Integrated Regional Econometric and Input-Output Modeling

Sergio J. Rey12 Department of Geography San Diego State University San Diego, CA 92182 [email protected]

January 1999

1Part of this research was supported by funding from the San Diego State Uni- versity 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 out- lined. Directions for future research on integrated econometric and input- output 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 input- output/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- Integrated Regional Econometric+Input-Output Modeling 2 ing 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. Sec- ondly, 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),1 while 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) Integrated Regional Econometric+Input-Output Modeling 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 en- joyed 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 Integrated Regional Econometric+Input-Output Modeling 4 sense 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: xij aij = . (2) Xi 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: Xn C = Ci (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. Integrated Regional Econometric+Input-Output Modeling 5

Table 2: Single Region Input-Output Accounts

Interindustry Final Total Sales Demand Output x11 x12 ··· x1n C1 I1 G1 NE1 X1 x21 x22 ··· x2n C2 I2 G2 NE2 X2 ...... xn1 xn2 ··· xnn Cn In Gn NEn Xn Wages w1 w2 ··· wn W Other ov1 ov2 ··· ovn OV Total Outlays X1 X2 ··· Xn CIGNE

the so called household open models, or endogenous in the closed models. Both of these treatments of consumption suffer from theoretical shortcom- ings. In the open IO models there are no induced effects since the income- consumption link is severed. On the other hand, approaches towards endo- genizing 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- Integrated Regional Econometric+Input-Output Modeling 6 ment 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. Integrated Regional Econometric+Input-Output Modeling 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., a- theoretical) 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. Integrated Regional Econometric+Input-Output Modeling 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.3 This 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

3It may even be possible to use the accuracy of integrated models, based on different IO models, as an indirect test of the accuracy of the underlying IO tables. Integrated Regional Econometric+Input-Output Modeling 9 taxonomy of models based on the underlying integration strategy employed as a way to structure the diversity of implementations. In addition to using these integration strategies to distinguish among empirical models, the approaches towards model calibration offer a second dimension to use in comparing these models. In this paper we use both of these dimensions to highlight the main differences across modeling methodologies and the implications these differences hold for the implementation of these models in practice.

3.1 Integration Strategies An integration strategy defines the manner and extent to which the EC and IO components are combined in the final framework.4 Three classes of integration strategies exist: linking; embedding; and coupling. Figure 1 portrays the general channels of integration in the coupling strategy which serves as a useful point of comparison for these three strategies. In the coupling approach, there is full two-way feedback between the IO and EC components, with the two central channels being the FinalDemand ⇒ IO flow and the IO ⇒ Labor Market connection. A number of subsequent interactions between the labor, demographic and final demand components closes the IO ⇔ EC interaction. In the linking strategy, only one of the IO-EC linkages is present as the integration is of a recursive form. In the embedding approach, the interaction between the EC and IO components is simultaneous, however, the number of the channels of integration is much fewer than is the case in the coupling strategy. The specific implementation of these strategies is outline below.

Linking In the linking strategy the integration between the EC and IO components has been accomplished in two ways. In the EC ⇒ IO approach (L’Esperance, 1981) the final demand shock is specified as endogenous rather than being specified exogenously by the analyst. This is done by modeling aggregate components of demand in the EC model, for example personal consumption: C = ZC βC + (5) where ZC is a vector of determinants of consumption with associated parameters βC and is a stochastic error term. Estimates for βC are obtained through the application of an appropriate econometric method to (5).

4For a more detailed analysis of integration strategies see Rey (1998). Integrated Regional Econometric+Input-Output Modeling 10

FINAL DEMAND COEFFICIENT CHANGE INTERINDUSTRY RELATIONS

Consumption Trade Coefficients

U.S. Economy

Exports Federal Technology Regional Input-Output Module Government

International Investment Economy

Labor Productivity Employment Demand

S&L Govt.

