Tests for consistency, Financial Management

Tests for Consistency

The consistency of the index numbers have been tested over the years. The most important of these tests are:

  1. The time reversal test

  2. The factor reversal test

  3. The circular test.

Time Reversal Test

Time reversal test has been developed by Prof. Irving Fisher. The test implies that for a price/quantity index, if the time periods are reversed, the resulting index should be the reciprocal of the original price/quantity index. 

If I0,1 denotes the original index for the current year with a given base year, and if I1, 0 denotes the resulting index, with time periods reversed, for the base year with the current year as a base year, then according to the time reversal test,

I0, 1 = 

1571_time reversal test.png  (or) I0, 1 x I1, 0 = 1

Let us test the consistency of the indices by interchanging 0 and 1 with 1 and 0 respectively.

It can be shown that Fisher's Ideal Index, Marshall-Edgeworth Index and Fixed Weights Aggregate Index satisfy this test. Laspeyres Index and Paasche Index do not. 

Factor Reversal Test

This test was also suggested by Prof. Irving Fisher. According to Prof. Fisher just as each formula should permit the interchange of the two time periods without giving inconsistent results, it ought to permit interchanging of the prices and quantities without giving inconsistent result, i.e. the two results multiplied together should give the true value ratio.

The product of change in prices in the current year and the change in quantities in the current year should be equal to  246_time reversal test1.png  (Value ratio)

where,

P1=Prices in the current year

P0=Prices in the base year

Q1=Quantities in the current year

Q0=Quantities in the base year

The test can be applied to the index numbers by interchanging P to Q and Q to P.

Except Fischer's Ideal Index, all other elementary indices, simple as well as weighted, fail to satisfy this test. 

Circular Test

Circular test is an extension of the time reversal test. This test is used while measuring price changes over a number of years with the shifting of base occurring frequently. According to this test, an index constructed for the year 'X' on base year 'Y' and for the year 'Y' on base year 'Z' should yield the same result as an index constructed for 'X' on base year 'Z'.

i.e. I0,1 x I1,2 x I2,0 = 1.

Laspeyres, Paasche and Fisher's indices fail to satisfy this test. Only the fixed weight aggregates method and simple aggregates method satisfy this test.

The indices satisfying the circular test would be amenable to change from year to year without referring to the base year. The indices have the advantage of reduced computational work in the event of a change in the base year.

Posted Date: 9/17/2012 3:13:49 AM | Location : United States







Related Discussions:- Tests for consistency, Assignment Help, Ask Question on Tests for consistency, Get Answer, Expert's Help, Tests for consistency Discussions

Write discussion on Tests for consistency
Your posts are moderated
Related Questions
a) Critical Path: A, B, E and F. Project completed in 11 weeks. Subtract one mark for each error made. Maximum marks can only be awarded if the candidate explicitly indicat


RWE Enterprises is a small manufacturer in Adelaide South Australia, feed suppliments for cattle. New production line NPV, Payback period and discounted payback period

Explain the Basis Risk Basis risk considers to the floating rates of two counterparties being pegged to two dissimilar indices.  In this situation, as the indexes are not compl

Define the both cash and share exchange Generally both cash and share exchange are used to make the offer more attractive. Other forms of consideration include: Paper consid

a choice is to be made between the two completing proposal which require an equal investment of Rs.50000.00 and we are expected t gererate net cash flow as under. Year Project A

Advantages and disadvantage of pacipatory style of budgeting

Which ratios would a banker be most interested in when considering whether to approve an application for a short-term business loan? Explain. Bankers and another lenders use li

One of the most important objectives of statistical analysis is to get one single value that describes the characteristic of the entire mass of unwieldy

The Option-Adjusted Spread (OAS) is a measure of the yield spread (expressed in basis points) which can be used to convert differences between the values an