Regional input-output models are, with few exceptions, now produced with computer estimating techniques commonly called "nonsurvey" techniques. This phrase refers to the fact that they are based on the technology embodied in the national input-output-table and that imports are estimated based on some supplementary technique not involving extensive survey work. This chapter briefly explains the most common of these approaches. In this introductory treatment, we specifically exclude mathematical procedures (such as the RAS balancing method) and we leave the operations embodied in various commercially available packages to their literature.
Let us start by restating the basic structure of the system.The equation system for a regional input-output model may be written as
The aij represent purchases from regional industry i by industry j (or xij) as a proportion of the output of industry j (or xj), yif is the local final demand for the products of industry i by final-demand sector f, and ei is the exports by industry i. The equation system might be illustrated with an algebraic table similar to that in Figure 5.1.
The system can also be outlined in terms of supply, describing the production technology of a region:
Here vfj is the value added by final-payments sector f to the product of industry i, and mij is the imports of the products of industry i by industry expressed as a proportion of the output of industry j. (Note that we have included t local final-payment sectors to match the t local final- demand sectors. This is for simplicity, since we normally have more final-demand sectors than final-payment sectors.
Now assume that we have augmented the interindustry portion of the system by treating the household sector as an industry, as in Chapter 4. The aij matrix, written as A, is called the regional interindustry coefficients matrix and is a critical part of the system since its constancy is a major technical assumption in input-output analysis. As is clear from Chapter 4, the solution to the equation system (10-1) may be written in matrix form as
(I - A)-1 *(Y + E) = X (10-3)
We will use this form of the system to avoid repetitive algebra in the discussion of estimating techniques.
The regional coefficients matrix, A, may be regarded as the difference between a technology matrix, P, and an imports matrix, M:
A = P - M (10-4)
The technology matrix records purchases from industry i (regardless of location) by industry j as a proportion of the output of industry j (pij). The imports matrix contains the mij elements in equation (10-2). The major problem confronting the regional analyst in constructing a transactions table is obtaining the P matrix and dividing it into its component parts, A and M. We now turn to this division problem.
Given the system described above, the regional analyst has several procedures available to him in constructing his empirical model. The choice between these techniques depends largely upon the resources available. This section briefly outlines these procedures and describes the means by which an inexpensive nonsurvey procedure may be evolved into a survey-based technique to fit whatever budget is available. (Schaffer 1972; Schaffer and Chu 1969)
Properly, an input-output model is based on a full survey of industries and final consumers which documents both sales and purchases. Each respondent is asked to designate sales to regional industries (xij) and to final users inside (yif) and outside (ei) the region. The respondents are also asked to designate their purchases from regional industries (aijqj), their purchases from industries outside the region (mijxj), and their final payments (vfj) to primary resource owners in the form of wages and salaries, profits, depreciation allowances, taxes, etc. These purchases and final payments outline the production technology of each industry in a usable format, already separated into a regional flows matrix and an imports matrix.
In acquiring data on both purchases and sales, the analyst has assembled the information required to produce a potentially reliable table. But the table is also very expensive and its construction is very time-consuming. Notice what happens if you don't have a complete census of firms and perfect reporting in each case. In this perfect case, the row estimates of xij will be identical to the column estimates. Now notice what happens if you have sampled only a few firms: the row estimates and the column estimates now vary widely. Sampling problems and reporting errors are substantial and the analyst is forced to achieve balance by tediously assaying the reliability of responses and by juggling numbers until totals finally match.
A basic alternative to this full-survey approach is the "rows-only" method. First used by Hansen and Tiebout, this method assumes
... that firms know the destination of their outputs far better than the origin of their inputs, especially where regional breakdowns are required. In other words, in terms of input-output flows, information for the "rows" is easier to obtain than information for the "columns." The reason for this is that the bundle of inputs is usually so varied and complex that their origins are difficult even for firms involved to track down accurately. However, the same firms are especially concerned with where and to whom they sell their output. (Hansen and Tiebout 1963)
This approach permits the analyst to avoid a complex data reconciliation. It produces only one entry per cell in the transactions table; the full-survey method forces the analyst to check his work by producing two estimates of cell values.
A second alternative to the full-survey approach is what is called the "columns-only" method. This approach assumes that business firms know their sources of supply better than they do their customers. Harmston and Lund argue that this approach takes advantage of the detailed knowledge of expenditures required by businessmen for control and tax purposes (Harmston and Lund 1967). Producing data in the same simple form as that of the rows-only method, the columns-only approach seems well-suited for use in small regions characterized by a relatively large number of locally-owned firms.
