NATIONALREGNSKABSNOTAT
Commodity
flow systems
and
construction of input -output
tables in Denmark
Bent Thage
6. KONTOR 1986
DANMARKS STATISTIK
ARBEJDSNOTAT NR.
_Da..2 ?
15
f
1
9 MAR. 1987
DAN MARKS STATISTIK
BIBLIOTEKET
PREFACE
Working Papers on National Accounts (Nationalregnskabsnotater) are
a
working
of
series
papers
from the national accounts division at
Statistik. They contain documentation or analyses related to
Danmarks
the Danish system of national accounts.
present
The
publication
gives
a
complete and detailed
fairly
of the functional part of the Danish system of national
documentation
accounts, both at current and at constant prices.
It
Danish
does
so
bringing together three conference papers on the
by
commodity flow system and on the use of this system as a basis
for the construction of annual input -output tables.
where
explained
how
have
they
In chapter
1
it is
these papers were first presented and reprinted,
been
adjusted
and
updated
and
to fit into the overall
framework of this publication.
Readers
are
invited
to
get in touch with the national accounts
dividion if they have comments on the papers or if they wish to obtain
further
(against
information
a service
on
the
It is also possible
system.
to acquire
charge) individual tables or time series of tables
of the kind described in the paper, i.e. input- output tables, matrices
of
capital formation, energy matrices and employment matrices,
fixed
which all fit together in a coordinated system of time series.
The
original
publication
have
papers
been
as
worked
national accounts division.
well
out
as
by
the adjustments made for this
Mr.
Bent Thage, head of the
5
Contents
1.
Introduction
2.
Balancing procedures in the detailed commodity flow system
at current prices
7
10
1.
Introduction
10
2.
The supply side
12
3.
The user side
15
values
a.
Estimating categories of use at purchasers'
b.
Estimating categories of use at basic values
19
c.
Commodity breakdown of categories of use at basic
values
22
16
4.
Subsystems and notional branches
24
5.
Balancing the system at basic values
28
6.
a.
The automatic balancing of commodities
28
b.
The manual balancing process
30
Balancing the system at purchasers'
a.
Calculation of final trade margin matrices
b. Final
7.
values
balancing of non -deductible VAT
The system as a basis for national accounts and
input- output tables
40
40
44
44
a.
National accounts tables
45
b.
Input- output tables
46
Diagrams and tables:
Diagram
3.
1
Stylized flow -chart for the functional part
of the final Danish national accounts
13
Table
1
A row of the user matrix
31
Table
2
A column of the user matrix
32
Techniques in the compilation of Danish input- output tables at
current prices
47
1.
Introduction
47
2.
The commodity -flow system
48
3.
The first version of the input- output tables 1966 -75
50
4.
Basic features of the present techniques
52
5.
The treatment of imports
55
6.
The treatment of domestic output
57
6
7.
Selected commodities
57
8.
A generalized treatment of imports
61
9.
Concluding remarks
66
Figures:
1.
The make matrix and the absorption matrix
53
2.
Breakdown of selected commodities into domestic output and
and imports
62
Illustration of symbols used in the definition of
"stripped" matrices
62
3.
Annexes:
4.
1600 commodity aggregation
1.
A technical note on the
2.
The treatment of scrap and waste materials
71
3.
Contents of the data bank for input- output matrices
74
Calculations of commodity flows and input- output tables
tables at constant prices
68
80
1.
Introduction
80
2.
Deflation in the detailed commodity flow system
81
3.
Construction of the input- output tables at constant prices
91
4.
Changes of base year
97
Figures:
1.
2.
The Danish deflation procedure illustrated in the SNA
accounting framework
84
The make and absorption matrices used in the compilation
of Danish input- output tables
93
Annex
1:
Some empirical illustrations
101
Tables:
1.
2.
3.
5.
Implicit price indices of the aggregated Danish
1975 input- output table at 1980 prices
106
Percentage growth of main components of gross domestic
product at constant prices
110
Percentage growth of components of private consumption at
constant prices
111
References
112
7
Chapter
1
INTRODUCTION
The present system of national accounts in Denmark starts with the
1966. From that year onwards the system and methods are based on
year
recommendations of the 1968 revision of the United Nations system
the
national accounts (SNA). There is now complete integration between
of
of
contents
the
tables
obtained
are
both
from
and
the
the
annual
more basic
contains about 2500 commodities and is
which
system
flow
accounts
national
and
tables,
input- output
commodity
the
balanced at this detailed level at both current and constant prices.
far no collected description of this system has been available
So
English. To remedy this shortcoming the present publication brings
in
together
three
of
this
use
papers on the Danish commodity flow system and on the
system
basis
as
for
the
construction
of
annual
input -output tables.
papers
The
have
presented at international conferences on
been
national
accounts
and input- output analysis over the period 1981 -86,
and
of
them
have been published in conference proceedings, cf.
two
adjusted
in
publication
this
the papers have been slightly
updated, but otherwise they are basically unchanged and
and
therefore
can
they
use
For
below.
still
considered
be
reprints
of the original
papers.
subsequent
of
use
comprehensive
a
description
of the
this
system
in
the compilation of input- output
also at both current and constant prices. It follows from the
of
nature
give
flow system at both current and constant prices, and of the
commodity
tables,
papers
the
Together
papers
the
that
this
exposition
cannot
be taken as a
documentation of the Danish system. For the
or
a
complete
reader
with
a
basic knowledge of national accounts and input- output
tables
and analysis,
textbook
good
insight
into
the contents of the papers will, however, give a
the
techniques used. In particular compilers and
users of national accounts figures and input- output tables
analytical
will find much useful information in the papers.
In chronological order the three papers are:
1)
"Techniques in the compilation of Danish input- output tables: A new
approach
to
Seventeenth
the
treatment
General
of
Conference
imports"
which was presented at the
of the International Association for
8
Research
in
was
paper
and Wealth held in Gouvieux, France in 1981.
Income
subsequently
input- output
tables,
printed
in
Skolka (ed.) Compilation of
J.
Springer -Verlag,
The
Berlin, Heidelberg, New York,
1982.
The paper is reprinted here as chapter 3, where the title has been
abbreviated
changed
and
somewhat
to
into
fit
the
logic
of the
publication. Furthermore two new annexes have been added.
"Balancing
2)
basis
in the detailed commodity flow system as a
annual input- output tables in Denmark" which was presented
for
International
the
at
procedures
Input- output
Meeting
on
Problems
of
Compilation
of
Tables in Baden, Austria in 1985. The paper is published
the proceedings from the conference: A. Franz and N. Rainer (eds.)
in
Problems
compilation
of
of
input- output
tables,
Orac -Verlag, Wien
1986.
paper
The
changed
where
3)
here as chapter 2, also with a slightly
On several points it has been extended to include the
title.
description
reprinted
is
of
some
new facilities introduced in the 1983 -balancing
new terminal based procedure came into use.
a
"Danish input- output tables at constant prices" which was presented
at
Eighth International Conference on Input- output Techniques in
the
Sapporo in Japan in 1986.
paper
The
"Calculations
reprinted
is
here
as
chapter
4
with
title
the
commodity flows and input- output tables at constant
of
prices ". Apart from the methodological aspects the paper also contains
some
empirical
calculations
carried
out
to
illustrate
the
inhomogeneity along the rows of an input- output table, and it analyses
consequences
the
of
using two more aggregated rebasing methods than
the one actually applied in change of base year for the constant price
calculations.
important new development in the functional part of the Danish
An
national accounts, namely the completion of annual investment matrices
the
for
briefly
in
a
front
period
1966 -83 at both current and constant prices, is only
mentioned in the papers. These matrices,
which are documented
separate volume of this series of working papers (see inside of
cover),
distinguishing
are
available
both
at
the
commodity
flow
level,
about 500 investment goods, and in a transformation to
9
the
input- output
the
one
the
investment
table
format as a set of matrices corresponding to
available for the detailed groups of private consumption. In
are
branches)
matrices 43 owner branches (an aggregation of the 117
The investment matrices are now produced as an
shown.
integral part of the annual commodity flow and input- output system.
Finally
complete
without
international
input-output
formal
an introduction to this collection of papers would not be
mentioning
community
tables
as
of
the
role
national
played by the members of the
accountants
and
compilers of
partners in many fruitful discussions and in
and informal communications on many different occasions. Their
encouragement and positive interest have provided much inspiration for
the writing of these papers.
10
Chapter 2
BALANCING PROCEDURES IN
THE DETAILED COMMODITY FLOW SYSTEM AT CURRENT PRICES
Introduction
1.
accounts
National
been
1930s
based
detailed
which
with
us
have
the commodity flow method.
on
functional
supplies
work in Denmark has since its beginning in the
national
accounts
a good basis for
figures
In addition to the
this
method
also
constructing input- output tables,
been compiled for the years 1930 -39, 1946 -47, 1949,
1953,
annually since the year 1966, when the present system of national
and
accounts
of
was established. This system is based on the recommendations
the
SNA (UN 1968) and has a complete integration between national
accounts and input- output tables.
present
At
accounts
though
start
in
1966,
cf.
time
series
Danmarks
of the Danish national
Statistik (1986a), and even
original national accounts figures for the years prior to
the
were
1966
comparable
the
based
distinguishing
on
commodity
the
flow method,
cf.
Bjerke (1956),
300 commodities, comparable revised figures for
about
the
period 1947 -65 which are now in the process of being finished are
not
backed
by
statistical
be
a
balanced set of commodity flows, (but the production
approach is used). Input- output tables will therefore not
produced in connection with the revised series, and the comparable
series
of annual input- output tables can consequently not be extended
back in time.
This paper will therefore be confined to treating the system which
has been in operation since 1966 (or rather used for producing figures
the
for
years
subsequently
we
could
since
made
a
1966,
as it became operative only in 1975 and
long catching up period necessary before in 1982
declare the work to be up to date, producing final national
accounts
and
covered).
Only the system at current prices will be discussed here, as
input- output
tables
2
1/2
-
3
years after the year
it
is in this system that the balancing takes place.
at
constant
where
it
within
also
of
a
prices
is
described
are
in chapter 4 of this publication
shown that that even though the calculations take place
balanced
system
of commodity flows at current prices they
require special methods and assumptions
this
paper
The calculations
is
the
aggregated
.
commodity
Also outside the scope
flow
calculations of preliminary national accounts figures.
system
used in
11
of
flow system consists of a main system and a number
commodity
The
the result of which are fed into the main system.
subsystems,
highly computerized as this is the only possible way to cope
work
is
with
data
at this level of detail. But the computer is not only used
it also plays an important role in the
as a means of storing the data,
process. The total size of the commodity flow system can be
balancing
by mentioning that it contains about 3.5 million elements
illustrated
(inclusive
could
ten
fulfilled
system
existence
of
years
This does not mean, however, that the
being further developed in response to new
currently
not
After
that the system has
concluded
be
can
it
expectations.
these
is
users of the data a maximum of flexibility.
allow
would
(as for example the adoption of a new
without being fundamentally affected, and
classification)
industrial
philosophy behind the
basic
kinds of specific information, which could endure
all
big definitional changes
rather
The
very detailed system was to create a framework which
this
utilize
which
cells).
zero -value
of
of
design
The
demands and experiences.
The commodities of the system were originally defined for the year
1966.
goods
agricultural
were
would fit together was chosen. For
statistics
production
industrial
services
detailed level at which foreign trade statistics and
most
The
similar
etc.
defined
were formed, and
groups
detailed
means of the most detailed service branch
by
nomenclature. Six -digit numbers are used for the identification of the
national
commodities.
accounts
those
with
identical
the
of
goods the first four digits are
For
CCC nomenclature. For 1966 a total of
4000 commodities were defined. The master files which translate
about
the foreign trade statistics and industrial production statistics into
the
accounts
national
commodities
must however be updated annually
because of changes in the commodity classifications
four
digits)
the basic statistics. If in the basic statistics an
in
number
existing
aggregated,
(yet not the first
replaced
just
is
by
a
new
one
or
further dis-
corresponding changes in the master file are
the
a
sheer
formality.
But if commodities In the basic statistics (still within a
four -digit
group)
classified
are
necessary
aggregated,
it
may
be
commodities
in
the
master
cannot
be
continued,
characteristics
are
and
not
according
to
to new criteria or are
aggregate
national
accounts
file too, as the earlier level of detail
as national accounts commodities with new
currently
being created. During the period
12
such
1966 -81
caused
changes
number
the
of
national
accounts
commodities to shrink from about 4000 to about 2500.
following exposition will be closely linked to the flow -chart
The
in
diagram
where
1,
independently
calculated
which
system,
it is illustrated how supply and use are first
and
then brought together in the balancing
several steps takes us from the balancing at basic
in
values1 to the balancing at purchasers' values.
2.
The supply side
The supply side of the system is contained in a 2500 (commodities)
by
inclusive
(branches,
121
of
four national branches) matrix for
domestic output. Imports and customs duties are aggregated to the 2500
commodities
value
of
well. Customs duties are considered part of the basic
as
imports
of
goods,
and the supply side is in general only
estimated in basic values, as the concepts of output or value added at
market
prices
not
are
applied
Danish
in
national
accounts
at
industry1) level.
The main categories of supply and the way they are treated are set
out in diagram
cif and customs duties are fed directly into the national
Imports
accounts
system
master
The
commodities
used
1.
from
file
the tapes containing foreign trade statistics.
used
for
transformation
national
is updated annually and is of course identical
transformation of exports.
for
to
accounts
to the one
The sum of customs duties on the
tape usually exeeds the total known from government finance statistics
refunds
of
because
etc.
which are not distributed by commodities. A
proportional regulation eliminates the difference. Imports of services
are taken from the balance of payments statistics but some elaboration
is
required,
balance
of
accounts,
other
hand
as
the
payments
and
also
national
borderline
is
different
because
accounts
between
from
goods and services in the
the one needed in national
much more detail is needed here. On the
follow
the
balance
of
payments in
generally only showing trade in services as net items.
1)
The terms values and prices are used synonymously in this paper,
and the same is the case with the terms industry and branch.
-
Diagram
1.
Stylized flow -chart for the functional part of the final Danish national accounts
SUPPLY
BALANCING
Indus ries
Basic values
^
_e-
Imports:
Imports c.i.f.
Customs duties
Services etc.
Domestic output:
Manufacturing
USES
Commod -ties
Basic values
Commodities
Basic values
Total use by branch /purpose
Purchasers values
Basic values
s,
Masterfile
/P
Masterfile +
balancing
JO
Predetermined
values
Energy
Repair
Insurance
Special cells
Supply side at
basic values
2500 x 124
matrix and sum
by commodity
--
Masterfile
User side at
basic values
2500 x 19B
matrix and sum
by commodity
ud Made
margin file
Exports:
Exports f.o.b.
Services etc.
(117 + 4 branches)
Inputs:
Establishments in industrial
statistics (turnover concept)
(a) Commodity stat. (2 6 empi.)
(b) Accounts
20 empi.)
stet..
Manufacturing industries
Aggr.
Supply less use = 2500 differences.
All column totals are at their
initial estimate
Masterfile
iFdF
---Aggr.
-
41.
Aggr.
Commodity distriOther establisments
(c) Register based (S 5 empi.)
(d) Special branches (S, V)
Aggr.
bution
keys
Proportional horizontal distribution
in the user matrix of commodity
differences. Exports and stock
changes are not affected
o
Branches directly on national
accounts form:
i
ft
Agriculture
Government services
All commodities are now balanced,
but column totals will differ
Branches based on comprehensive
calculation systems:
I
,
Correc-
Other branches:*
Forestry (S)
Fishing (S)
Extraction of oil and gas (S)
Electricity, gas, steam
and water (S)
Trade (A, V)
Restaurants and hotels (V)
Transport (A, V, S)
Finance and insurance (A)
Business services (V)
Education and health,
market services (S)
Recreation and cultural
services (V, A, S)
Household services (V)
Domestic services (S)
Private non -profit services (S)
Notional branches (S)
Corrections
supply side
Manual balancing process. The
result is the complete system
balanced at basic values
o
for year
user
aide
411-
4
Notional
Special system
for initial estimate
66 groups.
Deduction of
commodity taxes,
net,
Goverment consumption:
VAT and
One total only
trade margins
(1st VAT balance)
(1st margin bal.)
Gross fixed capital formation;
y
-01
statistics
V= VAT -statistics
S= Special calculations
1
I
4-
i
I
Machinery and equipment
Transport equipment
Construction
Breeding stocks
Change in stocks:
Commodity distribution keys
by category
1
Special stock changes
Stock changes based on
accounts statistics
(a) Wholesale, retail,construc
tion and manuf. industries
excl. (b)
Final VAT balancing
Complete balanced system at
all value levels. Output from
manuf. industries changed from
turnover to production concept.
Supply side: 2500 x 124 matrix
User side: 4 x (2500 x 198 matrix)
Value added at factor cost as residuals
branches (4)
Private consumption:
c
1
Special calculations
Small units (4 5 empl.)
Special branches
t
1
Vertical
distribution by
commodity as
in year t -1 at
t- prices
(Predetermined
cells excluded)
Industrial statistics:
Establishments (2 20 empi.)
Enterprises (' 20 empi.)
Establish,. (k 6 empl.) Estimate
All other actual branches
l
Final trade margin balancing.
Complete matrices for wholesale
an retail trade margins
Compensation of
employees
Complete balanced
system for year t -1
inflated to t- prices
and including all predetermined values and
commodity taxes, net,
41
from their initial estimates, i.e
there is about 190 differences
Construction
Use of dwellings
Repair of motor vehicles
*A= Accounts
(117 + 4 branches)
industries:
4--
-
(b) Finished products and
work-in-progress in ma-
{
Non -commodity
taxes, net
nufacturing
industries
indirect
**
Calculation of indirect production costs
in manufacturing industries and repair
and maintenance balancing.
14
steps.
quarterly
The
employing
more than
commodities
file
are
file
is
manufacturing
from
Output
calculated in several
is
statistics cover all establishments
commodity
persons. It contains the turnover of about 7500
5
(following
an 8 -digit CCCN -based code) which by a master
transformed
to
updated
also
industries
national accounts commodities. This master
annually. The data are fed directly from tape
into the national accounts system. The fact that the turnover
production)
the
treatment
of
concept
changes
is
in
here
used
stocks
has
of
consequences
finished
(and not
for
the
products
and
work -in- progress, to which we shall later return.
in establishments employing less than 6 persons (or
turnover
The
more precisely: those establishments in manufacturing industries which
are
by
covered by the quarterly commodity statistics) is determined
not
matching
is
value
figures,
turnover
with
the
as
added
there
tax
statistics
(which
is a single -rate VAT system in Denmark)
commodity statistics at establishment level.
the
also contain
In this way it
possible
to
remove from the VAT -based turnover those units which
covered
by
the
are
usually
also
commodity statistics. As these bigger units are
where the VAT- registration unit may deviate from
those
the establishment concept, we are left with a turnover by branch which
it
reasonable
is
commodity
to
interpret
as output in the smaller units.
The
mix of this output is not known, but for each branch (there
are about 100 branches at this stage) a commodity mix is assumed based
on
kind of branch and on the commodities known to be produced in
the
the bigger establishemnts
Up
till
industries,
have
not
this
stage
in the branch.
the
accounts
which cover establishments employing at least 20 persons,
been utilized. These statistics are grossed up to cover all
establishments employing at least
branch
statistics for manufacturing
between
the
turnover
in
6
persons, by using the relations by
the
commodity
statistics and the
accounting statistics. As will be seen later this is primarily done in
order
to
estimate
input
by
branch.
At the output side only three
"commodities" are taken from this enlarged statistics, namely
(1)
work done on materials belonging to other establishments (until
1982)
(2)
repair and installation work done for others (until 1982)
(3)
production of fixed investment goods for own use.
15
From
onwards
1983
statistics
are
they
as
and (2) are taken from the quarterly turnover
(1)
longer shown separately in the accounts
no
statistics.
machinery
and
publishing
slaughter
repair
shops
houses,
some branches in
from other
calculated
are
total supply from manufacturing industries has
which
after
sources,
to
additions
some
Finally
been estimated both by commodity and by branch.
sources
methods
estimation
and
are distinguished.
groups
accounts
and
form,
extreme
which
for
vehicles,
adjustments
construction,
as
of different
number
In diagram
used.
specialized
the
few
only
areas
are
are
great
a
1
three broad
For agriculture and government services the
from
received
are
figures
motor
industries
non -manufacturing
For
divisions
are
on national
required.
The other
use of dwellings and repair of
calculation
comprehensive
systems
are
established in the national accounts division. For the third category,
which
almost
contains
all
services,
methods are indicated in diagram
1.
the most important sources and
It is,
however, not possible to go
into any detail in describing these estimates, although a good deal of
the resources of the national accounts division go into this work.
accounts
national
The
commodities
for
services are in general
defined
by the most detailed service branches in the national version
of
ISIC
the
about
1968.
defined,
activity
particular
total we have about 300 services produced by
industries. All service branches are assumed to be
service
30
In
i.e.
service
is
there
is
no
secondary production, and one
in one and only one service
produced
branch.
on the other hand implies that the goods producing branches as a
This
are
also activity defined. The trade activity of manufacturing
industries
employing at least 20 persons is explicitly transferred to
whole
trade,
apart from this it is conveniently assumed that the trade
but
activity in small manufacturing establishments cancel out against what
production of goods there might be in trade, repair services, etc.
3.
The user side
In
chapter
basic
prices
total
use
confronted
three
2
was
saw how the supply of the 2,500 commodities at
determined.
We
now have to make estimates of the
each of these commodities, also at basic prices, to be
of
with
steps.
we
the
supply
in the balancing process. This involves
Firstly each category of use (input into an industry,
a
16
group
household
of
consumption
expenditures,
at purchasers
etc.)
prices
must
prices
must be calculated, and thirdly this total at basic values for
estimated. Secondly the corresponding value at basic
be
each category of use must be distributed by commodity.
3.a Estimating categories of use at purchasers'
exports
Total
balance
and
of goods and services are known from foreign trade
payments
of
values
statistics,
what is said above about
cf.
imports.
Total intermediate consumption in each branch is based on much the
same
sources
problem
complicated.
more
is
coverage
mentioned for supply, but in general the estimation
as
is
some
good,
Even
kinds
enterprise
and
not
at
statistics
are
not
very
purchases
shown
expenditures
of
establishment
helpful
there
cases where the statistical
in
the
comprise
both
only given at
Furthermore
level.
on
are
input
side
the
VAT
because the
expenditures
current
and
expenditures for fixed capital formation.
manufacturing
For
and a few other items (direct production costs) are taken from
energy
establishment -based
grossed -up
the
above.
than
industries the expenditures for raw materials,
accounts
statistics
mentioned
direct production costs for establishments employing less
The
persons are in general estimated by using the same output /cost
6
ratio as for the bigger establishments in the branch. The expenditures
indirect
for
maintenance
covering
which
only
given
are
in enterprise -based accounts statistics
enterprises employing at least 20 persons. These statistics,
also have a detailed breakdown by branch, are aggregated to the
natonal
costs,
accounts
and
buildings,
turnover
in
costs (i.e. mainly services) and repair and
production
branches,
respectively,
defined
branches
branch.
Having
arrived
at
national
commodities
the
added
estimated
these
total
as
percentages
of
total
and these percentages are subsequently used
calculate
to
accounts
used
the
calculated
are
of own products,
with
for each branch indirect production
for repair and maintenance of machinery and
expenditures
connection
and
to
purchase
definition
outputs
these
three
the establishment
from
cost elements for each
the direct production costs we have
of
of
inputs
by
each branch. As the
intermediate
consumption
is
rather than purchased the net increase in stocks of
raw materials, purchased semi -manufactures etc. must be deducted.
17
the establishment -based accounts statistics the value of these
In
stocks
the
at
and
beginning'
of the year (more precisely:
end
the
accounting year, which might deviate from the calendar year) is given.
It
assumed that the stocks are valued at the prices at which they
is
have
been
and that on average they have been purchased in
purchased,
(corresponding to the observation that stocks are on average
November
turned over ten times per year). As no commodity details are given, we
further
assume
mix equals the input structure of
into the branch in the preceding year. As we have price indices
goods
for each commodity
to
possible
materials
purchasers'
at
industries
at
both
current
and
column totals of this matrix are deducted from
The
purchase
it is now
matrix of stock changes of raw
complete
the
manufacturing
in
prices.
total
uses
for November and for the year on average,
calculate
etc.
constant
the
product
the
that
by branch mentioned above to arrive at the total
prices.
row
(The
totals in this stock change
form part of total stock changes by commodity - a final demand
matrix
category).
For
costs
branches outside manufacturing
are
and
repair
and
ment)
separately
already
not
singled
maintenance,
buildings
for
each
and
industries indirect production
out at this stage,
but the two categories of
of machinery (inclusive of transport equip-
structures,
branch.
respectively,
are calculated
As repair and maintenance are balanced
at this stage in a separate subsystem, cf.
below, the initial
estimates might have been changed in this process. Seen from the point
of view of the system at large these adjusted values are however still
initial estimates of intermediate consumption.
For quite a number of subbranches in the service industries it has
necessary to resort to estimating total intermediate consumption
been
as
a
rather unfounded fixed percentage of output. Even in cases where
there is access to some statistics it can be difficult to utilize them
because the extent of intra- industry sales, subcontracting etc. is not
known.
As
vary
work).
there is only one branch for construction its input ratio will
depending
on
the output mix (structures, new buildings, repair
The initial input total for this branch is therefore of a very
preliminary
character,
balancing process.
and
may
be
changed
considerably
in
the
18
initial
The
consumption
car
either
are
of
final
growth
the
groups of private
66
made directly as an absolute figure (energy,
rates at current prices which are multiplied by
several
classifications
of
of
figures for the preceding year. These growth rates are the
of
results
the
each
for
repair, insurance etc., cf. about special subsystems later) or as
estimates
the
estimates
accounts
transformation
of
processes
which
the retail turnover index,
translate
the
the VAT statistics and
statistics for retail trade into the SNA classification
household
consumption expenditures.
In this way several different
growth rates can be obtained for one particular consumption group, and
taking into consideration the price index for each group it is
also
matter
for
experienced
the
national
a
accountant to choose the most
likely growth rate for each group.
Data
are
the final consumption expenditures of general government
on
received
statistics.
sales
from
expenditures
specialized
the
the
At
government
output
from
same
of
we
of
general
receive
which
commodities,
producers
of
time
division
a
is
government
government.
on government finance
detailed breakdown of
the difference between
services
The
breakdown
and
consumption
by
purpose of
government consumption is not applied in the commodity flow system.
For gross fixed capital formation construction
are
determined
construction
changed
groups,
connection
branch
the
in
and
the estimates of output for the
with
agriculture,
respectively, and will not be
balancing process. The initial estimates for the two
machinery
traditionally
the
in
and breeding stocks
and
been of
a
equipment,
and
transport
equipment,
rather poor quality, as basic statistics
have
from
user side are scarce. In the balancing process the commodity flow
system for investment goods has therefore been allowed to overrule the
initial
However,
has
estimates
more
than
in any other category of final demand.
from the year 1982 a new system for making initial estimates
been
established.
The system is based on the experience obtained
by constructing annual investment matrices for the years 1966 -81.
