3.0 A Competitive Regional CGE Model

In a market economy there is generally a large number of homogeneous goods and services, which include not only consumption items but also factors used in production. Each of these goods and services has a market price, determined by the forces of supply and demand. Every market is assumed to clear at this set of prices. The perfectly competitive model further assumes zero transactions cost, a large number of price taking market participants (consumers and suppliers), and existence of perfect information, all of which support the law of one price (Nicholson).

Under these conditions, computable general equilibrium (CGE) models are similar to multimarket models, in which agents’ decisions are price responsive and markets reconcile supply and demand. Because they also encompass macroeconomic components, such as investment and savings, balance of payments and government budget, they are best chosen for policy analysis when the socioeconomic structure, prices, and macroeconomic phenomena all prove important (Sadoulet and de Janvry). CGE models have been built to simulate the economic and social impacts of various scenarios. Examples of alternative scenarios include foreign trade shocks, changes in economic policies, and changes in domestic economic and social structure.

In a regional CGE model, production creates demand for value-added factors and goods and services used as intermediate inputs. Intermediate inputs consist of both imports and locally produced goods and services. Demand for value-added factors interacts with available factor supplies to determine factor prices. Margins, such as taxes and transportation costs, increase factor costs to firms, which in turn increase product prices. Factor rates of return and ownership of factor supplies determine personal income, which in turn influences demand for imports and locally produced goods and services. Equilibrium occurs at prices which equate the demands for goods and services with supplies, and the demands for factors with factor supplies.

Because the CGE model attempts to look at all adjustments simultaneously, it is inherently an extensive formulation. To enhance understanding by students and prospective users of CGE analysis, the model here is split into components and each component is explained separately. The components include commodity markets, factor markets, production systems, institutional agents, and welfare measures.

3.1 Production system

Unlike regional input-output and SAM models, which are based on Leontief technology, neoclassical theory guides specification of production in regional CGE models. In consequence, the CGE model does not represent factor demands as linear functions of output. Instead, factor demands depend on both output and relative prices. The only exception, however, is in relation to treatment of those goods and services that are used as intermediate inputs. The Leontief input-output production function is used to represent production of regional output with fixed proportions of composite primary factors and composite intermediate inputs.

The composite primary factors generally enter the production process in a manner allowing factor substitution. Thus, production is best described as a multi-level or nested production process. Note that all factors in a constant elasticity of substitution (CES) function have the same elasticity of substitution between any pair of factors. To allow for differing elasticities between sets of factors, multi-level or "nested" production function forms are used in CGE, with each level containing a different set of factors and their own corresponding elasticities of substitution. That is, the use of a multi-level structure allows for use of both fixed-coefficients and price responsiveness in the CES form.

3.1.1 Composite value-added and intermediate inputs

The Leontief input-output production function that represents the non-substitutability between intermediate and primary inputs constitutes the first level of the three-level production process characteristic of most CGE models. For a single industry/sector, the Leontief production function is presented as:

(3.1.1)

where X_i is gross output of sector i, VA_i is composite factor (value-added) inputs of industry i and is composite intermediate inputs of industry i. Constants and represent industry i’s input-output coefficients for composite factor inputs and composite intermediate inputs.

By rearranging terms in equation (3.1.1), the (input-output coefficient) parameters of the Leontief production function are calibrated as follows:

, and

(3.1.2)

For each calculation in equation (3.1.2), values of the variables on the right-hand-side (RHS) are given in the SAM. For the agricultural sector in Table 2.1, for example, total output X_i = 4,344,160,000 (the column or row total), composite factor inputs = 1,713,668,000, and composite intermediate inputs (locally produced plus imports) = 2,534,191,000. Therefore, Leontief parameter values are = 0.40 and = 0.58 (click here for graphic presentation of Leontief production function). Although an industry is an aggregation of many producers, it is treated as a single firm in the CGE framework.

3.1.2 Substitution among primary factors of production

What generally distinguishes a regional CGE production structure from a simple input-output model is that value-added (primary) factor usage is responsive to factor costs, and imports of intermediate goods are price responsive (Partridge and Rickman). At the second level of production, nesting allows different treatment of intermediate goods from that of value-added factors.

Primary inputs and their demands

Cobb-Douglas (CD) or constant-elasticity-of-substitution (CES) functions are commonly specified to represent substitution among primary factors of production in a sector - land, labor, and capital. Here production technology is assumed to possess constant returns to scale (CRS). The CD function implicitly specifies unitary factor substitution elasticities, while the CES is a more general case that allows different from unitary elasticities of substitution. For simplicity, the Cobb-Douglas functional form is used to represent the second level of production:

, (3.1.3)

where, , and are labor, capital, and land inputs for industry i, respectively. Coefficient is the total factor efficiency parameter for composite primary factor inputs in sector i. Parameters , , and are production elasticities (click here for CD production elasticities) and correspond to labor, capital and land, respectively. Constant returns to scale are imposed by assuming that the sum of the elasticities in equation (3.1.3) is equal to unity. Individually, the production parameters are also assumed to have values that lie between zero and one. By substituting and rearranging terms in equations (3.1.2) and (3.1.3), sectoral gross output () can be expressed in the Cobb-Douglas production function form:

, (3.1.4)

or

, where (3.1.5)

Assuming that labor, land, and capital are the only value-added (or primary) inputs in the production of sector i's output X_i, the sector’s profit function is

(3.1.6)

where p _i is profit (click here for example of profits) for sector i, PN_i is net price of output (i.e. output price less cost of intermediate inputs and indirect business taxes), PL is wage rate, PK_i is capital rent (assuming capital is fixed by sector), and PT is land rent.

