When the product of price index and the quantity index is equal to the...
Factor Reversal Test: It says that the product of a price index and the quantity index should be equal to value index. In the words of Fisher, just as each formula should permit the interchange of the two times without giving inconsistent results similarly it should permit interchanging the prices and quantities without giving inconsistent results which means two results multiplied together should give the true value ratio.
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When the product of price index and the quantity index is equal to the...
Factor Reversal Test
The factor reversal test is a statistical test used to check the accuracy of the price and quantity indices used in measuring changes in the value of a product or group of products over time. It is based on the relationship between the price index, the quantity index, and the value index.
Understanding the Test
The factor reversal test states that if the product of the price index and the quantity index is equal to the corresponding value index, then the test holds. In other words, if the formula Price Index * Quantity Index = Value Index is satisfied, then the price and quantity indices are accurate and reliable measures of changes in the value of a product.
Interpreting the Test
When the factor reversal test holds, it indicates that the changes in the value of a product or group of products are accurately reflected in the price and quantity indices. This means that the indices are consistent and reliable in measuring the changes in value over time.
Implications of the Test
The factor reversal test is an important tool in validating the accuracy of price and quantity indices. If the test does not hold, it suggests that there may be errors or inconsistencies in the measurement of changes in value. In such cases, further analysis and adjustments may be required to ensure the accuracy of the indices.
Example:
Let's consider an example to illustrate the factor reversal test. Suppose we have a product with an initial value of $100, a price index of 1.2, and a quantity index of 0.8.
Using the formula Price Index * Quantity Index = Value Index, we can calculate the value index as follows:
1.2 * 0.8 = 0.96
The calculated value index is 0.96, which indicates that the value of the product has decreased by 4% compared to the initial value.
By comparing the calculated value index with the actual value index, we can determine whether the factor reversal test holds. If the calculated value index matches the actual value index, then the test holds, and the price and quantity indices accurately reflect the changes in value.