The
calculation
semi -finished
described
changes
way,
stock
of
products
etc.
changes
in
for raw materials,
manufacturing
industries
purchased
has been
above. For finished products and work -in- progress the stock
in
manufacturing
industries
are calculated in an analogous
but in this case the output matrix of the preceding year is used
19
to
the distribution by commodity. As the supply side throughout
form
process is on turnover (sales) basis for manufacturing
balancing
the
these stock changes are not introduced into the commodity
industries,
flow system, but only (as indicated in diagram
1)
used at branch level
to transform the final figures from sales to production concept.
changes
Stock
are
on accounts statistics of the same kind as found for
based
also
wholesale trade, retail trade and construction
in
industries,
manufacturing
value
the
i.e.
of
stocks
detailed
by
subbranch at the beginning and end of the accounting period is known.
wholesale
For
thereof
seems
the
of
likely
most
construction
and
with
matched
is
stocks.
trade
a
subbranch
each
or part
branch in manufacturing industries which
of the kind of commodities held in
producer
Thus the same system as used for calculating changes in stocks
finished products and work -in- progress in manufacturing industries
can be used to calculate these stock changes by commodity.
retail trade the subbranches are matched with the consumption
For
groups
same
(the
key as used in connection with the
transformation
estimates of consumption groups), and the composition of each group by
commodity
retail
on
the
in
preceding
is used as a distribution key for
year
stocks. Again by using price indices for November and the year
the complete matrix of retail stock changes is calculated
average
at both current
stock
Special
products
and constant prices.
and
calculations
change
made
changes
stock
physical
energy,
are
for
being
agricultural
multiplied by
average prices.
3.b Estimating categories of use at basic values
Whereas
of
categories
obvious
that
consumption
demand)
it
we
of
is
obvious
use
at
purchasers'
at
this
each
an initial estimate of each of the
that
level
industry,
of
prices
is necessary,
aggregation
totals
for
intermediate
(total
each
it is less
category of final
should calculate initial values at basic prices, as trade
margins and commodity composition of each of these (vertical) totals
a
composition
balancing
simplifying
which
process.
is
not
yet
Therefore,
assumptions
to
what
avoid
-
known, as it is determined in the
we
the
do in this step is based on
complication
of
explicitly
20
entering into a simultanous balancing procedure where all price levels
open to change at the same time. On the other hand what we do now
are
is
labelled the first set of balances for VAT, other commodity taxes,
and wholesale and retail trade margins, respectively. During the
net,
balancing
process
purchasers'
basic
at
and
basic
prices
values
these first differences between
might
changed,
be
after
and
the
completion of the basic price balancing the second and final balancing
of
commodity
VAT,
taxes,
and
net,
trade margins takes place, cf.
below.
first
The
categories
step
of
now
is
For
use.
calculate
to
non -deductible
use we know the VAT
each
VAT
by
for the preceding
year,
and if the VAT rate has not been changed the same percentage is
taken
of the category at purchasers'
changed
percentages
the
construction
of
known
changed
are
same proportion. For
the
in
the theoretical VAT rate is used in any case. If the sum
calculated
this
prices. If the VAT rate has been
is within reasonable closeness
VAT
from government finance statistics,
to the total
the difference is left open
at this stage. This is usually the case.
Commodity
commodity
taxes,
(primarily
preceding
the
been estimated by user category and
by using the horisontal distribution known from
year).
commodity -by -use
have
net,
So
this
at
stage
we
have
a
complete
of commodity taxes, net, and these taxes are
matrix
balanced, although the specific distributions will be changed somewhat
in the balancing process.
For
a
number og commodities the detailed distribution by user of
basic
value, wholesale, and retail trade margins and commodity taxes,
net,
is
compiled
predetermined
except
in
values
cases
in
separate
are
not
where
subsystems,
changed
cf.
below.
These
during the balancing process
errors are detected and corrected at a later
stage.
Exports f.o.b. of goods are aggregated by means of the master -file
to
the
assumed
level
that
of
the
the
national
accounts commodities and it is then
percentage rates of wholesale trade margins of the
preceding year are still valid (retail trade margins on exports are by
definition
exports
at
calculated.
nil).
basic
Commodity
values,
taxes,
both
net,
total
on
and
exports are known, and
by
commodity,
can
be
21
stock changes the calculation methods described earlier imply
For
also the link between purchasers' and basic values. Both trade margins
and commodity taxes, net, but not VAT, might be part of stock changes.
As
for
values
commodity
the
exports,
immediately
is
known.
of the totals at basic
composition
same is the case for gross fixed
The
capital formation in construction and breeding stocks.
we
Still
retail
trade
categories
initial estimates of basic values, wholesale, and
lack
margins
of
of
the
balanced commodity flow system from year
is
created.
Before
commodities
in
all other
.
this purpose a file containing the complete
For
use.
most
for
inflated to year
t -1
t
prices
all predetermined values were entered into
1983
this file where they replaced the inflated values. This "mixed" system
was
then
basic
added
values,
so that for each column we obtained (1)
column,
by
wholesale trade margins, (3) retail trade margins,
(2)
and (4) commodity taxes, net.
For intermediate consumption, private consumption, and gross fixed
capital
formation
commodity
(other
are
net,
taxes,
construction
than
first
deducted
and
breeding
from purchasers'
stocks)
values
exclusive of non -deductible VAT (cf. above). Before 1983 the remaining
total
each
for
wholesale,
and
category
retail
of
trade
use
were subdivided into basic value,
margins
the
in
same
calculated from the inflated "mixed" system for year
From
the
the
in
variations
by
t -1.
onwards this method has been changed in order to avoid
1983
distortions
caused
proportions as
in
breakdown on basic values and trade margins
the
share
of
predetermined commodities.
of entering the predetermined values into the inflated system
Instead
for
year
now
removed
all cells containing predetermined values in year t are
t -1,
from
the inflated system for year
t -1.
Commodity taxes,
have been estimated at an earlier stage and are removed from the
net,
system
in
the
same
way
as
the predetermined values.
The file now
contains inflated basic values, wholesale, and retail trade margins of
the
preceding
year
for those cells in the system,
where a value for
the current year has not been calculated separately.
For
intermediate
consumption
and gross fixed capital formation,
residual purchasers' value (exclusive of non -deductible VAT, commodity
taxes, net, and also all predetermined basic values and trade margins)
is
calculated
for
each
category
of
use.
This
residual
is then
22
subdivided between basic value, wholesale, and retail trade margins in
calculated
proportions
the
mentioned
above.
estimates
of
When
basic
from
the
file
predetermined
the
wholesale,
value,
with
inflated
values
values are added, initial
and retail trade margins are
found for each category of use.
private
For
consumption
accounts
estimates
consumption
group
calculated in
are
statistics,
cf.
of
retail
trade margins by
separáte system that utilizes
a
the description in section 6 of the use of
accounts statistics for retail trade. For 16 of the consumption groups
wholesale
margins can be estimated in
trade
a
similar way. From 1983
onwards these estimates are used, when basic values are calculated for
consumption groups.
For
government
consumption expenditures there is just one figure
and no difference between purchasers' prices and basic prices.
totals
the
When
calculated
for
of wholesale and retail trade margins have been
all uses,
they can be compared to the total supply of
If there are big differences the
each of these kinds of trade margins.
matter is looked into. This may result in adjustments of trade margins
certain
for
categories
demand
final
(primarily
private
but at this stage a complete balance between supply and
consumption),
use
of
of trade margins is not aimed at, as they will anyway be modified
in the balancing process.
have
We
now
arrived
at
total
use
by
category (industry for
intermediate consumption, purposes for final demands) at basic prices.
3.c Commodity breakdown of categories of use at basic values
As results of earlier calculations, exports of goods and services,
stocks and, for fixed capital formation, construction and
changes
in
changes
in breeding stocks have already been broken down by commodity
at basic prices.
For
they
all
other categories of use it is now initially assumed that
are distributed by commodity in the same way as in the preceding
year, represented by the inflated final commodity
Before
this
commodities
that
they
(vertical)
distribution
flow system for
t -1.
takes place, the predetermined
are removed from the totals and the distribution keys,
are
not
overruled
by
this
so
automatic distribution. For
23
industries the totals for indirect production costs are
manufacturing
separately,
distributed
cost
category
the goods and services belonging to this
as
develop
might
from the direct production
differently
costs.
what is here carried out is the first step in a modified
fact,
In
procedure,
RAS
basic assumption is that the physical input
the
and
structures composition of final demands from the preceding year is the
of
point
best
departure.
assumption
alternative
the
prices
would
carry
out
in
decisions
taken
hand
other
such
results
of
the
whole
test would be almost impossible to
a
manner because of all the discretionary
be a priory expectation that the
must
presumably
there
different
the manual part of the balancing process. On the
in
followed
procedure
and
controlled
a
constant input structures at current
of
significantly
give
procedure,
balancing
however, never been tested whether
It has,
does bias the final figures towards more constant
input structures than those actually found in the real world.
For years where figures are available from censuses on inputs into
manufacturing
fifth
every
industries
year)
from
or
budget surveys
household
(about
the above procedure is different, as in principle
automatic distribution by commodity can be replaced by the actual
the
values.
from these censuses, which have a very detailed
figures
The
by commodity (in most cases more detailed than the national
breakdown
commodities),
accounts
must
however
grossed up and adjusted in
be
ways before they can be fed into the commodity flow system.
different
calculations often happen in ad hoc systems which might also be
These
influenced
the data already in the final national accounts system
by
preceding
for
the
new
information
year. An important principle when introducing the
is
make the maximum use of it while at the same
to
time securing a minimum break in continuity. The needs of the national
accounts division are taken very much into consideration in the design
of
both
the
input
census and the household budget survey, and this
facilitates the introduction of the data into the system.
The
structure
input
originally
been
producers
for
estimated
by
accounts
for
repeated
at
structure
is almost exclusively
central
(many)
and
years
digging
local
of
government services has
down into the details of the
governments,
interval.
For
and this procedure is
constructidn
the
input
determined by kinds of commodities in
24
the commodity flow system,
in
this
as input censuses have never been conducted
area. So both these important branches are in ordinary years
treated
together
with
the
other branches in the automatic vertical
distribution process.
We have now arrived at the 2500 (commodities) by 198 (uses) matrix
at basic prices mentioned at the beginning of this chapter and are now
ready
to confront the user side with the supply side in the balancing
process.
Before proceeding to this it will however be useful to say
a
few words about the predetermined values and the national distribution
branches.
4.
Subsystems and notional branches
notional
A
serve
we
as
artificial branch which is created to
to identify in detail.
intermediate
its
to
an
is
distribution instrument for commodities, the use of which
unable
are
equal
a
branch
The output of such a branch is
consumption
so
that
no value added is
created. In the Danish system there are three notional branches:
-
notional branch for goods
-
notional branch for services
notional
-
branch
for
some
goods
and services for repair and
maintenance
(As a fourth notional
imputed
the
input
bank
not
is
branch might be mentioned the one which receives
service
later
charges.
distributed
This is however atypical as its
as
output and therefore creates a
negative value added).
In the calculation sequence from total
to
breakdown
of
inputs
by
commodity
input at purchasers' prices
at basic prices the n *tional
branches are treated in the same way as ordinary branches.
notional
The
things
small
like
part
branch
branch for goods receives as input office supplies,
electric bulbs and some advertising expenditures. Only
of
the
total supply of goods is channelled through this
and its level and growth rate is not a cause of worry.
however,
for
communication
household
the
a
notional
expenditures,
Not so,
branch for services, which receives most
business
services
and
a
good deal of
services (to the extent that these are used by business, as
notional branches do not deliver to final demand categories). About 25
25
per
of
cent
imputed
bank
branch.
Its
growth
in
such
financial
services
computer
as
leasing).
leasing
(in
service industries receive
many
As
and
input from the notional branch for services, its size
consequences
unfortunate
some
than trade, dwellings and
other
rate has been extremely high because of the fast
growth
dominant
has
services
charges are now (1983) channelled through this
service
services
particular
their
market
all
the
in
construction
of
the
input- output table, cf. below.
As mentioned earlier, there is a complete subsystem for repair and
where
maintenance,
commodity
balanced
are
commodities
is
for each "repair
"unspecified
repair
of
The total expenditures for repair and maintenance of
follows:
as
use
which is the "output" of a notional branch. The procedure
machinery ",
is
and
these
of
One
".
supply
machinery and transport equipment are estimated for each branch. After
deduction
repair
for
motor
of
vehicles,
repair done by machinery
repair shops, shipyards, repair shops of airlines and public transport
companies,
etc.,
and
branch,
the
is assumed to come from the notional
residual
sum total of these residuals then defines the total
the
size of the notional branch. Inputs into this branch will be all kinds
of
spare
repair
parts,
done
work
for
balancing process in the system at large
real
other
subsystem
by
branches
in
industries etc., and this input mix will be modified in
manufacturing
the
others
the case for all
notional branches - and is therefore not part of the
and
repair
for
- as is
and maintenance, which also contains the final
balance for repair og buildings and structures.
In
the
preserved,
balanced
commodity flow system the notional branches are
their
existence causes no problems in relation to the
as
construction of the ordinary national accounts tables. In principle it
would also be possible to preserve them in the input- output table, but
in
practice
it
is
calculations
which
input- output
table,
each
the
element
input
procedure
structures
run
transform
these
the
branches
commodity
flow
Therefore in the
matrices
to the
are eliminated by assuming that
of
the particular notional branch. The drawback of this
course
that
we
pretend
(in particular for services)
solution
for users.
in the output row has the same commodity composition as
into
is
inconvenient
rather
to
to know more about input
than we actually do. The long
this problem is obviously to try to distribute more
26
services directly, as even the sole use of common sense can often give
us
distribution
better
a
than
calculated
one
the
on
the above
assumption.
from
Apart
subsystem for repair and maintenance three other
the
subsystems exist. They are: the motor vehicle distribution system, the
energy system and the insurance distribution system.
vehicle
motor
The
system
contains
a
distribution of all motor
vehicles by owner branch or household. Eleven different kinds of motor
are distinguished. From the official motor vehicles register
vehicles
the
number
total
owner
rather
motor
vehicle
fuel
of
categories
these
of
cars is known
but the distribution
in the national accounts division and is based on
made
is
often
of
each
as the average number for the year),
(calculated
by
of
statistics for certain industries, the type of the
old
and many kinds of indirect information such as the use
All this and a good deal of heroic assumptions make it
etc.
possible to update the motor vehicle matrix (118 by 11) annually. This
matrix
with
is not used directly
of distribution keys to be applied to expenditures on fuel
a set
motor
for
insurance,
vehicles, lubricating oil, tyres, service charges for auto
repair of motor vehicles, and motor vehicle duties.
most
In
which
cases it is not just the actual number of motor vehicles
used
is
in the national accounts, but supplies us
as
a
distribution key. We also take into account the
kind of fuel used (petrol, diesel oil or LPG) and
per
year
household).
particular
any
for
assumptions
The
car
in
any
the average mileage
particular
branch
necessary to make these submatrices are
even more heroic than those used to construct the main car matrix,
it
none
is
but
less believed that this system yields a much better
the
distribution
(or
of
the
relevant
commodities than could otherwise have
been obtained. The basic assumption here as elsewhere in our system is
that the more detail you have the easier it becomes to apply all kinds
of
specialized
information,
expert
knowledge,
and
-
perhaps most
important - common sense.
The
use
of
values
about
time
20
energy
commodities.
Both physical quantities and
all price levels) are calculated.
(at
sophisticated
same
system gives a complete description of the supply and
energy
This system is the most
subsystem, where a comprehensive balancing model at the
takes
account of both quantities and values, depending on
27
of information is available. For manufacturing industries
kind
which
energy censuses are held with two or three years intervals, giving the
quantities of each kind of energy, whereas there is annual information
about
total expenditures on energy products for each branch. For
the
census
energy
years
this
is combined to calculate the
information
average price paid by each branch for each kind of energy, and for the
inter -census
total
years
costs
energy
price relations are used together with the
their
for
each
branch
to
estimate
the
physical
quantities. To this is added all available information from the energy
producing branches and what statistics are available from the Ministry
of
Energy.
energy
The
consumption
of small manufacturing units is
determined
by a set of differentiated grossing -up methods. For use of
energy
other
in
household
quinquennial
kinds
consumption
Energy
information
is
in
some
cases
by households can be checked against the
budget
surveys,
and it too is based on many
specific information. The energy taxes (other than VAT) are
of
calculated
the system, and the calculated total compared with the
in
actual total from government
margins
trade
annual
in other cases specific information is completely
whereas
available,
absent.
branches,
energy
on
finance statistics is a useful check. The
products are supervised continually by the
Danish Monopolies Commission and are therefore rather well documented.
Although
physical
the
national
accounts
separate
field
data
energy matrix is not part of the ordinary
is published together with them, and also as a
it
of energy statistics. Furthermore, the constant -price
energy are found by multiplying the quantities by base year
for
prices.
The
the
of energy used by motor vehicles takes place in
distribution
system
car
and is then transferred back to the energy system to
make this complete.
the
In
charges
for
the
which
system
for
distribution
of
accident insurance service
starting point is about 25 different kinds of insurance,
the service elements are calculated as gross premiums less
claims. For some kinds of insurance it is immediately obvious that the
users are some specific branches or households, whereas for the rest a
distribution
also
a
key
connection
been
constructed. As mentioned above there is
between
this system and the car system as far as
has
motor vehicle insurance is concerned.
28
commodity
All
predetermined
accounts
(not
taxes,
which
subsystems
the
in
system
commodity
distributions
just
net),
are
this
in
fed
into
have
way
the
been
main national
basic values, but also trade margins and
and
will only in exceptional cases be
they
changed in the subsequent balancing process.
5.
Balancing the system at basic values
We
now have the supply matrix (dimension 2,500
matrix
(dimension
balancing
2,500
system.
errors
are
almost
exclusively
Only
detected,
x
to
198)
x
confronted
be
in very few cases,
and the use
124)
in the central
for example where obvious
will changes be made at the supply side. So it
the
is
matrix
use
which is the object for the
balancing work.
different steps in the balancing procedure can be followed in
The
diagram
1.
5.a The automatic balancing of commodities
first
The
deduct
Of
to aggregate both matrices by commodity, and
is
estimated
the
obtained.
step
course
use
some
calculations
take
happen.
predetermined
The
from supply. Hereby 2,500 differences are
place
of
in
these
might
of
units
be
1000
commodities
are
zero,
Dkr.,
by
bub as
the
that will seldom
definition balanced
already at this stage.
Some
master
of
file
the
bigger
from
year
consideration
the
in
differences
t -1
year
to
(vertical)
appear
t
have
because changes in the
not
been taken into
distribution of each user total at
basic values (the first step in the modified RAS procedure,
which
done
is
existing
in
on
year
the
t -1.
basis
of
cf. above)
the national accounts commodities
This technical complication is dealt with by
explicitly making corrections in the user matrix depending on the kind
of
change in the master file (the most usual change being aggregation
of national accounts commodities, where the new commodity is given the
number
of
giving
this number a new content). The reason why this aggregation is
the
most important of the aggregated commodities, thereby
not made already in the inflated
the
master
file
is
t -1
user matrix is that the change in
often necessitated by some special developments
29
which
cannot
introduced
be
into
user
the
of the system by
side
automatic methods.
Also
other
commodity differences are studied, primarily for
big
the purpose of detecting errors either on the supply or the user side.
It
may
decided that big differences among commodities which have
be
dramatically
increased
Denmark
recent
in
construction
horizontal
natural
distribution
used
procedure,
cf.
connection with the
in
network)
gas
(for example in
year
last
kept
are
below,
outside
the
they would most
as
supply. The differences for the commodities "produced"
increased
the
commodities
years
the
since
be allocated to branches which are positively known not to use
likely
by
of
value
in
for goods and services, respectively, are
branches
national
the
always kept outside the horizontal distribution.
taken
Having
next
the
step
of these special differences we are ready for
care
the
in
automatic
procedure
second step in
(the
a
modified RAS procedure), in which the difference for each commodity is
commodity
particular
calculated
on
to
the
uses of that
in the first step. Exports of goods
services and stock changes are not involved in this distribution,
and
as
(horizontally)
proportionally
distributed
they have been given their final values earlier in the calculation
(Although here as elsewhere such categorical statements are
sequence.
never
true.
absolutely
level
commodity
can
In
fact
exports and stock changes at
both
be changed in the balancing process, but not by
means of automatic procedures).
The
will
matrix
user
which
results from the horizontal distribution
have column sums which in general differ from the initially
now
however,
we
still
believe
to be the best
estimated
sums,
estimates
we can produce a priori. So at the present stage the system
has
all
commodities balanced, but hase about 190 differences by user
category.
and
in
which,
now be tempting to go on with the RAS procedure,
might
It
many steps as necessary to balance the system completely.
as
Why don't we choose this easy solution?
The
balancing
answer
process
work and become
the
particular
reference
to
that
is
would
if
we
went on with the RAS procedure,
the
lose its character of empirical statistical
pure model exercise where the only way of explaining
a
size
the
of
an
individual
element
ex post would be a
system as a whole rather than available statistics
30
and the technical and economic development in that particular industry
or
category
demand.
To
take
an example,
is also consumed by a third branch in year t.
t -1
would
final
suppose that a
national accounts commodity which had two user branches in
particular
year
of
leave
element
the
A RAS
balancing
in the third branch still at zero,
and the
of this error would in an untraceable way have been spread to
effects
the
whole system. When, however, we stop after the second step of the
RAS
procedure, we will most probably find that the first two branches
received more than their initially estimated totals, whereas the
have
third branch is in deficit. In the manual phase of the balancing it is
possible
to
errors
the
correct this distribution by changing a few elements, as
in the automatic steps have not spread to the whole
made
system. Therefore, stopping after the second step of the RAS procedure
gives
to
us
be
a
good point of departure for detecting elements which need
and makes such changes manageable in practice, which
changed,
they would not have been if we had stopped after the first step of the
RAS
procedure,
where
we
would
have to cope with 2,500 differences
without having received the instructive clues about the differences by
industry or final demand category which result from the second step in
the RAS procedure.
5.b The manual balancing process
Having
carried
out the second step in the modified RAS procedure
the
automatic part of the balancing has come to an end, and it leaves
us,
as
mentioned above, with
altogether
about
190
a
difference for each category of use
differences,
whereas
all
commodities
-
are
balanced.
As
a
for the manual balancing two kinds of print -outs are
basis
produced:
-
A print -out showing
of
the
the supply and use of each commodity (the rows
the supply and use matrices). As illustration this balance for
commodity
is
shown
in
table
1.
It
is seen that also trade
margins and commodity taxes, net, are printed.
earlier
The commodity taxes
determined, but they must be redistributed if
are
those
the
commodity is redistributed. The trade margins shown have been
calculated by using the margin rate from the preceding year on the
Table
1.
Row (transposed)
for
the commodity "pesticides etc." in the user matrix 1981 (1000 Dkr.)
Supply /; Branch/
Commodity: user
purpose
:
year
no.
1
Domestic output
Imports c.i.f
Customs duties
Intermediate consumption
Private consumption
Raw materials ..
Stock changes
"
Whole sale trade
"
"
Retail trade
Exports
:
2
8
-- 381107
8
5
1010 35110
1010 35120
381107
81381107
- 81
381107
81
381107
-81 -- 381107
81
381107
81
381107
8
381107
81
381107
381107
818F - 381107
381107
81
-
1020
_
1021
-_--
201011103--
133.370(
19.701
9.553
29.412
:
'
Commodity taxes,: Purchasers vanet (excl. VAT)
lues (excl. VAT)
;
7
36.171
6.288
1.316
1.173
8.570
.
123-
1.26440647.450
2061
2062
2080
1
Retail
trade margins
302.004
39.658
21.017
10.726
42.795
1311.264 -
4.813
8---
1138.606
.
is printed out after the horizontal
both tables. The commodity
i
table
1
is balanced,
distribution in the user matrix at basic values, and this row intersects
shown in table
i.e. all supplies (Id -10)
2
at the element 33.370 which is framed in
sum to all uses (Id -20).
In table 2 columns 5 -7 show the results of the automatic part of the balancing carried out by the first
two steps in
modified RAS -procedure. For example the commodity no. 381107 has been reduced from 35.093 to 33.370 in the horizontal
distribution of the total commodity difference of
-
519 -
56. 56
and 2
the corresponding column for branch no. 11.103 (horticulture)
a
9
8
135
265.833
1
:
6
2010 11101
Comments to tables
:
66.847
50.790
285.754
-
2010 35120
2010 98099
2030 451
2060
-
Table
Basic values
4
3
Whole sale
trade margins
:
no.
id.
18.475. After the horizontal distribution the column sum is 1.365.672
to be compared with the original estimate of 1.374.314.
The changes from column 7 to column 8 in table 2 are the results of the manual balancing process. In this case rela-
tively few changes have been made, but the original estimate of total input at basic values has not been upheld,
figure being 1.407.244. The wholesale and retail trade margins and the commodity taxes, net, shown
i
the final
columns 9 -11 are the
results of the final balancing, and the purchasers values in column 12 are the sums of columns 8 to 11.
Columns for horticulture in the user matrix 1981 (1000 Dkr.)
Table 2.
Automatic balancing, basic values
:Commodity :User
Year :no.
:id.
:
Branch
:
:
no.
:
After vertical
distribution
Total commodity difference
:
:
Final figures
After horizontal
distribution
:
:
:
Whole sale
trade margins
Basic values
:
Retail
trade margins
:
:
.
2
1
7
3
4
7
5
000001
2010 11103
81 000002
81 000802
81 003621
81 003840
2010 11103
81'
- 201ff
-.44.&08_.___
-
0
20.000P
__ 26.010P _
2- 53.619P
15.611.535-DS
__13.825
70.7621.381P
2.959
_ _ 0_..
4.185P
190.402111.767
114.274 __ 29.000.821-DS
25.933116.099
38.680- .-5.041
2010 MOT.'
_
-
20111
11_
103
._-
2010 11103
006301
-
84 006303-_
81 007141
81 009001
81 060201
81 120309
81 250501
81 251707
81 270101
81 270305
81 271006
81 271008
81 271016
81 271018
81 271022
81 271024
81 271101
81 271701
81 310301
81 310501
81 321203
181 381103
81 381105
81 381107
81 390205
81 39 037
81 401111
81 401119
442103
480801
481601
620301
81 681601
81 691401
81
81
81
81
11101-
2010=11103
2010 11103
2010 11I03
2010 11103
2010 11103
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
7
r
7.727.724=111V
4.923.941-_DS
__
11.577-
_37.1411__.
15.863P
2010 11103
81 005210 81
-
2010 11103
81 004000
6
7
15.863
42.875_
20.000
_
26.0-1a
53.619.
__
1.381
___ 4.185__._
69.616_
13.023___.
11103
11103-
16.272P
114.274
113.737
42.775_
3.041
15.611
11103
11103
11103
11103
11103
10,122P
-
.
__-
-
-
8.155P
11103
11103
11103
11103
11103
11103
11103
11103
11103
11103
11103
11103
11103
11103
---_
___
86TP
10.454P
_28.35&P
... 8.698
--
2.141129.306--._
105.620__
4
_
115.080
-
-
---
35.091 -
_
- 867
10.454
28.35&.
1.713
-
1.809
255
--
0--
4
97
565-
1.621
8.155
68.638
328.600
._
3
2
68.63&_P-__
.._
30 _
.
329
3.8652.837
185.493
7.835_ _ 770-P-__ __ 29.5166.142
16.165-
522-.286
914
770-
.
_
_ 302
'la-
297
21.551
11103
742
13.653
13.4757.053
2.558
21.262
936
15.661
3.364
.
__
-1.676-
_
_____-
_
5.528
1.365.672
.
,
P
=
predetermined, D
:
=
Difference not horizontally distributed, S
See text to table
1
=
-
0
0
0
0
0
--
--
0
-
-
_
-
0
:
12
--------
Os=--
0
___
--
--_
---
0-
-
_ 0----0
-
-
_
-
0==__-.