Assuming all firms in the sector strive to maximize profits, differentiating equation (3.1.6) with respect to each of the inputs and equating the outcome to zero will give the first order conditions. Thus, the first order condition with respect to capital is:

. (3.1.7)

Rearranging terms in equation (3.1.7), the marginal product of capital is equal to the ratio of capital rent to output net price:

. (3.1.8)

Substituting equation (3.1.5) into equation (3.1.7) yields the following:

, (3.1.9)

which translates into:

. (3.1.10)

Rearranging terms in equation (3.1.10) and substituting for using equation (3.1.5), yields an expression for capital’s share parameter in the Cobb-Douglas production function:

, or (3.1.11)

This is equivalent to multiplying capital’s marginal product (see equation 3.1.8 above) by the ratio of capital to output, which is also the formula for elasticity. Therefore, expression (3.1.11) shows that factor shares are equal to production elasticities in a Cobb-Douglas function. Share parameters for labor and land are derived in a similar fashion. In equation (3.1.11), making the subject of the formula yields the conditional demand (i.e. fixed output level) for capital in the industry, given by:

. (3.1.12)

Similarly, conditional demands for labor and land can be expressed as:

, and (3.1.13)

. (3.1.14)

Calibration of the Cobb-Douglas production equation (3.1.5), involves determining and evaluating two sets of parameters – share parameters and the efficiency parameter, where all prices are normalized to one. The numerator and denominator in equation (3.1.11) are provided in the SAM as total capital returns and total value-added, respectively. For the agricultural sector in the above SAM (Table 2.1), capital returns and total value-added are $571,360,000 and $1,713,668,000, respectively. Substituting these values into (3.1.11) yields = 0.333. Similarly, = 0.253 and = 0.414. The efficiency parameter for the Cobb-Douglas production function is calculated by rearranging equation (3.1.5):

. (3.1.15)

Calibration of equation (3.1.15) proceeds by substituting the calibrated factor share parameters and the quantities for the factor variables obtained from the SAM. For the agricultural sector, = 7.46. Multiplying by a_oi yields the value . (Click here for graphic presentations of the calibrated production function and factor demands).

Intermediate inputs and their demands

By the Armington assumption (Armington), goods produced in different regions (and possibly countries) are assumed to be imperfect substitutes, usually specified as a constant elasticity of substitution (CES) function. These intermediate goods from different regions combine at the second level of production to form composite intermediate goods that enter the first level of production. The CES function representing the relationship between the two categories of intermediate inputs can be expressed as:

, (3.1.16)

where is the intermediate input efficiency parameter, is the share parameter, represents intermediate goods imported by sector i from sector j in the exporting region, is regionally produced intermediate goods for sector i from sector j, is the elasticity of substitution for industry j, and is the substitution parameter. The value of depends on the degree of substitutability between the two sources of intermediate inputs. If , the two are perfect substitutes. If , they are used in fixed proportions.

The following cost minimization problem is used to derive demand functions for regionally produced and imported intermediate inputs:

Minimize

Subject to: ,

where PM and represent, respectively, prices of imported and regionally produced intermediate inputs from sector j. Solving the first-order conditions of this problem and rearranging terms yields the following expression:

. (3.1.17)

Calibration of this equation requires knowledge of the elasticity of substitution and normalizing the two prices, PM and to one. As stated above, values of elasticities of substitution are obtained from other sources. For the Oklahoma agricultural sector, for example, manufacturing input has a value of 3.55 (Table 3.1). This leaves the share parameter as the only unknown in equation (3.1.17). The value of is calculated by substituting the elasticity of substitution and the base values for imported and regionally produced intermediate inputs (from SAM) in the rearranged form of equation (3.1.17):

. (3.1.18)

From the SAM, the known values for intermediate inputs from manufacturing to agriculture are =159,671,000 and =446,829,000. Thus, from equation (3.1.18), =0.359. The efficiency parameter is computed by rearranging terms in the CES function (equation 3.1.16) and making the relevant substitutions:

. (3.1.19)

Total intermediate inputs from manufacturing to agriculture is, = 606,500,000 (see the SAM). Thus, evaluating equation (3.1.19) yields the value = 1.931 for the agricultural sector. (Click here for graphic presentation of the substitution between the two sources of intermediate inputs).

3.1.3 Substitution among types of factor inputs

A third level in the nested production process may represent substitution among labor skills within the overall labor input, among classes of land within the overall land input for agriculture, or types of capital inputs within the overall classification of capital. (The SAM presented in Table 2.1 does not show subcategories of primary inputs.) A common procedure is to consider the CES form of production which allows elasticities of substitution to differ among industries but requires the elasticity of substitution among any two subcategories (i.e. labor skills, land classes or types of capital) to be the same. Alternatively, subcategories could be grouped into two parts, such as production labor and all other, with one elasticity of substitution between the two and then two different classes of production labor with a different elasticity of substitution.

The elasticities of substitution for this level of the production process must come from other studies. (Click here for modeling substitution among labor skills). The studies by Koh and Budiyanti classified labor into five skill levels following work by Rose. They then assumed the Cobb-Douglas elasticity of substitution (equal to one) for all combinations of skill levels and for all industries. No sensitivity analysis was completed to test the results of varying these elasticities.

3.1.4 Net output price

Net output price in the competitive model is regional output price minus the unit cost of intermediate inputs and unit value of indirect business tax:

(3.1.20)

where PN_i is commodity i's net price, PX_i is the composite regional output price, a_ji is the amount of the j^th commodity per unit output of the i^th commodity, P_j is the composite purchase price of the j^th commodity, and ibt_i is the indirct business tax per unit value of output. (See section 3.2.4 for explanation of composite regional output price and composite purchase price). The net output price is the per unit value of output available to compensate for primary factor use. Under conditions of constant returns to scale in production, the sum of the marginal value products for all primary factor use should exactly equal the commodity net price.

