Notes on estimating embodied
emissions in imports and exports
Phil Briggs1
October 2016
1
Phil Briggs is an independent researcher based in Wellington, New Zealand. He can be contacted at:
[email protected].
Contents
1 Introduction ........................................................................................... 3
2 General approach to estimating embodied emissions ................................... 3
3 Calculating embodied emissions for each New Zealand industry .................... 6
General method and results ...................................................................... 6
Domestic emissions ............................................................................... 10
Imported emissions ............................................................................... 11
Rearranging the imports table .............................................................. 11
Carbon intensity assumptions .............................................................. 11
Results .............................................................................................. 12
Improving the methodology ................................................................. 13
Estimates of domestic and imported emissions by industry ...................... 15
Exported emissions at the macroeconomic level ........................................ 15
4 A ‘ready reckoner’ approach to estimating total (scope 3) emissions for exports
............................................................................................................. 18
The method .......................................................................................... 18
A technical note .................................................................................... 20
5 Aspects of the input-output methodology ................................................. 22
6 References ........................................................................................... 24
Appendix A: An outline of the input-output model ........................................ 25
Capturing the full supply chain ................................................................ 28
Appendix B: A multi-regional input-output (MRIO) model .............................. 29
Appendix C: Exported emissions at the macroeconomic level ........................ 31
2
1 Introduction
These notes outline some initial work on estimating embodied emissions in
imports and exports. Most of this work involves the use of input-output models
and in the examples that are presented New Zealand data is used.
The note has four sections:




a brief section on the general approach to estimating embodied emissions,
including the use of input-output models
a section that documents how the embodied emissions have been calculated
for each New Zealand industry
a description of a ‘ready reckoner’ approach that an enterprise might use to
estimate the emissions in its own exports
a brief discussion of some aspects of the input-output model.
2 General approach to estimating embodied emissions
A country that uses border carbon adjustments will require that any enterprise
that is sending exports to that country will have to specify the embodied
emissions that are in those exports. Embodied emissions of a product are the
total greenhouse gases that are emitted in the process of making of that
product. These embodied emissions will include the emissions across the full
supply chain related to the product.
However, any figures for embodied carbon emissions will be estimates. We
cannot measure them directly each time a product or service is produced. We
therefore have to estimate the carbon emissions created based on the earlier
actual measures of emissions created using the same process to produce the
same product or service. Figures for embodied emissions will always be the
result of estimation processes. Nevertheless, the estimates need to be as
accurate as possible; they should be realistic values that exporters, customs
officials, and importers can have confidence in. Embodied emissions of exports
include:
a. emissions generated directly by the exporting enterprise in its own
production processes.
b. emissions that are produced by the exporter’s suppliers in the course of
making the goods and services that the exporter purchases from them.
c. emissions generated by other enterprises in the supply chain. These include,
for example, emissions of enterprises that are supplying the exporter’s
suppliers. But they also include emissions of the next level of suppliers, and
the next level, and so on.2
2
Suppliers and other enterprises in the supply chain can include enterprises that are located overseas. Hence
some of the emissions covered by (b) and (c) will be the emissions embodied in imports.
3
An exporter should have data on its own emissions – those covered in category
(a) above. The exporter may also be able to obtain data from its immediate
suppliers on the emissions that are contained in their supplies. So the exporter
may also be able to get data for emissions in category (b). However, it would
probably be an impossible task to obtain data for category (c), since this would
involve obtaining data from a large number of firms that the exporter doesn’t
normally have contact with.
There is a way of estimating the total emissions embodied in exports – including
category (c) emissions – and this involves using input-output tables. Virtually all
countries produce input-output tables showing the purchases made by each
sector of the economy from other sectors of the economy. By applying matrix
algebra to the input-output table it is possible to show how an increase in final
demand for products from one industry will flow through the economy and affect
the demand for products of all industries. The original increase in demand is
referred to as the increase in direct demand, while the flow-through effects are
referred to as an increase in indirect demand. In a similar way, the emissions in
category (a) above can be seen as being direct emissions, while the emissions in
categories (b) and (c) are indirect emissions.3
So the input-output approach can be adapted to calculate both direct and
indirect emissions for particular industries. It can also be adapted to calculate
direct and indirect emissions for particular products. However, this isn’t the only
way of calculating emissions. Some industries or firms, especially firms in the
most emission-intensive sectors (such as fuels, metals, transportation and
cement), will undertake detailed analyses of their various industrial processes in
order to measure the emissions that they produce. This process analysis is often
related to Life Cycle Analysis (LCA) where a firm will examine the full life cycle –
the making, delivery, servicing, and eventual disposal – of a product. Some
enterprises have used process analysis or LCA in combination with input-output
analysis in their efforts to estimate greenhouse gas emissions of products. This
hybrid approach, which uses both product level data and industry level data, is
often referred to as economic input-output based life-cycle assessment or EIOLCA.4
It seems that using only process analysis, without combining it with input-output
analysis, is not going to provide an adequate estimate of the embodied
emissions in products. This is because it is impossible to get right back up the
supply chain; no matter how far back up the chain the analysis goes there will
always be a part that is missing, and this part will be generating emissions that
3
The World Resources Institute (WRI) and the World Business Council of Sustainable Development (WBCSD)
use a slightly different approach. They define Tier 1 or Scope 1 emissions as being the direct emissions of an
entity. Tier 2 or Scope 2 emissions include the indirect emissions that are generated by purchased energy
(electricity, steam, and heat) that an entity purchases. Tier 3 or Scope 3 includes all other indirect emissions
not included in Tier 2. Taken together the three tiers include all direct and indirect emissions.
4
See Hendrickson et al (2006).
4
go uncounted. This is referred to as the boundary problem. The boundary for
domestic emissions is the full economy. It will always be necessary to use a
model, like the input-output model, to fill in the gaps in the supply chain that
process analysis doesn’t cover.5
The task then is to develop a set of rates for each type of export which when
applied to the export value will provide an estimate of the export’s embodied
emissions.
Points to note:

The value for embodied emissions for a product should include both direct
and indirect emissions. If it included for example only direct emissions, then
the total emissions related to making this product would be understated, and
the emissions levy would be too low.

This means that the exporter will need to provide information to customs
authorities on the total embodied emissions in the product, not just the
emissions produced directly by the exporter.

For most industries and enterprises, total embodied emissions will be
significantly higher than the exporter’s direct emissions.
So what exactly would be expected of exporters and their estimates of embodied
emissions? One possible set of requirements would be:

That exporters of high emission products – especially those that result in
process emissions while being made – be required to use EIO-LCA analyses in
order to assess the emissions content of their exports.

That other exporters are given two options:
o Using a set rate for emissions per unit of export sales. These rates would
be would be derived using the origin country’s official input-output table
and would reflect the supply chain structure of an ‘average’ domestic
producer of the product.
o Producing their own estimates of embodied emissions. Under this option
the exporter would need to provide documentation of the methodology to
customs officials.
If these two options are available a lower than industry average emitter is likely
to opt to use their own estimates. This will tend to increase the estimated
emission intensity of the producers using the set rate estimates. This is as it
should be, as the reason for introducing a charge on emissions is to encourage
producers and consumers to move to products and services with lower carbon
emissions embedded in their production. The next section of this paper sets out
how set rates for New Zealand have been derived. The section after that outlines
5
See Matthews et al (2008) and Pandy et al (2010).
