Lotze, Hermann: Integration and Transition on European Agricultural and Food Markets: Policy Reform, European Union Enlargement, and Foreign Direct Investment - Four Essays in Applied Partial and General Equilibrium Modeling -


Chapter 2. Applied General Equilibrium Modeling and the Global Trade Analysis Project

2.1. An Introduction to Applied General Equilibrium Modeling

Quantitative modeling of markets and policies has become ever more demanding in the process of economic development. Modern economies are characterized by multiple linkages between domestic input and output markets. In addition, international trade and factor movements establish further connections between countries and regions within the global economy. As the world economy becomes more integrated, there is also an increasing demand for quantitative policy analyses on a global scale. Important examples are the Uruguay Round (UR) negotiations under the General Agreement on Tariffs and Trade (GATT) as well as regional trade issues like the expansion of the European Union (EU), the Asia-Pacific Economic Cooperation (APEC), and Mercosur in Latin America (Hertel 1997, p.1.2).

Applied general equilibrium (AGE) models are powerful tools for analyzing these complex relationships. They provide a consistent framework, based on neoclassical economic theory, for conducting controlled experiments with respect to policy issues on the level of the whole economy (Powell 1997, p.iii). AGE models combine certain characteristics of disaggregated partial equilibrium models with those of highly aggregated macroeconomic models. Modern computer and software technology meanwhile allows the modeling of a large variety of disaggregated markets and sectors in an AGE framework, which was until recently the main feature of partial equilibrium models (Bauer and Henrichsmeyer 1989; Taylor et al. 1993). Moreover, AGE models establish linkages between all sectors within the economy, while taking into account the limited endowments with basic resources like land or labor. These models are closed in a macroeconomic sense, as they include the equalization of economy-wide savings with overall investment. Since policy measures are usually sector specific, disaggregated AGE models provide results with respect to costs and benefits for various economic agents which is usually not feasible with empirical macroeconomic models (Shoven and Whalley 1992, p.1).

Policy analysis with a focus on agriculture and food was traditionally a domain of partial equilibrium approaches. However, in this area the application of AGE models


can be useful for two reasons. First, if agriculture and the food industry have a large share in the economy, like in most developing countries and some transition countries, changes in agricultural policies or the development of the food industry may have a significant impact on the rest of the economy. Hence, it would be inappropriate to neglect corresponding factor movements between sectors and the effects on income redistribution. Changes in savings and investment also contribute to a more realistic picture of the economy-wide impact of sector policies. Second, changes in the macroeconomic environment, like monetary policy or exchange rates, or other exogenous shocks, like energy taxes, have an impact on the situation in the agricultural sector. Endogenous treatment of these issues usually goes beyond the capacity of partial equilibrium models.

AGE modeling started out with simple two-sector models of one country (Meade 1955; Johnson 1958; Johansen 1960; Harberger 1962). Gradually, the variety of sectors and markets in the models was increased, as improving computer technology and mathematical algorithms provided the means to solve these models consistently. Adelman and Robinson (1978) added another level of complexity by incorporating international trade between regions. A good survey of AGE modeling is given by Shoven and Whalley (1984).

The most important applications of multi-region AGE models were analyses of the distorting effects of taxes, tariffs and other policies on production, trade and resource allocation. "The value of these computational general equilibrium models is that numerical simulation removes the need to work in small dimensions, and much more detail and complexity can be incorporated than in simple analytic models" (Shoven and Whalley 1992, p.2). Many different policy interventions can be analyzed simultaneously, which is important as the total impact might differ from the sum of all the isolated effects. In order to provide meaningful analyses for policy makers, in many cases a detailed model structure with respect to regions, commodities, and policy instruments is required. The model developed by the Global Trade Analysis Project, which will be discussed in Chapter 2.2 , is an example of a multi-region, multi-commodity AGE model.


2.1.1. The Basic Structure of an Applied General Euqilibrium Model

The central idea of an AGE model is "to convert the Walrasian general equilibrium structure ... from an abstract representation of an economy into realistic models of actual economies. Numerical, empirically based general equilibrium models can then be used to evaluate concrete policy options by specifying production and demand parameters and incorporating data reflective of real economies" (Shoven and Whalley 1992, p.1).