3.2 Commodity markets

Commodity trade involves both regional and export markets. Within the region, commodity supplies are obtained from regional sources (regional production sectors) as well as from out-of-region sources (imports). Though differentiated by source, these commodities are bought by industries (intermediate inputs), households and other institutions. Inter-industry commodity flows have been discussed in Section 3.1 as intermediate input demands. In this section, we discuss regional output markets and household commodity demand systems.

3.2.1 Market outlets for regional output

Each industry in the region produces a composite commodity that can be exported or sold in the regional market. Export markets include other regions within the country and international markets. In CGE analysis, exports and regionally sold products are assumed to be differentiated by market, with the relationship between them represented by a constant elasticity of transformation (CET) function. Price ratios and elasticities of transformation determine the levels of output exported and sold in the region. The substitution possibilities are, thus, represented as

, (3.2.1)

where is industry i’s total output (as defined above), is the output efficiency parameter, is the share parameter, represents sector i’s supply for export, is the sector’s output supply to the regional market, is the elasticity of transformation for industry i, and is the output substitution parameter. The value of depends on the degree of transformability between the two market outlets. If , the two are perfect in their transformation. If , the two markets are not substitutable and further market behavior for each must be specified (see Berck et al. for an alternative to the CET).

Each firm allocates it's output between the regional and export markets so as to maximize revenue, subject to the CET function. Because the production process is assumed the same for each market, revenue maximization may be substituted for profit maximization. Thus, for given regional and export prices, the problem faced by the firm is to:

maximize

subject to: ,

where PE_i and are, respectively, prices of exported and regionally sold commodities from sector i. Solving the first-order conditions and rearranging terms yields the following:

. (3.2.2)

Calibration of this equation requires knowledge of the elasticity of transformation , which is obtained from other sources, and normalizing the two prices, and to one. For the Oklahoma agricultural sector in Table 3.2, . The value of , the only unknown in equation (3.2.2), is calculated by substituting the elasticity of transformation and the benchmark values for exported and regionally sold commodities (from SAM) in the rearranged form of equation (3.2.2):

. (3.2.3)

For the agricultural sector (see SAM in Table 2.1), = 1,752,557,000 and = 2,591,603,000. Thus, from equation (3.2.3), = 0.47. The efficiency parameter is computed by rearranging terms in the CET function (equation 3.2.1) and making the relevant substitutions:

. (3.2.4)

For the agricultural sector, = 4,344,160,000 (see the SAM). Thus, evaluating equation (3.2.4) yields = 2.01 for the agricultural sector. (Click here for graphic presentation of the calibrated CET function for regional product and exports.)

3.2.2 Commodity consumption by households

Regional household income available for commodity expenditure is calculated as gross income minus government taxes, savings and, in this case, payments for labor employed by households. Equation (3.2.5) is an algebraic representation of this relationship:

, (3.2.5)

where is household expenditure, is household disposable (minus government taxes) income, represents household savings, PL is wage rate, and is labor employed directly by households. The subscript h represents household category (low, medium or high income). The current SAM (Table 2.1) shows only total households.

The regional consumption by households is nested in two levels. At the first level, households maximize utility from leisure and consumption of composite market commodities, subject to total time (work plus leisure), household budget constraints and prices. At the second level, they choose optimal combinations of imported and locally produced commodities, which are imperfect substitutes, so as to minimize their cost of purchasing predetermined amounts of market commodities. Substitution between these commodity groups is captured in a CES function. A detailed presentation of each of these levels of the household consumption follows below.

Household commodity demand systems

Several alternative formulations have been used to represent household demand systems in the literature. Examples include the almost ideal demand systems (AIDS) by Deaton and Muellbauer, the Rotterdam model by Theil, and Barten, and the linear expenditure system (LES) by Stone. In general, a theoretically consistent demand system permits imposition of the general restrictions of classical demand theory. These restrictions are a) adding-up: value of total demands equals total expenditure, b) homogeneity: demands are homogeneous of degree zero in total expenditure and prices, c) symmetry: cross-price derivatives of the Hicksian demands are symmetric, and d) negativity: direct substitution effects are negative for the Hicksian demands.

The linear expenditure system is the most commonly used in CGE analysis due, in part, to convention and because it allows representation of subsistence consumption, in addition to satisfying the above restrictions. In this subsection, we provide an overview of the LES demand system and its adaptation to the CGE framework. Readers interested in more detail about the LES and other demand systems are referred to Deaton and Muellbauer.

In the LES, demand equations are assumed to be linear in all prices and incomes and the set of demand functions is expressed in expenditure form:

, (3.2.6)

where is the price of the i^th commodity, is the quantity of the commodity demanded, is the i^th intercept, are the price parameters, is the marginal budget share for the commodity, and y is the household’s income. Empirically, the LES is derived from constrained maximization of the Klein-Rubin (also known as Stone-Geary) utility function, whose general form is

(3.2.7)

where U is the utility level, is level of commodity i, is as defined above, and , if positive, is subsistence minima as perceived by the consumer.

