Measuring Price Change

A single-item price index time series can be created from a series of prices over time.

**Single Item Index Number**

This can be done by:

- choosing one period as the reference period and giving it an index value of either 100 or 1000.
- scaling all the other prices accordingly.

**EXAMPLE**

1. Take a time series of prices of mushrooms.

Taking a time series of prices | ||||
---|---|---|---|---|

Item | Month |
|||

Jan | Feb | Mar | Apr | |

Mushrooms ($ per kg) | 5.00 | 5.60 | 6.00 | 7.00 |

2. Choose an index reference period (e.g. January).

Taking a time series of prices | ||||
---|---|---|---|---|

Item | Month |
|||

Jan | Feb | Mar | Apr | |

Mushrooms ($ per kg) | 1000 | ... | ... | ... |

3. Calculate the index numbers using the increase in the price from the index reference period to each of the other months:

Feb =\frac{1000 \times 5.60}{5.00}
= 1120

Mar =\frac{1000 \times 6.00}{5.00}
= 1200

Apr =\frac{1000 \times 7.00}{5.00}
= 1400

Taking a time series of prices | ||||
---|---|---|---|---|

Item | Month |
|||

Jan | Feb | Mar | Apr | |

Mushrooms ($ per kg) | 1000 | 1120 | 1200 | 1400 |

This means that there has been a 40% increase in the price of mushrooms from January to April. What was the increase from January to February?

**The correct answer is %**

**EXERCISE**

Calculate an orange juice price index time series (Use June as the reference period with an index number of 100, Orange juice is in $ per litre).

Taking a time series of prices | ||||
---|---|---|---|---|

Item | Month |
|||

Jun | Jul | Aug | Sep | |

Orange Juice ($ per litre) | 3.00 | 2.40 | 3.00 | 3.60 |

Jul =

×

3.00

=
**The correct answer for the missing value is **

Aug =

×

3.00

=
**The correct answers for the missing values are and **

Sep =
=

×

**The correct answers for the missing values are , , and **

What was the increase from:

- a. Jun to Sep?

The answer is %

- b. Jun to July?

The answer is %

END SINGLE ITEM INDEX NUMBER

When there is more than one item included in the index number we use the multi-item index number.

**Multi-Item Index Number**

If there is more than one item included in the index number then each good or service in the basket is assigned an expenditure weight representing its (average) relative importance in household spending patterns.

Goods and services that are more important to households are given higher weights and have a greater influence on the CPI.

The weight assigned determines how much impact a price movement for a particular good has on the overall CPI. For example, if households spend more on petrol than on milk, a 5 percent increase in the price of petrol would have a greater impact on the CPI than a 5 percent increase in the price of milk.

**Calculating Weights**

A sample survey of households is usually undertaken to work out the average household expenditure.

The proportion of the total expenditure on items in a '*Subgroup*'
or '*Group*' is its '*Expenditure Weight*'.

**EXAMPLE**

The weights for each Group in the table below are calculated showing the percentage of total expenditure on goods in that Group.

Group | Spending ($) |
Proportion/Weight |

Food | 856 | 26.11% |

Housing | 1234 | 37.64% |

Household Operations | 326 | 9.95% |

Clothing & Footware | 124 | 3.78% |

Transport | 576 | 17.57% |

Tobacco & Alcohol | 84 | 2.56% |

Miscellaneous | 78 | 2.38% |

TOTAL | $3278 | 100.00% |

The proportion/weight for Food is calculated as:

\frac{856}{3278} \times 100 = 26.11\%

**EXERCISE 1**

Calculate the weights for the items in the following expenditure table

For all of these exercises answers are to one decimal place. Click 'Check' after you have entered all values in each table, any correct responses will be highlighted with a green border.

**From top to bottom the answers are: , , , , , **

**EXERCISE 2**

*New Zealand*

The following table has the Groups and Subgroups in New Zealand's CPI. Estimate (or collect) your quarterly spending in each Group and fill in the table below. If you have not spent anything in a subgroup then just leave it blank.

You can *view the table here* but you should use **Excel** to calculate the percentage you spent on each Group. These
are **YOUR** expenditure weights.

You can compare your weights to those for the average New Zealand household, these are given below.

*View the table here* or download a copy in Excel using the button below.

More information on the Statistics New Zealand site here: *www.stats.govt.nz*

- a student sharing a flat may have cheap rent and smaller weight for housing
- a non-drinker, no-smoker will have a very small, possibly zero weight, for alcohol and tobacco
- a person who works from home may have small costs and a small weight for transport

END MULTI-ITEM INDEX & CALCULATING WEIGHTS