A nonsurvey technique commonly used in the United States, the supply-demand pool technique relies on the national input-output table as a reasonable estimate of the production-technology matrix, or P matrix, of a region and proceeds to estimate regional flows and imports using the concept of regional commodity balances (Isard 1953). This method is sometimes called the Moore-Petersen technique since it was first applied to a study of Utah by Moore and Petersen (Moore and Petersen 1955). (The term "supply-demand pool" actually originated in discussions with a programmer in 1968 as we were developing tests of nonsurvey procedures (Schaffer and Chu 1969)).
The only additional data assumed to be available are gross outputs for the n regional industries, qj, and the gross purchases of t final-demand sectors. Now, to avoid more complex addition, let us assume that the P matrix includes both industries and final demand sectors, so A is of dimension n*(n+t). Value added is three rows in the national table and has been excluded from P.
Let di be the row sum of total demands for the products of industry i, computed from A as follows:
Here, of course, the pij have been computed from the national input-output table and we have simply reduced national flows to regional size.
A commodity-balance ratio comparing regional production or supply (qi) with regional demand can be computed as
bi = qi/di (10-6)
and the P matrix can be divided into its A and M components through a simple set of rules. If b is greater than or equal to one, then all inputs can be supplied by local producers and we can set aij = pij, mij = 0, and ei = qi - di. If bi is less than one, inputs must be imported, so aij=bipij, mij = pij-aij and ei=0.
This pool procedure allocates local production, when adequate, to meet local needs; when the local output is inadequate, it allocates to each purchasing industry i a share of regional output qi based on the needs of the purchasing industry itself (p ijqj) relative to total needs for output i (di).
One of the major characteristics of a regional input-output model is its openness. Exports and imports are substantial, if not dominant, parts of the typical regional transactions table. Since simulated exports are so greatly at variance with the survey-based exports in the above comparison, it seems reasonable to believe that correction of this discrepancy could lead to a much better estimate of regional transactions.
If we can afford neither of the more powerful alternatives to a full survey as discussed above, then an export survey combined with a supply-demand pool procedure may be an adequate substitute. This approach requires that we simply canvass firms in the region, asking for three bits of information: their industry classification, value of sales for the year, and the proportion of their sales going to out-of-region purchasers. The first two answers permit the analyst to classify replies and to properly weight export proportions in constructing the transactions table.
The procedure, then, involves setting exports of each industry i at the survey-estimated value and simulating the remainder of the table. For the balance ratio used above, we simply substitute a ratio which excludes exports from the supply available for local use:
This approach satisfies export requirements first and then allocates the remainder of local production to satisfying local needs in proportion to requirements. If be i is greater than one, the technology matrix may have to be adjusted, but this proves to be a minor problem.
Two observations are appropriate. One is that a procedure developed by the late Ben Stevens, the Regional Purchase Coefficients (RPC) procedure, is an attempt to estimate these balance ratios from a combination of Census of Transportation data, other product characteristics, and econometric equations. RPC's are in common use now.
The other observation regards the term "minor problem" in the previous paragraph. Actually, that is an understatement. In the Nova Scotia Study described in Chapters 7 and 8, columns for imports and exports appear in the commodity origins table and accumulate the data required for estimating regional trade coefficients. This is great conceptually, but recall that rows in the origins table represent actual supply and demand equations for each of 600 commodities and all degrees of freedom are gone - there is no room for error. Even though we had, in many cases, census data, none of the equations balanced and we had to insert columns for estimated imports and exports for each commodity. The greater part of a year was spent unraveling these estimates (DPA Group Inc. and Schaffer 1989)
Now, if more trade information than just export estimates can be assembled, the method can be extended to permit a setting of selected values in the transactions table. We simply set observed values xig, xih, ..., xik and estimate the remaining regional flows using an adjusted balance ratio:
9.3 Commodity-by-industry procedures
The above notes are sufficient to show the general problem associated with constructing regional models from published data, that of estimating imports and exports. It is beyond the scope of this exposition to explore the details of constructing modern input-output models. To understand the process requires a thorough knowledge based on a standard reference such as Miller and Blair [, 1985 #190], on the current U.S. interindustry tables, and on a recent exposition of problems associated with regionalization [for example ,Jackson, 1998 #197]
Several sources of assistance are available.
The Regional Economic Analysis Division of the Bureau of Economic Analysis produces models of states, counties, and multi-county areas on request. These models are available in detailed or aggregated format. Information can be obtained at their web site:
The Minnesota Implan Group, Inc. provides a wide variety of services in impact analysis, including software and data. Full details are available at:
Guy West of the University of Queensland provides software and data for construction and analysis. Called IO7, it is available through Randall Jackson at West Virginia University (Randall.Jackson@mail.wvu.edu). A DOS based version is available at no charge via:
IOPC is a product of the Regional Science Research Instutute and the late Benjamin H. Stevens. It is software for manipulating models produced by RSRI and is temporarily unavailable.
Data, software, and related reports will soon be available at my web site:
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