Given a fixed amount of household income that can be allocated to consumption, , the household faces the following constrained maximization problem:

Maximize

subject to: ,

where the subscript h represents a particular category of households.¹ Solving the first order conditions of the Lagrangean to this problem produces the following results:

, and (3.2.8)

. (3.2.9)

Rearranging terms in (3.2.8), summing across i, and solving for the Lagrangean multiplier yields

, (3.2.10)

where, as stated above, . Substituting (3.2.10) into (3.2.8) produces an expression for the expenditure on commodity i by household category h:

. (3.2.11)

As expected, the first derivative of equation (3.2.11) with respect to total expenditure is the marginal budget share, . The linear expenditure system (equation 3.2.12) is obtained by dividing equation (3.2.11) by :

. (3.2.12)

To evaluate equation (3.2.12), we need values for and , prices, and total consumption expenditure data from the SAM. Because cannot be directly estimated from empirical data and because cannot be calculated from a one-period data set in the SAM, equation (3.2.12) is often implemented using a simplified version of the Stone-Geary LES. Rearranging equation (3.2.12) gives

. (3.2.13)

If we assume that the average budget share is equal to the marginal budget share, equation (3.2.13) implies the following:

, and (3.2.14)

. (3.2.15)

Because and , the relationship in equation (3.2.15) is guaranteed only if the minimum/subsistence consumption for all commodities. If this is the case, the LES demand function, equation (3.2.12), simplifies to:

. (3.2.16)

Coefficients are calculated from equation (3.2.14) by using the benchmark data in the SAM. This process is accomplished by normalizing the prices to one, which transforms the expenditure results in the SAM to physical quantities. In our example (Table 2.1), total household expenditure on both imported and regionally produced commodities, = $50,665,679,000 and expenditure on agricultural commodities is $328,760,000. Thus, the marginal (equal to the average) budget share for agriculture is 0.0065. (Click here for a graphic presentation of the calibrated commodity demand.)

As you notice, equation (3.2.16) is based on very restrictive and somewhat unrealistic assumptions. It implies that income elasticities of demand are unitary for all commodities. Although the results are not appropriate for dynamic analysis, this assumption does not pose serious problems for comparative static analysis, particularly if expenditure patterns for several household income groups are embodied in the model. For the interested reader, click here for a more general case of the LES demand system, which provides for leisure, household labor supply, and varying commodity income elasticities.

Commodity substitution of imports for domestic product

The second level of household commodity demand involves determination of the minimum cost combination of regional and imported commodities. For each commodity i, substitution between the two sources is captured in the following CES function:

, (3.2.17)

where is the household consumption efficiency parameter, is the share parameter, represents household demand for imports, household demand for regional products, is the elasticity of substitution, and is the substitution parameter. The determination of the domestic (regional) and imported amounts of a fixed total household demand is the same as presented in equations (3.1.16) to (3.1.19). (Click here for a graphic presentation of the substitution relationship between imported and regionally produced commodities as shown in the form of a household indifference curve).

3.2.3 Institutional markets

Governments and capital formation are the two remaining commodity markets represented in the Oklahoma SAM. Quantity demanded is assumed exogenous for each of these markets. However, price is endogenous and, hence, expenditure by governments and for capital formation varies with price. Similar to intermediate commodity inputs and household commodity demands, imported and regionally produced commodities are imperfect substitutes in meeting the composite commodity demands. Exogenous commodity demand for governments (QG_i) and capital formation (QC_i) from the two sources (regional and imported) is given by the following CES function:

(3.2.18)

where QX_i = QG_i + QC_i, QXM_i is quantity imported and QXR_i is quantity domestically produced. All parameters are identified similar to those for equation (3.1.16). The elasticities of substitution are the same as for intermediate inputs and household demand (see Table 3.1). Solution to quantities imported and domestically produced is similar to equations (3.1.16) to (3.1.19).

3.2.4 Commodity prices

Composite purchase price

Commodity purchase prices are a composite of regional and import prices:

(3.2.19)

The composite purchase price (P_i) is the unit value for household consumption goods, intermediate inputs, and institutional purchases. PR_i is the regional purchase price and PM_i is the import price. R_i is the total amount of commodity regionally produced and consumed and M_i is the total amount of commodity imported:

(3.2.20)

(3.2.21)

The right hand side terms are as previously defined.

Composite output price

Commodity output prices are a composite of regional and export prices:

(3.2.22)

The composite output price (PX_i) is the weighted unit value of revenue received from regional and export sales. PR_i is the regional price and PE _i is the export price. R_i is the regional quantity and EXP_i is the export quantity.

3.2.5 Commodity market equilibrium

Total commodity demand is the sum of intermediate demand, institutional demand, and export demand. Total commodity supply is the sum of regional production and imports. Market equilibrium for commodity i is the following:

(3.2.23)

where X_i = regional production, M_i = imports, TV_i = total composite intermediate input demand, TQ_i = total composite household demand, QX_i = total composite exogenous commodity demands (governments plus capital formation), and EXP_i = export demand.

3.3 Factor markets and factor incomes

In section 3.1, we derived factor demands for a profit-maximizing firm. However, these industries are not the only participants on the demand side of the factor markets. Institutions such as governments and households demand factor services. In addition to discussing institutional demand for factors, this section also describes the supply side and equilibrium conditions for the factor markets.

In the CGE framework, market behavior for primary factors is studied from both short-run and long run perspectives. In the short run, capital is assumed to be fixed by sector while labor is assumed to be mobile between sectors and between regions. In the long run, both capital and labor are mobile between sectors and regions. Land is assumed fixed in both short- and long run.

Factors are assumed to migrate in search of interregional quantity-price equilibrium. Higher wage rates and capital rents relative to out-of-region levels encourage in-migration while lower rates induce out-migration. Few regonal CGE studies have attempted to incorporate interregional mobility in factor markets. In their national trade model, de Melo and Tarr derived an endogenous labor supply by incorporating leisure as a commodity in the household utility function. Lee endogenized labor supply by allowing the labor-leisure choice and labor migration through a labor migration elasticity in his Oklahoma regional CGE model. In modeling the U.S. economy, Rickman incorporated both labor and capital migration. Budiyanti adapted Lee’s endogenous household labor supply and incorporated labor and capital migration in a regional CGE model.

