4.0 Model Execution

In this section the procedure for implementing the regional CGE is presented as discussed in section 3.0. Because section 3.0 explains and derives the equations for a competitive regional CGE, there are more equations than needed for actual model execution. Section 4.1 puts in tabular form the actual model equations needed for execution (Table 4.1). Also, subscript notation is in Table 4.2; summary of endogenous variables is in Table 4.3; summary of exogenous variables is in Table 4.4; and summary of parameters is in Table 4.5.

A brief discussion of the General Algebraic Modeling System (GAMS) solution is presented in section 4.2 with reference to more detailed procedures. The actual model construction in GAMS is presented in section 4.3. The model itself can be downloaded for purposes of experimenting with model changes and model simulation. (Click here to download GAMS input file).

Results of a simulation of increased terms of trade for the region is presented in section 4.4.

4.1 Competitive CGE model equations

Table 4.1 Competitive CGE Model Equations

Table 4.2 Subscript Notation

Table 4.3 Summary of Endogenous Variables

Table 4.4 Summary of Exogenous Variables

Table 4.5 Summary of Parameters

4.2 GAMS Solution

A CGE Model is an integrated system of equations whose simultaneous solution determines values of endogenous variables. The underlying equations are derived from economic theory of the behavior of economic agents and markets – producers, institutions, factor markets, etc. Several approaches have been used to solve these models. Dervis, de Mello and Robinson have classified these algorithms into fixed point theorem based, tatonment process based and Jacobian approaches. Most recent CGE applications have used General Algebraic Modeling System (GAMS) whose solvers fall in the third category.

GAMS is a high-level modeling system consisting of a language compiler and a stable of integrated high-performance solvers. It is specifically designed for modeling linear, nonlinear and mixed integer optimization problems and is tailored for complex, large scale modeling applications. This permits building of large maintainable models that can be adapted quickly to new situations. One of the advantages of GAMS is that it is designed to accept equations in almost the same format as presented in Table 4.1. The use of subset notation allows implementation of different functional forms and closure rules for different subsets (in a variable vector) without having to introduce dummy variables. By eliminating the need to think about purely technical machine-specific problems such as address calculations, storage assignments, subroutine linkages, and input-output and flow control, GAMS increases the time available for conceptualizing and running the model, and analyzing the results. Detailed programming procedures are provided in Brooke, Kendrick and Meeraus.

Because of the presence of nonlinear functions in CGE model formulations, finding solutions requires use of nonlinear algorithms. Several such solution algorithms are present in GAMS. The syntax of optimization characteristic of GAMS requires an objective function with the rest of the CGE equations treated as constraints. Because none of the equations has an inequality sign in CGE, the model solution is invariant to choice of objective function. Therefore, any equation is eligible to be an objective function, as long as it is a scalar equation.

For empirical implementation, (two) positive slack variables are introduced in one of the equations (in our case, the production function). To equate the number of endogenous variables to the number of equations and, hence, to ensure full identification of the system, an extra equation is introduced which sums up the two slack variables. In the optimization process, the sum of the slack variables is minimized subject to all other equations (equality constraints). This ensures that the optimal solution is attained when the sum of the slack variables is equal to zero, a condition necessary to satisfy all the simultaneous equations in the model. With benchmark exogenous variable values, the program will replicate exactly the values of the endogenous variables contained in the SAM at the optimum. Thus, the introduction of slacks only facilitates the optimization process and does not affect the solution values. Brooke, Kendrick and Meeraus also recommend this (slack variable) technique in nonlinear optimization, arguing that it helps to address the infeasibility problem that frequently occurs during iterations in such models.

4.3 Model construction in GAMS

The model construction is presented in the syntax of the GAMS software program. For a guide to the GAMS-input-file click in this link {user’s guide to GAMS-input-file}. To execute a GAMS program the reader must have the GAMS software program. For more information on how to obtain, install and run the GAMS software see this link {http://www.gams.com/}.