-
0
0
0
1.296
-0- -=-
0
0
0-
0
0
19.995
93.284
993
3.771
6.509
3.681
1.417
227
897
2.517
23.002
0
1.621
8.155
22.879
328.600
867
1.241
28.358
1.713
105.620
97
522
286
607
2.010
0
0
523
72
0
0
0
0
0
70
0
7.097
669
22.279
16
10.757
0
0
0
914
770
5.528
297
155
314
0
0
0
0
0
21.262
936
15.661
3.364
3.587
1.407.244
Supply not entered in the system
0
0
6---
0
--
-
0
-
0
---
-
_
-
0
-- 0
8.796
-
0
--
0
0
0
0
998
602
4.185
14:350='=-
0
1.721
53.619
12.586
2.677
-- -
0
0
0
0
0
51.140_-15.863
15.806
20.000
26.010
___
-27.06f= =__
--
Cy
0-
0
0
0
0
____
--- 0
-
10
values
(excl. VAT)
:
1.381
_
For comments
t
Purchasers
:
taxes, net
(excl. VAT)
11
4.185
108.596
158.176
133.737
42.775
3.041
19.253
16.272
30.588
10.122
43.370
20.552
44.412
39.412
.
11103
_1.374.314
-
:.
.
201
_
-
97
..
.
1.381.740-D
--_32.680
__. 914P
--3.756-
_-
-.
18.475.-.
20.552
11103
11103
__
10.122
2
328.600 P
_
16.272
_-30.588
4.897--_
_1.62.1P
11103
_.
0
.
-33.824.
_
108.596
6.404
2.766
__
U-586.____
-
9
51.140
15.863
42.875
20.000
26.010
53.619
12.586
-37-140-
-
.
11103
11103
8
Commodity
_.
-...___
-
0
-
-
Q
_
- 0---- 0
0
0
---_
0
0
0
0
0
0
0
0
0
0
3.422
364
0
0
0
Cr
207.398
4.158
0
-2.627
1.848
9.575
25.396
351.602
2.472
3.853
28.358
2.382
127.899
113
594
356
0
0
0
0
108.596
172.526153.732
136.059
4.034
23.024
22.781
34.269
22.056
_
50.467
20.552
55.169
1.383
770
5.528
297
24.849
936
19.083
3.728
1.616.173
-
33
new basic values, except for exports and stock changes where trade
margins have been determined earlier, cf. above.
-
print -out showing the calculated input of commodities into each
A
industry
and
matrix).
As
of
final
demand (the columns of the use
illustration the print -out for horticulture is shown
table
in
category
rows
first
three
The
2.
have
the
following
interpretation:
procedure.
Its
created
column
the
is
This
(5)
total
the
is
in
initial
the first step of the RAS
estimate of intermediate
consumption at basic value.
(6)
This column shows the total difference between supply and use
for
each
commodity after the first step of the RAS procedure. So
this difference is the one which is distributed in the second step
of
the RAS procedure.
The figures in this column are not specific
for horticulture but for the commodities and are just printed here
for information.
(7)
This is the input column created in the second step of the RAS
and the point of departure for the manual balancing. It
procedure,
is
estimate
we
the
that
seen
sum
of
this column differs from the initial
the first column.
in
In the following balancing process
must adjust the figures in this column in such a way that they
with
together
the
derived changes in trade margins permit us to
hit the total at purchasers' values, but not necessarily the total
at basic values that we started out with in column 5.
from
Apart
these two prints the "balancer" will also have at his
disposal a detailed version of the master file system, which shows the
connection
between
the
national
accounts commodity numbers and the
most detailed commodity classification in foreign trade and industrial
production
statistics, and this print also gives the text belonging to
each commodity. In the balancing process this is a tool for going back
to
the
most detailed primary statistics if necessary. Also available
is a collection of notes describing the special treatment which should
be
given
containing
preceding
and
some
available.
to
a
year
certain commodities or industries in the balancing,
list
the
special
and
of checks etc. which must be carried out. For the
final versions of the two prints mentioned above
work
sheets
from
the
balancing process will be
34
the
Then
capacity
his
rest
is
the
in
hands of the "balancer ", who in this
is deemed omnipotent. He may of course discuss problems with
colleagues,
the final results of whatever considerations or
but
investigations he makes are usually not written down, and what happens
in
the
another
manual
balancing
person.
This
process
usually not be reproduced by
can
where the art of national accounting takes
is
over from the techniques of national accounting.
Usually
out
by
the manual balancing work (which may very well be carried
means
of
computer terminal, cf. below) is shared between
a
three or four persons (economists) in a way which experience has shown
to be fruitful. The main idea is here to distinguish between different
"complexes"
much
is
the
in the economy,
where the interaction within complexes is
more intense than between complexes. When one particular complex
allocated
extent
interfere
to one person in the balancing work this also minimises
which
to
members
the
of
the
balancing
team have to
each others' work. The most clearly separable complexes
in
are:
-
Agriculture,
horticulture,
industries,
restaurants
and
fishing,
the
food
the
and
beverage
food
and
beverage
groups of
private consumption.
-
The
metal
shops,
and
machinery
fixed
equipment,
capital
formation
notional
the
government
industries,
purchases
branch
construction,
machinery
in
and
transport
repair goods and services,
for
military
of
auto repair
equipment,
and
private
consumption of most durable goods.
-
Forestry,
mining
of
rocke, sand etc., industries producing wood
products and non -metallic mineral products, construction, and some
private consumption groups.
-
Manufacture
of
clothing
textiles,
and
footwear,
and
the
corresponding groups of private consumption.
-
Chemical
industries,
including
plastic products and a number of
groups of private consumption.
-
Service
the
industries,
notional
branch
including
for
producers of government services,
services
and
private
consumption of
services.
The two last- mentioned complexes are characterized by having their
35
output
distributed
inputs
mainly
complex
to
come
from
energy
for
have
commodities
a
large
within
already
of the economy, whereas their
the groups themselves. There is no
stage,
this
at
part
as
energy branches and energy
been finally balanced in the subsystem for
energy.
each
Within
about
the
complex
has
there
over time developed a knowledge
most appropriate order to make changes. Generally speaking
the
most
commodities
basic
with
commodities
and /or branches will usually be treated
few uses or branches with few dominant
first,
and
inputs
will usually be treated early in the balancing process. Before
making
any changes,
the person responsible
for a certain complex will
some time to look through all the details of the area to get some
use
ideas about what are the main balancing problems and perhaps also make
some
important
within
for
complex,
the
solutions. Also at this stage it is
their
find out whether there is an overall surplus or deficit
to
this
as
may
imply either a more than average
with other complexes or already now acceptance of changes
interaction
in
design
summary
one or more of the initial totals for user categories belonging to
This overall check might also lead to detection of errors
the complex.
in the data input into the system on either the supply or user side or
to the conclusion that some significant new developments have happened
must be further investigated
which
before the ordinary balancing can
begin.
In
order
keep
to
the manual balancing process under control, a
i.e. if an industry or a category
commodity
is never left unbalanced,
of
demand is given more of a commodity,
final
decided
which
redistribution
or users it must be taken away from. During this
user
of
it is at the same time
commodities
it often happens that a user category
gets its difference increased rather than decreased, but of course the
general tendency is towards decrease of differences. When a difference
has
been
brought down to a very small size, for example one per cent
or less of total input into an industry, the residual is eliminated by
(additional) changes in the inputs received from the notional branches
for goods or services.
During
estimate
new
the
balancing
process it may be decided that the initial
for an input total at purchasers' values is not valid,
and a
one is explicitly fixed as the target. This happens primarily for
36
industries
service
(exclusive
have
balancing.
exports
of
are
the
results
of
For the categories of final
and stock changes) the initial totals
status and are more often than not changed during the
weaker
a
totals
the
founded calculations.
well
statistically
demand
where
industries,
manufacturing
construction, but in practice never for
for
and
the commodity flow method has a decisive influence not
So
on the commodity composition, but also on the total sizes of the
just
categories.
demand
final
developments
price
of
private
of
groups
the
in
means
By
indices
the
real
consumption are kept under
surveillance.
Although
of
exports
goods
and
stock
changes
have already in
principle
been finally calculated by commodity, some changes are none
the
possible in the manual balancing process. For exports it is
less
possible
between basic value and wholesale
for exports f.o.b. in the foreign trade statistics).
figure
will
This
change the amount at basic value available for domestic use. For
changes it is felt permissible to make counterbalancing changes
stock
commodities
in
borderline
the
margin (but keeping the purchasers' value unchanged, as this is
trade
the
move
to
belonging
the
to
broad
same
commodity group. For
one kind of semi -manufactured metal product can be exchanged
example,
for another in the stock column, but it cannot be exchanged for coffee
clothes.
or
Total
manipulations,
but
changes
comes
which
"technical"
stock
stock
they
changes
are
not
affected
by
these
are affected by a special category of stock
into
existence in the balancing process. These
changes
are
used
as
the last resort to solve a
balancing problem. Only few commodities enter these stocks every year,
and it is strictly forbidden to use them as a general means of solving
problems.
timing
They
between
domestic
sale
for example be used to offset differences
can
registration
or
purchase.
in
in the
foreign trade statistics and either
Commodities such as soyabeans, tobacco,
ships and airplanes are frequently entered at these stocks. Taken over
a
number
years
of
these stock changes must add up to approximately
zero.
It
manual
cent
years
is
not
easy
to say how many elements are changed during the
balancing process, but
a
qualified guess is that about ten per
of the elements (not counting the zero elements) are changed. In
with
either
input
censuses
for
manufacturing industries or
37
household
budget
comprehensive.
in
small
are
left
surveys
changes
the
are
of
course
much
more
In general more changes are made in large figures than
and many small commodities are not touched at all but
ones,
at the values determined by the automatic calculations. But
of course these figures have a statistical or other empirical basis in
earlier
some
year, as elements different from zero cannot be created
automatically by the RAS method if there is not
principle
aim
concerned
making
at
value there already.
heading of this section indicates we are at this stage in
the
As
a
with the balancing at basic values only, i.e. we
such changes as will eliminate the deviation from the
original estimate of the total basic value of each user category. From
onwards
1983
which
some improvements were however introduced in the system
permit
between
us
changes
following
currently take into account the interconnection
to
in basic values and changes in trade margins.
procedure
the
used
for
the
In the
years 1966 -82 will first be
described, and afterwards the new procedure will be presented.
Even
though
principle
later
of
the
stage,
borderline
was
it
between
receive
margin,
the period 1966 -82 was in
for
"second" trade margin balancing to be solved at a
course
of
total
specific user category.
should
used
concerned only with the basic values of the system, leaving
whole
the
procedure
the
basic
possible
at
any time to move the
value and total trade margins for a
If for example it was decided that an industry
as input a new commodity with a relatively high trade
it was usually at the same time decided to decrease the basic
value total and increase the trade margin total (but leaving the total
for
purchasers'
commodity
values
taxes
unchanged). Also when commodities subject to
were
redistributed
the
commodity
taxes
were
redistributed as well, thereby influencing the total for basic values.
Such movements of the "borderline" were however only made on an ad hoc
basis, and often not very systematically, and the overwhelming part of
the
changes
the
in
balancing process were restricted to figures at
basic values only.
From
computerized
had
a
1983
the
"manual
balancing"
became
further
in
the sense, that each person engaged in the balancing
computer
terminal in front of him, by means of which he could
communicate
that
year
the
changes
directly
with
the
central commodity balance system, so
to the system should no longer take place by filling in
38
punched card forms, as had earlier been the case. The basic print outs
described
based
tables
in
were not changed, but the new terminal
2
it possible to build into the balancing work a
made
procedure
and
1
number of facilities which it would earlier had been too cumbersome to
handle,
spite of the fact that they had all the time been seen as
in
very desirable.
The most important new facility is one which automatically changes
margins in the same proportion as the corresponding basic value
trade
elements
are
desired,
it
changed.
during the balancing process (a check which because of
margins
trade
different change in the trade margin is
is just a way of keeping a closer check on the
facility
this
glance
a
course also possible to specify this. At a first
of
is
If
the work it involved was not possible in the earlier system). A closer
look
the system unveils however, that a much more profound change
at
taken place, namely a shift from a balancing at basic values to a
has
balancing at all value concepts simultaneously, where the total we are
at
totals
for
basic
to
just
reduced
is
of
stage
change
and
values
being
trade
margins
(For
procedure.
as
at
least
group is usually predetermined
consumption
have had their status
supporting variables at a certain
necessary
pronounced,
less
values, and where the initial
at purchasers'
calculation
the
is
one
the
aiming
private consumption the
total
retail
margin by
from separate sources, cf.
above).
quality
the
be obvious that this new procedure in general improves
should
It
in
the
balancing
work,
in particular by avoiding the
distortions which the earlier almost complete separation between basic
value balancing and trade margin balancing introduced. It must however
also be underlined, that the final balancing of the trade margins
(cf.
next section) is not made superfluous by this new facility, as it
the
does
total
that all the individual trade margins add up to the
secure
not
output
from
the
trade
branches
(wholesale trade and retail
trade). But the final balancing of the margins becomes a lot easier to
carry out.
Apart
from
the new facility for trade margins the terminal based
system allows many checks to be carried out currently in the balancing
process
specific
so that errors can immediately be corrected.
Also a number of
files which form part of the terminal based balancing system
39
(such
possible to follow exactly which
it
have been made (and by whom), and what are their consequences
changes
the differences we are trying to eliminate.
for
So each person has in
of him a permanently updated status report.
front
written
also
the
make
commodities and the "file for
for
file"
differences ")
and
totals
"correction
the
as
text which is necessary to explain the reasons for
any
complete
documentation
balancer,
which
is
year
for
of
changes
the
made
to
a
individual
each
by
compared
forward
step
big
a
system supplies us also with
the earlier
standard. The "correction files" including the relevant
documentation
text
based
terminal
the
So
change.
Into these files is
very helpful as background reference in the
are
t -1
work for year t, and substitute a rather complicated system
balancing
of handwritten notes, the purposes of which were among other things to
ensure
commodity is not by sheer coincidence year after year
that
a
in
the
changed
same direction away from the statistical base in the
census year.
"complexes ",
commodities
of
the system. Different controls were printed out (do all
into
entered
fact balance, and are all input totals and categories
in
demand
final
manual
balancing
system
used
target
the
at
were
rounds
correction
values were in the pre -1983 system punched and
new
the
in the balancing have finished their
involved
persons
the
When
necessary
process
onwards
1983
had
Usually
levels ?).
three
or four
before all errors made during the
eliminated.
been
The terminal based
makes most of these checks superfluous as
they are currently made by the system.
At
example
branches
balanced.
and
for
will
usually
still be some branches (for
of
government services and the
producers
goods
and services) which are not completely
final operations necessary to arrive at the completely
The
system
balanced
at
basic
values
(which
interacts
with the final
of trade margins and VAT, cf. below) are now carried out by
balancing
or
there
construction
notional
one
stage
this
persons
two
who
have
the
responsibility
for solving all
remaining problems and for the final outcome of the balancing work.
The
manual
man -months
or
go
household
amount.
balancing
usually
takes
4 -5
weeks,
into the work. In years with industrial
and
about
5
input censuses
budget surveys the use of resources might be twice this
40
Balancing the system at purchasers' values
6.
have complete and balanced matrices for supply and use at
now
We
basic
values
exclusive
final
and
of
complete (use) matrix for commodity taxes, net,
a
To arrive at the system at purchasers'
VAT.
matrices
(use)
respectively,
must
be
of
wholesale
constructed
and
retail
prices the
trade
margins,
as well as the final row for the
distribution of non -deductible VAT by user category.
6.a Calculation of the final trade
First
the method used in the final balancing of trade margins for
period
the
which
marin matrices
1966 -82
follow
from
the
and afterwards the modifications
described
are
introduction of the terminal based balancing
system from 1983 onwards.
The method used for 1966 -82
In chapter 3 the preliminary trade margin balancing was described.
It
resulted
trade
wholesale
margins
and
retail trade margins, but no
for
one
of trade margins were created at that stage, and there might
matrices
be
two absolute figures for each user category, one for
in
differences
between
the
and the calculated use of trade
supply
margins.
been
manual
the
In
made
which
borderline
margins
explicitly
between
for
percentage
balancing process two kinds of decisions may have
total
category
a
trade
influence
use
of
basic
at
use
trade
may
margins.
Firstly the
values and the total trade
have been moved. Secondly the
margins for specific elements may have been changed
if an element formerly zero at basic prices is given a value the
(and
trade
into
margins
the
must explicitly be decided). These changes are entered
system
in the same process as the corrections to the basic
value matrix.
The first step is now to calculate complete matrices for wholesale
and
retail
percentage
they
trade
margins from the balanced basic value matrix by using the
trade
margins from the preceding year, to the extent that
have not been replaced by new ones in the balancing,
margins
have
been
put
into
the
system
or absolute
together
with the
41
predetermined values. The column totals of these trade margin matrices
can now be compared with the initial estimates of
estimates)
(second
the totals (as modified in the manual balancing).
There
now
are
for a category of use may be different from the
totals
margin
trade
balancing problems to solve. Firstly the new
two
initial estimates (they usually are), and if they were kept at the new
initial estimates of use by category at purchasers' prices
level
the
could
not be upheld.
margins
will
calculated
so
supplies
Secondly the sum total of the two kinds of trade
wholesale
from
output
(the
different
be
from
corresponding
the
retail trade industries,
and
to which they must eventually be adjusted.
respectively)
To help solve these problems the accounts statistics for trade are
again
utilized.
statistics
retail
for
margins
detailed subbranches in the
by
are first reduced by retail margins on
trade
consumption and gross fixed capital formation, according
intermediate
to
gross
The
preliminary trade margin balancing. The remaining margins are
the
then transformed to private consumption groups by'the same key as used
earlier
and
with initial estimates of private consumption
connection
in
changes
stock
retail
in
trade.
These
results
are
used
in
connection with similarly calculated figures for the preceding year to
calculate
group,
are in turn multiplied by the final
rates
growth
these
and
rates for retail margins by consumption
growth
of
set
a
retail margins for the preceding year to obtain a new (third) estimate
of
margins
retail
topsy -turvy
seemingly
accounts
statistics
way
do
precisely
transformed
consumption).
wholesale
consumption groups in the current year.
by
not
into
is necessary because the
calculation
have
total
the
nor can they be
coverage,
classification
of
household
is not possible in the same way to make estimates of
It
margins
trade
classification
of
(This
in
these
by
consumption
statistics
groups
is different,
because the branch
and a much larger
share of these margins is derived from intermediate consumption, fixed
capital
formation and exports.
Still for 16 consumption groups margin
totals are estimated from the wholesale accounts statistics.
Still at the level of total trade margins by categories of use the
following assumption are made:
-
The
second
estimates
of
retail
trade
margins on intermediate
consumption and fixed capital formation are final.
42
-
The second estimate of wholesale trade margins on exports is final
(here are no retail trade margins).
-
second estimate of both wholesale and retail trade margins on
The
stock changes are final.
-
estimate
third
The
made
wholesale
for
trade
margins
on
16
consumption groups is only changed in exceptional cases.
-
estimate
second
The
consumption
groups
fixed
and
trade
wholesale
of
capital
margins
formation
other
on
is
usually
accepted.
-
third estimate made for retail trade margins on all groups of
The
private
goods is usually preferred to the second
of
consumption
estimate.
leads to the following procedure for balancing trade margins
This
at category level:
-
margins
trade
Wholesale
intermediate
on
consumption
into all
industries except construction are calculated as residuals, as all
other
values
in
sequence
the
from basic values to purchasers'
values are given, and purchasers'
-
retail
The
with
which
margins on all uses are summed up and compared
trade
target
total
usually
values are final.
(output
not
does
retail trade). The difference,
from
exceed
few per cent of the total,
a
is
distributed proportionally on all groups of private consumption.
-
The wholesale trade margins on all uses are summed up and compared
with
the target total (output from wholesale trade). Also in this
case
the
trading
difference
building
in
studied
before
is
usually
materials
more
or
small.
and
in
The wholesale branches
fixed capital goods are
arbitrarily
less
eliminating
this
difference.
result of this balancing is the final distribution by the two
The
kinds
of
category
trade
totals
construction,
margins
at
private
by category of use.
purchasers'
consumption
prices
and
In
the same process the
exclusive
fixed
capital
of
VAT
for
formation in
machinery and transport equipment are determined.
What
margins
is
for
now
missing is the calculation of two matrices of trade
which we have just determined the column totals.
This is
simply done by multiplying (for each column) the trade margin matrices
43
of the second set of estimats by the ratios of the final column totals
to
of the second estimate, still leaving predetermined margins
those
the
row
are no further balancing problems involved here,
There
unchanged.
as
of the trade margin matrices have no counterparts on
totals
the supply side.
As
illustration the balanced columns at all price levels are also
shown in table
2.
The method used 1983 onwards
It
in
from what is said about the new terminal based method
follows
section
that the earlier method for calculations of final trade
5
margins must be modified on the following points:
1.
From
use
left
and
value" balancing both wholesale and retail
are already final (both as totals by category
margins
trade
of
"basic
the
commodity) for all industries which are not
by
play a role in the final balancing operations, such
to
as construction and producers of governemnt services.
2.
For
consumption
private
above as the third estimate
the
trade margin totals described
(all retail margins and 16 groups
of wholesale margins) have been introduced already before the
balancing,
value"
"basic
have as far as possible been
and
kept unchanged (as totals by category of private consumption)
in
the
balancing process, where on the other hand the trade
margin rates by commodity have had the burden of adjustment.
3.
freedom in the final trade margin balancing
The
degrees
are
now
the
sum total of the two kinds of trade margins are equal to
the
known
of
fewer than before, but still we must make sure that
output totals from the wholesale and retail trade
branches, respectively.
4.
For
the
wholesale trade margins the adjustment can take place in
construction
in
fixed capital formation.
government
whereas
in
producers
of
government
the unrestricted categories of private consumption
services,
and
industry,
In the case of producers of
services purchasers' values are completely fixed,
they
can
be
permitted
categories mentioned above.
to
change
for
the other
44
For
5.
trade margins there is at this stage very little
retail
room for manoeuvre, but on the other hand the introduction of
"third
the
estimate"
already
the
in
trade margin
balancing
secures
that
difference to the output total will be quite small
the
connection
first
in
with the balancing method
can be eliminated by insignificant changes in the retail
and
trade margins in private consumption.
before
As
6.
trade
margin
changes
final
now have the final total wholesale and retail
we
have
"basic
taken
compared to the results from the
place
value" system, the differences must as earlier
distributed
be
category. For those categories where
user
by
by
commodity
proportional
to the existing
trade margin elements, leaving out any predetermined margins.
6.b Final balancing of non -deductible VAT
As
of Denmark's single -rate VAT system, a complete VAT
result
a
matrix is not very interesting, and the estimate of non -deductible VAT
is
of
-
confined to one row, showing
therefore
Non -deductible
use.
capital
fixed
levied
VAT
formation
a
figure for each category
on intermediate consumption and
found only for a few industries such as
is
dwellings, passenger transport, private medical services and producers
of
government
obvious
services.
the balancing process has not given any
If
cause for change, the figures from the first VAT estimate are
retained for these groups, and the final VAT balancing is consequently
limited
to
area of private consumption. Here it is ensured that
the
the same VAT rate is applied to all fully taxed consumption groups and
at the same time that non -deductible VAT on all categories of use adds
up
to
the
resulting
target
average
figure
VAT
in
government
finance
statistics.
The
rate on private consumption is always somewhat
below the theoretical rate.
7.
The
system
as
a
basis
for
national accounts and input- output
tables
The
balanced
dimension
for
basic
commodity
flow
system contains
a
supply matrix of
2500 by 124 and four user matrices of dimension 2500 by 198
values,
wholesale trade margins, retail trade margins and
45
commodity taxes, net, respectively. When these four matrices are added
the
user
matrix
at purchasers'
the
column
sums
When
of
values exclusive of VAT is obtained.
matrix
this
added
are
the
to
row of
VAT by user category, each use (intermediate or final)
non -deductible
is obtained at purchasers' prices.
In
order
get
to
the
necessary basis for the ordinary national
accounts tables and the input- output table we must further:
-
Add the stock changes of- finished products and work -in- progress in
manufacturing industries to (1) sales by manufacturing industries,
in
order to move from the sales concept to the production concept
side, and to (2) stock changes at the user side
at the output
the
in
in
of the national accounts tables just as one figure, and
case
case
the
-
of
the
table distributed by branch. So the
input
commodity decomposition of these stocks, cf. earlier, is only used
as a technical remedy in their calculation at current and constant
prices.
-
Calculate other indirect taxes, net, (non- commodity indirect taxes
or
taxes)
production
motor
Taxes on land and buildings,
industry.
by
vehicle duties and deficits in government owned enterprises
account for the dominant part of these taxes.
-
compensation
Calculate
interrelated
with
the
of
employees
industry. This task is
by
estimation of employment by industry, but
will not be discussed here.
-
Consumption
in
this
of fixed capital by industry, which belongs naturally
list,
is
not
yet
estimated
in
Danish national
the
accounts.
7.a National accounts tables
From this data base it is now possible to construct:
-
The goods and services account
-
The production account
-
The generation of income account
for
also
basic
the
for
whole economy, and in the case of the two last mentioned
each
value
and
industry. At industry level the output concept is
value
added
is
calculated
at
factor prices
46
(although
might
it
actually
done
in
also
calculated
be
basic values as is
at
sector accounts). In the accounts for the
the
whole economy all the standard value concepts are applied,
as they
can be constructed by aggregations in the data base. All the usual
supporting
gross fixed
purpose,
by
showing private final consumption expenditures
tables
capital
formation by type of goods etc.
are also taken directly from the system.
7.b Input- output tables
As mentioned above the 2,500 national accounts commodities are not
comparable over time, so even though it is useful to work at
strictly
this
level
calculations
containing
changed
constant
of
about
constant -price
price
figures
procedures
figures,
commodities,
1600
earlier
for
commodity
the
(2)
balancing
the
in
and
in
used
years,
"current"
more aggregated level,
a
is
the
for
when
the
(1)
rebasing
base year is
system in the preliminary national
flow
accounts and (3) the construction of the input- output tables.
commodity level is obtained by aggregating all national
1600
The
accounts
goods
exceptions)
the
to
four -digit
CCCN
nomenclature
(with
a few
and keeping the services as they are. At this level there
is theoretically complete comparability over time.
From
this
level
calculated,
200
supply (make) matrix and the use (absorption)
the
i.e.
table
follows
method
commodities
of
input- output table is automatically
matrix
to
obtain
an industry x industry
on the assumption of an industry technology. This
the recommendations of the SNA, and as no aggregation
to
characteristic
commodities
is done prior to the
multiplication in order to avoid loss of information caused by
matrix
procedure,
this
the
117 x 1600 make matrix is multiplied by a 1600 x
a
absorption
(approx.)
input- output
aggregation
of
matrix at
the choice of an industry technology is the only one
possible.
The
tables
3
techniques
used
in
the construction of Danish input- output
from the two basic matrices are described in detail in chapter
of this publication.
47
Chapter 3
TECHNIQUES IN THE COMPILATION OF
DANISH INPUT -OUTPUT TABLES AT CURRENT PRICES
1.
Introduction
Accounts work in Denmark has since its initiation in the
National
1930's
and
tables,
method
commodity -flow
the
method
- or
production statistical
has been the core of the technique.
-
tables for Denmark have been published for the years
Input- output
1930 -39
1948),
(DSD
1962)
(DSD
connected with the construction of input- output
closely
been
1953
(DS 1973) at still higher levels of detail and
1966
and
1947 and 1949 (DSD 1955),
1946 (DSD 1951),
sophistication.
