Input/Output analysis - Shortcuts to life cycle data?
4. Uncertainty in IO-based LCI
Manfred Lenzen, University of Sydney
Parts of this article has been submitted for publication in Journal of Industrial Ecology.
4.1 Abstract
Conventional process-analysis-type techniques for compiling life-cycle inventories (LCIs) suffer from a truncation error, which is caused by the omission of resource requirements or pollutant releases from higher order upstream stages of the production process. The magnitude of this truncation error can be in the order of 50%. The only way to avoid such significant errors is to incorporate Input-Output Analysis (IOA) into the assessment framework, resulting in a hybrid LCI method. Uncertainties of such IO-based LCIs can be calculated using Monte-Carlo simulations.
4.2 Introduction
The inventory phase of a life-cycle assessment (LCA) requires the assembly of a database on resource requirements and pollutant releases occurring in the life of a product or process. The system boundary of the inventory is to be chosen to include, at a minimum, all regions involved in the various stages of the life cycle, including countries supplying inputs . In LCAs performed as set out by the Society for Environmental Toxicology and Chemistry (SETAC), the inventory is set up using process analysis or similar bottom-up techniques. Within process analysis, the resource requirements and pollutant releases of the main production processes and some important contributions from suppliers of inputs into the main processes are assessed in detail (for example by auditing or using disparate data sources), and the system boundary is usually chosen with the understanding that the addition of successive upstream production stages has a small effect on the total inventory.
LCAs based on process analysis and IOA yield considerably different results (see and ). In general, even extensive process analyses will not achieve reasonable system completeness, given the high number of significant input paths. As a result, environmental impacts will be systematically underestimated in conventional LCAs, thus leading to unreliable or incorrect conclusions (compare . In contrast, LCAs based on IOA inherently cover infinite orders of upstream production stages. IOA, however, suffers itself from errors from various sources. In this article these sources will be discussed, and attempts of quantifying the associate standard errors of IO-based LCIs will be presented for the example of Australian data.
Figure 4.1
Process-based LCA only cover a limited amount of the whole system. What is excluded
due to the truncation of the system boundary is usually not known. It can be shown
quantitatively that the outside contribution to the functional unit - illustrated by the
question mark – is of the same order of magnitude as the contribution of the
processes contained within the conventional system boundary. Thus, conventional LCA
carries truncation errors.
Figure 4.2
Energy-intensive sectors tend to be more complete at lower orders of upstream
production stages than energy-extensive sectors. However, even for second-order analyses,
that is considering about 10,000 input chains, system completeness is only between 50% and
80%. This means that the truncation error of even extremely detailed process analyses can
be in the order of 20-50%.
Figure 4.3
Convergence towards system completeness in detail: acceptable completeness is reached
for electricity generation at first order, that is after evaluating 100 suppliers.
However, for all other systems, even evaluating 10,000 inputs of second order will yield
completeness below 80%. Note that the convergence to system completness is
sector-dependent!
Figure 4.4
Convergence towards system completeness revisited: kf(k)
shows the (sector-average) relative growth in system energy with when progressing from
order k-1 to order k. In other words: kf(3)=75%
means that when progressing from order 2 to 3, the additional embodied energy (in order 3)
is about 75% of that contained in order 2. Dkf(k)
shows the variation of kf(k) across
sectors. Note that even for orders 2 and 3, there is a considerable fluctuation in
convergence speed. This means that a process-based LCA of, say a plastic bottle and a
glass bottle, are not necessarily comparable, even when the system boundary was truncated
in a systematic and comparable way. This is simply because the "plastic system"
might, at a specified order k, be more (or less) complete than the "glass"
system.
