Final Report
Deriving Measures of Plant-level Capital
Stock in UK Manufacturing, 1973-2001a
Submitted to the DTI by
Professor Richard Harris
(Independent Economic Consultancy Services Limited)
a
This work contains statistical data from ONS which is Crown copyright and reproduced with the
permission of the controller of HMSO and Queen's Printer for Scotland. The use of the ONS statistical
data in this work does not imply the endorsement of the ONS in relation to the interpretation or analysis
of the statistical data.
i
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ii
Executive Summary
E1.
In order to estimate total factor productivity (TFP) (the preferred measure of
productivity vis-à-vis labour productivity) and other supply-side analysis based
on the use of production functions, reliable measures of capital stock a are a
necessary prerequisite.
E2.
Currently, the capital stock series used by the Business Data Linking (BDL)
section at the ONS measures capital stock using what is known as Reporting
Unit (RU) data, and various methods based on the perpetual inventory approach.
The series were computed by Martin (2003). The use of RU data, and the
assumptions used to derive capital stock series need to be carefully analysed, and
the drawbacks and limitations considered. This is the major purpose of this
study, to consider such issues.
E3.
An accurate measure of the capital stock that is intended for use in estimating
production relations should represent the total amount of capital services
available for producing output. This means taking into account efficiency losses
due to deterioration (including obsolescence). This requires the use of an
appropriate rate of deterioration of capital goods that reduces their efficiency
through time as they are used to provide capital services and as they age.
E4.
It was argued by Denison (1972) that the expected time pattern of deterioration
of a capital good is expected to exhibit a slow rate of deterioration at the
beginning, becoming more rapid as the expected length of life of the good
approaches. Thus gross and net (of straight-line deterioration) plant and
machinery capital stock figures are calculated in this study using the perpetual
inventory method and the expected length of life of capital goods adopted by the
ONS since 1983. Once gross and net stock figures have been calculated, the
i
approach used by Denison (1972) of weighting these in the ratio of three to one
is adopted to obtain net stock figures which incorporate the desired pattern of
deterioration, at first slow, followed by more rapid deterioration.
E5.
Other authors have advocated the geometric depreciation pattern as an
alternative approach to the Denison approach method used in this study.
However, this implies a far higher rate of deterioration than is likely in economic
terms, involving a much higher rate of capital-embodied technical progress than
those typically found in the empirical literature.
E6.
Thus, the Denison approach with ONS asset lives was used, with the perpetual
inventory approach, to produce plant and machinery capital stock estimates
using gross investment data for plant and machinery taken from the Annual
Respondents Database (the ARD).
E7.
The technical details of how this was done are presented, along with the
statistical routines required to estimate UK manufacturing plant and machinery
capitals stocks for each plant in operation between 1970 and 2001.
E8.
The list of issues that were then considered include the following:
1. Whether plant (LU) or establishment (RU) level data should be used
2. Implementation of the Perpetual Inventory method and specifically:
i. What depreciation series should be used?
ii. What start values are needed (i.e. the first year of gross investment data
used) in order to derive an accurate series
iii. The availability of plant level gross investment data (acquisitions net of
disposals)
iv. How to take account of plant closures
E9.
These issues were considered mainly by contrasting the preferred approach used
in this report with the approach used by Martin (2003). Various evidence is
presented to show that the methods used here to calculate the plant and
ii
machinery capital stock have advantages over those employed by Martin since
they:
•
are based on LU data and thus avoid the problem that LU’s can be reallocated
between RU’s for accounting purposes by firms, or when plants are bought
and sold, or when they are opened and closed;
•
the Denison approach to calculating economic deterioration seems more
realistic when compared to using a geometric depreciation series, especially if
the purpose of calculating capital stock estimates is to use these when
estimating a production function or when estimating total factor productivity;
•
post-1969 data at the plant level is used here, while Martin uses post-1979
data, and thus the influence of benchmark data is lower in the present
estimates, especially from 1980 onwards. The benchmark series used here
were also more disaggregated, and thus likely to have been more accurately
distributed to those plants that were open in 1970 (and thus required pre-1970
capital stocks to be allocated to them), especially as Martin uses the average
value of intermediate inputs of RU’s based on their entire operating life to
allocate the benchmark data (rather than investment and employment shares
linked to the benchmark period);
•
investment data is interpolated (when necessary) using a population estimate
of investment in a 5-digit industry in any particular year (after subtracting
investment already identified to belong to those plants that were selected for
inclusion in the ABI), while Martin simply interpolates linearly between
observed investment levels for each RU;
•
the capital stock produced here takes account of plant closures, while Martin
does not.
iii
E10.
However, ‘spreading back’ investment data from selected RU’s based on LU
employment shares does introduce an unknown level of bias into the capital
stock estimates produced at the plant level, because of inaccuracies in plant level
employment estimates for the smallest firms. Improvements in the accuracy of
measuring the capital stock using the perpetual inventory approach would be
achieved if the ONS were to consider the following changes:
•
collecting information on capital expenditure at the local unit level (in
addition to employment data) when conducting the ABI;
•
increasing the frequency with which LU employment estimates are updated
for smaller firms. The National Assembly for Wales has for some years
funded a top-up to the ARI for the region and Scotland has recently agreed
the same with the ONS.
•
obtaining more up-to-date estimates of economic depreciation of assets by
industry, in order to provide better estimates of the rate of deterioration and
obsolescence.
iv
Table of Contents
Executive Summary
i
Chapter 1:
Introduction
1
Chapter 2:
Measuring the Capital Stock
7
Chapter 3:
Plant Level Estimates of the Capital Stock
17
Chapter 4:
Issues in Measuring the Capital Stock
25
References
39
Statistical Appendix
42
v
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1
1. Introduction
1.1
Given the availability of the panel micro-level database on enterprises in UK
manufacturing comprising the Annual Respondents Database (the ARD),
various analyses relating broadly to issues such as productivity and growth can
now be undertaken. This is directly relevant to the building up of the evidence
base needed by government in this area in order to achieve its goal of boosting
UK productivity levels and overall GDP.
1.2
With such micro panel data it is possible to measure such variables as labour
productivity, and efficiency, and consider related issues such as entry and exit,
and the impacts of changes in ownership. All of these topics have been
previously looked at (sometimes for all UK manufacturing but also separately
for different sectors) by Harris and others.1
1.3
However, in order to undertake studies related to total factor productivity (TFP)
(a preferred measure of productivity vis-à-vis labour productivity – see below)
and other supply-side analysis based on the use of production functions, reliable
measures of capital stock are a necessary prerequisite. How the capital stock is
measured in terms of the use of the perpetual inventory method, and the data
needed to undertake such calculations, results in a number of significant and
important issues that have to be considered.
1.4
Currently, the capital stock series used by the Business Data Linking (BDL)
section at the ONS measures capital stock using what is known as Reporting
1
For a detailed description of the ARD see Oulton (1997), Griffith (1999), and Harris (2002). Analysis
using the database covers a range of areas; cf. Disney, Haskel and Heden (2003a,b), Harris and
Drinkwater (2000), Harris (2001), Harris and Collins (2002), Harris and Robinson (2002, 2003,
2004a,b), and Harris and Hassaszadeh (2002). The counterpart to the ARD in the US is the
Longitudinal Research Database – or LRD - for US manufacturing provided through the US Bureau of
Census. This has been analysed fairly extensively in recent years, covering various areas linked to
productivity (e.g., Bahk and Gort, 1993; and Bartelsman and Dhrymes, 1998); the impact of ownership
change on productivity (McGuckin and Nguyen, 2001); capital efficiency (e.g., Doms, 1996) and entry
and exit (e.g., Doms, et. al, 1995; Olley and Pakes, 1996; Kovenock and Phillips, 1997)
1
Unit (RU) data, and various methods based on the perpetual inventory approach
(see Martin, 2003).2 The use of RU data, and the assumptions used to derive
capital stock series need to be carefully analysed, and the drawbacks and
limitations considered. Evidence is presented here (based on Harris and
Drinkwater, 20003) showing that Local Unit (LU) data should be preferred, as
well as different assumptions regarding lengths-of-life of assets, how they
depreciate, how data is weighted, and historical information on gross investment
at the plant (i.e. LU) level.
1.5
Therefore this project looks at the different methods used to calculate the capital
stock (concentrating on the BDL approach and that used by Harris and
Drinkwater, op. cit.), and the consequences of using these approaches. In
addition, an up-to-date series of plant level (plant and machinery) capital stock
has been compiled for the ONS for inclusion in the BDL database, along with
the statistical algorithms that can be used to update the series when new ABI
data becomes available to the ARD. Those proposing to calculate their own
capital stock measures or to update the data produced from this report are
advised to consult existing documentation on the ARD available in the BDL at
the ONS.
2
Others have calculated their own estimates of capital stock using similar approaches to Martin (e.g.
based on RU data, a benchmark series often starting in 1980 or later, and an assumption that
depreciation has an exponential distribution). Examples include Griffith (1999) and Disney et. al.
(2003a, 2003b). Given that their approaches are very similar and/or less detailed than Martin’s, only
the latter is considered in any detail here.
3
This current study uses the same approach as that employed by Harris and Drinkwater, but updates
the series to cover 1994-2001. It also differs from the previous study in that it compares the approach
used to that employed by Martin (and others – see footnote 2).
2
Measuring productivity – the preferred approach
1.6
As stated in par. 1.3, capital stock measures are necessary in order to obtain
estimates of total factor productivity rather than, say, labour productivity. This
sub-section sets out why measures of TFP are preferred vis-à-vis labour
productivity. It is useful to start with a simple Cobb-Douglas4 production
function:
y = α 0 +α E e +α M m +α K k +αT t
(1.1)
where y refers to the logarithm of real gross output; e refers to the logarithm of
employment (with αE measuring the elasticity of output with respect to
employment – i.e.∂y/∂e); m refers to the logarithm of real intermediate inputs
(with corresponding elasticity of output, αM); and k refers to the logarithm of
capital stock (with corresponding elasticity of output, αK). Totally
differentiating this function with respect to time to obtain rates of change (and
expressing terms such as dy / dt as y& ), a measure of total factor productivity
growth can be obtained as:
TF&P = α T = y& − α E e& − α M m& − α K k&
(1.2)
Note, this measures the increase in output that is not attributable to increases in
e, m, or k; rather it measures the contribution to growth of all influences other
than the factors of production, capturing such determinants as technological
progress and/or increases in efficiency (note, inefficiency also captures any
under-utilising of factor inputs). Thus, if any factor input increases, then via
4
Other forms of the production function (e.g. CES or translog), or indeed a general function, could be
used, and the points to be illustrated will not alter in any significant way.
3
(1.1) output increases by a value depending on the elasticity of output with
respect to the factor increasing, and the impact on TFP in (1.2) is zero.
1.7
In terms of labour productivity growth, a relationship can be obtained by
subtracting the logarithm of employment from both sides of (1.1) and
expressing the result in terms of rates of change with respect to time:
y& − e& = (α E − 1)e& + α M m& + α K k& + TF&P
(1.3)
This shows that increases in labour productivity ( y& − e&) are negatively related to
increases in employment [since (αE−1)<0], and positively related to increases in
intermediate inputs, capital stock and TFP. Indeed, if over time there is an
increase in capital deepening (cet. par. the K/E ratio rises as capital is
substituted for labour perhaps due to greater automation) or outsourcing (cet.
par the M/E ratio rises as less is made internally and more semi-finished and
finished products, and services, are bought from suppliers), then labour
productivity will increase as relatively less labour is used to produce output.5
Thus, increases in labour productivity do not depend on just technological
progress and/or gains in efficiency, since what happens with the other factors of
production is also important.
1.8
Figure 1.1 provides some insights with regard to what has been happening in
UK manufacturing in recent decades;6 labour productivity (based on the gross
output measure) rose fairly constantly throughout the 1973-1998 period;
however, this was likely to have been at least in part due to capital deepening
5
If a value-added production function were used instead of a gross output function (with VA=Y−M),
and constant returns-to-scale imposed with perfect competition in factor and output markets, then (1.3)
simplifies to:
y& − e& = (1 − α E )(k& − e&) + TF&P
(1.3a)
which shows that labour productivity growth depends positively on capital deepening and TFP growth.
6
Note the data in Figure 1.1 are based on (population weighted) totals for UK manufacturing, not
averages of plant or firm level data.
4
(increases in K/E), particularly in the 1970’s and early 1980’s, and outsourcing
(increases in M/E), which seems to have increased at a more significant pace
from the mid-1980’s onwards.
Figure 1.1: Real outputs and inputs in UK manufacturing, 1973-1998
3.30
2.80
gross output per employee
capital per employee
intermediate inputs per employee
M/E
1973=1
2.30
Y/E
1.80
K/E
1.30
0.80
1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
Source: based on own calculations using the ARD
1.9
In conclusion, the major weakness of using a measure of labour productivity
growth that is primarily intended to capture the impact of improvements in
technology and/or efficiency is that it is also significantly influenced by
substitution between the factors of production. In contrast, TFP measures
capture the ‘pure’ impact of shifts in the production possibility curve (due to
technical change) or movements towards it (due to improvements in efficiency).
1.10 It can also be seen that there is an issue of which labour productivity measure
should be used (i.e., based on gross output or gross value-added).7 The answer
depends on whether the production function is separable or not (i.e., whether
intermediate inputs be separated from K and E in the formulation of the
7
Of course, this same question arises when calculating TFP – should a gross output or value added
production function be used?
5
function) – and the empirical evidence strongly suggests not – while the
literature on outsourcing suggests that the gross output approach captures more
exactly measures of efficiency while value-added functions are more closely
related to profitability (Gorzig and Stephen, 2002).
6
2. Measuring the Capital Stock
2.1
An accurate measure of the capital stock that is intended for use in estimating
production relations should represent the total amount of capital services
available for producing output. This means taking into account efficiency losses
due to deterioration (including obsolescence). However, there is a second
'economic accounts' measure of the capital stock that takes into account capital
that is 'used up' in production; that is, depreciation. Triplett (1996) provides a
comprehensive account of the differences between these two concepts of the
wealth and productive capital stock, which has been the source of much debate
in the literature. Essentially, Triplett (op. cit., p. 100) shows that while
deterioration and capital used up in production (depreciation) have similarities,
they are not equal. The main difference between them is that deterioration
measures the current services lost from using the capital stock in any one
period, and thus the loss in potential for next period's production; depreciation
measures (in value terms) the lifetime deterioration in the capital stock that
reduces the long run income flow from that stock. That is, deterioration refers:
"… to the loss of capital services in the following period that arise from the use
of the capital good in any period, t + i" while depreciation is "… the diminution
of the total stock of services embodied in a capital good because it has been
used in production for one period" (p. 100, italics from original). Triplett notes
that:
Capital used up is not the appropriate concept for production
analysis… deterioration is not the appropriate definition for the
purposes of economic accounts… These are not mere semantic
7
differences, or issues that arise from differences in the use of
language; they are conceptual distinctions that arise because the
production function use of capital and the economic accounts use
are different purposes (p. 103)
2.2
Here we concentrate on a 'production analysis' concept of the capital stock that
takes account of deterioration. This requires the use of an appropriate rate of
deterioration of capital goods that reduces their efficiency through time as they
are used to provide capital services and as they age. Essentially, we define the
net stock of capital as8:
t
K(t) =
E (υ )
∫ E (t ) . D(t − υ ). I (υ ). dυ
(2.1)
−∞
where I(ν) is constant price gross investment of year ν, weighted by both
physical decay D between time ν and t,
and by accumulated embodied
technical progress (obsolescence) E between time ν and t. Therefore, vintages
installed in year ν provide less capital services as the age of I(ν), i.e., t − ν,
becomes sufficiently large due to (i) wear and tear, resulting in D → 0,9 and (ii)
accumulated technical progress means that the newest vintages in time t embody
more capital services than do older fixed assets, thus over time E(ν)/E(t) → 0.
Physical decay and obsolescence combine to produce deterioration. Therefore,
information is required on the rate of deterioration that reduces the capital
services available from any vintage and eventually removes the ageing asset
from the remaining capital stock.
8
A simpler way of thinking of the capital stock is based on the perpetual inventory formula:
K t = (1 − δ ) K t −1 + I t where K is the capital stock, δ is economic depreciation, and I is investment.
D(t − ν) can be thought of as an index of decay equal to 1 when t = ν, but becoming equal to 0 when t
− ν becomes sufficiently large.
9
8
2.3
Ideally, we require empirical estimates of the level of known deterioration to
enable us to calculate both the rate (or pattern) of deterioration and the value of
the actual length of life of a capital good. Unfortunately, this information is not
available and therefore some other technique must be used to estimate the
expected life of a capital good, which provides an indication of the period over
which deterioration must take place. The perpetual inventory method is
typically adopted for this purpose, with the rate of deterioration assumed to
follow some simple pattern such as straight-line or exponential decline. If rates
of physical decay and embodied technical progress are assumed to be stable
over long periods of time, then the expected length of life will remain the same
and using expected length of life is an accurate indication of how long
deteriorating capital goods remain in a net stock measure. However, these
assumptions appear more appropriate for physical decay, and not technical
progress, and this is presumably the major reason why the ONS adopt the
procedure of shortening asset lives every five years for plant and machinery
expenditure undertaken since 1950.10 The length of life assumptions do not take
account of premature scrapping, which is mainly caused by obsolescence. This
occurs when a capital good ceases to earn a positive quasi-rent, often caused by
a lack of demand for the firm’s product or a sharp change in relative factor
prices, and is scrapped in advance of the period when repairs to combat physical
decay become too great.
2.4
As to the discussion over the appropriate rate of deterioration, it was argued by
Denison (1972) that the expected time pattern of deterioration of a capital good
10
Asset lives decline depending on which 5-year period the asset was purchased between 1950 and
1970 (assets bought since 1970 are assumed to have the same lengths of lives as 1970 assets). For
example, the average life assumption for all manufacturing plant and machinery declined from around
29 years in 1949 to 22 years by 1970.
9
is expected to exhibit a slow rate of deterioration at the beginning, becoming
more rapid as the expected length of life of the good approaches.11 The reasons
for this are that firms typically undertake maintenance and repair in order to
maintain the same performance level as when the machine was new (Jefferson,
1971), with this activity increasing with the age of the capital goods, while the
effect of obsolescence on the rate of deterioration is probably small (Barna,
1962).12 This assumption is more applicable when the rate of capital-embodied
technical progress is low over time since equation (1) shows that obsolescence
not only affects the length of life of an asset but it also makes older vintages less
productive than newer ones. Thus lowering the length of life of assets, on the
assumption that technical change has increased in more recent years is
presumed to reduce any impact of obsolescence on the rate of deterioration.
2.5
Given the above discussion, gross and net (of straight-line deterioration) plant
and machinery capital stock figures are calculated using the perpetual inventory
method and the expected length of life of capital goods adopted by the ONS
since 1983.13 As set out in Hulten and Wykoff (1996 p.15), if ϕs represents the
efficiency (or remaining capital services) of an s-year-old asset as a function of
the productive capacity of a newly produced asset, then the deterioration pattern
for the gross stock measure is:
ϕ0 = ϕ1 = …. = ϕT-1 = 1, ϕT+t = 0
t = 0, 1 ,2 ……
(2.2)
11
Note, Denison referred to depreciation rather than deterioration, but failed to distinguish between the
production analysis use of capital stock and the economic accounts measure.
12
Barna (1962) is concerned with capital stocks in the 1950s, when there was a large amount of heavy
industry.
13
Note, there are up to 6 different classes of assets covering plant and machinery capital goods
purchased by each of the 18 industries, each with a different average length of life (which also changes
over time although post-1970 lives are used throughout in this study). Table A2.1 in the appendix
presents the lengths of life assumptions used since 1970. Gross investment figures by industry were
available for the 1948 to 1969 period and individual plant level estimates were available from 1970;
see the next chapter for details, including how the two datasets were merged.
10
That is, assets retain full efficiency until retirement at time T, the service life of
the asset. If straight-line deterioration is adopted then the pattern for the net
stock is:
ϕ0=1, ϕ1=1-(1/T), ϕ2=1-(2/T), … ϕT-1= 1-[(T-1)/T], ϕT+τ = 0
τ = 0, 1 ,2
2.6
(2.3)
For completeness, choosing the exponential distribution, deterioration (and in
this instance depreciation) would occur at a constant rate δ=(ϕt-1-ϕt)/ϕt-1 so that:
ϕ0=1, ϕ1=(1-δ), ϕ2=(1-δ)2, …. ϕt=(1-δ)t
(2.4)
Note, the exponential distribution is not (directly) determined by the service life
of the asset, and only asymptotically declines to zero. Thus under the
exponential distribution the efficiency function and the age-price function are
identical and deterioration and depreciation are equal.
2.7
Once gross and net stock figures have been calculated, the approach used by
Denison (1972) of weighting these in the ratio of three to one is adopted to
obtain net stock figures K(t), which incorporate the desired pattern of
deterioration, at first slow, followed by more rapid deterioration.14
2.8
Other authors have advocated different deterioration and/or depreciation
patterns or an alternative approach to the perpetual inventory method used in
this study.15 For instance, Oulton and O'Mahony (1994) use an exponential rate
of depreciation (which is equivalent to exponential deterioration) together with
14
It is possible to use weighting ratios other than the preferred 3:1 ratio. However, other ratios would
move the distribution closer to the distribution for the gross stock or closer to straight-line
deterioration, while it is argued here that the Denison approach is more appropriate. Figure 2.1
illustrates this point.
15
Those interested in an economic accounts measure of capital stock need to measure depreciation. As
pointed out in the text, only when the exponential distribution is used do depreciation and deterioration
coincide. Thus using the exponential distribution results in an internally consistent measure of capital
stock in that the two concepts are then the same (see Jorgenson, 1996, who gives this argument in
favour of using the exponential distribution).
11
the ONS length of life assumptions.16 They justify the use of the exponential
distribution with reference to Hulten and Wykoff (1981), in which the prices of
second-hand assets were found to decline geometrically with an asset’s age in
the US.17 Oulton and O'Mahony (1994) nevertheless argue that the rise in
efficiency of new assets (or equivalently the increased obsolescence of older
ones) leads to an overall geometrically declining deterioration pattern even
though they accept that for plant and machinery, physical deterioration is
unlikely to follow such a pattern (the ‘light bulb’ or one-hoss shay pattern being
more likely). Advocates of the exponential distribution usually favour its use for
reasons other than just to take account of obsolescence; e.g., because its is
consistent with the economic accounts definition of the capital stock; it is
implied by second-hand US capital price data; and it also incorporates various
factors that can lead to a wide-band distribution of retirements in practice (e.g.,
the loss of assets due to fires, explosions, pre-mature scrapping). Hulten and
Wykoff (1996) state:
…it may well be true that every single asset in a group of 1000
assets depreciates as a one-hoss shay, but that the group as a whole
experiences
near-geometric
depreciation.