A summary of the early Danish experiences is given in
Bjerke,
and
Milhoj
input- output
series
of
Summary
tables
of
versions
on
Rasmussen
have
worked
cover
tables
publications
Nerregaard
been
years
the
these
national
(1956). Since 1966 annual
out.
At the moment the time
1966 -83
on a comparable basis.
tables
are
now published in the annual
accounts
and
on
input- output tables and
analyses.
with the earlier tables the 1966 table represented a new
Compared
of
generation
industry
1966
table
next
4 -5
current
partly
by its size (130 indus-
namely as an industry- industry table on the assumption of
techniques,
"first
tables,
and partly by being worked out according to precisely defined
tries),
an
input- output
technology
in the terminology of new SNA (UN 1968).
The
was completed in 1972 and published in 1973, and over the
years
version"
prices
comparable
of
and
the
tables
tables
for
1967 -75 were compiled. This
1966 -75 were available at both
for
constant 1970 -prices. For practical reasons they
were however not published but made available in a data bank, and were
used extensively for analytical purposes in the following years.
To
some
supply
description
of
the
background
information this paper gives a brief
commodity -flow
system on which the input- output
tables are based and of the techniques used for constructing the first
version
the
tables
for
1966 -75.
Its
main
contents are however
a
description of the more disaggregated techniques which is now used. It
was
introduced
tables
for
the
at
the time the 1976 -table was compiled, but all the
period
1966 -75
were
also
completely recalculated
according to the new method.
The modified technique is still following the SNA recommended pro-
48
cedure, but it differs from the methods first used in the construction
of
1966 -1975
the
tables
especially
concerning
the degree of dis -
aggregation of the two basic matrices (the make matrix and the absorption matrix), and the treatment of imports. The basic matrices are now
rechtangular
contain
and
about
1600
commodities.
The treatment of
imports, which is a very important question in input- output tables for
countries with
the
table
a
high rate of foreign trade, has been modified to make
more
connection
flexible
question
the
non -competitive
difficult
of
distinguishing
(complementary)
handle
to
for different analytical purposes.
imports
In this
between competitive and
which
particularly
is
time series of input- output tables has been
in
solved by introducing more flexibility in the treatment of imports.
2.
The commodity -flow systeml
there
Denmark
In
integration
between
as
is,
proposed
the new SNA, a complete
in
national accounts and the detailed commodity and
production
accounts which form the basis for the input- output tables.
The
yearly
final
accounts
three
service
account
contain
about
4000 commodity
gradually declining to 2500, cf. below) and 121
are redistribution accounts and one contains imputed
charges.
imports
for
categories
accounts
accounts inclusive of four artificial production accounts,
which
of
bank
time
(over
production
national
of
final
the supply side there are furthermore one
On
c.i.f.
use,
and two for customs duties. There are 77
of which private consumption represents 66
categories. The complete system is thus made up of a 4000
supply and a 4000
for
element
x
198 matrix for use.
is further subdivided into element
x
124 matrix
In the latter matrix each
for basic value, wholesale
margin, retail trade margin and commodity taxes, net. The total
trade
number of elements in the commodity -flow system is therefore about 3.5
million (inclusive of empty cells).
The
calculation at constant prices takes place also at this level
of detail, i.e. price indices for imports and for domestic production,
respectively,
and
the
assumption
uses
are
at
determined
constant
(mainly from wholesale price material)
prices
are
calculated
roughly
on the
that exports are made up of domestic output, and all other
uses have identical import contents.
1)
comprehensive description of the commodity flow system at current prices
is given
in
chapter 2, and at constant prices in
chapter 4, of this publication.
A
49
of the figures published for the final national accounts are
Most
obtained by aggregations in this data system, but of course figures on
income
separately
final
figures
is
this
are
etc. must be calculated
taxes
After a long period of catching up,
the
system.
now
ready 33 months after the year to which they
the input- output table can be produced immediately after,
and
refer,
as
outside
indirect
other
distribution,
purely
a
technical
which does not require any
matter
further estimation work on the data.
principle
In
after 1966, but in practice it has over time been necessary to
period
and to accept other kinds of discontinuities.
tures)
As a consequence
the total number of commodities decreased from about 4000 in
this
1966
of changes in the basic commodity nomencla-
(because
some
aggregate
of
4000 commodities are comparable over the whole
the
2500 in 1982. Nonetheless it has been found extremely
about
to
useful to carry out the balancing in the commodity -flow system at this
detailed level, where each commodity has an immediately clear meaning.
course
Of
the
balancing
the commodity flows and production
of
accounts is carried out by extensive use of computer based procedures,
eventually
but
procedures.
As
production
of
the
emphasis
in
this
paper
on the subsequent
is
table, these procedures will not be
input- output
here, but it is important to realize that it is in this ba-
described
lancing
last
the
are eliminated by conjectural
differences
the
process
that the material contents of the input- output table
are
established, i.e. the national accounts picture of the real world
is
determined
whereas
here,
following
the
construction
of
the
input- output table is basically a question of presenting these data in
a
more
aggregated
and
form
operational
with
a
minimum
loss of
information.
As mentioned above, the most detailed
over
comparable
level
figures,
the
the
in
a
time,
initial
even
so
commodities are not strictly
though it is useful to work at this
and
balancing
calculation of constant -price
higher level of aggregation has been found appropriate for
purpose
of recalculating the figures to a new base year for con-
stant prices. This level contains about 1600 commodities, of which 500
are
services
temporal
which
are
comparability.
not aggregated, as there are no problems of
The
goods
four -digit CCCN nomenclature (i.e.
is
are
simply
aggregated
to
the
the former BTN- nomenclature), which
possible because the first four digits at the 4000 -commodity level
50
identical with the code numbers of the CCCN headings. In this way
are
intertemporal comparability is secured at the 1600 -commodity
complete
These
level.
current
series
prices
available on an annual basis since 1966 in
are
and in constant prices.
(See annexes
1
and
2
for some
modifications to this aggregation procedure).
3.
The first version input- output tables 1966 -75
method
The
applied
in
these tables is summarized
construction
below and fully explained in (DS 1973).
each of the 4000 commodities an identification code for one of
To
the
characteristic
130
industry
is
Here
elsewhere
as
applied
as
an
obtained,
consumption
figure
1
role
is
attached. The characteristic
the main producer of the commodity in 1966.
the paper the term "industries"
in the SNA meaning of the term.
aggregation
and
the
also includes
This code was then
criterion, and 130 commodity groups were
make
matrix
as
well
as the intermediate
part of the absorption matrix became square matrices (see
for an illustration of make and absorption matrices). So the
above -mentioned
no
as
in
producers"
"other
thus
defined
industries
medium level of aggregation (1600 commodities) played
at that time. Most commodities without Danish production (at
the
4000 -commodity level) were classified as non -competitive imports,
and
not
given any code for characteristic industry.
commodities
were
Imports of these
in all subsequent calculations treated as a primary
input.
By
means of the well known SNA procedure an input- output table of
the industry- industry type on the assumption of an industry technology
was
2)
then
calculated.2
The
final demands were also included in this
industry x industry table has industries, which are ideally
made up of establishment kind units, in both rows and columns of
intermediate consumption
the
part of the table, whereas a
commodity x commodity table has rows and columns defined in terms
of a commodity classification.
An
Both kinds of tables can be constructed from the make and
absorption matrices using either the assumption of an industry
technology or the assumption of a commodity technology. In the
first
case
it
is
assumed that an industry has the same input
structure whatever its product mix, whereas in the second case, it
is
assumed that a commodity has the same input structure in
whichever industry it is produced.
is
not possible
at this
place to summarize the intense
discussion the last
10 -15
years on the pros and cons for these
different
kinds of tables, but this article can be seen as a
strong case for choosing the Danish solution.
It
51
In this way a complete input- output table with
final demand.
negative
imports
according
treated
to
method
"Input- output Tables and
C in
(UN 1973) was obtained.
Analysis"
table was named the "exogenous" version, because competitive
This
imports
applications
useful.
in
some
for price models it was in some cases easier to
basis
a
although
problems,
for example calculation of energy contents it proved
as
As
some
raised
this
model
quantity
on it would be an exogenous variable. As a
based
models
in
apply because of the limited number of exogenous prices it required.
many
In
imports
competitive
separation
demands.
the
had
whereas
variable,
endogenous
for
required
which
a
from domestic production in each
imports
consumption
intermediate
all
other
of
uses
between
proportion
same
the
final
and
each
characteristic
imports
and
domestic
imports were treated according to method D in (UN
Hereby
production.
it was desirable to be able to calculate
done on the assumption that exports had no direct
was
This
commodity
an
matrices
contents,
import
as
competitive
of
of
element
however,
uses,
1973).
"endogenous"
PASSION
the
a
(the
were
respectively)
version
connection with
tables
input- output
of
sets
Both
"exogenous"
placed
in
a
and
the
data bank in
special computer programme for IO- analysis (based on
developed
programme
at
the
Harvard Economic Research
Project in the sixties). The complete set of matrices for one year was
made up of 46 matrices,
23 for the current -price tables and 23
matrices.
constant -price
from
Apart
for the
the column totals all matrices
were stored in coefficient form only.
These
tables
with
nection
physical
were used for many kinds of analysis, often in con-
data matrices, for example of energy use in
supporting
terms
and /or
employment
figures, which were fitted to the
classifications of the input- output table.
these
When
they
the
under pressure of time and resources
-
1966
cedure
basic
tables became the "first version" only it was because
procedure,
(cf.
below)
although
which
-
had been produced using
it was planned to work out a new pro-
could
take full advanage of the detailed
data source, and also because a change in the classification of
branches
was
constant -price
planned
(from 1958 ISIC to 1968 ISIC).
Furthermore the
tables would be recalculated from 1970 to 1975 as base
52
year,
which
-
taking place only at the 1600 -commodity aggregation
-
would invalidate the concept of characteristic industry earlier used.
was
It
version
an
tables
starting
in
amalgating
exception
indispensible
that
1966.
new branch classification
The
from
branches
the
general
this
-
and present -
should constitute an unbroken time series
they
resequencing
or
requirement to the new
rule,
of
was established by
the
old
one.
As an
two new branches were created by
subdivision: "Extraction of coal, oil and gas" and "Domestic services"
(DS 1981).
In this process the total number of branches decreased from
130 to 117. All national accounts data from 1966 and onwards have been
reclassified according to the new classification.
4.
Basic features of the present techniques
with the detailed data base in the commodity flow system
Compared
it
is
obvious
input-output
that
above -mentioned
the
tables
introduced
method
unnecessary
constructing
for
aggregation
errors
by
taking the round -about route represented by the initial aggregation to
characteristic
avoid
this
commodities.
error
The
main
idea
in the new method is to
constructing the input- output matrices and the
by
import matrices directly from the 1600 -commodity level matrices.
The
basic
two
matrices
are
shown
in
figure
1
where numbers
indicate matrix dimensions.
These matrices exist for each year in current and constant prices.
To
facilitate
shown
of
the calculation of the input- output table the matrices
above have been slightly modified compared with the arrangement
the matrices in the basic commodity -flow system. This concerns the
following four points.
1.
Three
artificial
"unspecified
distribution
services"
and
"goods
sectors
and
for "unspecified goods ",
services
for
repair
and
maintenance ", each producing one commodity have been eliminated on the
assumption
that each sector receiving input of these commodities gets
a basket of
commodities equal to the input structure of the artificial
sector in question.
2.
Reexports
have been deducted from the figures in the total export
column. Ideally this can be done just using the reexport figures given
53
Figure
The make matrix and the absorption matrix.
1.
The
make matrix:
Commodities (1600)
Industries
Domestic output
(117)
(basic values)
Imports c.i.f..
(1)
Customs duties
(1)
The absorption matrix:
,.,
.,
v
c......,
Household cons.
1J
tn
6,
C
-0 O
CO
'ri
-0
.,-1
4-t
a
G)
E
E D
k
G)
4-3
C
1-1
N
C
O
U
.--1
O
C
CO
CO
CO
C
o
.-1
C)
t-t
17
>
C
r--t
(+-
O
O
.0
.0
CI- U)
.ri
.0
O
....I
O)
U) CI-
D
C O
=
U
O
O
La
O.
w E
UY-
U
U %
V
W H
x.
1Reexports
G)
!
91
Commodities (1600)
VO
(1)
Final demands (75)
Industries (117)
54
in the foreign trade statistics.
complicated,
more
the
commodity.
would
uses
output
first
second
the
output
such cases the direct import contents of domestic
negative. In other cases it happens that the domestic
commodity is less than total exports
reexports.
In the
it is assumed that reexports are equal to imports,
and in
a
case
because registered reexports can exceed imports of
In
be
of
In practice the matter is a good deal
case that total exports
(which
-
-
reexports are equal to domestic
defines the size of the reexports).
Solutions to other
complications which can emerge, have also been built into the computer
programme handling this procedure.
constant -price
the
In
reexports
and
residual
from
3.
total
exports
are divided into
and the rest, by deflating reexports by the prise index for
imports,
chapter
figures
calculating
the constant -price value for the rest as a
the given constant -price value for total exports. (Cf.
in the present publication).
3
the national accounts imputed bank service charges are treated
In
as intermediate consumption. Technically this is implemented by having
an
artificial
sector
with imputed bank service charges as input and
output equal to zero, which implies a negative gross operating surplus
equal to the input.
keep
To
cause
problems
therefore
would
two
for
sector in the input- output table would
reasons.
Firstly,
the
output is zero and
input- coefficients are not defined. Secondly, if the sector
aggregated
were
artificial
this
have
a
with
the
financial sector, this amalgamated sector
dominant own -delivery,
and the small proportion of bank
services which are actually paid for would have an enormous multiplier
effect, which could invalidate the results of model calculations.
Therefore it has been decided to move imputed bank service charges
to the final demand section of the table.
its
existence
financial
and
sector
the
(and
need
to
take
This will remind the user of
it into consideration if the
consequently other sectors) is to appear in
a
meaningful way in model calculations.
Finally
service
it must be underlined that this treatment of imputed bank
charges
calculated
as
implies
that total GDP in the input- output table is
the sum of value added in the individual branches less
this element of final demands.
55
of stock changes (exclusive of work- in -pro-
categories
five
The
4.
gress and finished own products in manufacturing industries, which are
by commodity) have been added together to one single
distributed
not
column,
mainly
subdivision
the
as
character,
technical
of
input- output
applied in the commodity -flow system is
tables.
For
the
and
samne
not
useful
reason
the
in the context of
two categories of
customs duties are added together
5.
The treatment of imports
The distinction between competitive and non -competitive imports is
not applied, but some special commodities which are not covered by the
foreign
trade
categories
statistics
primary
of
singled
are
inputs.
out
and
treated
as
three
The commodity contents of these rows
are:
1.
Goods and services imported directly to off -shore activities
in the Danish part of the North Sea. (In 1983 the coverage of
the foreign trade statistics was extended also to such goods,
so from this year the group contains services only).
2.
Purchases abroad by resident households and expenses for
business trips etc. and purchases in Denmark by non -resident
households etc.
3.
Expenses abroad for Danish ships.
In
and
isolated,
import
this
contents
absorption
showing
how
preceding
the
the
of
it
was
explained how reexports were
course is the same as calculating the direct
of exports. To make a complete disaggregation of the
matrix
uses
chapter
into
one
showing uses of domestic output and one
of imports, it is necessary to make an assumption as to
of
remainder
imports
(i.e. imports cif + customs duties -
reexports) are distributed among the categories of use.
For
the
lack
any specific information it is assumed (for each of
1600 commodities) that the ratio of domestic output to imports is
identical
and
of
in all domestic uses. Changes in stocks of work -in- progress
finished
own
products are of course always domestic output, and
are so treated in the input- output table.
It
is
important
to note, that this assumption for imports is in
the present system applied at the detailed commodity level, whereas in
the
earlier version it was applied at the level of 130 characteristic
commodities, and therefore could lead to import figures in cells about
56
which
instance
(for
agricultural input into dairies).
eliminated
almost
is
positively known that all input was of domestic origin
was
it
when
imports
This source of error
are singled out at the detailed
commodity level, and for model purposes it may often be more useful to
identical
assume
import
proportions
in
all
domestic
uses
of an
individual commodity than to use the actual more or less incidental or
random
for import contents - if we had knowledge about them,
figures
which we don't.
the above -mentioned procedures the total absorption matrix has
By
into two matrices of equal dimensions
subdivided
been
-
one for uses
of domestic output, and one for uses of imports.
of the resulting import matrix are
aggregations
different
Three
carried out:
means
By
1.
of
groups
industry
principle
commodities
aggregation
takes place to form
to the domestic industries. In
are
rearranged to suit
a
clas-
commodity is assumed to be supplied by indus-
each
where
matrix
corresponding
(117)
imported
the
sification
make
the
in the same proportion as the domestic output of the commodity.
tries
(Technically the absorption matrix for imports is premultiplied by the
make
matrix
explained
in
coefficient
a
form, the column totals being 1).
As
the following section on the treatment of domestic out-
in
put, a problem did arise in cases where no domestic output existed, as
such commodities are not contained in the make matrix. The problem was
solved by "assigning"
2.
domestic industry to these commodities.
All commodities contained in the CCCN nomenclature (i.e. all goods)
aggregated
are
yields
in
a
rows (CCCN groups 01 -99).
99
row
one
over the first two digits of this nomenclature,
(no.
100).
comparability
direct
which
All services are lumped together
The advantage of this classification is its
with current statistics, and the absence of any
questions of interpretation.
3.
A
special
aggregation for use in the macroeconometric model ADAM
showing the ten divisions of SITC and an 11th group for services. This
grouping
was
also worked out for exports. This aggregation is not in
the ordinary input- output data bank.
57
6.
The treatment of domestic output
matrix for domestic output (at the 1600 -commodity
absorption
The
level)
treated in a way parallel to the first kind of aggregation
is
mentioned above for the import matrix, i.e. it is premultiplied by the
matrix
make
in
which
technology,
when
assumption
Also
form.
is an industry x
result
The
input- output table calculated on the assumption of an indus-
industry
try
coefficient
a
practical
calculations are based on rectangular matrices.
the
case
this
in
sense
is the only possible technology
incidentally
commodity
a
commodity table would not make any
x
theoretically
- but
1600 x 1600 input- output table
a
could be calculated.
worth
is
It
assumption
technology
industry
maximum
when
taken
is
of
detailed
a
construction of the table (cf. also UN 1973,
earlier
mentioned
As
characteristic
concept
this
which
need
for
the
concept
of
construct the input- output table
imply
producer. Furthermore, for commodities
main
are
not
produced
it
has
been
level)
38).
commodity is defined as characteristic in the
the
is
no
is
p.
data base in the
The make matrix does however automatically
each
if
which
industry
there
products in order to
by the new procedure.
x
commodity tables are completely eliminated
x
advantage
whether to produce industry
and
choose
to
commodity
or
that the much discussed problems of which
noticing
in Denmark (about 300 at the 1600 -commodity
necessary
to assign a characteristic sector in
order to carry out the first aggregation of the import matrix. In this
way
the concept of a "characteristic sector" has been defined for all
commodities for the year 1975.
7.
Selected commodities
It is generally accepted, that the distinction between competitive
and
non -competitive
(complementary)
imports
important
is
in
input- output analysis. The distinction is set out in SNA (UN 1968) and
discussed
in
more detail in (UN 1973). From the latter the following
passage might be quoted:
"The
decision
on
complementary)
may
disaggregation
of
arbitrary
in
classification
thus
(because
commodities,
between competitive and
(i.e.
p.
it
depends
60),
on
the level of
to a certain extent,
be
particular cases and may need revision over time if
58
domestic
production
ceases
commences. Finally, it should be
or
noted that the classification will vary between economies and this
may cause slight problems in international comparisons" (p. 61).
of the Danish input-output tables 1966 -75
In
the
first
almost
all
commodities at the 4000 -level disaggregation for which no
version
Danish production took place in 1966 were classified as complementary.
This meant that about 30 per cent of imports were so classified.
compilation of time series of input- output tables and the
the
In
application of these in analysis, two problems showed up:
Firstly,
products
waste)
some product categories such as iron and steel work
for
which
are partly produced in Denmark
partly
imported,
commodities
were
classified
competitive,
even though this case might from
and
had
view
a
that about half of the
found
complementary
as
expected to show
been
was
it
(but only by recycling
a
and
the
rest
as
common sense point of
clear -cut example of complementary
imports,
as
analysis
the capacity limit for Danish output could not be taken into
consideration,
classify
arose
and
iron
no
ore
whereas
actual
the
produced
is
in Denmark.
In input- output
the other hand it would not make sense to
on
Danish
as complementary. Similar cases
output
many other primary products such as agricultural products,
for
lately in the case of Denmark also for crude oil and natural gas.
these
Clearly
marginal in
problems have no simple solution as their character is
system which is based on average ratios throughout.
a
Secondly,
over
complementary
had
to
imports
applications
where
commodity
complementary
competitive
words:
a
stick
to
it
imports
be
useful to interpret it as covering
this
-
the
for
would
be
the
case
both for
groups of imports classified as
In other
reclassification of the goods would be necessary to
yearly
the
groups
of
would impair the concept in
which
output of a specific domestic industry.
the
to
would
definition
applied would imply that commodities
yearly,
and
above -mentioned
the
strictly
reclassified
be
homogenous
time
ideal
reclassification
definition,
but
on
the
other
hand
such
a
would make the data more or less meaningless as time
series.
It
is
obvious that these problems can be solved in specific app-
lications
of
base
more
for
the
input- output tables, where they are used as
sophisticated
a
data
econometric models, and where marginal
59
effects
can
etc.
To producers of in-
into consideration.
taken
be
tables which are required to be comparable over many years
put- output
and
to
be useful in many different applications
not
be
known
the
at
(of which many might
the table is produced), the problem is,
time
however, a much more difficult one, as discussed in Thage (1973).
following
the
In
the
solution which was finally chosen to this
problem, is set out. It is based on three basic principles:
1.
flexibility.
Maximum
can
versions
The
former
obtained
be
as
"exogenous"
and
"endogenous"
special cases from a more general
system.
2.
The link to the detailed rectangular data matrices is utilized and
thereby makes clear to users that the input- output data system can
applied
be
connection with much more detailed data which are
in
available
also
in
represent
data
commodity -flow
standard
a
form.
(In fact to show that the
a system of
consistent statistics
are comparable over time and available in connection with
which
-
but also without - the input- output tables).
3.
To take into consideration that in many cases the user will be in-
terested
in analysing the effects on certain key commodities of a
specific
policy
and
in knowing whether the changes are of
also
domestic or foreign origin. In recent years analysis of energy and
raw
other
material
development
and
problems,
pollution
and
technological
general analysis of the inflationary process
in
are examples to be mentioned.
considerations
These
1600
the
(in
reasonably
commodities
to
the
data
called
be
It
key
a
number of commodities which might
commodities
in the Danish economy.
These
arranged in special matrices corresponding in format
are
input- output
bank.
version)
192
x
us directly to the concept of selected
simply meant to select from the absorption matrix
which
commodities,
led
is
matrices
important
and placed together with these in the
to
note
that no aggregation of these
commodities
take place, so that the rows in the matrices for selected
commodities
consist
have
a
other
clear
of
definition
statistical
four -digit CCCN groups. This means that they
for users and can easily be connected with
information (for example statistics on production,
foreign trade and prices).
A
total
of
99 commodities were selected.
Of the total supply of
60
these commodities, 67 per cent consisted of imports,
and these imports
made up 52 per cent of total imports of goods (in 1975).
practical reasons it was a priori decided, that the number of
For
selected commodities should not exceed 100. But for users with special
wishes it is possible to select other goods from the absorption matrix
by ad hoc procedures, as these matrices cannot be available in full in
input- output
the
data
The commodities selected can broadly be
bank.
said to consist of the following categories:
Agricultural products not produced in Denmark
Grain and other important feeding stuffs
Energy products
Fertilizers, basic plastics
Timber, pulp, paper
Wool, cotton, chemical fibres
Iron and steel (not fabricated)
Other metals (not fabricated)
Aircrafts and parts thereof, computers
Transistors, microchips
Tractors, motorcars and parts thereof.
annex
In
products
with
divided
only
are
the
full list of selected commodities is given.
a
3
input -output
all years since
for
Energy
into four commodities, but in connection
tables there are also special energy matrices
1966 which show 25 kinds of energy, both in value
and physical quantity terms.
annex
In
the set -up of the matrices in the input- output table
3
data bank is shown for one single year.
for
each
can
be
year
seen
-
In fact there are to such sets
one in current prises and one in constant prices.
that
It
the input- output table has been divided into many
submatrices to faciliate calculations. In the data bank there are also
two
inverse matrices (nos.
no.
1
of
and matrices
nos.
converted
and
14
13,
1 +4,
16 and
17)
which are the inverse of matrix
respectively. All matrices with the exception
15 are given in a coefficient form,
but can be
absolute figures by means of the absolute column totals
to
given in the three mentioned matrices.
The
nos.
total
coefficient
21 -23.
In
contents
matrices
this
of
for
selected commodities are shown as
form they can only be applied to calculate the
these
commodities
or
to trace price effects on
61
special
assumptions.
trices
with
by means of the supporting coefficient ma-
But
nos. 24 -26 they can be changed into forms which are compatible
matrices nos.
1 -6
and thereby allowing a more generalized treat-
ment of imports.
8.
generalized treatment of imports
A
mentioned
As
21 -23)
have
above,
rows
the matrices for selected commodities (nos.
consisting
of 4 -digit CCN groups.
By applying the
same procedure as described earlier for dividing the absorption matrix
into
a
matrix
for domestic production and a matrix for imports, the
21 -23
can each be so divided. The necessary information for
matrices
this
operation
uses)
matrix
and
contained
is
in matrix 25 (import ratio in domestic
(import ratios in exports).
26
procedure is illustrated in figure
described
As
selected
above,
The result of this
2.
breakdown of the original matrices for
the
commodities takes place by applying the actual import ratios
for the year in question given in the matrices 25 and 26. But it is of
course
also
possible
choose
to
different
ratios
for some or all
commodities in individual calculations, the two extremes being (1) the
import
ratios
commodities
all
original
are
matrices
conditions
all commodities are one (2) the import ratios for
for
and
zero.
This
makes
it
use
what
to
flexibility
possible
in
splitting
up the
to take into account marginal
external information the analyst might
possess.
After
the
above
procedure has been carried out, the two sets of
natrices are still on a commodity basis. From the total make matrix is
singled out
partial matrix which contains the information concerning
a
the 99 selected commodities. (Matrix no. 24 of dimension 117
means
of
this
matrix
x
99). By
is now possible to transform the matrices
it
21a -23a and 21b -23b into a form having industry identifications in the
matrices
with
rows,
i.e.
added
to
the
two
faciliate
the
following
sets
of
117
rows which can be subtracted from or
matrices
exposition,
1 -3
the
and 4 -6, respectively. To
relevant sets of matrices
(with the symbols used hereafter) are set out in figure 3.
62
Figure
2.
The breakdown of selected commodities into domestic output
and imports.
Original matrices for selected commodities (cf. annex 1):
(117)
Domestic output
and imports
(99)
21
(66).
22
After breakdown into domestic output and imports:
Domestic output
(99)
2la
22a
23a
Imports
(99)
2lb
22b
23b
Figure
3.
Illustration of symbols used in the definition of
"stripped" matrices.
