Types Of Index Numbers

20-2

A price index measures the changes in prices from a selected base period to another period.

EXAMPLE: Price index is widely applied in various economic and business policy formation and decision making.It is used to measure cost of living of teachers,farmers and weavers.It is also used to construct price index of securities in securities markets.

A quantity index measures the changes in quantity consumed from the base period to another period.

EXAMPLE: Federal Reserve Board indexes of quantity output.

A special-purpose index combines and weights a heterogeneous group of series to arrive at an overall index showing the change in business activity from the base period to the present.

EXAMPLE: Profits or sales or production,Price index of stock markets or productivity index

A value index measures the change in the value of one or more items from the base period to the given period. The values for the base period and the given periods are found by PxQ. Where p = price and q = quantity

EXAMPLE: the index of department store sales,agricultural production,export,industrial production.

A value index measures changes in both the price and quantities involved.

A value index, such as the index of department store sales, needs the original base-year prices, the original base year quantities, the present-year prices, and the present year quantities for its construction.

Its formula is:

8.117)100(000,9$

600,10$)100(

00

qp

qpV tt

The consumer price index (CPI) / cost of living index is a measure of the overall cost of the goods and services bought by a typical consumer.

It is used to monitor changes in the cost of living over time.

The inflation rate is calculated as follows:

1001 Year in CPI

1 Year in CPI - 2 Year in CPI Year2in Rate Inflation

Housing

Food/Beverages

Transportation

Medical Care

Apparel

Recreation

Other

Education andcommunication

40%40%

16%16%

17%17%

6%6%

5%5%6%6% 5%5% 5%5%

An aggregate index is used to measure the rate of change from a base period for a group of items

Aggregate Price Indexes

Unweighted/Simple

aggregate price index

Weighted aggregate price

indexes

Paasche Index Laspeyres Index

A simple price index tracks the price of a single commodity

The formal definition is:

Where pn = the sum of the prices in the current

periodpo = the sum of the prices in the base period

100p

pindexaggregateSimple

o

n

20-12

Unweighted total expenses were 18.8% higher in 2004 than in 2001

Automobile Expenses:Monthly Amounts ($):

Year Lease payment Fuel Repair TotalIndex

(2001=100)

2001 260 45 40 345 100.0

2002 280 60 40 380 110.1

2003 305 55 45 405 117.4

2004 310 50 50 410 118.8

118.8(100)345

410100

P

PI

2001

20042004

Airplane ticket prices from 1995 to 2003:

90)100(320

288100

P

PI

2000

19961996

Year PriceIndex

(base year = 2000)

1995 272 85.0

1996 288 90.0

1997 295 92.2

1998 311 97.2

1999 322 100.6

2000 320 100.0

2001 348 108.8

2002 366 114.4

2003 384 120.0

100)100(320

320100

P

PI

2000

20002000

120)100(320

384100

P

PI

2000

20032003

Base Year:

Prices in 1996 were 90% of base year prices

Prices in 2000 were 100% of base year prices (by definition, since 2000 is the base year)

Prices in 2003 were 120% of base year prices

90)100(320

288100

P

PI

2000

19961996

100)100(320

320100

P

PI

2000

20002000

120)100(320

384100

P

PI

2000

20032003

Unweighted aggregate price index formula:

100P

PI

n

1i

)0(i

n

1i

)t(i

)t(U

= unweighted price index at time t

= sum of the prices for the group of items at time t

= sum of the prices for the group of items in time period 0

n

1i

)0(i

n

1i

)t(i

)t(U

P

P

I

i = item

t = time period

n = total number of items

20-17

Weighted index no. Consists of –

Laspeyres index

The Laspeyres index is also known as the average of weighted relative prices

In this case, the weights used are the quantities of each item bought in the base period

The formula is:

Where:qo = the quantity bought (or sold) in the base period

pn = price in current periodpo = price in base period

100index Laspeyres

oo

on

qp

qp

20-18

20-19

The 1990 party The 2000 party

Drink Unit price Quantity Unit price Quantity

po qo pn qn

wine 2.50 25 3 30

beer 4.50 10 6.00 8

soft drinks 0.60 10 0.84 15

poqo = (2.5 x 25) + (4.5 x 10) + (0.6 x 10) = 113.5

So, Laspeyre's price index = (143.4/113.5) x 100 = 126.3

pnqo = (3 x 25) + (6 x 10) + (0.84 x 10) = 143.4

Laspeyres Index

Requires quantity data from only the

base period. This allows a more

meaningful comparison over time.

Laspeyres index assumes that the same

amount of each item is bought every year.

If I bought a radio one year, the index

assumes I bought one the next year.

If I bought 35 kg of oranges in Po, the

index assumes I bought the same amount

every year, when in reality if the price went

up, one might buy less.Does not reflect changes in buying

patterns over time. Also, it may

overweight goods whose prices

increase.

Paasche index The Paasche index uses the consumption in

the current period It measures the change in the cost of

purchasing items, in terms of quantities relating to the current period

The formal definition of the Paasche index is:

Where:pn = the price in the current periodpo = the price in the base periodqn = the quantity bought (or sold) in the current

period

100qp

qpindexPaasche

no

nn

20-22

64.135)100(36.598$

60.811$)100(

0

t

tt

qp

qpP

Paasche Index

Because it uses quantities from the current period, it

reflects current buying habits.

Paasche Index

It requires quantity data for the current

year.

Because different quantities are used

each year, it is impossible to attribute

changes in the index to changes in price

alone.

It tends to overweight the goods whose

prices have declined.

It requires the prices to be recomputed

each year.

Fisher’s ideal index Fisher’s ideal index is the geometric mean of

the Laspeyres and Paasche indexes The formal definition is:

100qpqp

qpqp

indexPaascheindexLaspeyresindexsFisher'

nooo

nnon

20-26

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.

(ii) Index numbers measure the relative

change in a variable or a group of related

variable(s) under study.

(iii) Consumer price indices are useful in

measuring the purchasing power of money,

thereby used in compensating the

employees in the form of increase of

allowances.

20-28

20-29