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Computable General Equilibrium Modeling for Regional Analysis
Eliécer Vargas, Dean Schreiner, Gelson Tembo, and David Marcouiller


1.0 Introduction

1.1 Introduction

Partial equilibrium analysis illustrates results for one market at a time. However, there often exist market interactions and thus market feedbacks. As Nicholson suggests, pricing outcomes in one market usually have effects in other markets, and these effects, in turn, create ripples throughout the economy, perhaps even to the extent of affecting the price-quantity equilibrium in the original market. To represent this complex set of economic relationships, it is necessary to go beyond partial equilibrium analysis and construct a model that permits viewing many markets simultaneously. The general equilibrium model is a framework for analyzing linkages between markets and thus interactions between industries, factor resources and institutions.

de Melo and Tarr argue that inter-industry linkages are best captured in a general equilibrium framework. Although partial equilibrium may yield accurate estimates for particular sectors, estimates of aggregate costs of regional policies across sectors, for example, require a general equilibrium model to account for region-wide budget and resource constraints.

In the past, implementation of general equilibrium analysis was constrained by inadequate data and computational resources. Currently, however, the existence of large-capacity computer technology has made possible applications of such models to actual market situations. By recommending general equilibrium analysis, we do not mean that econometric estimates representing different sectors have little value. Rather, the two approaches should be viewed as complementary because it is neither feasible nor desirable to estimate, as a system of simultaneous equations, the full set of conditions describing a multisector economy model (de Melo and Tarr). In many cases, general equilibrium analysis borrows parameter estimates from partial equilibrium econometric studies.

1.2 General equilibrium economic models

Several approaches have been used to represent the regional macroeconomy interactions among sectors and, hence, the analysis of impacts of alternative policies. Most general equilibrium procedures are broadly categorized into fixed-price (multiplier) impact analysis and the endogenous price, quantity and income computable general equilibrium (CGE) methods. This section provides an overview and comparison of these model types and their variants.

Input-output analysis, attributed to Leontief, has been used for assessing the impact of a change in the demand conditions for a given sector of the economy. The basic relationship in these models is represented by

, (1.1)

where , the amount of sector i’s output required for the production of sector j’s output, is assumed to be proportional to sector j’s output , and is the relevant input-output coefficient. Summing over sectors and adding final demand to equation (1.1) produces the I-O model:

, (1.2)

which is also assumed to hold in first-difference form (depicting changes in the variables). An increase in final demand in a particular sector by, say, D will initially increase production for that sector, which in turn raises the intermediate demand for all sectors. To produce these intermediate inputs, however, more intermediate inputs are required. Although sectoral outputs keep on rising in several rounds, these increases become smaller and smaller such that their total always has a limit (Sadoulet and de Janvry). Equation (1.2) is often written in matrix notation:

, (1.3)

where X is the vector of outputs, F is the vector of final demands, A is the matrix of input-output coefficients, and I is the identity matrix (with ones on the diagonal and zeros elsewhere). The matrix represents a multiplier used to calculate overall changes in sectoral outputs caused by changes in final demand. For a more complete discussion of input-output see the web text chapter by William A. Schaffer.

Input-output analysis hinges on the crucial assumption that sectoral production is completely demand-driven, implying that there is always excess capacity in all sectors that is capable of meeting increased demand with no price increase. Because this assumption is likely to be unrealistic, input-output models are more useful as guidelines to potential induced linkage effects, and as indicators of likely bottlenecks that may occur in a growing economy, than as predictive models (Sadoulet and de Janvry).

Further, I-O models assume a constant returns to scale production function with no substitution among the different inputs. Prices are also assumed constant, which is not a major problem as substitution among factors is expected to be induced only by nonexistent relative price movements.

Extension of the I-O model to a social accounting matrix (SAM) framework is performed by partitioning the accounts into endogenous and exogenous accounts and assuming that the column coefficients of the exogenous accounts are all constant. According to Sadoulet and de Janvry, endogenous accounts are those for which changes in the level of expenditure directly follow any change in income, while exogenous accounts are those for which we assume that the expenditures are set independently of income. In determining exogenous accounts, it is common practice to pick one or more among the government, capital, and the rest of the world accounts based on macroeconomic theory and the objectives of the study.

