How to Create a Sport Satellite Account

SportsEconAustria
Institut für Sportökonomie, Wien
How to Create a
Sport Satellite Account
Methodology Paper
for the EU Working Group
Sport and Economics
February 2012
Günther
Grohall,
Anna Kleissner und Bernhard Moser
Christian
Helmenstein,
Kontakt:
Christian Helmenstein
SportsEconAustria (SpEA)
Schottenfeldgasse 29, 1070 Wien
: +43/67684/8048-401
E-Mail: christian.helmenstein@spea.at
Anna Kleissner
SportsEconAustria (SpEA)
Schottenfeldgasse 29, 1070 Wien
: +43/67684/8048-600
E-Mail: anna.kleissner@spea.at
Günther Grohall
SportsEconAustria (SpEA)
Schottenfeldgasse 29, 1070 Wien
: +43/159991-246
E-Mail: guenther.grohall@spea.at
How to Arrive at a Sport Satellite Account
Contents
1
Short Overview ................................................................................................................... 2
2
Enlarging the Matrix ........................................................................................................... 3
2.1
Gross Value Added ..................................................................................................... 5
2.2
Gross Production Value/ Total Supply........................................................................ 6
2.3
Consumption ............................................................................................................... 6
2.4
Imports and Exports .................................................................................................... 7
2.5
Intermediate Goods Output ........................................................................................ 8
2.6
Intermediate Goods Input ........................................................................................... 8
3
Sport-relevant Shares ........................................................................................................ 8
4
Further Data Processing .................................................................................................... 9
5
General Traps and Pitfalls................................................................................................ 10
5.1
Numeric Methods of Certain Computer Programmes .............................................. 10
5.2
Try to Avoid Zeroes in the Vectors ........................................................................... 10
5.3
Try to Avoid Different Data Sources ......................................................................... 11
5.4
If using Excel, use its Enhanced Worksheet Functions ........................................... 11
5.5
Customers’ Scepticism concerning Data .................................................................. 11
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How to Arrive at a Sport Satellite Account
1 Short Overview
It is probably the best to start once again with the scheme of an I/O-Table. Figure 1 shows a
simplified table with some exemplary numbers in it. Note that in reality, “sectors” are “goods”,
as I/O-Tables are of dimension CPA x CPA. For the sake of simplicity, we are talking about
sectors here in this introduction.
Figure 1: A simplified I/O-Table with important data vectors having a coloured background.
Source: Meyer, Ahlert, 2000, page 86, small changes included.1
The matrix formed by the intersection of the sectors is the Intermediate Goods Matrix. The
sum of its columns forms the Intermediate Goods Inputs, the sum of the rows forms the
Intermediate Goods Outputs. The sum of the nth row does not have to equal the sum of the
nth column (sector 2 has inputs worth 29 and outputs worth 30), but the sum of all rows has to
equal the sum of all columns – as can be seen in the cell containing “54 / 54”.2
Since goods are not the only cost centre, additional rows are added below, containing Gross
Value Added in all its forms (tax deductions, taxes, wages, and profits in this example).
Intermediate Goods Input plus Gross Value Added sum to Total Supply, which is the last row
in Figure 1. This is the value of all goods of a sector supplied in a country, as it contains the
production costs (material and services, plus wages), taxes on products and production, and
the companies’ profits.
As goods and services are not just purchased by companies, extra columns are placed to the
right of the Intermediate Goods Output. Here we have private consumption, state
consumption, and investments, summing up to final Consumption. In the first row we thus
find the deliveries of goods of sector 1: either to other companies (intermediate goods), or to
1
Bernd Mayer and Gerd Ahlert, “Die ökonomischen Perspektiven des Sports“, Schriftenreihe des
Bundesinstituts für Sportwissenschaft, Band 100, Verlag Karl Hofmann, Schorndorf, 2000.
2
Both sums of sums are just different ways of summing up all elements of the same matrix. And since
A+B=B+A, the order of the elements does not matter.
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How to Arrive at a Sport Satellite Account
the final consumers. The sum equals the number of all products produced and is called
Gross production. As all goods are produced in one way or the other, Total Supply (the last
line) has to equal Gross production (last column).3
Foreign trade either enters as an own sector (Import as an input row and Export as an output
column), or as parts of the extensions below and to the right. In the Austrian I/O-Table,
foreign trade is listed between Gross Value Added and Total Supply (Import) and as part of
Consumption (Export).
Figure 2: A simplified enlarged I/O-Table.
Source: Own calculations based on Meyer, Ahlert, 2000, page 86.