4.4 Model simulation

A change in regional terms of trade is used to show the results of a model simulation. Export prices for all commodities were increased five percent with import prices remaining at base level. This is similar (but in the opposite direction) to the impact of a decrease in agricultural commodity export prices during the mid 1980s, which contributed to considerable stress and change in rural Oklahoma. An overall price index in 1982 of 100 for agricultural commodities produced in the state was 89.0 by 1986 (Schreiner, Lee, Koh and Budiyanti, p 64). This implied about an 11 percent decrease in export prices of agricultural commodities during a relatively short period of time.

Simulation results of a five percent increase in terms of trade (5 % increase in all export prices), assuming long-term adjustment and capital mobility, are presented in Table 4.6 (below). These results are based on a recent paper by Tembo, Vargas and Schreiner presented at the 30^th Mid-Continent Regional Science Association meetings, Minneapolis, MN, June 11-12, 1999.

Total exports increase by 13.8% and imports increase by 8.9%. Remember that exports and imports are constrained by constant elasticities of transformation (CET) and constant elasticities of substitution (CES), respectively. This means that producers respond not only to a change in the price ratio of export markets to domestic markets but also to their willingness to substitute (transform their product) between the markets. Consumers in the regional (domestic) market must also adjust to higher regional prices (not shown for individual commodities in Table 4.6). On the import side, consumers are faced with higher regional prices and thus substitute imports (which are at the same price as before the simulation because they are exogenously set) for regional products, based on their willingness to substitute (i.e. the CES parameter). The small region effect is assumed here where regional output and regional demand do not change external prices.

The index of the composite price, a weighted average of regional and import prices, increases by 1.6%. This is the price regional (state) consumers pay for purchases within the region (state). Regional consumers include households, intermediate input buyers and governments. Incomes of regional households increase by 8.1% in nominal terms. By deflating nominal income by the composite price index, real income increases by 5.06%.

Gross state product (GSP) increases by 10.3%. GSP is the compensation for all resources employed in the state, no matter whether the resource owners reside in-state or out-of-state. GSP is the result of the changes in resource prices (wages and rents) and quantity of resources employed. In this simulation, wages and rents increase (not shown in Table 4.6) and quantities of labor and capital increase through migration. The latter increase because resource prices in the state are higher relative to prices out-of-state. Again, the small region effect is assumed where the regional demand for resources does not stimulate price increases out-of-state.

Results similar to Table 4.6 could be calculated to show the change in all endogenous variables (see Table 4.3). Because CGE emphasizes relative changes, results are generally expressed by index form showing the percent change from the base. Hence, an index of 1.1032 for GSP indicates a 10.32% increase over the base, whereas an index of 0.9600 would indicate a 4% decrease in GSP. Absolute changes are easily calculated by applying the percent change to the base level. For example the 10.32% change in GSP applied to the factor payments, $57,551,174,000, in Table 2.1 results in a change in GSP of $5,939,281,157 (excluding indirect business taxes paid to governments).

5.0 Increasing Returns and Imperfect Competition in Regional CGE Modeling

The CGE framework presented so far expands beyond the assumptions of input-output (I-O) based models. By relaxing the assumption of fixed prices, which in I-O models implies that increased demand is always met with no price increase due to excess production capacity and limitless supply of labor and other factors, we have a more realistic empirical model of regional analysis. The CGE framework allows demand and supply of commodities and resources to depend on prices. Furthermore, resources may be substitutable in production.

However, the competitive regional CGE modeling presented above has two important limitations. First, it does not consider the presence of imperfect competitive market structure and, second, it ignores production technologies characterized by increasing returns to scale (IRS). We present here regional CGE modeling of increasing returns to scale and imperfect competition. An introduction to the theoretical difficulties brought about by the inclusion of returns to scale to the competitive CGE framework is presented. The purpose is to introduce the reader to limitations of the modeling techniques presented above. But first, the case of forest product production and wood processing in Oklahoma is used to show the potential for increasing returns to scale and imperfect competition.

The wood-products manufacturing sector in Oklahoma has several highly concentrated industries. For example, in the sawmills and planning mills industry (SIC 242) 70% of total employees work for one multinational company. Similarly, the paper mills (SIC 262) and the paperboard mills (SIC 263) industries are represented by seven establishments of which 82.5% of total labor force works for two multinational companies. In addition to the high concentration of the industry, Oklahoma timber producers have limited options on where to sell their timber because of costly transportation and long distances between processing centers. All of this propitiates some kind of imperfect structure for the timber market (raw materials market) in which wood processing industries are capable of affecting the price paid for timber.

