1 NBS-OECD Workshop on National Accounts 6-10 November 2006 Measuring Capital and Capital Services:...

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1 NBS-OECD Workshop on National Accounts 6-10 November 2006 Measuring Capital and Capital Services: An Overview Paul Schreyer OECD

Transcript of 1 NBS-OECD Workshop on National Accounts 6-10 November 2006 Measuring Capital and Capital Services:...

Page 1: 1 NBS-OECD Workshop on National Accounts 6-10 November 2006 Measuring Capital and Capital Services: An Overview Paul Schreyer OECD.

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NBS-OECD Workshop on National Accounts

6-10 November 2006

Measuring Capital and Capital Services:

An Overview

Paul Schreyer

OECD

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Purpose of capital measurement

2 main purposes:

• Capital as a storage of wealth

• Capital as a source of productive services

The two purposes correspond more or less to

• Capital in the balance sheets and in the income side of the national accounts, e.g., value of fixed assets, depreciation, net and gross income…

Relevant questions: what is the value of wealth in the economy? Is current income sustainable?

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Purpose of capital measurement

• Capital in the production side of the national accounts

Relevant questions: capital and multi-factor productivity, growth accounting, competitiveness

• In the SNA93, no explicit recognition of capital in the production account

• In revision to SNA 93, explicit recognition of capital income and capital services in the production account

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Stocks and flows – an integrated approach

• Key objective of new capital manual: present integrated and consistent approach towards capital measurement to link relevant flows and relevant stocks:

• Investment

• Depreciation

• Capital services

• Net stock

• Gross stock

• Productive stock

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System of capital in the SNA93

InvestmentGross stock

Retirement

function

CFC

Net value addedAge-price

function

Net stock

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System of capital in the new SNA

InvestmentGross stock

Retirement

function

CFC

Net value addedAge-price

function

Productive stock

Age-efficiency

function

Return on capital

User costs

Capital services

Net stock

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Stocks and flows – an overview Income and wealth perspective Production and productivity

perspective

Basic flow Investment Investment

Aggregation across assets of different age based on

Depreciation profile (Age-price profile)

Age-efficiency profile

Resulting stock for each class of assets

Net capital stock by asset type Productive stock by asset type

Derived flow Depreciation Capital services by type of asset

Aggregation across different classes of assets based on

Market prices Rental prices or user costs

Resulting stocks Total net capital stock Total productive stock

Derived measure Balance sheet entry, national wealth, net measures of income

Total capital services, multi-factor productivity

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Asset market equilibrium condition

Central economic relationship that links income and production perspective Walras (1874); Boehm-Bawerk (1888)

• Stock value of an asset = discounted stream of future rental payments that the asset is expected to yield

P0t: price of new asset purchased at the beginning of period t

fnt: nominal rental payable at beginning of period t

(1+rt): nominal discount factor

P0t=f0

t+1/(1+rt) + f1t+2/(1+rt)2 + f2

t+3/(1+rt)3+…

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Asset market equilibrium condition (2)

In a functioning market, purchase price of an asset equals the discounted stream of expected rentals

Purchasers will buy asset of flow of rental implies at least a rate of return that is as large as rt rt can also be considered the opportunity cost of investing in the asset = the return that the market would pay for investment of similar risk

Central equation for integrated system of stocks and flows of capital

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Rentals and asset prices – numerical example (1)

Assume: asset with

• Service life of 8 years

• Discount rate 5 %

• Rental for a new asset is 10$

• For simplicity, no general inflation

• Price of new asset and price of rentals are expected to rise by 2% per year: fn

t+1=fnt*1.02

• Productive services of the asset decline by a constant amount over its service life: linear age-efficiency pattern

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Rentals and asset prices – numerical example (2)

10*0.88*1.02 =8.93

10.0/1.05=9.52

Year (t)Age-

efficiency

Rental price

beginning of period

Rental price

discounted to

beginning of year 1

1 100%2 88% 10.00 9.523 75% 8.93 8.104 63% 7.80 6.745 50% 6.63 5.466 38% 5.41 4.247 25% 4.14 3.098 13% 2.82 2.009 0% 1.44 0.97