This
fallacy
of
composition arises from the fact that different assets in the group are
retired at different dates; some may last only a year or two, others
ten to fifteen years. When the experience of short-lived assets is
16
The approach taken by Martin (2003) when calculating the BDL capital stock series was also to use
the exponential rate, and an average rate of 0.06 for plant and machinery (see Chapter 4 for a
discussion and implications).
17
Such data is not available for the UK, and we would argue that it would not necessarily reflect
accurately both wear and tear and obsolescence. This is because second-hand asset price data reflects
the impact of depreciation and not just deterioration (the former taking account of deterioration over
the entire life of an asset), and it has been argued that using used-asset market price data as an indicator
of in-use asset values is problematic if the relatively small number of assets resold in second-hand
markets are not of as ‘good quality’ as those assets that remain with the plants that undertook the initial
investment.
12
averaged against the experience of long-lived assets, and the
average cohort experience is graphed, it will look nearly geometric
(p. 18).
2.9
However, this implies that a number of assets are pre-maturely scrapped,
destroyed or ‘lost’. That is, many assets have to be short-lived in order to
produce an exponential deterioration rate, especially if (as in this study) premature scrapping due to closure is accounted for separately.
2.10 A simple example demonstrates the implications of using the exponential
distribution. If an asset has an average service life of 20 years, then after five
years it will typically offer only 33 per cent of the capital services that would be
available from a new asset. After ten years, only 11 per cent of the asset’s initial
services are available, falling to 3 per cent in year 15. In other words, when
deterioration is assumed to be very high in the first few years after installation, a
new asset is three times more productive than an asset that is one-quarter of the
way through its life. This implies a far higher rate of capital-embodied technical
progress than those typically found in the empirical literature (e.g., Kalt, 1978,
estimated capital-embodied technical progress at 0.01 per cent per annum for
the USA over the 1929-67 period, while Hulten, 1992, reports a figure of 0.3
per cent per annum for 1949-83).
2.11 An alternative approach to the perpetual inventory method that has been
suggested is one which centres on the use of a putty-clay model of production
(e.g., Coen, 1980; and Anderson and Rigby, 1989). Basically this means using
an investment model to impute the ‘best’ rate of depreciation and service life
that fits gross investment data matched to employment levels through time.
Besides the untested hypothesis that once installed a capital good requires a
13
fixed amount of labour to operate it, the approach is also subject to other
theoretical and empirical limitations (see Fabricant, 1980 for a discussion).18
Figure 2.1:
Different distributions for deterioration: Iron and Steel industry
100
Net Stock
Gross Stock
Denison
Exponential
90
80
initial investment in year 0 = 100
70
average service life = 24.6 years
60
50
40
30
20
10
46
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
8
10
6
4
2
0
0
Years from original investment
2.12 To illustrate the use of the Denison deterioration pattern instead of the more
frequently used exponential pattern, Figure 2.1 shows various outcomes for the
Iron and Steel industry following the purchase of a single capital good (costing
£100 in real terms). The ONS assumes that investment in any year is subdivided (in this industry) into 4 sub-groups, each accounting for a different
proportion of the total investment and each with a different service life (see
Table A2.1 for details).19 For example, 77.9 per cent of the investment is
18
Note, the assumption of ‘putty-clay’ technology is not essential for this type of approach. For
instance, Nadiri and Prucha (1996) jointly estimate a labour-demand equation, based on a normalised
variable cost function in which Kt is a determinant, with the following identity: Kt ≡ It + (1 − δ)Kt-1,
where It denotes gross investment and δ the depreciation rate of capital. The authors found that δ took a
value of 0.059 using data on US manufacturing plant and machinery gross investment for 1960-88 (and
an initial benchmark estimate of the capital stock).
19
In theory, it is possible to use different lengths of life assumptions (and thus different rates of
deterioration). However, we only have information collected by the ONS on which to base asset lives,
with no evidence that alternative estimates should be used in their place.
14
presumed to belong to an asset class where the length of life is 26 years. For
Iron and Steel, the average length of life when combining all four sub-groups is
24.6 years. For the net and gross (and thus Denison) stock, assets are assumed to
be retired 10 per cent either side of the average length of life of each sub-group.
The exponential pattern is based on the ONS length of life of each sub-group
and the declining balance rate (DBR) derived from Hulten and Wykoff (1981)
with δ = DBR ÷ T.20
2.13 Figure 2.1 shows that when the asset is 6 years old (approximately one-quarter
of the way through its average length of life), none of the gross stock has
deteriorated, 89.9 per cent of the Denison stock remains, 69.8 per cent of the net
stock is intact, but only 58.5 per cent of the asset’s capital services remain in the
exponential measure. At the other extreme, when the asset is 28 years old only
4.6 per cent of the gross stock, 3.4 per cent of the Denison stock, and 1 per cent
of the net stock remains; however, 13.1 per cent of the asset is still in place
under the exponential distribution. Hence, for an industry like Iron and Steel,
where a large amount of investment took place in the 1950-1980 period, if the
exponential distribution is used a significant amount of old, non-depreciated
capital stock will still remain in place in the post-1980 period.
Oulton and O’Mahony (1994, Table 3.4) provide the estimates of δ employed here. See also
Fraumeni (1997) for an explanation of how DBR is combined with asset life to produce rates of
deterioration/depreciation.
20
15
Appendix
Table A2.1: Definitions of the 18 industries
Indust Name
SIC80
ry
codes
Asset class (and % distribution)
A
B
C
D
E
Iron and steel
221 – 223
13.8 3.7 77.9
Other metal
210, 224
1.4 10.0 20.0 56.5
manufacturing
3
Extraction, bricks,
231-239,
3.0 15.0 31.0 28.0
asbestos
241 – 246
4
Glass, pottery
247, 248
5.0 24.0 19.0 14.0
5
Chemicals
251 – 259
3.4
2.7
6.8 56.9
6
Man-made fibres
260
2.6 89.7
7
Other metal products
311 – 316
1.1 10.9 16.3 61.4
8
Electrical engineering
320 – 348
1.4 10.0 20.0 56.5
9
Motor vehicles
351 – 353
25.0 2.0
10.0 52.0
10
Shipbuilding
361
1.4 10.0 20.0 56.5
11
Other vehicles
362 – 365
3.0
13.0 69.0
12
Instrumental
371 – 374
1.4 10.0 20.0 56.5
Engineering
13
Food, drink, tobacco
411 – 429
2.0 22.0 68.0
14
Textiles
431 – 442
2.6 89.7
15
Clothing, footwear,
451 – 456
73.0 4.0
leather
16
Timber products
461 – 467
76.0 5.0
17
Paper, publishing
471 – 475
4.5 54.5
18
Other manufacturing
481 – 495
73.0 4.0
Average length of life for asset (in years): A=5; B=12; C=14; D=19; E=26; F=37.
Source: ONS
1
2
F
4.6
12.1
23.0
38.0
30.2
7.7
10.3
12.1
11.0
12.1
15.0
12.1
8.0
7.7
23.0
19.0
41.0
23.0
16
3. Plant level Estimates of the Capital Stock
3.1
Gross investment data for plant and machinery was taken from the Annual
Respondents Database (the ARD). The ARD basically comprises financial
information21 collected from some 14-19,000 manufacturing establishments (or
reporting units – denoted RU hereafter) for each year from 1973-200122, based
on a stratified sampling frame that is heavily biased towards the largest
establishments. Establishments (and the plants comprising such establishments)
can be linked through time to form a panel, and information is also available on
the population of establishments (or plants), which can be used to weight the
financial data to obtain population estimates.
3.2
For each year there are two files that can be merged to produce plant level data;
one file covers the sample of RU’s23, known as the ‘selected’ file, that were
asked questions about financial matters (e.g. amounts spent on capital
expenditure, including any pre-production expenditure), while the other
contains information (such as employment and ownership structure) on ‘nonselected’ establishments (the remainder of the population). Establishment level
data can be 'spread back' to local units (hereafter referred to as LU’s) using
employment shares24 and the unique reference number allocated to each plant
21
Such as sales, purchases of inputs, investment undertaken, as well as the characteristics of
respondents in terms of ownership and location. See footnote 1 for details.
22
Since 1998, data is available on an economy-wide basis and not just for production industries.
However, since the perpetual inventory method used here to calculate capital stocks requires
information on gross investment for up to 37 years, the economy-wide data cannot yet be used to
calculate reliable plant level capital stock estimates.
23
Establishments are either single plants or they make a return that covers several plants - details and
definitions are provided in the introductory notes for each annual census.
24
Note, employment data for local units is based on information supplied by respondents when they
make a return to the ABI. Tit is this information on local unit employment that is used here.
Employment data for non-selected local units is obtained from the IDBR (and before 1994 from the
register of plants keep by the ONS), and for especially smaller plants this information may be
interpolated or be based on information collected in previous years (thus making it less accurate). The
17
during the whole 1970-2001 period (with single unit establishments supplying
their own LU – i.e. plant level - information). Sample data can be grossed-up to
provide population estimates (using employment estimates for all plants)25 and
each non-selected plant's share of annual investment in each industry can be
apportioned back to these plants using employment share data.
3.3
Thus, plant-level (LU) estimates of capital expenditure are to some extent
derived from establishment level (RU) information. The next chapter provides
an analysis of the extent to which plants obtain their financial information
through pro rata allocations from the RU to which they belong. In particular,
large multi-plant establishments combine a significant proportion of their plants
into single financial returns to the ABI. The extent to which plant level
information on capital expenditure is biased cannot be measured, and especially
whether this biases the overall estimates. Of course, ‘spreading back’ RU
investment data to LU’s based on employment shares is to assume a constant
investment-labour ratio across the local units of an establishment, when
investment is usually ‘lumpy’ and for some plants is likely to involve ratios
above and below the average for the RU. Over a number of years, however, this
issue is unlikely to be too great a problem as there is a strong positive
correlation between investment and employment levels across plants, reflecting
the fact that large plants in employment terms on average tend to invest more
(and vice versa).
3.4
In any case, using RU’s as the base for analysis results in a different set of
issues which suggest that it is questionable whether using RU data is a viable
source of employment data for non-selected plants (and thus weaknesses associated with its use) is
discussed in the next Chapter.
25
The 'weights' were calculated at the 4-digit industry level and by RU size-band. Note, the 1980
Standard Industrial Classification was used throughout (requiring a ‘look-up’ table that reclassifies the
1992 SIC to the 1980 SIC), with plants from 1970-1979 reclassified from the 1968 SIC.
18
alternative to using plant-level data. As shown in Chapter 4, the main reason is
that the establishments are not 'stable' over time (an essential requirement for
the perpetual inventory measure of capital), since their composition (in terms of
the number of plants they cover) can change as companies open and close
plants, buy and sell plants, or simply change the way they report to the ONS
(i.e., reallocate plants into different establishments for accounting purposes).
Even those RU’s that have the same number of plants in different years
(typically the smallest establishments), the year of opening and closing for the
different plants in each RU are a mix of different dates. The largest RU’s, in
employment terms, are more likely to have different numbers of plants in
different years. The deviation in the opening and closing dates of the plants
contained in these establishments is significant. In addition, the change in
average employment in these establishments (and the standard deviation
associated with the employment in the plants contained in each establishment) is
very large.
3.5
Using plant-level estimates of capital expenditure (on plant and machinery),
based on acquisitions less disposals and including pre-production expenditure
(where available), it is possible to estimate the capital stock for each plant using
the perpetual inventory method based on the Denison approach to deterioration
and the length-of-life assumptions as used by the ONS when calculating the
'official' estimates for the UK (Chapter 2 provided details on the methods
employed). For plants in existence in 1970, these estimates do not take account
of pre-1970 investment. Thus, 1949-69 data supplied by the NIESR (based on
3-digit industries under the 1968 SIC) were used to calculate a 1969 benchmark
series that was then apportioned to the 1970 stock of plants using 1970-72
19
shares of employment and gross expenditure on plant and machinery. The
benchmark figures depreciate with no further new investment being added, and
these estimates are then merged with the post-1969 capital stocks calculated for
each plant. Plants in existence in 1970 that close after this date remove a
proportion of the benchmark capital stock from the aggregate.26,27
3.6
Plant and machinery price deflators (based on the 1980 SIC) supplied by the
ONS (and updated using information published annual in the MM14 series)28
were applied to the data, to produce real gross investment in plant and
machinery by industry. The most disaggregated industry breakdown available
which was consistent through time was used for 21 manufacturing sectors. The
1949-69 data supplied by the NIESR were in 1980 constant-prices.
Updating the Capital Stock Estimates post-2001
3.7
The rest of this chapter explains in detail how to update the plant and machinery
capital stock estimates produced here when ARD information for 2002 and
26
Specifically, the capital stocks of plants that closed were simply subtracted from the unadjusted
industry stocks on a year-by-year basis from the date when the plant closed. The method used to
measure the aggregate industry capital stock and individual plants capital stock is identical, being based
on the same length of asset life assumptions and the same deterioration patterns.
27
Note, if a plant that closes belongs to a multi-plant enterprise, it is possible that some at least of its
assets are distributed around the other plants in the establishment to which the plant belongs, without
disposals and acquisitions being recorded in the financial returns for the establishment. To the
(unknown) extent to which this happens, our estimates of scrapping will be biased upwards. However,
it is likely that the majority of capital is ‘sunk’ in the sense of having only a specific use in the plant for
which it was acquired.
28
Latest published figures are provided for the 1992 SIC, and these are matched as accurately as
possible to the 1980 SIC.
20
beyond becomes available. The SPSS code used to do this is attached
comprising four syntax files.29
3.8
The first step comprises merging the selected and non-selected files and
calculating weights to obtain a single plant-level ARD file for the year in
question. The syntax file that does this is labelled ‘2001 matching data.sps’, and
is attached at the end of this report in the Statistical Appendix. The individual
RU files for each sector (labelled dat2001xxx.sav or nul2001xxx.sav)30 are
amalgamated and checked to ensure that there are no duplicate cases. These are
then spread back to the LU data (after it has been merged into one file – each
file is labelled snul2001xxx.sav). At this stage turnover, gross output, GVA, and
gross investment in plant and machinery figures are obtained based on ONS
definitions. Such estimates for LU data derived from RU data are multiplied by
‘unitwt’ which is the share of LU employment in total RU employment.
3.9
Step two comprises maintaining a plant level link through time (labelled
CSO_REF), converting 1992SIC codes back to 1980SIC codes, and calculating
real gross investment figures for all plants (whether they were ‘selected’ or
‘non-selected’). The syntax file for this is labelled ‘setup K 2001.sps’. The
outcome is an updated file (labelled rnet_pm70xx.sav) which will be used to
calculate capital stocks for each plant based on post-1969 real gross investment
data.
3.10 Next, capital stock estimates based on the Denison approach are calculated for
each plant. The syntax file is labelled ‘capstock.sps’.
29
The BDL unit at the ONS creates data files using STATA but these can be converted to SPSS files
using the STAT TRANSFER software available at the BDL. Note, users can amend the programmes
provided to meet their own needs if, for example, they decided to use a different depreciation series.
30
The xxx refer to the different industry codes (e.g. ‘prg’ refer to production) while the ‘dat’ refers to
RU’s that were selected and sent forms for completing with regard to supplying financial information.
The ‘nul’ files refer to non-selected RU’s that were not selected for the ABI.
21
Table 3.1: UK manufacturing plant & machinery capital stock 1970-2001 (£m
1980 prices)
Year
Capital Stock
Real Gross Investment
No. of Plants
1970
61,419
5,763
99410
1971
64,106
5,241
99021
1972
66,303
4,596
99631
1973
68,770
5,038
112063
1974
72,276
6,348
119848
1975
74,440
5,531
122113
1976
76,012
5,169
125189
1977
77,837
5,480
125952
1978
80,141
6,102
125957
1979
83,337
7,023
124703
1980
82,505
4,945
124032
1981
80,738
3,829
123242
1982
79,000
3,723
116659
1983
77,768
4,017
115498
1984
74,453
4,769
148925
1985
74,552
5,296
155719
1986
74,706
5,081
161600
1987
75,632
5,843
166109
1988
78,154
7,189
170702
1989
80,393
8,084
173933
1990
82,105
7,532
167208
1991
82,430
6,589
162532
1992
82,060
6,015
173144
1993
78,179
5,016
159526
1994
77,297
6,445
183453
1995
77,554
8,223
211276
1996
72,099
7,195
190946
1997
69,478
8,070
198338
1998
66,813
8,322
182726
1999
63,666
7,694
191308
2000
66,186
7,888
189135
2001
66,831
8,525
181653
Total
2,376,576
195,634
4798652
22
3.11 Finally, the capital stock data for individual plants is merged to pre-1970
benchmark data, to obtain the final estimates for each plant. The syntax file is
labelled ‘capital stock final merge.sps’. The results for the 1970 to 2001 period
for all manufacturing plants are presented in Table 3.1
23
[this page is blank]
24
4. Issues in Measuring the Capital Stock
4.1
A list of issues that need to be considered include the following:
a. Whether plant (LU) or establishment (RU) level data should be used
b. Implementation of the Perpetual Inventory method and specifically:
i. What depreciation series should be used?
ii. What start values are needed (i.e. the first year of gross
investment data used) in order to derive an accurate series
iii. The availability of plant level gross investment data
(acquisitions net of disposals)
iv. How to take account of plant closures
4.2
These issues are considered mainly by contrasting the approach set out in
Chapters 2 and 3 with the approach used by Martin (2003).31
Table 4.1: RU Plant & Machinery Capital Stocks, 1980-1993, based on using LU and
RU data
Ratio of RU
capital stocks
LU data
RU data
£m 1980 prices
%
< 0.75
112,238
12.8
53,100
6.4
18,735
0.75 to <1
263,394
30.1
248,435
30.0
263,611
1
158,065
18.0
158,065
19.1
1,354,491
>1 to 1.25
319,201
36.4
331,845
40.1
271,688
> 1.25
22,929
2.6
36,312
4.4
11,744
Total
875,828
827,757
100
1,920,269
100
£m 1980 prices
%
No. of RU’s
in each
sub-group
See text for details (author’s own calculations using the ARD)
31
Note we cannot compare directly our estimates with those generated by Martin as he calculates a
measure including plant, machinery, buildings and vehicles and we only estimate a figure for plant and
machinery.
25
Local versus reporting unit estimates of the capital stock
4.3
The arguments set out in par. 3.3 show that there are problems when using RU
as opposed to LU data. The main reason is that RU’s are not 'stable' over time
since their composition (in terms of the number of plants they cover) can change
as companies open and close plants, buy and sell plants, or simply change the
way they report to the ONS (i.e., reallocate plants into different establishments
for accounting purposes).
4.4
In order to measure the implications of using RU’s (vis-à-vis LU’s) when
estimating the capital stock, the 1970-93 real investment data for plant and
machinery was re-assigned to RU’s. Then using the same procedures as in
Chapter 3 but with RU reference codes rather than LU codes, the capital stock
estimates were re-computed (referred to hereafter as the RU capital stock
estimates). Note, pre-1970 benchmark data at RU level was not available, and
thus for the present exercise only data from the ARD is used (covering plants
and establishments from 1970 onwards). Also, RU codes that have been linked
through time are not available post 1993 (when the ONS moved over to using
new IDBR codes for LU’s and RU’s), since the ONS did not provide a complete
look-up table to match local and reporting unit reference numbers in 1993 (the
last time the VAT register was used) with those used in 1994 (when the IDBR
was first used).32
4.5
Table 4.1 presents the results from aggregating plant level capital stock data to
the RU level and comparing the results with the RU capital stock estimates.
32
The present author has fully linked LU’s using the old CSO_REF codes to maintain a link through
time, but not RU’s, hence CSO_REF2 codes end in 1993.
26
Note, the extent to which the two series differ reflects the points noted in par.
4.3 that RU’s are often not stable over time (of course single plant enterprises
have de facto the same LU and RU reference codes, and therefore will have
identical capital stock estimates33). The first difference to note is that overall the
total UK manufacturing capital stock is lower when RU data is used, since a
number of RU’s were ‘closed’ during the period 1970-93 with (some or all) of
the plants they accounted for reassigned to other RU’s. The consequence of this
is that while the RU’s that gained these plants had higher levels of real
investment after ‘acquiring’ the LU’s, they did not gain the accumulated past
investments (i.e. the capital stocks) of such LU’s.
4.6
To recap, for each RU covering the 1980-1993 period included in Table 4.1,
two estimates of capital stock were available: (i) one based on using plant level
data aggregated to the RU level; and (ii) the other based on RU data. The
difference between the two for each RU was calculated as the ratio of the
estimate based on RU data to the estimate based on using LU data. During the
1980-93 period, over 70 per cent of RU’s were ‘stable’ in that they comprised
the same plants throughout the post-1969 period (indeed, most were single plant
enterprises – see the last column in Table 4.1), but these ‘stable’ RU’s only
accounted for some 18 – 19 per cent of the total real capital stock during 198093.
4.7
For some RU’s, the capital stock based on using LU data was larger (so that the
ratio is below 1 in Table 4.1). This was usually the result of RU’s that were
closed having their plants reassigned but not the capital stocks of these
reassigned plants (see par. 4.5 above).
33
Although this changes if they are acquired by a multi-plant firm.
27
Table 4.2: Plant & machinery capitals stock (1973=100) for single hypothetical RU,
1973-93
Year
Total capital stock (K)
No. of
plants
K lost due
to ‘closure’
K gained due to plant
reassigned from
different RU
1973
100.0
30
1974
102.5
30
1975
105.1
30
1976
107.7
30
1977
110.4
30
1978
113.1
30
1979
116.0
30
1980
116.0
30
1981
77.3
20
1982
77.3
20
1983
77.3
20
1984
58.0
15
1985
58.0
15
1986
59.1
15
1987
59.1
15
1988
60.3
15
1989
57.6
15
1990
60.6
18
1991
72.7
18
1992
24.2
5
1993
24.2
5
Source: ARD and author’s own calculations
4.8
38.7
19.3
12.1
48.5
For other RU’s, the capital stock based on using LU data is smaller (ratios
above 1 in Table 4.1). This typically resulted when some (but not all) of the
plants within a RU were closed, which reduces the capital stock estimate based
on using LU data but not the estimated obtained when using RU data (since the
28
RU does not close and thus none of the capital stock of closing plants is
removed).
4.9
Table 4.2 makes this clearer; information for a single (hypothetical34) reporting
unit is shown with capital stock data based on amalgamating the local units
included in the RU. Thus, capital stock estimates here are based on using LU
data. At the end of 1980, 1983 and 1991 several plants are ‘closed’35 (see the
column headed ‘number of plants’), and consequently the total capital stock for
the RU declines substantially. If the capital stock had been calculated using RU
data, none of this reduction due to ‘closure’ would have taken place, leading to
a significant overestimate of the actual capital stock available to this RU.
4.10 If a user of the ARD prefers to use RU data, then aggregating up LU estimates
to the RU level will at least avoid the problems of ‘stability’ discussed in this
section (although there still remains an issue with plant closures).
4.11 This sub-section concludes with a discussion of some of the problems
associated with using plant level estimates of capital stock that are based on
‘spreading back’ gross investment data from RU’s to LU’s based on
employment in local units.