The term general equilibrium was first elaborated by Arrow and Hahn (1971). A very simple AGE model would look like the following. Main economic agents in the economy are households and producers. Households have an initial endowment with resources and a set of preferences for various commodities. By maximizing their utility, household demand functions for commodities can be defined. Market demands are the sum of all individual households' demands. Commodity demands depend on all prices, and they are continuous, nonnegative, and homogeneous of degree zero. Moreover, they satisfy Walras' law which states: if, in an economy with n markets, n-1 markets are in equilibrium, then the last market also has to be in equilibrium. This is the same as to say that, at any set of prices, the total value of consumer expenditure is equal to total consumer income (Shoven and Whalley 1992, p.2). Producers have a certain technology, usually described by constant or non-increasing returns to scale, which they use for converting primary factors and intermediate inputs into final commodities. Producers are assumed to maximize profits. Since commodity demand is homogeneous of degree zero and supply is homogeneous of degree one, there is no money illusion in the economy and only relative prices matter within the model. One price is usually declared as the numeraire.

A standard AGE model is comparative static. The model is assumed to be in an equilibrium in the initial state. After an exogenous shock, like a policy intervention, a new equilibrium is achieved by searching a set of prices and production quantities for all commodities such that market demand equals market supply for all inputs and outputs. Under the constant-returns-to-scale assumption this assures that all output revenue is converted into factor income without extra profits. The mechanism is demonstrated in Figure 2.1 in an Edgeworth-box diagram for a simple two-person, pure exchange general equilibrium model. There are two individuals, A and B, with their


preferences and an initial endowment of two goods at point E. The size of the box defines the total endowment of the economy.

Figure 2.1: Simple pure exchange general equilibrium model

Source: Shoven and Whalley (1992, p.38).

Using individual preferences, a contract curve can be determine: Simple pure exchange general equilibrium model (Source: Shoven and Whalley 1992, p.38).d which is the locus of all tangencies of both individuals' indifference curves, like point Z. Trade can occur along the relative price line which runs through points E and Z. In a closed economy, any sales of good 1 by person A must be equal to purchases of good 1 by person B, and likewise for good 2. At point Z on the contract curve, the price line is tangent to the indifference curves, and net trade of both individuals is balanced (Shoven and Whalley 1992, p.38). Finding an equilibrium implies finding a price ratio where market excess demands for both goods are zero. In Figure 2.2 , the two market excess demand curves, g1 and g2, are shown depending on the price ratio P1/P2. In a two-goods economy it is actually sufficient to find a price ratio where excess demand on one market is zero. By Walras' law the other market is automatically in equilibrium. However, finding an equilibrium may be easy only in a very simple model. If the number of dimensions increases, a trial-and-error procedure becomes inappropriate. With higher dimensions, excess demand curves might be complex and the model might not converge to an equilibrium (Shoven and Whalley 1992, p.39). For solving


complex models, powerful solution algorithms and computer software have been developed.<4>

Figure 2.2: Excess demand curves for a simple general equilibrium model

Source: Shoven and Whalley (1992, p.39).

The major prerequisite and the basis of any AGE model is a social accounting matrix (SAM) of the economy or the regions under consideration. It is a square matrix that provides a picture of all economic transactions in a country or region at a given point in time, usually a certain base year. A stylized SAM is shown in Figure 2.3 . Linkages between sectors and agents in the economy are established by expenditures and revenues. Expenditures are listed in columns, while revenues are listed in rows. The SAM is based on the principle of double accounting which is applied to the economy as a whole. Each account must balance such that the row and column totals are equal (Brockmeier 1994, p.2; Sadoulet and de Janvry 1995, p.274-276).

Sources and destinations of all value flows in the economy can be identified in a SAM. It represents a closed system of a circulating economy, starting with the provision of factors of production by private households, followed by the generation of factor income, private consumption and commodity demand, and ending with production and


factor use by firms. This system is completed by government agencies, international trading relationships and the balance of savings and investment on a regional or global level. Thus, the SAM provides a mirror image of the functional relationships and identities in a corresponding AGE model.

Figure 2.3: Example of a stylized social accounting matrix



Factors of production



Capital account

Rest of the world



Intermediate demand


Private consumption

Government consumption



Total revenues

Factors of production

Factor demand






Factor income



Factor supply





Household income


Taxes and tariffs






Government revenue

Capital account



Private savings

Government savings


Capital transfers

Total savings

Rest of the world









Costs of production

Factor outlay

Household expenditure

Government expenditure

Total investment



Source: Adapted from Brockmeier (1994, p.2); Sadoulet and de Janvry (1995, p.274-276).