10 0.00 0.00Price of asset beginning of year 40.12

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Rentals and asset prices – numerical example (3)

7.80/1.052 =7.08

Rental price discounted to beginning of year

Year (t)Age-

efficiency

Rental price

beginning of period

1 2 3 4 5 6 7 8

1 100%2 88% 10.00 9.523 75% 8.93 8.10 8.504 63% 7.80 6.74 7.08 7.435 50% 6.63 5.46 5.73 6.02 6.326 38% 5.41 4.24 4.45 4.68 4.91 5.157 25% 4.14 3.09 3.24 3.41 3.58 3.76 3.948 13% 2.82 2.00 2.10 2.21 2.32 2.43 2.55 2.689 0% 1.44 0.97 1.02 1.07 1.13 1.18 1.24 1.30 1.37

10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00Price of asset beginning of year 40.12 32.12 24.81 18.24 12.52 7.74 3.98 1.37

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Rentals and asset prices – numerical example (4)

This example also shows a very important link between age-efficiency profile and the age-price profile

For a given rate of interest, a given rate of price change of new assets, there will be exactly one sequence of asset prices for each age-efficiency profile

Consider the following price history of an asset

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Rentals and asset prices – numerical example (5), Price history of asset

Diagonal price movement: total change in value of asset between two years e.g. 40.12-32.12 = 8

•Vertical movement: price change of new asset (2%) = 40.92-40.12=0.80

•Horizontal movement: price difference due to age = 40.92-32.12=8.80

Year (t) 0 1 2 3 4 5 6 7 8

1 40.122 40.92 32.123 41.74 32.77 24.814 42.57 33.42 25.30 18.245 43.43 34.09 25.81 18.61 12.526 44.29 34.77 26.32 18.98 12.77 7.747 45.18 35.47 26.85 19.36 13.03 7.89 3.988 46.08 36.18 27.39 19.75 13.29 8.05 4.06 1.379 47.01 36.90 27.94 20.14 13.56 8.21 4.14 1.39 0.00

Age of asset

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Rentals and asset prices – numerical example (6), Age-price profile

32.12/40.92=0.785

Year (t) 0 1 2 3 4 5 6 7 8

1 40.122 40.92 32.123 41.74 32.77 24.814 42.57 33.42 25.30 18.245 43.43 34.09 25.81 18.61 12.526 44.29 34.77 26.32 18.98 12.77 7.747 45.18 35.47 26.85 19.36 13.03 7.89 3.988 46.08 36.18 27.39 19.75 13.29 8.05 4.06 1.379 47.01 36.90 27.94 20.14 13.56 8.21 4.14 1.39 0.00

78.50%78.50% 59.43%78.50% 59.43% 42.85%78.50% 59.43% 42.85% 28.84%78.50% 59.43% 42.85% 28.84% 17.47%78.50% 59.43% 42.85% 28.84% 17.47% 8.82%78.50% 59.43% 42.85% 28.84% 17.47% 8.82% 2.97%78.50% 59.43% 42.85% 28.84% 17.47% 8.82% 2.97% 0.00%

Age of asset

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Rentals and asset prices – numerical example (7)

Note: Age-price profile does not depend on time here because age-efficiency profile is not time-dependent and because the expected rates of asset price change and discount factors are given for any point in time

However, as historical time moves on, it may well be that discount factors or price expectations change, in which case the age-price profiles of all assets would be affected.

