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Namaste! Friends, I heartily welcome you to read this post about the concept of Index numbers. The main purpose of this site is to provide concepts primarily. to learn more or to enquire more information, please research yourself in the internet.

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If you get any doubt, try to find out yourself. if it is not getting solved with you, then as a final step, ask your lecturer. Even your doubt is not cleared, you can learn something new while searching for your doubt. that's the best method to really learn something with your own efforts. If you like someone's teaching, take him as a model. It improves your learning productively.

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Studying and gaining more and more information is not necessarily needed. expressing or (writing) what you know qualitatively is more important. quality is > quantity.

Study and understand. compare concepts. relate to other topics. you will experience analysis.

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What topics are covered here?

Following topics are introduced in this blog.

Meaning of index numbers (Concept)
Its uses
Aspects or characteristics features of index numbers
Difficulties in the Construction of Index Numbers
Types of Index Numbers
Methods of Index Numbers

Methods include

Laspeyre
Paasche
Fisher.

Concept of index numbers

Index numbers are one of the main technique and tools of statistics which are widely in use today. It is also known as measurement of pulse of an economy. Generally index numbers are constructed to measure the effect of changes in prices. Now a days, we not only use index numbers to measure prices but also for number of measurements like cost of living, agricultural and industrial production, imports, exports, poverty, etc.

Index numbers refers to indicators which measures percentage change in one or a group of related variables over a particular period of time.

It is a single ratio or also known as percentage value which measures change between different variables in different times.

Index numbers are not only measured based on a particular time. it is also measured on geographical location and other characteristics.

Price index numbers

Price index numbers measure changes in the general price level or (value of money) over a particular period of time. generally money value changes due to a change in general price level.

Note

We are providing more concepts related to price index. That's why this concept is introduced primarily here.

Aspects of index numbers

(Characteristics of index numbers)

(Features of index numbers)

Following are the some main important features or aspects of index numbers:

Average: Index numbers are special kind of average which describes measurement of changes of levels of a phenomena from one time to another time. Index numbers are special average value because, it can measure the value which is not in the same unit. generally other statistical averages like mean, median, etc. can measure and compare the values of same units (numerical units). Values can be expressed in different units in case of index numbers.
Percentage values: Index numbers are expressed in terms of percentage values to show the amount of relative change.
Measures of relative changes: index numbers measure relative changes between values of 1 or a group of variable over a particular time or places.
Index numbers can measure which cannot be measured directly or (quantitatively). for example, cost of living, business activities in the country, etc. by measuring the variables or determining factors, it is possible to measure the values even they are not expressed quantitatively.
Index number technique is used to compare the level of changes of a phenomena with the change in level of other previous date. for example, The price level of 2018 can be compared with the price level of 2006. Even the technique is used to compare in different geographies like India and America price levels etc.
This technique can be used to measure changes in 1 variable in relation to a related group of variables. for example, 1 variable = change in price of milk and group of variables = prices of sugar, sweets, price of wheat, milk products, etc.

Uses of index numbers

Index numbers are widely in use today. whether in business activities or to understand economic status. that's why it is also known as the measurement of pulse of an economy.

Its uses

Following are some main uses of index numbers.

economic barometers
formulating economic policies and planning
studying trends
forecasting or (Predicting)
purchasing power of money

Economic barometer

Economic barometer means measurements of trend of an economy with a series of data. Index numbers are used to understand the economic status of a country by measuring business and economic activities. it also measures the economic fluctuations of markets, prices, etc. not only economic fluctuations, but also the economic cycles like trade cycles or (business cycles), inflation rate, deflation rate, etc.

Formulating economic policies and planning

Index numbers analysis is the main basis for formulating number of policies related to business and the economy. for example, Living index of employees, fixing DA of the employee to deal with inflation. If the salaries offered by the companies are not increased according to cost of living index, then it leads to strikes. So, index number analysis leads to issue of some minimum guidelines regarding salaries of employees.

Studying trends

Generally Index numbers measure the changes in one or group of a variable over a particular period of time. So, the time series will provide the clear analysis of trends of business or any variables.

Forecasting

Forecasting means using historical data as inputs to estimate or predict the future trends. Index numbers are not only useful to analyse present and past activities of our economy but also, enable economists to predict the future causes. so, with the forecasting technique, an economist suggest the government to take suitable measures. for example, predicting changes in inflation rate

purchasing power of money

Index numbers measure the purchasing power of money. Purchasing power of money is determined by real wages. real wages is the purchasing power of money. rising of real wages is determined or based on cost of living.

Formula: Money wages / price index * 100

Conclusion

Index numbers in various departments.

