Index Number

TAMIL NADU NATIONAL LAW SCHOOL TIRUCHIRAPPALLI

ACADEMIC SESSION: 2016-2017

BUSINESS STATISTICS PROJECT: INDEX NUMBER

SUBMITTED BY:

Gunjan Chandavat ROLL NO. –BC0140023

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Acknowledgement I take the opportunity to express my profound gratitude and deep regards to my guide for Dr.P.Kumaresan his exemplary guidance, monitoring and constant encouragement throughout the course of the project. The help and guidance given by him time to time shall carry me a long way in the journey of life which I will embark . I also express a deep sense of gratitude to our Vice Chancellor for giving me this opportunity. I am obliged to my parents for showing faith which helped me in completing the project on time. Lastly, I thank , my friends for their encouragement without which the assignment would have not been possible.

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TABLE OF CONTENTS: 1.

INTRODUCTION

4

2.

CHARACTERISTICS & USES

5

3.

IMPORTANCE OF INDEX NUMBER

7

4.

PROBLEMS IN CALCULATING INDEX NUMBERS

8

5.

LIMITATIONS

11

6.

METHODS OF CALCULATING

12

7.

PROBLEMS

14

8.

REFERENCES

21

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INTRODUCTION: INDEX NUMBER: A number that expresses the relative change in price, quantity, or value compared to a base period. DEFINITIONS: 1. “Index numbers are devices for measuring differences in the magnitude of a group of related variables”-Croxton & Cowden.1 2. “An index number is a statistical measure designed to show changes in a variable or a group of related variables with respect to time, geographic location and other characteristics such as income, profession, etc.”-Spiegel2 3. According to Patternson : " In its simplest form, an index number is the ratio of two index numbers expressed as a percent . An index is a statistical measure, a measure designed to show changes in one variable or a group of related variables over time, with respect to geographical location or other characteristics".3 OBJECTIVE OF STUDY: The objective of this research project is to analyse the index number calculated and to see the trend over the years , find out the different ways of calculating the index number and to make the layman understand in simpler terms the inflation and other market trends going on in the economy.

METHODOLOGY: The researcher has worked on this project “INDEX NUMBERS”. The researcher has used the secondary resources, which the researcher has taken from various mediajournals, online resources etc. and only secondary data has been used while making this assignment. The researcher has taken the prices and quantities of various consumer goods in order to calculate & analyze the index number.

1

S.P.Gupta,Statistical Methods,Sultan Chand & Sons.,2014,pg no.536 Ibid. 3 Ibid. 2

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SCOPE OF THE PROJECT : The project deals with index number and its calculation using different methods, the data has been obtained from various government departments relating to consumer goods and indexes of the same.

CHARACTERISTICS OF INDEX NUMBERS: Following are some of the important characteristics of index numbers : 

Index numbers are expressed in terms of percentages to show the extent of relative change.4



Index numbers measure relative changes.They measure the relative change in the value of a variable or a group of related variables over a period of time or between places. 5



Index numbers measures changes which are not directly measurable. 6



The cost of living, the price level or the business activity in a country are not directly measurable but it is possible to study relative changes in these activities by measuring the changes in the values of variables/factors which effect these activities.7

Index numbers may be classified in terms of the variables that they are intended to measure. In business, different groups of variables in the measurement of which index number techniques are commonly used are (i) price, (ii) quantity, (iii) value and (iv) business activity. Thus, we have index of wholesale prices, index of consumer prices, index of industrial output, index of value of exports and index of business activity, etc.In general, the present level of prices is compared with the level of prices in the past. The present period is called the current period and some period in the past is called the base period.8

4

http://download.nos.org/srsec311new/L.No.38.pdf Ibid 6 Ibid 7 Supra note 2. 8 http://www.emathzone.com/tutorials/basic-statistics/index-numbers-and-types-of-index-numbers.html 5

