This page is a learning resource for the food price index (FPI). It outlines the purpose of the index and its main uses, and provides a few practical exercises relating to the index.

- What is the food price index?
- How is the data collected?
- How is the FPI used?
- What are the common confusions?
- Statistical calculations
- Further reading
- Answers

## What is the food price index?

The food price index (FPI) measures the change in food prices faced by households over time. The food group is the only commodity group of the consumers price index (CPI) for which an index is prepared each month. The CPI is prepared quarterly.

The FPI consists of five subgroups:

- fruit and vegetables
- meat, poultry, and fish
- grocery food
- non-alcoholic beverages
- restaurant meals and ready-to-eat food.

These subgroups are broken down into 14 classes and 17 sections within selected classes.

Since July 2008, 157 different food goods and services are included in the FPI basket (see ‘Definitions’ below). The basket of goods and services is reviewed every three years, with the latest review being implemented in July 2008.

Each item in the basket is allocated an expenditure weight (see ‘Definitions’ below), which shows its importance in a household’s shopping basket relative to other food items. The more that households spend on a particular item the higher the weight assigned to that item is. Items with higher weights have a larger impact on the FPI. For instance, if households spend more on milk than on bread, a 5 percent increase in the price of milk would have a greater impact on the FPI than a 5 percent increase in the price of bread.

It is important to note that the FPI is not a measure of price levels or average prices, it is primarily a measure of price change. A price index is a series of numbers that show how a whole set of prices has changed over time. One index number by itself means nothing. Another index number is needed to compare it with in order to calculate the movement between the two time periods.

## How is the data collected?

Food prices are collected for the FPI in Whangarei, Auckland, Hamilton, Tauranga, Rotorua, Napier-Hastings, New Plymouth, Wanganui, Palmerston North, Wellington, Nelson, Christchurch, Timaru, Dunedin, and Invercargill.

Prices are collected from about 650 outlets in the 15 surveyed urban areas. Of these, about 75 are supermarkets, 30 are greengrocers, 30 are fish shops, 30 are butchers, 50 are convenience stores (half are service stations and the other half are dairies, grocery stores, and superettes), 120 are restaurants (for evening meals), and more than 300 are other suitable outlets (for breakfast, lunch, and takeaway food). Fresh fruit and vegetable prices are collected weekly while all other prices are collected monthly.

## How is the FPI used?

The FPI is used to report on the changing price of food and non-alcoholic beverages faced by New Zealand households. Percentage movements between different periods are calculated to show how much prices have changed.

In addition to publishing index numbers and percentage changes, Statistics New Zealand also publishes a table of average prices for selected food items each month (table 3 in the monthly FPI information release). These are weighted average prices that can be compared with previously published average prices. They are not statistically accurate measures of average transaction price levels, but do provide a reliable indicator of percentage changes in prices. However, it may be misleading to compare the FPI average prices with other prices, for instance prices collected directly from individual stores, because the FPI average prices are nationwide weighted averages that cover many brands, varieties, and types of stores.

## What are the common confusions?

A common confusion associated with the FPI is that it should exactly represent an individual's personal inflation experience. However, the goods and services used to calculate the FPI – and their relative importance – reflect purchases made by all New Zealand private households. The basket includes a large variety of food goods and services that is very unlikely to exactly match the purchases of any individual household. Furthermore, the FPI includes prices from throughout the country, whereas most households make the majority of their purchases in just one region. This means that movements in the FPI will not exactly match the inflation experiences of individual households.

## Statistical calculations

### Definitions

**Basket** – Commonly used term for the set of goods and services, specified in terms of commodity and quantity, whose prices are surveyed to compile the FPI.

**Expenditure weight** – The measure of the relative importance of an item, based on the expenditure of the item relative to expenditure on all items in the basket.

**Index number series** – For more information on index number series please see the CPI learning resource.

**Percentage change in index numbers** – The change in an index number time series from one period to another is expressed as a percentage. Percentage change can be calculated using the following formula:

percentage change = | current value - previous value x 100 ______________________ |

previous value |

### Example

#### Calculating a single-item price index time series

A price index gives information about how specific price levels change over time. The changes are commonly expressed as percentage changes.

