Improving capital measurement
using micro data
Abdul Azeez Erumban
24-02-2009
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 approach
Comparison: Earlier CBS estimates vs. new estimates
Comparison: Estimates for other countries vs. Estimates for the
Netherlands
• Conclusions
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)
3
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.)
4
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 recordsall 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
•
 ( x )
S ( x)  e
 u for x  0,
•
where =shape parameter, =scale parameter
= 1 => Exponential distribution
• And from the Weibull properties, the mean lifetime can be
derived as
1
1 
E ( x )    
1


  





8
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.
s tj ( x) 
K j ,t 1  D j ,t
K j ,t 1
• And the survival function (S) is calculated as the cumulative
distribution of survival rates, i.e.
x
S ( x )   s (i )
i 1
• This is exactly what the CBS followed before
• A crucial assumption (standard, but very strong) is Sj(x)=s(x)
9
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
K
 D1981,1990
1990
s1981
(10)  1981,1989
K1981,1989
•
Then the above approach assumes
•
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
•
1990
s1981
(10)  s (10) for all vintages
10
Alternative 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…!
60
Age
10
11
12
K81,90
50
40
30
D81,92
D81,93
20
Discard rate at Age 12=0.652
i.e. D81,93/K80,92
D81,91
10
0
60
Age 10
K80,90
Age 11
Age 12
K81,90
vintage
1981
1980
1979
D80,92
AVG
w.AVG
50
40
30
20
D80,91
10
0
Age 11
Age 12
Age
Discard rate
Disc.Rate
11
0.145
@age12
12
0.213
0.65
13
0.405
0.21 Discard rate at Age 12=0.213
D80,93
0.53 i.e. D80,92/K80,91
0.47
0.46
Age
12
13
14
K80,90
60
K81,90
K79,90
40
30
20
Discard rate
0.533
0.370
0.529
Discard rate at Age 12=0.533
D79,91/(K79,90)
D79,91
D79,92
10
0
Our approach
Age 13
70
50
Discard rate
0.100
0.489
0.652
D79,93
Age 12 Age 13 Age 14
11
Alternative Approach
• Average of more than one discard rate for each vintage (within
our data availability, 3 different vintages); more formally
s tj ( x) 
• where
s tj ( x) 
s tj ( x)  s tj11 ( x)  s tj22 ( x)
3
K j ,t 1  D j ,t
s tj11 ( x) 
s tj22 ( x) 
K j ,t 1
K j 1,t 1  D j 1,t  D j 1,t 1
K j 1,t 1  D j 1,t
K j 2,t 1  D j 2,t  D j 2,t 1  D j 2,t 2
K j 2,t 1  D j 2,t  D j 2,t 1
• 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
Data
• Estimate equation
regression
S ( x)  e
 ( x )
 u using a non-linear
• Dutch micro data
• Extensive use of Dutch firm level data on capital stock &
discards
• Lifetime estimates for three assetsMachinery, transport & computer
• 15 2-digit manufacturing industries
13
Results: Lifetime estimates for Dutch
manufacturing
Transport
1 year
3-year
Industry
discard
discard
Food, beverages & tobacco
8.1
6.3
Textile & leather pdts.
6.4
Wood & wood pdcts, medical & optical eqpt & Other mfg.
6.1
5.4
Paper and paper products
5.3
4.8
Publishing and printing
4.1
3.8
Petroleum products; cokes, and nuclear fuel
9.0
Basic chemicals and man-made fibers
Rubber and plastic products
Other non-metallic mineral products
Basic metals
7.8
Fabricated metal products
7.5
5.0
Machinery and equipment n.e.c.
7.6
5.2
Office machinery & computers, radio, TV & communication eqpt.
4.3
Electrical machinery n.e.c.
Transport equipment
8.3
Average
6.5
6.0
Computers
1 year
3-year
discard
discard
19.0
8.1
6.9
6.9
16.8
9.7
10.4
28.1
8.7
8.0
15.0
9.0
7.6
13.7
6.9
6.8
7.8
8.9
9.8
6.9
15.9
8.6
Machinery
1 year
3-year
discard
discard
31.2
27.9
28.4
22.8
34.7
24.9
22.5
22.6
13.6
30.0
24.7
34.7
29.5
35.8
28.7
33.0
28.5
29.2
24.5
19.6
13.6
16.7
41.0
39.9
23.7
29.4
25.5
Shorter lifetime in capital asset (?) lease effect and second-hand sale
Single-year survival rate vs. 3 year approach
14
Single year vs. 3 year discard approaches
Difference in life times (3 year –Single year)
Computer
Machinery
Transport Equipment
Average
Average
Average
Transport equipment
Transport equipment
Office mach,computers, TV etc.
