Understanding Time Reversal Test in Price Index Formulas

In the realm of price index formulas, the Time Reversal Test (TRT) plays a crucial role in determining the applicability of various index calculation methods. Professor Fisher introduces tests like TRT, FRT, and Circular Test to gauge formula efficiency. TRT demands that the calculated index remains consistent regardless of the base point chosen. Formulas like Laspeyre's and Paasche's fall short of meeting TRT requirements, while Fisher's Ideal Index, Marshall-Edgeworth Index, and the geometric mean of Price Relative succeed. Explore how different formulas fare in meeting TRT criteria and understand the significance of Fisher's formula in satisfying it.

• Price Index
• Time Reversal Test
• Professor Fisher
• Index Formulas
• Economics

valley Follow

Uploaded on Jul 18, 2024 | 1 Views

Download Presentation

Please find below an Image/Link to download the presentation.

The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.

Presentation Transcript

1. Dr Parmila Assistant Professor of Commerce Kanya Mahavidyalaya Kharkhoda Sonipat

2. Prof. Fisher has given the following tests to select an appropriate formula: Time Reversal Test TRT Factor Reversal Test- FRT Circular Test

3. Time Reversal Test TRT Illustrating this test, Prof Fisher remarks, The test is that the formula for calculating an index number should be such that it will give the same ratio between one point of comparison and the other, no matter which of the two is taken as base Time Reversal Test is satisfied when 1 P01= --------- or P01X P10= 1 P10 Where, P01 P10 = Price index for the year one with zero as base = Price index for the year zero with one as base

4. Time Reversal Test TRT This test is not satisfied by simple A.M. of price relative, Laspeyre and Paasche s formula. But this test is satisfied by Fisher s Ideal Index, Marshall-Edgeworth Index and simple G.M. of Price Relative. Laspeyre s Formula : p1q0 --------- X 100 p0q0 p0q1 --------- X 100 p1q1 The Laspeyre s Formula does not satisfied the TRT. P01= P10= Since P01X P10 1

5. Time Reversal Test TRT Paasche s formula p1q1 --------- X 100 p0q1 P01= p0q0 --------- X 100 p1q0 P10= Since P01X P10 1 The Paasche s Formula does not satisfied the TRT.

6. Time Reversal Test TRT Fisher s formula __________________ p1q0 --------- X p0q0 p1q1 ---------- p0q1 P01= X 100 __________________ p0q1 --------- X p1q1 p0q0 ---------- p1q0 P10= X 100 Since P01X P10= 1 The fisher s Formula does satisfied the TRT.

7. Time Reversal Test TRT Dorbish and Bowley s formula p1q0 --------- + p0q0 _____________________________ p1q1 ---------- p0q1 P01= 2 p0q1 --------- + p1q1 _____________________________ p0q0 ---------- p1q0 P10= 2 Since P01X P10 1 The Dorbish and Bowley s Formula does not satisfied the TRT.

8. Time Reversal Test TRT Marshall- Edgeworth s formula p1q0+ ---------------------------- p0q0+ p1q1 P01= X 100 p0q1 p0q1+ --------------------------- p1q1+ p0q0 P10= X 100 p1q0 Since P01X P10= 1 The Marshall- Edgeworth s formula does satisfied the TRT.

9. Factor Reversal Test FRT According to Prof Fisher, Just as our formula should permit the interchange of two times without giving inconsisting results, so it ought to permit interchange of prices and quantities without giving inconsistent results, i.e., the two results multiplied together should give the true value ratio. Factor Reversal Test is satisfied when p1q1 --------- p0q0 P01X Q01= Where, P01 Q01 = Price index for the year one with zero as base = Quantity index for the year one with zero as base

10. Factor Reversal Test FRT This test is not satisfied by Laspeyre, Paasche s formula and Marshall- Edgeworth. But this test is satisfied by Fisher s Ideal Index. Laspeyre s Formula : p1q0 --------- X 100 p0q0 q1p0 --------- X 100 q0p0 P01= Q01= p1q1 P01X Q01 --------- p0q0 The Laspeyre s Formula does not satisfied the FRT.

11. Factor Reversal Test FRT Paasche s formula p1q1 --------- X 100 p0q1 q1p1 --------- X 100 q0p1 p1q1 P01= Q01= P01X Q01 --------- p0q0 The Paasche s Formula does not satisfied the FRT.

12. Factor Reversal Test FRT Fisher s formula __________________ p1q0 --------- X p0q0 p1q1 ---------- p0q1 P01= X 100 ___________________ q1p0 --------- X q0p0 q1p1 ---------- q0p1 Q01= X 100 p1q1 --------- p0q0 P01X Q01= The fisher s Formula does satisfied the FRT.

13. Factor Reversal Test FRT Dorbish and Bowley s formula p1q0 --------- + p0q0 _____________________________ p1q1 ---------- p0q1 P01= 2 q1p0 --------- + q0p0 _____________________________ q1p1 ---------- q0p1 Q01= 2 p1q1 P01X Q01 --------- p0q0 The Dorbish and Bowley s Formula does not satisfied the FRT.

14. Factor Reversal Test FRT Marshall- Edgeworth s formula p1q0+ ---------------------------- p0q0+ p1q1 P01= X 100 p0q1 q1p0+ ---------------------------- q0p0+ q1p1 Q01= X 100 q0p1 p1q1 P01X Q01 --------- p0q0 The Marshall- Edgeworth s formula does not satisfied the FRT.

15. Circular Test According to this test, if there are three time periods 0,1,2 and price index od period 1 relative to 0 (P01), price index of period 2 relative to period 1 (P12) and price index of period 0 relative to period 2 (P20) are computed, then the product of these three indices must be unity. P2 P0 Symbolically: P1 P01X P12X P20= 1

16. Circular Test Circular test is satisfied by simple aggregative index only.

17. Thanks