4.12 The issue of ‘spreading back’ gross investment data from RU’s to LU’s, and
thus imposing the assumption that investment-labour ratios are constant across
the LU’s that make up a single RU, has already been discussed (par. 3.3). A
further issue (and potential source of bias) is that employment data for nonselected plants is not always up-to-date or directly collected.36
34
These numbers are ‘made-up’ and do not relate to any actual RU to ensure confidentiality.
Either closed in the sense of the plant(s) ceased production or the plant(s) were reassigned to another
RU (or RU’s).
36
Of course, this is also true for non-selected RU’s (e.g. single-plant enterprises). Note also, any microbased analysis of the data will used (weighted) data for ‘selected’ plants, where employment
information is up-to-date.
35
29
4.13 Since 1994, employment information is collected at local unit level by the
Annual Register Inquiry (ARI), with larger firms (with over 50 employees)
being covered annually and all firms updated at least every four years, from a
variety of sources including ARI, ABI and the PAYE register. However, for
very small firms where there is only VAT turnover information, employment is
interpolated (based on the turnover/employment ratios of plants that do provide
information on both measures). Moreover, smaller (usually single-plant) firms
will have their employment information updated less frequently than larger
firms, and therefore the employment information available for non-selected
plants (belonging to non-selected RU’s) is less reliable in the short-term.
4.14 Prior to 1994, employment data for non-selected RU’s in the 0-19 employment
size-band was based on interpolations using VAT turnover data and
turnover/employment ratios from the 20-49 employment size-band.
4.15 This issue of the accuracy of using plant-level employment (and the unknown
bias that may result) when ‘spreading-back’ data from RU’s needs to be
weighed against the problems of using RU’s when calculating capital stock
estimates (principally issues of the non-stability of RU’s and plant closures).
Issues relating to implementation of the Perpetual Inventory method
4.16 The first issue to be considered is the depreciation series that is used in the
present approach (based on Denison, 1967) compared to that used by Martin
(2003). The latter uses a geometric depreciation rate based on the average ONS
length of life for all manufacturing and thus δ = 0.06 in Martin (op. cit.) – see
par. 2.12 for further details. Note, Martin does not use the length of life
30
information for each of the sub-groups within the 18 manufacturing industries
for which data is available (see Table A2.1). Figure 2.1 (in Chapter 2) and the
discussion in par. 2.12 and 2.13 illustrate the implications of using a geometric
depreciation rate. It was argued that using such a depreciation rate removes
capital services from the asset stock at too fast a rate in the initial years and then
too slowly when the asset nears the end of its length of life. If we are interested
in the economic services available from an asset, then the Denison (1972)
approach produces a more appropriate deterioration patter (at first slow,
followed by more rapid deterioration).
4.17 The next issue is the start values that are used in the perpetual inventory
approach. In theory, we need gross investment data that extends back some 37
years before the first year for which we wish to calculate the plant and
machinery capital stock.37 Plant level data on real gross investment in plant and
machinery is only available from 1970, and this is linked to 3-digit industry
level estimates of gross investment that covers the 1948-1969 period (see par
3.4). Investment data at the 3-digit level is not available before 1948, although
more aggregated information can be obtained from the ONS (however, this was
not used since it is felt that this would not be accurate enough for linking to
plant-level data, and in any event much of the pre-1948 data covers the period
of WWII and much of this stock of capital is likely to subject to special factors
that make its use problematic38). Thus, the 1970-2001 plant level estimates of
the (plant and machinery) capital stock comprise two (merged) elements: (i)
estimates for each plant using the perpetual inventory method based on the
37
For estimates of the stock of industrial buildings, we would need gross investment data for at least 80
years before the first year for which we wish to estimate the capital stock, given the much longer length
of life of buildings.
38
E.g. some of this stock would have been destroyed in the war; much would have been obsolete after
the war and would have needed to be converted to peace-time use.
31
Denison approach to deterioration; and (ii) a 1969 benchmark series (based on
the 1948-1969 3-digit 1968 SIC investment data) that was then apportioned to
the 1970 stock of plants using 1970-72 shares of employment and gross
expenditure on plant and machinery. The benchmark figures depreciate with no
further new investment being added, and these estimates are then merged with
the post-1969 capital stocks calculated for each plant. Plants in existence in
1970 that close after this date remove a proportion of the benchmark capital
stock from the aggregate (further details are provided in par. 3.4).
4.18 Figure 4.1 shows what proportion of the total manufacturing capital stock (in
selected years) is accounted for by the (depreciated) 1969 benchmark data. In
the early years, plants that were open in 1970 dominate the aggregate stock and
in turn the benchmark series provides the largest share of capital stock for such
plants. By 1980, some 40 per cent of the aggregate stock is accounted for by
investment that occurred pre-1970 (and thus which is based on the 3-digit 1968
SIC industry aggregate investment data).
4.19 In contrast, Martin (op. cit.) uses 2-digit (rather than 3-digit) SIC real gross
investment data for 1948-1979 to calculate a 1979 benchmark series which is
then apportioned to 1980 RU’s using the average material usage over the
lifetime of a post-1979 RU.
4.20 The first difference to note when comparing the approach used here and
Martin’s is that his capital stock figures for the 1980’s will be dominated by the
benchmark series, as he only uses RU data from 1980 onwards.
4.21 Secondly, his method of apportioning the benchmark series to RU’s existing in
1980 is very different to the approach used in this study. It is unclear why
apportioning using intermediate inputs (rather than investment or employment
32
data) is preferred; it is even harder to understand why the average over the
lifetime of the RU should be used. For example, RU’s that are new in 1980 but
survive a long time and grow relatively large will be apportioned a large part of
the 1979 benchmark series in 1980, but RU’s that are relatively ‘old’ in 1980
and perhaps decline in size and close earlier will be allocated a smaller
allocation of the 1979 benchmark series.
Figure 4.1 Proportion of UK Plant & Machinery Capital stock in selected years
accounted for by (depreciated) 1969 benchmark data
100
%
90
80
70
60
50
40
30
20
10
19
70
19
71
19
72
19
73
19
74
19
75
19
76
19
77
19
78
19
79
19
80
19
81
19
82
19
83
19
84
19
85
19
86
19
87
19
88
19
89
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
0
4.22 The approach used in this study apportioned the 1969 benchmark capital stock
using the 1970-72 shares of investment and employment of 1970 plants (within
each 3-digit industry), giving equal weight to the investment and employment
shares.39
39
The problem with using investment shares is that investment (even covering a 3 year period) can be
‘lumpy’; the problem with using employment shares to proxy for the relative size of the plants within
each 3-digit SIC industry is that this assumes a fixed ratio between the size of the capital stock and the
size of the employment stock in 1969. So both series were used, although it was found that the two
were strongly correlated across plants suggesting that using either series would not be inappropriate.
33
4.23 The third issue associated with implementing the perpetual inventory method is
that it requires investment data (acquisitions net of disposals)40 in every year
that the plant (or RU) is open, not just those years when the unit was selected to
be included in the ABI (or Annual Census of Production). In this study, data for
‘non-selected’ years was interpolated by grossing-up sample data (provided in
the ‘selected’ file) to provide population estimates of gross investment for each
4-digit industry (using the 1980 SIC)41, subtracting the share of investment
attributable to the ‘selected’ plants so that what is left over comprises the nonselected share of annual investment in each industry, which is then apportioned
back to non-selected plants using employment share data. Figure 4.2 provides
an example of the procedure for one plant covering the 1973 – 1987 period (the
red diamonds denote the interpolated investment levels in each year).
4.24 In contrast, Martin (op. cit.) linearly interpolates between any two years where
selected data for an RU is available (and if data is missing prior to closure then
the last observed value is used). In terms of Figure 4.2, the equivalent estimates
using Martin’s approach would lie on the blue dashed lines in the diagram.
Clearly a major weakness of Martin’s approach is that it takes no account of the
level of total investment that took place in any year, since adding together his
estimates of selected and non-selected (interpolated) investment data is not
constrained to equal the total level of (population weighted) investment for an
industry. That is why in Figure 4.2 the interpolated data used here lies above
and below the estimates that would be obtained using Martin’s technique;
40
Note, from 1976 data on leasing of plant and machinery is available separately in the ARD. These
figures were not used here, but should added to the capital stock (after deflation) prior to use in any
econometric analysis (such as estimating TFP).
41
This is the procedure used by the ONS when publishing industry level investment data.
34
fluctuations are included here to reflect overall investment levels in each
industry in each year.
4.25 The final issue is how to take account of closures. The section above dealing
with the implications of using LU versus RU data (par. 4.3 to 4.14) shows that
when firms reduce their production capacity (through closing a plant) this
cannot be adequately dealt with if RU data is used. Estimates of the capital
stock using RU data will therefore be biased when closures occur, and the
extent of bias is likely to be relatively large.
Figure 4.2 Actual and interpolated/extrapolated gross investment for one plant in UK
manufacturing, 1973-1987 (1973=1)
3.5
3.0
interpolated data (Harris approach)
2.5
2.0
1.5
1.0
interpolated data (Martin)
0.5
0.0
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
-0.5
-1.0
-1.5
35
Conclusions and recommendations
4.26 To conclude, the methods used here to calculate the plant and machinery capital
stock are argued to have certain advantages over those employed by Martin (and
others using RU data) since they:
•
are based on LU data and thus avoid the problem that LU’s can be
reallocated between RU’s for accounting purposes by firms, or when
plants are bought and sold, or when they are opened and closed;
•
the Denison approach to calculating economic deterioration is argued to be
more realistic when compared to using a geometric depreciation series,
especially if the purpose of calculating capital stock estimates is to use
these when estimating a production function or when estimating total
factor productivity;
•
post-1969 data at the plant level is used here, while Martin uses post-1979
data, and thus the influence of benchmark data is lower in the present
estimates, especially from 1980 onwards. The benchmark series used here
were also more disaggregated, and thus likely to have been more
accurately distributed to those plants that were open in 1970 (and thus
required pre-1970 capital stocks to be allocated to them), especially as
Martin uses the average value of intermediate inputs of RU’s based on
their entire operating life to allocate the benchmark data (rather than
investment and employment shares linked to the benchmark period);
•
investment data is interpolated (when necessary) using a population
estimate of investment in a 4-digit industry in any particular year (after
subtracting investment already identified to belong to those plants that
36
were selected for inclusion in the ABI), while Martin simply interpolates
linearly between observed investment levels for each RU;
•
the capital stock produced here takes account of plant closures, while
Martin does not.
4.27 However, ‘spreading back’ investment data from selected RU’s based on LU
employment shares does introduce an unknown level of bias into the capital
stock estimates produced at the plant level. Improvements in the accuracy of
measuring the capital stock using the perpetual inventory approach would be
achieved if the ONS were to consider the following changes42:
•
collecting information on capital expenditure at the local unit level (in
addition to employment data) when conducting the ABI (this information
was apparently collected prior to 1994 when RU’s were asked to report on
employment and capital expenditure for the plants included in the return,
but the information was not made available in the ARD);
•
increasing the frequency with which LU employment estimates are
updated for smaller firms. The National Assembly for Wales has for some
years funded a top-up to the ARI for the region and Scotland has recently
agreed the same with the ONS. The additional costs are not large and it is
estimated that the benefits in terms of the improved accuracy of
employment and plant turnover information for smaller firms (below 50
employees) will be significant.43
42
The cost of such changes is not considered here and the ONS would need to balance costs against
gains in terms of the quality of the micro-data generated, given that the primary purpose of the ABI is
to generate information which is used to provide figures at a much more aggregated level (e.g. national
GVA statistics by industry). However, updating the IDBR through the Annual register Inquiry is also
important since the IDBR underpins analysis of business demography at the local level, which is
important to government in terms of policy aims and objectives.
43
The Scottish contact person is Gerhard Mors ([email protected]) who has further
information.
37
•
obtaining more up-to-date estimates of economic depreciation of assets by
industry, in order to provide better estimates of the rate of deterioration
and obsolescence.
4.28 An alternative might be for ONS to undertake a limited survey of plants and
firms in order to generate direct estimates of the capital stock. This would not
only confirm how accurate the methods used here are (especially in relative
terms across plants), but would also help to provide an alternative to the
perpetual inventory approach which comprises the standard means for
calculating capital stock in most countries.
38
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40
Haskel, J. and R. Martin (2003), Productivity Spreads Using Conventional Measures,
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Using Vintage Asset Prices: An Application of the Box-Cox Transformation,
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Hulten, C. R. and F. C. Wykoff (1996) Issues in the Measurement of Economic
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Jefferson, C. W. (1971) Capital Statistics for Irish Manufacturing Industry, Paper No.
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41
Statistical Appendix
2001 matching data.sps
* MERGE RU'S FOR DIFFERENT
SECTORS.
set mxmemory=2097151.
get file= 'h:\files\dat2001cag.sav' .
add files file=*
/file='h:\files\dat2001cng.sav'
/file='h:\files\dat2001mtg.sav'
/file='h:\files\dat2001pdg.sav'
/file='h:\files\dat2001prg.sav'
/file='h:\files\dat2001reg.sav'
/file='h:\files\dat2001stg.sav'
/file='h:\files\dat2001whg.sav'
/file='h:\files\nul2001cag.sav'
/file='h:\files\nul2001cng.sav'
/file='h:\files\nul2001mtg.sav'
/file='h:\files\nul2001pdg.sav'
/file='h:\files\nul2001prg.sav'
/file='h:\files\nul2001reg.sav'
/file='h:\files\nul2001stg.sav'
/file='h:\files\nul2001whg.sav' .
* dlink_re REFERS TO RU NUMBER.
sort cases by dlink_re.
compute n=1.
* CHECK FOR DUPLICATE CASES.
aggregate outfile='h:\files\del.sav'
/break=dlink_re/number=sum(n).
match files
file=*/table='h:\files\del.sav'/by
dlink_re.
frequencies vars=number.
compute ru_emp=empment.
save outfile='h:\files\ru2001gb.sav'.
sort files by number dlink_re.
* MERGE LU DATA FOR
DIFFERENT SECTORS.
get file= 'h:\files\snul2001cag.sav' .
add files file=*
/file='h:\files\snul2001cng.sav'
/file='h:\files\snul2001mtg.sav'
/file='h:\files\snul2001pdg.sav'
/file='h:\files\snul2001prg.sav'
/file='h:\files\snul2001reg.sav'
/file='h:\files\snul2001stg.sav'
/file='h:\files\snul2001whg.sav' .
sort cases by dlink_re.
save outfile='h:\files\snul2001gb.sav'.
descriptives dlink_r1.
* MERGE RU DATA BACK TO LU
DATA.
get file='h:\files\snul2001gb.sav'.
match files
file=*/table='h:\files\ru2001gb.sav' /by
dlink_re.
execute.
if (ru_emp gt 0)
unitwt=empment/ru_emp.
if (empment eq 0) unitwt=1.
if (missing(dlink_r1)) dlink_r1=dlink_re.
* RENAME LU AND RU CODES TO
luref AND ruref.
compute luref=dlink_r1.
compute ruref=dlink_re.
descriptives unitwt.
descriptives wq11.
save outfile='h:\files\capital
stock\2001gb_all.sav'/drop=dlink_r1
dlink_re.
* WEIGHT DATA.
get file='h:\files\capital
stock\2001gb_all.sav'.
compute selected=0.
if (wq11 gt 0) selected=1.
*means unitwt by selected.
compute number=1.
compute sic92a=trunc(sic92/10).
aggregate outfile='h:\files\weight1c.sav'
/break=sic92a selected
/pop4=sum(empment)
/nsamp4=sum(number).
aggregate outfile='h:\files\weight2c.sav'
42
/break=sic92a
/totpop4=sum(empment).
sort cases by sic92a selected.
match files
file=*/table='h:\files\weight1c.sav'/by
sic92a selected.
match files
file=*/table='h:\files\weight2c.sav'/by
sic92a .
compute totemp1=empment.
do if (selected eq 1 ).
compute nsamp=nsamp4.
compute popwt=totpop4/pop4.
end if.
recode nsamp (1 thru 5=1) (6 thru 10=2)
(11 thru 20=3) (21 thru high=4) into
nsamp5.
*crosstabs sic92a by nsamp5.
temporary.
select if selected eq 1.
descriptives empment /statistics=sum .
weight by popwt.
temporary.
select if selected eq 1.
descriptives empment /statistics=sum .
weight off.
compute
weight=popwt*(9621759/21623246).
descriptives weight popwt.
* COMPUTE TURNOVER etc DATA
FOR EACH PLANT, HAVING
MULTIPLIED BY unitwt.
compute turnover=wq399*unitwt.
if (missing(turnover))
turnover=wq346*unitwt.
if (missing(wq11)) turnover=-99.
missing values turnover (-99).
compute go=turnover+((wq500wq599)*unitwt)+(wq602*unitwt).
if (missing(go) and missing(wq602))
wq602=0.
if (missing(go)) go=turnover+((wq501wq502)*unitwt)+(wq602*unitwt).
if (missing(wq416)) wq416=0.
compute
gva=turnover+(wq317*unitwt)+((wq500
-wq599)*unitwt)+(wq602*unitwt)(wq499*unitwt)+(wq414*unitwt)(wq400*unitwt)+(wq416*unitwt).
if (missing(gva))
gva=turnover+(wq317*unitwt)+((wq501
-wq502)*unitwt)+(wq602*unitwt)(wq499*unitwt)+(wq414*unitwt)(wq400*unitwt)+(wq416*unitwt).
means wq11 gva turnover go gva by
sic92a/cells=sum count.
variable label gva'GVA at FC (x unitwt)'
go'gross output (x unitwt)'
turnover'turnover (x unitwt)'.
* RELABEL luref TO idbr_ref.
compute idbr_ref=luref.
sort cases by idbr_ref.
save outfile='h:\files\capital
stock\2001gb_all.sav'/drop=nsamp4
nsamp5 totpop4 pop4 sic92a totemp1
number
/compressed.
* CALCULATE PLANT AND
MACHINERY GROSS INVESTMENT.
get file='h:\files\capital
stock\2001gb_all.sav'.
descriptives wq515 wq516 wq527
wq530.
if missing(wq515) wq515=0.
if missing(wq516) wq516=0.
if missing(wq527) wq527=0.
if missing(wq530) wq530=0.
compute netpm=((wq527wq530)+(wq515-wq516))*unitwt.
descriptives netpm.
save outfile='h:\files\capital
stock\2001gb_all.sav'.
43
setup K 2001.sps
* STEP ONE IS TO LINK IDBR_REF
TO CSO_REF USING MOST RECENT
YEAR WHERE LINK EXISTS.
get file='h:\files\capital
stock\2000_merge.sav'/keep=cso_ref
idbr_ref .
aggregate outfile='h:\files\capital
stock\idbr look up.sav'
/break=idbr_ref
/cso_ref=min(cso_ref).
* STEP TWO IS TO LINK TO SIC80
AND CSO_REF, AND CREATE NEW
CSO_REFS FOR PLANTS THAT
OPENED THIS YEAR.
GET
FILE='h:\files\capital
stock\2001gb_all.sav'.
* SELECT JUST MANUFACTURING
PLANTS.
select if sic92 eq 74200 or (sic92 gt
14000 and sic92 lt 40000).
execute.
* MERGE IN DATA FOR MATCHING
1992SIC CODES TO 1980SIC CODES.
sort cases by sic92.
match files file=*/table='h:\files\capital
stock\post-93 SIC80 agg codes.sav'/by
sic92.
compute idbr_ref=luref.
* MATCH IN cso_ref LOOK-UP
DATA FOR PREVIOUS YEAR.
sort cases by idbr_ref.
match files file=*/table='h:\files\capital
stock\idbr look up.sav'/by idbr_ref.
descriptives idbr_ref cso_ref.
sort cases by cso_ref.
* FOR PLANTS WITH NO CSO_REF,
CREATE NEW NUMBERS
STARTING FROM HIGHEST
CSO_REF VALUE (denoted ?)
ALREADY EXISTING.
do if missing(cso_ref).
compute cso_ref=$casenum+?.
end if.
save outfile='h:\files\capital
stock\2001gb_merge.sav'.
*STEP THREE: SAVE NET PLANT
INVESTMENT EXPENDITURE INTO
NEW FILE.
get file='h:\files\capital
stock\2001gb_merge.sav'.
compute net_pm=netpm*1000.
* IF not yet in production
INVESTMENT DATA IS MISSING
THAT ASSIGN zero TO IT.
compute npm_nyip=0.
means net_pm npm_nyip by
sic80/cells=sum.
save outfile='h:\files\capital stock\2001
net cap.sav'/keep=cso_ref year sic80
net_pm npm_nyip popwt empment.
*STEP FOUR: COMPUTE
INVESTMENT FIGURES FOR NONSELECTED PLANTS AND DEFLATE
TO REAL PRICES.
get file='h:\files\capital stock\2001 net
cap.sav'.
if (missing(popwt)) popwt=0.
compute wnetpm=0.
compute wnetpm=net_pm*popwt.
compute emp=0.
if (popwt eq 0) emp=empment.
aggregate outfile='h:\files\capital
stock\delete.sav'
/break=year sic80
/totem=sum(emp)
/totnpm=sum(wnetpm)
/totanpm=sum(net_pm).
sort cases by year sic80.
match files /file=*/table='h:\files\capital
stock\delete.sav'/by year sic80.
execute.
if (popwt eq 0)
net_pm=(emp/totem)*(totnpm-totanpm).
temporary.
select if (sic80 ge 2000 and sic80 lt
5000).
44
means net_pm by year/cells=sum mean
count.
if missing(npm_nyip) npm_nyip=0.
compute net_pm=net_pm+npm_nyip.
sort cases by cso_ref year.
temporary.
select if (sic80 ge 2000 and sic80 lt
5000).
means net_pm by year/cells=sum mean
count.
* RECODE SIC80 INTO 21
INDUSTRY GROUPS FOR
DEFLATION LATER.
compute ind=trunc(sic80/100).
if (sic80 ge 4710 and sic80 le 4729)
ind=471.
if (sic80 ge 4750 and sic80 lt 4759)
ind=475.
recode ind (21=22) (26=25) .
select if (sic80 gt 2000 and sic80 lt
5000).
* GROUP INTO THE 18 INDUSTRIES
USED FOR LENGTH OF LIFE
DEPRECIATION.
recode sic80 (2210 thru 2239=1) (2100
thru 2199=2) (2245 thru 2247=2) (2300
thru 2399=3)
(2410 thru 2469=3) (2470 thru 2479=4)
(2480 thru 2489=4) (2500 thru 2599=5)
(2600=6) (3100 thru 3199=7)
(3200 thru 3499=8) (3500 thru 3530=9)
(3610=10) (3620 thru 3650=11) (3700
thru 3799=12) (4110 thru 4299=13)
(4300 thru 4399=14) (4400 thru
4599=15) (4600 thru 4699=16) (4700
thru 4799=17) (4800 thru 4999=18)
into ind1.
frequencies vars=ind ind1.
temporary.
select if missing(ind1).
frequencies vars=sic80.