Employment Labor Market

Income Population

Figure 1: A Coupled EC+IO Model Integrated Regional Econometric+Input-Output Modeling 11

Having possibly specified an econometric model for each additional endogenous component of aggregate final demand, total final demand at the industry level is obtained through the disaggregation of each component (endogenous and exogenous) using fixed shares taken from a base year IO model : Yj = hCjC + hIjI + hGjG + hNEjNE (6) P P P P n n n n where j=1 hCj =1= j=1 hIj = j=1 hGj = j=1 hNEj. The linkage between the IO and EC models works through the classic reduced form IO identity: − −1 ∆Xj =(I A)j. ∆Y (7) − −1 where (I A)j. represents the jth row of the Leontief inverse, ∆Xj is the change in gross output for industry j in response to a change in final demand, where the latter is obtained from equations (5)-(6). It is important to note, however, that there is no subsequent feedback from the solution of (7) to (5). In the IO ⇒ EC linking the direction of the recursion is reversed in that output from the IO identity (7) is used to drive a number of econometric equations. For example, a labor demand equation might take the following form: ei = Zeβ + αXi + i (8) where α is the parameter linking output to employment in sector i.Mod- els employing this form of the linking strategy are described in (Kort and Cartwright, 1981; Shields and Deller, 1998; Stevens et al., 1981). There are two subtle, but important, distinctions between the EC ⇒ IO and IO ⇒ EC types of linking that can be seen by comparing equations (5) and (8). The first thing to note is that in the IO ⇒ EC approach, the final demand shock in (7) is specified by the analyst, while in the other approach this shock is determined in the econometric module. The second distinction is that the econometric component is present in many more equations in the IO ⇒ EC type of linking compared to the former, since there are n (i.e., one for each industry) labor demand equations (8), but only m components of final demand each with an equation of the form (5).

Embedding The second type of integration strategy is largely dominated by its EC component in that information from the IO model is embedded within a series of econometric equations. This has been implemented in two general ways, Integrated Regional Econometric+Input-Output Modeling 12 either in a structural econometric framework or in a time-series approach. In the structural approach the focus is on theoretically inspired regional employment and income determination speciﬁcations, for example a typical employment equation appears may appear as:

ei,t = f(Zld,t,Zla,t,Zsup,t,β,)(9) where Zld,t is a vector of variables representing local disaggregate interindustry linkages, Zla,t is a vector of local aggregate or macro variables, Zsup,t are variables reflecting supraregional linkages, β, is the vector of parameters associated with these variables and is a stochastic error term. Within the structural embedding models there have been a number of ways the interindustry variables have been specified. The earliest approach, suggested by Moghadam and Ballard (1988), was to let this term be based on the interindustry demand variable (IDV): Xn IDVi,t = ai,jej,t. (10) j=6 i The IDV collapses all the possible n−1 (direct) linkages that industry i may have with the other industries in the region, into a single variable. Because of this parsimonious characteristic, the IDV has attracted much recent attention in the embedded literature with a number extensions having been suggested (Coomes et al., 1991a,b; Rey and Dev, 1997; Rey and Jackson, 1999; Stover, 1994). A somewhat different approach to the use of the IO table in structural embedding has been to use the size of the coefficients to select a subset of industries that appear as individual components of Zld,t in (9). For example, White and Hewings (1982) were early proponents of such an approach suggesting that the employment in the sectors associated with the two-three largest coefficients in the ith row of a regional IO appear as explanatory variables in (9). More recent modifications of this approach can be found in (Glennon and Lane, 1990; Glennon et al., 1987, 1986).5 In the Bayesian approaches towards embedding, the IO coefficients are treated as prior information on the interindustry relationships. The approach is similar to that in the second class of structural embeddings in that a subset of industries are ultimately included in the final specification. However, the Bayesian approach offers a much more consistent probabilis- tic framework for the incorporation of the interindustry restrictions in the

5An interesting use of IO tables for similar purposes at the national level can be found in Shea (1993). Integrated Regional Econometric+Input-Output Modeling 13 econometric model. The Bayesian applications have primarily emphasized forecasting (Fawson and Criddle, 1994; LeSage and Magura, 1991; Magura, 1990; Partridge and Rickman, 1998) although they have also been used to analyze the nature of dynamic relationships between regional economies, as in the question of identifying lagging-leading regions (Magura, 1987). In general terms, in the class of embedding approaches model speci- ﬁcation has largely been determined by which series are available at the regional scale. The implicit philosophy underlying the embedded approach is the minimization of measurement error at the expense of increased speciﬁ- cation error. As will be made clear below, this makes the embedded models distinct from the coupled models.

