Annex A: Indirect jobs methodology worked example
Published 15 October 2020
1. Introduction
For further transparency on the methodology used in the Indirect Jobs Supported by MOD Expenditure bulletin, Annex A has been designed to guide users through the process by a worked example.
2. Methodology in Practice
As a worked example, we can explore the indirect jobs in the Manufacturing of Metal Products (MOD SIC group 17) as a result of expenditure on Shipbuilding and Repairing (MOD SIC group 27).
From Table 6 of MOD’s Regional Expenditure bulletin’s supporting data tables we know that the direct spend on Shipbuilding and Repairing was £3,338 million in 2018/19. To see how many indirect jobs this sector alone supports we can take this figure as our MOD vector of final demand and set all other values to zero.
Let f be the MOD vector of final demand, where here we now have,
We then need to construct the aggregated Input-Output Table (IOT) according to MOD’s own 52 SIC groupings from the 100+ SIC codes used in the ONS’s IOT tables starting with the outlined IOT in Table 1. Note that this is a subset of the whole table for illustrative purposes.
Table 1: 2015 Input-Output Table (Domestic Use, Basic Prices, Product by Product, £ million)
01 | 02 | 03 | .. | 94n | .. | Total Demand for Products at Basic Prices | |
---|---|---|---|---|---|---|---|
01 | 2,203 | 10 | 0 | .. | 4 | .. | 23,521 |
02 | 2 | 282 | 0 | .. | 0 | .. | 1,069 |
03 | 0 | 0 | 40 | .. | 0 | .. | 1,968 |
.. | .. | .. | .. | .. | .. | .. | .. |
93n | 0 | 0 | 0 | .. | 0 | .. | 510 |
94n | 0 | 1 | 0 | .. | 177 | .. | 14,744 |
Total Consumption | 10,721 | 551 | 1,052 | .. | 5,000 | .. | 3,238,681 |
Imports of Goods and Services | 2,899 | 57 | 228 | .. | 835 | .. | 546,594 |
Taxes Less Subsidies on Products | 503 | -8 | 132 | .. | 959 | .. | 203,800 |
Taxes Less Subsidies on Production | -1,712 | 1 | 15 | .. | 0 | .. | 26,805 |
Compensation of Employees | 4,200 | 166 | 160 | .. | 7,497 | .. | 928,459 |
Gross Operating Surplus | 6,910 | 302 | 381 | .. | 453 | .. | 736,775 |
Total Output | 23,521 | 1,069 | 1,968 | .. | 14,744 | .. | 5,681,114 |
The ONS IOT displays domestic use in Agriculture, Forestry and Fishing against the separate SIC codes of 01, 02 and 03 respectively. For MOD expenditure these are grouped together as MOD SIC group 1, so we simply sum each entry in row and column for SIC codes 01, 02 and 03 to get the aggregated domestic use for MOD SIC group 1. This is repeated across all ONS SIC codes to transform the IOT into the now aggregated IOT table according to MOD’s 52 SIC groups as shown in Table 2.
Table 2: Aggregated 2015 Input-Output Table (Domestic Use, Basic Prices, Product by Product, £ million)
1 | 2 | 3 | .. | 48 | .. | 51 | 52 | |
---|---|---|---|---|---|---|---|---|
1 | 2,537 | 3 | 0 | .. | 0 | .. | 43 | 0 |
2 | 0 | 24 | 0 | .. | 0 | .. | 0 | 0 |
3 | 0 | 0 | 974 | .. | 0 | .. | 2 | 0 |
.. | .. | .. | .. | .. | .. | .. | .. | .. |
48 | 0 | 0 | 0 | .. | 0 | .. | 0 | 0 |
.. | .. | .. | .. | .. | .. | .. | .. | .. |
51 | 77 | 0 | 39 | .. | 0 | .. | 10,326 | 0 |
52 | 0 | 0 | 0 | .. | 0 | .. | 0 | 0 |
Total Consumption | 12,324 | 427 | 4,879 | .. | 44,318 | .. | 25,806 | 29,475 |
Imports of Goods and Services | 3,184 | 99 | 659 | .. | 11,204 | .. | 10,244 | 0 |
Taxes Less Subsidies on Products | 627 | 48 | 53 | .. | 9,365 | .. | 4,361 | 0 |
Taxes Less Subsidies on Production | -1,696 | 2 | 48 | .. | 0 | .. | 1,322 | 0 |
Compensation of Employees | 4,527 | 175 | 1,998 | .. | 56,978 | .. | 38,021 | 6,641 |
Gross Operating Surplus | 7,593 | -27 | 5,871 | .. | 21,045 | .. | 32,678 | 35 |
Total Output | 26,558 | 723 | 13,509 | .. | 142,911 | .. | 125,085 | 6,676 |
Since we are only interested in jobs supported in industry, figures under SIC group 48 for public administration and defence are then nilled out to remove later interactions within the public sector. We then create the A matrix by dividing each cell by the column sum in Total Output, with the result shown in Table 3. We also drop any rows and columns that do not directly relate to SIC groups to get the A matrix in the desired format of 52 rows by 52 columns for each SIC crosstab interaction.
