Appendix 1   Methods Used in SAM Construction

The Valuation of Transactions

In order to achieve a balance between the row and column sums of the SAM, the transactions in the matrix have to be valued in a uniform manner. The prices used to value purchases or expenditures (recorded in the column entries) have to be consistent with the prices used to value receipts (recorded in the row entries of the matrix). There are numerous reasons why differences may prevail, the most obvious being that purchasers' prices include margins to cover distribution costs, transport margins and commodity taxes. In fact, the requirement of uniform valuation arises as much from theoretical as accounting considerations because, if the SAM is to be used for Leontief modelling, it is assumed at the outset that the price of commodities does not vary between purchasers. Consequently, an important stage in the construction of a SAM is deciding how to value transactions.

In line with the previous Western Isles Regional Accounts study, as well as established guidelines for constructing regional accounts, the 2003 SAM was constructed on the basis of so called “approximate basic prices”.  This means that distributive margins, transport margins and net commodity taxes have been deducted from both intermediate and final purchases of domestic goods and reallocated to the distribution commodity group or the government row of the matrix as appropriate.

Net commodity taxes were estimated indirectly using data from the UK and Scottish input-output tables and adjusted to reflect the pattern of commodity demand in the Western Isles. Although not ideal, this use of secondary data sources was considered preferable to the alternative, i.e. not identifying net commodity taxes within the SAM, for the following two reasons. Firstly, it allows the Western Isles GDP to be calculated at factor cost, thereby facilitating comparisons of GDP estimates at the Scottish and UK level. More importantly it avoids bias in the multiplier analysis stage of the study (Bulmer Thomas, 1982).

Defining output from the majority of sectors in the SAM was straightforward. For all of the sectors producing goods and services, output was defined as the value of sales of these goods/services plus changes in the value of stocks. In the case of the banking and insurance sector, output was similarly defined as the value of services (measured by bank charges) plus net interest charges. The definition of output of the distribution sector and public sectors is less obvious. In the case of the former, output has been defined as gross margin on sales for whatever services were rendered. By including only the value of this margin as opposed to the value of actual sales from retailers and wholesalers, the database avoids double counting the value of output from the producing sectors.

With respect to the treatment of public sector activities, the approach followed that adopted in the 1997 study where services such as health, education and social work have been separately identified as sectors within the production boundary. These sectors then “sell” their output valued at cost to either central government or the local council. In the case of public administration activity, output is defined to be equal to the value-added by this sector, with there being no material inputs or intermediate sales.

 

The Treatment of Imports, Exports and Capital Transactions

The inter-industry transactions matrix and household consumption data in the 2003 SAM reflect only flows of locally produced goods and services, with the value of imports recorded separately in the matrix. In this way, the value of the database for investigating, for example, the potential advantages of increasing the degree of local sourcing of inputs has been improved considerably. Imports have been valued on a “free-on-board” basis so as to be consistent with their valuation in the Scottish and UK input-output tables.

The treatment of exports in the SAM is conventional. Exports represent an additional source of final demand and are recorded at the intersection of the production accounts with the rest of world accounts.

With respect to capital formation, the treatment adopted in the Western Isles SAM mirrors that used in the UK Input-output Tables. GFCF on an ownership basis is translated into GFCF on a producer basis by examination of the type of asset being produced (for example vehicle or buildings etc.) and then the resulting data entered as a column of final demand in the SAM. Ideally, the capital accounts would have been balanced so as to ensure all savings and investments relating to the region were accounted for. However, insufficient information was available to fully articulate capital-related transactions and it is left as an area for possible extensions.

 

Technology assumptions used in producing symmetric production accounts

In order to place the production accounts onto a symmetric basis (i.e. where the rows and columns relating to the production sphere of the economy have the same output dimensions), a link needs to be established between commodity and activity output. This requirement is brought about by: a) the nature of the raw data that can be collected - intermediate input flows are recorded only in the form of commodity purchases by industry groups, and b) the nature of production - except at extreme levels of aggregation, industries are commonly involved in the production of more than one commodity.  Although it is theoretically possible to directly estimate symmetric input-output coefficients using regression techniques, the practical difficulties encountered by such an approach can be insurmountable.  Thus modellers resort to using certain technology assumptions to develop symmetric tables and, in this study, the industry technology assumption was used to convert the inter-industry transaction data onto an industry by industry basis. When reviewing the level and nature of transactions relating to production activity, the fact that the figures include the value of purchases and sales relating to secondary production should be born in mind.