For simplicity in the current exposition, initial institutional endowments and migration are assumed to influence factor supply. Equilibrium factor prices result when factor demands equal corresponding factor supplies. Endogenous labor supply (labor-leisure choice) is assumed to be insignificant and, hence, ignored. In the rest of this section, we present equilibrium conditions for the three primary factors - labor, capital and land - under conditions of no endogenous factor supplies. However, a detailed explanation of the modeling procedures required to address leisure-augmented household demand systems and endogenous labor supply is presented in this clickable. Most CGE models assume perfectly competitive factor markets, in which both firms (factor demanders) and households (factor suppliers) are treated as price takers. In the remainder of this section, we use the framework of perfect competition to discuss labor, capital and entrepreneurship, and land as factors and as sources of income.

3.3.1 The labor market

The labor market is in equilibrium when quantity supplied equals quantity demanded. Assuming all labor is homogeneous, equilibrium is expressed as:²

, (3.3.1)

where LSO is total initial household labor, LMG is labor migration, is total industry demand for labor, and LDE is exogenous demand for labor. LDE is equal to:

, (3.3.2)

where LDH is labor demanded directly by households and LDG is labor demanded by all government agencies. The labor row total in the SAM (Table 2.1) shows that LSO = 37,489,772,000 and is equal to the sum of LDI (30,400,863,000) and LDE (7,088,909,000). This is true when the system is in benchmark equilibrium because LMG is then equal to zero.

As stated above, labor migration arises due to differences between regional and out-of-region wage rates. The degree of mobility depends on the labor migration elasticity. This relationship is:

(3.3.3)

where LS0 is initial labor supply, PL is regional wage rate, PLE is rest-of-the-world wage rate, and is labor migration elasticity. is obtained from external sources. For examples in this study, the parameter is (0.92) and is from Plaut. For a more complete discussionn of regional labor markets see the web text chapter by Stephan J. Goetz.

Labor income

Total regional labor income (LY) is the sum of the product of labor demanded and the wage rate:

(3.3.4)

where PL is wage rate, LAB_i is labor demanded by industry i, LDH is labor demanded directly by households, and LDG is labor demanded by all government agencies. If the labor market is disaggregated by skill type, total labor income is determined by summing across all skills. Net labor income (NLY) is determined by subtracting payroll tax from total (or gross) labor income in equation (3.3.4):

NLY = LY (1 – ss tax) , (3.3.5)

where ss tax is the labor payroll tax rate. All of net labor income (NLY = 31,363,057,000) is distributed to households (SAM, Table 2.1). Payroll tax rate is ss tax = 0.164.

3.3.2 The capital market

In the short run, when capital is assumed to be perfectly immobile, the capital market is in equilibrium when quantity demanded by each industry () is equal to that industry’s initial capital stock ():

. (3.3.6)

If capital is mobile (the long run solution), the capital market is in equilibrium when total capital supply, which is the initial quantity plus migrated capital, equals total capital demand:

, (3.3.7)

where is capital supply from migration, and and are as defined above. Capital mobility ensures uniform capital rents across industries.

Like labor, capital migration arises due to differences between region and out-of-region rental prices:

(3.3.8)

where KS0_i is industry i's initial capital supply, PK is regional capital rent, PKE is rest-of-the-world capital rent, and is capital migration elasticity. The parameter is obtained from external sources. For examples in this study, the parameter is 0.92 and is taken from Plaut.

Capital income

Total capital income (KY) is the sum of the product of capital demanded and capital rent:

(3.3.9)

where PK_i is capital rent and CAP_i is the quantity of capital demanded by sector i.

In this formulation, capital is fixed with capital rents differentiated by industry. The overall capital rent is:

(3.3.10)

When capital is mobile across sectors and regions, capital income is:

(3.3.11)

where PK is the overall capital rent of the region.

Capital is owned by enterprises and households. Enterprise ownership is by corporations. Household ownership is by self-employed businesses including agriculture. Government subsidies are treated as an aggregate payment to capital. Thus net capital income (NKY) is the following:

NKY = (PK - gsub) KY (3.3.12)

where PK is capital rent and gsub is the government subsidy. From the Oklahoma SAM (Table 2.1), gsub = 0.0494467, ENTK = 12,510,953,000 and HHK = 7,848,069,000. Therefore, NKY = 19,352,336,000 when PK = 1.0. This is the same as the row and column totals for capital in the SAM.

Other accounting procedures and assumptions could be used in determining net capital income. In particular, business subsidies could be attributed directly to an industry.

3.3.3 The land market

Land is immobile and is assumed perfectly inelastic both in the short- and long run. Thus, the land market attains equilibrium when land use (LAND_i) is equal to initial quantity of land TSO_i:

. (3.3.13)

Total land income (TY) is the sum of the product of quantity of land and land rent:

(3.3.14)

where PT_i is gross land rent and LAND_i is the quantity of land demanded by sector i. For the Oklahoma SAM, agriculture is the only user of land. Net land income (NTY) is total land income less land tax:

NTY = (1 - t tax) (TY) (3.3.15)

where t tax is the land tax rate. From the Oklahoma SAM, t tax = 0.0363379 and LAND = 709,066,000. Therefore, NTY = 683,300,000. Because households own all land in the Oklahoma SAM, net land income accrues to households.

3.3.4 Enterprise income

The source of enterprise income (ENTY) is gross capital rents:

ENTY = PK • ENTK (3.3.16)

where PK is capital rent and ENTK is the initial stock of enterprise capital.

