BUILDING INTERINDUSTRY MODELS

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 *a _{ij}* represent purchases from regional
industry

The system can also be outlined in terms of supply, describing the production technology of a region:

Here *v** _{fj}* is the
value added by final-payments sector

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
*a** _{ij}* matrix, written 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 *(p* _{ij}*). The imports
matrix contains the m

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
(*x _{ij}*) and to final users inside (

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
*x** _{ij}* 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, *q _{j}*, and the gross purchases
of

Let *d _{i}* be the row sum of total demands for the
products of industry i, computed from A as follows:

(10-5)

Here, of course, the *p** _{ij}*
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
(*q _{i}*) with regional demand can be computed as

* b*_{i}* = q*_{i}*/d** _{i}* (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
*a _{ij} = p_{ij}, m_{ij}* = 0, and

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* q _{i}
*based on the needs of the purchasing industry itself (

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:

(10-7) | |||

This approach satisfies export requirements first and then allocates the
remainder of local production to satisfying local needs in proportion to
requirements. If *b** ^{e }_{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 *x** _{ig}*,

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:

http://www.bea.doc.gov/bea/regional/rims/

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:

http://www.econ.gatech.edu/faculty/schaffer/

- What is the major problem in constructing a regional input-output table? Outline several means by which it may be solved.
- Discuss the statistical reliability of a regional input-output coefficient estimated with a full survey.
- What are the major drawbacks to the nonsurvey techniques for estimating regional interindustry transactions? How may their effects be minimized?
- Sketch the algebraic transactions table for equations 1 and 2.