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Rentals and asset prices – numerical example (8), linear age-efficiency

profile0 1 2 3 4 5 6 7 8

Age-efficiency profile 1.00 0.88 0.75 0.63 0.50 0.38 0.25 0.13 0.00

Age-price profile 1.00 0.79 0.59 0.43 0.29 0.17 0.09 0.03 0.00

Age

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8 9 10

Age-efficiency profile Age-price profile

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Rentals and asset prices – numerical example (9), constant age-efficiency

profile0 1 2 3 4 5 6 7 8

Age-efficiency profile 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Age-price profile 1.00 1.00 0.89 0.77 0.65 0.53 0.40 0.27 0.14

Age

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8 9 10

Age-efficiency profile Age-price profile

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Rentals and asset prices – numerical example (10), geometric age-efficiency

profile0 1 2 3 4 5 6 7 8

Age-efficiency profile 1.00 0.78 0.60 0.47 0.37 0.28 0.22 0.17 0.13

Age-price profile 1.00 0.78 0.60 0.47 0.37 0.28 0.22 0.17 0.13

Age

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8 9 10

Age-efficiency profile Age-price profile

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Rentals and asset prices – numerical example (11), hyperbolic age-

efficiency profile0 1 2 3 4 5 6 7 8

Age-efficiency profile 1.00 0.93 0.86 0.77 0.67 0.55 0.40 0.22 0.00

Age-price profile 1.00 0.82 0.66 0.50 0.36 0.23 0.12 0.04 0.00

Age

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 1 2 3 4 5 6 7 8

Age-efficiency profile Age-price profile

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Retirement and survival functions (1)

• Assets in a cohort are unlikely to retire all at the same moment

• Typically, there is a retirement distribution around an average retirement age

• To construct the age-efficiency function of a cohort, the age-efficiency function for a single asset has to be combined with a retirement distribution

• This is shown in the following slides

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Retirement and survival functions (2)

• Probability density function of retirement: shows the (marginal) probability for an asset to retire at age T

• For simplicity, log-normal distribution

Normal distribution, average service life = 8 years

0.00

0.05

0.10

0.15

0.20

0.25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

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Retirement and survival functions (3)

• Call the probability that an asset retires at age T, FT

• In our example with a linear age-efficiency function gs, we had gs=1-s/T.

• For a single asset, the service life was assumed T=8

• With a retirement distribution, for each age s, there is a possibility that the asset retires at age s, or at age s+1 etc.

• Calculate an average, with probability weighting where Tm is the maximum service life:

hs= ∑T=sTm[1-s/T]*FT

• This creates a new age-efficiency profile for the cohort that reflects both efficiency loss and retirement {hs}

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Retirement and survival functions (4), age-efficiency profiles

0.938 0.875 0.813 0.750 0.688 0.625 0.563 0.500 0.438 0.375

0.889 0.778 0.667 0.557 0.448 0.342 0.243 0.158 0.091 0.046

s--> 1 2 3 4 5 6 7 8 9 10

sh

sg

0.000

0.200

0.400

0.600

0.800

1.000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Single asset Cohort with retirement distribution

• hs is non-linear even with linear gs!

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Retirement and survival functions (5)A special case: one-hoss shay

• Suppose a class of assets follows a one-hoss shay pattern of efficiency loss: efficiency is constant until the asset retires

• Then, the combined age-efficiency/retirement pattern {hsG}

becomes hsG= ∑T=s

TmFT, i.e., only a retirement pattern.

• More precisely, hsG is the cumulative probability density

function that varies from h0G=1 for a new asset to hTm

G=0

• It is now possible to construct the gross capital stock on the basis of the perpetual inventory method:

• Gross capital stock = sum of past investments of a class of assets, with cohorts weighted by the retirement pattern {hs

G}

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Retirement and survival functions (6)A special case: one-hoss shay

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Single asset Cohort with retirement distribution

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Retirement and survival functions (7)Gross capital stock

• Gross capital stock = sum of past investments of a class of assets, with cohorts weighted by the retirement pattern {hs

G}

• Gross capital stock = stock of assets surviving from past investments that ignores deterioration of assets and considers past investment ‘as new’ - only retirement is taken into account

• Although the gross capital stock is often calculated in practice, it serves mainly as an intermediate step towards measuring depreciation and net stocks rather than as an analytical measure in itself.

• Note: net stocks and depreciation can but do not have to be calculated via the gross stock. In fact, the usefulness of the gross stock is relatively limited.