Updating and balancing the SAM

There are various alternative mechanical methods of adjusting the entries in initial SAMs so that they balance, each designed to minimise the changes that are made to the initial estimates in the SAM. All the methods share the attribute of being only as good as the control totals of the system with any errors in these totals being transmitted back into the elements in the matrix during the reconciliation procedure. Having considered alternative methods including entropy, the method adopted in this study was a “modified RAS procedure” (Bulmer Thomas, 1982).

Appendix 2  Structural Path Analysis

Defourny and Thorbecke (1984) were the first to illustrate how structural path analysis of a SAM database can be used to identify those ‘poles’ (sectors, factors or household groups) that are key to the transmission of effects within an economic system.

As noted in the text, structural path analysis differs fundamentally from the conventional SAM multiplier methods in that it focuses on how individual elements of the multiplier matrix come about. Starting with changes in exogenous variables, it is a means of identifying the paths through which structural relationships in an economy lead to ultimate effects on endogenous variables. It thus reveals aspects of an economy that are not apparent from an examination of either direct transactions between accounts or an examination of the solution multiplier matrix.

 

The approach is based on the assumption that the average expenditure propensity flowing from account j to account i in the system, a_ij­, reflects the magnitude of influence transmitted from j to i or the intensity of arc (j, i).

 

Three different measures of influence can be derived between any two accounts in a SAM, j and i: the direct influence of j on i, the total influence of j on i and the global influence of j on i. The nature of each of these is considered briefly below with reference to the diagrams in Figure A2.

 

Direct influence, J^D_(j,i):

 

The direct influence of account j on account i is the change in income of account i (the destination account) induced by a unitary change in j (the source account) assuming that all the other accounts except those along the elementary path connecting j and i remain constant. If there is an arc directly connecting the two accounts (see for example Figure 2(i)), then

 

                                                                                                                (1)

 

where a_ij are elements of the coefficient matrix A showing average expenditure propensities between the endogenous accounts in the system.

 

Alternatively, the two accounts may be linked by an elementary path of more than one arc (see Figure 2 (ii)). A path p(j,i) from account j to account i may take the form

 

 where  .

 

In this case, the direct influence transmitted along the path is given by the product of the intensities of the arcs constituting the path, that is

 

                                                                              (2)

 

 

Total Influence

 

Along any elementary path between two accounts there may be other linked accounts and other paths that form circuits (see Figure 2 (iii)). Such circuits will amplify the direct influence transmitted along the elementary path. The total influence measure takes account of such amplification through the calculation of a path multiplier. In particular, it can be shown that the total influence along a path with adjacent circuits is equal to the direct influence along each path (given by the product of the intensities of each arc constituting the path) multiplied by the path multiplier, .

 

                                                                    (3)

 

where the path multiplier, , is given by

 

 

Δ is determinant of the matrix (I-A) and Δ_p(j,i) is the minor of the matrix (I-A) with the rows and columns  removed[1].  In general, longer paths (with more arcs) would be expected to have higher path multipliers because of the possibility of more adjacent circuits.

 

 

Global Influence

 

The global influence of account j on account i is a measure of the total effects on the income of account i arising from a one unit increase in account j. As such, is it equal to the sum of total influences of account j on account i along all elementary paths joining the two accounts (see Figure 2 (iv)). This in turn can be shown to equal the ijth component of the SAM multiplier matrix. That is,

 

                                                                                        (4)

where b_ij is the ijth element of the inverse matrix B=(I-A)^-1 and m is the number of elementary paths between j and i.

 

Importantly, the global influence captures the influence transmitted along all elementary paths between accounts i and j where the paths are not considered in isolation but simultaneously.

 

 

 

 

 

 

 

Figure A2: Types of paths from source account j to destination account i in a network