* DEFLATE INVESTMENT DATA.
sort cases by year ind.
match files file=*/table='h:\files\capital
stock\capital deflators.sav'/by year ind.
compute rnet_pm=net_pm/def.
temporary.
select if sic80 ge 2100 and sic80 lt 5000.
means rnet_pm net_pm by year.
save outfile='h:\files\capital
stock\capex_01.sav'/keep=year cso_ref
ind1 rnet_pm.
* ADD 2001 DATA TO 1970-2000
REAL INVETMENT DATA.
get file='h:\files\capital
stock\rnet_pm_7000.sav'.
add files file=*/file='h:\files\capital
stock\capex_01.sav'.
select if (rnet_pm gt -20000000 and
rnet_pm lt 322000000).
select if (cso_ref ge 0 and cso_ref lt
9900000000000).
*descriptives all.
frequencies vars=year.
means rnet_pm by year/cells=sum.
descriptives ind1 .
* GROUP DATA INTO 22 SUBGROUPS AS FILE TOO BIG FOR
SINGLE RUN.
recode cso_ref (low thru 1397711=1)
(1397712 thru 1909602=2) (1909603
thru 2367495=3) (2367496 thru
2726899=4)
(2726900 thru 2962701=5) (2962702
thru 3188255=6) (3188256 thru
3373448=7) (3373449 thru 3615079=8)
(3615080 thru 3849495=9) (3849496
thru 4066445=10) (4066446 thru
4530242=11) (4530243 thru
4630730=12)
(4630731 thru 4659740=13) (4659741
thru 4702195=14) (4702196 thru
4765747=15) (4765745 thru
5004878=16)
(5004879 thru 6096082=17) (6096083
thru 6237839=18) (6237840 thru
6268857=19) (6268858 thru
9000000=20)
(9000000 thru 100000000=21)
(100000000 thru high=22) into group.
45
frequencies vars=group .
save outfile='h:\files\capital
stock\rnet_pm_7001.sav'/keep=cso_ref
year ind1 rnet_pm group.
46
capstock.sps.
set mxmemory=2097151.
get file='h:\files\capital
stock\rnet_pm_7001.sav'.
* RUN 22 TIMES FROM group eq 1
TO group eq 22 SINCE OTHERWISE
TOO BIG TO COMPLETE IN FEWER
RUNS.
* REMEMBER TO CHANGE group eq
x AND pmcx EACH RUN WHERE x=1
TO 22.
select if group eq 1.
execute.
* MATCH IN LENGTH OF LIFE
ASSUMPTIONS.
sort cases by ind1.
match files file=*/table='h:\files\capital
stock\length of life.sav'/by ind1.
execute.
compute test=g1+g2+g3+g4+g5+g6.
frequencies test.
if (year eq 1993 and cso_ref gt
80000000) cso_ref=cso_ref-90000000.
* THROUGHOUT IF DATA POST
2001 IS ADDED, NEW LINES NEED
TO BE ADDED FOR ADDITONAL
YEARS.
if (year eq 1970) g1_70=g1*rnet_pm.
if (year eq 1971) g1_71=g1*rnet_pm.
if (year eq 1972) g1_72=g1*rnet_pm.
if (year eq 1973) g1_73=g1*rnet_pm.
if (year eq 1974) g1_74=g1*rnet_pm.
if (year eq 1975) g1_75=g1*rnet_pm.
if (year eq 1976) g1_76=g1*rnet_pm.
if (year eq 1977) g1_77=g1*rnet_pm.
if (year eq 1978) g1_78=g1*rnet_pm.
if (year eq 1979) g1_79=g1*rnet_pm.
if (year eq 1980) g1_80=g1*rnet_pm.
if (year eq 1981) g1_81=g1*rnet_pm.
if (year eq 1982) g1_82=g1*rnet_pm.
if (year eq 1983) g1_83=g1*rnet_pm.
if (year eq 1984) g1_84=g1*rnet_pm.
if (year eq 1985) g1_85=g1*rnet_pm.
if (year eq 1986) g1_86=g1*rnet_pm.
if (year eq 1987) g1_87=g1*rnet_pm.
if (year eq 1988) g1_88=g1*rnet_pm.
if (year eq 1989) g1_89=g1*rnet_pm.
if (year eq 1990) g1_90=g1*rnet_pm.
if (year eq 1991) g1_91=g1*rnet_pm.
if (year eq 1992) g1_92=g1*rnet_pm.
if (year eq 1993) g1_93=g1*rnet_pm.
if (year eq 1994) g1_94=g1*rnet_pm.
if (year eq 1995) g1_95=g1*rnet_pm.
if (year eq 1996) g1_96=g1*rnet_pm.
if (year eq 1997) g1_97=g1*rnet_pm.
if (year eq 1998) g1_98=g1*rnet_pm.
if (year eq 1999) g1_99=g1*rnet_pm.
if (year eq 2000) g1_00=g1*rnet_pm.
if (year eq 2001) g1_01=g1*rnet_pm.
* E.G. IF 2002 DATA IS BEING
ADDED, ADD NEW LINE HERE AND
REPEAT FOR ALL OTHER ENTRIES
WHERE 2002 NEEDS TO BE ADDED.
if (year eq 1970) g2_70=g2*rnet_pm.
if (year eq 1971) g2_71=g2*rnet_pm.
if (year eq 1972) g2_72=g2*rnet_pm.
if (year eq 1973) g2_73=g2*rnet_pm.
if (year eq 1974) g2_74=g2*rnet_pm.
if (year eq 1975) g2_75=g2*rnet_pm.
if (year eq 1976) g2_76=g2*rnet_pm.
if (year eq 1977) g2_77=g2*rnet_pm.
if (year eq 1978) g2_78=g2*rnet_pm.
if (year eq 1979) g2_79=g2*rnet_pm.
if (year eq 1980) g2_80=g2*rnet_pm.
if (year eq 1981) g2_81=g2*rnet_pm.
if (year eq 1982) g2_82=g2*rnet_pm.
if (year eq 1983) g2_83=g2*rnet_pm.
if (year eq 1984) g2_84=g2*rnet_pm.
if (year eq 1985) g2_85=g2*rnet_pm.
if (year eq 1986) g2_86=g2*rnet_pm.
if (year eq 1987) g2_87=g2*rnet_pm.
if (year eq 1988) g2_88=g2*rnet_pm.
if (year eq 1989) g2_89=g2*rnet_pm.
if (year eq 1990) g2_90=g2*rnet_pm.
if (year eq 1991) g2_91=g2*rnet_pm.
if (year eq 1992) g2_92=g2*rnet_pm.
if (year eq 1993) g2_93=g2*rnet_pm.
if (year eq 1994) g2_94=g2*rnet_pm.
if (year eq 1995) g2_95=g2*rnet_pm.
if (year eq 1996) g2_96=g2*rnet_pm.
47
if (year eq 1997) g2_97=g2*rnet_pm.
if (year eq 1998) g2_98=g2*rnet_pm.
if (year eq 1999) g2_99=g2*rnet_pm.
if (year eq 2000) g2_00=g2*rnet_pm.
if (year eq 2001) g2_01=g2*rnet_pm.
if (year eq 1970) g3_70=g3*rnet_pm.
if (year eq 1971) g3_71=g3*rnet_pm.
if (year eq 1972) g3_72=g3*rnet_pm.
if (year eq 1973) g3_73=g3*rnet_pm.
if (year eq 1974) g3_74=g3*rnet_pm.
if (year eq 1975) g3_75=g3*rnet_pm.
if (year eq 1976) g3_76=g3*rnet_pm.
if (year eq 1977) g3_77=g3*rnet_pm.
if (year eq 1978) g3_78=g3*rnet_pm.
if (year eq 1979) g3_79=g3*rnet_pm.
if (year eq 1980) g3_80=g3*rnet_pm.
if (year eq 1981) g3_81=g3*rnet_pm.
if (year eq 1982) g3_82=g3*rnet_pm.
if (year eq 1983) g3_83=g3*rnet_pm.
if (year eq 1984) g3_84=g3*rnet_pm.
if (year eq 1985) g3_85=g3*rnet_pm.
if (year eq 1986) g3_86=g3*rnet_pm.
if (year eq 1987) g3_87=g3*rnet_pm.
if (year eq 1988) g3_88=g3*rnet_pm.
if (year eq 1989) g3_89=g3*rnet_pm.
if (year eq 1990) g3_90=g3*rnet_pm.
if (year eq 1991) g3_91=g3*rnet_pm.
if (year eq 1992) g3_92=g3*rnet_pm.
if (year eq 1993) g3_93=g3*rnet_pm.
if (year eq 1994) g3_94=g3*rnet_pm.
if (year eq 1995) g3_95=g3*rnet_pm.
if (year eq 1996) g3_96=g3*rnet_pm.
if (year eq 1997) g3_97=g3*rnet_pm.
if (year eq 1998) g3_98=g3*rnet_pm.
if (year eq 1999) g3_99=g3*rnet_pm.
if (year eq 2000) g3_00=g3*rnet_pm.
if (year eq 2001) g3_01=g3*rnet_pm.
if (year eq 1970) g4_70=g4*rnet_pm.
if (year eq 1971) g4_71=g4*rnet_pm.
if (year eq 1972) g4_72=g4*rnet_pm.
if (year eq 1973) g4_73=g4*rnet_pm.
if (year eq 1974) g4_74=g4*rnet_pm.
if (year eq 1975) g4_75=g4*rnet_pm.
if (year eq 1976) g4_76=g4*rnet_pm.
if (year eq 1977) g4_77=g4*rnet_pm.
if (year eq 1978) g4_78=g4*rnet_pm.
if (year eq 1979) g4_79=g4*rnet_pm.
if (year eq 1980) g4_80=g4*rnet_pm.
if (year eq 1981) g4_81=g4*rnet_pm.
if (year eq 1982) g4_82=g4*rnet_pm.
if (year eq 1983) g4_83=g4*rnet_pm.
if (year eq 1984) g4_84=g4*rnet_pm.
if (year eq 1985) g4_85=g4*rnet_pm.
if (year eq 1986) g4_86=g4*rnet_pm.
if (year eq 1987) g4_87=g4*rnet_pm.
if (year eq 1988) g4_88=g4*rnet_pm.
if (year eq 1989) g4_89=g4*rnet_pm.
if (year eq 1990) g4_90=g4*rnet_pm.
if (year eq 1991) g4_91=g4*rnet_pm.
if (year eq 1992) g4_92=g4*rnet_pm.
if (year eq 1993) g4_93=g4*rnet_pm.
if (year eq 1994) g4_94=g4*rnet_pm.
if (year eq 1995) g4_95=g4*rnet_pm.
if (year eq 1996) g4_96=g4*rnet_pm.
if (year eq 1997) g4_97=g4*rnet_pm.
if (year eq 1998) g4_98=g4*rnet_pm.
if (year eq 1999) g4_99=g4*rnet_pm.
if (year eq 2000) g4_00=g4*rnet_pm.
if (year eq 2001) g4_01=g4*rnet_pm.
if (year eq 1970) g5_70=g5*rnet_pm.
if (year eq 1971) g5_71=g5*rnet_pm.
if (year eq 1972) g5_72=g5*rnet_pm.
if (year eq 1973) g5_73=g5*rnet_pm.
if (year eq 1974) g5_74=g5*rnet_pm.
if (year eq 1975) g5_75=g5*rnet_pm.
if (year eq 1976) g5_76=g5*rnet_pm.
if (year eq 1977) g5_77=g5*rnet_pm.
if (year eq 1978) g5_78=g5*rnet_pm.
if (year eq 1979) g5_79=g5*rnet_pm.
if (year eq 1980) g5_80=g5*rnet_pm.
if (year eq 1981) g5_81=g5*rnet_pm.
if (year eq 1982) g5_82=g5*rnet_pm.
if (year eq 1983) g5_83=g5*rnet_pm.
if (year eq 1984) g5_84=g5*rnet_pm.
if (year eq 1985) g5_85=g5*rnet_pm.
if (year eq 1986) g5_86=g5*rnet_pm.
if (year eq 1987) g5_87=g5*rnet_pm.
if (year eq 1988) g5_88=g5*rnet_pm.
if (year eq 1989) g5_89=g5*rnet_pm.
48
if (year eq 1990) g5_90=g5*rnet_pm.
if (year eq 1991) g5_91=g5*rnet_pm.
if (year eq 1992) g5_92=g5*rnet_pm.
if (year eq 1993) g5_93=g5*rnet_pm.
if (year eq 1994) g5_94=g5*rnet_pm.
if (year eq 1995) g5_95=g5*rnet_pm.
if (year eq 1996) g5_96=g5*rnet_pm.
if (year eq 1997) g5_97=g5*rnet_pm.
if (year eq 1998) g5_98=g5*rnet_pm.
if (year eq 1999) g5_99=g5*rnet_pm.
if (year eq 2000) g5_00=g5*rnet_pm.
if (year eq 2001) g5_01=g5*rnet_pm.
if (year eq 1970) g6_70=g6*rnet_pm.
if (year eq 1971) g6_71=g6*rnet_pm.
if (year eq 1972) g6_72=g6*rnet_pm.
if (year eq 1973) g6_73=g6*rnet_pm.
if (year eq 1974) g6_74=g6*rnet_pm.
if (year eq 1975) g6_75=g6*rnet_pm.
if (year eq 1976) g6_76=g6*rnet_pm.
if (year eq 1977) g6_77=g6*rnet_pm.
if (year eq 1978) g6_78=g6*rnet_pm.
if (year eq 1979) g6_79=g6*rnet_pm.
if (year eq 1980) g6_80=g6*rnet_pm.
if (year eq 1981) g6_81=g6*rnet_pm.
if (year eq 1982) g6_82=g6*rnet_pm.
if (year eq 1983) g6_83=g6*rnet_pm.
if (year eq 1984) g6_84=g6*rnet_pm.
if (year eq 1985) g6_85=g6*rnet_pm.
if (year eq 1986) g6_86=g6*rnet_pm.
if (year eq 1987) g6_87=g6*rnet_pm.
if (year eq 1988) g6_88=g6*rnet_pm.
if (year eq 1989) g6_89=g6*rnet_pm.
if (year eq 1990) g6_90=g6*rnet_pm.
if (year eq 1991) g6_91=g6*rnet_pm.
if (year eq 1992) g6_92=g6*rnet_pm.
if (year eq 1993) g6_93=g6*rnet_pm.
if (year eq 1994) g6_94=g6*rnet_pm.
if (year eq 1995) g6_95=g6*rnet_pm.
if (year eq 1996) g6_96=g6*rnet_pm.
if (year eq 1997) g6_97=g6*rnet_pm.
if (year eq 1998) g6_98=g6*rnet_pm.
if (year eq 1999) g6_99=g6*rnet_pm.
if (year eq 2000) g6_00=g6*rnet_pm.
if (year eq 2001) g6_01=g6*rnet_pm.
if missing(g1_70) g1_70=0.
if missing(g1_71) g1_71=0.
if missing(g1_72) g1_72=0.
if missing(g1_73) g1_73=0.
if missing(g1_74) g1_74=0.
if missing(g1_75) g1_75=0.
if missing(g1_76) g1_76=0.
if missing(g1_77) g1_77=0.
if missing(g1_78) g1_78=0.
if missing(g1_79) g1_79=0.
if missing(g1_80) g1_80=0.
if missing(g1_81) g1_81=0.
if missing(g1_82) g1_82=0.
if missing(g1_83) g1_83=0.
if missing(g1_84) g1_84=0.
if missing(g1_85) g1_85=0.
if missing(g1_86) g1_86=0.
if missing(g1_87) g1_87=0.
if missing(g1_88) g1_88=0.
if missing(g1_89) g1_89=0.
if missing(g1_90) g1_90=0.
if missing(g1_91) g1_91=0.
if missing(g1_92) g1_92=0.
if missing(g1_93) g1_93=0.
if missing(g1_94) g1_94=0.
if missing(g1_95) g1_95=0.
if missing(g1_96) g1_96=0.
if missing(g1_97) g1_97=0.
if missing(g1_98) g1_98=0.
if missing(g1_99) g1_99=0.
if missing(g1_00) g1_00=0.
if missing(g1_01) g1_01=0.
if missing(g2_70) g2_70=0.
if missing(g2_71) g2_71=0.
if missing(g2_72) g2_72=0.
if missing(g2_73) g2_73=0.
if missing(g2_74) g2_74=0.
if missing(g2_75) g2_75=0.
if missing(g2_76) g2_76=0.
if missing(g2_77) g2_77=0.
if missing(g2_78) g2_78=0.
if missing(g2_79) g2_79=0.
if missing(g2_80) g2_80=0.
if missing(g2_81) g2_81=0.
49
if missing(g2_82) g2_82=0.
if missing(g2_83) g2_83=0.
if missing(g2_84) g2_84=0.
if missing(g2_85) g2_85=0.
if missing(g2_86) g2_86=0.
if missing(g2_87) g2_87=0.
if missing(g2_88) g2_88=0.
if missing(g2_89) g2_89=0.
if missing(g2_90) g2_90=0.
if missing(g2_91) g2_91=0.
if missing(g2_92) g2_92=0.
if missing(g2_93) g2_93=0.
if missing(g2_94) g2_94=0.
if missing(g2_95) g2_95=0.
if missing(g2_96) g2_96=0.
if missing(g2_97) g2_97=0.
if missing(g2_98) g2_98=0.
if missing(g2_99) g2_99=0.
if missing(g2_00) g2_00=0.
if missing(g2_01) g2_01=0.
if missing(g3_70) g3_70=0.
if missing(g3_71) g3_71=0.
if missing(g3_72) g3_72=0.
if missing(g3_73) g3_73=0.
if missing(g3_74) g3_74=0.
if missing(g3_75) g3_75=0.
if missing(g3_76) g3_76=0.
if missing(g3_77) g3_77=0.
if missing(g3_78) g3_78=0.
if missing(g3_79) g3_79=0.
if missing(g3_80) g3_80=0.
if missing(g3_81) g3_81=0.
if missing(g3_82) g3_82=0.
if missing(g3_83) g3_83=0.
if missing(g3_84) g3_84=0.
if missing(g3_85) g3_85=0.
if missing(g3_86) g3_86=0.
if missing(g3_87) g3_87=0.
if missing(g3_88) g3_88=0.
if missing(g3_89) g3_89=0.
if missing(g3_90) g3_90=0.
if missing(g3_91) g3_91=0.
if missing(g3_92) g3_92=0.
if missing(g3_93) g3_93=0.
if missing(g3_94) g3_94=0.
if missing(g3_95) g3_95=0.
if missing(g3_96) g3_96=0.
if missing(g3_97) g3_97=0.
if missing(g3_98) g3_98=0.
if missing(g3_99) g3_99=0.
if missing(g3_00) g3_00=0.
if missing(g3_01) g3_01=0.
if missing(g4_70) g4_70=0.
if missing(g4_71) g4_71=0.
if missing(g4_72) g4_72=0.
if missing(g4_73) g4_73=0.
if missing(g4_74) g4_74=0.
if missing(g4_75) g4_75=0.
if missing(g4_76) g4_76=0.
if missing(g4_77) g4_77=0.
if missing(g4_78) g4_78=0.
if missing(g4_79) g4_79=0.
if missing(g4_80) g4_80=0.
if missing(g4_81) g4_81=0.
if missing(g4_82) g4_82=0.
if missing(g4_83) g4_83=0.
if missing(g4_84) g4_84=0.
if missing(g4_85) g4_85=0.
if missing(g4_86) g4_86=0.
if missing(g4_87) g4_87=0.
if missing(g4_88) g4_88=0.
if missing(g4_89) g4_89=0.
if missing(g4_90) g4_90=0.
if missing(g4_91) g4_91=0.
if missing(g4_92) g4_92=0.
if missing(g4_93) g4_93=0.
if missing(g4_94) g4_94=0.
if missing(g4_95) g4_95=0.
if missing(g4_96) g4_96=0.
if missing(g4_97) g4_97=0.
if missing(g4_98) g4_98=0.
if missing(g4_99) g4_99=0.
if missing(g4_00) g4_00=0.
if missing(g4_01) g4_01=0.
if missing(g5_70) g5_70=0.
if missing(g5_71) g5_71=0.
if missing(g5_72) g5_72=0.
if missing(g5_73) g5_73=0.
if missing(g5_74) g5_74=0.