• Some countries (eg United States) do not publish gross stocks any more – they restrict themselves to net stocks and productive stocks (see later)

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Retirement and survival functions (8)Gross capital stock

Year (t)

Investment at historical

prices

Price index (new) capital goods

Investment in prices of

year 16Retirement

pattern

Investment in prices of year 16, weighted

with retirement

pattern

1 500 1.000 672.9 0.0060 4.0

2 800 1.020 1055.6 0.0225 23.8

3 1000 1.040 1293.6 0.0666 86.1

4 600 1.061 760.9 0.1584 120.6

5 500 1.082 621.7 0.3083 191.7

6 700 1.104 853.3 0.4998 426.4

7 750 1.126 896.3 0.6912 619.6

8 900 1.149 1054.5 0.8411 886.9

9 1200 1.172 1378.4 0.9330 1286.0

10 1000 1.195 1126.2 0.9770 1100.3

11 1100 1.219 1214.5 0.9936 1206.7

12 1200 1.243 1298.9 0.9984 1296.9

13 1100 1.268 1167.3 0.9995 1166.8

14 1000 1.294 1040.4 0.9997 1040.1

15 900 1.319 918.0 0.9998 917.8

16 800 1.346 800.0 1.0000 800.0

Gross stock at (current) prices of year 16 11173.6

Note three types of valuation of stocks:

•Historical prices = valuation in terms of prices of the year of

acquisition

•Constant prices = valuation in terms of

a base year

•Current prices = special case of

constant prices = valuation in terms of the current (typically

latest) year

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Net or wealth stocks (1)

• Net capital stock or wealth stock = market value of assets

• Net capital stock = stock of assets surviving from past investments that has been corrected for retirement and for loss in value due to ageing

• Net capital stock offers a wealth perspective. It is the capital stock that shows up in the balance sheets of the national accounts.

• Calculation of net stocks: 2 possibilities:

• Directly, as sum of past investments, weighted by age-price profile

• Derived from gross stock and depreciation

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Net or wealth stocks (2)

• Starting point: age-price profile, derived from combined age-efficiency & retirement profile

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Age-efficiency & retirement profile Age-price & retirement profile

Page 31: 1 NBS-OECD Workshop on National Accounts 6-10 November 2006 Measuring Capital and Capital Services: An Overview Paul Schreyer OECD.

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Net or wealth stocks (3)

Year (t)

Investment at historical

prices

Price index (new) capital goods

Investment in prices of

year 16

Combined Age-price + retirement

pattern

Investment in prices of year 16, weighted

with retirement

pattern

1 500 1.000 672.9 0.0000 0.0

2 800 1.020 1055.6 0.0001 0.1

3 1000 1.040 1293.6 0.0006 0.7

4 600 1.061 760.9 0.0020 1.5

5 500 1.082 621.7 0.0060 3.7

6 700 1.104 853.3 0.0154 13.1

7 750 1.126 896.3 0.0338 30.3

8 900 1.149 1054.5 0.0656 69.2

9 1200 1.172 1378.4 0.1141 157.3

10 1000 1.195 1126.2 0.1816 204.5

11 1100 1.219 1214.5 0.2691 326.9

12 1200 1.243 1298.9 0.3768 489.4

13 1100 1.268 1167.3 0.5042 588.5

14 1000 1.294 1040.4 0.6509 677.2

15 900 1.319 918.0 0.8163 749.4

16 800 1.346 800.0 1.0000 800.0

Net stock 31/Dec/year 16 at (current) prices of year 16 4111.9

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Depreciation (Consumption of fixed capital) (1)

•Depreciation is the loss in value of an asset or a group of assets as they age

•A flow concept

•Economic meaning: deduction from gross income to account for the loss in capital value owing to the use of capital goods in production

•SNA definition: « the decline, during the course of the accounting period, in the current value of the stock of fixed assets owned and used by a producer as a result of physical deterioration, normal obsolescence or normal accidental damage. »

•Excluded: value losses due to acts of war or as a consequence of exceptional events such as major natural disasters

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Depreciation (Consumption of fixed capital) (2)

Note:

•Depreciation must be measured with reference to a given set of prices, ie the average prices of the period

•“Used by producer” includes assets that are kept idle for whatever reasons

•“Normal obsolescence” is included in depreciation but not “abnormal obsolescence”. Example: scrapping of energy-intensive machines following an oil-price shock

Page 34: 1 NBS-OECD Workshop on National Accounts 6-10 November 2006 Measuring Capital and Capital Services: An Overview Paul Schreyer OECD.

