Chapter 6 (index) student

Index Numbers Index numbers allow relative comparisons over time  It measures the percentage change in the value of some economic commodity over time  Index numbers are reported relat

Chapter 6

Index numbers

Index Numbers

 Index numbers allow relative comparisons

over time

 It measures the percentage change in the

value of some economic commodity over time

 Index numbers are reported relative to a Base Period Index

 Base period index = 100 by definition

 ‘Economic commodity’: used to describe

anything measurable which has some economic relevance

 ‘Economic commodity’ can be: price, quantity, wage, productivity…

 Index numbers must always be related to some time period (i.e base time period and another time period)

Index Relatives

 Index relative or simple index number is

an index number which measures the change in a single distinct commodity

y I

y

where

Iy = index number of commodity ‘y’

yt = value of commodity ‘y’ at time t

y0 = value of commodity ‘y’ in the base period

Index Numbers: Example

 Company orders from 1995 to 2003:

Year Number

of Orders

Index

(base year = 2000)

Index Numbers: Interpretation

p I

q I

Time series of relatives

 Describe how the values of an index relative

change overtime

 There are two distinct ways in which relatives can

be calculated

- Fixed base relatives: each relative is calculated

based on the same fixed time point

- Chain base relatives: each relative is calculated

with respect to the immediately preceding time

point

Fixed base relatives

Chain base relatives

Changing the base of fixed base relative

 Used when the old base time point is no longer relevant (usually it is too far in the past or out of date)

 Step 1: Choose the required new base time

point and identify the corresponding relative

 Step 2: Divide each relative in the set by the

value of the relative identified above and multiply the result by 100

Changing the base of

fixed base relative

Year 2000 2001 2002 2003 2004 2005

Old Index

(1980=100) 244 260 270 285 300 315New Index

(2000=100) 100 106.56 110.66 116.80 122.95 129.10

Time series deflation

 A technique used to obtain index relatives that measure the changes in the real value of some commodity with respect to a given indicator

Time series deflation: procedure

 Step 1: Choose a base for the index of real

values of the series

 Step 2: For each time point, find the ratio of the current value to the base value

Time series deflation: procedure

 Step 3: Multiply by the ratio of the base indicator

to the current indicator

 Step 4: Multiply the result by 100

Real value Index (RVI)

Time series deflation: example

index

Composite index numbers

 A composite index number is an index number obtained by combining the information from a set

of economic commodities

 It measure the percentage changes of a group of items (not one item)

Weighting of components

 Usually, a composite index can be calculated by weighting each component

 A weighting factor is an indicator of the

importance of each component in calculating the composite index

 The need for weights (read in the textbook)

Types of composite index number

Weighted average of relatives

Weighting the index relative calculated for

each component Weighted aggregates

Weighted average of relatives

Formula:

AR

wI I

Weighted average of relatives

Weighted average of relatives

Items Price Standard

Weighted average of relatives

Weighted average of price index

relatives

wy I

Weighted aggregate: Example

Weighted aggregates

Weighted aggregate of price index:

Weighted Aggregate Price Indexes

 Paasche index

0

(100)

t t t

t

p q I

p q I

p q

�

 Laspeyres index

A Paasche price index uses

current time period

quantities as weights

A Laspeyres price index uses base time period quantities as weights

Weighted Aggregate Quantity Indexes

 Paasche index

0

(100)

t t t

t

p q I

p q I

p q

�

 Laspeyres index

A Paasche quantity index

uses current time period

prices as weights

A Laspeyres quantity index uses base time period prices

as weights