Revision for “InputOutput Analysis [IOA] (including Social Accounting Matrices [SAM])” created on April 27, 2014 @ 09:19:14
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InputOutput Analysis [IOA] (including Social Accounting Matrices [SAM])

Primary Source: Suomalainen, K., with contributions by Heijungs, R. (2006) <em>InputOutput Analysis SWOT Analysis</em> in Report on the SWOT analysis of concepts, methods, and models potentially supporting LCA. Eds. Schepelmann, Ritthoff & Santman (Wuppertal Institute for Climate and Energy) & Jeswani and Azapagic (University of Manchester), pp 96102
<strong>Level of analysis: </strong>Mainly macro, can be applied to mesolevel in some cases depending on the level of detail of available data and purpose of assessment. <strong>Assessed aspects of sustainability:</strong> Economic, generally national economic relationships. <strong>Main purpose of the assessment: </strong>To understand interdependencies of transactions between national industries/sectors in order to predict effects of a change in one industry on others. <strong>Description of the methodology</strong>: IOA is a method that systematically quantifies the mutual interrelationships between various sectors of an economy. The method uses national statistics of intersectorial transactions to construct a detailed statistical picture of the national economy in matrix form. The interdependence among the sectors is described by a set of linear equations expressing the balances between the total input and the aggregate output of each commodity and service produced and consumed over a defined period of time. The effect of an event at any one point is transmitted to the rest of the economy step by step via the chain of transactions that link the whole system together. <strong>The structure of IOA: IOtables</strong> IOA takes advantage of the relatively stable pattern of the flows of goods and services in an economy. National transactions are grouped into major departments or sectors of production, distribution, transportation and consumption. A matrix is set up consisting of rows and columns each representing inputs and outputs to and from a given sector over a certain period of time. The figures in the rows show how the output of each sector of the economy is distributed among the others. On the other hand, the figures in the columns show how each sector obtains inputs from the other sectors. The IOtable thus links each industry to all the others. The table may be developed in as much detail as available data permits and the purpose requires. <strong>Technical coefficients and the static inputoutput system</strong> Using national accounts as a reference, a matrix of technical coefficients is constructed (Leontief 1986). The physical output of sector <em>i </em>is represented by <em>xi</em>, and <em>xij </em>stands for the amount of product of sector <em>i </em>used as input to sector <em>j</em>. The amount of the product of sector <em>i</em> delivered to the final demand sector if represented by <em>yi</em>. The input coefficient of product of sector <em>i </em>going into sector <em>j </em>is then defined as the quantity of output of sector <em>i </em>consumed by sector <em>j </em>per unit of its total output <em>j</em>, and is given as <em>aij</em>; <a href="http://policydesign.org/wpcontent/uploads/2014/04/6.png"><img class="alignnone sizefull wpimage118937" src="http://policydesign.org/wpcontent/uploads/2014/04/6.png" alt="6" width="85" height="53" /></a> The total set of input coefficients gives the structural matrix of the economy. The balance between total output and the individual input of the products to the sectors can be described by a set of <em>n </em>(the number of sectors) linear equations, assuming general equilibrium between supply and demand; <a href="http://policydesign.org/wpcontent/uploads/2014/04/7.png"><img class="alignnone sizefull wpimage118943" src="http://policydesign.org/wpcontent/uploads/2014/04/7.png" alt="7" width="236" height="106" /></a> This states that the output of the product of sector <em>j </em>equals the sum of inputs of the product of sector <em>j </em>to all sectors plus final demand <em>yj</em>. This can be reformulated as: <a href="http://policydesign.org/wpcontent/uploads/2014/04/8.png"><img class="alignnone sizefull wpimage118945" src="http://policydesign.org/wpcontent/uploads/2014/04/8.png" alt="8" width="262" height="119" /></a> Given the matrix notation; <a href="http://policydesign.org/wpcontent/uploads/2014/04/9.png"><img class="alignnone wpimage118947 sizefull" src="http://policydesign.org/wpcontent/uploads/2014/04/9.png" alt="9" width="535" height="104" /></a> The system of linear equations above can be given in matrix form as; <a href="http://policydesign.org/wpcontent/uploads/2014/04/10.png"><img class="alignnone sizefull wpimage118951" src="http://policydesign.org/wpcontent/uploads/2014/04/10.png" alt="10" width="151" height="88" /></a> The last equation is the wellknown matrix representation of Leontief’s inputoutput analysis, the Leontief inverse. This can be understood as the amount of inputs needed from each sector to satisfy a given demand of products from one or several sectors, an application known as impact analysis. The column sums of (<em>I – A</em>)1 are the Leontief multipliers. The multiplier of one specific column provides information about the potential stimulus to the economy if the output of that sector is increased by one unit. Another main application of IO modelling is the imputation of primary inputs, which allows the imputation of labour and capital inputs to final demand. <strong>Social accounting matrices (SAM)</strong> An extension to an IOtable is the Social Accounting Matrix (SAM). In contrast to IOtables, a SAM is not used for doing imputation studies or impact analysis with Leontief multipliers, but rather restricts to the accounting functions, for a given year and a given region. It is a tableau économique of the macroeconomic structure of sales and purchases, with columns representing buyers and rows representing sellers. The columns and rows distinguished are factors of production (labour, operating surplus), households, companies, government, capital account (savings, investments), production activities (related to domestic transactions), and rest of the world (imports and exports). The focus of the SAM is the distributive