improving capital measurement using micro data abdul azeez erumban 24-02-2009 cbs, the hague
TRANSCRIPT
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
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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