Ideal or Not Ideal Interregional Input–Output Accounts and Model

Abstract

The significant role that Walter Isard played in regional analyses is well known at least among those of us conducting regional studies, as recently reviewed by Boyce. In this short article, we examine several aspects of Isard’s input–output accounts and models and raise two important points about his accounting framework and the underlying theory.

Keywords

input–output SAM CGE methods regional econometric models economic analysis spatial analysis integrated regional and multiregional models

Introduction

The significant role that Walter Isard played in regional analyses, as recently reviewed by Boyce (2003), is well known at least among those of us conducting regional studies. In this article, we raise two important points about his interregional accounting framework and the underlying theory. Our first point is that his interregional input–output (IRIO) accounts are excellent as a means for studying the vast number of transactions among industries in different regions. Analysts can use them to create detailed freight transportation plans if they need to know the origin and destination of a particular good. Such accounting data are needed for many transportation studies involving different trade flows in the United States and elsewhere; thus, they are a critical underpinning of planning and projection tools, especially for transportation studies. The IRIO account framework was formulated by Isard (1951) and given a prominent place in his book, Methods of Regional Analysis: An Introduction to Regional Science (1960, 309–373). The importance of Isard’s work can best be explained by noting that it took prior analysts many years to make other attempts, a few of the important ones we explain here, first for interregional accounts, then for multiregional accounts.

Our second point is that as a way to understand certain aspects of production theory, the Isard IRIO accounts are overly detailed for many uses and in view of the cost and complexity of preparing such accounts, analysts have sought alternatives that can meet their needs without these drawbacks. Some of these alternatives have proven to be so widely accepted that their use is now considered standard practice for regional impact analyses in the United States.

We present this article in four parts. In the first, we briefly recount Isard’s earliest beginnings in regional input–output economics. In the second, we describe his conception of interregional accounts. In the third, we discuss an important offshoot of the IRIO model, namely the multiregional input–output approach (MRIO). In the fourth section, we explain the IRIO and MRIO models in connection with models that have gained wide acceptance in regional economic impact studies.

Historical Background

Isard started to develop the field of regional science and construct the IRIO system while working at the Harvard Economic Research Project with Wassily Leontief at Harvard University in the late 1940s. In the 1950s, Isard continued his input–output work while briefly teaching at the Massachusetts Institute of Technology (MIT). From 1953 to 1956, he served as director of the Section of Urban and Regional Studies, and taught regional economics as an associate professor of Regional Economics, in the Department of City and Regional Planning (now the Department of Urban Studies and Planning) at MIT. Then, in 1956, he was hired as a professor by the University of Pennsylvania, where two years later, he founded their regional science department and simultaneously the Journal of Regional Science. In his book, Introduction to Regional Science, he defined regional science as encompassing economic, social, and political issues, and he laid out a system of equations that he said portrayed an “ideal” IRIO table.

According to Isard,

… regional science as a discipline concerns the careful and patient study of social problems with regional or spatial dimensions, employing diverse combinations of analytical and empirical research. (p. 2) [It is] [t]he study of a meaningful region (or systems of regions) as a dynamic organism. (Isard 1975, 5)

Isard stated that regional science revolves around economics, geography, political science, sociology, anthropology, and so on, but it is different in that

the regional scientist’s region or system of regions represents to him living organisms containing numerous and diverse behaving units—political, economic, social, and cultural—whose interdependent behavior is conditioned by psychological, institutional, and other factors. (Isard 1975, 3)

To examine Isard’s “ideal” IRIO model, we put it into the context of different types of regional input–output tables/models, all of which are based upon Leontief’s well-known national input–output model, which is depicted as follows:

X = (I - A)^{- 1} Y,

where X = vector of outputs, A = matrix of technology coefficients, Y = vector of final demands.

Based upon the input–output framework, the IRIO model is one of the four major types of regional models.

Regional input–output model.

Intranational input–output model.

IRIO model (Isard’s “ideal” model).

MRIO model.