Coupling The final, and most ambitious, integration strategy is the coupling approach which essentially extends the linking approach to a fully simultaneous EC ⇔ IO system. This has been accomplished in a number of ways, but a common theme has been to expand the econometric equations for final demand to include a feedback mechanism, for example, using the consumption function from (5): C = ZC βC + VAβVA+ (11) where VA = W + OV is value added from Table 2. There is an important difference between the generation of VA in the coupling and linking approaches. Both strategies solve for VAusing:6

VA= VXˆ (12) where Vˆ is a diagonal matrix of value added coeﬃcients. However, in the coupling approach, the IO identity (7) is re-expressed in its structural form (1). The solution of the coupled model relies on an iterative algorithm, such as Gauss-Siedel, that passes through equations (11) ⇒ (4) ⇒ (1) ⇒ (12) ⇒ (11) until the solution for the endogenous variables converges.7 This iterative solution can be seen as an approximation to the closed form solution of (7), with the important exception that the iterative solution includes

6It should be noted that the coupled models often decompose aggregate VA as determined by (12) using econometric equations that permit factor substitution (i.e., between labor and capital) in function of relative prices (Treyz, 1993). 7There are typically additional equations, associated with other regional subsystems, included in the sequence in most coupled models. Integrated Regional Econometric+Input-Output Modeling 14 additional equations that are designed to relax the fixed proportionality assumptions inherent in the IO model. While the coupled models clearly represent the most comprehensive approach towards integrated modeling at the regional scale, this comes at a potential cost. The final demand equations, as represented by (11), require a time series of both the endogenous and exogenous variables. In the case of the U.S., these series are typically not available below the national scale. Consequently, the modeler must first develop synthetic variables in order to implement these equations.8 Most often the development of these equations is based on a Kendrick and Jaycox (1965) approach which essentially propor- tions out a national series, for example in the case of personal consumption expenditures:

r r US PIt Ct = Ct US (13) PIt r 9 where PIt is personal income at time t in region r. . The philosophy here is the minimization of speciﬁcation error at the expense of measurement error, since the accuracy of the constructed series required for the implementation of the coupled models is largely unknown.

3.2 Approaches Towards Calibration One of the key features that distinguishes integrated EC+IO models from regional CGE and IO models is the their reliance on econometric estimation of key model parameters for the regions in question.10 There are three dimensions to consider in the calibration of an integrated model: what type of data to use, which estimation method to employ, and the interpretation of inference.

Data Three diﬀerent types of data have been used to estimate the parameters of integrated EC+IO models: [1] time series; [2] cross-sectional; and [3] panel data. When time-series for individual regions are used to estimate models,

8The construction of the synthetic variables can sometimes be omitted through the use of substitutions (Conway, 1979) 9It is important to note that the construction of synthetic regional variables is not specific to coupled models, but is a common practice in the implementation of regional models in general 10While some parameters used in CGE models are based on econometric studies, these estimates are rarely for the region of interest but rather taken from the literature. Integrated Regional Econometric+Input-Output Modeling 15 the interest typically is limited to the dynamic behavior of the interindustry relations in that single region. Models for Washington, (Conway, 1990)11 Ohio (L’Esperance, 1981) and Chicago (Schindler et al., 1997) represent examples of this approach. In contrast to the mainstream econometric literature, integrated modelers have largely ignored the issues that arise when estimating parameters using non-stationary variables. Related to this is the role of cointegration between the industry employment series which is to be expected given the theoretical interindustry relationships at the heart of the integrated framework. I return to these issues below.12 In models using cross-sectional data for calibration, the co-variation between the dependent and explanatory variables across the regions is the basis for parameter estimation. For example, the models in the Community Analysis and Planning Network (CPAN) (Scott and Johnson, 1998) utilize detailed county level data in the implementation of linked integrated models. The advantage of this approach is that a large number of variables are available from various population and industry census sources, in contrast to the smaller number of variables that are available as consistent time series at the regional scale. This permits the estimation of more complex behavioral specifications for key model equations. At the same time, however, this approach is based on an implicit assumption that the estimated parameters are identical across the cross-sectional units, in this case the different regional economies. While some attention has been given to the relaxation of this spatial homogeneity assumption (Swenson and Otto, 1998), there are often degrees of freedom constraints that limit the amount of spatial parameter variation that can be allowed for. The final type of data used in integrated models is based on the pooling of time series from multiple regions in the estimation of model parameters. The leading proponent of this approach has been Treyz (1993) who stresses the need to uncover structural relationships that hold over all regions as a way to provide scientific explanations of regional economies. From this view, time series approaches are not likely to produce reliable estimates of structural coefficients, due to the typically short nature of most regional time series and problems on non-stationarity. However, the parameters in question here actually have to be constant over the regions, in order for the gains in efficiency from the pooling of regional time series to be realized.