Once the price taking assumption is dropped, we face the challenges of modeling changes in the economic environment, government policies, technological advances, and external shocks. Researches have available to them considerable theoretical ground on how to model imperfect competition. Two approaches are partial equilibrium and general equilibrium. They differ in that the former considers regional wages and income of consumers to be determined outside of the model. As researchers in economics try to maximize their contributions to solving economic problems they are also constrained by time and data availability. CGE is more demanding on both time and data. Therefore, it is important for the profession to understand and contrast the benefits of using one approach over the other. Thus, using the Oklahoma’s forest products industry (FPI) we contrast empirically the strengths of partial and general equilibrium approaches when modeling imperfect competition. We estimate the effects on household welfare, gross state product, employment, raw material prices, wage rate, returns to capital, and so on, for different imperfect market structures of Oklahoma’s FPI.

5.1 Increasing returns, non-convexity, and competitive CGE models

The existence of increasing returns to scale (IRS) relies on the non-convexity of the production set. Non-convexity undermines the assumptions used to prove existence of general equilibrium. For the standard competitive general equilibrium, the equalization of prices and marginal rates of transformation is a necessary, and under the assumption of convex preferences and choice sets, a sufficient condition for optimality. This is not the case when non-convexity is present. To understand why, we may use the following line of thought. The presence of IRS leads to large-scale firms because at some price above minimum average cost, profits increase indefinitely with the scale of operation. This is a direct result of average cost always being greater than marginal cost under IRS. Thus, as firms increase the scale of operation the market becomes more and more concentrated which in turn leads to fewer and fewer firms (even one) in the industry and possible collusion of prices. Theoretically, the price mechanism loses its efficiency characteristics and the optimality and efficiency dichotomy that attracts us to competitive general equilibrium (Villar). Indeed, firms with IRS are not consistent with the hypothesis of perfect competitive markets.

The presence of IRS is not the only case that precludes the benefits of competitive equilibrium. Imperfect competition, for example, may be a direct consequence of limitations to entering the market or of a firm’s exclusive right to use a resource granted by the regional, federal, or local government. We concentrate in modeling increasing returns and imperfect competition while motivating the reader to investigate the extensions of our modeling description.¹

5.2. Modeling increasing returns and imperfect competition

Harris' work is considered by many as the first successful and compelling general equilibrium model to incorporate both imperfect competition and increasing returns to scale. His work deals with a small open economy and formulates for the first time the modeling of IRS using the dual approach (see below). After Harris’s work, imperfect competitive general equilibrium models have been extensively used, especially in trade liberalization issues.

Imperfect market structures that characterize the product side of the production system have been the major focus of the majority of theoretical and empirical work. Monopolistic competition and oligopolistic competition, for example, have extensively been applied in trade models. However, market imperfections related to the factor (input) side of the production system remain unexplored. The reason, at least in the opinion of these authors, is the international trade focus of most national CGE models where factor market imperfections are of less concern: i.e., how strong is the case for monopsony modeling when commodities are traded nationally and internationally?

However, at the regional level and particularly for agriculture and other natural resource based sectors, one may argue for modeling input side market distortions , i.e. monopsony and cooperative behavior (see Rogers and Sexton). Thus, the state of the art of CGE is very promising for output distortions of markets but less promising for distortions of input markets.

5.2.1 Increasing returns -- the dual approach

The modeling of IRS at regional levels is adopted from literature on international trade and national CGE formulations. Its implementation/adaptation to regional CGE models has been limited with few exceptions identified by Partridge and Rickman. Harris' basic approach is used here. The main characteristic of the approach is the use of the dual formulation of increasing returns to scale. Duality is less restrictive in modeling and allows treatment of the assumption of convex input requirement sets as compared to the primal approach.

Under constant returns to scale, marginal costs are assumed to be constant and equal to average variable cost (, where VC_i is variable costs and X_i is output for the i^th sector). Under increasing returns to scale, average cost is a monotonically decreasing function².

