Lecture 3: Cost of Living and Consumer Price Index (CPI)

Course Updates and Logistics

  • Course Pacing: The course starts slow (two chapters over three weeks) to allow students to get acquainted, especially due to Labor Day. Module 2 through 5 will move at a faster pace.

  • Lecture 5 Focus: Today's lecture will introduce the concept of the cost of living, specifically focusing on the Consumer Price Index (CPI).

  • Extra Credit: This week's extra credit assignment is for Chapter 2, titled "Think and Like and Condiments." It has no fixed points of view. It can be completed now or by the end of the month.

  • Schedule Shift: This Friday will be the second lecture of the week, deepening current investigations. Monday of next week will be the regular recitation session.

  • Cengage Issues: If Cengage is at fault for problems preventing homework completion, due dates will be extended to ensure students are not penalized. The Tech Checks website (Cengage's early warning system) is important to bookmark for checking service status. If Cengage is not at fault, check eCampus for announcements; otherwise, issues are likely computer-related, requiring TA assistance.

  • Calendar Priorities:

    • eCampus Calendar: This is the most reliable for due dates as it directly imports from campus and Cengage settings. Anything listed here as a due date is definitive. However, it is not fully completed for the entire semester (currently only through October 3rd) because not all modules are opened at once to prevent students from rushing too far ahead. Work is ongoing to integrate everything.

    • Internal Assignments Calendar: This preliminary calendar created by the course staff covers the entire semester (e.g., showing no class on Thanksgiving week, exam on Wednesday of that week). It is more comprehensive than the Ultra calendar for planning but may contain minor inconsistencies.

    • Syllabus: This is the least reliable source for specific dates. It provides a general idea of the semester's content, but dates are subject to change and may not be updated in the syllabus.

  • Special Accommodations: Students with special accommodation requests must speak with the instructor ASAP to review their letters and ensure arrangements are made before Exam 1. Emails will be sent early next week to those who haven't.

  • Attendance: Attendance is not required but is strongly encouraged. Students do not need to notify the instructor of absence unless it's an extended illness, or they need homework extensions, in which case they should contact their group TA directly.

  • Week 1 Results Overview:

    • Quick Quiz Participation: Mid-90s across both sections, higher than usual for the first week. Goal is to approach 100\%.

    • Homework Averages: 89\%-91\%. This is typical for the first week as students learn to use the three attempts effectively. Historically, homework averages are closer to 92\%-93\%.

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    • Clicking "Grade it now" constitutes one attempt. You have three attempts in total.

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Understanding Inflation and the Cost of Living

Revisiting Last Week: GDP and GDP Deflator

  • Last week focused on GDP, which measures the quantity of all goods and services produced. When adjusted for inflation, it provides the real quantity of production.

  • We calculated an approximate measure of inflation called the GDP deflator. This was a relatively simple calculation: obtaining two series, dividing them, multiplying by 100, and then finding the growth rate.

Shifting to CPI: Key Changes from GDP Deflator

This week, our approach to constructing inflation changes in two main ways:

  1. From Implicit/Approximate to Detailed Calculation: We move from the "back of the envelope" GDP deflator (a rough and dirty calculation) to a "very detailed, highly rich measure" created by the government, called the Consumer Price Index (CPI).

  2. From All Output Prices (Y) to Consumption Prices (C): The GDP deflator reflects the rate of change of prices for all output (Y), encompassing all four components of GDP:
    Y = C + I + G + NX (Consumption, Investment, Government Purchases, Net Exports).
    We will now focus on a deflator specific to Consumption (C), which represents consumer prices.

Deflators for GDP Components

  • While we primarily used the overall GDP deflator, implicit price deflators can be obtained for each component of GDP (C, I, G, NX).

  • Fred Series IDs:

    • GDP deflator: GDPDEF

    • Personal Consumption Expenditures (PCE) implicit price deflator: The mnemonic is not as simple as GDPDEF.

