Understanding Time Reversal Test
The time reversal test is a concept used in index number theory to assess how well an index number reflects changes in price or quantity over time.
Key Index Numbers
- Fisher Index Number: This is a geometric mean of the Laspeyres and Paasche index numbers. It satisfies the time reversal test, meaning if you calculate the index from one period to another and then back again, you should obtain the original values.
- Laspeyres Index Number: This index uses base-period quantities to measure price changes. It does not satisfy the time reversal test, as reversing the calculation can lead to inconsistencies.
- Paasche Index Number: This index uses current-period quantities to measure price changes. Similar to the Laspeyres index, it fails the time reversal test for the same reasons.
Why Fisher Index is Correct?
- The Fisher index is constructed to overcome the limitations of the other two indices. It provides a more balanced approach by taking into account both the base and current period quantities.
- When the Fisher index is calculated in both directions (from period 1 to period 2 and then back to period 1), it consistently returns to the original values, thus satisfying the time reversal condition.
Conclusion
In summary, the Fisher index number stands out as it fulfills the time reversal test, making it a reliable option for measuring changes in economic variables over time compared to the Laspeyres and Paasche indices. This property makes it particularly valuable in economic analysis and decision-making.