Table 3: The A Matrix (Matrix of Coefficients, Product by Product, Nilled Public Administration)
1 | 2 | 3 | .. | 48 | .. | 51 | 52 | |
---|---|---|---|---|---|---|---|---|
1 | 0.0956 | 0.0037 | 0.0000 | .. | 0.0000 | .. | 0.0003 | 0.0000 |
2 | 0.0000 | 0.0336 | 0.0000 | .. | 0.0000 | .. | 0.0000 | 0.0000 |
3 | 0.0000 | 0.0004 | 0.0721 | .. | 0.0000 | .. | 0.0000 | 0.0000 |
.. | .. | .. | .. | .. | .. | .. | .. | .. |
48 | 0.0000 | 0.0000 | 0.0000 | .. | 0.0000 | .. | 0.0000 | 0.0000 |
.. | .. | .. | .. | .. | .. | .. | .. | .. |
51 | 0.0029 | 0.0000 | 0.0029 | .. | 0.0000 | .. | 0.0827 | 0.0000 |
52 | 0.0000 | 0.0000 | 0.0000 | .. | 0.0000 | .. | 0.0000 | 0.0000 |
A MOD version of the Leontief Inverse matrix according to MOD’s own SIC groups is then generated using the equation (I – A)-1, where I is the identity matrix.
Calculate the Leontief Inverse matrix,
This constructs the Leontief Inverse matrix shown above. Since in this worked example we are looking at interactions on Manufacturing of Metal Products from Shipbuilding expenditure it has been expanded to highlight figures against SIC groups 17 and 27.
MOD total demand across all SIC groups is then calculated by multiplying the Leontief matrix by the MOD vector of final demand, i.e. (I – A)-1 f, where f is defined by MOD expenditure on Shipbuilding and Repairing.
Calculate MOD Total Demand,
To remove the impact of direct expenditure on demand we subtract the MOD vector of final demand from total demand to return intermediate demand, i.e. that which occurs throughout the supply chain.
Calculate Intermediate Demand,
Then, if we focus on only SIC group 17 for Manufacturing of Metal Products, from the latest ONS SUT Supply of Products table, published in 2017, we see that total domestic output of products in basic prices for this industry was £49,513,600,000. This total output figure includes products in iron and steel, other metals and casting, fabricated metal products, and further elements arising from the installation and repair of metal products.
Using employment data from the BRES, we can adjust full-time and part-time employees into FTE employment equivalents. For SIC group 17 this equates to 376,893 FTE employees in this industry. Dividing output by employment here provides the output at basic prices per FTE employment as £131,373 per FTE employment.
The estimate of indirect jobs supported in the Manufacturing of Metal Products solely as a result of MOD expenditure on Shipbuilding and Repairing is then given by dividing the respective intermediate demand for metal work, i.e. SIC group 17, by the industry’s output per FTE employment.
358,046,753 / 131,373 = 2,725 indirect jobs
In this case we therefore estimate that MOD’s £3.3 billion of direct expenditure with UK industry in the Shipbuilding and Repairing sector supported a further 2,725 indirect jobs in the Manufacturing of Metal Products industry group.
3. Contact Details
Defence Expenditure Analysis Head of Branch
Tel: 030 679 84442
Email: Analysis-Expenditure-PQ-FOI@mod.gov.uk
Defence Statistics (Defence Expenditure Analysis)
Ministry of Defence
Oak 0 West, #6028
MOD Abbey Wood North
Bristol
BS34 8QW
For general MOD enquiries, please call: 020 7218 9000