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USES OF INDEX NUMBERS: (i)Index numbers are economic barometers. They measure the level of business and economic activities and are therefore helpful in gauging the economic status of the country.9 (ii) Index numbers measure the relative change in a variable or a group of related variables under study.10 (iii) Consumer price indices are useful in measuring the purchasing power of money, thereby used in compensating the employes in the form of increase of allowances.11 Index Numbers have the following features : (i) Index numbers are specialised averages which are capable of being expressed in percentage.12 (ii) Index numbers measure the changes in the level of a given phenomenon.13 (iii) Index numbers measure the effect of changes over a period of time.14

TYPES OF INDEX NUMBERS:15 Index numbers are names after the activity they measure. Their types are as under : Price Index : Measure changes in price over a specified period of time. It is basically the ratio of the price of a certain number of commodities at the present year as against base year. Quantity Index : As the name suggest, these indices pertain to measuring changes in volumes of commodities like goods produced or goods consumed, etc.

9

Supra note.4 Ibid. 11 Ibid. 12 http://sol.du.ac.in/mod/book/view.php?id=1656&chapterid=1675 13 Ibid. 14 Supra no.13. 15 Supra no.4 10

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Value Index : These pertain to compare changes in the monetary value of imports, exports, production or consumption of commodities.

The importance or the uses of index numbers of prices are : (a) Measures Changes in Price Level and Standard of Living: Index number of prices is a method through which we can measure changes in the price level over time. This means that whether a country faces inflation or deflation can be known from the index number of prices. Thus, it helps to determine the changes in the economic conditions of people. Inflation reduces standard of living while deflation increases living standards. However, this statement is too simplistic and ignores many aspects. Anyway, as the price index changes, per capita income changes. A change in per capita income causes a change in the standard of living.16 (b) Regulation of Wage Rate: Salaries and wages and dearness allowances are revised by the government when price level changes. Higher wages and dearness allowances are often given by the appropriate authorities when index numbers of prices rise so as to protect the real income of the workers.17 In other words, a fall in real income consequent upon a rise in price level measured by the index numbers of prices is compensated in the form of higher wages and dearness allowances. Cost of living index can be made a basis for the regulation of wage rates and other allowances. (c) Determination of Government Policies: Index numbers of prices serve as guide to government policies. The price stability objective of the government policy is based on index numbers. It formulates policies to control inflation and deflation. Index numbers also enable governments to explain their population policies, agricultural and industrial policies, taxation policy, etc. 16 17

Ibid. Ibid.

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In addition, index numbers serve as a guide to the central bank (i.e., monetary authority) to take appropriate action against price changes.18 (d) Guide for Businessmen: Index numbers also serve as a guide to businessmen. Rising prices as indicated by index numbers may create an atmosphere of optimism. Now these people will be interested in investing more to have larger profit. Opposite reaction follows when prices fall.19 (e) International Comparisons: An index number facilitates international comparisons of economic variables. For instance, we want to make comparisons in living standards between different nations. We then construct real per capita of incomes of different nations on the basis of index numbers of prices. Thus, index numbers measure the levels of development of different countries.20

Problems in the Construction of Index Numbers While constructing Index Number, the following problems arise :21 1. The purpose of Index: Before constructing an Index Number, it is necessary to define precisely the purpose for which they are to be constructed. A single Index can not fulfill all the purposes. Index Numbers are specialised tools which are more efficient and useful when properly used. If the purpose is not clear, the data used may be unsuitable and the indices obtained may be misleading. If it is desired to construct a Cost of Living Index Number of labour class, then only those item will be included, which are required by the labour class.22

2. Selection of the items: The list of commodities included in the Index numbers is called the `Regimen'. Because it may not be possible to include all the items, it becomes necessary to 18