(5.1)

where FC is fixed costs and MC and AC are marginal and average cost, respectively. We assume that marginal costs are governed by the preferred constant returns to scale production function, but a subset of inputs are committed a priori to production and these costs must be covered regardless of the output level. Thus, increasing returns to scale takes the form of unrealized economies of scale in production. There is no customary procedure in defining fixed costs. Fixed costs may involve the same mix of inputs as marginal costs or, alternatively, fixed costs may be assumed to involve a different set of inputs. However, the specification of the fixed costs has important consequences for the calibration procedure (to be discussed).

As a measure of unrealized scale economies it is customary to use the concept of cost disadvantage ratio (CDR). The CDR provides an estimate of unrealized economies of scale (de Melo and Tarr). Depending on the value of this ratio, an industry may be facing economies/diseconomies of scale or it may be operating at the minimum efficient scale. The is calculated as:

(5.2)

where

and AC and MC are average cost and marginal cost, respectively. Thus, If , there are Economies of Scale; if , there are Diseconomies of Scale; and if, the firm is operating at the Minimum Efficient Scale³.

5.2.2 Increasing returns -- the primal approach

The primal approach in modeling increasing returns to scale has been infrequently used by CGE modelers. The reason is the indeterminacy under increasing returns to scale. Kilkenny, however, argues that "when factor markets are geographically segmented and the pool of labor is limited" factor costs will rise for an industry which is expanding operation using unexploited increasing returns to scale. Thus, existence of an optimal output level is thus obtained.

In the primal approach, increasing returns to scale are much easier to model. We adjust, for example, the coefficients of a Cobb-Douglas production function to exhibit increasing returns to scale: making, where f states for factor index and a is the exponential (share) parameters in the Cobb-Douglas technology specification.

5.2.3 Market power

Before modeling market power we require specification of the degree of product differentiation used in the model. We assume Armington preferences at the regional level. Thus, substitution in purchases is allowed between domestically produced consumer goods and out-of-region produced consumer goods. Traded goods are imperfect substitutes by origin and goods produced domestically are imperfect substitutes for imports. Also, goods supplied on the domestic regional market are imperfect substitutes for goods supplied for export. Armington specifications also apply to sectors with IRS. In those sectors, goods are produced by identical firms implying goods produced for domestic sales in these sectors are perfect substitutes.

Contestable pricing

Two pricing hypotheses are considered for the IRS sectors. First, we assume low-cost entry and exit such that the threat of entry forces firms to price at average cost. This is called the contestable pricing behavior:

(5.3)

where is the weighted sum of the unit sales prices on the regional (PR) and export () markets. Firms in a perfectly contestable market will be forced to operate as efficiently as possible, and to charge as low a price as long-run financial survival permits.

This pricing rule represents only a small departure from the competitive pricing rule because price also equals average cost in the long-run equilibrium of the competitive model (de Melo and Tarr). Another advantage of contestable pricing is that it is easy to calibrate. According to de Melo and Tarr, the calibration process is complete by just equating output price to average cost.

From monopoly to oligopoly

In the second alternative, we assume that each (identical) firm behaves in the regional market as if it is facing a downward-sloping demand curve. The equilibrium condition for each firm is given by:

(5.4)

where is the endogenous elasticity of aggregate sectoral demand, is the number of firms, and is the representative firm’s conjecture about the response of competitors to its output decision. This alternative is the conjectural variation specification where one may or may not have entry/exit assumptions.

In long-run equilibrium, entry/exit ensures zero profits. If represents the number of firms, then as we expect ; thus, firms behave competitively. Why should the representative firm’s conjecture banish as the number of firms increase? Two explanations are given. First, collusion is difficult if more firms arrive to the market, and second, more firms imply greater availability of varieties. A conjectures formulation that accounts for both product variety and effects on collusion of firms is given by:

(5.5)

where is the change in aggregate output of other firms due to a change in the j^th firm, and is an arbitrary number normalized to unity in the calibration.

On the other hand, with barriers to entry it is possible to have supernormal profit because firms sell in the domestic regional market at a price . If we define an exogenous rate of profit () per unit of regional sales, then the mark-up pricing equation (5.3) is replaced by:

(5.6)

This equation is the same for contestable market scenario when . In the conjectural variation case, we have .