50
if missing(g5_75) g5_75=0.
if missing(g5_76) g5_76=0.
if missing(g5_77) g5_77=0.
if missing(g5_78) g5_78=0.
if missing(g5_79) g5_79=0.
if missing(g5_80) g5_80=0.
if missing(g5_81) g5_81=0.
if missing(g5_82) g5_82=0.
if missing(g5_83) g5_83=0.
if missing(g5_84) g5_84=0.
if missing(g5_85) g5_85=0.
if missing(g5_86) g5_86=0.
if missing(g5_87) g5_87=0.
if missing(g5_88) g5_88=0.
if missing(g5_89) g5_89=0.
if missing(g5_90) g5_90=0.
if missing(g5_91) g5_91=0.
if missing(g5_92) g5_92=0.
if missing(g5_93) g5_93=0.
if missing(g5_94) g5_94=0.
if missing(g5_95) g5_95=0.
if missing(g5_96) g5_96=0.
if missing(g5_97) g5_97=0.
if missing(g5_98) g5_98=0.
if missing(g5_99) g5_99=0.
if missing(g5_00) g5_00=0.
if missing(g5_01) g5_01=0.
if missing(g6_70) g6_70=0.
if missing(g6_71) g6_71=0.
if missing(g6_72) g6_72=0.
if missing(g6_73) g6_73=0.
if missing(g6_74) g6_74=0.
if missing(g6_75) g6_75=0.
if missing(g6_76) g6_76=0.
if missing(g6_77) g6_77=0.
if missing(g6_78) g6_78=0.
if missing(g6_79) g6_79=0.
if missing(g6_80) g6_80=0.
if missing(g6_81) g6_81=0.
if missing(g6_82) g6_82=0.
if missing(g6_83) g6_83=0.
if missing(g6_84) g6_84=0.
if missing(g6_85) g6_85=0.
if missing(g6_86) g6_86=0.
if missing(g6_87) g6_87=0.
if missing(g6_88) g6_88=0.
if missing(g6_89) g6_89=0.
if missing(g6_90) g6_90=0.
if missing(g6_91) g6_91=0.
if missing(g6_92) g6_92=0.
if missing(g6_93) g6_93=0.
if missing(g6_94) g6_94=0.
if missing(g6_95) g6_95=0.
if missing(g6_96) g6_96=0.
if missing(g6_97) g6_97=0.
if missing(g6_98) g6_98=0.
if missing(g6_99) g6_99=0.
if missing(g6_00) g6_00=0.
if missing(g6_01) g6_01=0.
aggregate outfile='h:\files\capital
stock\flat.sav'
/break=cso_ref
/g1_70=sum(g1_70)
/g1_71=sum(g1_71)
/g1_72=sum(g1_72)
/g1_73=sum(g1_73)
/g1_74=sum(g1_74)
/g1_75=sum(g1_75)
/g1_76=sum(g1_76)
/g1_77=sum(g1_77)
/g1_78=sum(g1_78)
/g1_79=sum(g1_79)
/g1_80=sum(g1_80)
/g1_81=sum(g1_81)
/g1_82=sum(g1_82)
/g1_83=sum(g1_83)
/g1_84=sum(g1_84)
/g1_85=sum(g1_85)
/g1_86=sum(g1_86)
/g1_87=sum(g1_87)
/g1_88=sum(g1_88)
/g1_89=sum(g1_89)
/g1_90=sum(g1_90)
/g1_91=sum(g1_91)
/g1_92=sum(g1_92)
/g1_93=sum(g1_93)
/g1_94=sum(g1_94)
/g1_95=sum(g1_95)
/g1_96=sum(g1_96)
51
/g1_97=sum(g1_97)
/g1_98=sum(g1_98)
/g1_99=sum(g1_99)
/g1_00=sum(g1_00)
/g1_01=sum(g1_01)
/g2_70=sum(g2_70)
/g2_71=sum(g2_71)
/g2_72=sum(g2_72)
/g2_73=sum(g2_73)
/g2_74=sum(g2_74)
/g2_75=sum(g2_75)
/g2_76=sum(g2_76)
/g2_77=sum(g2_77)
/g2_78=sum(g2_78)
/g2_79=sum(g2_79)
/g2_80=sum(g2_80)
/g2_81=sum(g2_81)
/g2_82=sum(g2_82)
/g2_83=sum(g2_83)
/g2_84=sum(g2_84)
/g2_85=sum(g2_85)
/g2_86=sum(g2_86)
/g2_87=sum(g2_87)
/g2_88=sum(g2_88)
/g2_89=sum(g2_89)
/g2_90=sum(g2_90)
/g2_91=sum(g2_91)
/g2_92=sum(g2_92)
/g2_93=sum(g2_93)
/g2_94=sum(g2_94)
/g2_95=sum(g2_95)
/g2_96=sum(g2_96)
/g2_97=sum(g2_97)
/g2_98=sum(g2_98)
/g2_99=sum(g2_99)
/g2_00=sum(g2_00)
/g2_01=sum(g2_01)
/g3_70=sum(g3_70)
/g3_71=sum(g3_71)
/g3_72=sum(g3_72)
/g3_73=sum(g3_73)
/g3_74=sum(g3_74)
/g3_75=sum(g3_75)
/g3_76=sum(g3_76)
/g3_77=sum(g3_77)
/g3_78=sum(g3_78)
/g3_79=sum(g3_79)
/g3_80=sum(g3_80)
/g3_81=sum(g3_81)
/g3_82=sum(g3_82)
/g3_83=sum(g3_83)
/g3_84=sum(g3_84)
/g3_85=sum(g3_85)
/g3_86=sum(g3_86)
/g3_87=sum(g3_87)
/g3_88=sum(g3_88)
/g3_89=sum(g3_89)
/g3_90=sum(g3_90)
/g3_91=sum(g3_91)
/g3_92=sum(g3_92)
/g3_93=sum(g3_93)
/g3_94=sum(g3_94)
/g3_95=sum(g3_95)
/g3_96=sum(g3_96)
/g3_97=sum(g3_97)
/g3_98=sum(g3_98)
/g3_99=sum(g3_99)
/g3_00=sum(g3_00)
/g3_01=sum(g3_01)
/g4_70=sum(g4_70)
/g4_71=sum(g4_71)
/g4_72=sum(g4_72)
/g4_73=sum(g4_73)
/g4_74=sum(g4_74)
/g4_75=sum(g4_75)
/g4_76=sum(g4_76)
/g4_77=sum(g4_77)
/g4_78=sum(g4_78)
/g4_79=sum(g4_79)
/g4_80=sum(g4_80)
/g4_81=sum(g4_81)
/g4_82=sum(g4_82)
/g4_83=sum(g4_83)
/g4_84=sum(g4_84)
/g4_85=sum(g4_85)
/g4_86=sum(g4_86)
/g4_87=sum(g4_87)
/g4_88=sum(g4_88)
/g4_89=sum(g4_89)
/g4_90=sum(g4_90)
/g4_91=sum(g4_91)
52
/g4_92=sum(g4_92)
/g4_93=sum(g4_93)
/g4_94=sum(g4_94)
/g4_95=sum(g4_95)
/g4_96=sum(g4_96)
/g4_97=sum(g4_97)
/g4_98=sum(g4_98)
/g4_99=sum(g4_99)
/g4_00=sum(g4_00)
/g4_01=sum(g4_01)
/g5_70=sum(g5_70)
/g5_71=sum(g5_71)
/g5_72=sum(g5_72)
/g5_73=sum(g5_73)
/g5_74=sum(g5_74)
/g5_75=sum(g5_75)
/g5_76=sum(g5_76)
/g5_77=sum(g5_77)
/g5_78=sum(g5_78)
/g5_79=sum(g5_79)
/g5_80=sum(g5_80)
/g5_81=sum(g5_81)
/g5_82=sum(g5_82)
/g5_83=sum(g5_83)
/g5_84=sum(g5_84)
/g5_85=sum(g5_85)
/g5_86=sum(g5_86)
/g5_87=sum(g5_87)
/g5_88=sum(g5_88)
/g5_89=sum(g5_89)
/g5_90=sum(g5_90)
/g5_91=sum(g5_91)
/g5_92=sum(g5_92)
/g5_93=sum(g5_93)
/g5_94=sum(g5_94)
/g5_95=sum(g5_95)
/g5_96=sum(g5_96)
/g5_97=sum(g5_97)
/g5_98=sum(g5_98)
/g5_99=sum(g5_99)
/g5_00=sum(g5_00)
/g5_01=sum(g5_01)
/g6_70=sum(g6_70)
/g6_71=sum(g6_71)
/g6_72=sum(g6_72)
/g6_73=sum(g6_73)
/g6_74=sum(g6_74)
/g6_75=sum(g6_75)
/g6_76=sum(g6_76)
/g6_77=sum(g6_77)
/g6_78=sum(g6_78)
/g6_79=sum(g6_79)
/g6_80=sum(g6_80)
/g6_81=sum(g6_81)
/g6_82=sum(g6_82)
/g6_83=sum(g6_83)
/g6_84=sum(g6_84)
/g6_85=sum(g6_85)
/g6_86=sum(g6_86)
/g6_87=sum(g6_87)
/g6_88=sum(g6_88)
/g6_89=sum(g6_89)
/g6_90=sum(g6_90)
/g6_91=sum(g6_91)
/g6_92=sum(g6_92)
/g6_93=sum(g6_93)
/g6_94=sum(g6_94)
/g6_95=sum(g6_95)
/g6_96=sum(g6_96)
/g6_97=sum(g6_97)
/g6_98=sum(g6_98)
/g6_99=sum(g6_99)
/g6_00=sum(g6_00)
/g6_01=sum(g6_01).
get file='h:\files\capital stock\flat.sav'.
compute
gs6_01=g6_01+g6_00+g6_99+g6_98+g
6_97+g6_96+g6_95+g6_94+g6_93+g6_
92+g6_91+g6_90+g6_89+g6_88+g6_87
+g6_86+g6_85+g6_84+
g6_83+g6_82+g6_81+g6_80+g6_79+g6
_78+g6_77+g6_76+g6_75+g6_74+g6_7
3+g6_72+g6_71+g6_70.
compute gs6_00=gs6_01-g6_01.
compute gs6_99=gs6_00-g6_00.
compute gs6_98=gs6_99-g6_99.
compute gs6_97=gs6_98-g6_98.
compute gs6_96=gs6_97-g6_97.
53
compute gs6_95=gs6_96-g6_96.
compute gs6_94=gs6_95-g6_95.
compute gs6_93=gs6_94-g6_94.
compute gs6_92=gs6_93-g6_93.
compute gs6_91=gs6_92-g6_92.
compute gs6_90=gs6_91-g6_91.
compute gs6_89=gs6_90-g6_90.
compute gs6_88=gs6_89-g6_89.
compute gs6_87=gs6_88-g6_88.
compute gs6_86=gs6_87-g6_87.
compute gs6_85=gs6_86-g6_86.
compute gs6_84=gs6_85-g6_85.
compute gs6_83=gs6_84-g6_84.
compute gs6_82=gs6_83-g6_83.
compute gs6_81=gs6_82-g6_82.
compute gs6_80=gs6_81-g6_81.
compute gs6_79=gs6_80-g6_80.
compute gs6_78=gs6_79-g6_79.
compute gs6_77=gs6_78-g6_78.
compute gs6_76=gs6_77-g6_77.
compute gs6_75=gs6_76-g6_76.
compute gs6_74=gs6_75-g6_75.
compute gs6_73=gs6_74-g6_74.
compute gs6_72=gs6_73-g6_73.
compute gs6_71=gs6_72-g6_72.
compute gs6_70=gs6_71-g6_71.
compute
gs5_01=g5_01+g5_00+g5_99+g5_98+g
5_97+g5_96+g5_95+g5_94+
g5_93+g5_92+g5_91+g5_90+g5_89+g5
_88+g5_87+g5_86+g5_85+g5_84+g5_8
3+g5_82+g5_81+
g5_80+g5_79+g5_78+g5_77+g5_76.
compute gs5_00=gs5_01-g5_01+g5_75.
compute gs5_99=gs5_00-g5_00+g5_74.
compute gs5_98=gs5_99-g5_99+g5_73.
compute gs5_97=gs5_98-g5_98+g5_72.
compute gs5_96=gs5_97-g5_97+g5_71.
compute gs5_95=gs5_96-g5_96+g5_70.
compute gs5_94=gs5_95-g5_95.
compute gs5_93=gs5_94-g5_94.
compute gs5_92=gs5_93-g5_93.
compute gs5_91=gs5_92-g5_92.
compute gs5_90=gs5_91-g5_91.
compute gs5_89=gs5_90-g5_90.
compute gs5_88=gs5_89-g5_89.
compute gs5_87=gs5_88-g5_88.
compute gs5_86=gs5_87-g5_87.
compute gs5_85=gs5_86-g5_86.
compute gs5_84=gs5_85-g5_85.
compute gs5_83=gs5_84-g5_84.
compute gs5_82=gs5_83-g5_83.
compute gs5_81=gs5_82-g5_82.
compute gs5_80=gs5_81-g5_81.
compute gs5_79=gs5_80-g5_80.
compute gs5_78=gs5_79-g5_79.
compute gs5_77=gs5_78-g5_78.
compute gs5_76=gs5_77-g5_77.
compute gs5_75=gs5_76-g5_76.
compute gs5_74=gs5_75-g5_75.
compute gs5_73=gs5_74-g5_74.
compute gs5_72=gs5_73-g5_73.
compute gs5_71=gs5_72-g5_72.
compute gs5_70=gs5_71-g5_71.
compute
gs4_01=g4_01+g4_00+g4_99+g4_98+g
4_97+g4_96+g4_95+g4_94+
g4_93+g4_92+g4_91+g4_90+g4_89+g4
_88+g4_87+g4_86+g4_85+g4_84+g4_8
3.
compute gs4_00=gs4_01-g4_01+g4_82.
compute gs4_99=gs4_00-g4_00+g4_81.
compute gs4_98=gs4_99-g4_99+g4_80.
compute gs4_97=gs4_98-g4_98+g4_79.
compute gs4_96=gs4_97-g4_97+g4_78.
compute gs4_95=gs4_96-g4_96+g4_77.
compute gs4_94=gs4_95-g4_95+g4_76.
compute gs4_93=gs4_94-g4_94+g4_75.
compute gs4_92=gs4_93-g4_93+g4_74.
compute gs4_91=gs4_92-g4_92+g4_73.
compute gs4_90=gs4_91-g4_91+g4_72.
compute gs4_89=gs4_90-g4_90+g4_71.
compute gs4_88=gs4_89-g4_89+g4_70.
compute gs4_87=gs4_88-g4_88.
compute gs4_86=gs4_87-g4_87.
compute gs4_85=gs4_86-g4_86.
compute gs4_84=gs4_85-g4_85.
compute gs4_83=gs4_84-g4_84.
54
compute gs4_82=gs4_83-g4_83.
compute gs4_81=gs4_82-g4_82.
compute gs4_80=gs4_81-g4_81.
compute gs4_79=gs4_80-g4_80.
compute gs4_78=gs4_79-g4_79.
compute gs4_77=gs4_78-g4_78.
compute gs4_76=gs4_77-g4_77.
compute gs4_75=gs4_76-g4_76.
compute gs4_74=gs4_75-g4_75.
compute gs4_73=gs4_74-g4_74.
compute gs4_72=gs4_73-g4_73.
compute gs4_71=gs4_72-g4_72.
compute gs4_70=gs4_71-g4_71.
compute
gs3_01=g3_01+g3_00+g3_99+g3_98+g
3_97+g3_96+g3_95+g3_94+
g3_93+g3_92+g3_91+g3_90+g3_89+g3
_88.
compute gs3_00=gs3_01-g3_01+g3_87.
compute gs3_99=gs3_00-g3_00+g3_86.
compute gs3_98=gs3_99-g3_99+g3_85.
compute gs3_97=gs3_98-g3_98+g3_84.
compute gs3_96=gs3_97-g3_97+g3_83.
compute gs3_95=gs3_96-g3_96+g3_82.
compute gs3_94=gs3_95-g3_95+g3_81.
compute gs3_93=gs3_94-g3_94+g3_80.
compute gs3_92=gs3_93-g3_93+g3_79.
compute gs3_91=gs3_92-g3_92+g3_78.
compute gs3_90=gs3_91-g3_91+g3_77.
compute gs3_89=gs3_90-g3_90+g3_76.
compute gs3_88=gs3_89-g3_89+g3_75.
compute gs3_87=gs3_88-g3_88+g3_74.
compute gs3_86=gs3_87-g3_87+g3_73.
compute gs3_85=gs3_86-g3_86+g3_72.
compute gs3_84=gs3_85-g3_85+g3_71.
compute gs3_83=gs3_84-g3_84+g3_70.
compute gs3_82=gs3_83-g3_83.
compute gs3_81=gs3_82-g3_82.
compute gs3_80=gs3_81-g3_81.
compute gs3_79=gs3_80-g3_80.
compute gs3_78=gs3_79-g3_79.
compute gs3_77=gs3_78-g3_78.
compute gs3_76=gs3_77-g3_77.
compute gs3_75=gs3_76-g3_76.
compute gs3_74=gs3_75-g3_75.
compute gs3_73=gs3_74-g3_74.
compute gs3_72=gs3_73-g3_73.
compute gs3_71=gs3_72-g3_72.
compute gs3_70=gs3_71-g3_71.
compute
gs2_01=g2_01+g2_00+g2_99+g2_98+g
2_97+g2_96+g2_95+g2_94+
g2_93+g2_92+g2_91+g2_90.
compute gs2_00=gs2_01-g2_01+g2_89.
compute gs2_99=gs2_00-g2_00+g2_88.
compute gs2_98=gs2_99-g2_99+g2_87.
compute gs2_97=gs2_98-g2_98+g2_86.
compute gs2_96=gs2_97-g2_97+g2_85.
compute gs2_95=gs2_96-g2_96+g2_84.
compute gs2_94=gs2_95-g2_95+g2_83.
compute gs2_93=gs2_94-g2_94+g2_82.
compute gs2_92=gs2_93-g2_93+g2_81.
compute gs2_91=gs2_92-g2_92+g2_80.
compute gs2_90=gs2_91-g2_91+g2_79.
compute gs2_89=gs2_90-g2_90+g2_78.
compute gs2_88=gs2_89-g2_89+g2_77.
compute gs2_87=gs2_88-g2_88+g2_76.
compute gs2_86=gs2_87-g2_87+g2_75.
compute gs2_85=gs2_86-g2_86+g2_74.
compute gs2_84=gs2_85-g2_85+g2_73.
compute gs2_83=gs2_84-g2_84+g2_72.
compute gs2_82=gs2_83-g2_83+g2_71.
compute gs2_81=gs2_82-g2_82+g2_70.
compute gs2_80=gs2_81-g2_81.
compute gs2_79=gs2_80-g2_80.
compute gs2_78=gs2_79-g2_79.
compute gs2_77=gs2_78-g2_78.
compute gs2_76=gs2_77-g2_77.
compute gs2_75=gs2_76-g2_76.
compute gs2_74=gs2_75-g2_75.
compute gs2_73=gs2_74-g2_74.
compute gs2_72=gs2_73-g2_73.
compute gs2_71=gs2_72-g2_72.
compute gs2_70=gs2_71-g2_71.
compute
gs1_01=g1_01+g1_00+g1_99+g1_98+g
1_97.
compute gs1_00=gs1_01-g1_01+g1_96.
55
compute gs1_99=gs1_00-g1_00+g1_95.
compute gs1_98=gs1_99-g1_99+g1_94.
compute gs1_97=gs1_98-g1_98+g1_93.
compute gs1_96=gs1_97-g1_97+g1_92.
compute gs1_95=gs1_96-g1_96+g1_91.
compute gs1_94=gs1_95-g1_95+g1_90.
compute gs1_93=gs1_94-g1_94+g1_89.
compute gs1_92=gs1_93-g1_93+g1_88.
compute gs1_91=gs1_92-g1_92+g1_87.
compute gs1_90=gs1_91-g1_91+g1_86.
compute gs1_89=gs1_90-g1_90+g1_85.
compute gs1_88=gs1_89-g1_89+g1_84.
compute gs1_87=gs1_88-g1_88+g1_83.
compute gs1_86=gs1_87-g1_87+g1_82.
compute gs1_85=gs1_86-g1_86+g1_81.
compute gs1_84=gs1_85-g1_85+g1_80.
compute gs1_83=gs1_84-g1_84+g1_79.
compute gs1_82=gs1_83-g1_83+g1_78.
compute gs1_81=gs1_82-g1_82+g1_77.
compute gs1_80=gs1_81-g1_81+g1_76.
compute gs1_79=gs1_80-g1_80+g1_75.
compute gs1_78=gs1_79-g1_79+g1_74.
compute gs1_77=gs1_78-g1_78+g1_73.
compute gs1_76=gs1_77-g1_77+g1_72.
compute gs1_75=gs1_76-g1_76+g1_71.
compute gs1_74=gs1_75-g1_75+g1_70.
compute gs1_73=gs1_74-g1_74.
compute gs1_72=gs1_73-g1_73.
compute gs1_71=gs1_72-g1_72.
compute gs1_70=gs1_71-g1_71.
compute
ns6_01=.973*g6_01+.9459*g6_00+.918
9*g6_99+.8919*g6_98+.8649*g6_97+.8
378*g6_96+.8108*g6_95+
.7838*g6_94+.7567*g6_93+.7297*g6_9
2+.7027*g6_91+.6757*g6_90+.6486*g6
_89+
.6216*g6_88+.5946*g6_87+.5676*g6_8
6+.5405*g6_85+.5135*g6_84+.4865*g6
_83+.4595*g6_82+.4324*g6_81+.4054*
g6_80+
.3783*g6_79+.3514*g6_78+.3244*g6_7
7+.2973*g6_76+.2703*g6_75+.2433*g6
_74+.2163*g6_73+.1893*g6_72+.1623*
g6_71+.1352*g6_70.
compute
ns6_00=.973*g6_00+.9459*g6_99+.918
9*g6_98+.8919*g6_97+.8649*g6_96+.8
378*g6_95+.8108*g6_94+
.7838*g6_93+.7567*g6_92+.7297*g6_9
1+.7027*g6_90+.6757*g6_89+.6486*g6
_88+
.6216*g6_87+.5946*g6_86+.5676*g6_8
5+.5405*g6_84+.5135*g6_83+.4865*g6
_82+.4595*g6_81+.4324*g6_80+.4054*
g6_79+
.3783*g6_78+.3514*g6_77+.3244*g6_7
6+.2973*g6_75+.2703*g6_74+.2433*g6
_73+.2163*g6_72+.1893*g6_71+.1623*
g6_70.
compute
ns6_99=.973*g6_99+.9459*g6_98+.918
9*g6_97+.8919*g6_96+.8649*g6_95+.8
378*g6_94+.8108*g6_93+
.7838*g6_92+.7567*g6_91+.7297*g6_9
0+.7027*g6_89+.6757*g6_88+.6486*g6
_87+
.6216*g6_86+.5946*g6_85+.5676*g6_8
4+.5405*g6_83+.5135*g6_82+.4865*g6
_81+.4595*g6_80+.4324*g6_79+.4054*
g6_78+
.3783*g6_77+.3514*g6_76+.3244*g6_7
5+.2973*g6_74+.2703*g6_73+.2433*g6
_72+.2163*g6_71+.1893*g6_70.
compute
ns6_98=.973*g6_98+.9459*g6_97+.918
9*g6_96+.8919*g6_95+.8649*g6_94+.8
378*g6_93+.8108*g6_92+
.7838*g6_91+.7567*g6_90+.7297*g6_8
9+.7027*g6_88+.6757*g6_87+.6486*g6
_86+
56
.6216*g6_85+.5946*g6_84+.5676*g6_8
3+.5405*g6_82+.5135*g6_81+.4865*g6
_80+.4595*g6_79+.4324*g6_78+.4054*
g6_77+
.3783*g6_76+.3514*g6_75+.3244*g6_7
4+.2973*g6_73+.2703*g6_72+.2433*g6
_71+.2163*g6_70.
compute
ns6_97=.973*g6_97+.9459*g6_96+.918
9*g6_95+.8919*g6_94+.8649*g6_93+.8
378*g6_92+.8108*g6_91+
.7838*g6_90+.7567*g6_89+.7297*g6_8
8+.7027*g6_87+.6757*g6_86+.6486*g6
_85+
.6216*g6_84+.5946*g6_83+.5676*g6_8
2+.5405*g6_81+.5135*g6_80+.4865*g6
_79+.4595*g6_78+.4324*g6_77+.4054*
g6_76+
.3783*g6_75+.3514*g6_74+.3244*g6_7
3+.2973*g6_72+.2703*g6_71+.2433*g6
_70.
compute
ns6_96=.973*g6_96+.9459*g6_95+.918
9*g6_94+.8919*g6_93+.8649*g6_92+.8
378*g6_91+.8108*g6_90+
.7838*g6_89+.7567*g6_88+.7297*g6_8
7+.7027*g6_86+.6757*g6_85+.6486*g6
_84+
.6216*g6_83+.5946*g6_82+.5676*g6_8
1+.5405*g6_80+.5135*g6_79+.4865*g6
_78+.4595*g6_77+.4324*g6_76+.4054*
g6_75+
.3783*g6_74+.3514*g6_73+.3244*g6_7
2+.2973*g6_71+.2703*g6_70.
