types of index numbers
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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$)100(
00
qp
qpV tt
The consumer price index (CPI) / cost of living index is a measure of the overall cost of the goods and services bought by a typical consumer.
It is used to monitor changes in the cost of living over time.
The inflation rate is calculated as follows:
1001 Year in CPI
1 Year in CPI - 2 Year in CPI Year2in Rate Inflation
Housing
Food/Beverages
Transportation
Medical Care
Apparel
Recreation
Other
Education andcommunication
40%40%
16%16%
17%17%
6%6%
5%5%6%6% 5%5% 5%5%
An aggregate index is used to measure the rate of change from a base period for a group of items
Aggregate Price Indexes
Unweighted/Simple
aggregate price index
Weighted aggregate price
indexes
Paasche Index Laspeyres Index
A simple price index tracks the price of a single commodity
The formal definition is:
Where pn = the sum of the prices in the current
periodpo = the sum of the prices in the base period
100p
pindexaggregateSimple
o
n
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Unweighted total expenses were 18.8% higher in 2004 than in 2001
Automobile Expenses:Monthly Amounts ($):
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
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