To clearly identify sport in the economy, the I/O-table has to be enlarged. Each sector
containing sport-relevant activities is split in two parts. The non-sport part remains where it is,
the sport-relevant part gets its own row and column. In Figure 2 sectors 1 and 2 have such
activities, only sector 3 remains as it was. The non-sport parts are now called Sector 1’ and
2’, the sport-relevant parts are Sectors S1 and S2. The sum of Sector n’ plus Sector Sn
results in the original Sector n since nothing was added in or subtracted out of the country’s
economy. E.g.: intermediate goods from sector 1 delivered to sector 2 were worth 2, from
sectors 1’ to 2’ just 1. The remaining 1 is now in cell “1’ to S2”. Inputs into Sector 2 were
changed from (2; 17; 10)’ to (1; 11; 10; 0; 3)’. The remaining 4 are now inputs into S2, being
(1; 2; 0; 0; 1)’.
2 Enlarging the Matrix
After identifying all sport-relevant subsectors on a 6-digit level by applying the Vilnius
Definition, a number of steps have to be repeated to separate sport-relevant from non-sport
3
Differences in stocks are booked in “Investments”.
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How to Arrive at a Sport Satellite Account
data. These steps are the same for each data-vector you work on, intermediate goods inand output, Gross Value Added, Consumption, Import and Export, and so forth. The idea
always remains the same: since data often is only available on a 2-digit level, one has to
calculate the value of the relevant 6-digit activities, calculate their sport-relevant shares and
subtract these from the 4-digit values.
Example: Austria’s value added of sector “80 Education” amounts to 11,559 Mio €. The 6digit activity “80.10-02 Elementary Schools” appears in the Vilnius definition.
1. From the Austrian Working Place Count, WPC, we know that 15.96% of people
working in sector 80 actually work in elementary schools. We may conclude that the
corresponding value added equals 11,599 Mio € x 0.1596 = 1,844 Mio €.
2. According to the official time tables, 12% of the teaching time in Austrian primary
schools is sports.
3. Thus we have an estimate of 1,884 x 0.12 = 221 Mio € value added for 80.10-02.
4. Enter 221 Mio in the according “sport-relevant 80.10-02” cell of the extended Gross
Value Added vector.
5. Calculate 11,599 – 221 = 11,378 Mio € as the remaining Gross Value Added of the
non-sport part of sector 80 (Sector 80’).
Here the general layout of the steps:
1. Calculate the absolute value of the 6-digit activities within its 2-digit category.
2. Find the sport-relevant share in percent (which is easier than in absolute terms) of the
6-digit activity.
3. Multiply the absolute value of the 6-digit activity with its sport-relevant share to get the
absolute amount of sport-relevant activity within this 6-digit activity.
4. Enter this absolute sport-relevant number of the 6-digit activity as a new sector in the
vector.
5. Subtract this value from the respective 2-digit sector.
Knowing all the enlarged vectors around the enlarged Intermediate Goods Matrix (thus the
upper right and lower left quarter of Figure 2), one has to fill the enlarged Intermediate Goods
Matrix (the upper left quarter of Figure 2) with values such that the sums of its rows and
columns matches with the values in the vectors. But this is a purely mathematical problem
and can be solved by the TRAS-algorithm.
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How to Arrive at a Sport Satellite Account
2.1 Gross Value Added
Data on Gross Value Added in Austria can be found in the “Leistungs- und Strukturerhebung”
or “Structural Business Statistics” SBS (sectors 10 to 74 on a 4-digit level with many gaps
due to small numbers of companies) and in the IOT (all sectors on a 2-digit level, not
available for every year). The numbers can also be taken from the Supply and Use Table
SUT which coincide for the year 2005 with the IOT, but the SUT is available for every year.
To get from 2 digits to 4 digits, some checks within the SBS were done. It turned out that
within any one 2-digit sector the relation between Gross Value Added and number of
employees is very stable (correlation coefficient equals about 0.959, see Figure 3, red
crosses). Thus the 2-digit sum-of-intermediate-production values were split into its 4-digit
categories according to the number of employees within these 4-digits categories.
Figure 3: Relation between share of employees and Gross Production Values or Gross Value Added of
several exemplary 3- and 4-digit sectors within their 2-digit sectors (329 data points).
Source: SpEA, 2009.
Since the SBS only covers sectors 10 to 74, numbers taken from the Working Place Count
WPC were used for the remaining sectors. Data from the Austrian Employment Centre
turned out to be less reliable.
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How to Arrive at a Sport Satellite Account
2.2 Gross Production Value/ Total Supply
Gross Production Value and Total Supply equal in their numbers, so one can talk about the
related data-gathering in the same chapter – using some pragmatism.
Data for this vector can be found on a 2-digit level in the Austrian IOT and the SUT. The SBS
gives a “Production Value” without “Gross”, which is close to the “Net Production Value”
equalling Gross Production Value minus Gross Value Added. Still the numbers deviate a
little. Thus the IOT/SUT-values were chosen, but the 4-digit sector numbers from the SBS
were checked to calculate the correlation between numbers of workers and production value
within any 2-digit sector. The resulting coefficient equals 0.935 and the scatter plot can be
seen in Figure 3 in blue rings.
