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 I_0,1 denotes the original index for the current year with a given base year, and if I_{1, 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 =

(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    (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. I_0,1 x I_1,2 x I_2,0 = 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

Ask an Expert

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

Write your message here..

Related Questions

What can financial institution do for deficit economic unit, What can a fin... What can a financial institution Frequently do for a deficit economic unit (DEU) that it would have difficulty doing for itself if the DEU were to deal directly along with an SEU?

Determine the concept of cash flow to shareholders, Does financial leverage... Does financial leverage (debt) have any impact on the Free Cash Flow, on the Cash Flow to Shareholders, on the growth of the company and on the value of the shares? Debt has no

Explain taxonomy of financial intermediaries, Taxonomy of financial interme... Taxonomy of financial intermediaries We start by looking at the USA, the largest economy and financial system in the world. Subsequently we will turn to other countries. In the

Explain about receivables management, Q. Explain about receivables manageme... Q. Explain about receivables management? Receivable Management: - The term receivables demote to debt owed to the firm by the customers resulting from sale of goods or else ser

What do you mean by wealth maximization, Q. What do you mean by Wealth Maxi... Q. What do you mean by Wealth Maximization? This is also known as value maximization or net present worth maximization approach, it takes into consideration the time value of m

#titleCOST VOUME PROFIT.., Ask question #Minimum ed# what is cost volume pr... Ask question #Minimum ed# what is cost volume profits and what are the advantages and disadvantages?

Corrective action on variance analysis, Corrective Action: Once budget ... Corrective Action: Once budget figures are compared with those actually achieved, and a variance analysis carried out, management can then take steps to correct any problems id

Cash budget, We need to have done some exploration work on all of the major... We need to have done some exploration work on all of the major projects for inclusion in our prospectus, but of our $4m we need at least $1m in the bank to pay for all the listing

What do you meant by common stocks in the financial term, What do you meant... What do you meant by common stocks in the financial term? Common Stocks: Common stocks illustrate ownership interests into the firm. Common stockholders obtain dividends (wh

Securities analysis, 7. Bill Peters is the investment officer of a $60 mill... 7. Bill Peters is the investment officer of a $60 million pension fund. He has become concerned about the big price swings that have occurred lately in the fund’s fixed income sec