# Consumer Price Index

Consumer Price Index (CPI) is a statistic used to measure average price of a basket of commonly-used goods and services in a period relative to some base period. The base period price of the basket is marked to 100 and CPI value hovers above or below 100 to reflect whether the average price has increased or decreased over the period.

Once we have CPI values for two periods, we can determine the inflation rate over the periods as the difference between the two CPI values divided by the initial CPI value.

Producer Price Index (PPI) is a related index which measures average price level received by sellers. Its movement foretells the expected changes in CPI despite some differences that exist in their calculation methodology.

## Formula

Estimating CPI involves surveying people to identify what they purchase on regular basis. This helps determine the basket of commonly used goods and services. Total price of the basket is obtained from market for current period and base period and following formula is used to calculate CPI:

$$\text{Consumer Price Index} \\= \frac{\text{Current Period Price of the Basket}}{\text{Base Period Price of the Basket}} \times \text{100}$$

In practice many adjustments are made to CPI on account of seasonality, changes in composition of the basket, etc. and different versions of CPI are calculated to cater to real life needs.

In US, the Bureau of Labor Statistics estimates CPI on regular basis. IMF and World Bank provide CPI and other data for majority of countries.

## Example

In 1540, when Sher Shah seized control of India from Humayun, her average residents spent 40% of their total annual consumption budget on food, 20% on fuel, 20% on clothes and 20% on education. In 1545, the King sat down with his vizier to find out whether the standard of life has improved or worsened over the period. They pulled out some data:

Price in Rupees
Year 1545Year 1540
Food5250
Fuel2725
Clothes1715
Education90100

Over the five years, there was little change in the residents' spending preferences. Help the king determine whether people are feeling richer or poorer.

In order to calculate CPI, 1545 and 1540 prices are weighted according to consumers' spending preferences.

WeightPrice in Rupees
Year 1545Year 1540
Food40%5250
Fuel20%2725
Clothes20%1715
Education20%90100

Weighted Average Prices in 1545
= 0.4 × 52 + 0.2 × 27 + 0.2 × 17 + 0.2 × 90
= 47.60

Weighted Average Prices in 1540
= 0.4 × 50 + 0.2 × 25 + 0.2 × 15 + 0.2 × 100
= 48.00

Once we have total price of the basket for both periods, we can just plug in the figures in the following formula:

$$\text{Consumer Price Index} \\= \frac{\text{47.60}}{\text{48.00}} \times \text{100} = \text{99.17}$$

CPI in 1545 is 99.17 as compared to 100 in 1540. This tells that there is no deterioration in the purchasing power of the people. In fact, it shows that there has been a deflation.

## Limitations of CPI

Even though the consumer price index is the most common measure of inflation, it is generally believed that CPI overstated inflation by roughly 1 percentage point. This upward bias exists because:

• CPI doesn't incorporate the substitution effect into composition of the basket of goods. For example, when price of a good increases, consumer substitute away from it but the CPI doesn't include any mechanism to specifically reflect this.
• Even though the BLS attempts to address changes in quality, some quality changes such as improvement in safety, etc. are not quantifiable. Hence, CPI doesn't take into consideration such quality changes.
• Although new products generally have better quality, these goods are not included in the CPI basket of goods immediately but are included only when they are consumed by people fairly consistently. Another measure of inflation, the GDP deflator includes the effect of price changes of all person consumption expenditures (excluding imports).
• Many components of CPI such as food and energy are highly volatile which makes CPI a not so good measure of long-term inflation. Core inflation addresses this problem by considering only non-volatile items.