Standard coefficient matrices (cf. annex 1):
(66)
Total domestic
output (uses)
by industry
(117)
2
DC
Total imports
(117)
(uses) classified by producing industry
4
5
6
MA
MC
MD
Coefficient matrices for selected commodities:
Domestic output
(117)
of selected
commodities
by industry
Imports of
selected
commodities
by industry
SDA
SDC
SDD
SMA
SMC
SMD
(117)
63
by
following each of the four sets of matrices is symbolized
the
In
single variable name. D is the common name for the matrices DA,
a
DC and DD. Similarly the names M, SD and SM will be used for the three
and
other sets of matrices,
calculated
matrix
elements
for
the
actual import ratios and relevant make
in question.
year
the
It is then obvious that
matrices are completely contained in D and M, respectively, and
these
can
of
means
by
assume that the matrices SD and SM have been
shall
we
Initially
is defined as SD + SM.
S
be
subtracted from them without leaving negative elements in the
resulting matrices.
The
matrices D and M stripped of their
input- output
traditional
contents of selected commodities will then be:
And
what
D - SD
(2)
M - SM
adds
subtracted
have
we
(1)
up
to the total matrix for
selected commodities (both domestic and imported):
(3)
The
(SD,SM)
S
=
SD + SM
=
SD* + SM*
matrices in (3) can be either the actual matrices of the year
or
some specially constructed matrices SD* and SM* which can
be
obtained from the original matrices for selected commodities (fig.
2)
by
applying
partial
priori
make
ratios
import
other
and possibly also a different
matrix. This allows the user to take into account any a
information
he might possess, and to make special assumptions
regarding marginal changes.
Now
we
generalized
idea
is
selected
to
have
the
treatment
add
necessary
imports
of
instruments
for
illustrating
by some standard cases.
the
The basic
to the "stripped" matrices (1) and (2), matrices of
commodities.
The
only requirement to the matrices added is
that the column totals must be equal to the column totals of matrix S.
The
standard
cases are first shown using the actual
Line
shows
S,
SD and SM
matrices for delivery from
matrices
of
domestic
industries, line (b) endogenous imports exclusive of imports
of
selected
commodities.
the
year.
commodities
(a)
and line (c) endogenous imports of selected
64
"Stripped"
matrices
Case
Case
1
2
Case
+SD
M - SM
+S
+0
+0
+0
+0
(c)
0
+ 0
+ SM
+ S
Sum
D
(a)
D-
(b)
SD
+M
-
S
S
S
S
3
To exemplify how the above set -up is to be read the complete "case
2" model will be:
D - SD
(b)
M - SM + 0
(c)
0
three
The
"stripped"
it
+SD =D
(a)
+ SM
above
=
M - SM
=
SM
cases
according
cases
three
In all cases
imports of category (b), cf. above, are
the actual import ratios of the year. Through the
to
from
selected commodities to the
have the following characteristics.
matrices
is assumed that endogenous
used
adding
for
to
1
3
a
still
higher
proportion of selected
commodities are treated as endogenous imports.
case
In
commodities
1
it
zero
are
assumed
is
-
that
import ratios for all selected
or alternatively imports of these commodities
can be determined exogenously.
case
In
2
selected
commodities
are assumed to be domestically
produced (or exogenous) and imported according to the average rates of
actual
the
If SM is interpreted as complementary imports this
year.
case corresponds to the model which in the first version of the tables
was named "endogenous ".
case
In
3
it
is
assumed
that
import ratios for all selected
commodities are equal to one.
matrices in line (b) and line (c) can be added, it is possible
As
to
form
lumped together with other imports. It might be mentioned that in
are
cases
these
and
total import matrices, where imports of selected commodities
(c)
it
is possible to have import matrices in both line (b)
classified
according to
2 -digit
CCCN groups, or to keep ma-
trices in line (c) at the 4 -digit CCCN grouping of the original matrix
for selected commodities.
If
the
lines (a) and (b) are added we get three new cases, where
65
assumed that imports exclusive of what is specified as imports
it
is
of
selected
commodities
are
zero
alternatively
or
-
determined
For imports of selected commodities the assumptions will
exogenously.
be the same as in cases
1
-3.
The three new cases are:
"Stripped"
matrices
Case
Case 4
Case 6
5
(a +b)
D + M - S
+ S
+ SD
+ 0
(c)
0
+0
+SM
+S
Sum
D+ M-
S
S
S
S
is worth noticing that case 5 corresponds closely to the model
It
which in connection with the first version of the tables was named the
although
"exogenous ",
imports" is now defined from
"complementary
a
different point of view.
above six models the matrices SD and SM have been used to
the
In
the standard cases which could be commented upon by refer-
illustrate
ence to fairly simple model structures and to the treatment of imports
applied.
earlier
It is,
however, important to point out that the new
system gives an infinity of model possibilities if the matrices SD and
SM
replaced
are
by
SD*
and SM *, which can be tailored to specific
uses. In many instances the user will probably be interested in giving
a
special treatment to only one or a few of the selected commodities.
In this connection it is important to remember that in the calculation
of the "stripped" matrices it is always the actual S, SD and SM of the
year in question which must be deducted.
commodities
(M - SM)
for
imports
exclusive of imports of selected
has been considered in its entirety only. But of
it is possible to subdivide also in this matrix
course
M)
matrix
the
Above
into
(or the matrix
submatrices by separating out entire rows and to treat these
in a way parallel to the subdivided S- matrix.
few examples may give an idea about the possibilities of analy-
A
sis in models based on the above structure.
In an analysis of the marginal effects of an increase in output of
animal
the
products
selected
it would be appropriate to set the import ratios for
commodities
grain
and
feeding
stuff
at
one,
as no
66
additional supply of these commodities will be available from domestic
sources. On the other hand, if the harvest has been unusually large in
a
single year and an input- output table for an earlier year is used as
a
basis for model calculations, these ratios could be decreased on the
average.
that
Suppose
changed
capacity
the
drastically.
necessary
For almost any kind of analysis it will then be
change
to
of steel mills or oil refineries has
import
the
ratios
for
number of selected
a
commodities.
These
examples
structure
among
distinction
analysis,
things
input- output
in
kinds
many
of
the
makes
models
present
it
for
input- output data
meaningful to draw
average
a
and marginal
a
priori knowledge into the input- output
rather precise way. For more special applications it will
a
to
to almost any degree of detail by drawing on the
go
data in the basic commodity
9.
that
respectively, and generally speaking it will be possible to
possible
be
other
many
between
incorporate
model
illustrate
flow system.
Concluding remarks
the
In
production
more
development
economic
of
the
there
has been an enormous increase in the
input- output tables and in their applications in still
of
fields
increase
decade
last
size
the
in
general appearance,
of
the
analysis. Apart from a general tendency to
tables there has, however, not been much
techniques
of
producing the tables or in their
as this has been instituted by the recommendations
given in the SNA.
The
methods
concept
of
detailed
instrument
in the present paper (and implemented for
be seen as a step on the way to creating a more general
can
Denmark)
described
an
data
input- output table which in close connection with the
base
of the national accounts can serve as a flexible
for structural economic analysis at all levels.
67
ANNEXES
68
Annex
1
A technical note on the 1600 commodity aggregation
described above the main idea in the change in method from the
As
input- output
preliminary
tables for 1966 -75 to the final ones was to
the aggregation of the detailed commodity flows to characteris-
avoid
sectors (giving square make and use matrices) by constructing the
tic
input- output table directly from the detailed (rectangular) matrices.
Because
however
year,
but
1966,
commodity
digit
those containing the most detailed commodity flow system
not
each
for
problems of continuity these rectangular matrices are
of
but
aggregation from about 4000 commodities
an
gradually
declining
classification,
2500 in 1982) to the stable 1600
to
where all goods are aggregated to the four
classification,
CCCN
(in
whereas
services are left at their most
detailed level.
application
The
of
this
particular
level of aggregation gives
raise to some theoretical and practical problems. Whereas it is always
that
true
an
industry by industry input- output table constructed on
assumption
the
and
make
use
available
of
industry technology directly from rectangular
an
matrices
containing the most detailed commodity flows
be superior to the same kind of table constructed via
will
intermediate step of commodity aggregation to square make and use
the
matrices, it is not a given matter that a similar kind of input- output
table constructed from rectangular make and use matrices based on even
a
slight commodity aggregation, will have this property.
criterion
The
put- output
table
positively
be
world
will
known
contain
that
be whether the resulting in-
must
some
elements
simply
about
which
it can
they give a wrong description of the real
the sense that they contradict
in
tained
"goodness"
on
information which can be ob-
inspecting the most detailed commodity flow system
by
available.
The
does
obviously
above
occur.
tic
not lead to input- output tables which will fulfil the
criterion,
"safety
on
in
the
general
other hand this method has a build in
secures
that real disasters do not
This safety net is made up by the assignment of a characteris-
sector
fitted
but
which
net"
on aggregation to square make and use matrices
based
method
to
each commodity.
In other words the aggregation key is
to create as little turmoil as possible in the subsequent con-
struction of the input- output table.
69
from the 4000 (or 2500) commodities to the 1600
In the aggregation
groups
we
however
do
introduce
an
aggregation key (from the most
detailed commodities to the four digit CCCN groups) which basically is
to the subsequent calculations - the exceptions being such
irrelevant
where the added commodities happen to be mainly produced nn the
cases
same sector.
Even though the CCC Nomenclature is not very well designed for the
which
purpose
to
grouped
according
made,
its
digit
as the commodities are essentially
nature
of the material of which they are
the
to
that in each section or shapter it often contains a product
so
from
it is here put,
headings)
(the
level
to its most fabricated form,
crude
most
fortunately
most
it is at the four
often
the case that
important individual commodities are produced in the same sector (this
outcome
fication).
course
of
is
must
It
also
a
function of the given sector classi-
also here be mentioned that many of the most de-
tailed commodities are already at the four digit level
(and more so as
passes on), and for these there are by definition no aggregation
time
problems.
that two commodities which are grouped together in a
suppose
Now
have different producing sectors, different distri-
four -digit
group
bution
users, different import ratios and are both of a consider-
on
able size. In this case the resulting input- output table, and also its
subdivision
adversely
into
a
affected
domestic
in
matrix
and
an
import matrix will be
the sense that it will contain elements which
clearly contradicted by the information we have from the detailed
are
commodity flows.
milk delivered from farms were grouped together with milk
raw
If
delivered
from
we would have an example of such a group.
dairies
In
the input- output table the average distribution to users of this group
would
be
sector,
included
making
in
both the agricultural sector and in the dairy
sense
no
in either case.
The dairy sector would for
example be seen to deliver about half of its output to itself, whereas
farmers would have
In
a
big delivery of milk to final consumers.
such cases it is obviously necessary to deviate from the prin-
ciple of aggregating all goods to four -digit CCCN groups.
In
order
to detect cases where aggregation
would cause unaccept-
able distortions, two "partial" input- output tables for 1977 were constructed
for
each of the 1600 4 -digit groups (assuming for each par-
70
tial
table
first
one
all
commodities
group.
This
implies,
using
one
input- output table was con-
the
that
matrix with one column and one row re-
a make and use
and
spectively
of all de-
belonging to the 4 -digit group into one commodity
method
using
structed
A) was based on an initial aggregation
(method
tailed
commodities to be non existent). The
4 -digit
other
import
ratio.
The second one (method B)
omitted the initial aggregation, so in this case the number of columns
in
make
the
number
import
of
detailed
matrix,
the
number
respectively, were equal to the number of
ratios,
belonging
commodities
of rows in the use matrix and the
to that particular 4 -digit group. It
followed from the methods used that the two resulting tables will have
identical
vectors and identical column sum vectors, whereas
sum
row
the "interior" of the tables will be different.
should come as no surprise that the total IO table based on the
It
commodity classification could be obtained by adding up the 1600
1600
Method
IO tables,
A
commodity
detailed
most
and likewise that the total IO table based on the
level
(3000
in
1977) could be obtained by
adding up the 1600 Method B tables. Consequently the errors introduced
IO table by aggregating several detailed commodities
into
the
total
into
one 4 -digit group could be calculated as the differences between
the Method A and Method B table for that particular 4 -digit group.
two tables for each 4 -digit group were compared cell by cell,
The
the differences calculated both as absolute values and as percen-
and
about 45
of
column
cases
it
was found that the aggregation to the four digit level gave
raise
to considerable errors either in the total table or in its sub-
division
into
the
in
In
domestic matrix and the import matrix. The latter
of errors was seen as less serious than the former, which influ-
kind
ences
the
about
15
fic
sums
the total input- output table.
tages
technical
of
the input- output table. Finally
four -digit groups were disaggregatd to two (often one speci-
detailed
modification
years.
properties
commodity
to
the
and
"the rest ") or more subgroups, and this
simple aggregation key has been applied for all
This has of course required continuity for these more detailed
commodities to be kept over time.
Another deviation from the strict aggregation principle happens in
connection with the treatment of "scrap "commodities. This is explained
in annex 2.
71
Annex
2
The treatment of scrap and waste materials
Scrap and waste materials can arise from two basically different
sources.
First
as a result of demolishing existing
arise
can
it
capital goods, in which case it is supplied from
capital
fixed
productive
column.
Second
activity as
a
can
it
arise
form of by- product,
negative entry at
a
in
the
course
of
for example in cutting
processes etc. in the mashinery industry.
Even
the most detailed commodity level scrap and waste from
at
different
these
two
which
furthermore
particular
this
sources
will
are contained in the same commodity,
often also contain some ordinary supply of
But in most cases the dominant part of
metal etc.
the supply will come from negative fixed capital formation.
such
If
together
group,
with
constructing
domestic
how
is
other
after having being added
even
ordinary treatment in the process of
the
to
input- output
the
producer
table,
it
is
the distribution by
of supply of "production" waste products and any
ordinary
of
perhaps
with other commodities in the same four -digit
subjected
is
supply
commodity,
a
output of the commodity group which determines
the original negative entry in the fixed capital formation cell
finally assigned to sectors. As such "production" waste products
often
originate
sectors
will
from
very
given
be
different sectors, each of these
many
some
part
of
the negative fixed capital
formation in their row.
these
If
capital
formation,
positive,
table,
There
as
capital
consumption
do
-
other
figures
users
of
however
are
number
a
have
the
that
so
suspicious.
fixed
sectors
of
formation
(positive)
the cells may non the less be
in
the
deliveries to fixed
table
might
not
see anything
introduced some distortions in the
sectors will have too small deliveries to
and
too
big
deliveries to intermediate
often to the branch itself.
If some of these sectors
not have any ordinary deliveries to fixed capital formation,
negative
entry
will be visible in the input- output table in
a
the
cell
where nobody would expect such a figure.
Where
formation
should we then expect to find this negative fixed capital
in
the input- output table?
It is obviously not an output
72
from any ordinary sector, and we do not wish to create an artificial
sector
solely
order to solve this problem. So we are left with
in
two problems:
1.
We
subdivide those of the most detailed commodities which
must
contain scrap from demolished capital goods to isolate that part
of
commodity which is supplied from negative fixed capital
the
formation.
2.
We
sector
which
decide
must
is
to
be
chosen
as
the
characteristic producer of this kind of scrap materials.
As the most detailed commodities can by their vary nature not be
subdivided
fixed
negative
containing
procedure,
automatic
any
by
capital
and
the
commodities
formation cells like all other
commodities at the most detailed level lack continuity over time, it
has
been
decided
illustrated in figure
In
small
1.
(1) the original commodity balance is shown.
row
there
that
use an artificial subdivision process. It is
to
It is seen
are two domestic producers, each producing a relatively
share
of
the total amount available for use as intermediate
consumption and for exports.
In row (2)
it is shown how an artificial commodity is created by
assigning a negative output to wholesale trade equal to the negative
cell for fixed capital formation.
Table
1
Schematic illustration of the treatment of commodities containing scrap
Uses
Supply
Domestic output
Industry Value
Imports
Intermediate consumption
Fixed
capital
formation
Exports
100
250
-180
40
no.
1
Original commodity at the
most detailed level
2
-
Subdivision
Artificial new commodity
Is kept separate in
the construction of
the IO -table
Residual commodity
(-
1 -2)
aggregated with
any other commodity
38xx1
38xx2
7
3
38xx1
38xx2
7
3
Is
3
in the same
digit group,
except (2)
four -
-180
Wholesale -180
Wholesale
180
100
250
0
40
73
Finally row (3) is simply obtained by deducting row (2)
an
in row (3) is subsequently treated as
The "residual" commodity
(1).
from row
ordinary detailed commodity, i.e. it will be added together with
any other commodity in the same four -digit group.
Schematically
negative
capital formation
fixed
to.
wholesale trade as
a
reduction
(in order not to permit this playing around with scrap
in the output
to
have first delivered all scrap originating as
we
influence the totals of the wholesale trade sector), and then in
the
next round the wholesale trade sector acts as the "producer" of
the
scrap,
use
to a positive supply without affecting any of the totals of the
has in this way been transformed from a negative
which
system.
wholesale
the
trade
that
the
sum
of
all negative fixed
formation elements in the input- output table will be placed
capital
in
implies
treatment
This
margins
on
distortion
row.
fixed
capital formation of machinery etc., this
wholesale trade row, as the deliveries to fixed
the
in
not be visible, but there will of course be a
will
entry
negative
As there are considerable wholesale
trade
capital formation will be to small and the deliveries to the sectors
using
(and to exports) will correspondingly become
as inputs
scrap
to big. As the row for wholesale trade has rather high values in all
cells
will
distortions
the
be relatively small. Also the too big
deliveries to the scrap consuming sectors will not be without sense,
as
actually
arguments
or
part
biggest
the
metal
do
the value of scrap at purchasers' values
of
consist
of
wholesale trade margins. These last two
justifies that wholesale trade, and not for example steel
works,
has been chosen as the characteristic producer of
scrap from demolition materials.
Altogether
defined.
fixed
No
They
capital
negative
eight
are
such
all
artificial
scrap commodities have been
iron or metal products, which are negative
formation in the category "Machinery and equipment ".
fixed
capital formation is defined in connection with
the activity of demolition of buildings.
74
Annex
3
Contents of the data bank for input-output matrices
organization of the input- output matrices for
The
is
illustrated
input- output
in
the
following
table
has
been
diagram.
is
It
a
single year
seen that the
broken down into many submatrices to
facilitate the use. For each year two sets of matrices are placed in
data
the
At
bank
present
-
one in current prices, and one in constant prices.
(autumn
the
1986)
bank
contains annual data for the
period 1966 -83.
The data bank is placed at the computer center of the University
of Copenhagen in connection with
analysis which is
a
a
programme packet for input- output
further development of the PASSION packet worked
out at the Harvard Economic Research Project in the sixties.
way
the
data
the
statistical
In this
can be made directly available also to users outside
office. The programme packet and how to get access
to the data files is described in Folke (1981).
All matrices with the exception of nos. 13,
in
coefficient
a
form
14 and
15 are stored
but by means of the absolute column
only,
totals in these three matrices they can be transformed into absolute
figures if needed.
set
The
traditional
2,
5,
1,
3,
4,
6,
7,
9,
10 an
12 represents the
table in a coefficient form. The matrices
input- output
and
8
matrices
of
11 give a detailed breakdown of the column for
total
private consumption contained in matrices 3, 6, 9 and 12.
The
two
industries,
last
pages
groups
of
of
the
annex
further
not
need
any
4 -digit
CCCN
groups
a
complete list of
final demand and primary inputs used in the
input- output tables. The matrices where
do
give
of
2 -digit
explanation,
CCCN groups are used
whereas
a
list of the 99
selected commodities is given on the last
page of the annex.
In
but
in
principle all matrices are given in approximate basic value,
connection with indirect taxes, net, on uses, which are all
contained in the matrices for primary inputs,
values
for
a
total in purchasers'
each use is obtained. This implies that matrix 13 is in
approximate basic values, while 14 and 15 are in purchasers'
values.
75
Organisation of the input- output matrices in the data bank
Intermediate
consumption
Dim.:
Uses of domestic output
classified by producing
industry
Private
consumpt:
(subgroups)
117
Final
demands
(main groups:
66
9
117
1
2
3
117
4
5
6
Uses of imports of special
services etc.
3
7
8
9
Primary inputs
5
lo
11
_I
Column totals (absolute)
1
14
1
Uses of imports classified
in groups corresponding to
the output structure of
domestic industries
Uses of imports classified
by 2 -digit CCCN groups
loo
J
13
18
I
I
I
I
19
12
15
2o
(column totals equal to
totals in matrices 4, 5
and 6)
Selected commodities (domestic output and imports)
classified by 4-digit
CCCN groups
I
I
99
21
Dim.:
99
Transformation matrices to
be used in connection with
matrices for selected com117
modities:
24: Partial make matrix
25: Import ratios in domestic uses
26: Import ratios in exports
24
22
23
1
99
25
1
99
26
Matrices nos. 16 and 17 are not shown above. They are the inverses
corresponding to matrices nos. 1 and 1 +4, respectively.
76
Classification
1
11101
of
industries (117) in the input -output table
Agriculture
41
34210 Reproducing and composing services
42
34221 Book printing
2
11103 Horticulture
3
11109 Fur farming,
etc.
43
34222 Offset printing
4
11200 Agricultural
services
44
34223 Other printing
5
12000 Forestry and
logging
45
34230 Bookbinding
6
13000 Fishing
46
34240 Newspaper printing and publishing
7
20099 Extraction of coal,
47
34291 Book and art publishing
8
29000 Other mining
48
34292 Magazine publishing
9
31113 Slaughtering etc. of pigs and cattle
49
34293 Other publishing
10
31117 Poultry killing, dressing,
50
35110 Manuf. of basic industrial chemicals
11
31121 Dairies
51
35120 Manuf. of fertilizers and pesticides
12
31123 Processed cheese, condensed milk
52
35130 Manuf. of basic plastic materials
13
31124 Ice cream manufacturing
53
35210 Manuf. of paints and varnishes
14
31130 Processing of fruit and vegetables
54
35220 Manufacture of drugs and medicines
15
31140 Processing of fish
55
35230 Manufacture of soap and cosmetics
16
31151 Oil mills
56
35290 Manuf. of chemical
17
31152 Margarine manufacturing
57
35300 Petroleum refineries
18
31153 Fish meal manufacturing
58
35400 Manuf. of asphalt and roofing mater.
19
31160 Grain mill
59
35510 Tyre and tube industries
20
31171
60
35590 Manuf. of rubber products n.e.c.
21
31173 Cake factories
61
35600 Manuf. of plastic products n.e.c.
22
31174 Bakeries
62
36100 Manuf. of earthenware and pottery
23
31180 Sugar factories and refineries
63
36200 Manuf. of glass and glass products
24
31190 Chocolate and sugar confectionery
64
36910 Manuf. of structural clay products
25
31210 Manufacture of food products n.e.c.
65
36920 Manuf. of cement,
26
31229 Manuf. of prepared animal
feeds
66
36993 Concrete products and stone cutting
27
31310 Distilling and blending spirits
67
36998 Non -metallic mineral products n.e.c.
28
31338 Breweries
68
37101 Iron and steel works
29
31400 Tobacco manufactures
69
37102 Iron and steel
30
32118 Spinning, weaving etc.
textiles
70
37201
31
32120 Manuf. of made -up textile goods
71
37202 Non -ferrous metal casting
32
32130 Knitting mills
72
38121 Manufacture of metal
33
32158 Cordage, rope and twine industries
73
38138 Manuf. of structural metal products
34
32200 Manufacture of wearing apparel
74
38191 Manuf.
35
32300 Manufacture of leather products
75
38198 Manuf. of other fabr. metal
36
32400 Manufacture of footwear
76
38220 Manuf. of agricultural machinery
37
33100 Manuf. of wood products,excl.furnit.
77
38238 Manufacture of industrial
38
33200 Manuf. of wooden furnitute, etc.
78
38280 Repair of machinery
39
34110 Manuf. of pulp,
79
38293 Manufacture of household machinery
40
34128 Manuf. of paper containers,wallpaper
80
38298 Manuf.
oil
and gas
packing
products
Bread factories
paper,
paperboard
products n.e.c.
lime and plaster
casting
Non -ferrous metal works
furniture
of metal cans and containers
of
products
machinery
refrigerators, accessories
77
Classification of industries (continued)
100
71138 Other land transport
home appliances
101
71210 Ocean and coastal
83
38392 Manuf. of accumulators and batteries
102
71230 Supporting services to water trsp.
84
38398 Manuf. of other electrical supplies
103
71300 Air transport
85
38410 Ship building and repairing
104
71509 Services allied to transport,
86
38438 Railroad and automobile equipment
105
72000 Communication
87
38498 Manufacture of cycles, mopeds,
106
81000 Financial institutions
88
38500 Professional and measuring equipm.
107
82000 Insurance
89
39010 Manufacture of jewellery, etc.
108
83110 Dwellings
90
39098 Manuf. of toys,
109
83509 Business services
91
41010 Electric light and power
110
93109 Education, market services
92
41020 Gas manufacture and distribution
111
93300 Health, market services
93
41030 Steam and hot water supply
112
94000 Recreational and cultural services
94
42000 Water works and supply
113
95130 Repair of motor vehicles
95
50000 Construction
114
95299 Household services
96
61000 Wholesale trade
115
95400 Domestic services
97
62000 Retail
116
97099 Private non -profit
98
63000 Restaurants and hotels
117-
98099 Producers of government services
99
71118 Railway and bus transport, etc.
81
38320 Manuf. of telecommunication equip.
82
38330 Manuf. of electrical
etc.
sporting goods, etc.
trade
water transport
etc.
institutions
Classification of private consumption expenditures
1
001
Bread and cereals
16
120
Non -alcoholic beverages
2
002
Meat
17
131
Beer
3
003
Fish
18
132
Wine and spirits
4
004
Eggs
19
140
Tobacco
5
005
Milk,
20
210
Clothing
6
006
Cheese
21
220
Footwear
7
007
Butter
22
311
Gross rents
8
008
Margarine and lard
23
312
Water charges
9
009
Fruits and vegetables
24
321
Electricity
10
010
Potatoes, etc.
25
322
Gas
11
011
Sugar
26
323
Liquid fuels
12
012
Coffee,
27
324
Other fuels
13
013
Ice cream
28
410
Furniture, fixtures, carpets, etc.
14
014
Chocolate and sugar confectionary
29
420
Household textiles, furnishings etc.
15
015
Other foods
30
431
Major household appliances
cream,
tea,
yoghurt,
etc.
cocoa
78
Classification of private consumption exprenditures
(continued)
31
432
Repairs to major househ. appliances
50
714
Maintenance of recreational goods
32
440
Glassware, tableware,househ.utensils
51
720
Entertainment,
33
451
Non -durable household goods
52
730
Books, newspapers and magazines
34
452
Household services
53
740
Education
35
460
Domestic services
54
750
Day -care
institutions for children
36
510
Medical and pharmaceutical
55
811
Barbers,
beauty shops,
37
520
Therapeutic
56
812
Goods for personal care
38
530
Physicians, dentists, etc.
57
821
Jewellery, watches, rings, etc.
39
540
Hospital care and the like
58
822
Other personal
40
550
Accident and health
59
823
Writing and draving equipment
41
610
Personal transport equipment
60
831
Expenditure in restaurants
42
621
Maintenance of transport equipment
61
832
Expenditure for hotels and lodging
43
622
Gasoline and oils for trsp. equipm.
62
850
Financiel
44
623
Other expenditure on trsp. equipm.
63
860
Services, n.e.c.
45
630
Purchased transport
46
640
Communication
64
994 -Purchases in DK by non -res. househ.
47
711
Wireless and tv sets, gramophones
65
995
48
712
Photo and musical equipment,
49
713
Other
products
appliances and equipm.
insurance'
in
etc.
goods
services,
Consumption
n.e.c.
the domestic market
Purchases abroad by res. households
Consumption by resident households
boats
recreational goods'
cultural services,etc
66
Cons.
by private non -profit
inst.
Classifications of final demands and primary inputs
SPECIAL CATEGORIES OF IMPORTS
MAIN GROUPS OF FINAL DEMAND
1
Private consumption
consumption
1
Direct imports to continental
shelf
2
Tourist
3
Expenditures by Danish ships abroad
transactions
2
Government
3
GFCF,
machinery etc.