Our empirical example applies all of these modeling techniques to the Oklahoma region. For example, high concentration in the pulp manufacturing industry increases the likelihood of lower outputs and higher price than under a competitive structure. As well, its actions may distort the timber market, thus affecting the welfare of both forest land owners and consumers (Tillman).

5.3 Calibration

We calibrate our model using a modified social accounting matrix that identifies the forest complex. We have considered the forest complex to constitute the forestry sector and the forest product industry (FPI). Our calibration procedure depends on assumptions of market structure and strategic behavior by firms. Calibrating parameters of the model utilizes the information obtained from econometric work and/or economic theory.

Depending on the price rule and the exit/entry assumption, each alternative entails a different model calibration. In the case of normal initial profits (), we reduce the primary variable cost component of total costs by the amount of fixed costs. For the monopolistic case, equation (5.4) is solved to yield the value of the conjecture parameter.

In the case of supernormal profits, we allocate fixed costs as before. Then, given the profit rate, , and all quantities and out-of-region prices, we solve for the region (domestic) price which satisfies the firm’s profitability constraint. Finally, is solved from (5.4) but with the new set of regional prices.

Modeling IRS and imperfect competition requires additional parameters, mainly estimates of the following elasticities: elasticity of capital/labor substitution; import price elasticities of demand; and export supply price elasticities. Finally, the calibrated price elasticity of demand, , will depend on the functional form selected to represent import demand and export supply.

An example of the application of CGE to imperfect markets in the forest product industry is available in a paper presented by Vargas and Schreiner at the Mid-Continent Regional Science Association meetings, Minneapolis, MN, June 11-12, 1999 and published in The Journal of Regional Analysis and Policy (Vol. 29,2: 51-74, 1999)(see website http://www.agecon.okstate.edu/rcge/index.html).

6.0 Policy Applications and Summary and Conclusions

Regional development is a field of study requiring policy decisions. In a purely competitive economy, markets determine what is produced and what is consumed. Seldom do we permit markets in regions to operate completely unregulated. Externalities of production, public good nature of infrastructure, missing markets for amenities, and the importance of the distribution of benefits of economic growth enter into the political process of guiding regional development. Some policymakers view area development as an end in itself, irrespective of the results on measures of welfare for area populations.

In this chapter we presented a framework for analysis of regional development programs and policies. Markets were defined in terms of structure and behavior. Economic behavior of producers and consumers was specified, and ownership of resources was identified. The economic model is a form of regional general equilibrium where prices, quantities, and incomes are endogenous and changes in regional welfare are measured.

Examples of policy applications of regional general equilibrium studies completed in Oklahoma are presented in the next section. Examples of other studies are referenced in Partridge and Rickman. The last section is a summary and conclusion for this chapter of the webtext.

6.1 Policy applications

This section summarizes studies of regional welfare change associated with development issues by means of regional CGE. The first study is a state-level analysis of welfare losses due to agricultural export price decreases in the 1980s. Results explain why state policymakers were anxious to replace regional welfare losses. The second study is an effort to show the state economic impacts of potential damages a change in surface water quality may have on sport fishing in Oklahoma. The models are not presented, but are available in references cited.

6.1.1 Agricultural export prices ⁴

Agricultural commodity prices showed a sizable decrease during the mid1980s. Farm foreclosures and bankruptcies were several times higher than normal for the state. Low agricultural commodity prices and depressed energy prices decreased income and employment levels throughout the state, particularly in rural areas.

From 1982 to 1986 there was about an 11 percent decrease in export prices of agricultural commodities. In this context, a counterfactual experiment of a 10 percent decrease in export (national) prices of agricultural commodities was simulated for the Oklahoma economy focusing on welfare changes by household income group.

Welfare changes in terms of compensating variation (CV) amounted to a state loss of about $123,702,000 at the 1990 price level. Welfare losses equaled $83,525,000 for the high income household group and $51,281,000 for the middle income household group. Low income households showed a slight welfare gain of $11,104,000. The latter is a result of lower commodity prices, particularly for nontradable commodities. When compared to the initial level of expenditure for each household income group, welfare change for high income households was –0.86 percent, middle income households was -0.26 percent, and low income households was +0.10 percent.

