1. Item 8b Capital stock, capital services
ESTP course on National Accounts ESA 2010
Luxembourg, 30 May – 03 June Eurostat

2. Measuring capital
The fundamental role of capital [in economic growth] has been known at least since the writings of the physiocrat Anne-Robert-Jacques Turgot and Adam Smith in the 18th century
The practical measurement of capital is subject to opposing views. Therefore the statistician doing work on matters pertaining to capital should be prepared to meet criticism. However, as Hicks (1973) has it:
"Capital (I am not the first to discover) is a very large subject, with many aspects; wherever one starts it is hard to bring more than a few of them into view. It is just as if one were making pictures of a building; though it is the same building it looks quite different from different angles." 2

3. Capital in economic production
Capital combined with labour (and intermediate inputs) at some technology are used to produce economic output
Quantifying capital
- as a measure of wealth
- as an input into economic production (Growth accounting/Productivity measures)
What is capital? What is investment? 3

4. Capital stock Flows and stocks of capital
SNA93/ESA95 were very brief about capital stock. Better OECD (2001) Manual “Measuring capital” (updated in 2009).
In 2008SNA there is for the first time a chapter on “Capital services and the national accounts” (Ch. 20; the aim of the chapter is to establish a link between the value of assets used in production and the gross operating surplus generated)
In ESA2010 the analytical concept of capital services introduced for market production, so that it can be shown in a supplementary table as component of value added (NB. observation vs analysis?) 4

5. Defining capital: ESA2010 economic assets
Para. 7.15: "An economic asset is a store of value representing the benefits accruing to the economic owner by holding or using the entity over a period of time. It is a means of carrying forward value from one accounting period to another."
Types: Financial vs. Non-financial (produced or non-produced)
Excluded: human capital, natural assets that are not considered economic assets, consumer durables, contingent assets and liabilities which are not financial assets/liabilities 5

6. Non-financial assets (AN) Annex 7.1
- Produced non-financial assets (AN.1)
-- Fixed assets (AN.11)
-- Inventories (AN.12)
-- Valuables (AN.13)
- Non-produced non-financial assets (AN.2)
-- Natural resources (AN.21)
-- Contracts, leases and licences (AN.22)
-- Purchases less sales of goodwill and marketing assets (AN.23) 6

7. Capital stock measurement
Types of prices:
- historic prices (=capital goods are valued at the (“historical”) prices prevailing at the time they were purchased)
- current prices (=capital goods are valued at the prices prevailing in the current year)
- constant prices (=capital goods are valued at the prices of a selected base year) 7 7

8. Capital stock measurement
Problems in measuring capital stock
- Definition different from business accounts
- Valuation issues (Unique goods? ICT technological change?)
- Scarce sources of capital stocks (info on service lives, depreciation patterns, etc.) 8 8

9. Estimation of capital stock
Direct measurement:
- hard to observe & evaluate
- easier to observe capital purchases (GFCF)
Model based approach: Perpetual Inventory Model (PIM); pioneered by Raymond Goldsmith in 1951. 9

10. P51g: Gross fixed capital formation (GFCF)
Para 3.124:
"Gross fixed capital formation (P.51) consists of resident producers’ acquisitions, less disposals, of fixed assets during a given period plus certain additions to the value of non-produced assets realised by the productive activity of producer or institutional units. Fixed assets are produced assets used in production for more than one year"
Gross means gross of consumption of fixed capital (i.e. depreciation), which is the decline in the value of the asset due to its use in production

11. Example PIM 11 11

12. Calculating PIM: a real case (1)
For gross capital stock (GCS), important points:
- Working classification of asset types
- Assumptions about asset (service) lives
- Take inflation into account
- How many years back?
Gross capital stock (GCS) is the value of the capital used in production, valued at “as new” prices, i.e. regardless of age or actual condition, at a certain point of time:
GCS(t)=GCS(t-1)+GFCF(t)-R(t) 12 12

13. Example retirement functions
Usual retirement functions:
Winfrey
Weibull
Lognormal 13 13

14. P51c: Consumption of fixed capital
Para 3.139:
" Consumption of fixed capital (P.51c) is the decline in value of fixed assets owned, as a result of normal wear and tear and obsolescence. The estimate of decline in value includes a provision for losses of fixed assets as a result of accidental damage which can be insured against. Consumption of fixed capital covers anticipated terminal costs, such as the decommissioning costs of nuclear power stations or oil rigs or the cleanup costs of landfill sites. Such terminal costs are recorded as consumption of fixed capital at the end of the service life, when the terminal costs are recorded as gross fixed capital formation"
CFC shall be calculated for all fixed assets (except animals), including intellectual property rights, major improvements to land and costs of ownership transfer associated with non-produced assets

15. Calculating PIM: CFC & net stock
Roles of CFC in ESA2010:
- To estimate balancing items gross/net
- To calculate sum-of-costs of non-market producers
- Reported in capital account and balance sheets
CFC in close relation with capital stock
Calculation difficult in practice (gross values are more reliable than net values)
Assumption of depreciation rate
- straight line method
- constant geometric or exponential method
Net capital stock (NCS) is the market value of the capital in use:
CFC(t)=GFCF(t)-(NCS(t)-NCS(t-1)) 15

16. Capital services
Similarly as not the stock of labour per se, but the hours worked (weighted by their quality) is the ideal labour input measure also capital services is a better measure of capital input than capital stock
E.g. simply adding up a stock consisting of software and dwellings gives a skewed picture since these assets have different marginal products (intuitively: the computer software has a life of 3-5 years so it is in more of a hurry to generate capital income than a dwelling with a service life of 50 years)
Therefore the asset types are not weighted with their market prices but with so called user costs/rental prices to gain a measure of the appropriate capital input measure 16 16

17. Volume index of capital services
2-step calculation:
1) (productive) capital stock for each asset type
- retirement functions
- age-efficiency patters
2) aggregate assets
heterogeneity of assets
weighting with the user costs of capital 17 17

18. User cost of capital
where, r is the user cost, p designates the price index for new capital goods, q is the net rate of return, d is the rate of depreciation and π is the holding gain or loss, i.e. the change in prices from time t-1 to time t 18 18