11Conway (1990) has argued that his model uses cross-sectional data, but his use of the term relates to observations from different industries in the same region. In the current paper we use the term cross-section to denote observations from different economies. 12For overviews of the issues of non-stationarity and cointegration that are relevant to integrated modeling see Hamilton (1994) and Lütkepohl (1991). Integrated Regional Econometric+Input-Output Modeling 16

This assumption has rarely been checked in the integrated models using panel data. A final point to keep in mind in calibrating an integrated EC+IO model is that the inferences about regional economies produced by the models may be sensitive to the choice of data (i.e., time-series, cross-section or panel) used to calibrate the model. More specifically, it is generally agreed that in other areas of empirical econometric analysis, cross-sectional studies tend to yield long-run responses, while time-series studies tend to yield short-run responses (Baltagi, 1996, pg, 193). How these different types of data and views may be exploited in a complementary fashion in integrated modeling remains to be investigated.

Estimation Methods There are a number of issues associated with the choice of an econometric estimator in integrated models. The ﬁrst is the presence of substan- tial simultaneity in the integrated model and its proper treatment from an econometric perspective. As is well known, ordinary least squares (OLS) is inconsistent when applied to a system of simultaneous equations. There are a wide number of systems estimators that are consistent in such settings that can be employed13 as has been done in a number of integrated EC+IO models (Shields and Deller, 1998; Swenson and Otto, 1998). However, the type of simultaneity acknowledged in the integrated literature thus far is what can be referred to as traditional or feedback simultaneity. There is a second type of simultaneity that is present in multiregional integrated models that arises from the feedback between regions. This form of simultaneity has not been acknowledged, yet as shown in Rey and Boarnet (1998) this simultaneity is fundamentally distinct from traditional simultaneity and requires new types of estimators. As mentioned above, the use of non-stationary and/or cointegrated variables and the associated econometric implications have been largely ignored by integrated modelers. One of the major dangers is that the modeler picks up spurious relationships as a result of the non-stationarity. This would lead to a poorly speciﬁed model of limited worth for policy analysis. Interest- ingly, however, if the system of equations is estimated with two-stage least squares (TSLS), Hsiao (1994) has shown that the problems associated with non-stationarity and cointegration are mitigated. This would appear to provide further motivation for the use of TSLS over OLS in the calibration of integrated EC+IO models.

13For an overview of these approaches see Greene (1993). Integrated Regional Econometric+Input-Output Modeling 17

Approaches to Inference Related to the choice of data and estimation method is the role of inference in an integrated EC+IO model. As was indicated in section 2.1 there are a number of complications that arise from the integration of a deterministic IO model with a stochastic EC model in the same framework. It turns out that the well-structured inferential basis of an EC model does not have a straightforward translation to the integrated model. These complications must be addressed if the potential benefits of using an integrated EC+IO model for inference, identified in section 2.2, are to be realized. The complications can be highlighted by considering the IO identity (7) which specifies gross industry output as a function of intermediate and final demand. In the coupled model, certain elements of final demand are made endogenous, for example, as was done for the consumption function in (5). Substituting (11) into (6) and then (7) results in: ˆ X = AX + hc(ZC βC + βVAVA+ )+hFˆ F (14) − where hc is an n by 1 vector of share coefficients, hFˆ is an n by m 1matrix of share coefficients and:   I 00   Fˆ =  0 G 0  . (15) 00NE

This structural equation is further modified by taking into account the linkage between value added and industry output from (12): h i 0 ˆ ˆ X = AX + hc ZC βC + βVAinVX+ + hFˆF (16) where in is an nby1 unit vector. The reduced form for this system is: −1 ˆ −1 X =Γ hcZcβC + hFˆF +Γ hc (17) where: − − 0 ˆ Γ= I A hcβVAinV . (18) The integrated multiplier matrix Γ−1 poses some difficulties from an inferential perspective. The first is that even if unbiased estimates for βVA could be obtained for (11), their insertion into (18) would not likely lead to an unbiased estimate for the multiplier matrix, since it is well known that for a non-linear function: −1 E Γ−1 =6 E Γ . (19) Integrated Regional Econometric+Input-Output Modeling 18