Claims to enterprise income (ENTY) include regional households, governments and a broadly defined capital account. Governments receive revenues from corporate income taxation. The broadly defined capital account includes capital depreciation, retained earnings and capital payments to owners of capital (stock) outside of the region. Because the current regional CGE model is used as an analysis of comparative statics to marginal changes in the system, enterprise income is distributed to the three entities (regional households, governments and capital account) as fixed shares. This distribution of income may be realistic for households and governments but it is unrealistic for depreciation which is generally based on capital stock rather than capital income.

The assumed distribution is:

HENTY = h ENTY (3.3.17)

GENTY = g ENTY (3.3.18)

CENTY = c ENTY (3.3.19)

where h, g, and c are shares of gross enterprise income distributed to households, governments and capital account, respectively. These shares are computed from the SAM and are h = 0.1386, g = 0.1359, and c = 0.7255.

3.3.5 Household income

Most household income comes from factor payments. As noted above, gross factor payments are subject to government taxes and capital depreciation. It is, thus, the total earnings less the applicable deductions that are available for distribution to owners of factors. Other sources of household income include inter-household transfers, government transfers, and net remittances from the rest-of-the-world.

Gathering these sources of income for households, gross household income (GHY) is:

where NLY is net labor income, PK is capital rent, HHK is capital stock owned by households, NTY is net land income, HENTY is household enterprise income, GOVTH is government transfers to households, and ROWTH is net transfers and remittances to households from rest-of-world. The latter two sources do not depend on regional resource ownership and factor prices. These sources are exogenous and assumed constant for the following analyses. All values may be read directly from the household row in the SAM.

Disposable household income (DHY) is:

DHY=(1 – hh tax) · GHY (3.3.21)

where ht is the household income tax rate. For the Oklahoma SAM, hh tax = 0.1294835.

Household savings (HSAV) is:

HSAV = mps · GHY (3.3.22)

where mps is the savings rate. Because this is negative in the Oklahoma SAM for 1993, it implies a negative savings rate for the aggregate of households. It is not uncommon for households to expend more than their income, particularly lower income households where inter-household transfers are large and expenditures are based on expected future earnings. In the Oklahoma SAM, because there is one household group, inter-household transfers are netted out of gross household income. In this case, mps = -0.0718137.

Because the model allows for labor and capital mobility, adjustments need to be made in factor compensations to households to assure that ownership of resources by households does not change with resource mobility. This is a major difference between regional and national CGE modeling. National models need not account for mobility of resources within the national boundary to hold original resource ownership constant by household group. For regions, households own labor, capital and land and receive transfers (inter-household, governments and rest-of-world). If labor moves, it is generally the household that relocates with its ownership rights to not only labor but also to capital and land. If resource adjustments are not made with labor mobility, changes in regional gross household income accounting may be the result of unintended changes in household resource ownership.

Consider household labor income with migration. Equation (3.3.1) shows regional labor market equilibrium with migration. Migration is shown in equation (3.3.3). Labor income (LY) for the benchmark (initial) regional households is the following:³

(3.3.23)

where all terms are as defined before. The first term on the right hand is regional gross labor compensation. The second term identifies out-migration and the compensation received when outmigrating. The third term identifies in-migration and the compensation received by immigrants. In-migration and out-migration are mutually exclusive as shown in the migration equation (3.3.3). Click here for two hypothetical examples of equation (3.3.23).

Household income from capital depends on household capital ownership and capital rents. Under the assumption of no capital mobility (short run with capital fixed by sector and region, i.e. equation 3.3.6), the initial regional households own capital resources equal to HHK = 7,848,069,000 and are compensated equal to PK · HHK where PK is the average regional price of capital.

Even though capital is immobile, with labor migration, households migrating out are assumed to take with them their proportion of capital rents which are further assumed to be spent out of the region. Those households remaining in the region will receive their proportionate share of capital compensation. Labor (household) in-migration is assumed to bring no other resource (capital and land) rents into the region. This assumption may be modified if further information is available.

Capital compensation to households is equal to:

YKH = PK · HHK (3.3.24)

The proportion of initial households associated with labor out-migration is:

(3.3.25)

where aLMG is used to show an adjustment amount to the following income variables. Only when LMG is negative (i.e. out-migration) will the numerator be greater than zero. When LMG is positive (i.e. in-migration) aLMG will be zero. The capital compensation to households remaining in region is:

RYKY = (1 – aLMG) YKH (3.3.26)

If aLMG = 0 , then all of YKH remains in region.

With capital mobile, capital resources owned by the initial households are used in-region or out-of-region depending on the proportion of capital out-migration to initial capital stock. The proportion of capital migration to capital stock is:

(3.3.27)

The assumption is that the same proportion of out-migration of capital applies equally to households and enterprises.

Capital compensation to households remaining in-region and with capital mobility is:

RYKH = (1-aLMG) (1-aKMG) YKH

+PKE^·aLMG ^· HHK (3.3.28)

The first term on the right adjusts capital compensation to households (YKH) for out-migration of labor (1-aLMG) and out-migration of capital (1-aKMG). The second term adds back in the compensation for out-migration of capital but at a higher capital rent because PKE>PK.

Compensation for capital in-migration adds to gross regional (state) product but is assumed to flow back out-of-state because ownership resides out-of-state.

Household income from land depends on land ownership and land rents. All net land income (eq.3.3.15) accrues to households:

NTYH = (1-t tax) TY (3.3.29)

However, with labor out-migration, a proportion of NTYH flows out of state. The proportion of NTYH remaining in-state is:

RNTYH = (1-aLMG) NTYH (3.3.30)

where the argument is the same as for capital income given in equation (3.3.26).

