# Consumer Price Index (CPI)

### From Baripedia

In this chapter we focus on how to measure the cost of living, and its evolution. This will be useful to compare the purchasing power of different incomes at different points in time. For example, a salary of 200 can buy more than a salary of 2000 if the cost of living in the first case is more than 10 times lower than in the second case.

The consumer price index allows us to measure changes in the cost of living. It is a measure of the evolution of the general price level faced by the consumer, and therefore of inflation, i.e. the percentage change in the price level from one period to the next).

# Construction and CPI issues

## Definition and construction of the CPI

The CPI is the measure of the cost of the basket of goods and services purchased by the 'typical consumer'. It tells us the evolution of its cost of living. If the CPI increases, the typical consumer will have to spend more money to consume the same basket of goods and services, and therefore his cost of living will have increased.

Construction of the CPI and the inflation rate :

1. the basket of the typical consumer is defined and fixed by conducting consumption surveys to determine the weight given to each good in the total expenditure ;
2. price surveys are conducted at regular intervals;
3. the value of the basket is calculated at different points in time based on the prices collected;
4. a base year is chosen and the value of the index is calculated in each year by taking the ratio of the cost of the basket to the base year and multiplying it by 100;
5. the percentage inflation rate is given by the annual change in the CPI: ${\displaystyle Inflation={\frac {IPC_{t}-IPC_{(t-1)}}{IPC_{(t-1)}}}\times 100}$.

## Construction of the CPI: example

1. We define the basket of goods purchased by a typical consumer:

Dépense d’un consommateur représentatif par catégorie de bien (pour nous: hamburgers et hot-dogs).

2. We do price surveys every year:

3. The cost of the (fixed) basket is calculated each year :

4. A base year is chosen for the index and the CPI is calculated:

5. The CPI is used to calculate the annual inflation rate :

## Problems with the CPI

The CPI is not a perfect measure of the cost of living. There are several reasons for this:

• substitution bias: price changes will affect the composition of the typical consumer's basket. The index overestimates the increase in the cost of living by not taking into account the ability of consumers to substitute goods.
• introduction of new goods: this gives more choice to consumers who can substitute the consumption of certain goods with new goods, thus reducing their cost of living (downloading films from the internet is not part of the CPI, but the cinema ticket is). The increase in the cost of living is again overestimated.
• Improved quality of goods: for the same price, the consumer can buy goods that give him greater satisfaction or that perform better. The CPI overestimates the increase in the cost of living by ignoring quality.
• It is not a "true" cost-of-living index: it does not take into account health insurance premiums, taxes, social security contributions, etc. It is not a "real" cost-of-living index. It does not take into account health insurance premiums, taxes, social security contributions, etc. (only consumer goods and services are considered).
• Heterogeneity of consumption baskets: young versus old, poor versus rich, etc. The average consumption basket does not really exist → limits of the average basket if the composition of society changes or the prices of the goods consumed by each group do not evolve in the same way → comparisons between difficult people (and even more so between countries!).

## CPI versus GDP deflator

The GDP deflator was given by : GDP deflator = ${\displaystyle {\frac {PIB{\text{nominal}}}{PIB{\text{real}}}}\times 100}$

Differences from the CPI

1. The CPI focuses on the price evolution of goods consumed in the economy, while the GDP deflator focuses on the price evolution of goods produced in the domestic economy: the price of imported goods is included in the former but not in the latter.
2. The CPI compares the evolution of the cost of a basket of goods that is fixed, while the GDP deflator looks at the evolution of the price of commonly produced goods in relation to the price of goods produced the previous year. (Paasche index versus Laspeyres index)

## Indice de Paasche et Laspeyres

The GDP deflator is a "Paasche index":

GDP deflator = ${\displaystyle {\frac {\Sigma _{j}^{t}p_{j}^{t}}{\Sigma _{j}p_{j}^{(base)}q_{j}^{t}}}}$

in the case of hot dogs and hamburgers = ${\displaystyle {\frac {p_{HD}^{t}\times q_{HD}^{t}+p_{H}^{t}\times q_{H}^{t}}{p_{HD}^{base}\times q_{HD}^{t}+p_{H}^{base}\times q_{H}^{t}}}}$

The consumer price index is a "'Laspeyres index'":

${\displaystyle {\frac {\Sigma _{j}p_{j}^{t}q_{j}^{base}}{\Sigma _{j}p_{j}^{base}q_{j}^{base}}}}$

in the case of hot dogs and hamburgers = ${\displaystyle {\frac {p_{HD}^{t}\times q_{HD}^{base}+p_{H}^{t}\times q_{H}^{base}}{p_{HD}^{base}\times q_{HD}^{base}+p_{H}^{base}\times q_{H}^{base}}}}$

## CPI versus GDP deflator

Two other alternative measures of price changes are the Producer Price Index (PPI), which measures changes in the cost of a (fixed) basket of goods and services purchased by producers (this is used to predict changes in the CPI), and the Import Price Index (IPI).

