LBSRE1021 Data
Interpretation
Lecture 1
Index Numbers
Objectives
• Calculate a Price Index (base or current
weighted).
• Explain the use and meaning of these.
• Explain the calculation and use of the
Retail price Index.
• Use a price index to deflate a series of
figures.
Simple One Item Index
Year
Price per kg
(p)
Quantity
purchased
1995
12
520
1996
14
500
A note on ‘n’
•
•
•
•
•
•
The letter ‘n’ denotes the year in a series of years
We use ‘0’ for the base year in the series
The next year is year 1, then year 2 etc
The example just shows base year and year one
But we often deal with many years in a series
pn is ‘price at year n where n=whatever year it is
in the series’
Base year is 1995 (p0)
Price Index (year n)=
pn / p0 x 100 = 14/12 x 100 = 117 (%)
Index is % but usually omitted
Index for base year always 100.
Quantity index calculated same way.
How can quantity be taken into account?
More than one item
1995
Item
1996
kg
Meat
Price/
kg (p)
250
kg
20
Price/
kg (p)
290
Bread
20
520
24
500
Beans 37
200
39
190
25
Individual Price Indices
1995
1996
Meat
100
290/250x100=
116.0
Bread
100
24/20x100=
120.0
Beans
100
39/37x100=
105.4
Aggregate Price Index
Aggregate Price Index =
Total cost at current prices/Total cost at
base year prices
BUT
What quantities to use?
Base year quantities (Laspeyres’ Index)
Current year quantities (Paasche’s Index)
Base Weighting (Laspeyres’)
Laspeyres’ Price Index=
Total cost of base year quantities at
current price/ Total cost of base year
quantities at base year price=
Σpnq0 x 100
Σp0q0
Current Weighting
(Paasche’s)
Paasche’s Price Index=
Total cost of current year quantities at
current price/ Total cost of current year
quantities at base year price=
Σpnqn x 100
Σp0qn
Compare Laspeyres’ &
Paasche’s
• Laspeyres’
• Paasche’s
• Easier to calculate
• Direct year to year
comparison
• Most commonly
used
• Base re-defined at
intervals
• Reflects current
consumption
Example (using data above)
p0
q0
250 20
p1
q1
290 25
p0q0 p0q1 p1q0 p1q1
5000
6250
5800
7250
20
520 24
500
10400 10000 12480 12000
37
200 39
190
7400
7030
7800
7410
Total 22800 23280 26080 26660
Calculations
• Laspeyres’
• Paasche’s
Σpnq0
Σp0q0
Σpnqn
Σp0qn
x 100
x 100
=26080/22800 x 100
=26660/23280 x 100
=114.3
=114.5
Retail Price Index (RPI)
•
•
•
•
•
•
Change in Price of ‘Basket of Goods’
600 items in 11 groups
Weights based on Family Expenditure Survey
Base weighted index
Base year change decided by Government
Used to calculate REAL change in e.g.
earnings or expenditure by deflating figures.
Deflated Figures Example (1)
1988 1989 1990 1991 1992
Company
Turnover
(£m)
6.6
RPI
106.9 115.2 126.1 133.5 138.5
8.2
8.4
8.8
9.4
Deflated Figures Example (2)
Calculate real turnover based on 1988 RPI
89:
8.2 x 106.9 = £7.6m
115.2
90:
8.4 x 106.9 = £7.1m
126.1
91:
8.8 x 106.9 = £7.0m
133.5
etc.
Deflated Figures Example (3)
1988 1989 1990 1991 1992
Company
Turnover
(£m)
6.6
RPI
106.9 115.2 126.1 133.5 138.5
Deflated
Company
Turnover
(£m)
6.6
8.2
7.6
8.4
7.1
8.8
7.0
9.4
7.3
Deflated Figures Example (4)
Turnover (£m)
Company Turnover 1988-92
10
9
8
Turnover
Deflated
7
6
88
89
90
Year
91
92
Index Numbers-Tasks
• Tutorial 1:
– Calculation of Laspeyres’ and Paasche’s
indices
• Tutorial 2:
– Deflating using RPI
• Read: Presentation of Data chapter of Oakshott
(and try exercises)
• Read: Web-page background notes
• Read: statistics.gov information
• Start part 1 of coursework.