Enterprise income, government transfers and rest-of-world remittances accruing to the initial regional households (equation 3.3.20) remaining in-region under conditions of labor out-migration is given as:

REYH = (1-aLMG) (HENTY + GOVTH + ROWTH). (3.3.31)

Benchmark data is in equilibrium with labor and capital migration equal to zero. However, changes in equilibriums under comparative statics should allow for mobility of labor (households) and capital. As a result, three possible household groups are identified, with their own sources of income and their own effects on regional variables including commodity demands, savings and taxation. Each household group is presented by a set of income accounting equations.

Regional households

This group of households is part of the initial set of regional households and remains in the region after resource mobility occurs and a new equilibrium is attained under comparative statics. It is this group that is of primary interest in measuring welfare change from a change in regional policy or regional structure. Income to regional households includes net labor income, gross capital income, net land income, enterprise income, government transfers and rest-of-world net remittances:

(3.3.32)

The first term is household labor income adjusted for payroll taxes (equation 3.3.5) and labor out-migration (equation 3.3.23); the second term is household capital income adjusted for capital rents following labor migration (equation 3.3.26); the third term is net land income adjusted for land rents following labor migration (equation 3.3.29); and the fourth term is household enterprise income, government transfers and rest-of-world remittances, all adjusted for labor out-migration (equation 3.3.31). Under the conditions of capital mobility in addition to labor mobility, (equation 3.3.26) is replaced by (equation 3.3.28) and this becomes the second term in (equation 3.3.32).

Regional household expenditure for commodity demand is equal to:

RHE = (1-hh tax-mps) RHHY PL (1 aLMG) LDH (3.3.33)

where hh tax = household income tax rate, mps = household savings rate, and PL · (1-aLMG)LDH is household payments directly to labor adjusted for out-migration. The latter is included because payments directly to labor are not part of the household demand (expenditure) system.

Labor out-migration households

Households associated with labor out-migration take with them the value of their labor plus their capital and land rents from the initial distribution of resource ownership. Similarly, the region has less government transfers and less rest-of-world remittances. These reductions translate into less expenditure in the region and less government tax revenue and regional savings.

Income of out-migration households is the following:

(3.3.34)

where the first term is the labor compensation received out of the region. Notice that payroll tax is not included because this tax would be paid in the region of employment. The second term is capital rents and the third term is net land rents associated with regional resource ownership of migrating households. Notice that capital subsidies flow out but that land tax remains within the region. The fourth term is enterprise income associated with out-migrating households. Because this income is from capital ownership, it is treated the same way as direct capital payments to households.

Although regions lose government income tax revenue on labor income, regions keep income tax revenue (OMGR) on capital and land rents and enterprise income:

OMGR = hh tax · aLMG(YKH + RNTYH+ H · ENTY) (3.3.35)

Labor in-migration households

Income associated with labor in-migration households is assumed limited to only their labor compensation:

(3.3..36)

Regional expenditure associated with this income is equal to:

IMRE = (1-hh tax-mps) IMHHY. (3.3.37)

It is this expenditure which accounts for the commodity demands of in-migrants in their linear expenditure system.

3.4 Measures of regional and household welfare

The primary purpose of CGE analysis is to evaluate policy and policy change. Policymakers frequently evaluate policy change using several criteria. Two broad criteria are presented here with each subdivided into more specific welfare measures. The first broad criteria is regional welfare and emphasizes policy change on regional macro-variables. Because of the openness of regions, these measures are prone to emphasize place prosperity (or growth) with little insight on how policy changes welfare of people. The second broad criteria is household welfare and emphasizes people prosperity irregardless of where people eventually reside. This criteria considers both income effects and price effects in evaluating welfare of households residing in the region.

3.4.1 Regional welfare

Gross regional product

The most comprehensive measure of regional change is gross regional product (GRP) or, if for a state, gross state product (GSP). This measure accounts for the quantity of primary factor inputs used and the compensation to each input. It generally includes the indirect business tax paid by industry. It includes total compensation for labor by industry including payroll taxes and employee benefits. It includes gross returns to capital (including profits) before depreciation.

GRP are payments to resources used (or employed) in the region irrespective of where resource owners reside. Thus, factor payments flow to resource owners located within the region and outside the region. It is not necessarily a good measure of welfare change of households residing within the region.

For Oklahoma, GSP is the sum of all factor payments ($57,551,174,000) plus indirect business tax ($5,268,195,000) for a total of ($62,819,369,000). The following variables account for GSP:

(3.4.1)

where the right hand terms are, respectively, gross labor income, gross capital income, gross land income, and indirect business tax. The following is the index of change in GSP:

(3.4.2)

where GSP is the benchmark value of GSP.

Regional expenditure

Regional expenditures are defined here as aggregate expenditures by households, governments for consumption and businesses for capital formation. If regional expenditures are expanding, one would expect the state's economy to be growing. Expenditures as defined here are not adjusted for regional commodity imports. Presumably, households and governments have increasing incomes and revenues to support increasing expenditures, and investment opportunities are available to support increased capital formation.

Several caveats prevent this regional welfare measure from portraying viable economic growth. First, increased expenditure may be the result of increased commodity prices. A separate regional welfare measure accounts for the overall increase in price level. Second, expenditures may be financed from short term dissavings, government transfers, or out-of-region remittances. The negative savings ratio by households for Oklahoma in 1993 implies a dissavings for purposes of current consumption. Third, because governments were combined in the Oklahoma SAM, we can not view expenditure of only state and local governments. Federal government expenditures are more appropriately classified with regional exports. Fourth, double counting occurs because of government transfers to households and household tax payments to governments. Fifth, for the current CGE model, government expenditures and capital formation are exogenous and change only as commodity prices change. Of course, other behavioral conditions can be modeled for describing these expenditures.

The following variables account for regional expenditures:

(3.4.3)

where the right hand terms are total regional household expenditures and total exogenous commodity demand expenditures. The following is the index of change in RE:

(3.4.4)

where REO is the benchmark regional expenditure.

