statistics: index numbers calculation

Consumer Price Index or commonly called index numbers are created to measure the impact of changes in the cost of selected group of goods and services on the buying power of a specific category of society at any point in time with reference to a fixed reference. The index numbers are updated each month with updated basket of goods and services for analysis according to changes in cost of living. A variety of different approaches are adopted for the compilation of index numbers like the retail price index, Purchasing Managers Index (PMI), Purchasing Manager Cost Index (PMC), Consumer Price Index (CPI) and the residual price index. All these compilations consider various aspects of the production processes, including pricing, quality, availability, and competition among the producers. In general, there are four index numbers: the Purchasing Managers Index (PMI), the Purchasing Manager Cost Index (PMC), the Index of Consumer Prices (ICP) and the Real Effective Market Currencies (REEMAC).

The first step in the process to calculate index numbers is to decide the classification of the products to be measured. Two variables are chosen to be used in these calculations; these variables are the prices of the products being measured and their quantities. Other methods may also be used to select two variables; however these two variables should be well chosen so as to get reliable estimates. Some other important criteria that need to be considered while calculating aggregate expenditure are: whether the prices of domestic products can be compared across countries and whether country-specific prices are needed.

Another important criterion in choosing the index number methodology is whether to use actual prices or implied prices. The former is a more accurate method than the latter because it takes into account the fact that costs of production are likely to be volatile and are subject to change with respect to the prevailing conditions in any country. The other important criterion in the determination of the index number is whether to use the consumer price index number or the index of personal expenditure. While using the latter, certain assumptions need to be made for statistical purposes; these assumptions form the basis of the aggregated index. If these assumptions are not correct then the entire statistical analysis will be incorrect.

One of the simplest ways to calculate index numbers is to follow data using the consumer price index number. This is an appropriate way to calculate aggregates if the volumes consumed are large. For example, if one wants to calculate the cost of living index numbers then one would have to obtain the ASI based from national accounts and then multiply this by the volume of production. Other approaches include the Price Index System and the Purchasing Managers Index (PMI).

The other common way to calculate index numbers is the annual percentage rate (APR) method which is based on the prices of the goods and services sold during a specific time period. The data needed for the calculation are the prices per transaction for goods sold on a typical scale for one year. One has to adjust these values according to the usual market conditions to get the APRs for each family in the economy.

The alternative measure of index numbers that can be used to calculate aggregates is the current price relative to the index number in the base year and compare this with the corresponding index number in the base year. This is the most widely used approach and is also the oldest methodology. Using this approach, the process is simplified to a great extent because there is no need to make any assumption about the nature of the items sold in the base years compared with the items sold in the base years. The approach makes it possible to calculate aggregates at different time periods since the prices of the products are usually updated every year. Another advantage of this method is that it gives a reasonable picture of the changes in prices over time.

For calculating the index numbers for the current year, the process is quite similar to what was done earlier. First, a set of product prices is obtained from the ASBES database using the source code of the product. These prices are then used to subtract the prices in the base years from the current prices to arrive at the index number. Next, the weighted mean of all the times the average prices minus the average prices in the previous years are called the index number.

The next step involves the calculation of the deviation of the weighted mean price relative to the target price. The price relative method was first introduced in macroeconomic theory by equilibrium point theory and it assumes that a macroeconomic equilibrium exists. For calculating the deviation, the standard deviation is used as an estimate of the deviation of the mean price from its equilibrium value. By following the steps mentioned above, one will be able to use the index number for estimation purposes and derive estimates of growth in GDP by applying the same method to obtain the index numbers for the current year.