4.3 Input-output analysis
Input-Output Analysis (IOA) is a top-down economic technique, which uses sectoral monetary transactions data to account for the complex interdependencies of industries in modern economies. The result of generalised IOA is an f×n matrix of factor multipliers, that is embodiments of f production factors (such as labor, energy, resources and pollutants) per unit of final consumption of commodities produced by n industry sectors. A multiplier matrix M can be calculated from an f×n matrix Q containing sectoral production factor usage, and from an n×n direct requirements matrix A according to
| M = Q (I-A)-1, | (1) |
where I is the n×n unity matrix. A should comprise requirements from current as well as capital intermediate demand of domestically produced and imported commodities. The f×1 factor inventory F of a given functional unit represented by a n×1 commodity inputs vector y is then simply
| F = M y. | (2) |
An introduction into the IO-method and its application to environmental problems can be found in papers by and .
4.4 Uncertainties in input-output-based LCI
While being able to cover an infinite number of production stages in an elegant way, input-output analysis suffers from potential uncertainties arising from the following sources: (1) uncertainties of basic source data due to sampling and reporting errors, and uncertainties resulting from (2) the assumption made in single-region IO-models, that foreign industries producing competing imports exhibit the same factor inputs as domestic industries, (3) the assumption that foreign industries are perfectly homogeneous, (4) the assumption of proportionality between monetary and physical flow, (5) the aggregation of IO-data over different producers, and (6) the aggregation of IO-data over different products supplied by one industry. The calculation of all components is described for the case of Australian energy multipliers in the following sub-sections.
4.4.1 Source data uncertainty
Standard errors for monetary values in all basic Australian IO-tables can be calculated from performance data collected by the Australian Bureau of Statistics , while those for energy data have to be obtained from informed judgment. Figure 4-5 shows for the example of performance data that standard errors decrease with increasing magnitude of the data item. This is because generally, large data values are obtained from a summation over a large number of survey data, and because the uncertainty D s of a sum s of n summands si with stochastic uncertainties D si decreases approximately with Ö n:
4.4.2 Imports assumptions uncertainty
In single-region IO-models, it is commonly assumed that foreign industries supplying imports for the domestic market have factor intensities, which are identical to those of domestic industries. The output of the motor vehicles industry, for example, consists partly of assembly work undertaken in Australia, while imports consist only of vehicles and vehicle parts. The energy multiplier of assembly work is likely to be about 4 MJ/A$, while the energy multiplier of producing vehicles and parts is probably higher at around 12 MJ/A$. Thus, by assuming equal energy multipliers for foreign and domestic motor vehicle industries, the energy embodied in motor vehicle imports is, in this case, underestimated. However, since information on factor inputs of Australian imports is not readily available, a worst-case standard error of 50% was used for all entries in the imports table.
Due to a lack of available information, it must be assumed that foreign industries are perfectly homogeneous, that is, that they produce only one (the primary) commodity type. In Australian IO-tables, secondary products usually represent less than 5% of each industry’s total output. Hence, assuming that foreign industries have a similar structure with regard to joint production, the assumption of perfect homogeneity for foreign industries introduces an uncertainty of that magnitude into entries in the imports table. This uncertainty is negligible compared to the uncertainty arising from the assumption of equal factor inputs for imported and domestically produced commodities.
Figure 4.5
Figure 4.6
Regression of standard deviations of energy and emissions intensities.
4.4.3 Proportionality assumption uncertainty
Using monetary IO-tables for the calculation of multipliers of physical quantities implies that the physical flow of commodities between industries can be represented by the monetary values of the corresponding inter-industrial transactions. For example, the content of 100 A$ of electricity supplied to aluminium smelters is assumed to be equal to the energy in 100 A$ of electricity supplied to travel agencies. However, electricity prices vary considerably amongst industries, thus violating the proportionality assumption. The associated uncertainty can in principle be overcome by replacing monetary entries in all basic IO-tables with entries in physical units. This cannot be achieved for most of the industries classified in the Australian IO-tables, partly because physical data is unavailable, and partly because many industries are too heterogeneous with regard to their product range. In this work, monetary entries could be replaced by entries in physical units only for coal, oil and gas mining, petroleum refining, electricity, gas and water supply, resulting in mixed-units tables (A $ for monetary flow, MJ for energy industries, and L for water supply).