4
GFCF,
transport equipment
5
GFCF,
construction
6
Agricultural breeding stock
2
VAT on uses (net system)
7
Increase in stocks
3
Other indirect taxes net
8
Exports of goods and services
4
Compensation of employees
9
Imputed bank service charges
5
Gross operating surplus
PRIMARY INPUTS
1
Commodity taxes net (excl. of VAT)
79
Selected commodities (row no. in matrices 21 -23)
No.
CCCN
Tropical fruits
Coffee
Wheat
51
52
53
Rye
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
5501
5505
5506
5509
5601
5605
5606
5607
5804
7105
7107
7301
7302
7303
7307
7308
7310
7312
7313
7314
7315
7316
7317
7318
7319
7320
7401
7403
7404
7405
7407
7408
7601
7602
7603
7604
7606
8408
8453
8455
8508
8509
8521
8701
8702
8706
8709
8802
8803
No. CCCN
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
0801
0901
1001
1002
1003
1004
1005
1201
1507
1512
2205
2209
2304
2307
2401
2510
2701
2709
2710
2711
2816
2840
3102
3103
3104
3105
3814
3901
3902
4001
4002
4011
4403
4404
4405
4413
4414
4418
4701
4801
4807
5101
5104
5301
5305
5306
5307
5310
5311
5405
Barley
Oats
Maize
Oil seeds and oleaginous fruits
Fixed vegetable oils
Animal or vegetable oils and fats
Wine
Spirituous beverages
Oil -cake
Preparations used in animal feeding
Unmanuf. tobacco or tobacco refuse
Natural calcium phosphates
Coal
Crude oil
Refined oil products
Gaseous hydrocarbons
Ammonia
Phosphites and phosphates
Nitrogenous fertilizers
Phosphatic fertilizers
Potassic fertilizers
Mixed fertilizers
Additives for mineral oils
Condensation products
Poly- and copolymerisation products
Natural rubber
Synthetic rubber
Rubber tyres and cases
Wood in the rough
Wood roughly squared
Wood sawn lengthwise
Wood, planed etc.
Wood, veneer and plywood sheets
Reconstructed wood in sheets etc.
Pulp
Paper and paperboard
Paper and paperboard, impregnated
Yarn of man -made continuous fibres
Woven fabrics of man -made c. fibres
Wool, unmanufactured
Wool or other animal hair, manuf.
Corded woollen yarn, not ret. sale
Combed w. yarn, not retail sale
Wool or other anim. hair, ret. sale
Woven fabrics of w. or anim. hair
Woven fabrics of flax or ramie
Cotton, not carded or combed
Cotton yarn, not for retail sale
Cotton yarn, for retail sale
Other woven fabrics of cotton
Man -m. fibres, not prep. f. spinn.
Yarn of man -m. fibres, not ret. s.
Yarn of man -m. fibres, retail sale
Woven fabrics of man -m. fibres
Woven pile and chenille fabrics
Silver, unwrought or semi -manuf.
Gold, unwrought or semi -manuf.
Pig iron, cast i. and spiegeleisen
Ferro -alloys
Waste + scrap metal of iron /steel
Blooms, billets etc. of iron /steel
Iron or steel coils for re- rolling
Bars and rods of iron or steel
Rolled hoop and strip of i. /steel
Rolled i. /steel plates and sheets
Iron or steel wire, not insulated
011ay steel
Track construction mat. of i. /steel
Tubes and pipes of cast iron
Tubes and pipes etc. of i. /steel
High -press. hydro -el.steel conduits
Tube and pipe fittings of i. /steel
Copper, unwrought or waste /scrap
Copper bars, rods, wire, etc.
Copper plates, sheets and strips
Copper foil (0.15 mm)
Copper tubes and pipes, and blanks
Tube and pipe fittings of copper
Aluminium. unwrought or waste /scrap
Wrought alu. bars, rods, wire, etc.
Wrought alu. plates, sheets, etc.
Aluminium foil (0.20 mm)
Aluminium tubes, pipes, blanks
Engines for aircrafts
Data processing machines
Parts, access. for office machines
Starting equipment for motors
El. equipment for motor vehicles
Transistors and el. microcircuits
Tractors
Motor vehicles
Parts and access. for m. vehicles
Motorcycles, auto -cycles, etc.
Aircrafts
Parts for aircrafts
80
Chapter 4
Calculation of commodity flows and
input -output tables at constant prices
Introduction
1.
The main emphasis in this chapter will be on describing the system
approach
based on
deflation
to
detailed commodity flow system and
a
properties which this implies for the derived input- output tables
the
constant
at
involved
are referred to the standard texts in the SNA, UN (1968), the
readers
detailed
more
technical and practical problems
the
actual deflation work are therefore disregarded and
the
in
of
Most
prices.
and
(1979)
"Manual
ESA,
the
to
Danmarks
Statistik
index
Danish
(1979).
Eurostat
readers are further
chapters on national accounts at constant prices in
the
referred
reason
National Accounts at Constant Prices ", UN
on
(1985b)
and
formulas
(1986a)
respectively. For the same
mathematical
derivations are completely
and
avoided.
there
Denmark
In
is
a
long
tradition
for
compilation
input- output tables. Tables for the years 1930 -39, 1946,
of
1947 and 1949
were
published during the years 1946 -55 cf. Bjerke et al. (1955), and
this
"early
period" of input- output work in Denmark was concluded in
when the table for 1953 appeared.
1962,
and
prices,
calculated
was
1947 -table,
the
also
constant
at
analytical
early
Of these tables only one,
prices,
namely
the
1949
input- output work in Denmark was
based on the two comparable tables for 1947 and 1949. All these tables
were compiled by the Danish Statistical Office as part of the official
tables
input- output
-
have
statistics,
accounts
national
been
-
and
it
is
interesting to note that
and more fundamentally:
commodity flow method
central feature of national accounts work in Denmark
a
right from the beginning.
period" of national accounts in Denmark starts with
"present.
The
the year 1966. From that year onwards the system and methods are based
on
recommendations
the
there
the
1968 -revision
of
the
SNA.
Annual
tables are compiled at both current and constant prices,
input- output
and
of
is
integration
complete
between
the
contents of the
national accounts tables and the input- output tables. In fact both are
obtained
about
from
the
more
basic
commodity flow system which contains
2500 commodities and is balanced at this detailed level at both
current and constant prices.
81
annual
The
with
input- output
tables
are only produced in connection
the final national accounts, and they now appear
after
2
1/2 - 3 years
reference year. The size of the tables can be indicated by
the
mentioning that the number of industries is 117, that there are
groups
main
final demand, of which again private consumption is broken
of
down into 66 functional groups, and each of the
formation
capital
9
broken
are
down
3
main groups of fixed
approximately 40 purchasing
by
industries. So the total number of final demand categories exeeds 200.
Methodologically
tables
the
industry -by- industry tables on the
are
assumption of an industry technology.
published
national
the
Whereas
figures
accounts
constant prices are
at
their most detailed level only very aggregated versions
at
the input- output tables are published in the annual publication on
of
national
accounts,
Statistik
(1986a),
and users are
required to obtain the tables either on magnetic tape or by
therefore
direct
Danmarks
cf.
to the computer where the data are stored. However,
access
to
show
the
analytical possibilities there is also annually published
set
of
detailed
input- output
impact
multipliers,
cf.
a
Danmarks
Statistik (1986b).
exposition will fall into three parts. Firstly the
following
The
deflation procedure used in the detailed commodity flow system will be
set
out,
this
as
figures
constant -price
where
is
all
the
characteristics
of
the
are determined. Secondly it is described what
happens to the deflated figures in the transformation process from the
commodity
implications
used
in
system
balance
holds
this
connection
calculations
is
input- output
the
to
for the analytical uses.
with
change
explained.
of
Annex
base
1
table
and
what
Finally the method
for constant -price
year
contains
empirical
some
illustrations, and the results of two more aggregated rebasing methods
are analyzed.
2.
Deflation in the detailed commodity flow system
balancing and structure of the detailed commodity flow system
The
which
forms
accounts,
the
has
core
been
of the functional part of the Danish national
described
in
detail
in
chapter
2
of
this
publication. The contents of the present section is therefore confined
to
showing
the
basic
methods
by
which the balanced current -price
82
system
with
together
constant -price
information
price
system.
exposition
The
simplified illustration in figure
version
of
1.
transformed
is
will
heavily
draw
into
on
a
the
It is seen that this is a special
2.1 in the SNA, leaving out the transactions which
table
are not connected to the functional part of the system.
Both
it is recommended
SNA (chapter IV) and in UN (1979)
take
deflation
that
within
place
such
a
system, as the problem of
a
consistent set of accounts at constant prices reduces to
problem
of systematically revaluing all entries at the prices of
compiling
the
the
in
some
year
base
totals
column
time
preserving
while
the
balances between the row and
for individual commodities and industries.
At the same
method, which for industries implies double deflation, has
this
the
further advantage of being rather easy to explain to the users of
the
data
compared
as
to
for
different methods of single
example
and subsequent more or less arbitrary balancing between the
deflation
output side and the final demand side at an aggregated level.
Intuitively
idea of revaluing all entries at their base year
the
price is easy to grasp, and when we work at a detailed commodity level
this leads automatically to implicit price indexes of the Paasche type
and
quantity
and
properties
of the Laspeyres type. The well known formulas
indexes
of
these
indexes
will
not
be
discussed here and
reference to them only made when special needs arise.
The process of deflation must be thought of as an application of a
model by means of which we produce an outcome which has no counterpart
in
real
the
whether
to
It makes therefore no sense to ask the question
world.
constant -price figure is "true" or not, as there is nothing
a
test it against. The most we can do is therefore to make sure that
basic principles of logic and consistency are observed.
some
Examples
are that the supply of a commodity must equal its use also at constant
prices
and
value
same
that
prices used in the deflation must refer to the
the
concept
as the figure to be deflated (i.e.
producers' values or purchasers'
basic values,
values).
In the Danish system the deflation is fundamentally carried out at
the
level
balanced
of
basic
Only
after
the commodities have been
at constant prices at this value level are trade margins and
commodity
taxes,
rates
the
to
values.
net,
deflated
added by applying the base year margin or tax
basic
values.
This
makes
it
possible to
83
calculate
constant -price purchasers' values, and at this level a
the
number of checks are carried out, primarily by comparing the resulting
implicit
values derived from foreign trade statistics. But for reasons to
unit
be
indexes with prices from the consumer price index and
price
below, the level of purchasers' values is never used as
explained
the point of departure in the deflation process.
each
If
element
were
balance
deflated
by
commodity would still balance. As we request this
deflated
the
that
commodity
a
deflators it would only be by sheer coincidence
chosen
independently
in
identity to be fulfilled also at constant prices, we must
bookkeeping
introduce special constraints on the deflators,
a
requirement which in
practice usually is satisfied by calculating one of the deflators as a
residual.
important
An
a
deflation
system
each
industry,
where
of
characteristic
is
therefore the way this residual is chosen.
analogous
An
identity
bookkeeping
As
nature
cannot
for
total
that
some elements which by their very
contains
choice
the
is
made
easier.
accounts is considered an income flow rather than
branches
furthermore
deflated
is
deflator
physical
into
a
cost element which
employment and
a
wage rate (the
that compensation of employees in non -market service
being
exception
the
down
broken
be
As
such as
of employees also in the functional part of the national
compensation
can
the
must equal total
output
be separated into quantity and price elements,
surplus,
operating
requires
balance
this
input.
exists
problem
for
separately), this leads to the conclusion that
value
added
is
most appropriately chosen as the
residual or derived deflator for an industry, and this is also done in
Danish system for the element "gross value added at factor cost ".
the
(This
term
indicates
that
non -commodity
indirect
taxes,
net, are
deflated independently in the Danish system). This way of deriving the
deflator for value added is the very essense of the "double deflation"
It must,
method.
however, be pointed out that in a "system deflation"
the constraints put on the commodity deflators (cf. above) at the same
time create an interdependence between the derived deflators for value
added
industries.
of
probably
have
Therefore
the
result for each industry would
been different had the industry been "double deflated"
in isolation from the system.
In
the
following we shall go through the individual steps of the
deflation procedure based on the illustration in figure
1.
Figure
1
The Danisk deflation procedure illustrated in the SNA accounting framework
/
Basic values
(excl. trade)
Energy
2'
products
Wholesale trade margins
Commodities
Retail trade margins
klr istries
Commodities
Energy
products
Trade
Non
Market
2.500
Customs duties
\
Commodity taxes, net, on uses (excl. of VAT)
P
r
2.500
1
Compensation of employees
1
Gross operating surplus
1
i
PD
D
I
I
R
Ss
--
(S,)
R
v
as
R
R
A
Si
Total
(S2)
I
Explanation of symbols used:
P Deflation by price indexes
D Deflators derived from bookkeeping identities
PD Original'P- deflation followed by D- adjustment
I
P
1
Other indirect taxes, net
Sa
R
1
1
(SO
R
2.500
VAT on uses
P
P
2.500
117
cif.
Exports
76
117
-D-
Non- market
Imports,
Domestic
market
Market
Industries
Total
Final demands
1
P
(S3)
1
Sa
1
Base year rates for trade margins or net indirect taxes applied
Si Constant price values obtained as sums of deflated figures
(Si) Si transferred to serve as a bookkeeping restriction for deriving D
R
/A
I
S6
85
are marked with a letter are those for which
which
matrices
The
not denote
values
matrices,
are symbols indicating the method used to deflate each
but
calculated.
letters
constant -price
are
The
do
individual matrix. The methods are:
P
Deflation by price indexes
D Deflators are derived by utilizing bookkeeping
R
identities
Constant -price values are calculated by using base year rates for
trade margins or indirect taxes, net
S
Constant -price values are calculated as sums of other deflated
figures.
parenthesis
A
values
have
transferred
around
an
calculated
been
indicates that these constant price
S
somewhere
else in the system and then
to this new position in order to fulfil their function as
part of a bookkeeping identity in the further calculations.
or
column having an (S) as sum there will therefore also be found a D
symbol.
where
It
In any row
An
S
without parenthesis, but with the same subscript, shows
this constant -price value is actually calculated in the system.
at once seen that P- deflated matrices only appear in the basic
is
value
part
of
system and in the special case of value added in
the
areas
where
non -market
services.
information
external to the system plays a role in the deflation.
the
matrices
These
are
the
only
All
rest is determined by derived price indexes, base year rates, and
summing up in the system.
For
use)
an
individual
system
the
commodity
shows
balance (column
alternative
two
ways
supply and row
=
of
obtaining
=
the
corresponding constant -price balance.
Firstly
this
(and
is the predominant method used for almost all
commodities other than energy products) the supply which can come from
either
domestic
indexes,
values,
customs
and
or imports is deflated by means of price
industries
duties,
which
part of imports at basic
form
are obtained at constant prices by using the base year rates.
This allows us to calculate the total supply, S1, which is deemed also
to
be
constant -price
the
transferred
to
value
place
the
of
of
the
total
row sum.
use
and
subsequently
In the row,
exports are
deflated
independently
for
all
domestic uses is then derived (or rather: the total domestic
use
at
constant
distributed
values).
on
This
prices
individual
method
below) and the price index to be applied
(cf.
is
calculated
uses
implies
as
a
residual
which
is
proportionally to the current -price
that
for
each
individual
commodity
86
balance
domestic
all
uses will have identical price developments at
basic values.
Secondly
the
separately,
procedure
and
can
be
deflate each individual use
to
that the sum of the uses at constant prices,
decide
should be transferred to the supply side, and, again imposing the
S2,
restriction,
bookkeeping
derived
the
energy
item.
determine
the
In
the supply at constant prices as
Danish system this procedure is used for
for which a very detailed subsystem is worked out in
products
connection with the national accounts. As this subsystem also contains
calculation
physical
units
different
implicit prices for different uses, it is natural to demand
(tons
etc.)
the
and
method
implies
that for each individual element the constant price calculation should
result in a constant -price development identical to the development in
physical
is
quantity. The cost of obtaining this result at the user side
however usually that it cannot at the same time be obtained at the
supply
side.
different
users
sufficient
total
This
because
is
who
in
change
to
in the distribution between
changes
the base year paid different prices will be
total
uses at constant prices even though the
physical quantity is unchanged.
This socalled "shift effect" is
well known in the literature on deflation, and the usual justification
for placing the burden of adjustment on the supply side is that we are
concerned
really
commodities
not
just
with
commodity,
one
with as many
but
there are users paying different prices. The total at
as
the supply side is therefore a weighted average of all these different
commodities
physical
quantity.
theoretical
measured
in
Be
of
point
therefore
this
view,
compared
be
not
to
one single
argument as convincing as it may from
a
the users of national accounts are still
if for example they know that output of electric power
confused
left
should
and
GWH
has
increased
by
per
10
cent and they find the
constant -price value of the output of electricity generating plants to
per cent. Such cases have actually occurred in the
have decreased by
5
Danish
accounts, and we have chosen to accept such results.
national
which has been a pioneering country on the subject of shift
In Norway,
effects,
the
been chosen to leave such commodities unbalanced in
has
constant -price
effects
the
it
to
supply
effects
are
one
calculations
and
add
up the value of all shift
overall correction item which is shown separately on
side, cf. Flettum (1981).
usually
identified
for
It
is characteristic that shift
rather homogeneous commodities
87
can
which
measured in physical quantities. It is however
be
also
a
general problem, as price discrimination is perhaps more the rule than
most
in
Fortunately,
exception.
the
cases
do not have enough
we
information to identify the problem.
industry
The
accounts
figure
in
show how output at constant
1
from each industry is obtained as the sum, S3, of the constant
prices
The next step is to transfer S3 to
values of the commodities produced.
column sum (S3), which by using the bookkeeping identity makes it
the
possible
derive
to
producers
deflation ").
For
sequence
inverted,
is
last
inputs
all
case
being
summarily
from
directly
non -commodities
prices
(
"double
priced separately and the
In order not to overburden
somewhat
is
constant
at
non -market services this calculation
of
index derived.
price
output
added
value
to
1
routing
illustrated,
producers
the
figure
the
this
the
final demand
categories.
figure
From
by
duties),
are
estimate
output
(=
taxes.
The
commodity
in
matrices
taxes,
(with the exception of customs
net,
constant prices for the supply of trade
at
wholesale
and retail trade) and for indirect
wholesale
for
margins,
retail
margins
and
(exclusive of VAT) have the same dimension as
for uses at basic values, and for each individual element
matrix
the
rates
year
calculated from the user side. This means that there is
independent
margins
that also all constant -price values
seen
is
base
using
obtained
no
it
1
the rates relative to the basic values in the base year are applied to
the
values at constant prices in the current year.
basic
it
sometimes
is
decided
to
change
In practice
of the rates for real or
some
technical reasons.
there
As
usually
a
single -rate VAT system in Denmark, VAT on uses is
broken
not
construction)
prices
is
and
each
down
by
commodity
(the
exception
being
element in the row is calculated at constant
the assumption that the rate of the value exclusive of VAT
on
is the same as in the base year.
SNA it is assumed that "other indirect taxes,
In
the
be
deflated
separately but be included in the concept of value added
at constant prices, which would concequently
in
figure
is,
cost
1
in the case of the system
become gross value added at basic values. In Denmark there
however,
also
net" should not
at
a
long tradition for calculating value added at factor
constant
prices,
and
other indirect taxes, net, are
88
therefore
deflated
relative
total
to
special
separately
either
by
at purchasers' prices
input
the base year rate
using
for each industry or
base year taxes per motor vehicle etc. Constant -price figures
for value added at factor cost by industry are also calculated in some
for example the United Kingdom and Canada.
other countries,
now the description has been kept in rather general terms.
Untill
It
be appropriate also to give a brief outline of the
might, however,
price information actually used in the deflation.
About
series
3000
procedure.
detailed
Almost
primary
all
of
are
indexes
price
individual
information
used
go
index
into
the
series
deflation
from the most
compiling the official price
in
indexes published by Danmarks Statistik. This means that the weighting
schemes
applied
in
official
price
indexes
play
no
role
in the
deflation system.
Most of the indexes are those collected for the socalled wholesale
price
which
index,
is
first time a commodity is sold.
value
an index for the prices charged the
usually
These indexes correspond to the basic
Indexes based on prices (exclusive of indirect taxes)
concept.
for the consumer price index are also used. As these prices
collected
include
trade
concept,
but
margins,
as
this
they
type
do
not
correspond to the basic value
of index is almost exclusively used for
services, this problem is not a serious one. For agricultural products
special
detailed
construction
output
is
measures
prices
are
available.
As most of the output from
calculated at current prices by multiplying physical
by
prices,
the necessary price indexes are readily
available. The biggest deficiency in the price material is in the area
of
services mainly used by business, such as the services of auditors
and lawyers, advertising,
services.
indexes
are
as
constant
the
on
rather
used
the
it has been necessary to resort to constructing price
specifically
based
cases
of
Here
engineering services and many other business
many
for use in the national accounts. These indexes
different
kinds of indicators which are in some
farfetched in relation to the values for which they are
deflators.
For
non -market
services,
where
the output
at
prices is defined as being equal to the constant -price value
cost incurred in their production, it is necessary to deflate
factor costs directly. For this purpose a weighted wage index for
government employees has been constructed.
At
the
supply side the price indexes to be used as deflators for
89
domestic
output and imports c.i.f. at the commodity balance level are
calculated
levels
Paasche
as
which
price
indexes
from still more disaggregated
are essentially the most detailed industrial production
statistics (about 7500 commodities) and the most detailed level in the
foreign trade statistics (about 8500 commodities).
The keys connecting
the price indexes and the commodities at this very detailed level have
to
updated annually to take into account changes in the commodity
be
classifications.
deflator
used
several
for
advantage
commodities
this
at
very detailed level the
that the resulting currently -weighted price index to be
is
commodity
the
at
Even though one price index is in many cases used as
balance
level
is
to
be
preferred
to an
unweighted average of the price indexes for commodities falling within
a
given
commodity
indexes
with
whatever
gives
balance.
deflated
information
the
price
possible,
and
The
weighting
current -year
of the individual price
values makes the maximum use of
we have below commodity balance level, and this
indexes of the system as much
thereby
makes
the
constant
" Paasche
price
property" as
figures
as much
Laspeyres -type indicators as possible. This system implies that if the
domestic
supply
at the commodity balance level originates in several
industries
there
there
different
are
level.
calculations
vector
as many different output price indexes as
be
output
proportions
at
the detailed commodity
must be stressed that these very detailed commodity levels
It
domestic
for
will
output
of
and
the
for imports,
price
imports
are
only
used
to
support
the
matrix for domestic output and the price
respectively, at commodity balance level. So this
level of detail does not belong to the system at large.
At the supply side price indexes are given separately
for domestic
output and imports (this distinction being made in the wholesale price
There is therefore no reason to use unit values for imports as
index).
deflators in the system.
the
At
indexes
there
user, side
situation
at the level of purchasers'
An
easy
for all uses.
contents
is more complicated.
As price
values are not used in the system
almost by definition no price information which is directly
is
applicable.
index
the
in
exports
uses,
and
would
obviously
even
solution
This would, however,
were
though
be
would be to assume an identical price
of the same relative size as for domestic
there
wrong.
imply that the direct import
are some reexports such an assumption
Instead we have gone to the other extreme
90
deflate all exports at the commodity balance level by
and
chosen
the
average
deflators
for domestic output, arguing that practically
all
exports
originate
in domestic industries
price
to
statistics
distinction to be made between
any
allow
not
do
and that the available
selling prices to the domestic market and to exports.
solved
be
(The problems to
cases where exports exceed domestic output will not be
in
discussed here). The alternative of using unit values from the foreign
statistics
trade
deflators for exports has been rejected, partly
as
for
theoretical reasons, as unit values are not really price indexes,
and
partly
reasons, as the unit values in many cases
peculiar developments at the commodity balance level.
very
show
practical
for
Such
developments would then either have to be arbitrarily adjusted, or the
unlikely
indexes
developments
would
domestic
uses.
for
commodities
that
the
have
a
Because of the big export share for most
possible check on the validity of the method chosen is
a
derived price index for domestic uses of a commodity should
reasonable
constant
price
development
applied
is
which is generally the case. In the
-
of Canadian input-output tables the same
calculation
assumption
basic
be reflected in the derived price
also
deflation
the
in
of
exports,
cf.
Statistics Canada (1981).
now
Until
completely
current
the
automatic
prices,
procedure
deflation
where
process
indexes,
price
base
has
the
been
inputs
year
rates
described
are
for
as
a
the system at
margins and
indirect taxes and some keys connecting commodities and price indexes,
outputs
the
and
basically
each
true,
step
of
are
checks
the
constant -price
the
figures. Although this is
and controls are of course carried out after
calculation.
If
these
checks
reveal
unlikely
developments in constant -price figures or implicit price indexes it is
most
often
this
unit
calculations.
indexes
value
consumer
a
which are reconsidered, but also the
from
indexes
the
At
more
aggregated levels the implicit
constant -price calculations are compared to
for foreign trade
for imports and exports and to
price indexes for private consumption.
Laspeyres
really
indexes
respect serves as a final and rather efficient check for the
current -price
price
price
price figures will in some cases be changed, as the deflation
current
in
the
price
index,
and
the
As this last index is
unit values (cf. above)
are not
price indexes, rather big deviations from the implicit Paasche
price indexes are tolerated.
91
Construction of the input -output table at constant prices
3.
When
balanced
which
commodity
the
further
primary
of reexports,
information is introduced (apart from the separation
below), and no further balancing work is to be done.
cf.
tables,
emerge
from
which
it
possible
is
table
construction
the
post
ex
by
dividing
the
the current -price table have consequently
into
in
role
no
calculate
to
but they both
The implicit prices
deeper level of disaggregation.
the
constant -price
played
current -price input- output table,
the
from
calculated
prices,
the input- output table at constant prices is not
So
system.
constant
and
current
at
calculated by identical methods from the commodity
are
respectively,
system and the input- output table no
balance
input -output
balance
has been
is automatically constructed, so that
table
input- output
between
Two
1
both current and constant prices, we have the basis from
at
the
in figure
shown
system
balance
commodity
the
the input- output table at
of
constant prices.
The methods used in the construction of Danish input- output tables
from
balances are described in detail in chapter
commodity
the
of
understanding
only
and
publication
this
the
a
following
short
will
necessary
summary
here.
given
be
for
3
of
the
The general
principles for compilation of input- output tables according to the SNA
framework are found in UN (1973).
changes
of
Because
basic
the
in
commodity
classifications,
commodity balances are not completely comparable over time (in fact we
balances
started
with
4000
balances
in
1982).
four -digit
CCCN- headings
Services
down to about 2500
were
are
(with about 30 more disaggregated groups as
not
aggregated
as
their classification
constant over time. At this level of 1600 groups we
been
has
and
about 1600 groups, which for goods correspond to the
into
system
1966
Therefore the detailed balances are at this stage
aggregated
exceptions).
in
claim complete comparability over time.
