1. Puck Taminiau-van Veen
Measuring capital
Puck Taminiau-van Veen

2. Overview Relevance Non-financial balance sheets
Perpetual Inventory Method (PIM)
Types of capital stock
Results
Exercise
Conclusions

3. Relevance Consumption of fixed capital (depreciation)
More than only growth figures
Input for productivity measurement
OECD handbook “Measuring Capital”

4. Non-financial balance sheets
Produced assets
Capital stock (fixed assets)
Inventories
Consumer durables (memorandum item)
Non-produced assets
Land
Subsoil assets
In combination with financial balance sheets:  total net worth

5. Fixed assets
Fixed assets are produced assets used in production for more than one year.
The following asset types are distinguished:
Dwellings
Other buildings and structures
Machinery and equipment
Weapons systems (after ESA 2010)
Cultivated biological resources
Intellectual property products (including R&D after ESA )

6. Perpetual Inventory Method (1)
Basic idea: Measures capital stock by following changes in capital stock
Inputs required: time series of investments, price information, service lifes, other parameters

7. Perpetual Inventory Method (2)
Output:
Gross capital stock (replacement value)
Productive capital stock (productive value)
Net capital stock (market value)

8. Gross capital stock
The stock of assets surviving from past investment and re-valued at the purchasers prices of new capital goods of a reference period
The value of assets before deducting the consumption of fixed capital
Gross capital stock ignores decay of assets and considers past investment as new (only retirement is taken into account)
Capital stock measurement 8

9. Gross capital stock
Gross capital stock in year t of assets purchased in year j
Survival rate of t-j year old asset
Replacement value in year t of assets purchased in year j
Investments in historic prices
Cumulative price index to revalue investments in prices of year t 9

10. Gross capital stock (example)
In year 1, 20 cars are bought for € ,- each
Car prices rise with 2% each year
Suppose that cars have the following survival function:
Year (t) 1 2 3 4 5 6
Survival rate
100%
90%
80%
70%
60%
50%
What is the gross capital stock after 5 years?
Capital stock measurement 10

11. Gross capital stock (example)
In year 1, 20 cars are bought for € 20,000.- each
Car prices rise with 2% each year
Suppose that cars have the following survival function:
Year (t) 1 2 3 4 5 6
Survival rate
100%
90%
80%
70%
60%
50%
What is the gross capital stock after 5 years?
After 5 years, 60% of the cars are still in service
Replacement value of cars in year 5 is x € 20,000,- x (1.02)^5 = € 441,632.-
Gross capital stock = 0.6 x € 441,632.- = € 264,979.-
Capital stock measurement 11

12. Productive capital stock
The stock of a particular type of assets surviving from past periods, and corrected for loss in productive efficiency
Measured as the sum of past investments, weighted by an age-efficiency profile
Embodied volume of current and future capital services
Capital stock measurement 12

13. Productive capital stock
Productive capital stock in year t of assets purchased in year j
Gross capital stock in year t of assets purchased in year j
Age efficiency of all assets of the age t-j that are still used in production
Capital stock measurement 13

14. Example age-efficiency
Year (t) 1 2 3 4 5 6
Age-efficiency
100%
85%
65%
45%
20% 0%
During the first year the asset runs at 100 percent of its productive capacity, during the second period the figure is 85 percent and so on.
Capital stock measurement 14

15. Productive capital stock (example)
In year 1, 20 cars are bought for € 20,000.- each
Gross capital stock in year 5 is € 264,979.-
Suppose that cars have the following age-efficiency:
Year (t) 1 2 3 4 5 6
Age-efficiency
100%
85%
65%
45%
20% 0%
What is the productive capital stock after 5 years?
Capital stock measurement 15

16. Productive capital stock (example)
In year 1, 20 cars are bought for € 20,000.- each
Gross capital stock in year 5 is € 264,979.-
Suppose that cars have the following age-efficiency:
Year (t) 1 2 3 4 5 6
Age-efficiency
100%
85%
65%
45%
20% 0%
What is the productive capital stock after 5 years?
After 5 years, cars have 20% productive capacity
Productive capital stock is 0.2 x € 264,979.- = € 52,996
Capital stock measurement 16

17. Net capital stock
The stock of assets surviving from past periods, and corrected for depreciation
The net capital stock is valued as if the capital good (used or new) were acquired on the date to which a balance sheet relates
Similar to productive capital stock of a single asset if age-efficiency profile is identical with age-price profile (geometric)
Net capital stock is used for compiling the non-financial balance sheets
Capital stock measurement 17

18. Net capital stock
Net capital stock in year t of assets purchased in year j
Gross capital stock in year t of assets purchased in year j
Age-price profile of all assets of the age t-j that are still used in production
Capital stock measurement 18

19. Net capital stock (example)
In year 1, 20 cars are bought for € 20,000.- each
Gross capital stock in year 5 is € 264,979.-
Suppose that cars have the following age-price profile:
Year (t) 1 2 3 4 5 6
Age-price profile
0.96
0.79
0.58
0.38
0.16
What is the net capital stock after 5 years?
Capital stock measurement 19

20. Net capital stock (example)
In year 1, 20 cars are bought for € 20,000.- each
Gross capital stock in year 5 is € 264,979.-
Suppose that cars have the following age-price profile:
Year (t) 1 2 3 4 5 6
Age-price profile
0.96
0.79
0.58
0.38
0.16
What is the net capital stock after 5 years?
After 5 years, cars have an age-price profile of 16%
Net capital stock is 0.16 x € 264,979.- = € 42,396
Capital stock measurement 20

21. Balance sheets of net capital stock
Structure of balance sheet for fixed assets:
Opening balance sheet (stock 1/1)
Revaluation
Fixed capital formation (new)
Consumption of fixed capital
Acquisitions less disposals (existing)
Other changes in volume
Closing balance sheet (stock 31/12)

22. Consumption of fixed capital
Negative change in value as result of normal wear and tear and obsolescence
Annual change in net capital stock, before recording investments and other volume changes

23. Other items on balance sheet
Revaluation
Acquisitions less disposals (existing)
Other changes in volume

24. Results (2012) Opening stock Revaluation Investments Depreciation (-)
Opening stock
Revaluation
Investments
Depreciation (-)
2nd hand purchases, sales, etc
Closing stock
Billion €
Dwellings
964,0
-34,8
25,0
17,4
0,1
936,8
Industrial buildings
384,9
-0,1
16,0
16,2
384,5
Other structures
340,2
8,7
13,9
10,7
352,0
Transport equipment
46,8
0,8
11,5
8,3
-2,4
48,3
Computers
12,4
-0,4
4,4
3,7
12,8
Machinery and installations
163,8
1,6
15,9
15,3
166,0
Other tangible assets
32,2
0,7
7,7
7,8
-0,2
32,6
Intangible assets
33,0
10,1
9,5
33,8
Total
1977,4
-23,3
104,5
89,0
-2,6
1966,9

25. Exercise

26. Conclusions Important to measure capital/non-financial balance sheets
Use of PIM generates consistency
Growing interest for information on non-financial assets
Recommended by ESA

27. Questions?