Suppose you have a time series of index numbers that represents the price level of a packet of coffee over three months (the same size and brand is priced each time from the same outlets). The price of the coffee is represented as an index number in table 1.

The percentage change of an index can be calculated using the formula given above (see ‘Definitions’).

Column A gives the percentage movement from month to month and column B from the reference month to the current month.

Table 1

Calculating percentage changes from indexes |
|||

Month |
Index number |
A(month to month) |
B(reference to current month) |

Percent |
|||

Jan (reference) | 1000 | ... | ... |

Feb | 1500 | = 1500-1000 x 100 ________ 1000 = 50 |
= 1500-1000 x 100 |

Mar | 1650 | = 1650-1500 x 100 ________ 1000 = 10 |
= 1650-1000 x 100 ________ 1000 = 65 |

Symbol: ... not applicable |

This time series shows that the price of this brand of coffee increased by 50 percent from January to February. In March, the price was 10 percent higher than it was in February and 65 percent greater than it was in January.

However, the index numbers show nothing about the actual price of the coffee. It may have been $8.00 in January and increased to $12.00 in February, or it may have started at $15.00 and increased to $22.50.

#### Calculating percentage changes for periods that are not adjacent

In addition to the price movement from one period to the next, the price movement for the whole year, or for two years, may need to be known. A common mistake is to add the percentage movements of the four quarters together to arrive at the annual movement.

Index movements cannot be calculated by adding together the percentage changes of adjacent periods within the longer time period being considered. Movements must always be calculated from the start period to the end period under consideration.

Consider the index series in table 2:

Table 2

Calculating percentage changes from non-adjacent periods |
||||

Month | Index number | Monthly change | A Sum of months |
B Change from March |

Mar | 1000 | ... | ... | ... |

Apr | 1030 | 3.0 | 3.0 | 3.0 |

May | 1500 | 45.6 | 48.6 | 50.0 |

Jun | 1700 | 13.3 | 61.9 | 70.0 |

Jul | 1900 | 11.8 | 73.7 | 90.0 |

Symbol: ... not applicable |

The percentage movements for the months are:

March to April: 3.0% = | 1030 - 1000 x 100 _________ |

1000 |

April to May: 45.6% = | 1500 - 1030 x 100 _________ |

1030 |

May to June: 13.3% = | 1700 - 1500 x 100 _________ |

1500 |

June to July: 11.8% = | 1900 - 1700 x 100 _________ |

1700 |

The sum of the monthly percentage movements is 73.7%.

However, the index has moved from 1000 to 1900 since March, an increase of

90 percent = | 1900 - 1000 x 100 __________ |

1000 |

Clearly, the sum of the monthly movements does not equal the actual total movement from March to July.

### Activities

#### Calculate monthly percentage changes

The table below gives a time series of index numbers, which represents the price of a loaf of bread over five months (the same size and brand is priced each time from the same outlets). The price of the bread is expressed as an index number.

Using the percentage change formula, calculate the monthly percentage change from each month to the next month.

percentage change = | current value - previous value x 100 ______________________ |

previous value |

Monthly percentage change in bread prices |
||

Month |
Index number |
Monthly percentage change |

Jan | 1000 | ... |

Feb | 1200 | |

Mar | 1450 | |

Apr | 1700 | |

May | 1450 | |

Symbol: ... not applicable |

#### Calculate longer-term percentage changes

Using the same data from above, calculate the percentage change in the price of bread from January to each of the other months.

Percentage change in bread prices, reference to current month |
||

Month |
Index number |
Percentage change from January to current month |

Jan | 1000 | ... |

Feb | 1200 | |

Mar | 1450 | |

Apr | 1700 | |

May | 1450 | |

Symbol: ... not applicable |

## Further reading

Layperson's Guide: All About the Consumers Price Index

Updating the food price index basket

Food Price Index: December 2008

## Answers

Month |
Index number |
Monthly percentage change |
Percentage change from January to current month |

Jan | 1000 | ||

Feb | 1200 | 20.0 | 20.0 |

Mar | 1450 | 20.8 | 45.0 |

Apr | 1700 | 17.2 | 70.0 |

May | 1450 | -14.7 | 45.0 |