As shown in Figure 2.3 , commodities are used as intermediate inputs for the production of other commodities, for private and government consumption as well as exports and investment purposes. This generates revenue for producers in the first row account and causes expenditures in various column accounts. Factors of production like land, labor and capital are supplied by private households and used for final production. Thus, households generate income, while the government raises revenue by collecting taxes and tariffs. Moreover, households and the government provide savings to the capital account. External relationships to the rest of the world are established through exports and imports as well as capital transfers.

The intermediate input relationships between various industries in the upper left-hand corner of the SAM can be summarized in an input-output table. The square matrix design allows additional sector disaggregation, if this is required for specific model applications. For example, if the focus is on agriculture and the food industry, several sub-sectors may be defined for these sectors, while the rest of the economy remains highly aggregated (Wiebelt 1990, p.10-11; Brockmeier 1994, p.2; Sadoulet and de Janvry 1995, p.276).


2.1.2. Procedure of a Typical Model Application

A typical application of an AGE model would include the following steps as shown in Figure 2.4 . First, the base data for countries or regions which are covered in the model have to be collected. Second, the data have to be organized in a SAM and to be adjusted in order to achieve an initial equilibrium, i.e. overall income must be equal to overall expenditures, bilateral trade flows between regions have to be balanced, and producers' revenues have to be equal to total factor income. This is not a trivial point, as real world data often reveal inconsistencies and deficiencies.<5>

Figure 2.4: Flow-chart for a typical AGE model application

Source: Adapted from Shoven and Whalley (1992, p.104).


The third step in the model application is the calibration of unspecified model parameters. The term calibration means specifying the model in such a way that it is capable of reproducing exactly the numbers from the initial equilibrium data set. In essence this involves solving the model backwards for the parameter values while taking the initial data as exogenous. A complex AGE model is very demanding with respect to the number of model parameters. Most often not all of the necessary parameters are available from external estimates in other studies. Even if estimates are available, they might not be appropriate for a specific model. Hence, after the functional forms in the model are chosen and the available exogenous elasticity values are implemented, in the calibration run the model is solved for the missing parameters (Shoven and Whalley 1992, p.115-118). Very often this requires a parsimonious approach with respect to the overall number of parameters in the model, as the number of unknown parameters must not exceed the number of independent equations in the model. One method of reducing the number of parameters is the choice of so-called nested structures for the functional forms in the model (Shoven and Whalley 1992, p.94-100; Hertel and Tsigas 1997, p.20-28). In a replication run the model has to generate the initial data using the calibrated parameters.

Once the model is calibrated, the scenarios under consideration have to be defined and translated into the modeling framework. After policy shocks, or other exogenous changes, have been implemented in the model, a new counterfactual equilibrium is computed and the initial database is updated. Finally, the results are reported as changes in the updated database compared to the initial situation. Results may be presented in percentage changes or in levels. These include changes in output quantities, factor use and prices as well as overall summary indicators like changes in trade balance, consumer utility or regional welfare. Welfare measures are usually based on the underlying utility functions in the model. Although not without problems, the Compensating and Equivalent Variation measures developed by Hicks (1939) are widely used in AGE modeling (Shoven and Whalley 1992, p.123-128; Hertel and Tsigas 1997, p.35).

2.1.3. Critical Issues in Applied General Equilibrium Modeling

Several difficulties arise with the construction of complex AGE models. First of all, while AGE models are very demanding with respect to the number of exogenous


parameters, empirical estimates of most elasticities are scarce and often contradictory or inappropriate for a specific model design. Of course, this generally reduces the reliability of model results. The potential of calibration procedures is often limited, when even the key parameters are not readily available. Moreover, the possibility of sensitivity analyses does not immediately alleviate this problem. Complex AGE models contain such a large number of parameters that a meaningful sensitivity analysis often seems not manageable in a reasonable time frame. However, recently there has been some progress in developing automated procedures for systematic sensitivity analysis in large models. The approach by Arndt and Pearson (1996) will be briefly discussed in Chapter 2.4 .