Therefore we used the 4-digit employee numbers from SBS and WPC again for splitting up
the 2-digit sectors.
2.3 Consumption
Consumption data can be found within the IOT and the SUT on a 2-digit level. Since there is
absolutely no 4-digit data related to consumption in Austria, we interviewed experts (mainly
from the Chamber of Commerce) or searched for other sources. If nothing helped, we
assumed that most people work in sectors which produce the most bought goods – thus
applying employment data again.
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How to Arrive at a Sport Satellite Account
Figure 4: Relation between employees and Consumption of 43 sectors from 30 to 74 on 2-digit level.
Source: SpEA, 2009.
Figure 4 shows the relation between number of employees and Consumption in absolute
terms on 2-digit level. The correlation equals 0.621, which indicates some relation. That the
correlation within the 2-digit sectors is stronger due to the homogeneity within these groups
can only be assumed.
2.4 Imports and Exports
As with Consumption, there is no data which could give a hint on 4-digit foreign trade.
Imports may be calculated by knowing that Gross Production Value, Gross Value Added, and
Intermediate Goods Input correlate strongly with employment and can thus be estimated
quite well. Imports are then the difference
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How to Arrive at a Sport Satellite Account
+ Total Supply
- Gross Value Added
- Intermediate Goods Input
---------------------------------------+ Imports
Exports are far less simple, since there is Consumption, which cannot be approximated by
employment data that well.
2.5 Intermediate Goods Output
This is simply the difference (Gross Production Value) – (Consumption + Export).
Intermediate Goods Output and Gross Production Value are production based and can thus
be estimated by employment data rather well (if one estimates Intermediate Goods Output
e.g. for calculating Exports).
2.6 Intermediate Goods Input
This is the difference (Gross Production Value) – (Gross Value Added + Import). Since it is
production based, one should be able to estimate its 4-digit values well by using employment
data, but there is no way to show that with Austrian data.
There is one additional thing worth mentioning: directly below the Intermediate Goods Matrix
in the Austrian IOT, you can find a row called “C Insgesamt” or “C Total”. However, this is not
the Intermediate Goods Input! One has to subtract the row “CNTS Gütersteuern abzüglich
Gütersubventionen” meaning “CNTS Taxes on goods minus subsidies for goods” to arrive at
vector needed to create the SSA.
If you are not sure whether you chose the correct rows, just check the sums of your
Intermediate Goods Output vector and your Intermediate Goods Input vector (Foreign trade
must not be part of the matrix!). If the sums are equal, you are most likely right. If not, T/RAS
will not be able to find a solution.4
3 Sport-relevant Shares
After knowing the absolute values of the sport-relevant 4 and 6-digit categories, one has to
collect their respective sport-relevant shares. As a benchmark one may use numbers from
Meyer, Ahlert, 2000, who write on pages 20 to 23 (57 to 60 in German and 39 to 41 in
French) that private spending on sport articles was around 1.9% of all private spending in
4
The sum over the elements of a matrix must always be the same, no matter whether you add the
rows first or the columns – or in whatever order you add the elements. Therefore the two Intermediate
Goods vectors must sum to the same value, 54 in the example, too!
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How to Arrive at a Sport Satellite Account
1998 and 1.5% of public spending. Austrian Consumption Survey of 2004/05 attributes
12.6% of private consumption to “Spare Time, Sports, Hobbies”. Out of that, 2.6 percent
points go to “Spare Time, Sports, and Hobby Goods” and another 2.3 percent points to
“Spare Time, Sports, and Hobby Events”.
A big part of Austria’s private consumption is housing and energy (23%). This number can be
excluded right away, increasing the average share of money spent for all other goods.
Taking into account that sport goods wear off quicker, one may assume an average share of
probably 2% to 4%, which may be used as a first approximation for the production side too.
Detailed numbers were either found by searching respective articles (like annual reports), or
by asking people directly involved. These were again members of the Chamber of
Commerce, other similar institutions, or representatives of important companies. As Austria
is not that big, these interviews proofed to be very useful (comparably huge companies like
KTM – producing sport motor bikes – dominate the production side, but the consumption side
can look quite different).
Numbers about public sectors were available especially for education. Time tables,
employment data, costs, and so on are published by the Austrian state and the federal states
too. Data on the Austrian health sector was not that transparent, but numbers are available
for “Leisure Time Accidents” including sport accidents, providing at least an upper limit.
Interviews with hospital doctors and administration personnel showed some interesting cost
relations (internal medicine uses about 90% of all pharmaceuticals, much higher than the
respective share of patients).