Supra note 12. Ibid. 20 Ibid. 21 Supra note 18 22 Supra note 17 19

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decide what items are to be included. Only those items should be selected which are representative of the data, e.g. in a consumer Price Index for working class, items like scooters, cars, refrigerators, cosmetics, etc. find no place. There is no hard and fast rule regarding the inclusion of number of commodities while constructing Index Numbers. The number of commodities should be such as to permit the influence of the inertia of large numbers. At the same time the numbers should not be so large as to make the work of computation uneconomical and even difficult. The number of commodities should therefore be reasonable. The following points should be considered while selecting the items to be included in the Index : (i) The items should be representative. (ii) The items should be of a standard quality. (iii) Non-tangible items should be excluded. (iv)The items should be reasonable in number.23 3. Price Quotations: It is neither possible non necessary to collect prices of the commodities from all markets in the country where it is dealt with, we should take a sample of the markets. Selection must be made of the representative places and persons. These places should be well known for trading these commodities.24 It is necessary to select a reliable agency from where price quotations are obtained. 4. Selection of the Base period: In the construction of Index Numbers, the selection of the base period is very important step since the base period serves as a reference period and the prices for a given period are expressed as percentages of those for the base year, it is therefore necessary that (i) the base period should be normal and (ii) it should not be too far in the past.

23 24

Ibid. Ibid.

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There are two methods by which base period can be selected (i) Fixed base method and (ii) Chain base method.25 Fixed base Method: According to this any year is taken as a base. Prices during the year are taken equal to 100 and the prices of other years are shown as percentages of those prices of the base year. Thus if indices for 1998, 99,2000, and 2001 are calculated with 1997 as base year, such indices will be called as fixed base indices. Chain base Method: According to this method, relatives of each year are calculated on the basis of the prices of the preceding year. The Chain base Index Numbers are called as Link Relatives. 5.The choice of an average: An Index number is a technique of `averaging' all the changes in the group of series over a period of time, the main problem is to select an average which may be able to summaries the change in the component series adequately. Median. Mode and Harmonic Mean are never used in the construction of index numbers. A choice has to be made between the Arithmetic Mean and the Geometric Mean. Merits and demerits of the two are then to be compared. Theoretically a .M. is superior to the A.M. in many respects but due to difficulty in its computation, it is not widely used for this purpose.26 6. Selection of appropriate weights: The term weight refers to the relative importance of the different items in the construction of index numbers. All items are not of equal importance and hence it is necessary to find out some suitable methods by which the varying importance of the different items is taken into account. The system of weighting depends upon the purpose of index numbers, but they ought to reflect the relative importance of the commodities in the regimen. The system may be either arbitrary or rational. The weight age may be according to either : (1) the value of quantity produced, or (2) the value of quantity consumed, or (3) the value or quantity sold or put to sale. There two methods of assigning weights.

25 26

Supra note 17. Ibid.

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(i) Implicit and (ii) Explicit. Implicit: Under this method, the commodity to which greater importance has to be given is repeated a number of times i.e., a number of varieties of such commodities are included in the index numbers as separate items. Explicit: In this case, the weights are explicitly assigned to commodities. Only one kind of a commodity is included in the construction of Index umbers but its price relative is multiplied by the figure of weights assigned to it. There has to be some logic in assigning such type of weights.

Limitations of Index numbers 1 They are approximations: They cannot be taken as infallible guides. Their data are open to question and they lead to different interpretations.27 2. International comparisons are difficult, if not impossible, on account of the different bases, different sets of commodities or difference in their quality or quantity.28 3. Comparison between different times are also not easy. Over long periods, some popular commodities are replaced by others. Entirely new commodities come to figure in consumption or a commodity may be vastly different from what it used to be. Think of a modern railway engine and one of the early times. Ford car 1984 is a different commodity from the 1975 Ford.29 4. Index numbers measure only changes in the sectional price levels. An index number that helps us to study the economic conditions of mill hands or railway coolies will be useless for a study of the conditions of college lecturers. An entirely different set of commodities will have to be selected. Different people use different things and hold different assets.

