Improving capital measurement using micro data

Abdul Azeez Erumban24-02-2009

CBS, the Hague

Structure of the presentation

• Issues in the Measurement of aggregate capital• Standard practice and its problems• Measurement of depreciation and problems• Asset lifetime estimation

• Estimation of lifetime using Dutch micro data• Standard methodology• Our alternative approach• Data• Results

Comparison: standard approach vs. new approachComparison: Earlier CBS estimates vs. new estimatesComparison: Estimates for other countries vs.

Estimates for the Netherlands

• Conclusions

3

Issues in the measurement of Aggregate capital

Co-existence of multiple vintages

=Different vintages have different marginal productivities

=Each generation of capital assets will embody different levels of

technology, and are therefore not homogenous

And

Heterogeneity of Capital Assets

=Aggregating computers, machines, trucks and many more!

=Cambridge Controversy (aggregating money value vs. impossibility of

aggregation)

4

Standard Practice & its problems

• Perpetual Inventory Method• Aggregate money value of different assets (value of

computers + value of trucks)• Problems• Aggregation of vintages:• Use efficiency weights (under the assumption

that newer vintage embody newer technology). Takes account of differences in vintages to some

extent, given that depreciation and asset prices are properly measured

• Aggregation across assets:• Aggregate money value of different assets.

Takes no account of asset heterogeneity• Measures of Capital services (Capital assets,

weighted by their marginal productivities.)

Depreciation and lifetimes: Major ingredients in capital measurement

Whether it is aggregation across vintages, or across assets, an important factor is

loss of value due to ageing

Measurement of depreciation

• But• Scarce empirical evidence on depreciation• Common Depreciation across countries & over time

=Same age-price profile across countries & over time

• Empirical Measurement of Depreciation-two prominent methods

• Used -asset price model (Hulten and Wykoff 1981)

depreciation can be isolated by comparing prices of same asset at various ages

• Asset lifetime based

Declining balance rate (straight line, double declining, sum of year digit) Hulten and Wykoff, 1981; Fraumeni, 1997

6

Problems in Empirical Measurement of Depreciation

• Used-price approach• Lack of data

• Lifetime based approach• Availability of reliable estimates of life time

Rely on expert advice, tax information, company records- all have potential bias

An important deviation - Estimation of asset lifetime from actual data

Meinen et al 1998; Meinen, 1998; van den Bergen et al, 2005; Nomura, 2005)

• This presentation • Lifetime estimation using actual data for Dutch manufacturing (improving

on earlier Dutch studies)

7

Estimating lifetimes using Dutch unit level data Methodology: The Weibull function

• Lifetime estimation using survival function (the probability that the asset survives until a given age)• Survival function with a longer tail-The Weibull• Weibull is a flexible distribution

• According to Weibull, the survival function S at a given age x can be written as

• • for x 0,

where =shape parameter, =scale parameter

= 1 => Exponential distribution

• And from the Weibull properties, the mean lifetime can be derived as

8

uexS x )()(

1

11

)(xE

Remaining question: Measuring survival function from actual data

• Survival function is the cumulative distribution of survival rate (s), which is the rate at which an asset scurvies until any given age x, i.e.

• And the survival function (S) is calculated as the cumulative distribution of survival rates, i.e.

• This is exactly what the CBS followed before

• A crucial assumption (standard, but very strong) is Sj(x)=s(x)

9

1,

,1,)(

tj

tjtjtj K

DKxs

x

i

isxS1

)()(

Why this assumption

• No information on K& D in ‘all’ vintages over a ‘long’ span of time• Therefore, for all vintages the survival rate at any given age is assumed to be the same!

• An Example• Suppose there exists 3 vintages, 1979, 1980 & 1981, of an asset in year 1990. • The survival rate of these 3 vintages at age 10 can be calculated if we have

information about their discard in 1989, 1990 & 1991. In practice this may not be available

• Suppose, we have this information since 1991, then we can calculate the survival rate of only vintage 1981 at age 10, as

• Then the above approach assumes for all vintages

• But, the discard pattern could be different for each vintage, threatening the assumption sj(x)=s(x).

• Is it possible to account for vintage heterogeneity completely?