The second difficulty relates to the expected value of the third term in (17) which, in general, will not be equal to zero even though E[]=0.This is because some of the elements of Γ will be stochastic. As a result of these complications, the estimates of the policy multipliers of the exogenous variables Zc are likely to be biased as are the estimates of gross sectoral output X. As a consequence the standard methods for impact analysis using either a stand alone IO model or an EC model cannot be directly applied to the case of an integrated EC+IO model. While IO models are deterministic, their integration with a stochastic EC model results in a stochastic EC+IO model. On the other hand, when using EC models for impact analysis, the property of unbiasedness typically holds and this simplifies the development of confidence intervals to attach to estimated impacts. In the case of the EC+IO model, however, one can no longer rely on the unbiasedness property. In order to exploit the inferential capabilities of integrated EC+IO models alternative approaches need to be considered. There are two general possibilities. The first would be to rely on asymptotic results to provide an- alytical results that could form the basis for developing confidence intervals (Goldberger, 1990). However, such an approach may be difficult to implement in practice due to the nonlinearity of (17) and the question of how relevant large sample results would be in the finite sample situations facing most regional modelers. The second alternative approach could be based on a resampling strategy such as a bootstrap (Efron and Tibshirani, 1993; Jeong and Maddala, 1993) or a stochastic simulation perspective (Fair and Taylor, 1990; Murinde, 1992; Rey, 1997c). In these approaches one creates an artificial sampling distributions for the βC and/or , based on their estimated variance-covariance matrices and assumed parametric densities, and substitutes realizations from these distributions into (17) to generate sampling distributions for the industry outputs X. Theses distributions can be examined to construct empirical confidence intervals for the estimated impacts and forecasts generated by the integrated model.

4 Spatial Linkages in Integrated Modeling

The implementation of integrated EC+IO models at the regional scale raises a number of issues that, to date, have not received much attention. These relate to the special nature of space and the proper treatment of multiregional linkages both from a conceptual and methodological perspective. Integrated Regional Econometric+Input-Output Modeling 19

One of the key distinguishing features of regional economies is the increased degree of openness relative to that exhibited by most national economies. This openness reflects many different substantive processes including: labor and non-labor migration; interregional trade; information flows; and inter- governmental fiscal transfers. In addition to these substantive processes, the manner in which the data used in a regional economic model is recorded and organized creates several difficulties when the administrative boundaries do not coincide with the boundaries of the substantive processes (i.e., markets). In this case, there is a form of spatial measurement error present in the data that requires special attention from an econometric perspective. These substantive and nuisances form of spatial dependence have been at the core of the recent explosion of research in the field of spatial econometrics (Anselin, 1988; Anselin and Florax, 1995; Anselin and Rey, 1997). Curiously, however, there has been very little crossfertilization between spatial econometrics and integrated EC+IO models. In the following sections, I first outline the treatment of space in existing integrated models and then suggest some ways in which this cross fertilization may be strengthened.

4.1 Representation of multiregional linkages in integrated models Despite the importance of spatial interactions at the regional scale, there have only been a few approaches that have been taken towards the representation of multiregional linkages in integrated models. These models consider not only the interindustry relations that are at the core of the integrated framework, but also the interregional linkages. There are, however, differences in the degree of detail given to either of these dimensions (i.e., the spatial or interindustry) in these efforts. More formally, consider the specification of the interindustry-interregional linkages as: r r,s ≈ ∂Zi βi,j s (20) ∂Zj

s r,s were Zj,t represents an activity of industry j in region s,andβi,j represents r the eﬀect of this activity on Zi,t. The question of disaggregation centers on r,s whether the βi,j are allowed to vary across all activities and regions. Table 3 summarizes the four possible cases of spatial-industry disaggregation found in regional EC+IO models. Models that are aggregate in both their spatial and industrial representations restrict the eﬀect of a unit change to be the same irrespective of what industry or region the change occurs in. Using an example from the U.S. Integrated Regional Econometric+Input-Output Modeling 20