27

https://economics-the-economy.knoji.com/uses-and-limitations-of-index-numbers/. Ibid. 29 Ibid. 28

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Therefore, different classes of people are affected differently by a given change in the price level. Hence, the same index number cannot throw light on the effects of price changes on all sections of society.30 5 The first major problem is concerned with the choice of a base year. Two criteria for the selection of’ base year are that it must show economic stability and it must not be too distant from the given year. The base period must not coincide with abnormally high or low prices. But it is very difficult to get a ‘normal year’ free from any economic disturbances. Further, if the base year is too distant from the current year, it is possible that the pattern of consumption may change considerably. New types of commodities may be introduced and consumers may change over to these types of commodities which are not comparable with the similar types used in the base period. 6. Data or statistics collected are often unreliable and less accurate. As a result, estimates based on such data are bound to be unreliable.

METHODS OF CALCULATING:

Simple Aggregative Method

30

Ibid.

12

This is a simple method for constructing index numbers. In this, the total of current year prices for various commodities is divided by the corresponding base year price total and multiplying the result by 100. Simple Aggregative Price Index :P01=( ΣP1/ ΣP0)*100 Where P01= Current price Index number Σp1 = the total of commodity prices in the current year Σp0 = the total of same commodity prices in the base year

Limitation of this method: 

The units used in the price or quantity quotations can exert a big influence on the value of index.31



No consideration is given to the relative importance of the commodities.32

Simple Average of Price Relatives Method In this method, the price relatives for all commodities is calculated and then their average is taken to calculate the index number. Thus, P01 =

P1*100 P0 N

where P01 is the price index N is the number of items, p0 is the price in the base year

31 32

S.P.Gupta,Statistical Methods,Sultan Chand & Sons.,2014 Ibid

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p1 of corresponding commodity in present year (for which index is to be calculated) WEIGHTED AVERAGE METHOD Laspeyre’s price index Laspeyre's price index, also known as base-weighted index or fixed-weighted index, calculates the index number using the weight of the base year as weight while ignoring the weight of subsequent year. Professor Ernst Louis Étienne Laspeyres (November 28, 1834 – August 4, 1913), an academic of economics and statistics in Germany came up with this index. It was one of the many contributions made by the German mathematician into the field of economics. Laspeyre's price index = [ΣPiW0] / [ΣP0W0] X 100 Since only the base quantities are used for the calculations, the changes which are only due to price changes can be studied through this index. Paasche's price index Paasche's price index price index, also known as end-year-weighted index, calculates the index number using the weight of the end year as weight while ignoring the weight of the base year. Professor Hermann Paasche (February 24, 1851 – April 11, 1925), an academic of economics and statistics in Germany came up with this index. He was a gifted statistician and economist. Paasche price index = [ΣPiWi] / [ΣP0Wi] X 100 Fisher’s Ideal Index Number: Geometric mean of Laspeyre’s and Paasche’s index numbers is known as Fisher’s ideal index number. It is called ideal because it satisfies the time reversal and factor reversal test. Laspeyre's Index × Paashe's P01=√∑P1qo∑Poqo×∑P1q1∑Poq1×100

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1. The indexes has been collected from various cities which shows Consumer Price Index of Industrial workers:33 Major Cities

Year (2010-11)

Year(2011-12)

Bengaluru

185

195

Delhi

166

179

Kolkata

176

187

Mumbai

178

196

Jaipur

183

195

Solution: Major Cities

Year (2010-11)

Year(2011-12)

Bengaluru

185

195

Delhi

166

179

Kolkata

176

187

Mumbai

178

196

Jaipur

183

195

ΣPo=888

ΣP1=952

Simple Aggregative Price Index :P01=( ΣP1/ ΣP0)*100

33

Labour Bureau, Ministry of Labour & Employment, Government of India.RBI Monthly Bulletin November 2012

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P01=(952/888)*100 P01=107.20(Ans.)

The simple inference from the above table is that there has been an increase in the cost of living in major cities of India, the overall increase is 7.20% from the base year. Thus, there has been a hike in prices of commodities which leads to increase in expenditure for the industrial workers.

2. The below table shows the indexes collected for different commodities in the year of 2013 & 2014 in the month of January for the consumer.34

Commodity

YEAR(JAN,2013)

YEAR(JAN,2014)

CEREALS

108.4

119.6

MILK

104.4

114.1

OIL

105.1

106.8

FRUITS

103.2

113.9

PULSES

106

108.9

The method used here will be Simple average of Price Relatives Method: using arithmetic mean.