compute
ns6_95=.973*g6_95+.9459*g6_94+.918
9*g6_93+.8919*g6_92+.8649*g6_91+.8
378*g6_90+.8108*g6_89+
.7838*g6_88+.7567*g6_87+.7297*g6_8
6+.7027*g6_85+.6757*g6_84+.6486*g6
_83+
.6216*g6_82+.5946*g6_81+.5676*g6_8
0+.5405*g6_79+.5135*g6_78+.4865*g6
_77+.4595*g6_76+.4324*g6_75+.4054*
g6_74+
.3783*g6_73+.3514*g6_72+.3244*g6_7
1+.2973*g6_70.
compute
ns6_94=.973*g6_94+.9459*g6_93+.918
9*g6_92+.8919*g6_91+.8649*g6_90+.8
378*g6_89+.8108*g6_88+
.7838*g6_87+.7567*g6_86+.7297*g6_8
5+.7027*g6_84+.6757*g6_83+.6486*g6
_82+
.6216*g6_81+.5946*g6_80+.5676*g6_7
9+.5405*g6_78+.5135*g6_77+.4865*g6
_76+.4595*g6_75+.4324*g6_74+.4054*
g6_73+
.3783*g6_72+.3514*g6_71+.3244*g6_7
0.
compute
ns6_93=.973*g6_93+.9459*g6_92+.918
9*g6_91+.8919*g6_90+.8649*g6_89+.8
378*g6_88+.8108*g6_87+
.7838*g6_86+.7567*g6_85+.7297*g6_8
4+.7027*g6_83+.6757*g6_82+.6486*g6
_81+
.6216*g6_80+.5946*g6_79+.5676*g6_7
8+.5405*g6_77+.5135*g6_76+.4865*g6
_75+.4595*g6_74+.4324*g6_73+.4054*
g6_72+
.3783*g6_71+.3514*g6_70.
compute
ns6_92=.973*g6_92+.9459*g6_91+.918
9*g6_90+.8919*g6_89+.8649*g6_88+.8
378*g6_87+.8108*g6_86+
57
.7838*g6_85+.7567*g6_84+.7297*g6_8
3+.7027*g6_82+.6757*g6_81+.6486*g6
_80+
.6216*g6_79+.5946*g6_78+.5676*g6_7
7+.5405*g6_76+.5135*g6_75+.4865*g6
_74+.4595*g6_73+.4324*g6_72+.4054*
g6_71+
.3783*g6_70.
compute
ns6_91=.973*g6_91+.9459*g6_90+.918
9*g6_89+.8919*g6_88+.8649*g6_87+.8
378*g6_86+.8108*g6_85+
.7838*g6_84+.7567*g6_83+.7297*g6_8
2+.7027*g6_81+.6757*g6_80+.6486*g6
_79+
.6216*g6_78+.5946*g6_77+.5676*g6_7
6+.5405*g6_75+.5135*g6_74+.4865*g6
_73+.4595*g6_72+.4324*g6_71+.4054*
g6_70.
compute
ns6_90=.973*g6_90+.9459*g6_89+.918
9*g6_88+.8919*g6_87+.8649*g6_86+.8
378*g6_85+.8108*g6_84+
.7838*g6_83+.7567*g6_82+.7297*g6_8
1+.7027*g6_80+.6757*g6_79+.6486*g6
_78+
.6216*g6_77+.5946*g6_76+.5676*g6_7
5+.5405*g6_74+.5135*g6_73+.4865*g6
_72+.4595*g6_71+.4324*g6_70.
compute
ns6_89=.973*g6_89+.9459*g6_88+.918
9*g6_87+.8919*g6_86+.8649*g6_85+.8
378*g6_84+.8108*g6_83+
.7838*g6_82+.7567*g6_81+.7297*g6_8
0+.7027*g6_79+.6757*g6_78+.6486*g6
_77+
4+.5405*g6_73+.5135*g6_72+.4865*g6
_71+.4595*g6_70.
compute
ns6_88=.973*g6_88+.9459*g6_87+.918
9*g6_86+.8919*g6_85+.8649*g6_84+.8
378*g6_83+.8108*g6_82+
.7838*g6_81+.7567*g6_80+.7297*g6_7
9+.7027*g6_78+.6757*g6_77+.6486*g6
_78+
.6216*g6_75+.5946*g6_74+.5676*g6_7
3+.5405*g6_72+.5135*g6_71+.4865*g6
_70.
compute
ns6_87=.973*g6_87+.9459*g6_86+.918
9*g6_85+.8919*g6_84+.8649*g6_83+.8
378*g6_82+.8108*g6_81+
.7838*g6_80+.7567*g6_79+.7297*g6_7
8+.7027*g6_77+.6757*g6_76+.6486*g6
_75+
.6216*g6_74+.5946*g6_73+.5676*g6_7
2+.5405*g6_71+.5135*g6_70.
compute
ns6_86=.973*g6_86+.9459*g6_85+.918
9*g6_84+.8919*g6_83+.8649*g6_82+.8
378*g6_81+.8108*g6_80+
.7838*g6_79+.7567*g6_78+.7297*g6_7
7+.7027*g6_76+.6757*g6_75+.6486*g6
_74+
.6216*g6_73+.5946*g6_72+.5676*g6_7
1+.5405*g6_70.
compute
ns6_85=.973*g6_85+.9459*g6_84+.918
9*g6_83+.8919*g6_82+.8649*g6_81+.8
378*g6_80+.8108*g6_79+
.7838*g6_78+.7567*g6_77+.7297*g6_7
6+.7027*g6_75+.6757*g6_74+.6486*g6
_73+
.6216*g6_76+.5946*g6_75+.5676*g6_7
58
.6216*g6_72+.5946*g6_71+.5676*g6_7
0.
compute
ns6_84=.973*g6_84+.9459*g6_83+.918
9*g6_82+.8919*g6_81+.8649*g6_80+.8
378*g6_79+.8108*g6_78+
.7838*g6_77+.7567*g6_76+.7297*g6_7
5+.7027*g6_74+.6757*g6_73+.6486*g6
_72+
.6216*g6_71+.5946*g6_70.
compute
ns6_83=.973*g6_83+.9459*g6_82+.918
9*g6_81+.8919*g6_80+.8649*g6_79+.8
378*g6_78+.8108*g6_77+
.7838*g6_76+.7567*g6_75+.7297*g6_7
4+.7027*g6_73+.6757*g6_72+.6486*g6
_71+
.6216*g6_70.
compute
ns6_82=.973*g6_82+.9459*g6_81+.918
9*g6_80+.8919*g6_79+.8649*g6_78+.8
378*g6_77+.8108*g6_76+
.7838*g6_75+.7567*g6_74+.7297*g6_7
3+.7027*g6_72+.6757*g6_71+.6486*g6
_70.
compute
ns6_81=.973*g6_81+.9459*g6_80+.918
9*g6_79+.8919*g6_78+.8649*g6_77+.8
378*g6_76+.8108*g6_75+
.7838*g6_74+.7567*g6_73+.7297*g6_7
2+.7027*g6_71+.6757*g6_70.
compute
ns6_80=.973*g6_80+.9459*g6_79+.918
9*g6_78+.8919*g6_77+.8649*g6_76+.8
378*g6_75+.8108*g6_74+
.7838*g6_73+.7567*g6_72+.7297*g6_7
1+.7027*g6_70.
compute
ns6_79=.973*g6_79+.9459*g6_78+.918
9*g6_77+.8919*g6_76+.8649*g6_75+.8
378*g6_74+.8108*g6_73+
.7838*g6_72+.7567*g6_71+.7297*g6_7
0.
compute
ns6_78=.973*g6_78+.9459*g6_77+.918
9*g6_76+.8919*g6_75+.8649*g6_74+.8
378*g6_73+.8108*g6_72+
.7838*g6_71+.7567*g6_70.
compute
ns6_77=.973*g6_77+.9459*g6_76+.918
9*g6_75+.8919*g6_74+.8649*g6_73+.8
378*g6_72+.8108*g6_71+
.7838*g6_70.
compute
ns6_76=.973*g6_76+.9459*g6_75+.918
9*g6_74+.8919*g6_73+.8649*g6_72+.8
378*g6_71+.8108*g6_70.
compute
ns6_75=.973*g6_75+.9459*g6_74+.918
9*g6_73+.8919*g6_72+.8649*g6_71+.8
378*g6_70.
compute
ns6_74=.973*g6_74+.9459*g6_73+.918
9*g6_72+.8919*g6_71+.8649*g6_70.
compute
ns6_73=.973*g6_73+.9459*g6_72+.918
9*g6_71+.8919*g6_70.
compute
ns6_72=.973*g6_72+.9459*g6_71+.918
9*g6_70.
compute
ns6_71=.973*g6_71+.9459*g6_70.
compute ns6_70=.973*g6_70.
compute
ns5_01=.9615*g5_01+.9231*g5_00+.88
46*g5_99+.8462*g5_98+.8077*g5_97+.
7692*g5_96+.7308*g5_95+
.6923*g5_94+.6538*g5_93+.6154*g5_9
2+.5769*g5_91+.5385*g5_90+.5*g5_89
+
.4615*g5_88+.4231*g5_87+.3846*g5_8
59
6+.3462*g5_85+.3077*g5_84+.2692*g5
_83+.2308*g5_82+.1923*g5_81+.1538*
g5_80+
.1154*g5_79+.0769*g5_78+.03848*g5_
77.
compute
ns5_00=.9615*g5_00+.9231*g5_99+.88
46*g5_98+.8462*g5_97+.8077*g5_96+.
7692*g5_95+.7308*g5_94+
.6923*g5_93+.6538*g5_92+.6154*g5_9
1+.5769*g5_90+.5385*g5_89+.5*g5_88
+
.4615*g5_87+.4231*g5_86+.3846*g5_8
5+.3462*g5_84+.3077*g5_83+.2692*g5
_82+.2308*g5_81+.1923*g5_80+.1538*
g5_79+
.1154*g5_78+.0769*g5_77+.03848*g5_
76.
compute
ns5_99=.9615*g5_99+.9231*g5_98+.88
46*g5_97+.8462*g5_96+.8077*g5_95+.
7692*g5_94+.7308*g5_93+
.6923*g5_92+.6538*g5_91+.6154*g5_9
0+.5769*g5_89+.5385*g5_88+.5*g5_87
+
.4615*g5_86+.4231*g5_85+.3846*g5_8
4+.3462*g5_83+.3077*g5_82+.2692*g5
_81+.2308*g5_80+.1923*g5_79+.1538*
g5_78+
.1154*g5_77+.0769*g5_76+.03848*g5_
75.
compute
ns5_98=.9615*g5_98+.9231*g5_97+.88
46*g5_96+.8462*g5_95+.8077*g5_94+.
7692*g5_93+.7308*g5_92+
.6923*g5_91+.6538*g5_90+.6154*g5_8
9+.5769*g5_88+.5385*g5_87+.5*g5_86
+
.4615*g5_85+.4231*g5_84+.3846*g5_8
3+.3462*g5_82+.3077*g5_81+.2692*g5
_80+.2308*g5_79+.1923*g5_78+.1538*
g5_77+
.1154*g5_76+.0769*g5_75+.03848*g5_
74.
compute
ns5_97=.9615*g5_97+.9231*g5_96+.88
46*g5_95+.8462*g5_94+.8077*g5_93+.
7692*g5_92+.7308*g5_91+
.6923*g5_90+.6538*g5_89+.6154*g5_8
8+.5769*g5_87+.5385*g5_86+.5*g5_85
+
.4615*g5_84+.4231*g5_83+.3846*g5_8
2+.3462*g5_81+.3077*g5_80+.2692*g5
_79+.2308*g5_78+.1923*g5_77+.1538*
g5_76+
.1154*g5_75+.0769*g5_74+.03848*g5_
73.
compute
ns5_96=.9615*g5_96+.9231*g5_95+.88
46*g5_94+.8462*g5_93+.8077*g5_92+.
7692*g5_91+.7308*g5_90+
.6923*g5_89+.6538*g5_88+.6154*g5_8
7+.5769*g5_86+.5385*g5_85+.5*g5_84
+
.4615*g5_83+.4231*g5_82+.3846*g5_8
1+.3462*g5_80+.3077*g5_79+.2692*g5
_78+.2308*g5_77+.1923*g5_76+.1538*
g5_75+
.1154*g5_74+.0769*g5_73+.03848*g5_
72.
compute
ns5_95=.9615*g5_95+.9231*g5_94+.88
46*g5_93+.8462*g5_92+.8077*g5_91+.
7692*g5_90+.7308*g5_89+
.6923*g5_88+.6538*g5_87+.6154*g5_8
60
6+.5769*g5_85+.5385*g5_84+.5*g5_83
+
3+.5769*g5_82+.5385*g5_81+.5*g5_80
+
.4615*g5_82+.4231*g5_81+.3846*g5_8
0+.3462*g5_79+.3077*g5_78+.2692*g5
_77+.2308*g5_76+.1923*g5_75+.1538*
g5_74+
.4615*g5_79+.4231*g5_78+.3846*g5_7
7+.3462*g5_76+.3077*g5_75+.2692*g5
_74+.2308*g5_73+.1923*g5_72+.1538*
g5_71+
.1154*g5_70.
compute
ns5_91=.9615*g5_91+.9231*g5_90+.88
46*g5_89+.8462*g5_88+.8077*g5_87+.
7692*g5_86+.7308*g5_85+
.1154*g5_73+.0769*g5_72+.03848*g5_
71.
compute
ns5_94=.9615*g5_94+.9231*g5_93+.88
46*g5_92+.8462*g5_91+.8077*g5_90+.
7692*g5_89+.7308*g5_88+
.6923*g5_87+.6538*g5_86+.6154*g5_8
5+.5769*g5_84+.5385*g5_83+.5*g5_82
+
.4615*g5_81+.4231*g5_80+.3846*g5_7
9+.3462*g5_78+.3077*g5_77+.2692*g5
_76+.2308*g5_75+.1923*g5_74+.1538*
g5_73+
.1154*g5_72+.0769*g5_71+.03848*g5_
70.
compute
ns5_93=.9615*g5_93+.9231*g5_92+.88
46*g5_91+.8462*g5_90+.8077*g5_89+.
7692*g5_88+.7308*g5_87+
.6923*g5_86+.6538*g5_85+.6154*g5_8
4+.5769*g5_83+.5385*g5_82+.5*g5_81
+
.4615*g5_80+.4231*g5_79+.3846*g5_7
8+.3462*g5_77+.3077*g5_76+.2692*g5
_75+.2308*g5_74+.1923*g5_73+.1538*
g5_72+
.1154*g5_71+.0769*g5_70.
compute
ns5_92=.9615*g5_92+.9231*g5_91+.88
46*g5_90+.8462*g5_89+.8077*g5_88+.
7692*g5_87+.7308*g5_86+
.6923*g5_84+.6538*g5_83+.6154*g5_8
2+.5769*g5_81+.5385*g5_80+.5*g5_79
+
.4615*g5_78+.4231*g5_77+.3846*g5_7
6+.3462*g5_75+.3077*g5_74+.2692*g5
_73+.2308*g5_72+.1923*g5_71+.1538*
g5_70.
compute
ns5_90=.9615*g5_90+.9231*g5_89+.88
46*g5_88+.8462*g5_87+.8077*g5_86+.
7692*g5_85+.7308*g5_84+
.6923*g5_83+.6538*g5_82+.6154*g5_8
1+.5769*g5_80+.5385*g5_79+.5*g5_78
+
.4615*g5_77+.4231*g5_76+.3846*g5_7
5+.3462*g5_74+.3077*g5_73+.2692*g5
_72+.2308*g5_71+.1923*g5_70.
compute
ns5_89=.9615*g5_89+.9231*g5_88+.88
46*g5_87+.8462*g5_86+.8077*g5_85+.
7692*g5_84+.7308*g5_83+
.6923*g5_82+.6538*g5_81+.6154*g5_8
0+.5769*g5_79+.5385*g5_78+.5*g5_77
+
.4615*g5_76+.4231*g5_75+.3846*g5_7
4+.3462*g5_73+.3077*g5_72+.2692*g5
_71+.2308*g5_70.
.6923*g5_85+.6538*g5_84+.6154*g5_8
61
compute
ns5_88=.9615*g5_88+.9231*g5_87+.88
46*g5_86+.8462*g5_85+.8077*g5_84+.
7692*g5_83+.7308*g5_82+
compute
ns5_84=.9615*g5_84+.9231*g5_83+.88
46*g5_82+.8462*g5_81+.8077*g5_80+.
7692*g5_79+.7308*g5_78+
.6923*g5_81+.6538*g5_80+.6154*g5_7
9+.5769*g5_78+.5385*g5_77+.5*g5_78
+
.6923*g5_77+.6538*g5_76+.6154*g5_7
5+.5769*g5_74+.5385*g5_73+.5*g5_72
+
.4615*g5_71+.4231*g5_70.
compute
ns5_83=.9615*g5_83+.9231*g5_82+.88
46*g5_81+.8462*g5_80+.8077*g5_79+.
7692*g5_78+.7308*g5_77+
.4615*g5_75+.4231*g5_74+.3846*g5_7
3+.3462*g5_72+.3077*g5_71+.2692*g5
_70.
compute
ns5_87=.9615*g5_87+.9231*g5_86+.88
46*g5_85+.8462*g5_84+.8077*g5_83+.
7692*g5_82+.7308*g5_81+
.6923*g5_80+.6538*g5_79+.6154*g5_7
8+.5769*g5_77+.5385*g5_76+.5*g5_75
+
.4615*g5_74+.4231*g5_73+.3846*g5_7
2+.3462*g5_71+.3077*g5_70.
compute
ns5_86=.9615*g5_86+.9231*g5_85+.88
46*g5_84+.8462*g5_83+.8077*g5_82+.
7692*g5_81+.7308*g5_80+
.6923*g5_79+.6538*g5_78+.6154*g5_7
7+.5769*g5_76+.5385*g5_75+.5*g5_74
+
.4615*g5_73+.4231*g5_72+.3846*g5_7
1+.3462*g5_70.
compute
ns5_85=.9615*g5_85+.9231*g5_84+.88
46*g5_83+.8462*g5_82+.8077*g5_81+.
7692*g5_80+.7308*g5_79+
.6923*g5_78+.6538*g5_77+.6154*g5_7
6+.5769*g5_75+.5385*g5_74+.5*g5_73
+
.4615*g5_72+.4231*g5_71+.3846*g5_7
0.
.6923*g5_76+.6538*g5_75+.6154*g5_7
4+.5769*g5_73+.5385*g5_72+.5*g5_71
+
.4615*g5_70.
compute
ns5_82=.9615*g5_82+.9231*g5_81+.88
46*g5_80+.8462*g5_79+.8077*g5_78+.
7692*g5_77+.7308*g5_76+
.6923*g5_75+.6538*g5_74+.6154*g5_7
3+.5769*g5_72+.5385*g5_71+.5*g5_70
.
compute
ns5_81=.9615*g5_81+.9231*g5_80+.88
46*g5_79+.8462*g5_78+.8077*g5_77+.
7692*g5_76+.7308*g5_75+
.6923*g5_74+.6538*g5_73+.6154*g5_7
2+.5769*g5_71+.5385*g5_70.
compute
ns5_80=.9615*g5_80+.9231*g5_79+.88
46*g5_78+.8462*g5_77+.8077*g5_76+.
7692*g5_75+.7308*g5_74+
.6923*g5_73+.6538*g5_72+.6154*g5_7
1+.5769*g5_70.
compute
ns5_79=.9615*g5_79+.9231*g5_78+.88
46*g5_77+.8462*g5_76+.8077*g5_75+.
7692*g5_74+.7308*g5_73+
62
.6923*g5_72+.6538*g5_71+.6154*g5_7
0.
compute
ns5_78=.9615*g5_78+.9231*g5_77+.88
46*g5_76+.8462*g5_75+.8077*g5_74+.
7692*g5_73+.7308*g5_72+
.6923*g5_71+.6538*g5_70.
compute
ns5_77=.9615*g5_77+.9231*g5_76+.88
46*g5_75+.8462*g5_74+.8077*g5_73+.
7692*g5_72+.7308*g5_71+
.6923*g5_70.
compute
ns5_76=.9615*g5_76+.9231*g5_75+.88
46*g5_74+.8462*g5_73+.8077*g5_72+.
7692*g5_71+.7308*g5_70.
compute
ns5_75=.9615*g5_75+.9231*g5_74+.88
46*g5_73+.8462*g5_72+.8077*g5_71+.
7692*g5_70.
compute
ns5_74=.9615*g5_74+.9231*g5_73+.88
46*g5_72+.8462*g5_71+.8077*g5_70.
compute
ns5_73=.9615*g5_73+.9231*g5_72+.88
46*g5_71+.8462*g5_70.
compute
ns5_72=.9615*g5_72+.9231*g5_71+.88
46*g5_70.
compute
ns5_71=.9615*g5_71+.9231*g5_70.
compute ns5_70=.9615*g5_70.
compute
ns4_01=.9474*g4_01+.8947*g4_00+.84
21*g4_99+.7895*g4_98+.7368*g4_97+.
6842*g4_96+.6316*g4_95+
.5789*g4_94+.5263*g4_93+.4737*g4_9
2+.421*g4_91+.3684*g4_90+.3158*g4_
89+.2632*g4_88+.2105*g4_87+
.1579*g4_86+.1053*g4_85+.0526*g4_8
4.
compute
ns4_00=.9474*g4_00+.8947*g4_99+.84
21*g4_98+.7895*g4_97+.7368*g4_96+.
6842*g4_95+.6316*g4_94+
.5789*g4_93+.5263*g4_92+.4737*g4_9
1+.421*g4_90+.3684*g4_89+.3158*g4_
88+.2632*g4_87+.2105*g4_86+
.1579*g4_85+.1053*g4_84+.0526*g4_8
3.
compute
ns4_99=.9474*g4_99+.8947*g4_98+.84
21*g4_97+.7895*g4_96+.7368*g4_95+.
6842*g4_94+.6316*g4_93+
.5789*g4_92+.5263*g4_91+.4737*g4_9
0+.421*g4_89+.3684*g4_88+.3158*g4_
87+.2632*g4_86+.2105*g4_85+
.1579*g4_84+.1053*g4_83+.0526*g4_8
2.
compute
ns4_98=.9474*g4_98+.8947*g4_97+.84
21*g4_96+.7895*g4_95+.7368*g4_94+.
6842*g4_93+.6316*g4_92+
.5789*g4_91+.5263*g4_90+.4737*g4_8
9+.421*g4_88+.3684*g4_87+.3158*g4_
86+.2632*g4_85+.2105*g4_84+
.1579*g4_83+.1053*g4_82+.0526*g4_8
1.
compute
ns4_97=.9474*g4_97+.8947*g4_96+.84
21*g4_95+.7895*g4_94+.7368*g4_93+.
6842*g4_92+.6316*g4_91+
.5789*g4_90+.5263*g4_89+.4737*g4_8
8+.421*g4_87+.3684*g4_86+.3158*g4_
85+.2632*g4_84+.2105*g4_83+
.1579*g4_82+.1053*g4_81+.0526*g4_8
0.
compute
ns4_96=.9474*g4_96+.8947*g4_95+.84
63
21*g4_94+.7895*g4_93+.7368*g4_92+.