aspects of the economy: who pays, who receives. As a SAM is used for revealing the structure rather than for doing modelling, its role in sustainability analysis is restricted to monitoring and benchmarking of developments, not to the analysis of scenarios. The formulation of a SAM builds on Leontiefs IOtables. In addition, it considers an unspecified number of households that jointly own an endowment of F different types of primary factors. Three assumptions govern this economy. First, there are no tax or subsidy distortions, or quantitative restrictions on trade. Second, the households act collectively as a single representative agent who rents out the factors to the industries in exchange for income. Households then spend the latter to purchase the N commodities for the purpose of satisfying D types of demands (e.g., demands for goods for the purposes of consumption and investment). Third, each industry behaves as a representative firm that hires inputs of the F primary factors and uses quantities of the N commodities as intermediate inputs to produce a quantity <em>y </em>of its own type of output. Letting the indices <em>i </em>= {1, …, N} denote the set of commodities, <em>j </em>= {1, …, N} the set of industry sectors, <em>f </em>= {1, …, F} the set of primary factors, and <em>d </em>= {1, …, D} the set of final demands, the economic flows in the economy can be completely characterized by three data matrices: an N×N inputoutput matrix of industries’ uses of commodities as intermediate inputs, denoted by X , an F×N matrix of primary factor inputs to industries, denoted by V, and an N×D matrix of commodity uses by final demand activities, denoted by G. The elements of the three matrices may be arranged to reflect the logic of the economic flows (table 1). Commodity market clearance implies that the value of gross output of industry <em>i</em>, <em>yi,</em> must equal the sum of the values of the <em>j </em>intermediate uses of that good, <em>xij</em>, and the <em>d </em>dinal demands <em>gid </em>that absorb that commodity. Similarly, factor market clearance implies that the firms in the economy fully employ the representative agent’s endowment of a particular factor, <em>Vf</em>: The assumption that industries make zero profit implies that the values of gross output of sector <em>j</em>, <em>yj</em>, must equal the sum of the benchmark values of inputs of the <em>I </em>intermediate goods <em>xij </em>and <em>f </em>primary factors <em>vff </em>that the industry employs in its production. The representative agent’s income, <em>m</em>, is made up of the receipts from the rental of primary factors and must balance the agent’s gross expenditure of satisfaction of commodity demands. Together, these conditions imply that income must equal the sum of the elements of V, which in turn must equal the sum of the elements of G. <a href="http://policydesign.org/wpcontent/uploads/2014/04/11.png"><img class="alignnone wpimage118953 sizefull" src="http://policydesign.org/wpcontent/uploads/2014/04/11.png" alt="11" width="455" height="307" /></a> <strong>Applications</strong> IOA has been commonly used in national economy planning, but applications have also reached areas such as energy planning (Tia et al 2006), regional analysis (Pietroforte et al 2000), trade issues (Machado et al 2001) etc. IOA can be used for forecasting to some extent, assuming that the main structures between the sectors remain constant over the period analysed. For more robust analysis over time, annual IOtables can be used in time series, but this has commonly not been done due to the expenses of gathering so many data intensive tables. A widerange of variations exist including the expansion of the model to environmental analysis (see SWOT on Environmental IOA / Extended Environmental IOA). IOA is relevant from a sustainability point of view in its analysis of macrolevel systems, where real quantities of physical flows may be easier to track by looking at monetary transactions. It has strength in its coverage of the entire economic realm of the country or region with a welldefined boundary; there are no significant underestimations of background systems. The method is consistent with an international accounting standard, allowing comparability between countries (if resolutions are similar). IOA also has potential to be integrated with other methods, models and data sources. <strong>Methodology (robustness, validity & reliability)</strong> IOA is a mathematically robust method, and highly based on real empirical data providing reliable results at the macro level, to which it is designed. However, it is methodologically possible to apply IOA to smaller scale systems as well, if relevant data is available. Also the relatively easy and transparent analysis of results is a strength of the method; it is possible to track back results in the calculations and check where specific results arise from. IOA is based on a static accounting system, which makes it less suitable for long term sustainability analysis. It is quite difficult to include consequences of technological change in the system unless a more complex model is built e.g. in timeseries. Although the direct effect of one action somewhere in the economy are evaluated in IOA, it is the average effect and not necessarily the real effect, which would be the marginal effect of a change. In IOA the product of a sector is assumed to be homogeneous, when in reality the range of products of a sector can be quite diversified from the aspect of environmental impacts. IOA also has the problem of data availability and lack of consistency among the available IOtables – differences in sectoral resolution make comparison difficult. Typically it takes one to five years to publish IOtables based on industry surveys. <strong>Methodology</strong> IOA is based on linear dependencies, giving constant scaling. This can give misleading results the bigger the studied changes or consequences are. One must remember that prices are given in production costs and marginal costs are equal to average costs in this method. Also no price elasticities are included, or consumer behaviour as how a consumer will react to price changes. The model is based on the assumption of general equilibrium. Data collection and model construction may be costintensive and timeconsuming tasks. 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