Table 3: Typology of Spatial and Industry Linkages

Industrially Industrially Aggregate Disaggregate r,s r r,s r Spatially βi,j = βi βi,j = βi,j Aggregate ∀j, s ∀s r,s r,s r,s Spatially βi,j = βi βi,j Disaggregate ∀j

this would mean an increase in manufacturing activity in California would have the same impact on the service industry in Texas as would an increase in manufacturing in Texas. A model that is aggregate in the industrial but disaggregate in its spatial representation would allow the impact of Texas manufacturing to be greater than that same level of change in California manufacturing. Models that are disaggregate in their industrial dimension allow for dif- ferential effects across industries in the same region. Continuing on with the California-Texas example, such a model would allow the effects of the same level increase in California manufacturing and agriculture to have unique impacts on services in Texas. Finally, models that allow for disaggregation in both their industrial and spatial representation would allow the differences between the effects of manufacturing and agricultural activity in California on Texas services, to be distinct from the differences of the effects of Texas manufacturing and agriculture on Texas services. Because the heart of any integrated EC+IO model is its depiction of interindustry relations, none of these models can be classified as industrially aggregate. Indeed, this is what distinguishes them from other non-integrated models. Consequently, we can further compare the existing EC+IO models with regard to their representation of space. Table 4 classifies a sample of existing integrated models with regard to the number of regions considered in the model, if the regional linkages are represented in an EC or IO approach, and whether the linkages are specified in a spatially disaggregated fashion or not. At first glance it seems that models that are calibrated using more than a single region of data would have to be classified as spatially disaggregate. However, this is not necessarily the case for those models that impose spatial homogeneity in the econometric estimation of model parameters, such as those based on pure cross-sectional data (Shields and Deller, 1998) or those Integrated Regional Econometric+Input-Output Modeling 21

Table 4: Spatial Representation in EC+IO Models

Number of Spatially Model Regions EC Disaggregate √ Conway (1990) 1 √ Dewhurst and West (1990) 4 √ Israilevich et al. (1997) 1 √ √ Kort and Cartwright (1981) 48 √ L’Esperance (1981) 1 √ Moghadam and Ballard (1988) 1 √ Prastacos and Brady (1985) 9 √ √ Rey and Dev (1997) 7 √ Schantz (1995) 3 √ Shields and Deller (1998) 99 √ Treyz (1993) 48 √ West (1991) 1 √ White and Hewings (1982) 5

using panel data (Prastacos and Brady, 1985; Treyz, 1993). In an effort to allow for some spatial disaggregation in the framework, the role of distance is sometimes given an explicit representation. In general, this is reflected in the so called spatial interaction variable defined as: Xn Zs Zr = i (21) i,sup dλ s=R rs where drs is the distance between regions r and s,andλ is the distance decay exponent. The spatial interaction variable is introduced into equation (9) to allow for interregional interactions. This variable is specified so that the strength of interaction between two regions declines as the distance between them increases. This approach does allow for a spatially disaggregate treatment of spatial spillovers. Variants of this approach have been used in Kort and Cartwright (1981) and Rey and Dev (1997). However, it still may enforce a form of spatial homogeneity if the parameter on the spatial interaction variable (21) is restricted to be spatially invariant. This is typically the case for models estimated on cross-sectional data, but can also be true for models based on panel data. In the latter case, an additional assumption is often also made regarding the temporal stability of the coefficient on the spatial interaction variable.14

14In addition to the spatial parameter, the other coeﬃcients in these models are typically assumed to be temporally invariant. Integrated Regional Econometric+Input-Output Modeling 22

