1. Description of dynamical processes
Jacek Szanduła

2. Lecture plan Average changes. Aggregate indices.
Fixed base and chain base measures.
Changes and individual indices.
Average changes.
Aggregate indices.
Lowe index.
Laspeyres price and quantity indices.
Paasche price and quantity indices.
Other price indices: Fisher, Walsh, Marshall–Edgeworth,Törnqvist.
Deflator.
Coping with inflation.
Jacek Szanduła

3. Fixed base (jednopodstawowy, o stałej bazie) and chain base (łańcuchowy) measures
Fixed base – a particular period t0 is chosen arbitrarily and measures of dynamics are calculated with the use of values of the current period t and the base period t0.
Chain base – measures of dynamics are calculated with the use of values of the current period t and the previous period t – 1.
Jacek Szanduła

4. Changes and individual indices
Fixed base
Chain base
Absolute change
Percentage change
Index
Jacek Szanduła

5. Some relations between measures of dynamics
Jacek Szanduła

6. Changes and indices – example
Average monthly wages in PLN (X). t0 = 2002
Year X
2002
2133 
2003
2201 68
3.2
1.032
2004
2290
157 89
7.4
4.0
1.074
1.04
2005
2380
247 90
11.6
3.9
1.116
1.039
2006
2477
344 97
16.1
4.1
1.161
1.041
2007
2691
558
214
26.2
8.6
1.262
1.086
2008
2944
811
253
38.0
9.4
1.38
1.094
2009
3103
970
159
45.5
5.4
1.455
1.054
2010
3225
1092
122
51.2
1.512
2011
3400
1267
175
59.4
1.594
Jacek Szanduła

7. Average changes Average Rate of Change (zmiana średniookresowa)
Compound (Annual) Growth Rate (średniookresowe tempo zmian)
Jacek Szanduła

8. Aggregate indices
An aggregate index measures relative changes in values ​​of several variables taken as a combination.
Example: Monthly expenditures
Month
May
June
Food
Price
Quantity
Bread 2 30
2.50 25
Butter 5 10 6 12
Tomato 4
Ham 20 3
Cheese
2.5 22
How to measure growth of prices using single index?
Jacek Szanduła

9. Lowe price index – Lowe price index
– price of ith good in the tth moment
– quantity of ith good in the tth moment
Jacek Szanduła

10. Laspeyres price index Month May June Food Month May June Food SUM 270
Quantity
Bread 2 30
2.50 25
Butter 5 10 6 12
Tomato 4
Ham 20 3
Cheese
2.5 22
Month
May
June
Food
Price
Quantity
Bread 2 30
2.50 25
2  30 = 60
2.5  30 = 75
Butter 5 10 6 12
5  10 = 50
6  10 = 60
Tomato 4
4  10 = 40
Ham 20 3
20  3 = 60
Cheese
2.5 22
20  2.5 = 50
22  2.5 = 55
SUM
270
290
Jacek Szanduła

11. Laspeyres quantity index
Month
May
June
Food
Price
Quantity
Bread 2 30
2.50 25
Butter 5 10 6 12
Tomato 4
Ham 20 3
Cheese
2.5 22
Month
May
June
Food
Price
Quantity
Bread 2 30
2.50 25
2  30 = 60
2  25 = 50
Butter 5 10 6 12
5  10 = 50
5  12 = 60
Tomato 4
Ham 20 3
20  3 = 60
Cheese
2.5 22
20  2.5 = 50
20  2 = 40
SUM
270
Jacek Szanduła

12. Paasche price index Month May June Food Month May June Food SUM 296.5
Quantity
Bread 2 30
2.50 25
Butter 5 10 6 12
Tomato 4
Ham 20 3
Cheese
2.5 22
Month
May
June
Food
Price
Quantity
Bread 2 30
2.50 25
2.5  25 = 72.5
2  25 = 50
Butter 5 10 6 12
6  12 = 72
5  12 = 60
Tomato 4
4  12 = 48
Ham 20 3
20  3 = 60
Cheese
2.5 22
22  2 = 44
20  2 = 40
SUM
296.5
270
Jacek Szanduła

13. Paasche quantity index
Month
May
June
Food
Price
Quantity
Bread 2 30
2.50 25
Butter 5 10 6 12
Tomato 4
Ham 20 3
Cheese
2.5 22
Month
May
June
Food
Price
Quantity
Bread 2 30
2.50 25
2.5  25 = 72.5
2.5  30 = 75
Butter 5 10 6 12
6  12 = 72
6  10 = 60
Tomato 4
4  12 = 48
4  10 = 40
Ham 20 3
20  3 = 60
Cheese
2.5 22
22  2 = 44
22  2.5 = 55
SUM
296.5
290
Jacek Szanduła

14. Fisher price index
Jacek Szanduła

15. Other price indices Walsh Marshall–Edgeworth Törnqvist
(share of ith good in all expenditures at the tth moment)
Jacek Szanduła

16. Törnqvist price index – example
Month
May
June
Food
Price
Quantity
Bread 2 30
2.50 25 60
72.5
1.25
0.222
0.245
0.233
1.053
Butter 5 10 6 12 50 72
1.2
0.185
0.243
0.214
1.040
Tomato 4 48
0.8
0.162
0.174
0.962
Ham 20 3 1
0.202
0.212
Cheese
2.5 22 44
1.1
0.148
0.167
1.016
SUM
270
296.5 
Jacek Szanduła

17. Deflator
Deflator (deflator) – value used to convert current prices into inflation-adjusted prices. One uses a deflator when one seeks to determine whether or not prices are rising in real terms.
Jacek Szanduła

18. Coping with inflation Year X CPIt/t-1 Y Z
X – average monthly wages in PLN. t0 = 2002
CPIt/t-1 – Consumer Price Index year to previous year
Y – real average monthly wages in PLN (base year 2002)
Z – real average monthly wages in PLN (base year 2011)
Year X
CPIt/t-1 Y Z
2002
2133
1.019
2715
2003
2201
1.008
2201 : = 2184
2779
2004
2290
1.035
2290 : : = 2195
2793
2005
2380
1.021
2234
2844
2006
2477
1.01
2302
2930
2007
2691
1.025
2440
3106
2008
2944
1.042
2562
3261
2009
3103
2609
3103   = 3321
2010
3225
1.026
2643
3225  = 3364
2011
3400
1.043
2672
Jacek Szanduła

19. Exercise 1 Year Profit [mln PLN] CPIt/t-1
2007
1.9
1.025
2008
2.1
1.042
2009 2
1.035
2010
1.026
2011
1.043
Present the company's profit in prices of 2009.
Jacek Szanduła

20. Exercise 2 Calculate indices: Laspeyres, Paasche, Fisher. Year 2010
2011
Good
Price
Quantity
Bread
2.50
200
2.00
Bus tickets
500
400
Beer
100
120
Calculate indices:
Laspeyres,
Paasche,
Fisher.
Jacek Szanduła