5
an alternative approach to estimating embodied emissions that is likely to
produce more accurate estimates than the set rate method.
3 Calculating embodied emissions for each New Zealand
industry
General method and results
Statistics New Zealand’s input-output table for the year ended March 2006 has
been used to calculate the embodied emissions in industries’ deliveries to ‘final
demand’. Final demand includes exports, private consumption, government
consumption, and investment. It excludes intermediate consumption –
sometimes called business consumption – which is output that businesses
provide to other businesses.
The New Zealand economy is divided into 106 industries (see Table 1). Other
economies, especially large ones, would use a finer division, with more
industries.
The method of estimating embodied emissions uses the standard matrix
equation that is used to estimate the direct and indirect effects of a change in
final demand:
X = [I - A]-1 F
X is gross output, [I - A] -1 is the inverse of the Leontief matrix, and F is final
demand. More details on this equation are included in Appendix A.
6
Table 1 Estimated carbon intensities of New Zealand industries
Industry
Carbon intensity
1 Horticulture and fruit growing
2 Sheep, beef cattle and grain farming
3 Dairy cattle farming
4 Poultry, deer and other livestock farming
5 Forestry and logging
6 Fishing and aquaculture
7 Agriculture, forestry and fishing support services
8 Coal mining
9 Oil and gas extraction
10 Metal ore and non-metallic mineral mining and quarrying
11 Exploration and other mining support services
12 Meat and meat product manufacturing
13 Seafood processing
14 Dairy product manufacturing
15 Fruit, oil, cereal and other food product manufacturing
16 Beverage and tobacco product manufacturing
17 Textile and leather manufacturing
18 Clothing, knitted products and footwear manufacturing
19 Wood product manufacturing
20 Pulp, paper and converted paper product manufacturing
21 Printing
22 Petroleum and coal product manufacturing
23 Basic chemical and basic polymer manufacturing
24 Fertiliser and pesticide manufacturing
25 Pharmaceutical, cleaning and other chemical manufacturing
26 Polymer product and rubber product manufacturing
27 Non-metallic mineral product manufacturing
28 Primary metal and metal product manufacturing
29 Fabricated metal product manufacturing
30 Transport equipment manufacturing
31 Electronic and electrical equipment manufacturing
32 Machinery manufacturing
33 Furniture manufacturing
34 Other manufacturing
35 Electricity generation and on-selling
36 Electricity transmission and distribution
37 Gas supply
38 Water supply
39 Sewerage and drainage services
40 Waste collection, treatment and disposal services
41 Residential building construction
42 Non-residential building construction
43 Heavy and civil engineering construction
44 Construction services
45 Basic material wholesaling
46 Machinery and equipment wholesaling
47 Motor vehicle and motor vehicle parts wholesaling
48 Grocery, liquor and tobacco product wholesaling
49 Other goods and commission based wholesaling
50 Motor vehicle and parts retailing
51 Fuel retailing
52 Supermarket and grocery stores
53 Specialised food retailing
54 Furniture, electrical and hardware retailing
55 Recreational, clothing, footwear and personal accessory retailing
7
(kg CO2e per dollar
of final demand)
2.200
3.588
3.066
0.531
0.363
0.711
0.416
0.367
0.225
0.400
0.308
1.908
0.491
1.883
0.586
0.500
1.129
0.485
0.403
0.537
0.398
0.367
1.485
0.621
0.457
0.555
1.005
1.681
0.645
0.293
0.424
0.378
0.407
0.295
1.891
0.490
0.761
0.192
0.142
0.226
0.309
0.368
0.313
0.273
0.341
0.178
0.189
0.372
0.223
0.138
0.176
0.268
0.244
0.164
0.179
Table 1 (continued) Estimated carbon intensities of New Zealand
industries
Industry
Carbon intensity
(kg CO2e per dollar
of final output)
56 Department stores
0.148
57 Other store based retailing; non-store and commission based retailing
0.210
58 Accommodation
0.278
59 Food and beverage services
0.297
60 Road transport
1.876
61 Rail transport
1.702
62 Other transport
0.750
63 Air and space transport
1.448
64 Postal and courier pick up and delivery services
0.298
65 Transport support services
0.262
66 Warehousing and storage services
0.272
67 Publishing (except internet and music publishing)
0.411
68 Motion picture and sound recording activities
0.149
69 Broadcasting and internet publishing
0.117
70 Telecommunications services including internet service providers
0.084
71 Library and other information services
0.072
72 Banking and financing; financial asset investing
0.056
73 Life insurance
0.060
74 Health and general insurance
0.063
75 Superannuation funds
0.127
76 Auxiliary finance and insurance services
0.078
77 Rental and hiring services (except real estate); non-financial asset leasing
0.118
78 Residential property operation
0.109
79 Non-residential property operation
0.188
80 Real estate services
0.160
81 Owner-occupied property operation
0.082
82 Scientific, architectural and engineering services
0.151
83 Legal and accounting services
0.070
84 Advertising, market research and management services
0.153
85 Veterinary and other professional services
0.107
86 Computer system design and related services
0.126
87 Travel agency and tour arrangement services
0.192
88 Employment and other administrative services
0.126
89 Building cleaning, pest control and other support services
0.165
90 Local government administration
0.169
91 Central government administration and justice
0.137
92 Defence
0.189
93 Public order, safety and regulatory services
0.116
94 Preschool education
0.077
95 School education
0.103
96 Tertiary education
0.164
97 Adult, community and other education
0.177
98 Hospitals
0.138
99 Medical and other health care services
0.093
100 Residential care services and social assistance
0.117
101 Heritage and artistic activities
0.128
102 Sport and recreation activities
0.244
103 Gambling activities
0.086
104 Repair and maintenance
0.193
105 Personal services; domestic household staff
0.104
106 Religious services; civil, professional and other interest groups
0.159
Sources: Input-output data for the year ended March 2007 is from Statistics New Zealand. Domestic
emissions data is based on data from Romanos, Kerr and Will (2014). Imported emissions data is
based on WRI data.
8
The equation is used to calculate the effect of a $1 increase in final demand for a
particular industry’s output – say the printing industry’s output – on the output
of all the industries in the economy. The results reflect not only the initial $1
increase in the printing industry’s output – the direct effect – but also the
indirect effects on the output of other companies, most of which will be in other
industries. These indirect effects are the result of the printing industry’s higher
demand for supplies from these companies, given that it now needs these
supplies in order to satisfy the rise in its own output.
We now take the results – the rises in each industry’s output due to the $1
increase in the printing industry’s output – and calculate the emissions related to
these rises in output. For each industry, we take its calculated rise in output and
multiply it by the industry’s emissions rate. Each industry’s carbon emissions
intensity rate would have been calculated earlier, as total emissions divided by
total output. So we now get, for each industry, the emissions that result from
the initial $1 rise in the printing sector’s output. Summing all these we find that
the total emissions from this $1 rise in printing sector output are 0.398
kilograms of CO2 equivalents (see industry 21 in Table 1). This figure – 0.398
kgCO2e per dollar of final demand – is a measure of the printing industry’s
‘carbon intensity’. In general, carbon intensity can be thought of as being
embodied emissions per unit of demand. Note these can also be expressed as
embodied emissions per unit of production for example 48 kilograms per tonne
of alumina or aluminium.