As pointed out earlier, both EC and IO models have been extended from single region to multiple region formulations. In a multiregional model, both EC and IO models cannot coexist in their multiregional forms, and so a choice must be made between the two ways to specify these linkages. In the EC approach to multiregional modeling the advantage of being able to use formal statistical inference to specify the strengths of the linkages is gained, as well as the potential for modeling the evolution of the multiregional linkages in a dynamic setting. On the other hand, the EC models are highly aggregated representations of the interindustry economies. IO approaches would offer a highly disaggregated representation to the interindustry-interregional linkages, however at a cost of using a static and deterministic framework. To date the empirical evaluation of these two op- tions has not been examined. To a large extent, data availability has conditioned the choice of how to represent interregional linkages in EC+IO models. For example, in the work on the Queensland model, data to implement region specific econometric consumption functions were not available, so the linkages between the regions were treated in an interregional IO model (Dewhurst and West, 1990, 1991). In the majority of cases, however, the lack of multiregional IO models necessitates the use of econometric equations to consider the regional interactions (Prastacos and Brady, 1985; Kort and Cartwright, 1981; Rey and Dev, 1997). Recent advances in MRIO modeling seem to be addressing the high costs associated with the implementation of MRIO models as a number of non-survey MRIO approaches have recently been suggested (De- ichmann, 1989; Hulu and Hewings, 1993; Olson, 1998; Robinson and Miller, 1991). This opens up the possibility of further consideration of the IO versus EC choice to multiregional linkage specification in integrated models.

4.2 Spatial Econometrics and Integrated EC+IO Models There are a number of areas where a tighter integration between developments in spatial econometrics and integrated EC+IO models could benefit current practice. The first concerns the spatial interaction variable in (21) in an integrated EC+IO model. This is a special case of a spatially lagged dependent variable, which has attracted much attention in the spatial econometrics literature. The presence of the spatial lag introduces a form of spatial simultaneity which, as was pointed out in section 3.2, requires specialized econometric techniques. To date, however, this spatial simultaneity has not been acknowledged by integrated modelers, and the application of spatial econometric approaches towards calibration of model parameters remains Integrated Regional Econometric+Input-Output Modeling 23 an open area for inquiry. A second area of fusion between the two fields relates to the similarities between the use of IO matrices in integrated modeling, and the role of the spatial weights matrix in spatial econometric modeling. For example, a traditional spatial lag specification takes the following form: y = Xβ + ρW y + (22) where y is a dependent variable measured for R regions at one point in time, X is an R by k matrix of explanatory variables with associated parameter vector β, ρ is a scalar spatial autoregressive coefficient, and W is an R by R spatial weights matrix. The individual elements of W reflect the potential interactions between observations on the dependent variable across the regions. The spatial lag Wy thus plays an analogous role to the IDV (10) in an integrated model, in that the lag (IDV) collapses all potential R − 1 (n − 1) linkages between region R (industry i) and the remaining regions (industries) into a single variable. Recognition of the similarities between the spatial lag and the IDV may offer some opportunities to address the problems with the specification of multiregional linkages identified in section 4.1. One avenue recently suggested by Rey and Dev (1997) is the spatial intermediate demand variable (SIDV): X X r rs s s SIDVi,t = θ ψijaijej,t (23) j=i s=6 r where θrs is a parameter reflecting the cost of overcoming distance between s regions r and s, ψij is the import propensity for good i by industry j in region s and all other terms are as previously defined. The SIDV then replaces the interregional variable Zsup,t in equation (9). The SIDV essentially extends the traditional IDV to a multiregional context, however in contrast to the IDV, the SIDV collapses n (R − 1) linkages into a single measure. At the same time, the SIDV, allows for both spatially and industrially disaggregated linkages in the specification of interregional interactions. The similarities between the spatial lag and the IDV may also be exploited to develop new measures of interconnectedness. This could benefit integrated models by developing analogies to the recently implemented Local Indicators of Spatial Association (LISA) (Anselin, 1995), that provide location specific measures of spatial dependence, for the interindustry context. Going in the other direction, Anselin (1988) has suggested the potential benefits to the study of spatial weights matrices that might be gained by drawing on the well established measures for interconnectedness in IO models (Di- etzenbacher, 1992; Szyrmer, 1985). To date this has not been investigated. Integrated Regional Econometric+Input-Output Modeling 24

Moreover, if such measures could be extended to dynamic EC+IO models, then some interesting paths for the analysis of space-time models may open up. A ﬁnal area for fruitful research that combines spatial econometrics and integrated EC+IO modeling concerns the three dimensions that are present in multiregional integrated models. These are industry, space and time. The interactions across these three dimensions as well as the diﬀerent types of intradimensional dependencies (i.e., interindustry linkages, spatial autocorrelation, temporal autocorrelation) will require new approaches towards model calibration. One possible approach would be to view the multiregional integrated EC+IO model as a special case of a three-dimensional panel data model (Beierlein et al., 1981; Wan et al., 1992). This along with other approaches are likely to lead to new advances in both spatial econometrics and integrated modeling.