6842*g4_91+.6316*g4_90+
.5789*g4_89+.5263*g4_88+.4737*g4_8
7+.421*g4_86+.3684*g4_85+.3158*g4_
84+.2632*g4_83+.2105*g4_82+
.1579*g4_81+.1053*g4_80+.0526*g4_7
9.
compute
ns4_95=.9474*g4_95+.8947*g4_94+.84
21*g4_93+.7895*g4_92+.7368*g4_91+.
6842*g4_90+.6316*g4_89+
.5789*g4_88+.5263*g4_87+.4737*g4_8
6+.421*g4_85+.3684*g4_84+.3158*g4_
83+.2632*g4_82+.2105*g4_81+
.1579*g4_80+.1053*g4_79+.0526*g4_7
8+0*g4_77.
compute
ns4_94=.9474*g4_94+.8947*g4_93+.84
21*g4_92+.7895*g4_91+.7368*g4_90+.
6842*g4_89+.6316*g4_88+
.5789*g4_87+.5263*g4_86+.4737*g4_8
5+.421*g4_84+.3684*g4_83+.3158*g4_
82+.2632*g4_81+.2105*g4_80+
.1579*g4_79+.1053*g4_78+.0526*g4_7
7+0*g4_76.
compute
ns4_93=.9474*g4_93+.8947*g4_92+.84
21*g4_91+.7895*g4_90+.7368*g4_89+.
6842*g4_88+.6316*g4_87+
.5789*g4_86+.5263*g4_85+.4737*g4_8
4+.421*g4_83+.3684*g4_82+.3158*g4_
81+.2632*g4_80+.2105*g4_79+
.1579*g4_78+.1053*g4_77+.0526*g4_7
6+0*g4_75.
compute
ns4_92=.9474*g4_92+.8947*g4_91+.84
21*g4_90+.7895*g4_89+.7368*g4_88+.
6842*g4_87+.6316*g4_86+
.5789*g4_85+.5263*g4_84+.4737*g4_8
3+.421*g4_82+.3684*g4_81+.3158*g4_
80+.2632*g4_79+.2105*g4_78+
.1579*g4_77+.1053*g4_76+.0526*g4_7
5+0*g4_74.
compute
ns4_91=.9474*g4_91+.8947*g4_90+.84
21*g4_89+.7895*g4_88+.7368*g4_87+.
6842*g4_86+.6316*g4_85+
.5789*g4_84+.5263*g4_83+.4737*g4_8
2+.421*g4_81+.3684*g4_80+.3158*g4_
79+.2632*g4_78+.2105*g4_77+
.1579*g4_76+.1053*g4_75+.0526*g4_7
4+0*g4_73.
compute
ns4_90=.9474*g4_90+.8947*g4_89+.84
21*g4_88+.7895*g4_87+.7368*g4_86+.
6842*g4_85+.6316*g4_84+
.5789*g4_83+.5263*g4_82+.4737*g4_8
1+.421*g4_80+.3684*g4_79+.3158*g4_
78+.2632*g4_77+.2105*g4_76+
.1579*g4_75+.1053*g4_74+.0526*g4_7
3+0*g4_72.
compute
ns4_89=.9474*g4_89+.8947*g4_88+.84
21*g4_87+.7895*g4_86+.7368*g4_85+.
6842*g4_84+.6316*g4_83+
.5789*g4_82+.5263*g4_81+.4737*g4_8
0+.421*g4_79+.3684*g4_78+.3158*g4_
77+.2632*g4_76+.2105*g4_75+
.1579*g4_74+.1053*g4_73+.0526*g4_7
2+0*g4_71.
compute
ns4_88=.9474*g4_88+.8947*g4_87+.84
21*g4_86+.7895*g4_85+.7368*g4_84+.
6842*g4_83+.6316*g4_82+
.5789*g4_81+.5263*g4_80+.4737*g4_7
64
9+.421*g4_78+.3684*g4_77+.3158*g4_
76+.2632*g4_75+.2105*g4_74+
.1579*g4_73+.1053*g4_72+.0526*g4_7
1+0*g4_70.
compute
ns4_87=.9474*g4_87+.8947*g4_86+.84
21*g4_85+.7895*g4_84+.7368*g4_83+.
6842*g4_82+.6316*g4_81+
.5789*g4_80+.5263*g4_79+.4737*g4_7
8+.421*g4_77+.3684*g4_76+.3158*g4_
75+.2632*g4_74+.2105*g4_73+
.1579*g4_72+.1053*g4_71+.0526*g4_7
0.
compute
ns4_86=.9474*g4_86+.8947*g4_85+.84
21*g4_84+.7895*g4_83+.7368*g4_82+.
6842*g4_81+.6316*g4_80+
.5789*g4_79+.5263*g4_78+.4737*g4_7
7+.421*g4_76+.3684*g4_75+.3158*g4_
74+.2632*g4_73+.2105*g4_72+
.1579*g4_71+.1053*g4_70.
compute
ns4_85=.9474*g4_85+.8947*g4_84+.84
21*g4_83+.7895*g4_82+.7368*g4_81+.
6842*g4_80+.6316*g4_79+
.5789*g4_78+.5263*g4_77+.4737*g4_7
6+.421*g4_75+.3684*g4_74+.3158*g4_
73+.2632*g4_72+.2105*g4_71+
.1579*g4_70.
compute
ns4_84=.9474*g4_84+.8947*g4_83+.84
21*g4_82+.7895*g4_81+.7368*g4_80+.
6842*g4_79+.6316*g4_78+
.5789*g4_77+.5263*g4_76+.4737*g4_7
5+.421*g4_74+.3684*g4_73+.3158*g4_
72+.2632*g4_71+.2105*g4_70.
compute
ns4_83=.9474*g4_83+.8947*g4_82+.84
21*g4_81+.7895*g4_80+.7368*g4_79+.
6842*g4_78+.6316*g4_77+
.5789*g4_76+.5263*g4_75+.4737*g4_7
4+.421*g4_73+.3684*g4_72+.3158*g4_
71+.2632*g4_70.
compute
ns4_82=.9474*g4_82+.8947*g4_81+.84
21*g4_80+.7895*g4_79+.7368*g4_78+.
6842*g4_77+.6316*g4_76+
.5789*g4_75+.5263*g4_74+.4737*g4_7
3+.421*g4_72+.3684*g4_71+.3158*g4_
70.
compute
ns4_81=.9474*g4_81+.8947*g4_80+.84
21*g4_79+.7895*g4_78+.7368*g4_77+.
6842*g4_76+.6316*g4_75+
.5789*g4_74+.5263*g4_73+.4737*g4_7
2+.421*g4_71+.3684*g4_70.
compute
ns4_80=.9474*g4_80+.8947*g4_79+.84
21*g4_78+.7895*g4_77+.7368*g4_76+.
6842*g4_75+.6316*g4_74+
.5789*g4_73+.5263*g4_72+.4737*g4_7
1+.421*g4_70.
compute
ns4_79=.9474*g4_79+.8947*g4_78+.84
21*g4_77+.7895*g4_76+.7368*g4_75+.
6842*g4_74+.6316*g4_73+
.5789*g4_72+.5263*g4_71+.4737*g4_7
0.
compute
ns4_78=.9474*g4_78+.8947*g4_77+.84
21*g4_76+.7895*g4_75+.7368*g4_74+.
6842*g4_73+.6316*g4_72+
.5789*g4_71+.5263*g4_70.
compute
ns4_77=.9474*g4_77+.8947*g4_76+.84
21*g4_75+.7895*g4_74+.7368*g4_73+.
6842*g4_72+.6316*g4_71+
.5789*g4_70.
compute
ns4_76=.9474*g4_76+.8947*g4_75+.84
65
21*g4_74+.7895*g4_73+.7368*g4_72+.
6842*g4_71+.6316*g4_70.
compute
ns4_75=.9474*g4_75+.8947*g4_74+.84
21*g4_73+.7895*g4_72+.7368*g4_71+.
6842*g4_70.
compute
ns4_74=.9474*g4_74+.8947*g4_73+.84
21*g4_72+.7895*g4_71+.7368*g4_70.
compute
ns4_73=.9474*g4_73+.8947*g4_72+.84
21*g4_71+.7895*g4_70.
compute
ns4_72=.9474*g4_72+.8947*g4_71+.84
21*g4_70.
compute
ns4_71=.9474*g4_71+.8947*g4_70.
compute ns4_70=.9474*g4_70.
57*g3_96+.7143*g3_95+.6429*g3_94+.
57154*g3_93+
compute
ns3_01=.9286*g3_01+.8571*g3_00+.78
57*g3_99+.7143*g3_98+.6429*g3_97+.
57154*g3_96+
.5*g3_90+.4286*g3_89+.3571*g3_88+.
2857*g3_87+.2143*g3_86+.1429*g3_8
5+.0714*g3_84.
compute
ns3_95=.9286*g3_95+.8571*g3_94+.78
57*g3_93+.7143*g3_92+.6429*g3_91+.
57154*g3_90+
.5*g3_95+.4286*g3_94+.3571*g3_93+.
2857*g3_92+.2143*g3_91+.1429*g3_9
0+.0714*g3_89.
compute
ns3_00=.9286*g3_00+.8571*g3_99+.78
57*g3_98+.7143*g3_97+.6429*g3_96+.
57154*g3_95+
.5*g3_94+.4286*g3_93+.3571*g3_92+.
2857*g3_91+.2143*g3_90+.1429*g3_8
9+.0714*g3_88.
compute
ns3_99=.9286*g3_99+.8571*g3_98+.78
57*g3_97+.7143*g3_96+.6429*g3_95+.
57154*g3_94+
.5*g3_93+.4286*g3_92+.3571*g3_91+.
2857*g3_90+.2143*g3_89+.1429*g3_8
8+.0714*g3_87.
compute
ns3_98=.9286*g3_98+.8571*g3_97+.78
.5*g3_92+.4286*g3_91+.3571*g3_90+.
2857*g3_89+.2143*g3_88+.1429*g3_8
7+.0714*g3_86.
compute
ns3_97=.9286*g3_97+.8571*g3_96+.78
57*g3_95+.7143*g3_94+.6429*g3_93+.
57154*g3_92+
.5*g3_91+.4286*g3_90+.3571*g3_89+.
2857*g3_88+.2143*g3_87+.1429*g3_8
6+.0714*g3_85.
compute
ns3_96=.9286*g3_96+.8571*g3_95+.78
57*g3_94+.7143*g3_93+.6429*g3_92+.
57154*g3_91+
.5*g3_89+.4286*g3_88+.3571*g3_87+.
2857*g3_86+.2143*g3_85+.1429*g3_8
4+.0714*g3_83+0*g3_82.
compute
ns3_94=.9286*g3_94+.8571*g3_93+.78
57*g3_92+.7143*g3_91+.6429*g3_90+.
57154*g3_89+
.5*g3_88+.4286*g3_87+.3571*g3_86+.
2857*g3_85+.2143*g3_84+.1429*g3_8
3+.0714*g3_82+0*g3_81.
compute
ns3_93=.9286*g3_93+.8571*g3_92+.78
57*g3_91+.7143*g3_90+.6429*g3_89+.
57154*g3_88+
.5*g3_87+.4286*g3_86+.3571*g3_85+.
2857*g3_84+.2143*g3_83+.1429*g3_8
2+.0714*g3_81+0*g3_80.
66
compute
ns3_92=.9286*g3_92+.8571*g3_91+.78
57*g3_90+.7143*g3_89+.6429*g3_88+.
57154*g3_87+
.5*g3_86+.4286*g3_85+.3571*g3_84+.
2857*g3_83+.2143*g3_82+.1429*g3_8
1+.0714*g3_80+0*g3_79.
compute
ns3_91=.9286*g3_91+.8571*g3_90+.78
57*g3_89+.7143*g3_88+.6429*g3_87+.
57154*g3_86+
.5*g3_85+.4286*g3_84+.3571*g3_83+.
2857*g3_82+.2143*g3_81+.1429*g3_8
0+.0714*g3_79+0*g3_78.
compute
ns3_90=.9286*g3_90+.8571*g3_89+.78
57*g3_88+.7143*g3_87+.6429*g3_86+.
57154*g3_85+
.5*g3_84+.4286*g3_83+.3571*g3_82+.
2857*g3_81+.2143*g3_80+.1429*g3_7
9+.0714*g3_78+0*g3_77.
compute
ns3_89=.9286*g3_89+.8571*g3_88+.78
57*g3_87+.7143*g3_86+.6429*g3_85+.
57154*g3_84+
.5*g3_83+.4286*g3_82+.3571*g3_81+.
2857*g3_80+.2143*g3_79+.1429*g3_7
8+.0714*g3_77+0*g3_76.
compute
ns3_88=.9286*g3_88+.8571*g3_87+.78
57*g3_86+.7143*g3_85+.6429*g3_84+.
57154*g3_83+
.5*g3_82+.4286*g3_81+.3571*g3_80+.
2857*g3_79+.2143*g3_78+.1429*g3_7
7+.0714*g3_76+0*g3_75.
compute
ns3_87=.9286*g3_87+.8571*g3_86+.78
57*g3_85+.7143*g3_84+.6429*g3_83+.
57154*g3_82+
.5*g3_81+.4286*g3_80+.3571*g3_79+.
2857*g3_78+.2143*g3_77+.1429*g3_7
6+.0714*g3_75+0*g3_74.
compute
ns3_86=.9286*g3_86+.8571*g3_85+.78
57*g3_84+.7143*g3_83+.6429*g3_82+.
57154*g3_81+
.5*g3_80+.4286*g3_79+.3571*g3_78+.
2857*g3_77+.2143*g3_76+.1429*g3_7
5+.0714*g3_74+0*g3_73.
compute
ns3_85=.9286*g3_85+.8571*g3_84+.78
57*g3_83+.7143*g3_82+.6429*g3_81+.
57154*g3_80+
.5*g3_79+.4286*g3_78+.3571*g3_77+.
2857*g3_76+.2143*g3_75+.1429*g3_7
4+.0714*g3_73+0*g3_72.
compute
ns3_84=.9286*g3_84+.8571*g3_83+.78
57*g3_82+.7143*g3_81+.6429*g3_80+.
57154*g3_79+
.5*g3_78+.4286*g3_77+.3571*g3_76+.
2857*g3_75+.2143*g3_74+.1429*g3_7
3+.0714*g3_72+0*g3_71.
compute
ns3_83=.9286*g3_83+.8571*g3_82+.78
57*g3_81+.7143*g3_80+.6429*g3_79+.
57154*g3_78+
.5*g3_77+.4286*g3_76+.3571*g3_75+.
2857*g3_74+.2143*g3_73+.1429*g3_7
2+.0714*g3_71+0*g3_70.
compute
ns3_82=.9286*g3_82+.8571*g3_81+.78
57*g3_80+.7143*g3_79+.6429*g3_78+.
57154*g3_77+
.5*g3_76+.4286*g3_75+.3571*g3_74+.
2857*g3_73+.2143*g3_72+.1429*g3_7
1+.0714*g3_70.
compute
ns3_81=.9286*g3_81+.8571*g3_80+.78
67
57*g3_79+.7143*g3_78+.6429*g3_77+.
57154*g3_76+
.5*g3_75+.4286*g3_74+.3571*g3_73+.
2857*g3_72+.2143*g3_71+.1429*g3_7
0.
compute
ns3_80=.9286*g3_80+.8571*g3_79+.78
57*g3_78+.7143*g3_77+.6429*g3_76+.
57154*g3_75+
.5*g3_74+.4286*g3_73+.3571*g3_72+.
2857*g3_71+.2143*g3_70.
compute
ns3_79=.9286*g3_79+.8571*g3_78+.78
57*g3_77+.7143*g3_76+.6429*g3_75+.
57154*g3_74+
.5*g3_73+.4286*g3_72+.3571*g3_71+.
2857*g3_70.
compute
ns3_78=.9286*g3_78+.8571*g3_77+.78
57*g3_76+.7143*g3_75+.6429*g3_74+.
57154*g3_73+
.5*g3_72+.4286*g3_71+.3571*g3_70.
compute
ns3_77=.9286*g3_77+.8571*g3_76+.78
57*g3_75+.7143*g3_74+.6429*g3_73+.
57154*g3_72+
.5*g3_71+.4286*g3_70.
compute
ns3_76=.9286*g3_76+.8571*g3_75+.78
57*g3_74+.7143*g3_73+.6429*g3_72+.
57154*g3_71+
.5*g3_70.
compute
ns3_75=.9286*g3_75+.8571*g3_74+.78
57*g3_73+.7143*g3_72+.6429*g3_71+.
57154*g3_70.
compute
ns3_74=.9286*g3_74+.8571*g3_73+.78
57*g3_72+.7143*g3_71+.6429*g3_70.
compute
ns3_73=.9286*g3_73+.8571*g3_72+.78
57*g3_71+.7143*g3_70.
compute
ns3_72=.9286*g3_72+.8571*g3_71+.78
57*g3_70.
compute
ns3_71=.9286*g3_71+.8571*g3_70.
compute ns3_70=.9286*g3_70.
compute
ns2_01=.9167*g2_01+.833*g2_00+.75*
g2_99+.6667*g2_98+.5833*g2_97+.5*g
2_96+.4167*g2_95+.3334*g2_94+
.25*g2_93+.1667*g2_92+.0833*g2_91.
compute
ns2_00=.9167*g2_00+.833*g2_99+.75*
g2_98+.6667*g2_97+.5833*g2_96+.5*g
2_95+.4167*g2_94+.3334*g2_93+
.25*g2_92+.1667*g2_91+.0833*g2_90.
compute
ns2_99=.9167*g2_99+.833*g2_98+.75*
g2_97+.6667*g2_96+.5833*g2_95+.5*g
2_94+.4167*g2_93+.3334*g2_92+
.25*g2_91+.1667*g2_90+.0833*g2_89.
compute
ns2_98=.9167*g2_98+.833*g2_97+.75*
g2_96+.6667*g2_95+.5833*g2_94+.5*g
2_93+.4167*g2_92+.3334*g2_91+
.25*g2_90+.1667*g2_89+.0833*g2_88.
compute
ns2_97=.9167*g2_97+.833*g2_96+.75*
g2_95+.6667*g2_94+.5833*g2_93+.5*g
2_92+.4167*g2_91+.3334*g2_90+
.25*g2_89+.1667*g2_88+.0833*g2_87.
compute
ns2_96=.9167*g2_96+.833*g2_95+.75*
g2_94+.6667*g2_93+.5833*g2_92+.5*g
2_91+.4167*g2_90+.3334*g2_89+
.25*g2_88+.1667*g2_87+.0833*g2_86.
compute
ns2_95=.9167*g2_95+.833*g2_94+.75*
68
g2_93+.6667*g2_92+.5833*g2_91+.5*g
2_90+.4167*g2_89+.3334*g2_88+
.25*g2_87+.1667*g2_86+.0833*g2_85+
0*g2_85.
compute
ns2_94=.9167*g2_94+.833*g2_93+.75*
g2_92+.6667*g2_91+.5833*g2_90+.5*g
2_89+.4167*g2_88+.3334*g2_87+
.25*g2_86+.1667*g2_85+.0833*g2_84+
0*g2_83.
compute
ns2_93=.9167*g2_93+.833*g2_92+.75*
g2_91+.6667*g2_90+.5833*g2_89+.5*g
2_88+.4167*g2_87+.3334*g2_86+
.25*g2_85+.1667*g2_84+.0833*g2_83+
0*g2_82.
compute
ns2_92=.9167*g2_92+.833*g2_91+.75*
g2_90+.6667*g2_89+.5833*g2_88+.5*g
2_87+.4167*g2_86+.3334*g2_85+
.25*g2_84+.1667*g2_83+.0833*g2_82+
0*g2_81.
compute
ns2_91=.9167*g2_91+.833*g2_90+.75*
g2_89+.6667*g2_88+.5833*g2_87+.5*g
2_86+.4167*g2_85+.3334*g2_84+
.25*g2_83+.1667*g2_82+.0833*g2_81+
0*g2_80.
compute
ns2_90=.9167*g2_90+.833*g2_89+.75*
g2_88+.6667*g2_87+.5833*g2_86+.5*g
2_85+.4167*g2_84+.3334*g2_83+
.25*g2_82+.1667*g2_81+.0833*g2_80+
0*g2_79.
compute
ns2_89=.9167*g2_89+.833*g2_88+.75*
g2_87+.6667*g2_86+.5833*g2_85+.5*g
2_84+.4167*g2_83+.3334*g2_82+
.25*g2_81+.1667*g2_80+.0833*g2_79+
0*g2_78.
compute
ns2_88=.9167*g2_88+.833*g2_87+.75*
g2_86+.6667*g2_85+.5833*g2_84+.5*g
2_83+.4167*g2_82+.3334*g2_81+
.25*g2_80+.1667*g2_79+.0833*g2_78+
0*g2_77.
compute
ns2_87=.9167*g2_87+.833*g2_86+.75*
g2_85+.6667*g2_84+.5833*g2_83+.5*g
2_82+.4167*g2_81+.3334*g2_80+
.25*g2_79+.1667*g2_78+.0833*g2_77+
0*g2_76.
compute
ns2_86=.9167*g2_86+.833*g2_85+.75*
g2_84+.6667*g2_83+.5833*g2_82+.5*g
2_81+.4167*g2_80+.3334*g2_79+
.25*g2_78+.1667*g2_77+.0833*g2_76+
0*g2_75.
compute
ns2_85=.9167*g2_85+.833*g2_84+.75*
g2_83+.6667*g2_82+.5833*g2_81+.5*g
2_80+.4167*g2_79+.3334*g2_78+
.25*g2_77+.1667*g2_76+.0833*g2_75+
0*g2_74.
compute
ns2_84=.9167*g2_84+.833*g2_83+.75*
g2_82+.6667*g2_81+.5833*g2_80+.5*g
2_79+.4167*g2_78+.3334*g2_77+
.25*g2_76+.1667*g2_75+.0833*g2_74+
0*g2_73.
compute
ns2_83=.9167*g2_83+.833*g2_82+.75*
g2_81+.6667*g2_80+.5833*g2_79+.5*g
2_78+.4167*g2_77+.3334*g2_76+
.25*g2_75+.1667*g2_74+.0833*g2_73+
0*g2_72.