Table 1 gives us a carbon intensity figure, and in effect a ‘set rate’, for each
industry. Suppose that an enterprise in the printing industry was exporting
products worth $NZ100,000 in 2015.6 The exporter would first need to express
this amount in 2006/07 dollars, since the figures in Table 1 were calculated
using the input-output table for the year ended March 2007. This would be done
using the producer price outputs index for the printing industry. This index
shows that output prices increased by just over 14.5% between the base year
and the start of 2015. Using this gives a value of $NZ87,323 for the exports in
terms of 2006/07 dollars. The exporter would now multiply this figure by the
printing industry’s carbon intensity from Table 1, which is 0.398. This gives an
estimate for total embodied emissions of 34,755 kilograms, or 34.755 tonnes, of
CO2 equivalents.
Note that the carbon intensities in Table 1 cover both domestic emissions and
imported emissions. Domestic emissions are those made by New Zealand
enterprises. Imported emissions are the emissions that are embodied in the
products imported by New Zealand enterprises. Details on how these two types
of emissions were handled are outlined below.
6
We will assume that this value of $NZ100,000 excludes indirect taxes, subsidies, and transport costs related
to delivering the exports; this makes it consistent with values used in the input-output table.
9
Domestic emissions
Data for domestic emissions was based on data from Romanos et al (2014). This
data covered fuel emissions and process emissions for each industry.
However, the domestic emissions for two industries – ‘other transport’ (which
includes sea transport) and ‘air and space transport’ were modified. Formerly
the data covered only domestic emissions made by these industries. We
estimated the emissions from international transport activities that enterprises in
these industries were undertaking. These estimates were derived using data
from the input-output use table on each industry’s total purchases of fuel. The
adjustments made the coverage of emissions consistent with the coverage of
economic activity in the input-output table.
The modified dataset for emissions was used to calculate an emissions rate –
CO2 equivalents per NZ dollar of gross output – for each industry.
Direct and indirect output was calculated using the formula:
X = [I-A]-1F
where X is total output, [I-A]-1 is the Leontief inverse, and F is final demand.
For more details on this and worked examples of input-output calculations see
Dowling (2001).
For each industry, the cell value of F for an industry, say industry i, was set to 1,
with the other cells of F being set to 0. So X, as calculated, is a vector showing
the increases in each industry’s output that stems from a $1 increase in final
demand for products from industry i.
The column vector X is then used to calculate emissions. Each cell is multiplied
by its corresponding emissions rate. So the first cell, which shows the increase in
output in the ‘horticulture and fruit growing’ industry, is multiplied by the
emissions rate for that industry.
We do the same thing for all the other cells of X and sum the results. The final
value is the total emissions that have resulted from a $1 increase in output from
industry i. This result includes emissions made by direct and indirect output and
is industry i’s capital intensity. If we subtract from this industry i’s emissions
rate – which is in fact the direct demand component of carbon intensity – then
we get the indirect demand component of industry i’s carbon intensity. This
component covers the emissions generated by industry i’s domestic supply
chain.7
Note that the carbon intensity that has been described here covers only
domestic emissions. We will refer to it as the domestic carbon intensity.
7
An industry’s supply chain includes its suppliers, its suppliers’ suppliers, and so on.
10
Imported emissions
Each column of the input-output table includes a cell showing an industry’s
imports. For a particular industry, such as the ‘horticulture and fruit growing’
industry, the industry’s imports will have been incorporated into the industry’s
output. That is, they will have been incorporated into the values that are shown
in the industry’s output row of the table, although they are not pulled out and
identified separately in that row. An industry’s imports will contain embodied
emissions. So these imported emissions need to be estimated, and added to the
domestic emissions.
The general approach taken in estimating the imported emissions incorporated
in each industry’s output was to:
1. Estimate the embodied emissions in each industry’s imports.
2. Derive an ‘imported emissions intensity rate’ for each industry, calculating
this as imported emissions divided by the industry’s total output.
3. Use these imported emissions intensity rates, together with output from
the formula X = [I -A]-1, to calculate direct and indirect emissions for
each industry. This is the same approach as used for domestic emissions.
Note that an industry’s indirect imported emissions are the imported
emissions in products that it obtains from its domestic supply chain.
Step 1, estimating the embodied emissions in total imports, was the difficult
part. While some estimates have been produced, these should be regarded as
being interim estimates only. They can certainly be improved upon.
Nevertheless, here is an outline of what was done.
Rearranging the imports table
The supporting tables that accompany the New Zealand input output table
include one that shows the types of products that each industry is importing. We
modified this so that it showed the industries that were producing these
imported products. We did this using information from Statistics New Zealand
which showed a rough concordance between product types and the types of
industry that were making these products. In doing this, we assumed that this
concordance between products and industries, which was based on
classifications used for New Zealand data, would also provide a reasonable
picture of the concordance between overseas products and the industries that
make them.
The modified table showed exports from overseas industries across the rows and
imports to New Zealand industries down the columns.
Carbon intensity assumptions
It was assumed that each overseas industry would the same carbon intensity as
the domestic carbon intensity of the corresponding industry in New Zealand.
11
Each row of the modified imports table was multiplied by the appropriate
domestic carbon intensity. Summing the columns of the table gave us initial
estimates of the imported emissions for each New Zealand industry. It also gave
us estimates of the emissions in imported products that went straight into final
demand categories i.e. New Zealand consumption and investment.
Results
Total imported emissions were estimated at 22,565 ktonnes CO2e.
Clearly these estimates are rough, since we have relied on New Zealand data to
estimate overseas emissions. We might expect the emissions for imported
products to be somewhat higher than our initial estimates, given that a
substantial proportion of New Zealand imports are from China, where carbon
intensities tend to be high.
As a check on our initial figure for total emissions, another approach was used.
UN data on GDP and total imports, both in nominal US dollars, was obtained for
virtually every country for 2006. ‘GDP plus imports’ was used as a measure of a
country’s final demand.8 Data on total emissions in each country in 2006 was
obtained from the World Resources Institute. Dividing emissions by ‘GDP plus
imports’ gave a value for each country of the average emissions in final demand
categories. Exports make up one of these final demand categories, so we can
apply the average emissions rate to a country’s exports.
These average emission intensity rates were then weighted by each country’s
merchandise exports to get an overall average. This average was then multiplied
by New Zealand’s total imports, as shown in the New Zealand input output table.
This gave a value of 23,224 ktonnes CO2e for total imported emissions, which
was 2.9% higher than the initial total that had been derived.
The difference between the two values was not as large as expected. The high
emissions in imports from China were offset to some extent by lower emissions
in imports from more developed countries.
As a final step in deriving estimates of imported emissions by industries, we
factored up the initial estimates by 2.9% to bring them into line with the higher
aggregate estimate. The final estimates show total imported emissions of
23,224 ktonnes CO2e, with 14,606 ktonnes CO2e being imported by industries,
and 8,618 ktonnes CO2e being imported directly into final demand. Given that
domestic emissions by industry are estimated at 72,345 ktonnes CO2e,
industry’s imported emissions account for around 17% of total industry
emissions.