MachineryNEC
MachineryNEC
Office mach,computers, TV etc.
Fabricated metal
pdt
Fabricated metal pdt
MachineryNEC
Non-metallic mineral
Publishing and
printing
Rubber & plastic
Fabricated metal pdt
Paper and paper
products
Chemicals
Chemicals
Publishing and printing
Wood & medical
&Other
Wood & medical &Other
Publishing and printing
Textile & leather pdts.
Food, beverages & tobacco
-20.0
Food, beverages &
tobacco
Food, beverages & tobacco
-15.0
-10.0
-5.0
0.0
-18.0
-13.0
-8.0
-3.0
2.0
-2.6
-2.1
-1.6
-1.1
-0.6
-0.1
15
Single year vs. 3-year approach
Comparing new estimates with earlier Dutch studies
New
Machinery
New
Computer
Meinen
Transport Equipment
Meinen
van Den Bergen et al
New
van Den Bergen et al
van Den Bergen et al
Average
Average
Transport eqpt
Transport eqpt
Average
Machinery&eqptNEC
Electrical Mach
Machinery&eqptNEC
Metal Pdts
Metal Pdts
Basic metal
Basic metal
Non-metallic min
Chemicals
Chemicals
Petroleum
Metal Pdts
Basic metal
Publish&Print
Publish&Print
Paper
Paper
Petroleum
Publish&Print
Paper
Textile & leather
Textile & leather
Textile & leather
Food, beverag&tobac
Food, beverag&tobac
Food, beverag&tobac
0
10
20
30
40
0
2
4
6
8
10
12
14
16
0
2
4
6
8
Methodological differences: Less discard information vs. more
discard information
Other differences: Treatment of data
16
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
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
Computer
Machinery
Transport
1-year discard
•
3-year discard
Tota # of industries in the
Sample
Better Fit
Three Discard Years
1
.8
.8
Survival Function
Survival Function
Single Discard Year
1
.6
.4
.6
.4
.2
.2
0
5
10
Age
15
20
0
5
10
Age
15
20
___ Actual _ _ Estimated
•
And More realistic Estimates
17
Average life time in Manufacturing,
comparing with other countries
NLD (New)
NLD (Bergen etal)
NLD (Meinen)
Japan (Nomura)
US (BLS)
Computers
Machinery
Canada (Baldwin et al)
Transport
0
5
10
15
20
25
30
35
Usual assumption of a common lifetime across countries (e.g. Caselli, 2005) doesn’t seem
to be true
18
Does it matter which lifetime one uses?
Capital stock in Netherlands under various lifetime Assumptions
Computer
Transport Equipment
3000
New Estimates
200
180
2500
160
140
2000
120
1500
100
80
1000
60
40
500
20
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
0
1970
0
Machinery
350
Canadian Est
US Est
Japan Est
NLD (Meinen Est)
NLD (Bergen etal Est)
NLD (New Est)
300
250
200
150
100
50
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
0
Source: EU-KLEMS
19
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.
20
Are lifetimes endogenous?
Determinants of Discard: Marginal coefficients from probit regression
Dependent variable = 1, if discard rate>0, and 0 otherwise
Variable
YG
WG
AGE
PCSIN
TURN
HTEK
Pseudo R2
Long likelihood
Chi2
Machinery
-0.221
(0.136)
-0.52
(0.347)
0.007 ***
(0.003)
0.079 **
(0.039)
0.008
(0.071)
0.002
(0.036)
0.06
-129.7
17.3 ***
Computer
Transport Eqpt
-0.024
-0.094
(0.144)
(0.252)
-0.008
-0.056
(0.533)
(0.637)
0.049 ***
0.064 ***
(0.011)
(0.012)
-0.067
-0.043
(0.059)
(0.071)
0.142
0.072
(0.122)
(0.144)
0.116 *
0.056
(0.059)
(0.069)
0.06
-232.2
30.0 ***
0.11
-129.1
31.8 ***
21
Differences in discard probabilities
Innovative firms have higher discard probabilities for machinery,
High-tech firms are more prone to discard computers at average age
Machinery
Computer
0.20
Avg Age:15.1
0.20
0.15
0.15
0.10
0.05
0.10
0.00
-0.05
0.05
-0.10
15
14
12
10
9
7
5
4
2
35
31
27
24
20
13
10
6
3
17
P c s - No n_P c s
1
0.00
-0.15
Hite k- No n_Hite k
22