Solution:

34

mospi.nic.in/mospi_new/site/PressRelease.aspx

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Commodity

YEAR(JAN,2013)Po

YEAR(JAN,2014)P1

PRICE RELATIVES

CEREALS

108.4

119.6

119.6/108.4 *100=110.33

MILK

104.4

114.1

109.29

OIL

105.1

106.8

101.61

FRUITS

103.2

113.9

110.36

PULSES

106

108.9

102.73 Σ534.32

P01 =

P1*100 P0 N

By applying the formula, Σ534.32/5=106.86(Ans.) Although arithmetic mean and geometric mean both can be used, but arithmetic mean is often preferred because it is easier to compute and much better known. From the above solution of index number it can be concluded that there is 6.86% increase in prices of commodities from previous year and hence consumer price index shows a hike in prices.

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3. The below table shows the data relating to cereals , non- alcoholic beverages, prepared meal and snacks and pulses with its price & quantity over the two years 2014 January & 2014 June.35Taking the below information , the index number will be calculated by weighted method.

COMMODITY

PRICE (2014)

QUANTITY(2014) PRICE (2014)

QUANTITY(2014)

CEREALS

122.4

12.35

124

6.59

NON-

117.3

1.37

116.1

1.13

124.8

5.56

127.6

5.54

116.3

2.95

120.1

1.73

ALCOHOLIC BEVERAGES PREPARED MEALS & SNACKS PULSES & PRODUCTS

35

http://pib.nic.in/newsite/PrintRelease.aspx?relid 18

Solution: Commodity

CEREALS

2014(Jan)

2014(June)

po

qo

p1

q1

122.4

12.35

124

6.59

p1qo

poqo

p1q1

poq1

1531.4

1511.64

817.16

806.6 1

NON-

117.3

1.37

116.1

1.13

159.05

160.70

131.19

ALCOHOLIC

132.5 4

BEVERAGES PREPARED

124.8

5.56

127.6

5.54

709.45

693.88

706.90

MEALS &

691.3 9

SNACKS PULSES &

116.3

2.95

120.1

1.73

354.29

PRODUCTS

343.08

207.77

201.1 9

Σ2754.19

Σ2709.3 Σ1863.02 Σ183 1.73

Laspeyre's price index = [ΣPiW0] / [ΣP0W0] X 100 P01=( Σ2754.19/ Σ2709.3) X 100 P01=101.65

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Paasche price index = [ΣPiWi] / [ΣP0Wi] X 100 P01=( Σ1863.02/Σ1831.73) X 100 P01=101.70

Laspeyre's Index × Paashe's P01=√∑P1qo/∑Poqo×∑P1q1/∑Poq1×100 P01=√ Σ2754.19/ Σ2709.3×Σ1863.02/Σ1831.73×100 P01=√(1.0165) ×(1.0170) ×100 P01=1.0167 ×100 P01=101.67

The analysis of the above problem shows that there has been an increase by 1.67%, which is not a substantial increase, this indicates that there has been fairly equal amount of consumption and also the variation in the price has also not been much that is why the overall expenditure has remained fairly the same and as a result not much variation can be seen in the index number.

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REFERENCES: BOOKS: S.P.Gupta,Statistical Methods,Sultan Chand & Sons.,2014 WEB SOURCES: 

http://download.nos.org/srsec311new/L.No.38.pdf



http://pib.nic.in/newsite/PrintRelease.aspx?relid



http://sol.du.ac.in/mod/book/view.php?id=1656&chapterid=1675



http://www.emathzone.com/tutorials/basic-statistics/index-numbers-and-types-of-indexnumbers.html



https://economics-the-economy.knoji.com/uses-and-limitations-of-index-numbers/.



Labour Bureau, Ministry of Labour & Employment, Government of India.RBI Monthly Bulletin November 2012



mospi.nic.in/mospi_new/site/PressRelease.asp

s

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