8
The identity for GDP is: GDP = consumption + investment + exports – imports.
Hence GDP + imports = consumption + investment + exports (i.e. final demand).
12
We now turn back to our input-output model of the New Zealand economy. Our
final estimates of industrys’ imported emissions were used in steps 2 and 3 as
outlined earlier, at the start of this section on imported emissions. That is, we
derived ‘imported emissions rates’ for each industry, and used these to calculate
both direct and indirect imported emissions for each industry.
Improving the methodology
Clearly the methodology outlined here produces only approximations of imported
emissions and needs to be improved upon.
Ideally, emissions data would be available for imports by each New Zealand
industry, broken down by both country and industry of origin. An international
database – combining both national input-output tables and emissions data –
would be needed in order to produce such data. There are a number of
databases that cover such data, with most of these having been assembled for
use by multi-regional input-output (MRIO) models.
MRIO models generally include industries for a number of countries. For example
a model may include 20 industries in each country. If the model covers say 20
countries, then it will include a total of 400 industries. All of these industries are
linked, with industries supplying intermediate products to other industries,
including industries in other countries. Each industry also supplies ‘final demand’
products to consumption and investment in its own country and also to
consumption and investment in other countries.
In an MRIO model, a country’s exports to other countries are split between
intermediate products and final products, with only final products being part of
final demand. This is problematic since in an input-output model the final
demand categories are the exogenous variables, the ones whose values are set
outside the model and then fed into the model to see what the results are. Since
intermediate exports are not part of final demand in an MRIO model, we cannot
set a value for an intermediate product and then use the model to see what the
supply chain looks like.
In contrast, in a single region input-output (SRIO) model, like the one we have
been using for the New Zealand economy, all exports – including exports of
intermediate products and final products – are exogenous. So we can use this
type of model to estimate the supply chains of exports, and the emissions made
by their supply chains.
MRIO models can be used to model the supply chains of final products, which
are products used in consumption or investment.9 An MRIO model can be used
for example to model the global supply chain of a car, where the final product is
assembled in say Germany.
9
MRIO modellers tend to use the term ‘consumption’ to cover both consumption and investment products.
13
Extensive work is being done on analysing MRIO supply chains so that
intermediate exports from a country can be traced to final demands in other
countries. 10 Still, estimating the supply chains and the embodied emissions of
exports of intermediate-type products, as well as final products, will require the
use of an SRIO-type model.
In the case of estimating the emissions imported by New Zealand industries, a
way of doing this would be to calculate the embodied emissions in the products
of each of the countries that are exporting to New Zealand. This would involve
using a SRIO model for each of these countries. This would clearly take a lot of
work.
This approach is used in Ahmad and Wyckoff (2003). This study used SRIO
models for all of the major economies of the world, with the emissions in a
particular country’s imports being calculated as the sum of emissions exported
to that country from other countries.11 Note that each country’s exported
emissions will contain both domestic emissions and imported emissions. So
including new estimates of imported emissions in the SRIO for a particular
country will affect its exported emissions. These will in turn affect the exported
emissions of other countries, and so on. The authors use an iterative process in
order to account for this. The individual SRIO models are rerun until all the
results stabilise. This study was extended and updated in Nakano et al (2009).
These studies demonstrate the value of using an international input-output
database for obtaining accurate estimates of imported emissions for a particular
country. With respect to estimating imported emissions for New Zealand, this is
an area for further work.
Robust estimates of imported emissions would certainly be needed if an official
country table of industries’ carbon intensities was to be produced for use by
exporters. Inaccurate estimates of imported emissions would affect the accuracy
of the figures in the official table.
Over recent years, a number of international input-output databases have been
developed. Most of these have been developed in the light of growing interest in
MRIO modelling. 12 Nevertheless, such databases could also be used to run a
suite of linked SRIO models that would provide accurate estimates of imported
emissions by industry. Interestingly, some of the recently developed databases
have been based on GTAP data, partly because this data has detailed
breakdowns of the agricultural sector.
Appendix B contains an example of a very simple international MRIO model.
10
See for example Meng, Peters, and Wang (2014).
The Ahmad and Wyckoff model is sometimes referred to as being an MRIO model. However, it is in effect a
suite of linked SRIO models.
12
Sato (2012) and Tukker and Dietzenbacher (2013) review the major international models.
11
14
Estimates of domestic and imported emissions by industry
While our estimates of imported emissions for New Zealand are rough they do
give us some indication of the likely scale of these emissions, and how they
might compare with domestic emissions.
Figure 1 breaks down total emissions rates, showing the imported components
of both direct and indirect emissions. The total emissions rates in this chart are
the same as those in Table 1.
Exported emissions at the macroeconomic level
The general focus in this report is on looking at how calculated industry rates for
embodied emissions could be used at the enterprise level. However, industry
rates can also be used at the macroeconomic level to estimate the total
emissions that are embodied in a country’s exports. For more on this see
Appendix C.
15
0
Horticulture, fruit growing
Sheep, beef cattle & grain
Dairy cattle farming
Poultry, deer, other livestock
Forestry and logging
Fishing and aquaculture
Agriculture, forestry, fishing support
Coal mining
Oil and gas extraction
Metal ore and non-metallic minerals mining
Exploration and other mining support
Meat and meat product manu
Seafood processing
Dairy product manufacturing
Fruit, oil, cereal and other food …
Beverage and tobacco product …
Textile and leather manufacturing
Clothing, knitted products,footwear …
Wood product manufacturing
Pulp, and paper product manufacturing
Printing
Petroleum and coal product manufacturing
Basic chemical and basic polymer…
Fertiliser and pesticide manufacturing
Pharmaceutical, cleaning & other chem …
Polymer product and rubber product…
Non-metallic mineral product…
Primary metal and metal product…
Fabricated metal product manufacturing
Transport equipment manufacturing
Electronic and electrical equipment …
Machinery manufacturing
Furniture manufacturing
Other manufacturing
Electricity generation and on-selling
Electricity transmission and distribution
Gas supply
Water supply
Sewerage and drainage services
Waste collection, treatment and disposal …
Residential building construction
Non-residential building construction
Heavy and civil engineering construction
Construction services
Basic material wholesaling
Machinery and equipment wholesaling
Motor vehicle and motor vehicle parts …
Grocery, liquor and tobacco product…
Other goods and commission based …
Motor vehicle and parts retailing
Fuel retailing
Supermarket and grocery stores
Figure 1 Estimated embodied emissions in final output of New Zealand industries
Kg CO2e per dollar of final output
4
3.5
3
Indirect, imported component
Indirect, domestic component
2.5
Direct, imported component
2
Direct, domestic component
1.5
1
0.5
Source: See Table 1
16
0
-0.5
Specialised food retailing
Furniture, electrical and hardware retailing
Recreational, clothing, & footwear retailing
Department stores
Other store based retailing; non-store and …
Accommodation
Food and beverage services
Road transport
Rail transport
Other transport
Air and space transport
Postal and courier pick up and delivery services
Transport support services
Warehousing and storage services
Publishing (except internet and music …
Motion picture and sound recording activities
Broadcasting and internet publishing
Telecommunications & internet services
Library and other information services
Banking and financing; financial asset investing
Life insurance
Health and general insurance
Superannuation funds
Auxiliary finance and insurance services
Rental and hiring services & non-financial …
Residential property operation
Non-residential property operation
Real estate services
Owner-occupied property operation
Scientific, architectural and engineering …
Legal and accounting services
Advertising, market research, management…
Veterinary and other professional services
Computer system design and related services
Travel agency and tour arrangement services
Employment and other administrative services
Building cleaning, pest control & other services
Local government administration
Central government administration and justice
Defence
Public order, safety and regulatory services
Preschool education
School education
Tertiary education
Adult, community and other education
Hospitals
Medical and other health care services
Residential care services and social assistance
Heritage and artistic activities
Sport and recreation activities
Gambling activities
Repair and maintenance
Personal services; domestic household staff
Religious services; civil, professional & other …
Figure 1 (continued) Estimated embodied emissions in final output of New Zealand industries
Kg CO2e per dollar of final output
4
3.5
3
Indirect, imported component
2.5
Indirect, domestic component
Direct, imported component
2
Direct, domestic component
1.5
1
0.5
Source: See Table 1.