In Table 1, we show the differences among the four regional models and the national input–output model in terms of the interindustry input coefficients and the interregional trade flows. We note the sharp contrast in amount of data required to implement Leontief’s intranational and MRIO models versus Isard’s IRIO model. The added detail has benefits for those who want to study particular industries and regions. Isard’s IRIO model requires a separate input–output table for each region, and the analyst must specify the inputs and outputs for each region and industry of origin as well as each region and industry of destination. Leontief’s intranational (1965) and the Leontief and Strout (1966) MRIO models both require far less data. In the MRIO model, for example, the analyst needs only know how much of each input is used for a given industry in a given region; thus, the region of origin of the input is not required to implement the MRIO model, just the total input from all regions.

Table 1.

Regional Input–Output Models.

Type of model	Interindustry matrices			Trade matrices
	Number	Dimension	Flows	Number	Dimension	Flows
	(1)	(2)	(3)	(4)	(5)	(6)
National	1	m × m	x _ij	0	na	na
Regional	1	m × m	x _ij,rr	2	1 × m	x _io,no , x _io,or
Intranational	n	m × m	x _ij,gh	l	1 × mn	[x _io,go − x _io,oh ]
Multiregional	n	m × m	x _ij,oh	m	n × n	x _io,gh
Interregional	n	m × m	x _ij,rr	l	mn × mn	x _ij,gh

Source: Polenske 1995.

Note: Where, for the flow x_ij,gh , i = producing industry, i = 1, … , m; j = purchasing industry, j = 1, …, m; g = shipping region, g = 1, … , n; h = receiving region, h = 1, … , n; r = a given region; m = number of industries (commodities); n = number of regions; o = summation over producing (or purchasing) industries or shipping (or receiving) regions, for example, $x_{i j, o h} = \sum_{g = 1}^{n} (x i_{j, g h})$ ; x = interindustry or trade flows; na = not applicable.

The vectors of final demand are exogenous.

In viewing the range of regional models shown in Table 1, as the amount of regional trade detail increases, the amount of data needed for implementation rises; thus, the costs and time required to use them are augmented. For the intranational and MRIO models, the analyst uses the same concept of a technical coefficient for each region, where the regional source of the input is not identified. The technical coefficients in the Leontief intranational model are based upon the national input–output coefficients.

Interregional Input–Output Accounts

Isard’s IRIO conceptual interregional accounts are highly detailed. He argued that two related sets of accounting flows would provide for a complete system of accounts (Isard 1960, 314–16). First, he proposed the interregional current account flows, including interregional trade of goods and services by producing and consuming industry (i.e., what we now generally call IRIO), and he then proposed a second set, interregional capital account flows, which he discussed only briefly, but which are structured in a tabular fashion similar to the current account information only for capital goods. Together, these offer a detailed view of linked regional economies including local production technology and factor utilization, along with interregional trade flows and technology transfers. With both sets of flow data, an analyst’s ability to conduct studies of the labor and capital intensities of traded goods would be powerful indeed.^1,2

In the late 1950s, the Japanese first used Isard’s IRIO accounts by assembling regional data for Japan for nine regions and forty-seven sectors. Japanese officials constructed IRIO tables for 1960 and then extended them for 1965 and 1970 and every five years from then to 2005 (Japan Ministry of Economy, Trade, and Industry, Research and Statistics Department (METI) 2012). The 2005 accounts are for nine regions and fifty-three sectors. For certain portions of the accounts, METI makes nonsurvey-based approximations. For example, they approximate region-specific input purchases by certain (basic) industries first using average industry purchase coefficients for those inputs. Thus, the Japanese assume that regional production technologies for some industries are spatially invariant until analysts make later adjustments.

To our knowledge, the Japanese IRIO model is the only one regularly updated and maintained for ongoing use. That is not to say that other IRIO models have not been constructed. One significant effort is by Guilhoto and Sesso-Filha (2005) who used an IRIO accounting system for their detailed interregional study of ten Amazon states in Brazil. They found, among other things, that the ten states are highly dependent on imported production of intermediate goods from the rest of Brazil (which generated more than 90 percent of gross domestic product, and that the production technology of the ten states differs markedly from the rest of Brazil). Guilhoto has also made estimates of interregional trade for Brazil.

