# The official CPI and bias

## Summary

This activity aims for students to gain insights about the problems in measuring a price index.

## Context for Use

Student Learning Outcomes:

Students are able to calculate the price index, and the inflation rate.

Students are able to explain why the official CPI (CPI-U) can have some problems, namely the substitution bias and the new good bias.

Text that students see:

Sheldon is calculating his food price index using the items of foods that he consumes. Being a picky eater, he eats three items; Thai food, Chinese food, and pizza. He sets Year 1 as a base year.

 Quantity (unit) year 1 Price per unit year 1 Quantity year 2 Price year 2 Thai food 10 \$10 3 \$30 Chinese food 20 \$5 30 \$7 Pizza 50 \$2 50 \$3

His friends are arguing about Sheldon's food price index. Whose argument is correct?

A. Raj said "Obviously, Sheldon's food price index went up by 50% in 2018. He must spend more money on his food due to the price increase."

B. Leonard said "Wait, Sheldon spends much more money on his food. He is experiencing 96% inflation from 2017 to 2018."

C. Howard said "Who cares this number? He ate Greek food last week, remember? This was not even a part of his food price index item. This number is not accurately reflecting Sheldon's food price index."

D. Penny said "So, we need to be careful which inflation index we use because the Bureau of Labor Statistics has several ones to choose from. Right?"

Facilitation guide:

The way to calculate price index is to use a fixed basket, in this example, using base year quantity as a fixed basket. (Note: this is different from Real GDP calculation, where price was with a base year price.)

In this example, BLS uses a fixed basket. (Note: BLS has C-CPI-U to eliminate substitution bias. https://www.bls.gov/cpi/additional-resources/chained-cpi-questions-and-answers.htm)

## Teaching Notes and Tips

Using a fixed basket (official CPI)

Price Index Year 1:

Cost of basket in Year 1 = 10 x \$10 + 20 x \$5 + 50 x \$2 = \$300

Price index in Year 1 = (300/300) x 100 = 100

Price Index Year 2:

Cost of basket in Year 2 = 10 x \$30 + 20 x \$7 + 50 x \$3 = \$590

Price index in Year 2 = (590/300)x100 = 196.7

Inflation from Year 1 to Year 2 = {(196.7-100)/100 }x 100 = 96.7%

Allowing substitution: Comparing Quantity to Experienced Quantity in Sheldon's Food Basket

 Quantity in Fixed Basket (unit) Year 2 Price (per unit) Experienced Quantity Year 2 (unit) Thai Food 10 \$30 3 Chinese 20 \$7 30 Pizza 50 \$3 50

Price Index Year 2:

Cost of basket in Year 2 = 3 x\$30 + 30 x\$7 + 50 x\$3 = \$450

Price index in Year 1 = (450/300) x 100 = 150

Inflation from Year 1 to Year 2 = {(150-100)/100} x 100 = 50%

Then, experienced or true cost of the basket in Year 2 becomes \$450 (= 3 x \$30 + 30x \$7 + 50 x \$3). Experienced or trueprice index in Year 2 would be 150 (= (450/300)x 100).

It is interesting to note that the official cost of the basket in Year 2 is 196; however, experienced or true cost of the basket in Year 2 is a much lower number at 150, as Sheldon substitutes a relatively expensive item, Thai food, with a relatively cheaper item, Chinese.

This is called substitution bias, an inflation rate calculated using a fixed basket of goods over time tends to overstate the true rise in the cost of living because it does not take into account that the person can substitute away from goods whose prices rise by a lot.

Due to substitution bias, officially calculated inflation rate may systemically over-estimate (or overstate) the actual rate of inflation.

When Sheldon had Greek food, which was not a part of fixed basket, the cost of basket increased. Price index increases as the size of the basket of goods and services gets larger due to newly introduced goods (i.e. Greek food). Therefore, a new good bias may systemically over-estimate (or overstate) the actual rate of inflation.

Below is the summary that an instructor can use as a debriefing.

1) people shift from items with greater price increases to show with lesser price increases. Using the original market basket causes the index to be higher. But using the later market basket may understate well-being because people may have shifted to less desirable purchases. (Substitution bias)

2) people buy entirely different items (Greek food)

3) The Bureau of Labor Statistics is well aware of this issue, mentioned in item (2). They have adjusted both the official CPI and created the chained-CPI.

From BLS website

(In particular, please see Question #2, What is substitution and substitution bias? And does the C-CPI_U eliminate it?.)

4) The issue often is politicized especially with indexing. Those wanting to living government payouts sometimes argue for indexes that measure lower inflation. Advocacy groups for seniors argue that their benefits should use a higher index reflecting seniors' higher spending on high inflation items such as health care.

(In particular, please see Question #3, When did you decide to use a cost of living (COL) index as a framework for the CPI and why is the CPI still not a COL?.)

## Assessment

A, B, C, or D can be correct answer. As long as students understand why they are correct, the learning outcome is achieved.