Not with the limited data available

10

1989,1981

1990,19811989,198119901981 )10(

K

DKs

)10()10(19901981 ss

11

Alternative approach:

K81,90

D81,91

D81,92D81,93

0

10

20

30

40

50

60

Age 10 Age 11 Age 12

Discard rate at Age 12=0.652i.e. D81,93/K80,92

Age Discard rate 10 0.10011 0.48912 0.652

K80,90K81,90

D80,91 D80,92D80,93

0

10

20

30

40

50

60

Age 11 Age 12 Age 13

Discard rate at Age 12=0.213i.e. D80,92/K80,91

Age Discard rate 11 0.14512 0.21313 0.405

K79,90

K80,90

K81,90

D79,91

D79,92 D79,93

0

10

20

30

40

50

60

70

Age 12 Age 13 Age 14

Discard rate at Age 12=0.533D79,91/(K79,90)

Age Discard rate 12 0.53313 0.37014 0.529

Disc.Ratevintage @age12

1981 0.65 1980 0.21 1979 0.53 AVG 0.47

w.AVG 0.46 Our approach

Suppose we have information on discards in more years, so that we can calculate discard rate for these years more for all these vintages…!

Alternative Approach

• Average of more than one discard rate for each vintage (within our data availability, 3 different vintages); more formally

• where

• Assumes absence of second hand investment

• Advantages: the assumption sj(x)=s(x) becomes more reliable as s(x) now carries information on more than vintage j, and helps make generalization more accurate

12

1,2,21,2

2,21,2,21,222

,11,1

1,1,11,111

1,

,1,

)(

)(

)(

tjtjtj

tjtjtjtjtj

tjtj

tjtjtjtj

tj

tjtjtj

DDK

DDDKxs

DK

DDKxs

K

DKxs

3

)()()()(

22

11 xsxsxs

xstj

tj

tjt

j

13

Data

• Estimate equation using a non-linear regression

• Dutch micro data• Extensive use of Dutch firm level data on capital stock &

discards

• Lifetime estimates for three assets-

Machinery, transport & computer

• 15 2-digit manufacturing industries

uexS x )()(

14

Results: Lifetime estimates for Dutch manufacturing

1 year 3-year 1 year 3-year 1 year 3-yearIndustry discard discard discard discard discard discardFood, beverages & tobacco 8.1 6.3 19.0 8.1 31.2 27.9Textile & leather pdts. - 6.4 - - 28.4 22.8Wood & wood pdcts, medical & optical eqpt & Other mfg. 6.1 5.4 - 6.9 34.7 24.9Paper and paper products 5.3 4.8 - 6.9 - 22.5Publishing and printing 4.1 3.8 16.8 9.7 22.6 13.6Petroleum products; cokes, and nuclear fuel - 9.0 - 10.4 - -Basic chemicals and man-made fibers - - 28.1 8.7 30.0 24.7Rubber and plastic products - - - 34.7 29.5Other non-metallic mineral products - - - 8.0 35.8 28.7Basic metals - 7.8 - 15.0 - 33.0Fabricated metal products 7.5 5.0 9.0 7.6 28.5 29.2Machinery and equipment n.e.c. 7.6 5.2 13.7 6.9 24.5 19.6Office machinery & computers, radio, TV & communication eqpt. - 4.3 6.8 7.8 13.6 16.7Electrical machinery n.e.c. - - - 8.9 - 41.0Transport equipment - 8.3 9.8 6.9 39.9 23.7

Average 6.5 6.0 15.9 8.6 29.4 25.5

Transport Computers Machinery

Shorter lifetime in capital asset (?) lease effect and second-hand

sale Single-year survival rate vs. 3 year approach

15

Single year vs. 3 year discard approachesDifference in life times (3 year –Single year)

Computer

-20.0 -15.0 -10.0 -5.0 0.0

Food, beverages & tobacco

Publishing and printing

Chemicals

Fabricated metal pdt

MachineryNEC

Office mach,computers, TV etc.

Transport equipment

Average

Machinery

-18.0 -13.0 -8.0 -3.0 2.0

Food, beverages & tobacco

Textile & leather pdts.

Wood & medical &Other

Publishing and printing

Chemicals

Rubber & plastic

Non-metallic mineral

Fabricated metal pdt

MachineryNEC

Office mach,computers, TV etc.