# Correction of macroeconomic variables for inflation

## Inflation correction

To be able to compare the purchasing power of a certain income in different years, the (nominal) value of this income must be corrected by the evolution of the cost of living. Ex: ${\displaystyle salary_{2004}^{2000}=salary^{2000}\times {\frac {CPI_{2004}}{;}}{CPI_{2000}}={\text{purchase power of salary 2000 in 2004}}}$.

Example 1 :

• George Washington's income in 1789 was USD 25,000.
• George Bush's income in 2007 was USD 450'000.
• The consumer price index with base 100 in 1789 is 2000 in 2007.

Which of the two George's has a higher real income (higher purchasing power)? ${\displaystyle {\text{Washington's income in 2007 = Washington's income in 1789}}\times {\text{CPI in 2007}}{\text{CPI in 1789}}=25000\times {\frac {2000}{100}}=500000}$.

Eexample 2 :

• LeBron James' salary in 2003 (his first year in the NBA) is $4 million. • Michael Jordan's salary in 1984 (his first year in the NBA) is$550,000.
• CPI in 2003 with base 100 in 1984 is \$200.

James has a real salary almost 4 times higher than Jordan's in his first year of the NBA.

## The base year

Price indices are generally set arbitrarily at 100 for a reference period: beware of comparisons!

If one index is 174 and another is 130, it is necessary to have the same base year (or index year or "year 100") in order to know which one has moved the fastest.

For example:

${\displaystyle IPC1995=102.6}$ and ${\displaystyle IPC1997=103.9}$ (1993 = 100)

Inflation rate (between 1995 and 1997) = ${\displaystyle {\frac {103.9-102.6}{102.6}}=0.01267=1.267\%}$ Or more simply, by approximation:

Inflation rate (between 1995 and 1997) = ${\displaystyle 103.9-102.6=1.3\%}$

(approximation valid only for small variations, i.e. < 10%)

## Inflation and deflation

It can be seen that inflation is low between January 2010 and December 2009 and that there is deflation between January 2009 and January 2010.

## Importance of measuring the CPI correctly

The CPI is used continuously in the political and economic life of countries and economic policy authorities as well as individuals rely on the observation of the CPI to make their decisions.

By "revising" the CPI downwards (see the biases we saw earlier), the government can show a larger increase in real wages than the actual increase and justify existing economic policies. The monetary policy adopted by the Central Bank is chosen, among other things, on the basis of the evolution of the CPI.

The CPI is used to index certain contracts, such as pensions, wages, electricity price regulation, etc. The CPI is also used for the indexation of certain contracts.

To evaluate the profitability of an investment we need a measure of the evolution of the cost of living:

Real interest rate = nominal interest rate - inflation rate.

# Summary

The CPI shows the cost of a basket of goods and services in a given year compared to the cost of the same basket in a base year. The percentage change in the CPI gives us the rate of inflation.

The CPI is an imperfect measure of the cost of living for four reasons:

• substitution bias;
• the importance of new goods;
• unmeasurable changes in the quality of goods;
• heterogeneity in the consumption baskets of different individuals.

The GDP deflator differs from the CPI in two respects:

• The CPI focuses on a standard consumption basket and the deflator focuses on the goods produced in the economy;
• The CPI uses a fixed basket of goods and services while the GDP deflator adjusts the composition of the basket to reflect the structure of production each year.

Monetary variables measured at different points in time must be adjusted by their purchasing power (CPI) in order to be compared. In order to say something about the evolution of individuals' purchasing power over time, the CPI must be measured correctly.

The CPI is used to set wages, pensions, the price of certain goods under public regulation.

The real interest rate is what determines the decision to invest and is given by the nominal interest rate minus the inflation rate.