Integrated Regional Econometric and Input-Output Modeling

Integrated Regional Econometric and
Input-Output Modeling

Sergio J. Rey^{1 2}

Department of Geography San Diego State University
San Diego, CA 92182

January 1999

¹Part of this research was supported by funding from the San Diego State University Foundation Defense Conversion Center, which is gratefully acknowledged.
²This paper is dedicated to the memory of Philip R. Israilevich.

Abstract

Recent research on integrated econometric+input-output modeling for regional economies is reviewed. The motivations for and the alternative methodological approaches to this type of analysis are examined. Particular attention is given to the issues arising from multiregional linkages and spatial eﬀects in the implementation of these frameworks at the sub-national scale. The linkages between integrated modeling and spatial econometrics are outlined. Directions for future research on integrated econometric and inputoutput modeling are identiﬁed.
Key Words: Regional, integrated, econometric, input-output, multiregional.

Integrated Regional Econometric+Input-Output Modeling

1

1 Introduction

Since the inception of the field of regional science some forty years ago, the synthesis of different methodological approaches to the study of a region has been a perennial theme. In his original “Channels of Synthesis” Isard conceptualized a number of ways in which different regional analysis tools and techniques relating to particular subsystems of regions could be integrated to achieve a comprehensive modeling framework (Isard et al., 1960). As the field of regional science has developed, the term integrated model has been used in a variety of ways. For some scholars, integrated denotes a model that considers more than a single substantive process in a regional context. Examples include models that combine regional economic components with environmental or ecological concerns (Briassoulis, 1986; Hafkamp and Nijkamp, 1981) or models that consider demographic and labor market interactions (Ledent and Gordon, 1981; Madden and Batey, 1980). These are referred to as substantively integrated regional models.
A second way in which a model can be considered integrated is if it treats multiple spatial scales and/or interacting regions within the same framework. Examples of these spatially integrated models include the work by Courbis (1979, 1980, 1982a,b) who developed a spatially hierarchical model for France that considers the interactions between the national, regional and urban scales. More recently, Jin and Wilson (1993) have suggested a multispatial integrated model which emphasizes interactions between urban zones within a larger interregional context. A further example of a spatially integrated model would be one where the interactions between multiple regions, at the same scale, are considered within the framework. This could include the so called interregional (IRIO) (Beyers, 1989; Oosterhaven, 1981) and multiple (MRIO) (Shao and Miller, 1990) input-output models as well as multiregional econometric models (Beaumont, 1989; Lienesch and Kort, 1992; Treyz et al., 1992).
The final manner in which a model can be considered integrated is if it combines more than a single modeling methodology in the same framework. This has been done in a wide variety of ways such as: extended inputoutput/demo-economic models (Madden and Batey, 1980); combined linear programing and input-output models (Anselin et al., 1990); optimization and spatial interaction models (Harris, 1988), among others.
In a recent update of his conceptualization Isard has identified the integration of econometric and input-output as a new approach to synthesis (Isard et al., 1998). This recognition stems from the recent heightened level of activity on integrated econometric and input-output (EC+IO) model-

2ing over the last two decades (Anselin and Madden, 1991; Beaumont, 1990; Rey, 1998). This paper presents an overview of recent research on integrating econometric and input-output models at the regional scale. The focus is mainly on efforts in the U.S., with an emphasis on the issues to be faced in the implementation of these frameworks in practice. As such the objectives of this paper are threefold. First, the paper will outline the main approaches that can and have been used to implement EC+IO models in practice. Secondly, a number of outstanding methodological issues associated with this type of modeling at the regional scale are discussed. Finally, a number of promising directions for future research are highlighted. Given these objectives, the paper is intended for regional analysts who may be considering the development of such models for their own regions, as well as for theoretical and applied regional modelers interested in recent developments in integrated EC+IO modeling.
In the following sections of the paper, I first discuss the motivations for integrated EC+IO modeling at the regional scale, where the focus is on both theoretical and practical concerns. Next, the different approaches that have been taken towards the implementation of integrated models are reviewed, with attention given to the relative merits of the alternative approaches. This is followed by the identification of a number of issues that arise in integrated modeling at the regional scale that are distinct from national efforts in that they are associated with multiregional linkages and other spatial issues. I then outline a series of promising new directions in integrated modeling, and I close with some more general remarks.

2 Motivations for Integrated Modeling

Given the wide variety of regional economic models that are available, it is important to properly situate integrated EC+IO within this larger ﬁeld. EC+IO models can be viewed in a variety of ways. For example, some scholars (West and Jensen, 1995) see a competition arising between the EC+IO models and regional computable general equilibrium models (CGE),¹while others have tended to stress the similarity between EC+IO and CGE models (Treyz, 1993). Even within the ﬁeld of EC+IO modeling there is some debate about the distinctions between the integrated EC+IO model and its individual components (i.e., EC and IO) (Beaumont, 1990). Therefore, as a way of trying to situate EC+IO models it is useful to focus on the mo-

¹For an excellent survey of recent work on regional CGE models see Partridge and
Rickman (1999)

3
Table 1: Comparative Characteristics of IO, EC and IO+EC Models
Characteristic IO EC EC+IO

√

√√√√√

Dynamic
Disaggregate
Price Responsive Impact Analysis Demand Driven
Forecasting

√
√√√√√√
√√

Inferential
Multiregional
??