17
4 A ‘ready reckoner’ approach to estimating total (scope
3) emissions for exports
The method
We saw earlier how a printing firm could estimate the embodied emissions in its
imports using the set rate method. In the example used, the embodied
emissions were calculated as being equal to 34.755 tonnes of CO2 equivalents.
This estimated figure will be substantially higher than printing company’s figure
for its own emissions, since the estimate includes not only the enterprise’s direct
emissions but also indirect emissions – that is, those that are made by other
enterprises in the supply chain. We will refer to the combined rate for direct and
indirect emissions as either total emissions or Scope 3 emissions, which is the
term used by the WRI and WBCSD.
Getting an initial figure for an enterprise’s total emissions using the set rate
method is straightforward. However, such a figure may not be particularly
accurate. This is because:



The printing firm’s own (direct) emissions in relation to its output may be
either higher or lower than the ‘average’ emissions rate for the printing
industry that has been used to derive the figures in Table 1.
The distribution of inputs from other industries into the printing firm’s
production processes may be quite different from the distribution shown in
the input-output table. For example inputs from the pulp and paper industry
as a proportion of the printing company’s total output may be lower than that
shown in the input-output table, which is based on company averages.
The carbon intensities the enterprise’s suppliers may differ from the average
industry intensities that have been calculated using the input-output table,
and which are shown in Table 1. For example, the enterprise’s electricity
supplier may have a lower carbon intensity than the industry average.
An enterprise could probably get a more accurate estimate of its scope 3
emissions using an alternative method, which can be called a ‘ready reckoner’
approach. This approach also uses pre-prepared data like that in Table 1, but in
a more targeted way.13 This approach is similar to building an extra column and
13
In the examples that follow we refer to data shown in Table 1. However, as shown by Berners-Lee et al
(2011) this data should be modified before it is used by businesses. Some of the industries in Table 1 – those
that provide wholesale and retail services – are ‘margin companies’. They generally do not transform products
– they simply buy and sell them. So in the input-output table their purchases and sales do not include the
products that they buy and sell for profit. They relate mainly to the margins that they make. Berners-Lee et al
(2011) get around this issue with respect to UK data by distributing the emissions for margin industries across
the industries that they serve (i.e. those that are supplying the products for resale). Berners-Lee et al also
modify the embodied emissions rates for each industry so that the ‘rate per dollar’ applies to prices including
direct taxes. Similar adjustments could be made to the figures in Table 1, but this has not yet been done.
row in an input-output table in order to represent an enterprise. But it avoids the
need to run an input-output model. Instead the calculations can be done in a
spreadsheet.
An enterprise using this approach would first estimate its total scope 3
emissions, and its total emissions rate. It would then modify the approach in
order to estimate the emissions rates for particular products. This would involve
apportioning a share of the enterprise’s inputs to each product type.
The alternative method for estimating scope 3 emissions for an enterprise is as
follows:
1. Collect data on the enterprise’s own emissions over the period that is being
looked at. This data will cover the emissions related to fossil fuel use, and
any greenhouse gas emissions that result from particular industrial
processes. Some organisations will already be producing this data and
supplying it to the government agency that compiles national greenhouse gas
inventories.
2. Collect data on the embodied emissions on all imports that have been
consumed or transformed in the enterprise’s production processes. Excluded
from this will be purchases of fixed assets (plant and machinery) that will be
owned and used by the enterprise itself. Getting this data on imports should
be easy once an international agreement on charging is in place, since the
enterprises that are supplying the imports will have to provide estimates of
the embodied emissions in their products. Before then, the enterprise should
ask the suppliers of the imports to provide estimates, or alternatively use
overseas input-output tables to estimate the embodied emissions.
3. List all the purchases from all immediate domestic suppliers that were used
or consumed in the period. Exclude from these purchases any indirect tax
component, like GST. Again, fixed assets – including land and buildings as
well as plant and machinery – should be excluded. Include purchases from
the enterprise’s bank, accountant, and other service agencies. Identify the
industry group to which each of these suppliers belongs, and find the
industry’s carbon intensity in Table 1. For example the figure for gas supply is
0.806 kilograms of CO2e per dollar of output. Multiply this by the enterprise’s
spending on gas to get the total amount of CO2e. Note that this amount
includes the total direct and indirect emissions that are produced in delivering
this amount of gas. That is, it covers all the emissions made by the gas
industry and the gas industry’s supply chain. Similarly the figure of 1.915
kilograms of CO2e per dollar of output for the road transport industry includes
all the emissions made by the road industry and the road industry’s supply
chain. Once the figures for each industry have been calculated, these are
added up to get a figure for the enterprise’s full domestic supply chain.
19
4. Adding the figures for emissions obtained from stages 1, 2, and 3 gives an
alternative estimate of the enterprise’s scope 3 emissions. We can divide this
by the total output or sales of the enterprise over the period to get the
enterprise’s carbon intensity. A firm might find that its alternative figure is
substantially different from the figure for its industry that is in Table 1. If so,
this will reflect the different method: the alternative figure includes the actual
figure for the enterprise’s direct emissions and it also takes account of the
distribution of inputs across immediate suppliers. However, more fine tuning
to the alternative estimate will still be possible. It may be that the total
emissions rate for say the road transport industry looks a little high. The
enterprise may be using a road transport operator that seems more efficient
than other operators. In this case the enterprise could contact its road
transport operator and ask what its carbon intensity is. The road transport
operator could calculate its own figure using a similar process to the one we
are describing here. It would of course need to cover indirect as well as direct
emissions. If the road transport operator’s figure was actually lower, and
certification of this could be provided, our enterprise could use this lower
figure in its own calculations. And it could take a similar approach with
respect to its figures for other suppliers.
Enterprises will tend to focus on the total emissions of their energy suppliers –
especially electricity companies. In a country like New Zealand, they will also
focus on suppliers in agricultural industries, since as the Table 1 shows,
emissions in these industries are relatively high.14
A technical note
We can use the framework of the input-output model to better understand what
we are doing in using this alternative approach.
The standard model is
X = [I - A]-1 F
And as outlined in Appendix A this is equivalent to
X = [I + A + A2 + A3 + ...] F
where the I in the bracket represents the direct component of output, and the
remaining terms represent the indirect component.
