Time Reversal Test and Marshall-Edgeworth Formula

Time Reversal Test is a statistical test used to check the consistency of an index number formula. It examines whether the index number formula satisfies the property of time reversibility. Time reversibility means that if the formula is used to calculate an index number for a period of time, say from year 1 to year 5, and then the formula is applied to calculate the index number for a different period of time, say from year 5 to year 1, the two index numbers should be equal.

Marshall-Edgeworth Formula is an index number formula used to measure the changes in the prices of a basket of goods and services over time. The formula is based on the concept of weighted averages and uses the arithmetic mean of the price relatives to calculate the index number.

The Time Reversal Test is satisfied by the Marshall-Edgeworth formula. This means that if the formula is used to calculate an index number for a period of time and then the formula is applied to calculate the index number for the same period but in reverse order, the two index numbers will be equal. The test is satisfied because the Marshall-Edgeworth formula is based on the weighted arithmetic mean of the price relatives and is time-reversible.

Other Index Number Formulas

There are several other index number formulas used to measure changes in prices over time. Two of the most commonly used formulas are the Laspeyres Index Number and the Simple Arithmetic Mean of Price Relative Formula. However, these formulas do not satisfy the Time Reversal Test.

The Laspeyres Index Number is based on the prices of a fixed basket of goods and services in a base period. The formula uses the quantity of goods and services consumed in the base period to calculate the index number. The Laspeyres Index Number is not time-reversible because it uses fixed quantities of goods and services.

The Simple Arithmetic Mean of Price Relative Formula is based on the arithmetic mean of the price relatives. The formula does not use weights, which means that all items in the basket are given equal importance. The Simple Arithmetic Mean of Price Relative Formula is not time-reversible because it does not use weights to account for changes in the quantities of goods and services consumed over time.

Conclusion

In conclusion, the Marshall-Edgeworth formula satisfies the Time Reversal Test because it is based on the weighted arithmetic mean of the price relatives. The formula is time-reversible, which means that if it is used to calculate an index number for a period of time and then the formula is applied to calculate the index number for the same period but in reverse order, the two index numbers will be equal. Other index number formulas, such as the Laspeyres Index Number and the Simple Arithmetic Mean of Price Relative Formula, do not satisfy the Time Reversal Test.

None