Page 263 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 20: Test of Consistency: Unit Test, Time Reversal Test, Factor Reversal Test and Circular Test

20.5 Summary Notes

• A number of mathematical criteria for judging the adequacy of an Index Number formula have
been developed by statisticians. In fact, the problem is that of selecting the most appropriate
one in a given situation.
• This test requires that the formula for constructing an index should be independent of the units
in which the prices are quoted. All formulae of weighted aggregate method except simple
aggregative method satisfy this test.
• Time Reversal means that if we change the base year to the current year and vice versa then the
product of the indices should be equal to unity. In other words, Simple Aggregative Method
does not satisfy this test. The index number reckoned forward should be the reciprocal of that
reckoned backward’. Thus, an ideal Index Number formula should work both ways, i.e., forward
as well as backward.
• According to Fisher Just as our formula should permit the interchange of two factors without giving
inconsistent results, so without to permit interchange of prices and quantities without giving
inconsistent results, i.e., the two results multiplied together should give the true value ratio.
• Another test of adequacy is circular test. This test is an extension of the time reversal test. It
requires that if an index is constructed for the year ‘b’ on year ’a’ and for the year ‘c’ on base
year ‘b’ we should get the same result as if we calculate directly an Index for ‘c’ on base year ‘a’
without going through b as an intermediary.
20.6 Key-Words

1. Coefficient of variation (CV) : The standard deviation divided by the mean.
2. Collinearity : The condition in which the independent variables are (usually
highly) correlated with each other.
3. Column totals : The total number of observations occurring in a column of a
contingency table.
20.7 Review Questions

1. Explain time reversal test and factor reversal tests. Show that Fisher’s Ideal index number satisfies
both.
2. What do you mean by time reversal test for index numbers ? Show that laspeyre and paasche
index numbers do not satisfy it and that Fisher’s Ideal index does.
3. What are the various tests of adequacy of index number formulae ? Describe each briefly.
4. Distinguish between Laspeyre's and Paasche's index.
5. What are the differences between time reversal test and factor reversal test?
Answers: Self-Assessment
1. (i)(e) (ii)(b) (iii)(c) (iv)(b) (v)(a)

20.8 Further Readings

1. Elementary Statistical Methods; SP. Gupta, Sultan Chand & Sons,
New Delhi - 110002.
2. Statistical Methods — An Introductory Text; Jyoti Prasad Medhi, New Age
International Publishers, New Delhi - 110002.
3. Statistics; E. Narayanan Nadar, PHI Learning Private Limied, New Delhi - 110012.

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