4 Further Data Processing
The sport-relevant shares of each 4 or 6-digit sector have to be multiplied with their total size
to calculate the absolute sport-relevant value. E.g.: category 80.10-02 was calculated to have
a Gross Value Added of 1,884 Mio € and a sport-relevant share of 12%. Thus the sportrelevant Gross Value Added equals 1,884 Mio € x 12% = 221 Mio €.
Subtract these numbers from their original, now non-sport, 2-digit categories (in the example
sector 80). After doing so, you have a new vector of length n+m where n equals the number
of 2-digit sectors and m is the number of sport-relevant 4 and 6-digit categories (57+124 for
Austria). Since this extension is just a “zoom” into the data, the sum over all elements of the
new vector equals the sum over all elements of the old vector.
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How to Arrive at a Sport Satellite Account
If you have all vectors (Intermediate Goods Input, Intermediate Goods Output, Import,
Export, Gross Value Added, Consumption, Total Supply, and Gross Production Value5), you
copy them into a spread sheet. In case you have foreign trade outside the Intermediate Good
Matrix (which is probably to be preferred) Intermediate Good Input and Output vectors are
the target values for the column and row-sums of the Intermediate Goods Matrix.
Some additional precautions:
1. Check the sums of the elements of corresponding vectors for equality (see Figure 2).
2. Check for zeroes or even negative entries in the target vectors.
3. Check for negative values in all other elements of matrices and vectors (they are
allowed in stock changes or tax deductions, but not in private consumption etc.).
4. If you run the T/RAS yourself, work with TRAS first. This allows you to keep the
values of those sectors which have no sport-relevant subcategories constant. RAS
would change these values!
5. Use the standard IOT as starting values with tiny values in the enlarged quadrants of
the matrix. This seems to be best starting point ready at hand.
6. TRAS usually converges within 100 steps to a maximum deviation of around 2% from
its target value. Check for sectors which “get stuck”.
7. If rows/columns converge toward 0% deviation, but columns/rows have a non-zero
average deviation from their target value, the sum of one target vector does not equal
the sum of the other.
5 General Traps and Pitfalls
5.1 Numeric Methods of Certain Computer Programmes
Working with an IOT sometimes requires inverting the matrix. For matrices as big as those
used by us, this is no trivial task anymore. Open Office Calc (a spreadsheet) was and
probably still is not able to do the job. Excel reports slightly different results, depending on
the version. Matlab seems to be a good, but expensive, alternative. The statistic program R
is freely available, but there are reports in the internet that it is not perfectly precise in
inverting large matrices.
5.2 Try to Avoid Zeroes in the Vectors
If a zero appears in one of the sum-vectors of the Intermediate Goods Matrix (e.g. in private
households), the T/RAS-algorithm does not find a solution due to a division by zero. A
5
For both, input side and output side, you may skip one of those vectors, since it calculates as a
difference of the other vectors.
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How to Arrive at a Sport Satellite Account
pragmatic solution is to add some 10.000 € or so to one cell (e.g. Imports) and after
convergence to subtract it again. T/RAS is extremely in-sensitive to such manipulations, the
result is thus at least a very good approximation (biggest deviations can be found in the order
of magnitude of a few Cents).
5.3 Try to Avoid Different Data Sources
This sounds very natural, but proofed to be a necessity for another satellite account. We had
two different, but in general very reliable sources for Gross Production and Consumption. But
after subtracting Consumption from Gross Production it turned out that the Intermediate
Goods Matrix should contain negative values. Several other strange results were found, like
Gross Value Added per employee should vary by a factor of more than 100 within one 2-digit
sector and the like. Even employment data from the Austrian Employment Centre turned out
to be plainly wrong sometimes.
5.4 If using Excel, use its Enhanced Worksheet Functions
If you want to or have to use Excel, use the “INDIRECT” and “MATCH” functions to collect
data. Each entry of a 6-digit activity requires data of the according 2-digit sector. E.g. if you
have the six 6-digit rows from sector 33, you would have to copy sector 33’s Gross Value
Added next to each of the six entries. If you change something, you have to change it
everywhere within you worksheets, which is a classic source for mistakes. Using $-signs to
use constant addresses, you only shift the problem to within each cell (after getting out of the
six 33-entries, you have to alter the address behind the $-sign – and you have more than 120
entries for each of the four to eight vectors!).
Use the above mentioned functions instead, with which Excel can find the correct data for
each 6-digit activity automatically.
5.5 Customers’ Scepticism concerning Data
We worked with some customers who believed that it is necessary to check all companies
individually. E.g.: When we discussed a culture satellite account for a specific Austrian
region, they were waiting for us to call each and every event manager. After explaining that
this is not necessary since we rely on data from Statistic Austria, they claimed that no one
ever was called by Statistic Austria. It seems to be a good idea to prepare a few slides on
data collection and availability before presenting – just to have them with you.
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