Also
system
by
this
at
of the foreign trade statistics. This subdivision is needed
for the following calculations.
is
subdivision
calculating
exports in the current -price
subdivided into reexports and exports of domestic output,
are
means
level of aggregation,
a
made
by
In the constant price system a similar
deflating
reexports
by
import prices and
derived price index for other exports. This ensures that
92
total
at constant prices of each commodity at the 1600 group
exports
level are not changed by the subdivision.
shown
As
117
1600
x
figure
in
and
disregarding
we now have a make matrix of the dimension
2,
absorption
an
the
investment
step
is
matrix of the dimension 1600
matrices,
as
they
x
192,
calculated
are
separately.
next
The
the breakdown of the absorption matrix into a
matrix for domestic output and
clear
that reexports belong in the import matrix only, and that other
exports
and
products
of
matrix for imports. It is immediately
a
stock
changes
of
work -in- progress
and
finished
own
belong in the matrix for domestic output only. The splitting
all
elements
other
absorption
the
in
matrix must for lack of
specific information be based on assumptions, and the most simple one,
namely
all
that
uses
these
procedure
prices
ratio of domestic output to imports is identical in
the
that all elements in the import matrix at constant
ensures
are
results
the
consequently
only
that
constant -price
the
deflation
procedure,
between
with import prices only, and
domestic output prices have played
domestic
for
cf. chapter 2,
output.
in
As
a role
the
in
main
all exports have been deflated with
output prices, but later, at the 1600 commodity group level,
broken
are
deflation
of
matrix
system,
domestic
of the 1600 commodities) is chosen. This
each
(for
down
above,
cf.
the
into
reexports
and
there
however, a slight lack of symmetry
is,
exports
other
by
a
special
matrices. This is best illustrated in the case of a
two
commodity which has passed through the whole calculation sequence from
being
subjected
matrix
the
commodity
detailed
the
the input- output table without
to
any aggregation or transformation.
to
In the import
have a uniform price index along the row, whereas in
will
it
balances
domestic output matrix the derived price index for exports, which
will
usually
implicit
price
deviation.
deflate
level.
deviate
The
index
obvious
reexports
with
from
for
the average output price, will cause the
domestic
solution
import
uses
to
prices
this
to
show
problem
a
compensating
is of course to
already at the most detailed
In spite of some practical problems such a change in the system
is at the moment being considered.
The
by
final step is to premultiply the subdivided absorption matrix
the make matrix to obtain input- output tables with separate import
matrices
at
both
current
and constant prices. By multiplying these
93
Figure 2. The make and absorption matrices used in the compilation of Danish
input- output tables.
The make matrix:
Commodity groups (1600)
Industries
Domestic output
values)
(basic
1)
(117)
(1)
Imports c.i.f.
(1)
Customs duties
2)
CO
>
o
CD
m É
C
a-)
L.
C
CL
X
Cd
Q)
=
(1)
(.
(1)
(
sive of
ate non-
v
Imputed bank service
charges
;1
Exports
reexports
C
Gross fixed
formation
t1ous0h
o
U
changes
Covernm. cons.
r
6)
'Stock
(1)
Cons. of
profit inst.
s.
odiate
ption
dity groups (1600)
(6
....-,
(4)
Final demands (75) 3)
Industries (117)
apital
The absorption matrix:
Notes:
1.
Here as elsewhere in the paper the term "industries" also includes
"other producers" in the SNA meaning of the term.
2.
Cf.
figure 1 the absorption matrix is in the actual calculation
composed of four submatrices: (a) basic values exclusive of trade,
(b) wholesale margins, (c_) retail margins, and (d) net commodity
texas.
3.
The connection between the 77 categories of final demand in figure
and the 75 categories above is that 5 categories of stock chan1
ges have been aggregated into one, whereas on the other hand the
new categories reexports and imported bank service charges have
appeared. The subdivision of fixed capital formation by owner branch
has been disregarded in both figures.
94
detailed rectangular matrices directly we avoid the aggregation errors
inherent
in an aggregation to the level of characteristic commodities
(square matrices) before the multiplication.
terminology
the
In
of
industry -by- industry
table
technology,
it
manufacturing
outside
need
although
not
have
part"
"domestic
of
SNA
on
the
should
be
the
resulting
assumption
table
of
an
is
an
industry
mentioned that all "industries"
are really activity defined. The import matrix
same
classification
in the
front column as the
the input- output table, as the premultiplication
the make matrix is only necessary if the import matrix must have
with
a
the
the
which
form
it additive to the domestic matrix,
makes
a
procedure
which is useful in many kinds of analysis.
Now the question is which kind of implicit price indexes does this
of input- output tables contain, and what are the implications for
set
the different uses to which the tables can be put?
the basic commodity balances to the rows of the input- output
From
we have passed through first a simple aggregation procedure and
table
combined
aggregation
transformation procedure. The
secondly
a
implicit
price indexes for the balances at the three different levels
and
have the following characteristics:
(1)
the commodity balance level (2500 commodities) each source of
At
supply,
different domestic industries and imports, will usually
i.e.
have different prices (because of the weighting of price indexes at an
even
two
detailed level), and at the user side we will usually have
more
different
prices,
one for exports and one for domestic uses. So
at this level there is no uniform price index in a row, although
even
all elements for domestic uses will show identical price movements for
commodities other than energy products.
(2)
the
After
indexes
in
aggregation
balance
a
to
will
the 1600 grouping all implicit price
usually
be
different,
and
after the
of reexports we will also have two different export prices
separation
in each row.
(3)
premultiplication
The
matrix
the
by
make
at the
1600 group level of the absorption
matrix means first a splitting of the commodity
groups (according to the market shares of industries given in the make
matrix)
with
all
the
and
next an aggregation of these subdivided commodity groups
producing
industries as keys, resulting in 117 rows, where
implicit price indexes in
a row must
be expected to be different,
95
we have now not only further aggregated commodities with different
as
implicit price indexes, but also by the transformation procedure added
parts
which may in commodity classification terms be
commodities
of
rather far apart. This is illustrated in table
this
On
such
statements
it
is
that simplistic theoretical
obvious
as the one that each row in an input- output table is
to consist of a homogeneous kind of output and therefore also
assumed
have
to
background
1.
identical
removed
implicit
empirical
practical
from
indexes in all elements,
price
are far
work in this area. And it must be
underlined that this would also have been the case if the input- output
table
had
table
on
alternatively been constructed as a commodity -by- commodity
the assumption of a commodity technology. The conclusion of
compilers of input- output tables rather trivial, namely
this
is
that
no input- output table will ever fulfil the assumptions which are
for
underlying
usually
view
this problem is found in Olsen (1985), where the question of
on
to construct and use input- output tables is seen as being part of
how
a
use in input- output analysis. An interesting
its
more
general
aggregation
rather
problem
than
choice between
a
alternative technology assumptions.
point
This
can
elaborated
be
on an article by Rae,
comments
a
little
more
by making a few
Chakraborty and Small (1984), to which
also been made in two recent papers by Viet (1985) and
reference
has
UN (1986),
respectively. By a numerical example the authors illustrate
the consequences of a change in a base year price of one commodity for
an
industry -by- industry
table
calculated
on
the
assumption of an
industry technology. Not surprisingly this price change will influence
many
makes
all) elements in the input- output table, which
the example:
(in
conclude
authors
the
input- output
has
tables
been
that
proved
this
method
of
methodologically
constructing
unsound and
therefore be rejected. This argument is hard to accept, as the
should
question
empirical
of
one
considerations
whether
and
an
can
industry
therefore
technology
not
is valid or not is an
be excluded from theoretical
alone, and similarly the question of whether the table
should be given in industry -by- industry or commodity -by- commodity form
practical one, depending on the needs of the users. It must also
is
a
be
underlined
table
is
that
constructed
if in order to avoid some aggregation errors the
directly
from rectangular make and absorption
96
matrices,
industry -by- industry
an
table
the
on
assumption
of an
So the conclusions of the
industry technology is the only possibility.
article
seem to rest firstly on a too simplistic view of the relation
between
commodities
equal to the number of industries thereby leaving out the
commodities
commodity
and industries, the example having the number of
enters,
unavoidably
which
problem,
aggregation
secondly
and
where
is
on
inhomogeneity
the
assumption that implicit
the
output prices should be uniform over the row, which seems to
industry
be mixing up table and model considerations.
The
remarks
above
also
should
draw
the attention to the very
important difference between an input- output table and an input- output
model.
taken by itself cannot be theoretically wrong, nor
table
The
are the usual input- output model assumptions of constant coefficients,
based on the full cost principle etc. part of the input- output
prices
table.
assumptions
Such
input- output
however,
can,
especially
data,
be
there
if
tested
time
exist
against
series
the
of
input- output tables at both current and constant prices.
models
it
prices
are
industry
price
index
of
the
by
cost
structure of each
price indexes for value added in
It is
consequently assumed that the
same for all elements in a row,
the
is
problem
left out here).
is
that developments in industry output
exclusively
special
(the
i.e. that there
uniform industry output price index which is valid for all
an
of
assumed
determined
models
exists
usually
is
price
users
where input- output tables are used as a basis for price
cases
In
output
from
that
particular industry. A look at the time
series
of implicit price index matrices derived from the input- output
tables
immediately
indicate,
not
convinces us that this is not so. Still this does
however,
that something is wrong with the input- output
table, but only that we have made simplifying assumptions in the model
which may or may not prove to be acceptable.
If time series of input- output tables were long enough we could in
principle estimate special relations for the prices of each individual
cell.
Simple
expected
to
input- output
reproduce
price
models
should
therefore
not
be
the actual implicit matrices of price indexes
outside the base year, but they may none the less serve rather well in
predicting
input
price
price
for
indexes for more aggregated variables such as total
an
industry or prices for individual categories of
97
final
The functioning of the input -output price model in the
demand.
Danish
model
econometric
ADAM
has
been
used to analyse the above
problem in detail, cf. Danmarks Statistik (1985a).
Price
models
based
industry -by- industry
on
tables
on
the
of
an
industry technology exhibit one feature of seeming
inconsistency,
as
prices are properties (also in the construction of
assumption
the input- output table) connected to commodities, whereas in the price
model
appear
they
individual
basically connected to industries even though
as
have
industries
different
of
uses
different
output
their
commodity
compositions
in
and over time. This implies that a
commodity (say at the level of 1600 commodity groups) in
a
implicitly
developments,
will
depending
problem
the
number
avoided
in
on
is
assumption of
problems
model
a
both
of
different
industries
model
a
in
the
based
construction
primary
as
price
producing
it. This formal
on a commodity table on the
of the table (cf. above) and in
inputs
are connected to industries
In practice the problems inherent in the
to commodities.
than
industry
several
commodity technology, which will, however, cause other
applications,
rather
given
be
price model
by industry price model are usually disregarded,
as compared
to
many other simplifications they are only of minor importance. Also
it
is
still
possible
to keep a separate import matrix in commodity
terms even though the table for domestic output is in industry terms.
The
problems outlined in the two above paragraphs would have been
nonexistent
if
we
constant -price
the
input- output
had chosen a much simpler deflation
had been carried out directly at the
calculation
table level,
scheme, where
each row being deflated by one single price
index constructed in some more or less obscure way outside the system.
Apart
crude
from
method
assumptions
data
the problems involved in defining the price indexes, this
of
is
hardly
to
a
simple
input- output price model directly into the
be
recommended,
imposes
the
1.
Changes of base year
Internationally
five
it
structure. The distortions caused by such a simplified deflation
method are illustrated empirically in annex
4.
as
years
because
representative
of
it
is
base
recommended to change the base year every
year prices gradually become less and less
the current flows. Basically there are two ways of
98
carrying
a
set
new
The first method is to calculate
out the change in practice.
constant
of
figures which completely replace the
price
previous ones and give an unbroken time series which extends on either
side
of
new base year. The second method is to use the new base
the
year prices only for calculating constant -price figures from this year
leaving comparisons back in time to be done by chain indexes
onwards,
-
approach which gives rise to the well known additivity problem,
an
cf.
for example UN (1979).
two
These
dimension,
methods
must
however
supplemented
be
by
a
third
the level of detail at which the calculations take
namely
place. If the second method is applied at detailed commodity level, it
comes very close to the first one and permits the additivity condition
to
fulfilled by calculating all aggregates as sums in the rebased
be
system.
is the essence of the procedure used in the rebasing of
This
the Danish constant -price figures.
present system of national accounts in Denmark had originally
The
as the base year and has been rebased twice.
1970
First the base year
was changed to 1975 in 1980 and next the base year 1980 was introduced
in
In both instances
1985.
national
accounts
back
1966,
to
figures
the rebasing was carried out both for the
and the input- output tables for all years
resulting in new sets of consistent national accounts
tables and input- output tables at constant prices.
the original deflation took place in a detailed commodity flow
As
as described in chapter
system
2
above,
it might seem a natural thing
just to repeat the whole procedure substituting new base price indexes
and trade margins and indirect tax rates for the old ones. For several
reasons such a procedure can however not be carried out automatically.
of
number
the
Firstly,
commodities
at the most detailed commodity
balance level decreases over time because of aggregations necessitated
by
changes
in
the
basic commodity nomenclatures (cf. above), which
means that the commodities which "disappeared" before 1980 do not have
any
price indexes in the new base year. Secondly problems of the same
kind
will
indirect
earlier
redone
show
taxes,
up
for the new base year rates for trade margins and
and
constant -price
thirdly
all
the
specific changes made in the
figures in the checking phase will have to be
in the course of the new deflation,
some other elements.
but probably now affecting
99
For these reasons the rebasing from 1970 prices to 1975 prices was
done at the 1600 commodity aggregation (which also forms the basis for
the construction of the input- output tables, cf. above). At this level
of
aggregation most of the problems mentioned above will not show up.
fact
The
first rebasing was carried out at this level of
this
that
aggregation is a further and rather decisive argument for carrying out
rebasing
the
system
1980 prices at the same level, as the constant price
to
prices does not exist at the more detailed level for
1975
at
the years 1966 -74.
concerns
valid
explanation
following
The
the
for
the
method
used in the rebasing
from 1975 prices to 1980 prices, but it is also
change
the
of
rebasing
first
with
the
exception that the second
rebasing implicitly contains two chainings and the first just one.
For each element of output by industry, imports and exports at the
1600
commodity
1980
at
1980
conversion
conversion factor is calculated as value in
divided by value in 1980 at 1975 prices. These
are then multiplied by the corresponding elements
of the years 1966 -79. The growth rates of these elements at
prices will therefore be identical to those at 1975 -prices. This
1980
of
a
prices
factors
each
for
level
just illustrates the simple fact that growth rates are not
course
changed
at
level. The domestic use at 1980 prices for
chaining
the
commodity balance is then calculated as the residual which makes
each
use
proportions
prices
constant
values
the
as
at
1975 prices,
and the growth rates at
elements will usually be changed by this
these
for
is distributed on uses in the same
residual
The
supply.
equal
procedure.
Trade margins at 1980 prices are not calculated simply by applying
rates to the 1980 -price basic values as this would overrule
the
1980
the
variation
which
for
time
over
different
in
reasons
the constant -price trade margin rates,
have
been
introduced in the original
constant -price calculations at 1975 prices. Instead conversion factors
are
calculated
for
basic
trade margin elements in 1980 in the same way as
for
values,
and
these
factors are in turn multiplied by the
absolute margin elements at 1975 prices for the earlier years.
For all categories of indirect taxes the rates in 1980 are used to
calculate the 1980 values for the earlier years.
In
the
same
way
as explained for the original deflation system
100
illustrated
figure
in
is now possible to calculate all other
it
1
values and aggregates at constant 1980 prices. These will usually show
growth rates which differ from the growth rates at 1975 prices and the
expectation is to find lower growth rates at 1980 prices, at least for
the period 1975 -80, cf. annex
rebasing
The
commodity
1600
course
each
of
implies
method
whereas
level,
aggregates)
all
the
are
chaining of some elements at the
a
all
other
rebased elements
(and of
derived. Furthermore commodities within
are still weighted by 1970 prices for the
groups
1600
1.
period 1966 -74 and with 1975 prices for the period 1975 -79. But as the
relative
price changes within groups are usually smaller than between
groups,
what
result of the rebasing is believed to come very close to
the
would
have
been
obtained
rebasing
by
at
the most detailed
commodity balance level.
Although
rebasing
the
is carried out rather mechanically,
necessary
for example to decide which
which
have
do
values
some
in
it is
1980 prices to use for elements
earlier
years but not in 1980, and
generally to make checks and controls in almost the same way as in the
original
deflations,
consequences
of
possible
in
this
made
the
to
current
unless
the
results
interactions
many
process
extent
price
unexpected
as
in
the
always
turn
system.
up
as
It is also
to correct errors which have earlier been
that they only concern the deflation system, as
figures
may
not
be
changed in the rebasing process
coincides with revision at current prices, which was not
this
the case for the rebasing to 1980 prices.
After
rebased
the
to
commodity
1980
prices,
balances
at the
1600 group level have been
the constant price input- output tables are
compiled again in exactly the same way as described in section
3.
101
Annex
1
Some empirical illustrations
data
The
accounts
are
base
functional
the
of the Danish national
part
now contains the following sets of annual data which
system
mutually
of
consistent
and
comparable
over
time
for
the years
1966-83:
1.
commodity balance system at the 1600 commodity group level at
The
current prices and at constant 1980 prices.
2.
Input- output
constant
tables at the 117 industry level at both current and
1980
prices.
Of
the 9 main categories of final demand
private consumption is broken down in a consumption matrix showing
functional
66
gross
categories,
capital
fixed
each of the
and
formation
broken
is
3
main categories of
down
in
investment
matrices according to about 40 owner branches.
and for the years 1966 -80 there are furthermore:
3.
commodity
The
balance
system
the
at
1600
commodity level at
constant 1975 prices.
4.
Input- output
with
the
1975
prices
as mentioned in (2) at constant 1975 prices,
tables
exception that the investment matrices are not found at
as
their
compilation
was
only finished after the
rebasing to 1980 prices in the national accounts had taken place.
current -price
As
figures
process
of
sets
1975 prices and at
at
caused
left completely unchanged in the
rebasing to 1980 prices, all differences between the data
by
rebasing
the
investigate
rebasing
1980 prices, respectively,
techniques
used.
are exclusively
This makes it possible to
detail the consequences for volume and price measures
in
of the rebasing.
of
were
(A similar investigation
to
1975
prices,
as
was not possible at the time
main revision of current price
a
estimates and industrial classifications took place at the same time).
section
In
3
it was explained how the sequence of aggregation and
transformation which takes place between the constant -price figures at
the
2500
commodity
balance level and the rows in the constant -price
input- output table causes the implicit price indexes in different uses
to
that
become
more
process.
more
and
and more different, which is just mirroring the fact
more
inhomogeneity
in
rows
is created during this
so r
Within
illustrate
indexes
table
these
the
following
level,
1.
indexes
are shown for the standard 27 industry group
though this aggregation adds further inhomogeneity
Even
rows
steps or even to show the implicit price
input- output table at the 117 industry level, but in
these
1
different
the
in
aggregation.
to
scope of this paper it is not possible to empirically
the
table
the
rather illustrative.
is
which
observations,
are
also
valid
Amongst others the
at the 117 industry
can be made:
price
Implicit
indexes
do
to
a
considerable extent vary along
rows. Exceptions are cases where commodities at the detailed level
and
as industry outputs are identical, such as for example repair
and
maintenance
of
buildings
intermediate consumption of
(all
output from the construction industry, which is activity defined).
2.
price indexes for corresponding elements of the domestic
Implicit
output matrix and the import matrix are usually different.
3.
Whereas
domestic
and the import matrix (in the column "Total ") do
output
show
not
price indexes for corresponding rows of the
average
the
much
corresponding
correlation,
have
rows
the patterns of variation along the
many
similarities.
This
is obviously
the commodity structure of imports is more
because
in
similar
to the structure of domestic inputs than are the averages
each
use
which are further blurred by the aggregation along rows.
As
at
the
in chapter 4 the rebasing to 1980 prices took place
described
the 1600 commodity group level.
results
aggregated
of
method
this
to
It might be of interest to compare
the
results
of
alternative more
methods. Two such methods have been tested, they
rebasing
are:
1.
element factor method ", where an implicit price index matrix
"The
is calculated directly at the input- output table level by dividing
each
element
of the 1980 input- output table at current prices by
the
corresponding
all
aggregates
index
matrix
table
at
prices by
of
all
1975
a
and
elements at 1975 prices.
for
The price indexes for
value added are disregarded. This price
can in turn be used to recalculate the input- output
prices for any other year to form a table at 1980
term -by -term multiplication and subsequent calculation
aggregates
respectively.
and
value
added
as
sums
and differences,
103
2.
"The
row factor method ", where an implicit price index vector for
each
row sum is calculated following the same procedure as above.
index
The
value
for
added
disregarded.
is
By multiplying an
input- output table at 1975 prices rowwise by this price vector and
subsequently calculating the missing aggregates and value added as
sums
and
differences,
input- output tables
different
price
table
a
1980 prices is obtained.
at
(As
1975 prices for other years than 1975 have
at
indexes along
a row,
their recalculation to 1980
prices by the row factor method will not remove this variation).
Both
methods
input- output
are
table
consumption
used
with
broken
down
the
at
separate
a
into
117
import
groups,
66
industry
matrix
i.e.
the
level
of
and
the
private
most detailed
input- output table available at 1975 prices.
input- output
The
tables
1966
for
(at
prices) and 1975,
1975
respectively, are rebased to 1980 prices by both method
implicit
The
(2).
tables
can
method
and
actually
applied.
in
functional
groups
table
are
made
the main
for
for private consumption subdivided into
and
2
comparisons
The
(aggregations
In both tables growth
3.
developments in the resulting
1980 prices, according to the detailed rebasing
(B)
aggregates
table
price
and
and method
compared to those implicit in the three tables at (A)
be
prices
1975
volume
(1)
of the 66 functional categories) in
rates are shown for the two subperiods
1966 -75 and 1975 -80 and for the whole period 1966 -80.
When
national
expectation
(because
is
figures
are
rebased
the
a
priori
growth rates of volume indicators will decrease
that
substitution
of
relatively
accounts
in price),
away from commodities which have increased
at least for the period between the old and the
new base year. By comparing columns (A) and (B) for the period 1975 -80
in
tables
the
for
2
and
3
this expectation is seen to be fulfilled, but also
subperiod
1966 -75
change can be found, although less
this
pronounced.
For
and
3,
the
in
results
of method (C) we can, by inspection of tables
particular
for
the
subperiod
1975 -80,
arrive
2
at the
conclusion that the growth rates generally lie somewhere between those
of (A) and (B), and usually closest to the first ones. This is what we
would
expect, as the more aggregated rebasing method is less "Paasche
type"
than
the
results
(B),
come
and this for some aggregates to such an extent that
close
to
those
we would have obtained if we had
104
chained
directly
consumption
detailed
rate.
at the level of the main aggregates.
represented
is
commodity
rebasing
the
figure
also
at the most
does not affect its growth
is the case with gross rents and purchases
same
The
level,
one
just
by
(As government
abroad by
resident households in table 3).
It is difficult to have any a priori expectation
method
as
(D),
which
method
industry
rebasing
the
takes place at
which
the
chaining takes place by row, it is output by
its growth rate (not shown in our tables), and
keeps
not the final demand categories which are column sums
which
determined
is
averaging
added
higher level of
a
which should give us growth rates even closer to those of
however,
As,
influence the results in two ways compared to
can
Firstly
(C).
aggregation
(A).
averaging of the price developments in the rows
the
implies
it
to the results of
or value added
as a residual also in this method. Secondly the
the price developments in the rows will influence value
of
and
-
final demand categories in an unpredictable way as it
the
depends
on
row.
further reason for the unpredictability is that at this level
A
the degree of price index variation actually found in the
aggregation
of
intermediate
often
differences
the
exports
consumption,
between
price
domestic
and
considerable (as can be seen in table
be
developments
in
final demands will
1,
though at
a
higher
level of aggregation than used in the calculations).
An inspection of the results of method
as
in tables 2 and 3 gives
(D)
expected no basis for general conclusions. Surprisingly the growth
rates
of
the aggregates in table
those
of
(B),
but
growth
rate
for
growth
rate
as
must
it
private
method
2
are in many cases rather close to
be deemed a sheer coincidence that the
consumption
works out at exactly the same
whole
(B)
for
the
of
the
results
confirmed
by
subgroups
of private consumption in table
method
inspection
gives
(D)
results
which
are
period
of
3,
the
1966 -80, as is
two
methods for
where for some subgroups
clearly
unacceptable
by any
standards.
The
the
observation
detailed
deflation
that
compared
level
methods
method (D) gives unsatisfactory results at
is
in
to
the
outcome of more sophisticated
agrement with the findings made by Richter
(1985) in a similar experiment
with Austrian input- output tables.
105
Although
of
the
a lot more can be said about the comparative achivements
different deflation methods the above should be sufficient to
illustrate
calculations
the
importance
from
of
building
up
the
constant
price
the most detailed level possible while keeping the
whole procedure within a consistent system approach. When this is done
the
otherwise
input- output
tremendous
tables
into
work
of
constant -price
recalculating
current-price
tables is reduced to being
just one of many possible applications of the basic data set.
Table
1.
1 11000
2
12000
13000
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
28
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
80
61
62
83
Implicit price
indices of
1975 input- output table at
Intermediate consumption
11000
12000
13000
20000
the aggregated danish
DANISH GOODS AND SERVICES
Agriculture, horticulture, etc.
Forestry and logging
Fishing
Mining and quarrying
Manuf. of food, beverages, tobacco
Textile, clothing, leather industry
Manuf. of wood products,incl. furnit.
Manuf. of paper,printing,publishing
Chemical and petroleum industries
Non -metallic mineral products
Basic metal industries
Manuf. of fabricated metal products
Other manufacturing industries
Electricity, gas and water
Construction
Wholesale and retail trade
Restaurants and hotels
Transport and storage
Communication
Financing and insurance
Dwellings
Business services
Market services of education,health
Recreational and cultural services
Household services, incl. auto repair
Other producers, excl. government
Producers of government services
IMPORTS INCL. CUSTOMS DUTIES
Agriculture, horticulture, etc.
Forestry and logging
Fishing
Mining and quarrying
Manuf. of food, beverages, tobacco
Textile, clothing, leather industry
Manuf. of wood products,incl. furnit.
Manuf. of paper,printing,publishing
Chemical and petroleum industries
..
Non -metallic mineral products
Basic metal industries
Manuf. of fabricated metal products
Other manufacturing industries
Electricity, gas and water
Construction
Wholesale and retail trade
Restaurants and hotels
Transport and storage
Communication
Financing and insurance
Dwellings
Business services
Market services of education,health
Recreational and cultural services
Household services, incl. auto repair
Other producers, excl. government 7777
Producers of government services
imports
20000
31000
32000
33000
34000
35000
36000
37000
38000
39000
40000
50000
60099
63000
71000
72000
80099
83110
83509
93009
94000
95009
95399
98099
11000
12000
13000
20000
31000
32000
33000
34000
35000
36000
37000
38000
39000
40000
50000
80099
63000
71000
72000
80099
83110
83509
93009
94000
95009
95399
98099
Other
Sum (1 -55)
Purchases in Denmark by non -resid. household
Net taxes on commodities
Value added tax
Uses at market prices (56 -59)
Other indirect taxes, net
Gross domestic product at factor cost
Gross output at basic values (60 -62)
.
.
.