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Computing depreciation (1)

Two avenues: directly and indirectly via net stock

Direct computation: main tool: age-price profile and investment series

•Rate of depreciation of an s-year old asset = price difference between an s-year old asset and an s+1 year old asset divided by price of an s-year old asset:

ts

t1s

tst

s P

PPd

{P0t, P1

t, P2t,…} is the age-price profile, so ds

t can be derived directly

Page 35: 1 NBS-OECD Workshop on National Accounts 6-10 November 2006 Measuring Capital and Capital Services: An Overview Paul Schreyer OECD.

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Computing depreciation (2)

•When applied to past investment, depreciation rates apply in a cumulative way:

•Depreciation for a new capital good: d0It

•Depreciation for a one-year old capital good: d1(1-d0)It-1

•Depreciation for a one-year old capital good: d2(1-d1)(1-d0)It-2

•Etc.

Total depreciation = d0It + d1(1-d0)It-1 + d2(1-d1)(1-d0)It-2 + …

Note: investment {It, It-1,…} is expressed in constant prices of a particular base year, therefore total depreciation is also in prices of this base year.

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Computing depreciation (3)Age-price profile Depreciation rates Depreciation profile

Age0 46.01 1.00 0.18369 0.18371 37.56 0.82 0.20268 0.16552 29.94 0.65 0.22538 0.14673 23.19 0.50 0.25269 0.12744 17.33 0.38 0.28564 0.10765 12.38 0.27 0.32517 0.08756 8.36 0.18 0.37181 0.06757 5.25 0.11 0.42526 0.04858 3.02 0.07 0.48412 0.03179 1.56 0.03 0.54602 0.0185

10 0.71 0.02 0.60813 0.009311 0.28 0.01 0.66786 0.004012 0.09 0.00 0.72348 0.001413 0.03 0.00 0.77489 0.000414 0.01 0.00 0.82538 0.000115 0.00 0.00 0.88736 0.000016 0.00 0.00 1.00000 0.0000

ts

t1s

ts

s P

PPd

)d1)...(d1)(d1(dD 02s1sss

(46.01-37.56)/46.01=0.184

Page 37: 1 NBS-OECD Workshop on National Accounts 6-10 November 2006 Measuring Capital and Capital Services: An Overview Paul Schreyer OECD.

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Computing depreciation (4)

Year (t)

Investment at historical

prices

Price index (new) capital goods

Investment in prices of

year 16Depreciation

profile

Investment in prices of year 16, weighted

with depreciation

profile

1 500 1.000 672.9 0.0000 0.0

2 800 1.020 1055.6 0.0001 0.1

3 1000 1.040 1293.6 0.0004 0.6

4 600 1.061 760.9 0.0014 1.1

5 500 1.082 621.7 0.0040 2.5

6 700 1.104 853.3 0.0093 8.0

7 750 1.126 896.3 0.0185 16.6

8 900 1.149 1054.5 0.0317 33.5

9 1200 1.172 1378.4 0.0485 66.9

10 1000 1.195 1126.2 0.0675 76.1

11 1100 1.219 1214.5 0.0875 106.3

12 1200 1.243 1298.9 0.1076 139.8

13 1100 1.268 1167.3 0.1274 148.7

14 1000 1.294 1040.4 0.1467 152.6

15 900 1.319 918.0 0.1655 151.9

16 800 1.346 800.0 0.1837 147.0

Depreciation during period 16 at (current) prices of year 16 1051.5

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Computing depreciation (5)

Net capital stock for period 17 at prices of period 16

Year (t)