Although I-O and SAM models have typically been used for impact analyses, they do not consider the special case where productive capacity of a sector is curtailed or eliminated (Seung, et al.). This concern has led to the emergence of mixed exogenous/endogenous I-O models where the production capacity of a sector is exogenously reduced (Petkovich and Ching). To examine the impacts of timber production potentials on income distribution, Marcouiller, Schreiner and Lewis (1993) demonstrated an application of a SAM version of the mixed exogenous/endogenous model, the supply-determined SAM (SDSAM) model, to the analysis of forest products.

However, these mixed exogenous/endogenous models, though relatively easy to implement, have limitations similar to fixed-price models. These are fixity of prices and no factor substitution in production and no commodity substitution in consumption. Seung et al. contend that, by these restrictive assumptions, the SDSAM model lacks microtheoretic foundation. Thus, such models are internally inconsistent because outputs for some sectors are forced to be fixed and final demands for the same sectors are assumed endogenous.

To circumvent the limitations posed by the SDSAM model, regional economists have turned to using the more theoretically sound computable general equilibrium (CGE) models as a tool for policy and impact analyses. In CGE analysis, output in all sectors is endogenously determined and prices are assumed sufficiently flexible to clear the commodity and factor markets. An empirical comparison of the SDSAM and CGE approaches by Seung et al. indicates that, compared to the CGE model, the SDSAM model tends to overestimate the policy impacts and to estimate production decreases in sectors where production may not change or may increase. The authors conclude that a regional CGE model is theoretically more sound than mixed exogenous/endogenous fixed price models for impact analyses where productive capacity of sectors is curtailed or eliminated.

Partridge and Rickman argue that fixed-price regional models are limiting cases of the more general Walrasian general equilibrium system. In fixed-price models, which are characterized by perfectly elastic supply, the total change in the regional economy is always predicted to be proportionate to the exogenous change. The Walrasian general equilibrium procedure, which is grounded in neoclassical theory, specifies less than elastic supply with equilibration of demand and supply achieved through flexible prices. In these models, the total response in an economy to an exogenous change is not necessarily proportionate and depends upon the various elasticities of demand and supply.


2.0 Overview of CGE Analysis

The CGE framework offers an alternative for regional analysis. It encompasses both the I-O and SAM frameworks by making demand and supply of commodities and factors dependent on prices. A CGE model simulates the working of a market economy in which prices and quantities adjust to clear all markets. It specifies the behavior of optimizing consumers and producers while including the government as an agent and capturing all transactions in circular flow of income (Robinson, Kilkenny and Hanson).

In the Walrasian neoclassical general equilibrium approach, the main equations are derived from constrained optimization of the neoclassical production and consumption functions. Producers are assumed to choose their level of operation so as to maximize profits or minimize costs using constant returns to scale production technology. Production factors – labor, capital and land – are all paid in accordance with their respective marginal productivities. Consumers are assumed to choose their purchases to maximize their utility subject to budget constraints. At equilibrium, the model solution provides a set of prices that clears all commodity and factor markets and makes all the individual agent optimizations feasible and mutually consistent (Bandara).

CGE analysis has been applied to a wide range of policy issues, which include, among others, income distribution, trade policy, development strategy, taxes, long-term growth and structural change in both developed and less developed countries (LDCs). Dixon and Parmenter associate the proliferation of these models in LDCs with two major conditions. First, growing realization that CGE models, unlike a number of other types of economic models, allow the simulation of policy alternatives in a way which is readily understood and perceived to be both relevant and useful by policy makers. Second, vast progress in the development of user friendly, readily transferable high capacity computer software, which has greatly increased researchers’ ability to handle models with considerable detail.

2.1 CGE analysis at national and regional levels

Most CGE models have been used to capture the effects of policies and economic shocks at the national level. Application of the technique to regions (such as states) is more recent. Examples of regional applications in Oklahoma include Koh, Lee, Budiyanti, and Amera.1

Regional CGE models differ from their national counterparts in several respects. Most of these differences stem from the fact that regions are relatively more open economies compared to nations. Because of regional openness, commodity trade and resource migration are more important in regional CGE models. For example, regional households and entrepreneurs would not invest within the region if other regions offered higher rates of return. Thus, while national CGE models require that savings be equal to investment, regional CGE models permit excess savings to flow out of the region and vice-versa. This is not to say that regional policymakers cannot influence rates of return to investments but that control over major components of monetary policy is mainly determined at the national level.