Most policymakers seek strategies that are short- to intermediate-term. Such strategies have limited success because most regional development issues are structural and require long-term changes in comparative advantage. When Oklahoma lost aggregate income and employment because of the decrease in agricultural prices, policymakers sought to replace the loss as quickly as possible. The strategies proposed, however, were long-term. Investments in value-added activities, international trade development, and development of alternative crop and livestock enterprises require long-term commitment – results of such development strategies are not felt immediately. Rural development research has not adequately recognized the differences between proposed development strategies and policy expectations. In part this is because rural development research has not focused on how factor and commodity markets work in rural regions in the short to intermediate term versus the long term.

The regional equilibrium model developed and applied at the state level in this study simulates the short-run conditions for markets by holding land and capital fixed by sector. Labor is assumed mobile between sectors and between regions. Hence, simulation results approach the short- to intermediate-term effects that correspond with expectations of policymakers.

A major conclusion of the study is that resource owners have a large stake in the re-establishment of economic activity. Land owners had a 20.9 percent reduction in land rents, and capital owners had a reduction of capital rents ranging from 20.9 percent in agriculture to 0.5 percent in services. Labor compensation was reduced 0.5 percent which, because of mobility between sectors and regions, was significantly less than the losses by land and capital resource owners. Labor that migrated had the lowest loss in resource compensation.

6.1.2 Sport fishing trip demand ⁵

Growth in sport fishing and the associated increase in angler expenditures have heightened the need for understanding how variations in expenditure can affect a regional economy and the welfare of economic participants. In Oklahoma the number of anglers increased 14 percent from 1980 to 1990, compared to a 20 percent increase nationally. Fedler and Nickum estimate that angler expenditure in Oklahoma was $387.3 million or 0.6 percent of gross state product in 1991. The fixed price multiplier impact was estimated by Fedler and Nickum to equal $793.5 million in output for all Oklahoma sectors, $202.2 million in job earnings, and 11,606 in employment. But what are the general equilibrium results, when both price and quantity are endogenous, from a change in the demand for sport fishing trips? Such general equilibrium results are important for measuring policy implications of changes in quality of sport fishing and subsequent changes in trip demands.

Agriculture accounted for about 5 percent of gross state product (GSP) in Oklahoma in 1992. Scifres and Osborn estimate that 15.4 percent of GSP is associated directly and indirectly with agriculture. Natural resource systems provide valuable services in support of agricultural production and sport fishing activities. Boosting agricultural production by applying more fertilizer and other chemical products could substantially affect the quality of water in natural resource systems and negatively impact sport fishing.

This study utilizes information on sport fishing trips and sport fishing expenditures in Oklahoma to measure welfare gains/losses due to a change in trip demand. The National Survey of Fishing, Hunting and Wildlife Associated Recreation shows that 803,700 U.S. anglers fished in Oklahoma during 1991 with a total angler expenditure of $387,326,000.

Model experiments focused on decreased trip demands. The premise is that if quality of sport fishing decreases, trip demand decreases. Quality of sport fishing is hypothesized to be associated with number of fish caught per trip. The number of fish caught per trip is hypothesized to be associated with fish population which, in turn, is hypothesized to be associated with water quality. Hence, a decrease in water quality (i.e., an increase in chemical discharge) reduces fish populations which reduces fish caught per trip and thus decreases the quality of sport fishing and number of trips in Oklahoma. Presumably anglers have alternative sites outside of the state at which they can replace their desire for sport fishing. These experiments begin to address the general equilibrium policy implications of the fixed price impact analyses by Fedler and Nickum for sport fishing expenditures and by Scifres and Osborn for cash receipts of agriculture.

Two scenarios were analyzed: a 10 percent and 50 percent quality tax imposed on the price (costs) of in-state trips. This increases the cost of in-state relative to out-of–state trips. Regional welfare was measured by gross state product and household welfare. Loss in GSP with a 10 percent quality tax on in-state fishing trips was estimated at $14,910,000 and at $55,670,000 with a 50 percent quality tax. These loses are due to outmigration of resources and lower resource returns (wage rate and capital and land rents).

