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Saturday, October 27, 2018

Business Statistics Notes: Index Number

Unit – 3: Index Number
Index Number and Its Features
Index number is an indicator of changes in prices and quantities. It is a specialized average designed to measure the change in a group of related variables over a period of time. These index numbers are also known as barometers of economic activity. It offers a device of estimating the relative changes of a variable when measurement of actual changes is not possible.  It is also an indicator of inflationary or deflationary tendencies.
Following are the various feature of index number:
1. Measures of relative changes: Index number measure relative or percentage changes in the variable over time.
2. Quantitative expression: Index numbers offer a precise measurement of the quantitative change in the concerned variable over time.
 3. Average: Index number show changes in terms of average.
Utility and Limitations of Index numbers
Utilities or Importance: Index numbers are highly valuable in business and economics. They provide a good basis for comparison as they are expressed in abstract units of measurement. Some of the utilities of index numbers are given below:
1.       Measurement of change in the price level or the value of money: - Index number can be used to know the impact of the change in the value of money on different sections of the society.
2.       Knowledge of the change in standard of living: - Index number helps to ascertain the living standards of people. Money income may increase but if index number show a decrease in the value if money. Living standard may even decline.
3.       Adjustment in salaries and allowances: - Cost of living index number is a useful guide to the government and private enterprises to make necessary adjustment in salaries and allowances of the workers.
4.       Useful to business community: - Price index numbers serve as a useful guide to the business community in planning.
5.       Information regarding foreign trade: - Index of exports and imports provides useful information regarding foreign trade.
Index numbers are called barometers of economic activity because of the above mentioned utilities.
Limitations of index number
1. Not completely true: Index number not fully true. The index number simply indicate arithmetical tendency of the temporal changes in the variable.
2. International comparison is not possible: Different countries have different bass of index numbers; these do not help international comparisons.
3. Difference of time: With the passage of time, it is difficult to make comparison of index number. With the changing time man’s habits.
4. Limited use: Index numbers are prepared with certain specific objective. If they are used for another purpose they may lead to wrong conclusion.
5. Lack of retail price index number: Most of the index numbers are prepared on the basis of wholesaler prices. But in real life, retail prices are most relevant, but it is difficult to collect retail prices.
Main Problems in the construction of index number
a.       Purpose of index number: There are various types of index number, constructed with different objectives. Before constructing an index number, one must define the objective.
b.       Selection of base year: Selection of base year is another problem in the construction of index number. Base year is the reference year. It is the year with which prices of the current year are compared.
c.       Selection of goods and services: Having defined the objective, the problem is of the selection of goods or services to be included in the index number.
d.      Selection of price: whether wholesale or retail prices are used is also a problem in construction of index number.
e.       Other problems:
a) Choice of average (simple, weighted or geometric average).
b) Selection of appropriate weights.
c) Selection of appropriate formula.
Methods for calculation of index number
Index numbers are constructed in a number of ways. These are broadly divided under two heads:
i) Method of Aggregates                              ii) Method of Relatives
i) Method of Aggregates are of two types:
a) Simple Aggregative method
b) Weighted Aggregative method
ii) Method of Relatives are of two types:
a) Simple Average of Price Relatives
b) Weighted average of price relatives
a) Simple Aggregative method: Under this method, Price index will be the aggregate of prices of the given period expressed as a percentage of that of the base period.  Here,
I = ∑Pn / ∑P0 x 100
b) Simple Average of Price Relative: A price relative is ratio of current year price expressed as a percentage with respect to the base year price. Under this method price relative of various items are calculated individually and average of price relative are obtained by dividing sum of price relative with number of items.
iii) Under Weighted Average Method
a) Laspeyre’s Method
b) Paasche’s Method
c) Marshall-Edgeworth Method
d) Fisher’s Ideal Index
Simple and weighted index number.
Simple and weighted are the two broad categories of index numbers which can be defined as:
Simple index number: - These are the index number in which all items of the series are given equal weighted or importance. It is a simple average of prices of different goods and services, as in case of simple price index
Weighted index number: - These are the index number in which different items of the series are given different weight age, depending upon their relative importance. It is not a simple average of prices of different goods and services, as in case of simple price index.
Difference between Price index and Quantity index
A measure reflecting the average of the proportionate changes in the prices of a specified set of goods and services between two periods of time. Usually a price index is assigned a value of 100 in some selected base period and the values of the index for other periods are intended to indicate the average percentage change in prices compared with the base period. A quantity index is built up from information on prices of various commodities.
A measure reflecting the average of the proportionate changes in the quantities of a specified set of goods and services between two periods of time. Usually a quantity index is assigned a value of 100 in some selected base period and the values of the index for other periods are intended to indicate the average percentage change in quantities compared with the base period. A quantity index is built up from information on quantities such as the number or total weight of goods or the number of services.
Time reversal and factor reversal test
Time Reversal Test:-The test is that the formula for calculating the 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. Symbolically P01 * P10 = 1
Factor Reversal Test:-Just as each formula should permit the interchange of the two items without giving inconsistent results so it ought to permit interchanging prices and quantities without giving inconsistent results, i.e. the two results multiply together should give the true value ratio. In other words the change in price multiplied by change in quantity should be equal the total change in value. P01 * Q01 =∑P1Q1 / ∑P0Q0
Cost of living index number (CLI)
Cost of living index numbers generally represent the average change in prices over a period of time, paid by a consumer for a fixed set of goods and services. It measure the relative changes over time in the cost level require to maintain similar standard of living. Items contributing to consumer price index are generally:
i)           Food
ii)          Clothing
iii)        Fuel and Lighting
iv)        Housing
v)         Miscellaneous.
                Uses of cost of living index:-
i)           CLI numbers are used for adjustment of dearness allowance to maintain the same standard of living.
ii)          It is used in fixing various economic policies.
iii)        Its helps in measuring purchasing power of money.
iv)        Real wages can be obtained with the help of CLI numbers.
Fixed base method and Chain base method
Fixed Base Method: - Under this method index number is calculated with a fixed base year. By this method the index number of a given year is not influenced by the variation of prices of any other year.
Chain Base Method: - Under This method the price of any period or year is related with the price of the immediate previous period or year. It has no relation with the price of fixed based period.
Use of Chain base index number:-         
i)        Direct comparison between two successive periods is possible through link indices.
ii)       This method is useful when weights are changing rapidly.
iii)     It facilitates introduction in new item replacing old one.
Disadvantages of Chain base index number:-
i)        This Method involves immense calculation.
ii)       Easy interpretation is lacking.
                Uses and limitations of fixed base index number: - Same as index number
Difference between chain base method and fixed base method:-

No fixed base is there.
Base Period is fixed.
Immediately preceding period is taken as base. 
Base period is arbitrarily chosen.
Calculation is too long.
Calculation is easy.
During Calculation if there is any error then the
Entire calculation is wrong.
This is not so in this method.
If data for any period is missing then subsequent chain indices cannot be computed.
This problem does not arise here.
Fisher’s index is regarded as ideal index because:-
i)        It considers both base year and current year’s price and quantity.
ii)       It satisfies both time reversal and factor reversal test.
iii)     It is based on Geometric mean which is theoretically considered to be the best average of constructing index number.
iv)     It is free from bias as it considers both current year and base year price and qty.
vii) Prove that fisher’s index satisfies both time reversal test and factor reversal test.

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