In general, CGE models require considerable data, which, in most cases, is difficult to obtain. This problem is more severe at the regional level, where data in most cases is virtually non-existent. In fact, one of the possible reasons for the relatively slow start of regional CGE modeling is the paucity of regional data, in addition to unresolved theoretical issues of regional specification2 (Partridge and Rickman). Most of the limitations of regional CGE models are also inherent in alternative empirical regional modeling, such as I-O, SAM, and econometric.

Although regional CGE models have grown in popularity in recent years as an alternative method for examining regional economies and policy issues, their contribution has yet to be assessed. Partridge and Rickman present an extensive review of literature related to regional CGE modeling and conclude that regional CGE models, though still with unclear conclusions on issues of quantitative accuracy, represent a significant advancement in regional economic analysis. For details on the current state of the art of regional CGE modeling, readers are referred to Partridge and Rickman.

The greater openness of regional economies suggests some desired divergence in structure between national and regional CGE models. In spite of the differences between national and regional CGE models discussed above, the general formulation used in most studies is basically the same. While some studies have been designed to capture the added complexity, others have relied on the specifications common to the national CGE literature.

Most empirical applications of CGE models have been developed on the simplifying assumption of constant returns to scale production technology and perfectly competitive market structures. This has made these models fail to adequately represent industries with declining unit cost structures. Recently, de Melo and Tarr used the theory of duality to develop and apply a production modeling technique that accommodates imperfect competition in the U.S. auto and steel industries. Tembo has suggested and demonstrated an application of this technique to regional economies. Vargas and Schreiner show an application to monopsony markets in the regional timber industry.

The purpose of this chapter is to present and illustrate application of the salient features of the regional CGE model and to provide a step-by-step example of their empirical implementation. In this endeavor, the more traditional perfectly competitive constant returns to scale version of the CGE model is presented first. This is then followed by a variation that accommodates imperfect competition (see section 5.0).

2.2 Data and data organization

CGE models are very data intensive. Thus, the first step in implementation of a CGE model is identification and organization of data into a social accounting matrix (SAM). The SAM is a square matrix representing a series of accounts which describe flows between agents of commodity and factor markets and institutions. It is a double-entry book-keeping system capable of tracing monetary flows through debits and credits and constructed in such a way that expenditures (columns) and receipts (rows) balance. King distinguishes two objectives for the SAM: 1) to organize information about the economic and social structure of a country, region in a country, city or any other geographic unit of analysis; and 2) to provide a "fixed point" basis for the creation of a plausible model.

Regionalized economic datasets that can serve as a basis for regional CGE models are now available. This section describes the types of data required for building regional CGE models. These data needs include regional social accounts and parameters required for incorporating economic relationships among industries, in production and factor usage, among institutions, and in the generation of regional economic output. Each is addressed in-turn in the following sections.

2.2.1 Social accounting matrices

The base data upon which a regional CGE model is constructed relies on a static accounting for economic transactions taking place in a base year and specific to the region under examination. Input-output (I-O) tables provide one data framework but lack the comprehensive accounting of income flows. Base data on these income flows are necessary to address labor components, production structures, and government interaction necessary to conduct policy analysis. A more comprehensive accounting structure for regional economies is provided through an I-O extension known as a social accounting matrix (or SAM.) SAM extensions were initially developed during the late 1960's and early 1970's as a result of general dissatisfaction with the manner in which income flows were treated. A good overview of SAM development and analytical background for the interested reader can be found in Pyatt and Round and Hewings and Madden. SAMs as a basis for CGE models is addressed in Isard et al.

What is a SAM?

Like input-output accounts, social accounting matrices provide a comprehensive accounting structure of regional market-based productive activities and utilize similar double-counting book-keeping entries. Unlike input-output, however, social accounts focus on the household as the relevant unit of analysis and provide a comprehensive, and additional, set of accounts that track how household income is generated and distributed. Where input-output tables are focused on industries and their respective relationships with regional output, SAMs extend this into a more complete range of market mechanisms associated with generating household income. The relevant focus thus shifts from how regional output is produced to also address how regional income is generated and distributed. This comprehensive element is particularly important in regional CGE models that focus on both production processes and the economics of household factor supply, commodity demand, and government interaction.

How are SAM’s useful for policy analysis?