A more revealing welfare measure was the compensating variation loss to households. This loss is a measure of the income it would take to bring households back to their original level of welfare before the fishing trip quality tax. The distribution of welfare loss showed that high income households had the greatest percentage loss when compared to the before quality tax income level. Low income households had a higher percentage loss compared to middle income households. The 50 percent quality tax had about four times the percentage welfare loss compared to the 10 percent quality tax. If a dollar of welfare loss is valued equally across the household income groups, then for all households in the state the welfare loss was $16,556,000 with the 10 percent quality tax and $64,070,000 with the 50 percent quality tax.

6.2 Summary and conclusions

We need better analyses of regional development programs and policies as they impact the welfare of households. We need better and more integrated policy frameworks in which to perform analyses. We need better analytical models to evaluate programs and policies that allow prices, quantities, and incomes to be endogenously determined for regions. We need more and better regional data including estimates of structural parameters.

Regional economies are characterized by complex variable interdependencies and market interactions. This makes the general equilibrium framework a more appropriate analytical method compared to partial equilibrium methods. In this chapter, an attempt was made to present the salient features and a step-by-step illustration of the implementation of a regional computable general equilibrium (CGE) model. Because of the rigid nonsubstitution assumptions and absence of the role of price in alternative general equilibrium models, such as input-output and SAM multiplier models, we argue that the more flexible and theoretically sound CGE approach is the more appropriate framework of analysis.

A typical CGE model incorporates the core of neoclassical features of a well functioning economy that is characterized by perfectly competitive markets and constant returns to scale production technologies. This chapter has demonstrated CGE modeling for such an economy, using Oklahoma’s 1993 social accounting matrix (SAM). Because this material is intended for a wide range of readership – including upper-class undergraduate students, graduate students, and practitioners – several additional assumptions have been adopted to simplify the scope and size of the model. For example, the Oklahoma regional economy is aggregated into four industrial sectors, and a single household income group. Also, local, state and federal governments are all represented by a single government institution. Household commodity demand functions are assumed to be derived from a non-leisure-augmented Stone-Geary (linear expenditure system) utility function. The aggregated Oklahoma CGE model was used to simulate an increase in terms of trade. Results of the simulation were used to interpret the workings of regional CGE.

While the assumptions adopted in this model help to reduce the scope and complexity of the model to levels that are relatively easy to comprehend, such ideal economies seldom exist in reality. Relaxing some of the assumptions of this basic structure is likely to result in a more representative picture of the economy. However, the general modeling techniques remain the same. In section 5.0 of this chapter, a monopsonistic market structure was proposed for the forest products industry and the model was respecified. We encourage the readers to extend the basic model in ways to address real world regional impact and policy problems.

Although a CGE model is generally theoretically sound, it is not clear whether its quantitative predictions are superior to alternative models. Most of the specification problems in CGE analysis emanate from its reliance on one year of data implied by the calibration process. This tends to make the system underidentified, making it imperative for the researcher to use external parameters, which in most cases are estimated in a framework that is inconsistent with general equilibrium analysis.

ENDNOTES

1. Several issues are still not totally clear on theoretical grounds. First, the selection of the numeraire has no implication for the competitive CGE framework; however, this issue is still controversial when imperfect competition is involved (see, Ginsburgh). Furthermore, the possibility of non-uniqueness of equilibrium is "a potentially serious problem" for applied general equilibrium models with imperfect competition and economies of scale (Mercenier). Finally, regional CGE modeling has adapted concepts and specifications from the national and/or trade CGE literature; however, the implications of its implementation at the regional level has been greatly criticized (i.e., the Armington assumption on product differentiation).

2. An alternative specification states average cost as where represents the cost function for a homogenous bundle of primary and intermediate inputs. This alternative formulation is used to specify scale economies due to returns from specialization.

3. For multi-product scale economies we carry out the following modification: where are, respectively, cost and output of the i^th product.

4. This section draws on the methods and results presented in Koh and Lee. The basic regional general equilibrium model is available in Koh, Schreiner, and Shin but was modified by Lee to include a labor migration elasticity, the labor-leisure relationship, and measures of welfare change. The basic social accounting matrix also was updated to 1990.

5. This section draws on methods presented in a paper for the Sixth International CGE Modeling Conference (Budiyanti, Schreiner, and Li) and on modeling methods in Lee. Results are from Budiyanti.

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