Investment at historical

prices

Price index (new) capital goods

Investment in prices of

year 16

Combined Age-price + retirement

pattern

Investment in prices of year 16, weighted

with retirement

pattern

1 500 1.000 672.92 800 1.020 1055.6 0.0000 0.0

3 1000 1.040 1293.6 0.0001 0.2

4 600 1.061 760.9 0.0006 0.4

5 500 1.082 621.7 0.0020 1.2

6 700 1.104 853.3 0.0060 5.1

7 750 1.126 896.3 0.0154 13.8

8 900 1.149 1054.5 0.0338 35.7

9 1200 1.172 1378.4 0.0656 90.4

10 1000 1.195 1126.2 0.1141 128.5

11 1100 1.219 1214.5 0.1816 220.6

12 1200 1.243 1298.9 0.2691 349.6

13 1100 1.268 1167.3 0.3768 439.8

14 1000 1.294 1040.4 0.5042 524.5

15 900 1.319 918.0 0.6509 597.5

16 800 1.346 800.0 0.8163 653.0

17 1000 1.373 980.4 1.0000 980.4

Net stock 31/Dec/year 17 at prices of year 16 4040.8

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Computing depreciation (6)

Indirect way of computing depreciation via net stocks and the following identity:

Net stock 31/Dec/year 16 4111.9+ Gross investment during year 17 980.4- Depreciation during year 16 1051.5Net stock 31/Dec/year 17 4040.8

Note: specific lags in this identity (depreciation year 16) disappear when everything is formulated in mid-year

valuations

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Computing depreciation (7)

Note: depreciation is in prices of period 16

•To obtain depreciation at current prices, apply investment goods deflator between years 16 and 17

• This is also an easy solution to split depreciation into price and volume components – the deflator for depreciation always equals the asset price deflator

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Computing depreciation (8)

Empirical basis for depreciation rates

1. Derived from age-efficiency functions. This raises the issue of how age-efficiency parameters are constructed. Needed: average service lives and retirement distributions surveys or assumptions

2. Measured directly.

• Service lives and retirement distributions from surveys, combined with some assumptions about the functional form of age-price functions

• Most frequent assumption: linear profile (constant amount of depreciation)

Ps/P0=1-s/T

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Computing depreciation (9)

• Geometric profile (constant rate of depreciation):

Ps/P0 = (1-)s where = DBR/T

DBR: declining balance parameter, often set to equal 2 (“double declining balance”)

For example, BEA uses DBR=2.2 for computers, DBR=1.65 for machinery and equipment, DBR=0.9 for structures

T: expected mean service life

• Econometric estimates based on used asset prices (Hulten Wykoff 1981)

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Productive stocks and capital services (1)

Net stock and depreciation have to do with the value side of capital and income

Productive stocks and capital services have to do with the quantity side of capital and its role in production, i.e. as capital input

The flow of capital services is normally assumed to be a constant proportion of the productive capital stock

The productive stock is the stock of cumulative investment of a particular type, corrected for retirement and efficiency losses, as captured by the age-efficiency and retirement function

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Productive stocks and capital services (3)

Productive stock of asset type i at the beginning of period t+1, and in constant prices of period t:

...IhIhIhIhK 3t3

2t2

1t1

t0

1t,i

{hs} s=0,1,2,… is the combined age-efficiency/retirement profile

By way of the numerical example used earlier, the productive stock is computed as follows:

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Productive stocks and capital services (4)

Year (t)

Investment at historical

prices

Price index (new) capital goods

Investment in prices of

year 16

Combined Age-

efficiency + retirement

pattern

Investment in prices of year 16, weighted

with retirement

pattern

1 500 1.000 672.9 0.0001 0.1

2 800 1.020 1055.6 0.0005 0.5

3 1000 1.040 1293.6 0.0021 2.7

4 600 1.061 760.9 0.0071 5.4

5 500 1.082 621.7 0.0197 12.2

6 700 1.104 853.3 0.0459 39.2

7 750 1.126 896.3 0.0914 81.9

8 900 1.149 1054.5 0.1580 166.6

9 1200 1.172 1378.4 0.2434 335.6

10 1000 1.195 1126.2 0.3420 385.1

11 1100 1.219 1214.5 0.4478 543.9

12 1200 1.243 1298.9 0.5570 723.5

13 1100 1.268 1167.3 0.6674 779.1

14 1000 1.294 1040.4 0.7782 809.6

15 900 1.319 918.0 0.8891 816.2

16 800 1.346 800.0 1.0000 800.0

Productive stock 31/Dec/year 16 at (current) prices of year 16 5501.6

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Productive stocks and capital services (5)

