  • When comparing salaries across regions, consider both dollar pay and local prices, especially housing costs.

Indexation in contracts and laws (COLA)

• Indexation occurs when a monetary amount is automatically adjusted for changes in the price level.
• Common examples:
  • Wages with cost-of-living allowances (COLA) tied to the CPI.
  • Social Security benefits indexed to CPI increases.
  • Tax brackets and other tax parameters indexed to inflation.
• Caveat: not all aspects of the tax system are perfectly indexed; some provisions are indexed, while others are not.
• These indexation practices help protect people against inflation, but imperfect indexing can still create distortions.

Real vs. nominal interest rates

• Core idea: nominal rates measure the rise in the number of dollars; real rates measure the rise in purchasing power.
• Key formula:
  • Real interest rate ≈ Nominal interest rate − Inflation rate
  • Exact relation in the simplest form:
    r = i - \pi
    where $r$ is the real rate, $i$ is the nominal rate, and $\pi$ is the inflation rate.
• Why it matters for savers and borrowers
  • If inflation exceeds the nominal interest rate, purchasing power falls despite higher nominal balances.
• Illustrative example (ticket purchase metaphor)
  • If a cinema ticket costs $10 and one starts with $1{,}000:
  • Zero inflation: 1000 dollars buys 100 tickets today and will buy 110 tickets after earning 10% interest.
  • 6% inflation (price rises to $10.60): purchasing power increases only about 4% (approx. 104 tickets).
  • 10% inflation (price rises to $11): still 100 tickets; real purchasing power unchanged.
  • 12% inflation (price $11.20): purchasing power falls to about 98 tickets; real wealth declines.
  • Deflation (e.g., price falls to $9.80): purchasing power rises to about 112 tickets; real wealth increases more than the nominal gain.
• Takeaway: If inflation is higher than the nominal return, real purchasing power can fall; if deflation occurs, purchasing power can rise even without higher nominal returns.

Real and nominal rates in the US economy (historical perspective)

• Nominal rate: e.g., three-month Treasury bills.
• Real rate: nominal rate minus inflation rate (CPI-based).
• Observations:
  • Nominal rates typically exceed real rates because inflation has been positive on average.
  • When inflation is high, real rates can be negative (as in much of the 1970s).
  • When inflation is low, real rates can be higher (e.g., late 1990s).
  • The 2020 pandemic era showed that nominal rates fell toward zero, and real rates turned negative as inflation dynamics shifted.
• Implication for policy and expectations
  • The interaction of real and nominal rates helps explain savers’ behavior, borrowing costs, and macroeconomic policy responses.

Conclusion and implications

• A dollar today is not worth the same as a dollar in the past or future due to persistent inflation.
• Price indexes (CPI, GDP deflator) are essential for comparing money across time and adjusting for inflation in contracts, wages, and policy.
• The CPI, while widely used, has notable measurement problems (substitution bias, new goods, quality changes) that can overstate true inflation.
• The GDP deflator complements the CPI by including domestic production and changing baskets, helping to explain divergences in inflation readings.
• The next chapters will build on these ideas to explore how long-run determinants of real GDP and the price level interact with money, inflation, and nominal rates.

Chapter review (key concepts and terms)

• Key concepts:
  • Consumer price index (CPI)
  • Inflation rate
  • Core CPI
  • Producer price index (PPI)
  • Indexed / indexing / COLA (cost-of-living allowance)
  • Nominal interest rate
  • Real interest rate
• Equations to remember:
  • CPI: \text{CPI}t = \frac{P{\text{basket},t}}{P_{\text{basket},base}} \times 100
  • Inflation rate: \text{Inflation rate}{t} = \frac{\text{CPI}t - \text{CPI}{t-1}}{\text{CPI}{t-1}} \times 100
  • Real interest rate: r = i - \pi
  • GDP deflator: \text{GDP Deflator} = \frac{\text{Nominal GDP}}{\text{Real GDP}}
• Important distinctions:
  • CPI vs GDP deflator: fixed basket and imports (CPI) vs changing basket and domestically produced goods (GDP deflator).
  • Substitution bias, new goods, and quality change as major reasons CPI may overstate inflation.
  • Regional price parities measure cross-state cost-of-living differences; housing dominates regional variation.

Practice prompts (questions to test understanding)

• How would updating the CPI basket to include new goods (like smartphones or streaming services) affect measured inflation over time?
• Explain why CPI can overstate inflation relative to the GDP deflator in the presence of rising imports.
• If the CPI in year t is 220 and in year t+1 is 231, what is the inflation rate between those years?
• Given nominal interest rate 6% and CPI inflation of 3%, what is the approximate real interest rate? Show the calculation.
• Why might Social Security cost-of-living adjustments (COLAs) create budgetary pressures if inflation spikes unexpectedly?

Connections to prior and future topics

• This chapter links to the GDP and price level discussions in the preceding chapter by comparing CPI and GDP deflator as measures of inflation.
• The framework sets up later sections on the determinants of real GDP, the money supply, and short-run fluctuations, where inflation and price levels influence macroeconomic dynamics.