So
[I - A]-1 F = [I + A + A2 + A3 + ...] F
14
The emissions rates for the electricity industries in New Zealand, which are shown in Table 1, will probably
seem low when compared to other countries. This is due to the relatively high proportion of electricity that is
generated from hydro and geothermal sources in New Zealand.
20
If we now premultiply F by A on both sides we get
[I - A]-1 AF = [I + A + A2 + A3 + ...] AF
And then we get
[I - A]-1 AF = [A + A2 + A3 + ...] F
We can see that the expression on the right side of this equation is simply
indirect demand.
So we can calculate an industry’s indirect demand by premultiplying AF by the
Leontief
inverse
[I - A]-1. And when F represents output of say $NZ1 for one industry, like the
‘horticulture and fruit growing industry’, then AF is simply the column of A for
that industry. The cells of this column will show the amount of each supply
industry’s output that is being purchased in order to satisfy final demand of
$1NZ. If F represented final demand for one industry’s products of say $NZ1500
then AF would be a vector where each cell would show the amount of each
supply industry’s output that is being purchased in order to satisfy final demand
of $NZ1500.
We could apply the [I-A]-1 matrix to this AF vector, and follow this by applying
industry emissions rates to get emissions. Instead though we could apply [I-A]-1
matrix, in turn, to each cell of the AF vector, then apply emissions rates, and
finally add all the results. The end result will be the same as that obtained by
applying the [I-A]-1 matrix to AF in one go. This second approach is equivalent
to multiplying each cell of the AF vector by the supply industry’s carbon
intensity.
This second approach is the one we are using in our alternative method for
estimating an enterprises carbon intensity. In our alternative approach though,
we don’t use the coefficients of A to calculate the first round of purchases from
the supply chain (i.e. to calculate the vector AF). Instead we use actual values of
purchases. However, we do in effect use values from the A matrix to calculate
subsequent rounds of purchases that occur within the supply chain.
The alternative method makes use of all the data that an enterprise has – data
on its own emissions, data on imported emissions (assuming these are
available), data on purchases from domestic suppliers, and actual total
emissions rates of domestic suppliers (where available) – in order to calculate its
own emissions. It should produce a more accurate, and more useful, result than
that obtained by using the set industry emissions rate.
As noted earlier, it should also give results that are very similar to those
obtained from an input-output model, where the enterprise is treated as a
separate industry in the context of that model.
21
5 Aspects of the input-output methodology
The alternative method outlined above takes into account an enterprise’s direct
and imported emissions, and also the distribution of an enterprise’s suppliers
across industries. However, it still depends on the results from an input-output
model, like those in Table 1, to calculate the emissions that are embodied in the
supply chains of an enterprise’s suppliers. Just how good are these input-output
results? It is difficult to know, without extensive empirical testing being done.
We have already seen from our example above regarding a printer, that inputoutput tables are often dated, even by the time they are published. Compiling
accurate input-output tables takes a long time. As we have seen, we got around
this problem to some extent in our example by adjusting the value of the
printer’s exports so that they were in 2006/07 dollars and hence were consistent
with the values used in the input-output table. However, it’s possible that the
economy that the input-output table describes could have changed in structure
since the table was compiled, although it could also be argued that any
structural changes are likely to occur gradually rather than suddenly.
Many economists are uneasy about using input-output models since they use
‘fixed coefficients’. A basic assumption of the input-output model is that a
change in an industry’s output will produce the same proportionate change in its
purchases of supplies. So an industry’s supplies from other industries will remain
constant, or ‘fixed’, relative to its own output. But the world doesn’t necessarily
work that way. Prices of products change. And if the prices of products from a
supply industry show a sharp rise, then the purchasing industry is likely to take
steps that will allow it to purchase fewer of the supply industry’s products.
Computable general equilibrium (CGE) models introduce prices into an inputoutput type framework. But they are complex, and tend to become ‘black
boxes’, with users not having a very clear idea of what is going on inside the
model. In general CGE models are used mostly for ‘what if’ type analysis of
economic policy changes.
CGE models are unlikely to be a satisfactory
substitute for input-output models in calculating embodied emissions.
A strength of the input-output approach is that it provides an estimate of the
additional output that occurs across the whole domestic supply chain. The basic
equation that it uses, X = [I - A]-1 F, can also be expressed as a power series
of A.15 The first term of this series accounts for the additional output arising
from the initial shock to final demand, F. The second term accounts for the
additional output arising from immediate suppliers. The third term accounts for
the additional output arising from suppliers to the suppliers, and so on. The
additional output from the initial shock gets smaller the further back we get in
the supply chain. So the value of series converges towards a final value, and
that value is equal to [I - A]-1.
15
For more on this, see Appendix A.
22
So the trade off with input-output analysis is that while it estimates the
additional output of the full supply chain it does this by assuming that the cells
of A – the coefficients representing inputs to output – remain fixed.
An alternative to using input-output estimates is for an enterprise to work back
up the supply chain, especially along branches that ultimately produce a large
amount of embodied emissions, and to measure the emissions at each stage.
This would in effect be an exercise in Life Cycle Analysis (LCA). However such
analyses can be time-consuming and expensive. Also at some point, the analysis
will probably have to stop. It would be impractical to keep tracing the supply
chain back further and further. So the LCA will have a boundary. Ironically,
input-output results – like those in Table 1 – could be used to estimate the full
supply chain emissions of each enterprise that was at the boundary of the full
LCA analysis. The input-output results will fill in the missing bits, and will in fact
be helpful in determining just how much of the full supply chain the LCA
managed to cover.
As noted earlier, the reality is that figures for embodied emissions are always
going to be estimates. And despite the shortcomings of input-output analysis, it
does give us a framework for analysing the flow of embodied emissions through
the economy. Also, it allows us to make estimates of indirect emissions that
cover an industry’s full supply chain, and to do this in a consistent way, for all
industries. The input-output methodology is transparent and the results are
reasonably understandable. Without the use of input-output tables, estimates of
embodied emissions will almost always be understated, because of the boundary
problem.
23
6 References
Ahmad, Nadim, and Andrew Wyckoff (2003) Carbon dioxide emissions embodied
in international trade of goods, OECD science, technology and industry working
paper 2003/15.
Berners-Lee, M, D C Howard, J Moss, K Kaivanto, W A Scott (2011) ‘Greenhouse
gas foot printing for small businesses – the use of input output data’, Science of
the Total Environment, 409, pp883-891.
Dowling, Edward T (2001) Schaum’s outline: Introduction to mathematical
economics, third edition, McGraw Hill.
Gillmore, David and Phil Briggs (2010) ‘World trade interdependencies: a New
Zealand perspective’, Bulletin, vol 73 no 2, Reserve Bank of New Zealand, June.
Hendrickson, C. T., Lave, L. B., Matthews, H. S. (2006). Environmental life
cycle assessment of goods and services: an input-output approach. Resources
for the Future Press.
Matthews, H Scott, Chris T Hendrickson, and Christopher L Weber (2008) ‘The
importance of carbon footprint estimation boundaries’, Environment Science and
Technology, 42, pp5839-5842.
Meng, Bo, Glen Peters, Zhi Wang (2014) Tracing CO2 emissions in global value
chains, Office of Economics working paper no 2014-12A, US International Trade
Commission.