Social accounting matrices have been employed in a wide array of situations arising in policy development to address key issues of economic structure and impact assessment. A good overview of SAM applications in policy analysis was written by Erik Thorbecke and found in the recent text by Isard et al. (pages 317-331.) Basically, SAMs are useful in assessments that require a more comprehensive accounting of circular flows of an economy.

Particularly useful for addressing issues of income distribution, SAMs have been widely employed in assessing development effectiveness in attaining equity-based outcomes of policy. Applications, however, are not limited to assessing redistributive income policies. This is particularly true in the United States as national and state level policies that support the redistribution of income to the poor are largely out of favor. Increasingly, welfare reform legislation has emphasized the role of private markets to provide for individual welfare. SAMs have been employed to assess the relative impacts of alternative market-based changes on the distribution of income within regions. Thus SAMs will continue to be relevant tools to address a wide array of policy situations and development issues.

The major strength of regional SAMs include accounting comprehensiveness. Although still widely used, it is important to note that SAMs have some rather serious theoretical shortcomings when used to model economic change. These modeling caveats have, in part, driven the movement toward developing more flexible modeling systems. As such their use in computable general equilibrium models remains the focus of this chapter.

How is a regional/state SAM constructed?

SAMs can be constructed in a variety of ways. The manner in which a SAM is specified is typically driven by the problem being addressed. A thorough assessment of the various types of SAM structures is beyond the scope of this chapter. Rather, for this discussion a generic SAM structure will be discussed illustrated by a modest empirical SAM constructed for the Oklahoma economy.

Data elements for constructing a SAM. An illustrative SAM framework is provided in Figure 2.1. From an input-output perspective, the rows and columns that correspond to industry and commodity are the focus. Whereas input-output is limited to this industrial perspective, social accounting matrices extend the dataset to more fully capture income distribution resulting from returns to primary factors of production (land, labor, and capital.) In this way, the circular flow of goods and services to households from firms and the corresponding factor market flows to firms from households are captured.

In the SAM, row totals and column totals are equal thus representing a regional economy in equilibrium. For example, total industry output just equals the outlay used in its production. Institutional income (to households for example) just equals the outlay required for the use of institutionally-owned land, labor, and capital in the factor markets. In general, total income equals total cost of inputs. SAM accounts are constructed to balance outputs with inputs.

Data sources for SAM building. Once again, the specific data requirements for constructing a regional SAM vary depending on the type of problems being addressed. However, some generalizations can be made. In addition to standard input-output data (industry production, interindustry transactions, final demands, factors of production and imports/exports), typical SAMs require additional data on total factor payments, total household income (by income category), total government expenditures and receipts (including intergovernmental transactions), institutional income distribution, and transfer payments (both to households and to production sectors.) SAMs are typically built as static snapshots of a region thus, data elements will need to be generally consistent in temporal and geographic specificity.

2.2.2 Using IMPLAN to construct a SAM

For purposes of illustration, discussion will center on a readily available dataset for the initial regional static equilibrium. A good example of this base economic equilibrium data is found in the county-level files available from the Minnesota IMPLAN Group (or MIG.) 3 This consultancy group develops relational datasets built from secondary data available at the national, state, and county-level from the BEA REIS, BLS ES202, County Business Patterns and other sources. Specifically, this group first gathers data at the national level, converts it to a standardized format, derives national input-output tables and national tables for deflators, margins and regional purchase coefficients. State level data is gathered and controlled totaled to the national. County level data is gathered and controlled totaled to each state. County or regional-level input-output tables are derived using various data elements employed in the model development software embedded within IMPLAN Pro.

Over the course of development, the Minnesota IMPLAN Group has endeavored to adapt, expand, and extend datasets into more comprehensive accounting structures and regional modeling approaches. For example, a set of social accounts has been added to the county-level IMPLAN datasets. These accounts are available for use both in assessing inter-institutional transactions and in regional CGE modeling. The latter application has been under development for the past few years. Notable discussions of these developments can be found in Robinson and Sullivan, McCollum, and Alward.

Specific data incorporated into the IMPLAN SAM begins with standardized elements of the National Income and Product Accounts (NIPA.) Household transfer payments and distributional breakdowns come from the Census of Population, BEA REIS dataset and the BLS Consumer Expenditure Survey. Government data requirements originate from the Annual Survey of State and Local Government Expenditures. This data source provides state and local revenues and expenditures by detailed category.