Example from Australia

100

110

120

130

140

150

160

170

180

1986 1988 1990 1992 1994 1996 1998

Capital services

Net (wealth) capital stock

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User costs and its elements (1)Price of capital services

Productive stock and capital services are the quantity/volume of capital input to production

What is the price of capital services?

Price of capital services = user costs or rental price

Basic idea: how much would an owner of a capital good charge if he rented out the capital good for one period under competitive conditions?

The rental price/user cost should cover:

• A ‘normal’ net return to the capital owner to account for opportunity costs

• Depreciation

• Expected revaluation

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User costs and its elements (10)

A reasonable approximation is:

u0t = [r*t + d0] P0

t.

where the user cost is the sum of a real rate of return and depreciation

This user cost formula, due essentially to Walras says that the user cost of capital is equal to the anticipated real interest rate plus the anticipated depreciation rate times the beginning of the period stock price of the asset.

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User costs and its elements (11)

There are two broad options (Diewert 1980 and Harper, Berndt and Wood 1989):

• Use of an endogenous (internal) rate of return (estimated capital services exactly corresponds to gross operating surplus and the capital element of gross mixed income)

• Use of an exogenous (external) rate of return (estimated capital services is unlikely to be exactly equal to gross operating surplus and the capital element of gross mixed income)

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Scope of assets and capital services

• Note: new asset classification proposed in revised SNA

• All fixed assets are within the scope of capital services

• Some special cases:

1. Research and development – not presently recognised as fixed assets, but SNA revision will bring them into asset scope statistical issues of how to measure R&D stocks, how to deflate them, how to depreciate them

2. Some assets are non-produced but sources of capital services, in particular land (see below for more extensive discussion)

3. Some assets are produced but not fixed inventories should they be part of the scope of capital services?

4; Government assets

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Valuation (1)

Valuation – an issue of practical importance

•SNA: flows should be valued at average prices of the period to which they relate

•SNA: stocks in the balance sheets should be valued at the prices of the point in time to which they relate

•The various flow measures (depreciation, value of capital services) should thus be measured at average prices of the period

•When there is a link to stock measures, stock measures should also be valued at average prices of the period for the purposes of carrying out calculations and preserving the link, but not as an entry into the balance sheet

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Valuation (2)

Example:

Net stock at the end of year t and at average prices of the year t =

Net stock at the beginning of year t, valued at average prices of year t

Plus

Gross investment during year t at average prices of year t

Minus

Depreciation during year t at average prices of year t

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Data requirements

Summary of data requirement:

•Benchmark estimate for capital stock, eg from capital survey

•Time series of investment expenditure by type of asset and by industry

•Deflators for investment goods, possibly separate deflators for new and for used assets

•Estimates of retirement or survival patterns

•Estimates of depreciation rates or age-efficiency rates

•Gross operating surplus (by industry)

•Split of mixed income into labour and capital part

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Overall conclusions on capital measurement

•Measurement and interpretation of capital has long occupied economists and statisticians

•Revision of SNA marks an important step forward in the harmonised treatment of assets and the associated flows in the national accounts

•Objective: consistent set of asset-related data with flows and stocks that fit together and that are analytically useful

•Capital measurement requires still many assumptions, and national accountants rightly try to minimise assumptions in measurement

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Overall conclusions on capital measurement (2)

•Additional empirical information concerning capital is key to improve quality of estimates and to reduce the number of assumptions

studies on depreciation or asset lives

Investment in investment goods deflators

Capital flow matrices for the economy

•Significant movement and willingness to move forward in this domain