√

tivations for this type of modeling, which are of two types: theoretical and practical.

2.1 Theoretical Motivations for EC+IO Modeling

One of the main theoretical motivations for implementing EC+IO models largely stems from the restrictive assumptions of each component model (i.e, EC or IO) when used in isolation. To illustrate the key assumptions, Table 1 summarizes the characteristics of the econometric and input-output models, as well as those characteristics that are inherited by the integrated framework.
During the early development of the field of regional science the classic regional IO model became a mainstay of the analyst’s toolkit. Yet with this widespread application came a growing awareness of the limitations of the behavioral representation offered by IO models. Chief among these were the assumptions of linear production technologies; constant returns to scale; homogeneous consumption functions; and price inflexibility.
Compared to IO models, regional EC models have historically not enjoyed the same level of popularity. This is explained, in part, by the more extensive data and calibration requirements of these models. Moreover, from a theoretical perspective, the modeler is additionally responsible for specification of the underlying theory, in contrast to the case for an IO model where the theoretical basis is inseparable from the framework.
While both IO and EC models are macroeconomic in nature, a crucial difference between these models pertains to their respective views of regional economies. IO models are essentially general equilibrium in nature in the

4sense that the markets clear. This occurs through supply adjustments to demand shocks, while prices play no role in the market response. On the other hand, regional EC models often depict regional economies in a partial and/or disequilibrium context, where the focus is typically on the dynamic adjustment path of the economy to exogenous shocks. However, despite this fundamental theoretical difference between the IO and EC models, both are essentially demand driven when applied at the regional scale (Beaumont, 1990).
Some of the theoretical differences have served as key motivations for combining IO and EC models. Specifically, the lack of price responsiveness in IO models has been the focus behind many integrated IO+EC models. Because this price rigidity is present throughout the IO model there have been multiple channels of integration between the EC and IO components. Table 2 shows the input-output accounts for a single region, with n industries, which provides the context to view these channels. Central to the integration of the IO and EC models is the following identity:²

X = AX + Y

(1) where X is an n by 1 vector of industry output, Y is an n by 1 vector of ﬁnal demands and A is an n by n regional input-output coeﬃcients matrix with a typical element:

x_ija_ij=

.

(2)

X_i

It is important to emphasize the role of aggregation in the integration. At the macroeconomic level, there are m elements of aggregate ﬁnal demand: personal consumption C; investment I; government expenditures G; and net exports (NE = Exports − Imports). Each of these aggregate components is obtained as the sum of the industry speciﬁc values, for example:

n

X

C =

C_i

(3)

i=1

and total gross regional product is:

Y = C + I + G + NE.

(4)
One of the more common channels of integration has focused on personal consumption C. In regional IO models this has either been exogenous in

²Unless explicitly noted otherwise, all variables are intended to be measured at the regional scale. Later in the paper, when discussing multiregional linkages, locational superscripts are added for clarity.

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Table 2: Single Region Input-Output Accounts
Interindustry
Sales
Final Demand
Total Output

X₁

x₁₁x₁₂· · · x_1nC₁I₁G₁NE₁

x₂₁x₂₂· · · x_2nC₂I₂G₂NE₂

X₂

...

.

x_n1x_n2· · · x_nnC_nI_nG_nNE_n
X_n

WOV

Wages Other Total

w₁w₂· · · w_nov₁ov₂· · · ov_n

Outlays X₁X₂· · · X_n

C

I

G

NE

the so called household open models, or endogenous in the closed models. Both of these treatments of consumption suffer from theoretical shortcomings. In the open IO models there are no induced effects since the incomeconsumption link is severed. On the other hand, approaches towards endogenizing the household sector, while internalizing the income-consumption linkage, have a number of restrictive assumptions including: income homogeneity, failing to distinguish between marginal and average consumption propensities, and treating existing residents, migrants, as well as employed and unemployed individuals uniformly (Batey and Weeks, 1989). In response, a number of modelers (Treyz, 1993; West, 1994) have endogenized consumption in econometric equations which then are used to generate predictions of consumption, reflecting some of these distinctions, and to drive the input-output model.
Related to the use of the integrated approach to achieve a more theoretically satisfying representation of regional personal consumption behavior is the specification of additional elements of final demand in econometric equations. For example, investment, exports, and governmental expenditures have all been endogenized in various integrated models. This is in contrast to the stand-alone use of IO models for which each of the demand components is treated as exogenous, or is specified in some ad-hoc fashion (L’Esperance, 1981). While it is true that the aggregate components of final demand are often found in regional EC models, in the integrated EC+IO model the advantage of increased sectoral disaggregation is gained, as is discussed below. Thus, the integrated approach represents an improve-