Miller, Ronald E and Peter D Blair (2009) Input-output analysis: foundations and
extensions, second edition, Cambridge University Press.
Nakano, Satoshi, Asako Okamura, Norihisa Sakurai, Masayuki Suzuki, Yoshiaki
Tojo, and Norihoko Yamano (2009) The measurement of CO2 embodiments in
international trade, OECD science, technology and industry working paper
2009/03.
Romanos, Carl, Suzi Kerr and Campbell Will (2014) Greenhouse gas emission in
New Zealand: a preliminary consumption-based analysis, Motu working paper
14-05, Motu Economic and Public Policy Research, Wellington.
Sato, Misato (2012) Embodied carbon in trade: a survey of the empirical
literature, Centre for Climate Change Economics and Policy working paper no 89,
Leeds.
Tukker, Arnold, and Erik Dietzenbacher (2013) ‘Global multiregional input-output
frameworks: an introduction and outlook’, Economic Systems Research, 25:1, 119.
24
Appendix A: An outline of the input-output model
Table A1 is a compressed version of the input-output table for New Zealand. The
full table contains 106 industries but here we combine them into just three:
primary producers, goods producers, and services.
Table A1 Three-industry input-output table for New Zealand
Values are NZ dollars, billions
Primary
Goods
Final
producers
producers
Services
demand
Primary producers
4.4
14.0
0.8
5.9
Goods producers
2.8
38.7
15.2
66.2
Services
5.6
19.6
58.6
110.9
Imports
1.9
14.7
11.0
23.1
Taxes on products
0.2
0.8
2.0
13.4
Labour
2.8
17.7
53.9
Other factor income
7.4
17.4
53.2
Total input
25.1
123.0
194.7
219.4
Total
output
25.1
123.0
194.7
50.6
16.3
74.4
78.1
562.2
Source: Derived from Statistics New Zealand's input-output table for the year ended March 2007.
The top three rows of the table show output, or sales, for each industry, and
which industry these sales go to.16 The first row for example shows sales by
primary producers. This industry makes sales of $4.4b to enterprises that are in
its own industry. It also makes sales of $14.0b to enterprises in the goods
producing industry and $0.8b to enterprises in the services industry. These sales
to industries are called intermediate demand or intermediate consumption.
Other sales go to satisfying final demand, which covers the end use of products.
Components of final demand include exports, private consumption, government
consumption, and investment.
The first three columns of the table show the inputs, or purchases, for each
industry. So primary producers purchase products worth $4.4b from other
primary producers. They also buy products worth $2.8b from goods producers
and products worth $5.6b from services. They also purchased imports worth
$1.9b and paid taxes on products that they produced of $0.2b. The labour that
they employed was paid $2.8b. ‘Other factor income’ is largely the gross income
earned by the owners of the businesses that make up the industry.
For any industry the table row reflects the following equation:
Sales to other industries + final demand = total output
16
Strictly speaking, output also includes changes in stocks, as well as sales. But changes in stocks are generally
small compared to sales.
25
Let’s label the total output of the first sector, the primary producers industry, x1.
As we can see from the table, x1 is equal to 25.1, where the units are billions of
dollars. We will also label total output for goods producers x2 and total output for
services x3.
We can see from the table that in order to produce output of 25.1 units, the
primary sector has to buy 4.4 units from other primary producers. So for every
unit that it produces it need to buy 4.4/25.1 units from other primary producers.
The total that it needs to buy can be expressed as (4.4/25.1) times x1.
Similarly, we can see that goods producers need to buy 14.0 units from primary
producers in order to produce total output of 123.0 units. So they buy
14.0/123.0 units of output from primary producers for every unit of output they
produce. The demand for primary sector output can be expressed as
(14.0/123.0) times x2.
Similarly the demand from services for primary sector output can be expressed
as (0.8/194.7) times x3.
We can now rewrite the equation from above to represent the components of the
first row of the input-output table. The rewritten equation is:
(4.4/25.1)x1 + (14.0/123.0)x2 + (0.8/194.7)x3 + final demand = x1
We will refer to (4.4/25.1), which is a coefficient, as a11. We will label
(14.0/123.0) as a12 and (0.8/194.7) as a13. We will also label the final demand
for the industry’s products as f1.
Using the same approach we can derive a similar equation for the sales or
output of the goods producing industry, and also the output of the services
industry. This gives us three equations:
a11x1 + a12x2 + a13x3 + f1 = x1
a21x1 + a22x2 + a23x3 + f2 = x2
a31x1 + a32x2 + a33x3 + f3 = x3
These three equations, which are a set of simultaneous equations, are an inputoutput model.
If we have values for f1, f2 and f3 – the final demands of each industry – then we
have three equations that each contain three unknowns – x1, x2 and x3. So we
can solve the equations to get values for x1, x2 and x3.
The variables f1, f2 and f3 are the exogenous variables for the model; if we set
these, we can solve the equations to find the total output of each industry.17 We
17
An exogenous variable is one that it not determined within a model but is set outside the model and is then
used as an input into the model.
26
can then use these values for x1, x2 and x3 in conjunction with the equation’s
coefficients to determine the purchases made by each industry from the other
industries.
The equations of an input-output model are usually solved using matrix
operations. The three equations of our model can be expressed in matrix form
as:
AX + F = X
where
𝑎11
𝐀 = [𝑎21
𝑎31
𝑎12
𝑎22
𝑎32
𝑎13
𝑎23 ]
𝑎33
𝑓1
𝐅 = [𝑓2 ]
𝑓3
𝑥1
𝐗 = [𝑥2 ]
𝑥3
To solve for X we rearrange the equation to get
X - AX = F
From this we can get
[I - A]X = F
where I is the identity matrix, with the property that IX = X = XI
Finally we get:
X = [I - A]-1F
[I - A ]-1 is the inverse of [I - A], with the property that [I - A]-1[I - A] = I
[I - A] is sometimes referred to as the Leontief matrix, with [I - A]-1 being the
Leontief inverse.
While we have used only three industries in our example, the matrix approach
can be used with any number of industries, provided that [I – A] is a matrix that
is invertible.
To use the model we specify the F matrix and calculate X. If we set F as follows:
1
𝐅 = [ 0]
0
then we will get the total output of each industry required in order to satisfy final
demand of 1 unit for the first industry, the primary producers’ industry. The F
matrix specifies that the final demand for the other two sectors is zero.
However, the results for the model – the calculated values for x1, x2, x3 – will
show that all three industries will be required to produce total output as a result
of the initial demand for 1 unit of primary producers’ output. These increases
reflect the purchases that the primary sector will make from each of the three
27
industries as it lifts its own output to meet final demand. The final total output
from the primary producers industry, x1, will be greater than 1 unit, because of
purchases that it makes from enterprises that are also in the primary producers
industry.
For more details on matrix algebra and examples of simple input-output models
see Dowling (2001). For more – much more – on input-output models see Miller
and Blair (2009).
Capturing the full supply chain
The increase in an industry’s output due to an initial rise in final demand is called
the direct increase in output. Other increases that occur as a consequence of
this – the increases in output as other enterprises supply the industry with what
it needs in order to meet the rise in final demand , are called indirect increases
in output.