4.4.4 Aggregation uncertainty
Input-output and factor data are generally aggregated over a number of producers within one industry. The fact that the number and identity of producers involved in a particular inter-industrial transaction is generally unknown leads to uncertainties in factor multipliers. In general, this uncertainty depends on the geographical and technological variability of production in the respective industry sector. Production scale may also influence factor multipliers, but this could not be confirmed by , who found "only minor differences between small and large pulp and paper plants in environmental efficiency".
Consider the case of energy as a factor to be analysed. One path contributing to the total energy multiplier of iron ore mining, for example, is the amount of energy required for the railway transport of iron ores. It is only a small portion of the monetary output of the Australian railway transport industry that is absorbed by iron ore mining, and iron ores are hauled by only a few railway freight operators. The amount of energy used by operators participating in the transport of iron ores might deviate from the average energy use of all railway freight operators, thus leading to an aggregation uncertainty in the energy requirement path "diesel for railway transport for iron ores". In contrast, the supply of meat from the beef cattle industry to the meat products industry, for example, represents almost the total output of the beef cattle industry. It can therefore be concluded that almost all beef cattle farms participate in the supply to the meat products industry. Hence, although individual beef cattle farms might vary with regard to their energy use, the amount of energy required per unit of output into the meat products industry is well described by the average energy use in the beef industry, and the aggregation uncertainty is low.
In general, the aggregation uncertainty associated with a particular inter-industrial transaction Aij from industry i into industry j decreases with (1) decreasing number Pi of producers in the supplying industry aggregate i, and (2) increasing number pij of producers participating in that transaction. Firstly, using energy multipliers of Danish manufacturing sectors (Danmarks Statistik 2000), energy and greenhouse gas multipliers of various Australian transport operators , and emission data for Swedish sulfate pulp mills and for Australian fossil-fuelled power plants ), a proportionality of the standard deviation of single-producer intensities to ln(P) can be established (see Fig. 4-6). Secondly, assuming that k=1,...,pij producers contribute aij,k to a particular inter-industrial transaction Aij=Sk aij,k, the aggregation uncertainty DAij/Aij of the transaction can be approximated as
 |
(4) |
where Daij,k/aij,k=SD is the relative standard deviation of the contribution aij,k of all producers as regressed in Fig. 4-6. In this approximation, it is assumed that aij,k/Aij» 1/pij, that is, all producers contribute about the same proportion to the transaction. Inserting for SD, the aggregation error of the transaction Aij can be expressed as
 |
(5) |
with the regression constant r =0.2. In practice, the number pij of participating producers can be estimated for any transaction from the ratio of the monetary value Aij of that transaction and the total inter-industrial output S j Aij of the supplying industry i, via pij» Pi×Aij/S j Aij.
4.4.5 Allocation uncertainty
Entries in IO-tables represent transactions of whole industry classes, and are aggregated over the product range in the respective class. This aggregation is equivalent to assuming that each industry class is perfectly homogeneous with regard to its product range, that is, it produces only one type of commodity. This assumption clearly ignores product diversity and joint production between industries, and leads to an allocation uncertainty in IO-data Aij, if the corresponding inter-industrial transaction involves only a few product types out of the whole output range of the supplying industry.
The Australian ship and boat manufacturing industry, for example, supplies ships and boats mainly for commercial fishing, water transport, defence, and private households. Obviously, this output is far from being homogeneous, since it comprises fishing boats, ferries, cruise liners, navy vessels, sailing boats, and aluminium dinghies. These different types of ships and boats might require different factor inputs, causing an allocation uncertainty in the output coefficients of the ships and boats manufacturing industry. In contrast, the water supply industry produces only one commodity, which is mains water, so that the allocation uncertainty for water supply is zero.
