Index Numbers

An index number measures the relative change in price, quantity, value, or some other characteristics of interest compared to a base period. It is a statistical value that measures the change in a variable with respect to the reference value of a variable for a specific period specific period such as a starting year, a specific factory or a specific location. 

A simple index number can be calculated using the following equation:

If the index number is greater than 100, it indicates an increase compared to the base period value while if it is less than 100, it indicates a decrease compared to the base period value. 

Depending on the number of variables included in the comparison, index numbers can be different. If an index number is used to measure the relative change in just one variable, this indicates a simple index. In the simple index calculation, the ratio of the two variables is converted to a percentage. In other words, index numbers are the percentage of a comparison with a reference value written without the percent symbol. It is important to determine what to write in the reference value field since the simple index calculations can be examined as a fixed based method and chain-based method. In applications, two types of indexes dominate, which are price and quantity indexes.

When you have a fixed period for the calculation of simple index values, all the index values are the division of their current observation values to the base period values of the variable that the index is calculated. Therefore, the equation for a simple index number can be re-written as follows to depict how to fix a base period for all index numbers to be calculated in the problem. Its equation is as follows:

Fixed based simple price index indicates the change in the price of a single item from a fixed base period to the period under consideration. It is calculated by dividing the price in the current period by the price in the fixed base period and expressed as percentage. This index allows the investigator to make comparison of prices of a specific product or characteristic from one period to other periods based on a starting period’s value. Its equation is as follows:

Fixed based simple quantity index indicates the change in the quantity of a single item from a fixed base period to the period under consideration. It is calculated by dividing the quantity in the current period by the quantity in the fixed base period and expressed as percentage. This index allows the investigator to make comparison of prices of a specific product or characteristic from one period to other periods based on a starting period’s value. Its equation is as follows:

A chain index is an index number where the value of any given period is relative to the value of the preceding period. Remember that in the fixed-base index, the index value of each period in a time series is directly related to the value of a fixed base period. In calculation of a chain-based index, the base period changes from year to year and this permits a comparison between two consecutive periods. The following equation is used to calculate chain-based simple index:

Chain-based simple price index indicates the change in the price of a single item between two consecutive periods. It is calculated by dividing the price of a product in the current period by the price of the same product in the preceding period and the result is expressed as percentage. The following equation is used to calculate chain-based index for price:

Chain-based simple quantity index indicates the change in the quantity of a single item between two consecutive periods. It is calculated by dividing the quantity of a product in the current period by the quantity of the same product in the preceding period and the result is expressed as percentage. The following equation is used to calculate chain-based index for quantity:

A composite index number is constructed to show the changes when there are a number of different items collected together. In some cases, it is desirable to develop an index to compare the aggregation of several substances and the cost of collecting these substances in two different periods. Composite index reflects the average change in the activity of a group of items from the base period to the period under consideration.

Composite indexes can be examined in two categories, namely weighted and non-weighted, based on the idea that the indexes take into account the importance of the products.

In order to calculate composite index number, one should be careful about how the items are included in the basket of goods or how the items are organized in in that basket. A basket of goods and services describes a fixed set of commodities for which we may measure changes in price and quantity. When it is assumed that there are no differences between the importance of the commodities in basket, unweighted composite indexes can be used to compare the changes.

A simple aggregate price index is simply based on accumulating the unit prices of several commodities in different periods. As the name suggests, in this index one looks at the total price of the products in a basket and makes a comparison of this total with another period or with a base period. Therefore, this index will show us the difference of the total price paid to the products in the basket from one period to another period. During the period, the price of some items may be increased while the price of others is decreased, the investigator does not consider the changes in the item price but s/he is interested in the total price change of the products. This index requires the prices of each product in the basket from one period to the other if the price of an item is missing in one period, then the simple aggregate index should not include this item in the final calculations.

In this method, first a fixed based or chain-based simple indexes are computed for different periods and then one of the averages such as arithmetic mean, geometric mean or median is used to find the averages of the found index values. This index also does not take into account the quantity of each item, but it is still a vast improvement on the simple aggregate index. The simple average of relative method is simpler and easier to apply than the simple aggregative method. The only disadvantage is that it gives equal weight to all items.

In some situations, it is not possible to look at all the items in a group for which an index calculation is planned, and some items might have more importance or weight than the others among the group members. When all commodities are not of equal importance, a weight of importance to each commodity might be assigned and an index number is computed then it is called weighted index numbers. The use of a weighted index allows the investigator to give greater importance to some of the items in the group. The importance is highlighted by assigning proper weighting to the values of items in proportion to their relative importance. Information other than the change in price over time can be used and can include such factors as the quantity sold or the quantity consumed for each item.

Laspeyres Index was created by the German economist Étienne Laspeyres. The technique designed by Laspeyres uses base-period weights. It consists of the information about the price and quantity of products in different periods. The weighting scheme makes it a better tool than simple indexes. By using the Laspeyres index, it is possible to make a comparison of today’s price and quantity between the price and quantity of items altogether for a base period. The Laspeyres price index is also known as the average of weighted relative prices since it is a composite index number of prices formed by the weighted sum method. The index is found by the ratio of the sum of prices in the current period to the sum of the prices in the base period, these sums are weighted by the respective quantities of the base period. In this case, the weights which are used are the quantities of each commodity in the base period. So, it measures the relative price change of the commodities when the respective quantities are considered unchanged.

In the calculation of the Paasche price index, the current period quantities are used as weights, so it is also known as the current year weighted index. This is another weighted index. The Paasche uses the quantities from the current period rather than a base period therefore it may be said that it reflects the buying habits of today’s customers. Overall, it measures the change in the price of commodities, in terms of quantities related to the current period.

There are advantages and disadvantages of both Paasche and Laspeyres indexes. In order to compensate, another index was created based on these two indexes. It is called Fisher’s ideal index. It is actually the geometric mean of these two indexes. Therefore, it is very easy to calculate Fisher’s ideal index using the results of Paasche and Laspeyres indexes.

The consumer price index (CPI) is a measure that is used to finds out the total cost of goods and services purchased by an ordinary consumer via examining the weighted average prices of goods and services in a heterogenous basket with many goods that a person might use in daily life. It is used to track the general price level of goods and services, and to determine changes in living costs over time.

Since it is used as an indicator of the cost of living, the consumer price index is the most commonly known of published indexes. It is generally accepted as a measure of inflation in a country. As an economic indicator, it gives information to understand the economic progress and changes, it also helps make decisions about the economy. When it increases, it means that an ordinary an ordinary family might spend more money to maintain the same standard of living. The consumer price index is published in monthly figures by the Institute of Statistics in Turkey.

The producer price index (PPI) is a family of indexes that measures the average change over time in selling prices received by domestic producers of goods and services. It is an output index and designed for domestic goods’ price changes; imports are not included. This index is based on the first commercial transaction of each product in non-retail markets.

The producer price index is frequently seen as as improved indicators of price changes in the economy and it is widely used as an important display of the future of the future trend of consumer price and the cost of living. When this index increases, it means there will be producer price increases that will ultimately pass to consumers with higher retail prices. Different from from the consumer price index, the producer price index measures price change from the seller’s perspective, not from the purchasers.