6ment over the traditional IO and EC models with regard to the treatment of the final demand components of regional economies. This is a key distinguishing feature of the integrated approach given the growing recognition by regional analysts of the importance of these components for the growth and functioning of regional economies (Hewings and Jensen, 1986).
In addition to the relaxation of the assumptions regarding final demand, the integration of EC and IO models has also been used to address the assumption of a fixed employment-output relation in the IO model. This has been done by situating the labor demand equations in an econometric module, in which industry output, generated by the IO model, appears together with other determinants of labor demand (Conway, 1990; West, 1991).
In many cases the objective of exploiting the complementary nature of the EC and IO components has been successfully achieved in the sense that the resulting EC+IO model provides distinct advantages over the use of either model in isolation. However, as indicated at the bottom of Table 1, there are two instances where the integration of these two models raises a number of complications. The first pertains to the inferential framework that may be used for the integrated model. This arises because the traditional view of a regional IO model is a deterministic one in the sense that the coefficients are fixed parameters with no associated uncertainty. In contrast, EC models have a well developed framework for dealing with uncertainty. How these two perspectives are combined raises a number of methodological issues that require further attention. The second complication relates to the treatment of multiregional linkages in the integrated model. In this case both IO and EC models are capable of representing multiregional linkages, however in the integrated model both representations cannot coexist and some decisions about how best to model these interregional linkages must be made. The complications associated with inference and multiregional linkages in integrated models have not received much attention and are revisited in sections 3.2 and 4, respectively.

2.2 Practical Motivations for EC+IO Modeling

In addition to the theoretical gains that are made possible from integration, research on EC+IO models has also been motivated by a number of practical concerns. These motivations fall into three categories: improved forecast performance; more comprehensive impact analysis capabilities; and measurement error concerns.

7

Forecast Performance

There is now a modest body of literature suggesting that integrated EC+IO models can offer more accurate forecasts than the traditional structural econometric models (Glennon et al., 1987; Moghadam and Ballard, 1988; Rey, 1998). The same appears to be true of the time-series models (i.e., atheoretical) in which labor market models employing a vector autoregressive (VAR) approach are often dominated by Bayesian VAR (BVAR) models in which IO relations are used to specify employment determination equations (LeSage and Magura, 1991; Magura, 1987).
In addition to the benefits of increased forecasting accuracy, the use of prior restrictions, either in a frequentist or Bayesian approach, can increase the precision of the econometric estimators used to calibrate these models. This would result in improved inferences about the interindustry relationships in the region. It is also possible that some of the increased forecasting accuracy might reflect this increased precision, yet the issue has not been fully explored by integrated modelers.

Impact Analysis Capabilities

The integration of EC+IO methods has also improved the scope and capabilities of impact analysis, over what was available using either model alone. A long recognized limitation of regional IO models in impact analysis is that the time path for the estimated impacts to work themselves through the regional economy is largely unknown. This is due to the comparative-static nature of the IO model. Econometric models, in contrast, have dynamics as a central feature of their impact analysis capabilities. On the other hand, EC models are much more industrially aggregate than are IO models, so the representation of dynamics comes at a cost (see Table 1). However, by combining the two in an EC+IO model, a dynamic and industrially disaggregated impact analysis tool can be developed.
A second limitation of IO models relative to EC approaches in impact analysis is the estimated impacts of the former are point estimates lacking any measurement of uncertainty. Forecast conﬁdence intervals, in addition to point estimates, of the impacts are commonly produced in EC analysis. Here again, the fusion of the two approaches oﬀers the potential for the mitigation of a shortcoming of the IO framework, as well as the ability to increase the level of disaggregation over what is available in EC analysis.

8

Measurement Error

A third practical motivation for the integration of EC+IO models relates to the issue of accuracy in the regional IO literature. Given the prohibitive costs of implementing full survey IO tables, the vast majority of regional IO models have been estimated using regionalization techniques (Lahr, 1993). Many of these techniques adjust a national IO coefficients for the region’s degree self-sufficiency, for example using location quotients. While these models are widely used, the accuracy of the various regionalization techniques has been questioned by some (Stevens et al., 1989).
A number of integrated modelers have suggested that by incorporating the econometric component in the integrated framework, some adjustments to the IO relathionships/coefficients are made possible through the estimation process. Moghadam and Ballard (1988) argue that there is an implicit form of regionalization of the national IO table that occurs in the integration. Indeed, their integrated EC+IO model relies on a national rather than a regional IO table. Conway (1990) makes a similar argument about the adjustment for regional trade over time in an integrated model of Washington State.
A related motivation for the integration of EC+IO models from a practical perspective is that model validation becomes much more comprehensive. In the context of stand alone IO analysis, model validation is often limited to the analyst’s view of the reasonableness of the multipliers and estimated impacts since there is no objective measure available to compare these with. EC+IO models have the advantage of being compared to observable series (i.e., typically income and employment), so the accuracy of the resulting predictions can be measured much more rigorously than can predictions from an IO model.³This is also a comparative advantage that EC+IO models have over regional CGE models, since the validation of the latter type of models is typically limited to how well the model fits the data on which it is calibrated.

3 Approaches Towards Integrated Modeling

A growing number of integrated models have been implemented at the regional scale in recent years. There are a number of dimensions that can be used to organize these eﬀorts. Recently, Rey (1998) has suggested a