Transport equipment

Average

Transport Equipment

-2.6 -2.1 -1.6 -1.1 -0.6 -0.1

Food, beverages &tobacco

Wood & medical&Other

Paper and paperproducts

Publishing andprinting

Fabricated metalpdt

MachineryNEC

Average

16

Single year vs. 3-year approachComparing new estimates with earlier Dutch studies

Machinery

0 10 20 30 40

Food, beverag&tobac

Textile & leather

Paper

Publish&Print

Chemicals

Non-metallic min

Basic metal

Metal Pdts

Electrical Mach

Transport eqpt

Average

New

Meinen

van Den Bergen et al

Computer

0 2 4 6 8 10 12 14 16

Food, beverag&tobac

Textile & leather

Paper

Publish&Print

Petroleum

Chemicals

Basic metal

Metal Pdts

Machinery&eqptNEC

Transport eqpt

Average

New

Meinen

van Den Bergen et al

Transport Equipment

0 2 4 6 8

Food, beverag&tobac

Textile & leather

Paper

Publish&Print

Petroleum

Basic metal

Metal Pdts

Machinery&eqptNEC

Average

New

van Den Bergen et al

Methodological differences: Less discard information vs. more discard informationOther differences: Treatment of data

17

Obviously there are differences: But are the new results better?

• More industries (with reliable estimates)Number of industries for which asset life could be computed

0123456789

10111213141516

1-year discard 3-year discard Tota # of industries in theSample

Computer

Machinery

Transport

.2

.4

.6

.8

1

Surv

ival

Fun

ctio

n

0 5 10 15 20Age

Single Discard Year

.2

.4

.6

.8

1

Surv

ival

Fun

ctio

n

0 5 10 15 20Age

Three Discard Years

___ Actual _ _ Estimated

• Better Fit

• And More realistic Estimates

18

Average life time in Manufacturing, comparing with other countries

0 5 10 15 20 25 30 35

Canada (Baldwin et al)

US (BLS)

Japan (Nomura)

NLD (Meinen)

NLD (Bergen etal)

NLD (New)

Computers

Machinery

Transport

Usual assumption of a common lifetime across countries (e.g. Caselli, 2005) doesn’t seem

to be true

19

Does it matter which lifetime one uses?Capital stock in Netherlands under various lifetime Assumptions

Computer

0

500

1000

1500

2000

2500

3000

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

Transport Equipment

0

20

40

60

80

100

120

140

160

180

200

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

Machinery

0

50

100

150

200

250

300

350

19

70

19

72

19

74

19

76

19

78

19

80

19

82

19

84

19

86

19

88

19

90

19

92

19

94

19

96

19

98

20

00

20

02

20

04

Canadian Est US Est

Japan Est NLD (Meinen Est)

NLD (Bergen etal Est) NLD (New Est)

New Estimates

Source: EU-KLEMS

20

Conclusions

• Choice of lifetime does matter for the estimation of capital stock

• Using survival information of more vintages in the lifetime calculation • improves the fit of the model• improves the estimates of lifetime• helps estimate lifetime for more industries

• Current adjustments followed by the CBS in order to account for second-hand and lease effect may be followed.

21

Are lifetimes endogenous?

VariableYG -0.221 -0.024 -0.094

(0.136) (0.144) (0.252)WG -0.52 -0.008 -0.056

(0.347) (0.533) (0.637)AGE 0.007 *** 0.049 *** 0.064 ***

(0.003) (0.011) (0.012)PCSIN 0.079 ** -0.067 -0.043

(0.039) (0.059) (0.071)TURN 0.008 0.142 0.072

(0.071) (0.122) (0.144)HTEK 0.002 0.116 * 0.056

(0.036) (0.059) (0.069)

Pseudo R2 0.06 0.06 0.11Long likelihood -129.7 -232.2 -129.1

Chi2 17.3 *** 30.0 *** 31.8 ***

Transport EqptComputerMachinery

Determinants of Discard: Marginal coefficients from probit regression

Dependent variable = 1, if discard rate>0, and 0 otherwise

22

Differences in discard probabilities

Machinery

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

3 6 10 13 17 20 24 27 31 35

P cs - Non_P cs

Avg Age:15.1

Computer

0.00

0.05

0.10

0.15

0.20

1 2 4 5 7 9 10 12 14 15

Hitek- Non_Hitek

Innovative firms have higher discard probabilities for machinery, High-tech firms are more prone to discard computers at average age