Generating a SAM from an IMPLAN model is rather straightforward given general knowledge of software and dataset operations. The SAMs generated from IMPLAN are not, however, without drawback. One key drawback of using the IMPLAN system to generate a social accounting matrix is the rather rigid categorization scheme used in dataset and model construction. For example, due to the manner in which the dataset was developed, value added remains in rather nebulous categories that match published secondary data sources. Instead of value added being separated into returns to land, labor, and capital, value added in IMPLAN is reported in categories that include employee compensation, other property type income, proprietary income, and indirect business taxes. One ad hoc method of conversion is to simply use employee compensation as a proxy for labor returns (which neglects proprietary income), other property type income as a proxy for land returns, and proprietary income as a proxy for capital returns (actually more a mixture of labor and capital returns). Although there exist procedures for disaggregating total value added into more standard categories of factor return, these methods tend to be data intensive and complex.

The aggregate SAM for Oklahoma

The number of sectors represented in the SAM and, hence, the number of markets in the CGE model depends to a large extent on the purpose of the study. Budiyanti, for example, aggregated the Oklahoma 1991 SAM to 14 industrial sectors of market goods, two sectors of non-market goods, three value-added sectors (capital, labor, and land), and three institutions (enterprises, households and government). The labor sector was further sub-divided into five skill levels. The household sector was also divided into low-, medium- and high-income classes. Government was represented by a state/local level and a federal level. Amera’s 1993 Oklahoma SAM has 30 industrial sectors, three factor sectors, three household sectors, two government sectors, one enterprise sector, one investment sector, and a rest-of-the-world sector. For illustration purposes in this chapter, a highly aggregated (four-industrial sector) version of Amera’s SAM is used as the data source (Table 2.1). This SAM also aggregates the household and government sectors into one sector each.

2.3 Determining parameter values

Once the economic agents are identified and their optimizing behavior specified by algebraic equations, the parameters in those equations must be evaluated. Data on endogenous and exogenous variables obtained at a snapshot point in time are typically used for this purpose. This process is referred to as calibration . Calibration or benchmarking determines the values of the normalizing (or free) parameters so as to replicate the observed flow values incorporated in the SAM (de Melo and Tarr). This process assumes that all equations describing market equilibriums in the system (model) are met in the benchmark period.

When dealing with flexible functional forms, such as the constant elasticity of substitution (CES) or the constant elasticity of transformation (CET), it is necessary to supplement the calibration process with these exogenously determined elasticities.4 Other parameters obtained from literature (econometric studies) include income elasticities, migration elasticities, and price elasticities of export demand. These parameters are used to illustrate the calibration process of the various components of the regional CGE model.

The calibration process starts with choice of units. Because in CGE analysis only relative prices matter, all prices and factor rents are normalized to unity in the initial equilibrium. With prices normalized to one, then the flow "values" in the SAM (Table 2.1) may be interpreted as a physical index of quantity in the commodity (industry) and factor markets (click here for further explanation of normalized prices). Once all the parameters are specified, the model is solved to reproduce the benchmark data. The solution obtained with the benchmark data is referred to as the "replication" equilibrium, assuming the benchmark represents an equilibrium outcome, given existing exogenous conditions (Partridge and Rickman). In addition to providing a check on the accuracy of the calibration, the replication also shows that the complete circular flows of income and expenditures are balanced, which is referred to as microconsistency of the data. Counterfactual equilibria are obtained by introducing shocks to exogenous variables, changes in market conditions, or changes in any policy variable and rerunning the model. The general algebraic modeling system (GAMS) software is used for solving the regional CGE model. The following sections in this paper outline the general features of a regional CGE model and demonstrate the calibration and solution processes under both perfect and imperfect competition.


ENDNOTES

1. These are all Ph.D. studies completed at Oklahoma State University. Results of the studies have been published in Koh, Schreiner and Shin; Schreiner, Lee, Koh, and Budiyanti; and Amera and Schreiner. Partridge and Rickman give an extensive review of many other regional studies.

2. Issues of functional form, elasticity specification, closure rules, sensitivity analysis, market structure, and dynamics.

3. The IMPLAN Pro software and county/state datasets are available from the Minnesota IMPLAN Group (accessed on the world wide web at www.implan.com.) Their mailing address is 1725 Tower Drive West, Suite 140, Stillwater, MN 55082, Voice: 651/439-4421 Fax: 651/439-4813.

4. Application of these elasticities in the CGE framework are discussed in section 3.0.


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