Circular Test and Index Number

Circular Test is a test of consistency of index numbers. It states that if an index number is calculated using two or more different methods, and if one of these methods is used to calculate the base value of the index, then the index number should return the base value when it is used to calculate the index number again.

An index number is a statistical measure that represents the changes in a variable over time. It is calculated by comparing the value of the variable at different points in time. Index numbers are widely used in economics and finance to measure inflation, productivity, and other economic variables.

Geometric Mean of Price Relatives

The geometric mean of price relatives is a method of calculating an index number. It is calculated by taking the nth root of the product of the price relatives for n periods. The price relative for a period is the ratio of the price of a commodity in that period to its price in the base period.

Weighted Aggregative with Fixed Weights

The weighted aggregative with fixed weights is another method of calculating an index number. It is calculated by taking the weighted average of the price relatives for n periods, where the weights are fixed and do not change over time.

Laspeyres, Paasches, or the Fishers Ideal Index

Laspeyres, Paasches, and the Fishers Ideal index are three commonly used methods of calculating index numbers. The Laspeyres index is calculated by using the prices of the base period as weights. The Paasches index is calculated by using the prices of the current period as weights. The Fishers Ideal index is a geometric mean of the Laspeyres and Paasches indexes.

Circular Test and Laspeyres, Paasches, or the Fishers Ideal Index

The circular test is not met by the Laspeyres, Paasches, or the Fishers Ideal index. This is because these methods do not use a fixed base period to calculate the index number. Instead, they use the prices of two different periods to calculate the index number. Therefore, if one of these methods is used to calculate the base value of the index, the index number will not return the base value when it is used to calculate the index number again.

Conclusion

In conclusion, the circular test is a test of consistency of index numbers. It states that an index number should return the base value when it is used to calculate the index number again using one of the methods that were used to calculate the base value. The Laspeyres, Paasches, and Fishers Ideal index do not meet the circular test because they do not use a fixed base period to calculate the index number.

Circular test is not satisfied by any of the index numbers