69
compute
ns2_82=.9167*g2_82+.833*g2_81+.75*
g2_80+.6667*g2_79+.5833*g2_78+.5*g
2_77+.4167*g2_76+.3334*g2_75+
.25*g2_74+.1667*g2_73+.0833*g2_72+
0*g2_71.
compute
ns2_81=.9167*g2_81+.833*g2_80+.75*
g2_79+.6667*g2_78+.5833*g2_77+.5*g
2_76+.4167*g2_75+.3334*g2_74+
.25*g2_73+.1667*g2_72+.0833*g2_71+
0*g2_70.
compute
ns2_80=.9167*g2_80+.833*g2_79+.75*
g2_78+.6667*g2_77+.5833*g2_76+.5*g
2_75+.4167*g2_74+.3334*g2_73+
.25*g2_72+.1667*g2_71+.0833*g2_70.
compute
ns2_79=.9167*g2_79+.833*g2_78+.75*
g2_77+.6667*g2_76+.5833*g2_75+.5*g
2_74+.4167*g2_73+.3334*g2_72+
.25*g2_71+.1667*g2_70.
compute
ns2_78=.9167*g2_78+.833*g2_77+.75*
g2_76+.6667*g2_75+.5833*g2_74+.5*g
2_73+.4167*g2_72+.3334*g2_71+
.25*g2_70.
compute
ns2_77=.9167*g2_77+.833*g2_76+.75*
g2_75+.6667*g2_74+.5833*g2_73+.5*g
2_72+.4167*g2_71+.3334*g2_70.
compute
ns2_76=.9167*g2_76+.833*g2_75+.75*
g2_74+.6667*g2_73+.5833*g2_72+.5*g
2_71+.4167*g2_70.
compute
ns2_75=.9167*g2_75+.833*g2_74+.75*
g2_73+.6667*g2_72+.5833*g2_71+.5*g
2_70.
compute
ns2_74=.9167*g2_74+.833*g2_73+.75*
g2_72+.6667*g2_71+.5833*g2_70.
compute
ns2_73=.9167*g2_73+.833*g2_72+.75*
g2_71+.6667*g2_70.
compute
ns2_72=.9167*g2_72+.833*g2_71+.75*
g2_70.
compute
ns2_71=.9167*g2_71+.833*g2_70.
compute ns2_70=.9167*g2_70.
compute
ns1_01=.8*g1_01+.6*g1_00+.4*g1_99+
.2*g1_98.
compute
ns1_00=.8*g1_00+.6*g1_99+.4*g1_98+
.2*g1_97.
compute
ns1_99=.8*g1_99+.6*g1_98+.4*g1_97+
.2*g1_96.
compute
ns1_98=.8*g1_98+.6*g1_97+.4*g1_96+
.2*g1_95.
compute
ns1_97=.8*g1_97+.6*g1_96+.4*g1_95+
.2*g1_94.
compute
ns1_96=.8*g1_96+.6*g1_95+.4*g1_94+
.2*g1_93.
compute
ns1_95=.8*g1_95+.6*g1_94+.4*g1_93+
.2*g1_92+0*g1_91.
compute
ns1_94=.8*g1_94+.6*g1_93+.4*g1_92+
.2*g1_91+0*g1_90.
compute
ns1_93=.8*g1_93+.6*g1_92+.4*g1_91+
.2*g1_90+0*g1_89.
compute
ns1_92=.8*g1_92+.6*g1_91+.4*g1_90+
.2*g1_89+0*g1_88.
compute
ns1_91=.8*g1_91+.6*g1_90+.4*g1_89+
.2*g1_88+0*g1_87.
compute
ns1_90=.8*g1_90+.6*g1_89+.4*g1_88+
.2*g1_87+0*g1_86.
70
compute
ns1_89=.8*g1_89+.6*g1_88+.4*g1_87+
.2*g1_86+0*g1_85.
compute
ns1_88=.8*g1_88+.6*g1_87+.4*g1_86+
.2*g1_85+0*g1_84.
compute
ns1_87=.8*g1_87+.6*g1_86+.4*g1_85+
.2*g1_84+0*g1_83.
compute
ns1_86=.8*g1_86+.6*g1_85+.4*g1_84+
.2*g1_83+0*g1_82.
compute
ns1_85=.8*g1_85+.6*g1_84+.4*g1_83+
.2*g1_82+0*g1_81.
compute
ns1_84=.8*g1_84+.6*g1_83+.4*g1_82+
.2*g1_81+0*g1_80.
compute
ns1_83=.8*g1_83+.6*g1_82+.4*g1_81+
.2*g1_80+0*g1_79.
compute
ns1_82=.8*g1_82+.6*g1_81+.4*g1_80+
.2*g1_79+0*g1_78.
compute
ns1_81=.8*g1_81+.6*g1_80+.4*g1_79+
.2*g1_78+0*g1_77.
compute
ns1_80=.8*g1_80+.6*g1_79+.4*g1_78+
.2*g1_77+0*g1_76.
compute
ns1_79=.8*g1_79+.6*g1_78+.4*g1_77+
.2*g1_76+0*g1_75.
compute
ns1_78=.8*g1_78+.6*g1_77+.4*g1_76+
.2*g1_75+0*g1_74.
compute
ns1_77=.8*g1_77+.6*g1_76+.4*g1_75+
.2*g1_74+0*g1_73.
compute
ns1_76=.8*g1_76+.6*g1_75+.4*g1_74+
.2*g1_73+0*g1_72.
compute
ns1_75=.8*g1_75+.6*g1_74+.4*g1_73+
.2*g1_72+0*g1_71.
compute
ns1_74=.8*g1_74+.6*g1_73+.4*g1_72+
.2*g1_71+0*g1_70.
compute
ns1_73=.8*g1_73+.6*g1_72+.4*g1_71+
.2*g1_70.
compute
ns1_72=.8*g1_72+.6*g1_71+.4*g1_70.
compute ns1_71=.8*g1_71+.6*g1_70.
compute ns1_70=.8*g1_70.
compute
gs01=gs1_01+gs2_01+gs3_01+gs4_01+
gs5_01+gs6_01.
compute
gs00=gs1_00+gs2_00+gs3_00+gs4_00+
gs5_00+gs6_00.
compute
gs99=gs1_99+gs2_99+gs3_99+gs4_99+
gs5_99+gs6_99.
compute
gs98=gs1_98+gs2_98+gs3_98+gs4_98+
gs5_98+gs6_98.
compute
gs97=gs1_97+gs2_97+gs3_97+gs4_97+
gs5_97+gs6_97.
compute
gs96=gs1_96+gs2_96+gs3_96+gs4_96+
gs5_96+gs6_96.
compute
gs95=gs1_95+gs2_95+gs3_95+gs4_95+
gs5_95+gs6_95.
compute
gs94=gs1_94+gs2_94+gs3_94+gs4_94+
gs5_94+gs6_94.
compute
gs93=gs1_93+gs2_93+gs3_93+gs4_93+
gs5_93+gs6_93.
compute
gs92=gs1_92+gs2_92+gs3_92+gs4_92+
gs5_92+gs6_92.
compute
gs91=gs1_91+gs2_91+gs3_91+gs4_91+
gs5_91+gs6_91.
71
compute
gs90=gs1_90+gs2_90+gs3_90+gs4_90+
gs5_90+gs6_90.
compute
gs89=gs1_89+gs2_89+gs3_89+gs4_89+
gs5_89+gs6_89.
compute
gs88=gs1_88+gs2_88+gs3_88+gs4_88+
gs5_88+gs6_88.
compute
gs87=gs1_87+gs2_87+gs3_87+gs4_87+
gs5_87+gs6_87.
compute
gs86=gs1_86+gs2_86+gs3_86+gs4_86+
gs5_86+gs6_86.
compute
gs85=gs1_85+gs2_85+gs3_85+gs4_85+
gs5_85+gs6_85.
compute
gs84=gs1_84+gs2_84+gs3_84+gs4_84+
gs5_84+gs6_84.
compute
gs83=gs1_83+gs2_83+gs3_83+gs4_83+
gs5_83+gs6_83.
compute
gs82=gs1_82+gs2_82+gs3_82+gs4_82+
gs5_82+gs6_82.
compute
gs81=gs1_81+gs2_81+gs3_81+gs4_81+
gs5_81+gs6_81.
compute
gs80=gs1_80+gs2_80+gs3_80+gs4_80+
gs5_80+gs6_80.
compute
gs79=gs1_79+gs2_79+gs3_79+gs4_79+
gs5_79+gs6_79.
compute
gs78=gs1_78+gs2_78+gs3_78+gs4_78+
gs5_78+gs6_78.
compute
gs77=gs1_77+gs2_77+gs3_77+gs4_77+
gs5_77+gs6_77.
compute
gs76=gs1_76+gs2_76+gs3_76+gs4_76+
gs5_76+gs6_76.
compute
gs75=gs1_75+gs2_75+gs3_75+gs4_75+
gs5_75+gs6_75.
compute
gs74=gs1_74+gs2_74+gs3_74+gs4_74+
gs5_74+gs6_74.
compute
gs73=gs1_73+gs2_73+gs3_73+gs4_73+
gs5_73+gs6_73.
compute
gs72=gs1_72+gs2_72+gs3_72+gs4_72+
gs5_72+gs6_72.
compute
gs71=gs1_71+gs2_71+gs3_71+gs4_71+
gs5_71+gs6_71.
compute
gs70=gs1_70+gs2_70+gs3_70+gs4_70+
gs5_70+gs6_70.
compute
ns01=ns1_01+ns2_01+ns3_01+ns4_01+
ns5_01+ns6_01.
compute
ns00=ns1_00+ns2_00+ns3_00+ns4_00+
ns5_00+ns6_00.
compute
ns99=ns1_99+ns2_99+ns3_99+ns4_99+
ns5_99+ns6_99.
compute
ns98=ns1_98+ns2_98+ns3_98+ns4_98+
ns5_98+ns6_98.
compute
ns97=ns1_97+ns2_97+ns3_97+ns4_97+
ns5_97+ns6_97.
compute
ns96=ns1_96+ns2_96+ns3_96+ns4_96+
ns5_96+ns6_96.
compute
ns95=ns1_95+ns2_95+ns3_95+ns4_95+
ns5_95+ns6_95.
compute
ns94=ns1_94+ns2_94+ns3_94+ns4_94+
ns5_94+ns6_94.
compute
ns93=ns1_93+ns2_93+ns3_93+ns4_93+
ns5_93+ns6_93.
72
compute
ns92=ns1_92+ns2_92+ns3_92+ns4_92+
ns5_92+ns6_92.
compute
ns91=ns1_91+ns2_91+ns3_91+ns4_91+
ns5_91+ns6_91.
compute
ns90=ns1_90+ns2_90+ns3_90+ns4_90+
ns5_90+ns6_90.
compute
ns89=ns1_89+ns2_89+ns3_89+ns4_89+
ns5_89+ns6_89.
compute
ns88=ns1_88+ns2_88+ns3_88+ns4_88+
ns5_88+ns6_88.
compute
ns87=ns1_87+ns2_87+ns3_87+ns4_87+
ns5_87+ns6_87.
compute
ns86=ns1_86+ns2_86+ns3_86+ns4_86+
ns5_86+ns6_86.
compute
ns85=ns1_85+ns2_85+ns3_85+ns4_85+
ns5_85+ns6_85.
compute
ns84=ns1_84+ns2_84+ns3_84+ns4_84+
ns5_84+ns6_84.
compute
ns83=ns1_83+ns2_83+ns3_83+ns4_83+
ns5_83+ns6_83.
compute
ns82=ns1_82+ns2_82+ns3_82+ns4_82+
ns5_82+ns6_82.
compute
ns81=ns1_81+ns2_81+ns3_81+ns4_81+
ns5_81+ns6_81.
compute
ns80=ns1_80+ns2_80+ns3_80+ns4_80+
ns5_80+ns6_80.
compute
ns79=ns1_79+ns2_79+ns3_79+ns4_79+
ns5_79+ns6_79.
compute
ns78=ns1_78+ns2_78+ns3_78+ns4_78+
ns5_78+ns6_78.
compute
ns77=ns1_77+ns2_77+ns3_77+ns4_77+
ns5_77+ns6_77.
compute
ns76=ns1_76+ns2_76+ns3_76+ns4_76+
ns5_76+ns6_76.
compute
ns75=ns1_75+ns2_75+ns3_75+ns4_75+
ns5_75+ns6_75.
compute
ns74=ns1_74+ns2_74+ns3_74+ns4_74+
ns5_74+ns6_74.
compute
ns73=ns1_73+ns2_73+ns3_73+ns4_73+
ns5_73+ns6_73.
compute
ns72=ns1_72+ns2_72+ns3_72+ns4_72+
ns5_72+ns6_72.
compute
ns71=ns1_71+ns2_71+ns3_71+ns4_71+
ns5_71+ns6_71.
compute
ns70=ns1_70+ns2_70+ns3_70+ns4_70+
ns5_70+ns6_70.
compute cap01=0.66*gs01+0.34*ns01.
compute cap00=0.66*gs00+0.34*ns00.
compute cap99=0.66*gs99+0.34*ns99.
compute cap98=0.66*gs98+0.34*ns98.
compute cap97=0.66*gs97+0.34*ns97.
compute cap96=0.66*gs96+0.34*ns96.
compute cap95=0.66*gs95+0.34*ns95.
compute cap94=0.66*gs94+0.34*ns94.
compute cap93=0.66*gs93+0.34*ns93.
compute cap92=0.66*gs92+0.34*ns92.
compute cap91=0.66*gs91+0.34*ns91.
compute cap90=0.66*gs90+0.34*ns90.
compute cap89=0.66*gs89+0.34*ns89.
compute cap88=0.66*gs88+0.34*ns88.
compute cap87=0.66*gs87+0.34*ns87.
compute cap86=0.66*gs86+0.34*ns86.
compute cap85=0.66*gs85+0.34*ns85.
compute cap84=0.66*gs84+0.34*ns84.
compute cap83=0.66*gs83+0.34*ns83.
compute cap82=0.66*gs82+0.34*ns82.
compute cap81=0.66*gs81+0.34*ns81.
73
compute cap80=0.66*gs80+0.34*ns80.
compute cap79=0.66*gs79+0.34*ns79.
compute cap78=0.66*gs78+0.34*ns78.
compute cap77=0.66*gs77+0.34*ns77.
compute cap76=0.66*gs76+0.34*ns76.
compute cap75=0.66*gs75+0.34*ns75.
compute cap74=0.66*gs74+0.34*ns74.
compute cap73=0.66*gs73+0.34*ns73.
compute cap72=0.66*gs72+0.34*ns72.
compute cap71=0.66*gs71+0.34*ns71.
compute cap70=0.66*gs70+0.34*ns70.
sort cases by cso_ref.
save outfile='h:\files\capital
stock\flat1.sav'/keep=cso_ref gs01 to
cap70.
get file='h:\files\capital
stock\rnet_pm_7001.sav'.
*CHANGE GROUP = TO MATCH
GROUP NO. AT START OF FILE.
select if group eq 1.
if (year eq 1993 and cso_ref gt
80000000) cso_ref=cso_ref-90000000.
sort cases by cso_ref.
match files file=*/table='h:\files\capital
stock\flat1.sav'/by cso_ref.
if (year eq 1970) K_pm=cap70.
if (year eq 1971) K_pm=cap71.
if (year eq 1972) K_pm=cap72.
if (year eq 1973) K_pm=cap73.
if (year eq 1974) K_pm=cap74.
if (year eq 1975) K_pm=cap75.
if (year eq 1976) K_pm=cap76.
if (year eq 1977) K_pm=cap77.
if (year eq 1978) K_pm=cap78.
if (year eq 1979) K_pm=cap79.
if (year eq 1980) K_pm=cap80.
if (year eq 1981) K_pm=cap81.
if (year eq 1982) K_pm=cap82.
if (year eq 1983) K_pm=cap83.
if (year eq 1984) K_pm=cap84.
if (year eq 1985) K_pm=cap85.
if (year eq 1986) K_pm=cap86.
if (year eq 1987) K_pm=cap87.
if (year eq 1988) K_pm=cap88.
if (year eq 1989) K_pm=cap89.
if (year eq 1990) K_pm=cap90.
if (year eq 1991) K_pm=cap91.
if (year eq 1992) K_pm=cap92.
if (year eq 1993) K_pm=cap93.
if (year eq 1994) K_pm=cap94.
if (year eq 1995) K_pm=cap95.
if (year eq 1996) K_pm=cap96.
if (year eq 1997) K_pm=cap97.
if (year eq 1998) K_pm=cap98.
if (year eq 1999) K_pm=cap99.
if (year eq 2000) K_pm=cap00.
if (year eq 2001) K_pm=cap01.
if (year eq 1970) nk_pm=ns70.
if (year eq 1971) nk_pm=ns71.
if (year eq 1972) nk_pm=ns72.
if (year eq 1973) nk_pm=ns73.
if (year eq 1974) nk_pm=ns74.
if (year eq 1975) nk_pm=ns75.
if (year eq 1976) nk_pm=ns76.
if (year eq 1977) nk_pm=ns77.
if (year eq 1978) nk_pm=ns78.
if (year eq 1979) nk_pm=ns79.
if (year eq 1980) nk_pm=ns80.
if (year eq 1981) nk_pm=ns81.
if (year eq 1982) nk_pm=ns82.
if (year eq 1983) nk_pm=ns83.
if (year eq 1984) nk_pm=ns84.
if (year eq 1985) nk_pm=ns85.
if (year eq 1986) nk_pm=ns86.
if (year eq 1987) nk_pm=ns87.
if (year eq 1988) nk_pm=ns88.
if (year eq 1989) nk_pm=ns89.
if (year eq 1990) nk_pm=ns90.
if (year eq 1991) nk_pm=ns91.
if (year eq 1992) nk_pm=ns92.
if (year eq 1993) nk_pm=ns93.
if (year eq 1994) nk_pm=ns94.
if (year eq 1995) nk_pm=ns95.
if (year eq 1996) nk_pm=ns96.
if (year eq 1997) nk_pm=ns97.
if (year eq 1998) nk_pm=ns98.
if (year eq 1999) nk_pm=ns99.
if (year eq 2000) nk_pm=ns00.
if (year eq 2001) nk_pm=ns01.
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if (year eq 1970) gk_pm=gs70.
if (year eq 1971) gk_pm=gs71.
if (year eq 1972) gk_pm=gs72.
if (year eq 1973) gk_pm=gs73.
if (year eq 1974) gk_pm=gs74.
if (year eq 1975) gk_pm=gs75.
if (year eq 1976) gk_pm=gs76.
if (year eq 1977) gk_pm=gs77.
if (year eq 1978) gk_pm=gs78.
if (year eq 1979) gk_pm=gs79.
if (year eq 1980) gk_pm=gs80.
if (year eq 1981) gk_pm=gs81.
if (year eq 1982) gk_pm=gs82.
if (year eq 1983) gk_pm=gs83.
if (year eq 1984) gk_pm=gs84.
if (year eq 1985) gk_pm=gs85.
if (year eq 1986) gk_pm=gs86.
if (year eq 1987) gk_pm=gs87.
if (year eq 1988) gk_pm=gs88.
if (year eq 1989) gk_pm=gs89.
if (year eq 1990) gk_pm=gs90.
if (year eq 1991) gk_pm=gs91.
if (year eq 1992) gk_pm=gs92.
if (year eq 1993) gk_pm=gs93.
if (year eq 1994) gk_pm=gs94.
if (year eq 1995) gk_pm=gs95.
if (year eq 1996) gk_pm=gs96.
if (year eq 1997) gk_pm=gs97.
if (year eq 1998) gk_pm=gs98.
if (year eq 1999) gk_pm=gs99.
if (year eq 2000) gk_pm=gs00.
if (year eq 2001) gk_pm=gs01.
descriptives cso_ref.
means rnet_pm k_pm by year/cells=sum
count.
compute lcapst=lag(K_pm).
if missing(lcapst) lcapst=0.
compute deprec=rnet_pm-(K_pmlcapst).
if (year eq 1970) deprec=.33*(rnet_pmnk_pm).
* CHANGE FILE HANDLE PMCx SO
x MATCHES GROUP NO.
save outfile='H:\files\capital
stock\pmc1.sav'/keep=cso_ref year
rnet_pm K_pm nk_pm gk_pm deprec.
get file='H:\files\capital stock\pmc1.sav'.
75
capital stock final merge.sps
set mxmemory=2097151.
* MERGE SUB-GROUP FILES.
get file='h:\files\capital stock\pmc1.sav'.
add files file=*
/file='h:\files\capital stock\pmc2.sav'
/file='h:\files\capital stock\pmc3.sav'
/file='h:\files\capital stock\pmc4.sav'
/file='h:\files\capital stock\pmc5.sav'
/file='h:\files\capital stock\pmc6.sav'
/file='h:\files\capital stock\pmc7.sav'
/file='h:\files\capital stock\pmc8.sav'
/file='h:\files\capital stock\pmc9.sav'
/file='h:\files\capital stock\pmc10.sav'
/file='h:\files\capital stock\pmc11.sav'
/file='h:\files\capital stock\pmc12.sav'
/file='h:\files\capital stock\pmc13.sav'
/file='h:\files\capital stock\pmc14.sav'
/file='h:\files\capital stock\pmc15.sav'
/file='h:\files\capital stock\pmc16.sav'
/file='h:\files\capital stock\pmc17.sav'
/file='h:\files\capital stock\pmc18.sav'
/file='h:\files\capital
stock\pmc19.sav'/file='h:\files\capital
stock\pmc20.sav'/file='h:\files\capital
stock\pmc21.sav'/file='h:\files\capital
stock\pmc22.sav'.
aggregate outfile=*
/break=cso_ref year
/rnet_pm=max(rnet_pm)
/ K_pm=max(K_pm)
/ nk_pm=max(nk_pm)
/ gk_pm =max(gk_pm)
/deprec=max(deprec).
save outfile='h:\files\capital stock\net
plant capital stock.sav'.
if (missing(nk_69)) nk_69=0.
if (missing(gk_69)) gk_69=0.
if (missing(dep_69)) dep_69=0.
compute k_tot=(k_pm/1000000)+k_69.
compute
nk_tot=nk_69+(nk_pm/1000000).
compute
gk_tot=gk_69+(gk_pm/1000000).
compute
dep_tot=dep_69+(deprec/1000000).
means k_tot k_pm k_69 by
year/cells=sum.
aggregate outfile=*
/break=cso_ref year
/rnet_pm=max(rnet_pm)
/k_tot=max(k_tot)
/nk_tot=max(nk_tot)
/gk_tot=max(gk_tot)
/dep_tot=max(dep_tot).
variable labels rnet_pm'real investment
in plant £1980 prices' k_tot'p&m capital
stock £m 1980 prices' nk_tot'net p&m
capital stock £m 1980 prices'
gk_tot'gross p&m capital stock £m
1980 prices' dep_tot'depreciation £m
1980 prices'.
save outfile='h:\files\capital stock\total
capital stocks
1970_01.sav'/keep=cso_ref year
rnet_pm k_tot nk_tot gk_tot dep_tot.
means k_tot rnet_pm by year/cells=sum
count.
title 'capital stock final merge'.
get file='h:\files\capital stock\net plant
capital stock.sav'.
*sort cases by cso_ref year.
* ADD BACK PRE-1970
BENCHMARK INFORMATION.
match files file=*/table='h:\files\capital
stock\benchmark.sav'/by cso_ref year.
if (missing(k_69)) k_69=0.
76