  • Comparison of Deflators in Fred:

    • The GDP deflator (blue line) and the Consumption deflator (PCE) (red line) are very similar in their level. This similarity is one reason why central banks often focus on consumer price inflation when conducting monetary policy and setting interest rates, as it broadly represents all prices and directly impacts households.

    • The Investment deflator (I deflator) (green line) shows significant differences from the C and Y deflators. This divergence is because the factors influencing the prices of capital goods (e.g., technology, AI, NVIDIA chips) are distinct from those affecting consumer goods like eggs or gasoline.

  • Inflation as a Growth Rate: A price index itself represents a level. To calculate inflation, we compute the annual growth rate of the index:
    ext{Inflation} = rac{Index{ ext{this year}} - Index{ ext{last year}}}{Index_{ ext{last year}}} imes 100

  • Why Abstract from I, G, and NX Deflators: We focus on the C deflator because its behavior (less volatility and different growth patterns compared to the I deflator) makes it a more suitable measure for general inflation, particularly since the economy's ultimate purpose is to benefit households through the purchase of goods and services.

Why We Need a Cost of Living Index

  • Comparison Across Time and Regions: A consistent cost of living index allows for meaningful comparisons of prices both across different time periods and different geographical regions (e.g., California vs. West Virginia). Without a fixed set of goods, changing consumption patterns make comparisons imprecise.

  • Defining Inflation Accurately: Inflation is the rate of change in the average price level of all goods and services, not the change in the price of any single item. For instance, high egg price inflation combined with falling computer prices may result in a stable average price level. Misrepresenting individual price increases as inflation is a common error.

  • Purpose: While complex to construct, a good measure is better than none. Price indexes are used to remove inflation from nominal variables to derive real variables (e.g., converting a nominal interest rate into a real interest rate).

The Consumer Price Index (CPI)

  • Definition: The CPI measures the overall cost of a representative "basket" of goods and services bought by the average or typical consumer in the domestic economy. It helps monitor changes in the cost of living over time and across different geographies.

  • Core CPI: This is a special version of the CPI that excludes highly volatile items, primarily food and energy prices. These prices can fluctuate dramatically (e.g., gas prices changing from 2.50 to 4 in weeks) due to specific industry factors, which can obscure the underlying, broader inflation trend. Central banks often pay close attention to core CPI.

  • Producer Price Index (PPI): Similar to CPI but measures the average change over time in the selling prices received by domestic producers for their output. It focuses on the costs faced by firms (raw materials, semi-processed goods, energy). While generally correlated with CPI, PPI can sometimes diverge or act as an early warning signal for future consumer price inflation due to supply chain effects. It is generally less focused on because firms ultimately pass most costs to final consumers.

How the CPI is Calculated

The Bureau of Labor Statistics (BLS) calculates the CPI using a three-step process:

  1. Define the Basket: The BLS identifies a representative "shopping basket" of goods and services purchased by the average consumer. This basket contains hundreds of items.

    • Typical Consumer Spending (Pie Chart Example):

      • Housing: Largest component.

      • Transportation: Second largest.

      • Food and Beverages: Third largest.

      • Medical Care: Significant portion.

      • These four categories combine to nearly 90\% of a typical consumer's spending.

  2. Collect Price Data: The BLS collects detailed price information for each good and service in the basket. This involves collecting unit prices (e.g., 1.89 per dozen eggs) and quantities purchased, often through consumer diaries.

  3. Calculate the Basket's Cost: For a given year, the cost of the basket is calculated by summing the product of the price (P) and quantity (Q) of each item in the basket.

