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
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
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.
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
amount of sector is output required for the production of sector
js output, is assumed to be proportional to sector js
and is the relevant
input-output coefficient. Summing over sectors and adding final demand
to equation (1.1) produces the
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:
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
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
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
computable general equilibrium
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
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
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
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
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
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
to develop and apply a production modeling
technique that accommodates
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
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.
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
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 SAMs
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
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
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
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
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
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
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. Ameras 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 Ameras SAM is used as the
data source (Table 2.1). This SAM also aggregates
the household and government sectors into one sector each.
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 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
and imperfect competition.
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.
back to Table of Contents