A feature of the input-output model is that it captures all of these indirect effects
– it captures the increases in output across an industry’s full supply chain. This
can be seen with the help of a little matrix algebra.
It can be shown that the Leontief inverse, [I – A]-1, is equal to [I + A + A2 + A3
+ ...], where A2 is A times A, and A3 is A times A times A, etc.18
This means that the input-output model can be expressed as follows:
X = [I + A + A2 + A3 + ...]F
= F + AF + A2F + A3F + ...
Let’s assume for now that F is as above, where it showed a value of 1 unit for
the final demand of the first industry, the primary producers industry.
The first term in the equation above, F, is simply the initial shock to the
industry’s final demand i.e. the direct effect. It can be shown that the second
term is the increase in output by the industry’s suppliers. And the third term is
the increase in output by the suppliers’ suppliers. And so on.
The terms tend to get smaller and smaller as they go on, since all the technical
coefficients in A are between 0 and 1. Hence the value of the series converges to
a limit. The final value captures all the effects of the initial change to final
demand as they ripple through the economy. The final value is the increase in
output across the full supply chain. And it is equal to [I – A]-1 F.
18
See Miller and Blair (2009), pp31-34, for a proof of this. The expansion of [I – A]-1 is analogous to the
expansion of the algebraic expression 1/(1-x), which is equal for 1 + x + x2 +x3 +... for |x| < 1.
28
Appendix B: A multi-regional input-output (MRIO) model
Table B1 shows a cut down version of the input-output table in Gillmore and
Briggs (2010). It is a multi-regional input-output (MRIO) table and differs from a
single region input-output (SRIO) table. In a single region model, all exports are
taken as being part of final demand. In a multi-regional model, exports are split
between intermediate products, which are products used by other enterprises,
and final demand products, or products that are used directly in consumption or
investment. In an MRIO model, each region supplies both intermediate products
and final products to all other regions. The links between the regions can be
seen in Table 2. As with single region models, the rows show sales the columns
show purchases.
An MRIO model is derived in a similar way to a single region model. Technical
coefficients are derived for the intermediate inputs to each region. The in-built
assumption here is that the output of a region’s intermediate products will move
in line with the region’s total output. A Leontief inverse matrix, or [I – A]-1
matrix, is then derived from the matrix of technical coefficients. This matrix can
then be applied to a vector for final demand to calculate the output required
from each region in order to produce this final demand. This gives us a picture of
the full supply chain related to this final demand.
Note though that model shown here is a very simple one, and in effect it treats
each country as having only one industry, with that industry being the full
economy. Most MRIO models incorporate a number of industries in each country.
The tables for these models tend to be large, since for each industry they show
the intermediate and final products being delivered to every other industry,
including the industries in other regions as well as industries in their own
regions.
29
Table B1: Example of a multi-regional input-output (MRIO)table
Data is for 2006, in billions of US dollars
Intermediate demand
US
Euro area China Australia
US
10,266.4
135.8
74.2
14.1
Euro area
209.7 8,851.3
87.5
14.1
China
168.4
101.7 4,677.4
12.0
Australia
7.7
6.7
17.9
662.9
New Zealand
2.5
1.5
1.6
3.6
Rest of World
945.7
952.4
545.3
46.9
Taxes
0.0
327.7
0.0
12.1
Value added
13,398.9 9,536.3 2,793.5
691.4
Total
24,999.3 19,913.4 8,197.4 1,457.1
NZ is New Zealand, RoW is Rest of World
NZ
2.6
1.9
1.5
5.0
102.4
7.2
0.8
98.9
220.3
Final demand
RoW
US
Euro area
697.8 13,307.1
103.2
1,152.0
137.7 8,898.5
431.0
110.6
77.3
68.6
5.0
5.1
10.2
1.6
1.1
18,257.2
621.3
723.4
212.5
0.0
764.3
20,487.1
41,316.4 14,183.3 10,572.9
China Australia
16.4
11.8
19.3
11.9
2,423.7
10.1
4.0
639.0
0.4
3.0
120.8
39.5
54.3
51.7
2,638.9
767.0
NZ
2.0
1.5
1.2
3.9
87.8
5.6
6.4
RoW
367.9
528.3
182.7
31.3
4.6
19,051.5
679.4
Output
24,999.3
19,913.7
8,197.6
1,457.1
220.3
41,316.8
2,109.2
108.4 20,845.7
Source: This is a condensed version of the table in Appendix 2 of Gillmore and Briggs (2010). The full table includes
additional countries, which are: Canada, Mexico, United Kingdom, India, Japan, Korea, Taiwan, Singapore, Philippines,
Vietnam, Thailand, Malaysia, and Indonesia. The full table therefore includes New Zealand’s major trading partners.
Appendix C: Exported emissions at the macroeconomic
level
Here we look at how industry rates for embodied emissions can be used to tell
us something about New Zealand’s total exports. If, for each industry, we take
its rate and multiply it by its annual value of exports, we get an annual total of
the industry’s exported emissions.
Figure B1 shows the emissions embodied in exports for various industries. Not
all industries are shown here; the chart includes the 25 industries which had the
highest values of exported emissions. It also includes results for three residual
categories – other primary industries, other goods producing industries, and
other service industries – so that the chart covers all exported emissions.
Figure B1 Embodied emissions in New Zealand exports
Kilotonnes of Co2 equivalents
16,000
14,000
Indirect emissions
12,000
Direct emissions
10,000
8,000
6,000
4,000
Other service industries
Road transport
Air and space transport
Accommodation
Food and beverage services
Basic material wholesaling
Other goods producing industries
Machinery manufacturing
Electronic and electrical equipment …
Fabricated metal product …
Transport equipment manufacturing
Primary metal and metal product …
Basic chemical and basic polymer …
Polymer product and rubber product …
Pulp, and paper product …
Petroleum and coal product…
Wood product manufacturing
Textile and leather manufacturing
Beverage and tobacco product …
Seafood processing
Dairy product manufacturing
Meat and meat product manu
Forestry and logging
Other primary industries
Dairy cattle farming
Sheep, beef cattle & grain
Horticulture, fruit growing
0
Fruit, oil, cereal and other food …
2,000
Sources: See Table 1
A number of features stand out:


Exported emissions come largely from three industries based on agriculture:
dairy products, meat products and horticulture/fruit growing. Together they
accounted for 60% of total exported emissions in the year ended March
2007.
Other industries with large exported emissions are air transport and primary
metal products – which includes the production of aluminium and steel.
31



Overall, indirect emissions (emissions generated by exporters’ suppliers) far
outweigh direct emissions (emissions made directly by exporters). Indirect
emissions account for nearly three quarters of all exported emissions. This
backs up the point that estimates of embodied emissions in exports have to
include indirect emissions as well as direct emissions.
The high level of indirect emissions for the dairy products industry is due
largely to the supplies that it gets from the dairy cattle farming industry.
These supplies have high emissions, since dairy cattle emit methane and
their body wastes result in the release of nitrous oxide. The chart indicates
that the dairy cattle farming industry does not export a lot of its production
directly; most of it is exported via the dairy products industry.
Similarly, the high level of indirect emissions for the meat products industry
is due to the supplies that it gets from the ‘sheep, beef cattle and grain’
industry. Sheep, like cattle, also emit methane and cause emissions of
nitrous oxide.
32