5 New Directions in Integrated EC+IO Modeling

Our review of the implementation of integrated models has highlighted a variety of approaches as well as a number of methodological issues that reflect a great deal of recent research on EC+IO models. At the same time, there have been several newly emerging research directions that have been made possible by this implementation. Here we briefly identify a number of these new directions. While the main applications of integrated models thus far have been for impact analysis and forecasting, a number of researchers have been applying these frameworks for the purposes of structural regional economic analysis. Work at the Regional Economic Applications Laboratory has been at the forefront of this activity, using their models of the midwestern states to analyze a fascinating set of issues including the hollowing out of those regional economies (Schindler et al., 1997; Israilevich et al., 1997) and the forecasting of regional structural change (Schindler et al., 1995). By definition integrated EC+IO models combine dynamic and static components. While this is viewed as a complementarity, a number of questions concerning how the dynamics are incorporated in the integrated model have recently attracted attention. Thus far, the evidence is somewhat mixed, with some results suggesting that the integration is relatively robust to the specification of the dynamics (Stover, 1994) while other studies indicate that care needs to be taken in this representation (Rey, 1997b; Rey and Jackson, 1999). A related stream of research is on the question of the choice of the IO Integrated Regional Econometric+Input-Output Modeling 25 model within the integrated framework. Here again the evidence is mixed with papers suggesting that the source of the IO table can matter a great deal (Israilevich et al., 1996), while other findings indicate that, in particular contexts, the integration can be robust to choice of regionalization scheme (Rey, 1997a). Given the mixed evidence on both of these questions, more research is clearly required. A somewhat related effort can be found in the work of researchers associated with CPAN who are using the same integration strategy to develop EC+IO models across 16 states. Using these models, the group is evaluating a common set of policy scenarios and plans to utilize the estimated impacts as a database to inform a comparative analysis of regional economic structure and functioning. This agenda offers the potential for a much tighter nexus between regional policy issues and regional modeling, which is important given the increasing application of IO+EC models for policy analysis (Coomes et al., 1991b; Deller and Shields, 1998). A fourth area of new investigation is the work examining a set of questions concerning the relative properties of integrated models, input-output models and CGE models at the regional scale (Rey, 1998; West, 1995; West and Jackson, 1998). Out of this work is emerging an improved understand- ing of how these frameworks may be used in a complementary fashion. The possibility of using the results of these comparisons to guide the modifica- tion and adjustment of input-output models is particularly interesting given the widespread application of IO models for regional analysis. The idea is to utilize these adjustments to address some of the limitations of the IO model while not having to implement a fully integrated model. A final area of research is focusing on using integrated EC+IO models to implement new diagnostics for regional analysis (Rey, 1999). Here the emphasis is not on developing improved integrated models per se, but rather exploiting the properties of these models to derive indicators that may provide deeper insights as to the structure and evolution of regional economies.

6 Conclusion

This paper has presented an overview of approaches to integrated EC+IO modeling at the regional scale. The field of EC+IO modeling is rapidly evolving on both theoretical and empirical fronts. While the integrated approach has resulted in improved regional analysis methods and offers much promise, there are a number of outstanding methodological issues that need Integrated Regional Econometric+Input-Output Modeling 26 to be further investigated. Highlighted in this paper were the issues arising from implementing these frameworks in a multiregional context; the problems of measurement and specification error; and the appropriate approach to inference in integrated models. Addressing these issues represents a chal- lenging research agenda for integrated modelers. Finally, it may be worthwhile to reconsider integrated EC+IO models in light of the recent “rediscovery” of regional economics by mainstream economists (Barro and Sala-I-Martin, 1991; Krugman, 1991). Thus far, this new interest seems to have stressed the application of well-developed techniques from national and international economic analysis to the new domain of the region. There is a growing recognition that perhaps these methods are not as well suited to the unique characteristics of regions, and that effort towards developing new tools for regional economic analysis may be required (Quah, 1993). In this regard, integrated EC+IO models are properly viewed as one of many avenues for future research. The field of regional analysis will be well served by viewing alternative methodological approaches as comple- ments rather than substitutes.

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