64.98
53.52
65.17
87.26
95.21
66.92
87.72
82.80
69.74
77.42
65.99
63.76
58.09
66.34
75.46
63.24
61.27
80.93
64.75
67.81
72.92
58.79
65.03
68.58
64.00
55.92
65.91
61.57
-
75.00
70.19
70.44
82.50
65.61
53.41
62.18
77.78
66.60
63.33
59.75
66.34
75.13
63.26
60.95
80.91
65.10
66.61
57.45
60.00
64.14
68.58
63.78
-
61.73
53.52
82.50
68.51
84.53
87.06
64.44
44.25
62.40
72.14
63.68
65.85
-
66.34
99.44
63.24
66.71
80.94
64.97
86.61
57.83
59.09
63.28
68.58
63.64
55.90
62.79
-
61.24
83.19
66.85
64.25
70.31
45.76
66.42
78.48
67.75
65.31
63.22
66.32
86.81
63.24
60.89
80.93
64.56
66.61
57.27
58.62
63.19
68.59
66.67
-
-
55.09
83.61
70.83
80.00
77.75
44.22
59.11
71.15
70.98
69.31
63.35
1980 prices
31000
32000
33000
34000
71.22
75.00
54.07
73.04
57.08
73.22
76.97
65.04
72.96
66.15
74.11
70.67
67.23
75.74
59.76
71.72
59.74
64.83
56.89
72.06
62.69
68.15
62.59
68.45
62.52
63.79
66.34
51.08
63.24
61.99
80.93
65.00
66.61
57.58
58.84
62.25
68.59
82.67
61.97
64.53
73.14
64.58
56.18
57.53
72.33
63.93
54.54
66.34
67.74
63.24
63.52
80.93
64.84
65.77
72.82
89.67
79.80
70.99
82.63
67.23
64.49
55.31
77.79
68.38
80.68
59.77
86.34
76.23
63.24
62.55
80.93
64.95
66.14
57.58
61.51
84.08
68.58
63.92
64.25
48.31
80.30
69.16
64.30
66.85
66.34
62.96
63.24
63.27
80.93
64.54
66.61
57.57
58.84
63.64
68.58
78.02
41.29
55.87
69.87
72.15
75.57
70.91
78.14
58.31
70.48
70.56
69.71
69.26
57.62
64.45
71.28
-
66.39
57.55
58.74
62.32
68.58
63.64
62.73
43.07
56.46
69.10
89.13
61.82
58.08
78.03
65.50
56.40
61.93
68.04
63.03
78.41
64.11
-
52.67
60.00
82.36
57.21
75.95
78.71
63.05
53.76
76.73
62.48
73.91
61.74
62.93
-
-
65.84
80.39
70.93
70.08
64.24
65.15
70.21
70.15
89.47
57.75
73.33
74.16
66.67
69.00
46.22
58.97
69.23
70.56
68.18
68.85
91.85
72.79
67.35
39.04
59.49
70.14
67.83
70.81
66.67
-
-
-
-
-
-
64.41
62.50
64.29
66.67
64.29
63.87
64.35
63.14
-
-
-
-
-
-
-
-
-
-
59.90
66.45
60.00
65.22
59.89
58.12
-
-
56.05
52.56
68.94
267.12
69.00
69.35
-
-
42.49
52.73
64.61
25.28
40.42
52.50
57.95
41.93
57.21
53.71
66.18
55.70
-
-
-
-
-
-
-
-
62.42
80.48
-
39.54
52.48
60.25
-835.81
61.72
59.02
-
-
59.90
70.27
-
-118.75
52.58
69.38
13.72
75.39
70.69
57.17
75.91
66.17
62.60
61.43
71.15
61.30
59.90
65.34
-
41.04
52.57
65.17
-61.31
75.02
68.87
-
-
-
-
59.89
64.28
59.90
69.54
44.37
52.59
64.16
936.59
71.29
66.87
42.28
52.62
69.25
-175.79
65.41
67.56
Table 1 continued
Intermediate consumption (continued)
35000
36000
37000
38000
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
28
27
28
29
30
31
32
33
34
35
38
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
81
62
63
39000
40000
50000
60099
63000
71000
72000
80099
83110
61.88
71.43
79.78
72.85
67.24
53.45
76.87
61.20
82.38
58.20
85.54
58.20
75.89
86.34
41.95
63.24
61.57
80.93
64.88
66.61
57.93
59.21
62.58
68.59
111.45
100.00
127.27
36.53
65.25
69.43
55.37
78.43
63.72
63.55
31.26
68.10
56.60
73.39
81.46
87.55
72.87
72.03
71.11
67.84
87.49
63.94
63.21
65.90
72.20
89.01
72.30
58.78
66.34
72.86
83.24
81.24
80.93
63.27
65.10
57.57
58.83
65.19
68.58
63.55
84.15
85.35
78.21
78.08
58.64
70.50
59.02
58.45
71.72
71.53
69.54
63.04
95.72
81.54
87.53
53.50
71.13
71.09
64.85
62.01
66.55
52.55
81.74
77.01
67.79
64.13
58.62
68.34
70.50
83.24
62.79
80.93
64.97
66.61
57.63
91.25
81.63
88.58
49.38
55.08
65.91
71.17
72.51
88.07
71.95
41.88
59.58
69.49
69.83
86.78
64.20
61.52
61.53
81.54
61.58
83.36
83.46
62.50
69.54
71.33
60.93
65.64
39.23
61.85
78.87
88.00
82.16
64.67
66.34
72.71
83.24
64.18
80.93
63.45
66.61
57.57
58.81
85.30
68.58
63.88
89.51
70.42
62.43
65.82
48.49
62.12
79.11
67.77
63.07
58.40
88.34
76.75
63.24
72.52
80.93
63.66
89.47
71.95
62.89
65.78
52.20
80.95
78.35
87.88
81.35
58.35
66.34
85.36
63.24
62.79
80.93
64.93
86.60
57.62
58.92
64.51
68.58
63.75
66.61
57.59
58.80
61.00
88.58
-
-
-
74.16
75.17
85.41
69.09
38.57
59.07
69.88
71.58
69.10
69.31
74.15
74.53
69.54
88.98
43.12
59.18
70.03
70.53
88.93
64.31
74.11
75.50
77.44
69.14
44.86
58.75
-
-
-
-
65.47
102.67
48.99
71.21
73.25
63.87
73.20
58.06
68.81
63.59
68.43
67.87
58.03
88.34
89.99
63.24
83.29
80.93
64.86
66.61
57.60
58.84
61.89
68.58
58.62
41.30
60.11
39.72
75.88
73.77
85.08
78.25
61.19
64.31
81.88
70.45
72.11
58.98
55.56
81.58
78.85
84.81
79.33
69.32
66.52
73.49
54.09
68.42
89.02
69.03
64.35
58.17
68.34
68.71
63.24
61.42
80.93
64.88
68.81
57.61
58.85
61.99
68.58
84.13
77.78
55.53
82.25
74.80
56.48
76.77
54.88
59.77
58.95
70.53
46.92
79.27
59.55
61.29
68.66
71.28
61.32
70.69
53.09
83.89
67.96
66.59
68.21
42.24
56.48
64.38
64.39
65.00
64.17
82.50
64.29
84.16
64.24
64.38
64.32
63.64
84.18
84.04
59.90
50.70
59.90
62.92
59.94
60.88
59.90
87.92
59.93
55.93
59-.90
59.90
66.34
59.90
64.67
59-.90
53.23
57.95
59.90
68.15
59.90
66.45
59.90
66.92
40.95
52.72
83.46
67.88
77.60
73.83
65.42
52.49
67.35
71.96
58.97
83.08
44.65
33.09
57.31
42.83
32.88
63.10
21.04
93.54
80.93
38.89
34.89
59.55
102.81
66.11
64.73
34.77
39.00
60.83
87.98
57.77
59.11
-
38.80
52.58
50.68
-176.56
71.28
55.32
-
32.42
52.55
82.70
83.95
69.07
65.87
81.95
-
70.87
73.51
67.36
82.11
69.78
55.46
53.44
58.27
68.55
84.05
56.56
88.34
58.71
83.23
83.51
80.93
85.06
66.61
57.50
58.73
62.29
68.59
62.50
-
48.98
52.53
60.66
81.28
98.97
69.87
81.54
73.28
100.00
83.93
73.63
70.10
63.22
70.59
63.12
60.20
71.12
86.97
64.23
81.99
86.34
74.07
83.24
62.32
80.93
64.82
66.61
57.58
58.80
62.37
68.58
41.47
59.31
57.14
54.78
87.79
74.29
59.93
73.52
65.41
54.61
67.63
68.98
52.42
89.09
64.28
_
-
63.78
69.47
68.08
62.37
65.57
44.32
82.11
79.23
87.75
64.54
82.98
66.34
100.67
63.24
87.09
80.93
64.94
68.61
57.85
58.93
67.15
88.59
83.64
-
75.32
74.16
72.55
68.00
88.58
44.18
59.21
70.28
70.87
68.58
63.02
57.80
54.19
_
_
_
43.41
52.56
67.71
41.28
52.56
55.81
46.51
52.89
66.16
140.48
67.79
67.79
54.72
59.37
57.57
2.10
52.57
51.08
82.99
91.28
65.55
1
27.96
88.20
87.02
-
83.55
89.48
82.38
64.43
70.55
54.12
72.07
80.20
68.31
63.14
59.72
88.34
72.88
63.24
62.61
80.93
63.88
66.53
57.58
58.81
64.87
88.58
63.67
-
74.12
75.28
63.53
72.99
49.05
89.52
76.46
69.20
69.58
84.20
-
67.82
-
58.49
67.92
83.00
89.49
72.27
83.33
65.83
49.14
51.81
75.00
68.89
80.85
58.29
68.34
88.74
63.24
62.79
80.93
65.87
86.61
57.65
58.87
72.00
88.58
63.75
63.49
-
74.03
75.73
100.00
89.17
43.09
54.84
66.87
86.41
69.26
84.45
69.34
69.24
69.25
64.18
continued
Table
1
continued.
Intermediate consumption (continued)
Imputed
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
28
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Si
62
11000
12000
13000
20000
DANISH GOODS AND SERVICES
Agriculture, horticulture, etc
Forestry and logging
Fishing
Mining and quarrying
Manuf. of food, beverages, tobacco
Textile, clothing, leather industry
Manuf. of wood products,incl. furnit.
Manuf. of paper,printing,publishing
Chemical and petroleum industries
Non -metallic mineral products
Basic metal industries
Manuf. of fabricated metal products
Other manufacturing industries
Electricity, gas and water
Construction
Wholesale and retail trade
Restaurants and hotels
Transport and storage
Communication
Financing and insurance
Dwellings
Business services
Market services of education,health
Recreational and cultural services ..
Household services, incl. auto repair
Other producers, excl. government
Producers of government services
IMPORTS INCL. CUSTOMS DUTIES
Agriculture, horticulture, etc.
Forestry and logging
Fishing
Mining and quarrying
Manuf. of food, beverages, tobacco
Textile, clothing, leather industry
Manuf. of wood products,incl. furnit.
Manuf. of paper,printing,publishing
Chemical and petroleum industries
Non -metallic mineral products
Basic metal industries
Manuf. of fabricated metal products
Other manufacturing industries
Electricity, gas and water
Construction
Wholesale and retail trade
Restaurants and hotels
Transport and storage
Communication
Financing and insurance
Dwellings
Business services
Market services of education,health
Recreational and cultural services
Household services, incl. auto repair
Other producers, excl. government
Producers of government services
imports
31000
32000
33000
34000
35000
36000
37000
38000
39000
40000
50000
60099
63000
71000
72000
80099
83110
83509
93009
94000
95009
95399
98099
11000
12000
13000
20000
31000
32000
33000
34000
35000
38000
37000
38000
39000
40000
50000
80099
63000
71000
72000
80099
83110
83509
93009
94000
95009
95399
98099
Other
Sum (1 -55)
Purchases in Denmark by non -resid. household
Net taxes on commodities
Value added tax
Uses at market prices (56 -59)
Other indirect taxes, net
Gross domestic product at factor cost
.
.
.
.
.
:
Total
bank
service
charges
83509
93009
94000
95009
95399
98099
61.53
61.64
62.94
61.51
61.67
-
-
-
-
-
65.27
48.46
53.49
70.43
70.96
69.77
82.27
85.48
61.44
81.37
65.52
65.72
86.58
-
70.21
72.59
54.36
58.06
72.07
66.66
66.06
68.15
56.75
65.99
69.45
67.66
65.78
-
59.88
86.31
71.81
63.22
63.51
80.93
64.84
59.11
66.28
75.51
65.22
64.90
68.58
69.95
58.87
56.01
42.74
-
-
57.14
69.48
72.27
65.52
65.52
53.42
56.19
73.56
87.22
62.68
62.50
71.35
71.91
62.50
65.62
50.13
61.39
78.87
63.43
61.57
58.56
68.34
69.80
63.24
62.79
80.93
64.12
88.81
72.67
58.51
61.64
68.59
62.98
85.38
9.39
1.09
2.46
5.35
53.75
2.14
9.13
68.80
2.99
-
-
-
74.13
75.87
90.00
60.84
45.93
57.14
64.62
64.43
88.36
77.18
75.46
74.19
69.12
45.35
59.20
31.99
68.06
69.27
64.11
64.10
-
-
58.40
88.34
86.72
83.24
68.24
80.93
64.88
66.55
57.59
62.42
62.70
68.58
63.55
-
-
58.42
6.34
7.64
3.24
1.75
0.93
4.80
62.50
69.30
62.03
59.69
71.60
64.08
57.26
55.55
68.30
65.77
58.83
66.34
66.65
63.24
61.56
80.93
63.49
-
-
-
100.00
69.49
72.28
64.52
65.63
83.59
58.00
75.00
68.07
60.95
57.92
66.35
85.68
63.24
62.79
80.93
64.87
66.61
57.55
58.90
60.35
68.59
62.50
-
-
74.22
82.58
69.23
69.00
46.60
59.20
70.06
70.56
65.13
64.22
72.67
63.46
71.20
72.60
54.25
55.97
58.25
67.57
68.39
74.38
75.71
88.89
69.18
55.40
56.76
66.67
67.92
69.03
59.07
88.20
90.82
63.17
65.91
80.94
64.85
59.11
66.77
76.14
89.80
63.14
88.58
55.80
45.83
54.94
65.88
69.77
73.29
73.22
71.69
54.46
62.17
65.92
67.87
73.44
64.08
64.10
64.15
-
-
-
6.27
7.56
2.29
2.16
-
8.58
5.18
-
66.61
57.55
58.88
65.03
-
68.58
63.68
-
-
-
-
-
-
64.19
64.41
59.77
64.32
65.22
62.10
-
-
-
-
-
-
-
-
59.90
66.10
-
37.44
312.87
66.47
34.17
66.79
-
-
-
59.88
63.18
59.89
64.20
59.90
65.66
40.95
30.38
57.21
-477.43
77.02
17.42
52.54
62.40
33.52
67.75
51.10
52.57
85.25
130.81
64.42
-
-
-
-
59.90
86.81
49.84
89.92
68.58
1137.27
57.94
-
-
59.90
68.32
24.30
38.69
63.24
50.69
68.76
-
64.91
-
-
-
-
-
64.91
-
64.91
-
64.91
69.08
69.42
57.97
75.79
55.14
59.47
65.69
69.31
66.07
58.78
58.74
-
-
-
60.34
-
-
54.42
64.97
30.18
39.39
63.83
194.07
89.30
Table
1
continued
Final
demands
Private :Govern- :Gross fixed capital
consump -:ment
:Machine -: Transtion
:consump -:ry and
port
:tion
:equipm.
equipm.:
:
:
:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
18
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
88.48
45.06
53.49
66.59
71.36
68.90
84.88
85.30
47.33
64.38
64.06
68.87
43.14
70.46
74.66
63.04
87.08
80.93
64.17
59.11
68.69
69.39
72.89
84.45
58.70
66.50
49.97
24.88
54.94
54.78
70.50
72.83
69.08
70.25
41.12
84.27
51.49
74.52
65.85
83.80
80.35
-
-
-
-
-
66.95
67.26
71.31
68.46
63.85
64.53
88.42
85.40
70.50
87.01
-
-
72.86
45.83
-
50.43
-
.
.
-
73.26
-
-
-
-
-
-
-
-
71.64
50.13
17.15
76.72
28.95
68.18
57.47
76.17
58.31
65.58
76.79
70.05
52.74
132.19
151.80
-
-
-
71.74
-
72.33
67.25
-
-
-
-
-
-
-
-
-
-
-
65.88
-
89.91
-
-
-
-
-
-
-
-
-
83.38
58.16
66.87
-
-
-
-
-
-
-
63.50
-
-
-
-
-
-
-
-
-
-
-
-
187.53
-
-
-
-
-
-
-
-
-
-
-
60.58
49.97
62.22
60.68
87.93
71.18
81.31
79.36
47.43
64.69
37.10
54.53
71.95
123.38
113.74
-
-
-
-
59.48
-
62.19
70.56
-
-
62.41
67.30
80.70
65.26
53.36
66.09
65.68
85.66
71.73
82.41
-
-
76.98
78.72
-
Total
.
!
tion
-
-
Total
-
-
64.33
-
-
-
-
-
84.45
58.71
57.57
64.47
89.20
70.21
68.53
71.54
58.99
84.45
71.00
88.14
83.97
66.33
75.88
60.99
65.70
84.72
59.18
68.58
48.88
55.53
55.82
53.20
70.22
70.28
61.01
67.37
89.50
81.23
59.51
70.60
51.20
67.24
60.08
64.05
53.86
57.08
64.23
70.19
69.52
67.53
66.05
54.13
64.22
70.49
67.85
56.44
70.31
67.25
74.88
63.04
62.57
80.93
64.18
59.11
88.52
69.39
72.41
84.45
58.70
66.86
50.43
50.13
55.22
59.64
70.52
72.73
66.98
65.02
44.79
63.86
61.65
70.23
65.24
86.25
81.14
69.35
86.18
55.70
59.02
70.69
68.87
66.87
67.56
55.32
65.87
69.87
67.79
57.57
65.55
67.02
73.83
63.08
63.00
80.93
64.73
59.11
88.57
73.15
71.20
64.86
58.70
66.88
59.39
56.67
55.87
43.29
89.57
71.04
59.63
74.82
51.95
60.32
85.48
69.84
65.46
87.27
59.45
81.32
80.84
60.40
-
59.96
86.15
57.27
65.68
-
-
-
-
51
60.51
52
53
54
55
-
57
58
59
59.90
65.25
83.83
55.74
41.61
60
61.61
58
-
:
formation
Changes: Exports:
:Breeding: in
Construt- :stock
stocks
66.87
-
-
66.87
-
119.38
88.27
70.81
-
73.12
102.32
-
-
-
35.86
35.48
80.78
17.62
48.12
-
84.08
73.12
-21072.22
-
118.28
66.27
83.63
51.49
-
-
-
53.84
43.11
49.38
42.43
88.48
84.15
64.03
O
CO
Table
2.
A
Private consumption
Government consumption
3 Gross capital formation
4 Domestic final uses
1
2
..
.
+3)
5
Exports
6
Final uses of goods and
services (4 +5)
Imports
Gross domestic product at
market prices (6 -7)
Indirect taxes, net
Gross domestic product at
factor prices (8 -9)
7
8
9
10
NOTE
:
Columns
Columns
Columns
Columns
marked
marked
marked
marked
A are at
B are at
C are at
D are at
8966-1975
D
I
A
32.0
97.5
31.9
97.6
11.3
31.9
97.5
8.0
11.4
8.9
9.6
26.2
41.7
98.1
38.4
94.3
39.5
95.1
38.7
98.0
14.7
15.6
13.2
15.9
52.8
69.9
48.9
59.7
50.0
62.7
49.7
63.7
13.2
-0.2
14.4
3.3
12.4
-0.4
48.0
26.8
45.5
25.0
46.1
24.0
45.5
23.5
16.0
16.7
15.1
51.2
50.1
51.0
50.4
35.2
97.5
25.4
13.2
13.3
14.5
1.0
16.5
1.7
26.6
56.9
11.6
27.9
9.9
24.9
30.8
40.8
32.2
41.2
15.3
18.0
28.6
25.2
27.7
20.0
29.5
23.9
29.3
29.5
30.7
22.9
57.5
8.6
21.0
57.5
8.8
23.6
57.5
9.3
9.2
25.4
377735
122256
27.0
54.9
26.0
55.5
25.0
55.6
499991
126205
32.4
43.9
31.5
41.0
373786
57797
29.2
25.6
315989
29.8
I
0
A
6.7
25.5
-0.4
25.4
2.5
23.8
57.5
9.5
1975
1980
1980
1980
D
7.3
25.4
-0.6
208814
99734
69187
o
1966-1980
1975-1980
Imi11980r.I
(1 +2
11
Percentage growth of main components of danish gross domestic product at constant prices
9.1
11.6
prices
prices calculated by commodity balance factors
prices calculated by IO element factors
prices calculated by IO row factors
Table 3.
Percentage growth of components of danish private consumption at constant prices
m111980
Food
Beverages
Tobacco
Clothing and footwear
Fuel and power
Other non -durable goods
35894
9215
7130
B966-1975
I
A
1975-1980
D
2.6
72.1
-1.5
4.5
i
A
1966-1980
D
9.4
5.2
-0.2
9.9
0.9
5.4
7.4
9.3
-6.8
39.3
25.5
9.7
9.6
-6.8
10.7
4.6
7.3
16.0
17.9
7.3
33.5
35.3
35.8
14.2
17.6
17.7
75.8
48.2
60.3
18403
38.6
28.8
38956
8598
9738
65.6
17.6
20.3
19224
(
A
I
C
88.5
-8.3
16.6
46.4
36.6
11.4
80.5
3.5
13.8
43.0
29.5
9.4
86.9
10.0
5.6
8.2
-13.7
-16.3
7.4
15.9
4.0
46.0
32.4
61.5
30.6
5.7
7.0
4.6
26.1
24.7
24.1
23.4
-6.6
-29.6
-9.9
-5.3
-29.6
-4.4
-4.8
-37.5
68.7
-5.3
-29.9
0.6
-14.1
28.7
-16.7
76.8
24.7
-19.6
33.6
28.0
-17.2
53.2
29.3
-26.5
45.0
33.4
35.1
-12.8
-16.8
-15.0
-21.6
20.8
7.1
13.4
5.9
65.6
16.0
20.2
-10.4
65.6
15.0
37.7
3.0
15.0
28.5
2.8
15.2
90.4
61.9
23.9
90.4
51.5
23.8
17.4
14.0
15.0
36.8
2.9
21.3
29.2
4.7
1.9
65.6
17.9
20.4
-1.4
18.5
19.6
12.5
90.4
58.7
23.7
8.7
90.7
51.2
25.9
17.9
-8367
63.3
62.4
63.3
63.3
1.6
2.2
1.6
-3.8
65.9
66.0
65.9
57.1
8402
61.2
61.2
61.2
61.2
37.5
37.5
37.5
37.5
121.5
121.5
121.5
121.5
Total of services excl.
gross rents
37595
6.7
5.3
-0.8
5.0
26.2
21.5
27.5
27.0
34.7
27.9
26.5
33.3
Total of services
76551
30.4
30.0
26.3
30.4
20.5
18.0
20.8
20.7
57.1
53.6
52.6
57.4
208814
23.8
22.9
21.0
23.6
9.2
7.3
9.1
6.7
35.2
31.9
32.0
31.9
3.1
1.8
1.8
12236
24419
24966
72.0
-1.5
5.3
39.9
27.3
71.6
3.7
3.5
41.7
22.9
71.0
-1.5
4.4
32.7
25.4
113860
17.5
18.0
5916
6234
6253
35.9
18.8
Total of durable goods
Gross rents
Transport and communication
Hotels and restaurants
Other services
Purchases in Denmark by
non -resident households
Purchases abroad by resident
households
Total of non -durable goods
.
Furniture, fixtures, carpets
Personal transport equipment
Other durable goods
Total of private consumption
NOTE
:
Columns
Columns
Columns
Columns
marked
marked
marked
marked
A
B
C
D
are
are
are
are
at
at
at
at
1975
1980
1980
1980
17.1
20.2
-0.6
10.1
prices
prices calculated by commodity balance factors
prices calculated by IO element factors
prices calculated by IO row factors
13.1
-8.1
14.9
11.1
48.5
-17.5
12.3
112
REFERENCES
Bjerke, K., P. Milhej and P. Nerregaard Rasmussen, 1956. "National
235 -57 in Barna, T. (ed.) "The
experiences, Denmark" pp.
structural interdependence of the economy ", New York and
Milano
Danmarks Statistik, 1973. Input- output tabeller for Danmark, 1966,
Vol. 1 and 2.
Danmarks Statistik, 1981. Klassifikation af brancher og privat konsum i nationalregnskabet. Nationalrégnskabsnotat nr. 4.
Danmarks Statistik, 1985a.
nr.
Input- output systemet
i
ADAM.
Arbejdsnotat
19
Danmarks Statistik,
1985b.
Indeksberegninger
i
Danmarks Statistik.
Danmarks Statistik, 1986a. Nationalregnskabsstatistik 1984.
Accounts 1984).
(National
Danmarks Statistik, 1986b. Import -, beskwftigelses- og energimultiplikatorer 1982. (Import -, employment- and energy multipliers
1982). Arbejdsnotat nr. 21
Det statistiske Departement, 1948. Nationalproduktet og nationalindkomsten 1930 -46.
Det statistiske Departement, 1951. Nationalproduktet og nationalindkomsten 1946 -49.
Det statistiske Departement, 1955. Nationalindkomsten
1947 -54.
Det statistiske Departement,
1938 og
1962. Nationalregnskabsstatistik
1947 -60.
Eurostat,
1979. 'European System of integrated economic accounts,
ESA, Second edition, Luxembourg
Flettum, E., 1981. National accounts of Norway. System and methods of
estimation. Rapporter 81/1, Statistisk Sentralbyr5, Oslo
Folke,
T.
1981. Brugervejledning for PASSION og nationalregnskabets
databank pá RECKU. Nationalregnskabsnotat nr. 5. Danmarks
Statistik.
Olsen, J.A., 1985. "Adaption of detailed input- output information:
Restructuring and aggregation ". Review og Income and Wealth,
no. 4, pp. 397 -411
Rae,
T.T., D. Chakrabarty and J.A. Small, 1984. "An alternative treatproducts in input- output analysis" The
ment of secondary
Review of Economics and Statistics, Vol. LXVI pp. 88 -97.
113
Richter,
"The role of import
price input- output tables ".
tional Meeting on problems
tables, Baden, Austria. May
Problems
(eds.)
Rainer
N.
tables, Wien 1986.
J.,
1985.
matrices in compiling constant
Paper presented at the Internaof compilation of input- output
1985. Reprinted in A. Franz and
of compilations of input- output
Statistics Canada, 1981. The input- output structure of the Canadian
economy in constant prices 1971 -77. Ottawa.
Thage,
B.
"Udenrigshandelen i input-output analysen". Nationalekonomisk Tidsskrift nr. 3, pp. 361-81.
1973.
Thage, B., 1982. "Techniques in the compilation of Danish input- output
tables: A new approach to the treatment of imports" in
J. (ed.) Compilation of input- output tables. Berlin,
Skolka,
Heidelberg, New York.
Thage,
"Balancing procedures in the detailed commodity flow
system used as a basis for annual input- output tables in
Paper presented at the International Meeting on
Denmark ".
Baden,
tables,
of Compilation of input- output
Problems
(eds.)
in
Franz
and
N.
Rainer
A.
Austria. May 1985. Reprinted
1986.
tables,
Wien
of
inputoutput
Problems of compilations
B.,
1985.
United Nations, 1968. A system of national accounts. Studies in
Method, Series F, No. 2, Rev. 3, New York
United Nations, 1973. Input- output tables and analysis.
Method. Series F, No. 14, Rev. 1, New York
Studies in
United Nations, 1979. Manual on national accounts at constant prices.
Statistical Papers, Series M, no. 64. New York
United Nations, 1986. "Study of country practices in implementing the
in the 70's ". Paper prepared by
SNA input- output framework
for
the Meeting of the ECE working party on national
UNSO
accounts and balances, Geneva 3 -7 March 1986
Viet,
V.
"Input- output standards in the SNA framework ". Paper presented at the 19th general IARIW conference, Noordwijkerhout,
Netherlands 25 -31 August 1985