Apart from above economic and business activities, index numbers are also used in various department for different purposes. like

Psychologist: measurement of Intelligent quotient IQ.
Sociologist: population index.
Education: school productivity.
Demographer: population policy

Basic concepts

Following are the few simple concepts to understand the formulas which are provided below.

simple index numbers: only year is given.
weighted index numbers: both year and quantity are assigned to the values.
P1: refers to price of current year.
P0: refers to price of previous year or the base year.
Q1: refers to quantity of current year.
Q0: refers to quantity of previous year or the base year.

Formulas

Following methods are used widely in constructing index numbers.

Laspayre: (∑P1Q0/∑P0Q0)*100.
Paasche: ∑(P1Q1/∑P0Q1)*100.
Fisher: √[(∑P1Q0/P0Q0) * (∑P1Q1/P0Q1)] *100

Simple, The geometric mean of Laspeyres’ and Paasche’s is the Fisher’s Ideal Price Index.

I.e. Fisher formula is the COMBINATION OF ABOVE 2 FORMULAS.

* by subtracting the base year value from the price index value , you will get the inflation rate. So, write inflation percentage at the end of your answer.
Price index value - base year value = inflation rate
An inflation rate is just the percentage change in a price index.

Techniques to remember these formulas

method - 1: simply remember 1000 number for Laspayre method. because, p1q1 / p0q0. once you observe, there are all zeros after 1. and for Paasche method, the formula is p1q1/p0q1. so, remember 1101 number to remember this formula.
Method - 2: This method provides some subject knowledge / information to easily remember the formulas. once you observe, for both the above formulas, common thing is p1/q0*100. here, you need to understand for which year the economists have given more importance. according to 1st formula, the Laspeyre has given more importance to base year or (last year) so, p1q0/p0q0. here, p1/p0*100 are unchanged. in case of Paasche method, he has given more importance to current year that is p1,q1. finally Paasche = P1Q1/P0Q1.
Fisher formula: Once if you are clear with above 2 formulas i.e. the Laspeyre and the Paasche method, remembering Fisher method is very easy. Fisher formula is nothing but L+P. In this case, we add only the square root. That is why Fisher method is also known as the geometric mean of Laspeyre and Paasche methods.

WHY FISHER METHOD OF INDEX NUMBER IS CALLED AN IDEAL INDEX NUMBER?

Laspeyre method is based on the values of base year prices and base year quantity. whereas, Paasche method is based on values of current year prices and current year quantity. But, in case of Fisher's price index, he equally considered the values of both base year and the current year. That is why Fisher method is also known as the geometric mean of Laspeyre’s index and Passche’s index. it satisfies the time reversal test and factor reversal test.. It is also very good at predicting consumer index or personal consumer index. Inflation is measured by using PCI which considers the household expenditure on consumer goods in an economy, and its changes in prices.

More information about Fisher's ideal price index

Fisher compared many index number formulas and finally, he concluded that the geometric mean of Laspayre method and Paasche method are the perfect methods to satisfy the tests. it is very useful for good prediction. He only called it as the Ideal Index. later, it is popularly known as Fishers ideal index.

Issues of Construction of Index Numbers

(Problems of constructing price index numbers)

(Steps in constructing index numbers)

*Index numbers refers to indicators which measures percentage change in one or a group of related variables over a particular period of time.

*Price index numbers measure changes in the general price level or (value of money) over a particular period of time.

Steps / Methods/ difficulties in the constructing an index number

Purpose.
Selection of base year.
selection of commodities.
selection of prices.
selection of an average.
selection of weights.
Selection of method.
selection of formula.

*Quick explanation.

Purpose

Purpose of an index number is the primary step in the construction of index numbers. purpose means objective. all other steps are followed by the purpose of the index. It is very important to be clear about the purpose of the index number because, index number of 1 purpose cannot be used for other purpose. i.e. there is no all purpose index.

Selection of base year

Selection of base year is another important step. base year refers to reference year. base year is the year where comparisons are made. the main thing in selection of base year is

* it should be normal. i.e. no unusual activities like wars, booms, earthquakes, depressions, etc.

* it should not be very recent or very far.

Selection of commodities

Generally commodities are to be selected based on the purpose of the constructing index number. but the number of commodities should not be very small or very large. it must be representative of the group of commodities. that means, as a representation of the people's taste, preferences, habits, etc based on the purpose. a decision regarding number of commodities and their quantities is necessary.

Selection of prices

After selection of commodities the next step is selection of prices. Care must be taken to consider the prices from different sources. selected prices must be reliable that means, they must be same or constant in price, quality, etc. The prices may be quoted in terms of money as RS 150 or in terms of quantity i.e. 1KG per RS 150. also a decision regarding including wholesale price or retail prices.

Selection of an average

Index numbers are a special kind of averages. after deciding on prices, the next step is to take decision on an average. there are many kind of averages like mean, median, mode,

Concept Of Index Numbers

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