Regional price level

Composite commodity prices are endogenous to the regional CGE. Therefore, growth in the monetary variables for the region may be because of quantity changes and/or price changes. Export and import commodity prices are exogenous but the composite price is endogenous because it is a weighted average of the domestic regional and import prices. The overall regional price level may be calculated as either a weighted index of the composite commodity prices or of regional output prices. The former is useful in measuring the effects of prices on regional expenditures. The latter is useful for comparing the overall regional price level to external price levels.

The price index presented here weights the price changes by the benchmark quantities. Other price indexes may be used to measure changes in the overall price level.

The composite commodity price level is the following:

(3.4.5)

where RO_i and MO_i are benchmark quantities of regional market supply and imports, respectively. The price level index relative to the benchmark price level (i.e. PO = 1.0) is the following

(3.4.6)

The regional output price level is the following:

(3.4.7)

where XO_i is benchmark quantities of regional output. Presumably, with an increase in PX, regional output would be expanding and regional growth would occur. Similarly, with a PX less than one, regional output is decreasing and regional growth is contracting. The effects of this price level is particularly important when evaluating productivity changes in a region.

Net government revenue

Another important regional welfare measure is the change in net government revenue. An important policy question is whether a regional change in structure or policy adds more to regional government costs than is received in regional government revenue. This welfare measure is not considered here because of the aggregation of all government units (including federal) in the SAM. Several CGE studies are available that have disaggregated the governmental jurisdictions to trace government expenditures and revenues in considerable detail. One of the most detailed is a California study by Berck, et al. It also contains a review of the current literature in this area of application of CGE modeling.

Other regional measures of welfare

The rest-of-the world current trade account compares a region's exports to its imports. The importance of the balance of trade account is not so much that the aggregate of exports exceeds the aggregate value of imports as that the sources of exports and imports are identified. This assists in evaluation of the regional terms of trade, a comparison of the aggregate export price with the aggregate import price. Frequently, a region has a more limited array of export commodities compared to its basket of import commodities. This may lead to highly volatile terms of trade for some (especially small) regions. More diversified regions have less volatile terms of trade. Regions that have large export values compared to import values will have counter balancing monetary flows in the financial markets. Agriculturally related regions and older matured regions frequently have large monetary flows out of the region to counteract revenue inflows from exports. This generally means these regions have fewer investment opportunities compared to other regions. These results may be captured by constructing a balance of payments account for regions.

3.4.2 Household welfare

Household income

The most widely used measure of household welfare is household income. This measure is available in government documents for states and regions by time periods. However, to reproduce this measure from a CGE analysis after simulating a policy or impact change is not straight forward. In the regional CGE framework, households have an initial resource ownership with initial unit values. In addition, they have other sources of income such as government transfers and transfers from other households. In the typical comparative static analysis of policy or impact change, resource ownership and transfer income are held constant by household with emphasis on changes in unit values of resources and regional mobility of resources (labor and capital). The result is an accounting of income for three household groups after the policy change: (1) initial (benchmark) households remaining in the region, (2) initial households that migrate form the region, and (3) households added to the region through in-migration. Incomes for these three household groups are given in the equations of section 3.3.5.

Household incomes generated from regional CGE models are in nominal terms. To express in real terms, regional household incomes should be adjusted for changes in regional price level. One price index that may be used is the composite commodity price level calculated from equation (3.4.6). This adjusts regional household incomes by the purchasing value of commodities in the region.

Compensating and equivalent variation

Utility measures for individuals and households are the result of preferences expressed through markets. Similar measures are not available for regions. Policymakers express preferences for regions. Regional policymakers frequently choose preferences (goals) such as maximizing regional employment growth or maximizing gross regional product (GRP) or income. Such goals have little relevance when how they affect the welfare of individual households or groups of household is unknown (Levin). Maximizing employment growth may lead to trading many low paying jobs for fewer high paying jobs. Maximizing GRP may lead to emphasizing a regional structure of large corporate ownership of resources with high regional outflows of factor payments versus a regional structure of local ownership of resources with low regional outflows of factor payments.

An alternative goal is to increase welfare of one or more household groups within the region. Moving from one market result to another market result presumes a welfare change for most, if not all, household groups. To measure this change from a policy or program change, welfare must be measurable. Because utility is not directly measurable, an alternative measure must be chosen. An observable alternative for measuring the intensities of preferences of an individual for one situation versus another is the amount of money the individual is willing to pay or accept to move from one situation to another (Just, Hueth, and Schmitz, p. 10). The two most widely accepted willingness-to-pay measures are compensating and equivalent variations first proposed by Hicks. Compensating variation (CV) is the amount of money which, when taken away from an individual after an economic change, leaves the person just as well off as before. Equivalent variation (EV) is the amount of money which, if an economic change does not happen, leaves the individual just as well off as if the change had occurred (Just, Hueth, and Schmitz, pp. 10-11). Which welfare measure is employed depends on whether initial prices or new prices are used. The CV measure is based on new prices, and the EV measure is based on initial prices. Information on the distribution of welfare gains and losses among household groups should be useful to policymakers in making judgments on whether this policy result is inferior or superior to an alternative policy result.

Application of these criteria in national CGE models is available in de Melo and Tarr. Application to regional CGE models for Oklahoma are in studies by Lee, Budiyanti, and Amera. The equational forms for CV and EV are presented in Table 4.1.

ENDNOTES

1. Often, households have been categorized into 'high income', 'medium income', and 'low income'. See, for example, Budiyanti. For simplicity, we assume here that all households are homogeneous (h = 1).

2. If labor is differentiated by skill, the relationships presented here would hold for each skill type.

3. This formulation appears in the Amera and Schreiner regional CGE.

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