Development of IRIO accounts continues to raise some barriers for many regional economic analysts and planners in need of quick analyses, in part because they are extremely expensive to construct and can be time consuming to prepare. Absence of intersectoral trade data is a limitation common to many regional modeling efforts. Hulu and Hewings (1993), for example, developed a synthetic IRIO model for an eleven-sector, five-region model of Indonesia that relied only on gross regional product, the national technology matrix, and intermediate outputs and inputs. They used a multistage estimation process to estimate and reconcile interregional trade balances followed by biproportional adjustments for technology and trade coefficients. In this instance, in their model exposition, they did not exploit the IRIO information in any significant fashion.

We note that Isard did not specify the technology nor the trade theory underlying the additional detail required for the IRIO accounts. Also, in terms of implementation, the use of so many subscripts and superscripts in the IRIO model created difficulties, especially in earlier times when the computer and printing systems were not able to handle these. At the time of its introduction, such complexity of the notation may have hindered many scholars from entering the regional input–output field.

Multiregional Input–output Accounts

We noted in the introduction that as a way to understand the theory of production, the Isard IRIO accounts are overly detailed for many uses. Although termed ideal by Riefler (1973) in the sense that they offer complete information on the spatial composition of interregional trade and production technology, they are not what many regional practitioners would call “ideal.” For technology studies, Leontief provided far less detailed accounts than Isard, for example, by not differentiating the place in which a commodity was produced. Leontief maintained that, for studies of technology, an analyst does not need to know the origin of an input. It usually does not matter, for example, from which state the wood used in building a house comes. Rather, what does matters in building the house is whether the carpenter used wood or brick or some other construction material, each of which requires a different building technology, and the type of wood used (e.g., whether it is hardwood or pine), its cost and whether (from the standpoint of the region in question) the inputs are obtained internally or from other regions.

Thus, for the study of technologies and changes in them, the detail in the Isard IRIO accounts is “ideal” as an accounting framework, but only for those researchers in need of production origin information. Origin information may be useful for differentiating product characteristics and market shares, as noted by Batten and Martellato (1985). When the concern is for origin-related product characteristics, expanding the number of industry or commodity categories in the accounts may be sufficient to meet such informational needs. When the spatial decomposition of production is at issue, then the full IRIO account transaction data are indispensable. We conclude therefore that in terms of data requirements, the Isard IRIO model can be considered “ideal” for those analysts who need details. For further discussion of the attributes of the various regional input–output modeling approaches, see Hewings and Jensen (1986).

Several alternatives to the IRIO system were developed since the 1960s. From 1966 to 1970, Polenske (1970) and her Harvard research team of ten, for example, obtained MRIO data from census and other publications that provide state data for the United States, they did the first full implementation of the Leontief–Strout MRIO model in 1970. At first, they intended to use the Leontief–Strout gravity model for the trade data. With this approach, an analyst estimates the flow of a good between region g and region h as being equal to the amount of production in region g and the amount of consumption in region h, divided by the total production/consumption in the nation and multiplied by a gravity coefficient, represented by the inverse of the distance between the two regions. This model, however, failed to converge, because as Bon (1975) determined, such gravity coefficients are estimated from demand and supply conditions (i.e., equilibrium ones), which were not mathematically compatible with the regional input–output coefficients, which are derived from demand-only information. That led the Polenske team to implement the MRIO model with the Chenery–Moses column coefficients (Chenery 1953; Moses 1955). For more detail, the reader is referred to Polenske’s (2004) paper “Leontief’s Magnificent Machine and Other Contributions to Applied Economics.”

The technical coefficients in the original US MRIO model vary from one region to another and were derived from various US census publications, such as those for the Census of Manufacturers, Census of Agriculture, Census of Wholesale and Retail Trade, and so on (Polenske 1980). Because they are based on actual state data, the technical input coefficients vary from one state to another due to product mix, price, and technology differences. For interregional trade flows, the MRIO model provides much more detail than the intranational model, providing gross trade flows among regions. For the intranational model, an analyst only obtains the net trade flows. As we noted earlier, Isard’s IRIO model is detailed both in terms of regional technologies and interregional trade, details which are extremely useful for some analyses, but which are not required for many studies.

