Index numbers: Part 2

1. Index numbers:Part 2 Marc Prud’Homme University of Ottawa Last update: 14/09/12

2. Index numbers recap • Though originally developed for measuring the effect of change in prices, index numbers have today become one of the most widely used statistical devices and there is hardly any field where they are not used. • Newspapers headline the fact that prices are going up or down, that industrial production is rising or falling, that imports are increasing or decreasing, that crimes are rising in a particular period compared to the previous period as described by index numbers.

3. Index numbers recap • Index numbers are used to feel the pulse of the economy and they have come to be used as indicators of inflationary or deflationary tendencies. • In fact, they are described as ‘barometers of economic activity’, i.e., if one wants to get an idea as to what is happening to an economy, he or she should look to important indices like the index number of industrial production, agricultural production, business activity, etc.

4. Index numbers recap • Some prominent definitions of index numbers are given below: • ‘Index numbers are devices for measuring differences in the magnitude of a group of related variables. —Croxton & Cowdert • “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 or other characteristics such as income, profession, etc. —Spiegel

5. Index numbers recap • “In its simplest form an index number is the ratio of two index numbers expressed as a per cent. An index number is a statistical measure—a measure designed to show changes in one variable or in a group of related variables over time, or with respect to geographic location, or in terms of some other characteristics.” —Patternson

6. Index numbers a definition • Index numbers are statistical devices designed to measure the relative change in the level of variable or group of variables with respect to time, geographical location etc. • In other words these are the numbers which express the value of a variable at any given period called “current period “as a percentage of the value of that variable at some standard period called “base period”.

7. Index numbers a definition • Here the variables may be • The price of a particular commodity like silver, iron or group of commodities like consumer goods, food, stuffs etc. • The volume of trade, exports, imports, agricultural and industrial production, sales in departmental stores. • Cost of living of persons belonging to a particular income group or profession etc.

8. Challenges in constructing indexes • Purpose of the index • Selection of products • Selection of a base period • Normal period • Not too distant from the given period • Fixed base or chained base

9. Characteristics of index numbers • Index numbers are specialized averages: • An average is a single figure representing a group of figures. • However to obtain an average, the items must be comparable. • Furthermore, the unit of measurement must be the same for all the items. (cont’d)

10. Characteristics of index numbers • However this is not so with index numbers. • Index numbers are types of averages which show in a single figure the change in two or more series for different items which can be measured in different units. • For example, while constructing a consumer price index number, the various items which are used are divided into broad headings namely food, clothing, fuel, lighting, house rent, and miscellaneous which are obviously measured in different units.

11. Uses of index numbers • Index numbers are indispensable tools of economics and business analysis. Following are the main uses of index numbers.

12. Uses of index numbers • Index numbers are used as economic barometers • Index number is a special type of averages which helps to measure the economic fluctuations on price level, money market, economic cycle like inflation, deflation etc. • G. Simpson and F. Kafka say that index numbers are today one of the most widely used statistical devices.

13. Uses of index numbers • Index numbers helps in formulating suitable economic policies and planning etc. • Many of the economic and business policies are guided by index numbers. • For example, while deciding the proper wage increase for employees, employer’s have to depend primarily on the CPI.

14. Uses of index numbers • They are used in studying trends and tendencies • Since index numbers are most widely used for measuring changes over a period of time, the time series so formed enable us to study the general trend of the phenomenon under study. • For example for last 8 to 10 years we can say that imports are showing an upward trend.

15. Uses of index numbers • They are useful in forecasting future economic activity. • Index numbers are used not only in studying the past and present workings of our economy but also important in forecasting future economic activity.

16. Uses of index numbers • Index numbers measure the purchasing power of money. • The CPI, an index number, determines whether the real wages are rising or falling or remain constant. • The real wages can be obtained by dividing the money wages by the corresponding price index and multiplied by 100. • Real wages help us in determining the purchasing power of money.

17. Uses of index numbers • Index numbers are used in deflating. • Index numbers are highly useful in deflating i.e. they are used to adjust the wages for cost of living changes and thus transform nominal wages into real wages, nominal income to real income, nominal sales to real sales etc. through appropriate index numbers. • Index numbers are widely used for deflating in the national accounts, e.g., nominal GDP to real GDP.

18. Classification of index numbers • Price index number • Quality index number • Value index number • Special purpose index number

19. Choice of formula • Axiomatic approach vs. Economic approach

20. Axiomatic approach • The axiomatic approach to the selection of an appropriate index formula specifies a number of desirable properties an index formulation should possess. • Seek to determine the most appropriate functional form for an index by specifying a number of axioms, or tests, that an index ought to satisfy. • Potential indexes are then evaluated against the specified properties and the index that passes the most tests is the preferred one.

21. Economic approach • With the axiomatic approach, prices and quantities were treated as separate independent variables. • Two price vectors and two quantity vectors • With the economic approach, the quantities are a function of the prices. • Two price vectors plus a functional relationship connecting the prices to the quantities in periods 1 and 2 respectively.

22. Economic approach • Two main functions relating Qs to Ps: • Utility functions • Production functions • The classic example of an economic theoretic index is the Cost-of-living-index (COLI). • COLI: “the ratio of the minimum expenditures required to attain a particular indifference curve (level of welfare or standard of living) under two price regimes or situations”.

23. END