    • ext{Basket Cost} = ext{Sum of } (P imes Q) ext{ for all items}

The CPI Formula

The Consumer Price Index (CPI) for a given year is calculated as follows:

CPI = rac{ ext{Cost of basket in current year}}{ ext{Cost of basket in base year}} imes 100

More specifically, for a given year T and a defined base year for the basket quantity (let's denote it as Q{ ext{base}}) ext{CPI}T = rac{ ext{Sum of } (PT imes Q{ ext{base}}) ext{ for all goods}}{ ext{Sum of } (P{ ext{base}} imes Q{ ext{base}}) ext{ for all goods}} imes 100

  • The numerator represents the sum of (current year price PT multiplied by the base year quantity Q{ ext{base}}) for all goods in the basket. This is sometimes described as the nominal consumption adjusted to current prices, holding the base year basket fixed.

  • The denominator represents the sum of (base year price P{ ext{base}} multiplied by the base year quantity Q{ ext{base}}) for all goods in the basket. This is nominal consumption in base year prices, for the base year basket.

Inflation Rate Calculation: Once the CPI for different years is obtained, the inflation rate between two years is calculated as:

ext{Inflation Rate} = rac{CPI{ ext{current year}} - CPI{ ext{previous year}}}{CPI_{ ext{previous year}}} imes 100

Contrast with GDP Deflator: The CPI calculation differs from the GDP deflator. The GDP deflator implicitly reflects price changes by dividing nominal GDP (using current quantities) by real GDP (using base quantities). The CPI, in contrast, uses a fixed basket of base-year quantities (Q_{ ext{base}}) in both the numerator (current prices) and the denominator (base-year prices), focusing specifically on how the cost of that fixed basket changes.

Understanding "Base Years" in CPI

There are two interpretations of the "base year" concept, and it's important to differentiate them for CPI:

  1. Index Base Year: This is the year in which the value of an index (like CPI or GDP deflator) is arbitrarily set to 100$$. Changing this base year (e.g., from 1982 to 2012) will shift the entire index level, but it will not change the calculated growth rates between any two periods.

    • For the GDP deflator, the base year is currently 2017.

  2. CPI Basket Base Year: This is the year in which the basket of goods and services used for the CPI calculation was selected. For the BLS, the most recent basket definition was based on consumption patterns from 1982 to 1984.

    • Significance: If the BLS were to update the basket to 2025, it would likely include different goods (e.g., no typewriters, but smartphones). When the basket of goods changes, the measure of inflation changes because the comparison is now based on a different set of items, reflecting different consumer purchasing habits.

Problems with the CPI (Overstating the Cost of Living)

The CPI tends to overstate the true cost of living increase due to three main biases:

  1. Substitution Bias:

    • Concept: Consumers naturally substitute away from goods whose prices have risen relatively quickly towards relatively cheaper alternatives (e.g., buying more chicken if beef prices rise significantly).

    • CPI Issue: The CPI uses a fixed basket of goods. It does not account for this consumer substitution.

    • Consequence: By not reflecting consumers' ability to switch to less expensive goods, the CPI makes the cost of maintaining a certain standard of living appear higher than it actually is.

  2. Introduction of New Goods:

    • Concept: Over time, new goods and services are introduced, often offering improved quality or new benefits at a given price point, or even fulfilling needs more efficiently.

    • CPI Issue: If new goods are not immediately incorporated into the fixed CPI basket, their price-reducing or value-enhancing effects are missed.

    • Consequence: The CPI overstates the cost of living by not reflecting the increased purchasing power that consumers gain from the choice and value offered by new products.

  3. Unmeasured Quality Change:

    • Concept: The quality of goods and services often improves over time (e.g., a car today is significantly more advanced than a car 20 years ago, even if its nominal price is similar).

    • CPI Issue: It is difficult for the BLS to fully adjust prices for every quality improvement. If a good's quality improves but its price remains the same, the effective cost per unit of quality has decreased.

    • Consequence: When quality improvements are not adequately measured and adjusted for, the CPI may mistakenly attribute price changes to pure inflation rather than improved value, thus overstating the cost of living.

Bottom Line: While a constant basket is crucial for consistent historical comparisons, the changing nature of consumer goods and buying habits means that the fixed basket approach inherent in CPI can lead to an overestimation of true inflation over long periods.