For applications, the question arises as to what is the theoretical underpinning of the different models? For the MRIO model, the underlying assumption is that the technology for making a good in a particular region depends only on the amount of a given input from a particular sector, not upon whether the input from that sector originates in region n or region m. By developing this model, Leontief was able to reduce significantly the amount of data required to implement the model, compared with the IRIO model, thereby lowering the costs of collecting data for its use. Not only are considerably more data required for the IRIO model, but, as we noted earlier, Isard did not specify the technology or the trade theory underlying the additional detail.

The MRIO framework has proven to be highly practical and has been adapted to many recent modeling efforts. One of the more ambitious uses in the context of international accounts is the World Input–Output Data Base (WIOD) system described by Timmer et al. (2012). This set of accounts links national input–output models for forty countries, with international trade data bridging bilateral transaction flows for thirty-five industries and fifty-nine commodities. Further, it augments current account data in ways not included in the Leontief/Polenske MRIO approach by distinguishing skill levels (classified as low, medium, or high) for the labor value-added inputs, factor-utilization detail (i.e., labor, capital, and energy), and environment emissions factors (e.g., carbon dioxide [CO₂], nitrogen oxides [NO _x ], sulfur oxides [SO _x ], carbon monoxide [CO], and several others) to form the basis for international social accounts, as well. By extending the model to include major environmental externalities, the WIOD model permits analysts to examine questions first raised in connection with Isard’s work and its negative impact on Puerto Rico’s environment, a matter we discuss later in this article.

Another attempt to approach a world-MRIO model is the four-region model estimated by Canning and Wang (2005) using data from the Global Trade Analysis Project at Perdue University. In this research, they test alternative estimation methods to the widely used biproportional balancing scheme when linking use and make transactions tables with international trade data. One approach they suggest is to use measures of interregional transportation impedance and/or transportation cost to establish parameter limits for selected technical and/or trade coefficients. In this way, the modeler can incorporate high-quality information (obtained either from survey or other means) into an MRIO or IRIO model rather than simple biproportional balancing.

Regional Economic Impact Analyses

Regional analysts are accustomed to the use of input–output accounts and models for the purpose of conducting regional economic-impact analyses. Frequently, these take the form of estimating the total job and income effects of a policy action that change with the level of activity in a certain sector. Very often, they use “off-the-shelf” models, such as those developed by the Minnesota IMPLAN Group with its IMPLAN model (Minnesota IMPLAN Group 2012a) or the Regional Economic Model, Inc.’s REMI model (Regional Economic Models, Inc. 2012). REMI incorporates input–output-based decomposition of policy actions into the affected sectors; then, it links output changes to other regions’ production and to factor markets, such that all regions’ production and prices are estimated in partial equilibrium fashion such that equilibrating adjustments occur over time. Currently, the REMI model structure is used for models of the United States, Canada, United Kingdom, Belgium, Italy, China, and South Korea. In the model, all interregional interactions (whether concurrent or feedback ones) occur through output-level changes in supplying regions, and changes in regional factor prices, which, in turn, generate demographic and investment responses, none of which are input–output based. The input–output models that are used are single-region ones estimated using regional purchase coefficients adjusted by transport impedance estimates between regions.

In the context of US regional modeling, a multiregional county-based modeling system from the Minnesota IMPLAN Group is now widely used for regional impact analysis. With this MRIO, users can conduct analyses of impacts across multiple regions, with full accounting for feedback and spillover effects (although not in the externality sense, directly). Originally, IMPLAN, based its model on commodity flows using “supply and demand pools” very much like Isard’s early attempts to estimate regional commodity production balances (Isard 1953) in which an analyst uses US production technology embedded in the 1947 national model to estimate regional commodity output and trade balances based on demand and supply requirements stemming from regional production.