Allocation uncertainties can be estimated by comparing factor multipliers calculated using IO-models of different aggregation level. Figure 4-7 shows the relative frequency distribution f(D ) of deviations D of multipliers for 43 production factors in a 132-commodity IO-model from averages over 2, 5, 10, and 100 randomly selected commodity groups. Each distribution contains about 500,000 draws. Deviations increase with increasing number of contained sub-groups, and are mostly below 50% for an aggregation of 2® 1, and mostly below 100% for an aggregation of 100® 1. The asymmetry of the distributions result from the fact that for most production factors, multipliers are high for a few commodities (such as coal for electricity, water for crops, and land for grazing), and low for all others. The deviations shown in Fig. 4-7 represent a worst case, because commodities were selected randomly. In practice, aggregation is usually based on similarity of commodities. Allocation uncertainties can in principle be overcome by further disaggregation of the IO-model.
Figure 4.7
Relative frequency distribution f(D ) of deviations D of multipliers for
43 production factors in a 132-commodity input-output model.
Table 4.8 Look here!
Truncation errors of primary energy multipliers for 0th to 3rd
order process analysis (PA 0-3), and total errors for input-output (IO) analysis.
4.4.6 Total uncertainty
The overall uncertainty of factor multipliers is calculated in two steps. Firstly, the total relative standard error d Rij=D Rij/ Rij of input-output coefficients Rij is calculated from relative standard errors d Rij,comp of components described in the previous sub-sections via
Note that the proportionality error could not be quantified in this study due to a lack of price data. The subsequent estimation of standard errors of multipliers is not so straightforward, because standard errors of the Leontief inverse (1-A)-1 in Equation (1) cannot be calculated analytically, but by using a Monte-Carlo technique to simulate the propagation of uncertainties (see . Following early work by , it is assumed that errors in the elements of Q and A are normally distributed. Such errors can be simulated by generating two matrices d Q and d A, which contain random, normally distributed perturbations of Q and A, with zero mean and standard errors {d Aj}i,j=1,...,n as in Equation (6). The uncertainty d M of a multiplier M resulting from a single perturbation is then
| d M = (Q+d Q) [I– (A+d A)]-1 – M. | (7) |
While relative standard errors d Aij of IO-data Aij range mostly between 20% and 80%, the relative standard errors of the IO-based energy multipliers are much smaller at about 10-20% (see Tab. 1). This can be explained as follows: considering that (I-A)-1=I+A+A2+A3+..., the calculation of multipliers involves numerous additions of coefficients Aij, so that the corresponding relative errors d Aij cancel out due to their stochastic nature. This feature is particularly helpful in IO-based LCAs of functional units with many components (for example an overseas holiday, or a residential dwelling), because the inventory uncertainty decreases with the number of components comprised in the inventory (travel agent service, air travel, accommodation, food, entertainment, or bricks, glass, concrete, structural metal, furniture, appliances, etc). Such reductions do not apply to the systematic truncation errors inherent in process analyses. While for energy supply, transport, and upstream manufacturing, IOA ranks between second and third order process analysis in terms of uncertainty, it is preferable to third order process analysis for raw materials extraction, downstream manufacturing, and services.
4.5 Conclusions
Conventional (SETAC) life-cycle assessments suffer from an irreducible, systematic error caused by the truncation of the production system boundary. This truncation error is case-dependent, but can be in the order of 50%, which can render results and conclusions of conventional life-cycle assessments unreliable or even invalid. Truncation errors can be avoided by employing a hybrid assessment method, which combines process and IOA. IOA in turn suffers from various errors, which can be estimated using Monte-Carlo simulations.
4.6 Acknowledgements
Thomas Bue Bjørner, AKF, København, calculated statistics for direct energy intensities of Danish manufacturing sectors at company level, shown in Fig. 4-6.
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