Circular Test:

The circular test is a test that determines the consistency of index numbers. It is also known as the reversal test or the inter-temporal consistency test. The circular test compares two index numbers that are calculated using two different base years.

Explanation:

The circular test is satisfied when the product of two index numbers, calculated using the same set of prices and quantities, is equal to 100. In other words, if we have two index numbers, A and B, both calculated using the same set of prices and quantities, then the circular test is satisfied if:

A x B = 100

If the circular test is not satisfied, it means that the index numbers are not consistent and may contain errors. The circular test is used to check the accuracy of index numbers and to ensure that they are reliable.

Index Numbers:

An index number is a statistical measure of the percentage change in a variable over time. Index numbers are used to track changes in prices, quantities, and other economic variables. There are different types of index numbers, including:

1. Laspeyres index number
2. Paasches index number
3. Fisher's index number

None of these index numbers satisfy the circular test. This is because the Laspeyres index number uses fixed quantities and the Paasches index number uses fixed prices, which makes them inconsistent. Fisher's index number is a weighted average of the Laspeyres and Paasches index numbers, so it also does not satisfy the circular test.

Conclusion:

In conclusion, the circular test is a test that determines the consistency of index numbers. None of the commonly used index numbers, including the Laspeyres, Paasches, and Fisher's index numbers, satisfy the circular test. It is important to use reliable and consistent index numbers to make accurate economic analysis and decisions.

Because it satisfied only by the index number formulae based on the simple gometric mean of the price relatives and Kelley's fixed weights or base method.