The IMPLAN model developers modified the commodity-balance approach to become a regional purchase coefficient. As in the REMI model, they augment the commodity balance figures with commodity-transportation survey data in a gravity-type formulation such that balance is achieved consistently from sources that are physically close to supply sources for each commodity. IMPLAN’s developers note that this approach does not apply to estimating trade in services, which are estimated by analyst judgment in combination with a gravitational constant derived from the US Bureau of the Census survey-based Commodity Flow Survey (CFS) data (see Minnesota IMPLAN 2012b).³ IMPLAN’s developers, in describing the sources of trade flow information, do not disclose the means by which this constant is derived except to say that it has its origins with the CFS data. In view of the likely growth of web-based services delivery that is largely divorced from the distance decay functions that can be derived from the CFS, the service commodity flows are certainly feasible, but the degree to which they reflect actual regional interdependency remains unknown. In so much as tradable services have grown from being 42 percent of the 1963 national economy modeled by Polenske to 60 percent in 2011, the need for a more transparent approach here is critical.

We note that the “supply and demand” pools (or commodity-balance information) that are used to develop MRIO models were not viewed by Isard as sufficient for a complete analysis of trade and production. As Isard noted:

… the determination of the basic industries to be nurtured and promoted in a region, input requirements, and commodity balances tables are of little help except as a source of statistical data. Rather, one must resort to comparative cost studies, location theory, and traditional market and regional analysis … It is clear that in regional analyses, we want to know not only total input requirements but also the extent to which any input requirement of a given region is furnished by that region and each other region. Additionally, we want to know how the output of each industrial sector of a given region is tied to every industrial sector in the same region and in every other region. ( 1953, 174–75)

Isard’s last point in the above quote (the need to know the full set of interregional interindustry relationships) remains the key justification for the IRIO framework.

His first, less-stringent, requirement in the above quotation is knowledge of whether an input requirement is supplied from within a region or some other region. This can be determined with the MRIO framework. The difference between the two approaches is vast when it comes to the data requirements for the accounting of trade flows. Whereas the IRIO approach remains largely a theoretical construct even after sixty years of rapid advances in information processing and development that could have supported its development, the MRIO approach is not only a reality, but has become a standard contemporary analysis tool.

Rather than to use the IRIO model, for most studies, we prefer to use a model for which the underlying technology and trade theories are clear, and many analysts may not find the effort worthwhile to gather and process the data required for the IRIO model. Even so, the Isard IRIO model remains extremely useful for transportation and other analysts who need details on commodity shipments.

Conclusion

Isard implies, in his discussion of Puerto Rico in Introduction to Regional Science, as to what truly “ideal” accounts would allow us measure:

As we have indicated previously, there is no way of evaluating the total effect. The only thing one can do is ask the people themselves whether it was worth it. We from the more advanced industrial regions can offer our opinions. But they mean very little. And we should go down to Puerto Rico and see the havoc wrought upon the environment. The Penuelas region of the petrochemical plants is a messy wasteland. The cities have not retained their traditional qualities, and all too often they exhibit congestion and squalor amid affluence. On the other hand, to repeat, the hundreds of thousands of pot-bellies have disappeared. (Isard 1975, 469)

When Isard acknowledges that the problems of development were not always evident even using the most detailed framework and data, it is not because the problems themselves were to be “swept under the rug.” Rather, he seems to despair that we can only measure so many things to put in our models. By 1975, modeling social and environmental externalities was still beyond current means, and, as such, no model could be considered truly ideal. We note, however, that some progress has been made on this front. The WIOD inclusion of emissions and labor skill levels, now nearly sixty years later, is evidence of progress toward Isard’s ideal, and although much work remains, we argue for following Isard’s own suggestion regarding his contribution to his field. Ask the people, and, in this case, ask those actively engaged in regional economic development work, whether Isard’s methods are valuable to them. We see his methods used nearly everyday, but now only very rarely without consideration of negative side effects. Despite detractors, Regional Science, including its tools and methods, and even its theories (admittedly not all of which are unified) have stood the test of time. The fact that there is a growing awareness of the consequences of economic development is a tribute to the pioneering work by Walter Isard. He deserves far more credit than that offered him by those who subsequently built on his foundation.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes

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