Second, some of the key assumptions in many standard AGE models have been widely criticized. Full employment and perfect competition are the most striking examples (Shoven and Whalley 1992, p.5). Usually these assumptions are imposed in order to simplify a model. The possibility of unemployment would require the introduction of market inequalities which in turn requires advanced algorithms to solve the model. With regard to imperfect competition there is no unique theoretical approach, and hence there are various ways how to implement monopolistic or oligopolistic behavior realistically in an applied policy model. In any case, imperfect competition can be introduced into an AGE model, but it inflates the size of the model and the number of additional parameters tremendously (Swaminathan and Hertel 1996). This again adds to the above mentioned problem of parameter specification. Another important assumption refers to international factor movements, especially of capital. In most models regional factor endowments are fixed at initial levels. However, in the process of economic globalization capital becomes more and more mobile between regions which has important implications for the effects of national trade policy interventions. The existence of multinational firms and foreign direct investment are rarely taken into account in AGE models.<6>

A third issue which is neglected in neoclassical simulation models is the existence of sunk costs and path dependence in economic systems (Balmann 1995). In many cases, certain rigidities, like investments in fixed assets, prevent economic agents from making


their decisions purely based on relative marginal costs. This may lead to persistent market structures which change very slowly over time. Path dependence could play an important role, for example, in the analysis of restructuring processes in transition countries. However, as yet these issues have not been taken into account in AGE modeling.

A fourth critique of standard AGE analysis concerns the representation of policy instruments in the models. This is especially important for modeling agricultural and food policies, where the variety of instruments is vast. Specific real-world taxes and tariffs are often difficult to translate into a model-equivalent form due to different aggregation levels with respect to sectors and agents. Hence, "... for each tax there is substantial disagreement in the literature as to the appropriate treatment" (Shoven and Whalley 1992, p.5). In trade models, non-tariff barriers and quantitative restrictions often cause difficulties. Recent advancements in modeling techniques have tackled these issues (Bach and Pearson 1996). However, aggregated multi-sector or AGE models have their limitations when farm specific policy measures are introduced, like upper limits for subsidy payments per individual farm. These policies can only be modeled consistently with farm-based sector models (Balmann et al. 1998).

Finally, meaningful tests of AGE model specifications in a statistical sense are lacking. In the calibration procedure of an AGE model, a deterministic framework based on rigorous assumptions is constructed such as to reflect an artificial equilibrium situation which corresponds to a real economy at a single point in time. However, "... with enough flexibility in choosing the form of the deterministic model, one can always choose a model so as to fit the data exactly. Econometricians, who are more accustomed to thinking in terms of models whose economic structure is simple but whose statistical structure is complex (rather than vice versa), frequently find this a source of discomfort" (Shoven and Whalley 1992, p.6).

Having discussed the potential as well as certain weaknesses of AGE models in general, in the remainder of this chapter the theory and structure of the GTAP model is provided as a specific example.


2.2. Theory and Structure of the Global Trade Analysis Project Model

The Global Trade Analysis Project (GTAP) was established in 1992 at Purdue University, West Lafayette, USA. The main objectives of the project were to combine research efforts of many international experts in quantitative policy modeling and to lower entry costs for researchers who are willing to conduct economy-wide analyses of international economic issues, but who have not been involved in applied general equilibrium modeling before (Hertel 1997, p.1.1). The start-up costs for model development, data collection and calibration are very high for complex multi-commodity, multi-region models. Therefore, GTAP aims to provide a standard modeling framework and a common database for AGE analysis which gives researchers the opportunity to focus on policy implementation problems and further model development rather than spending too many resources on setting up the basic requirements.<7>

2.2.1. A Graphical Overview

Because the GTAP model is very complex, it may be useful to provide a graphical overview of the basic structure, before going into further detail of the model equations.<8> Figure 2.5 presents the basic value flows for one model region. For simplicity, there is no depreciation in this Figure, and government intervention in the form of taxes and subsidies is also omitted. At the top of Figure 2.5 is the so-called regional household which has a fixed endowment with primary factors of production, i.e. land, labor and capital. Without government intervention, the only source of income for the regional household is from sales of endowment factors to producers which yields factor payments in return. The regional household has an aggregate utility function which allocates regional income across three broad categories, i.e. private expenditure, government expenditure and savings. The most important advantage of the formulation of a regional household in an AGE model is the provision of an unambiguous indicator for overall regional welfare. As regional income rises, the regional utility function which will be discussed below takes not only changes in private expenditures, but also savings and government purchases into account (Hertel and Tsigas 1997, p.10).


Figure 2.5: Value flows in an open economy model without government intervention

Source: Adapted from Brockmeier (1996).

Private households spend their income on domestic as well as imported goods. The same applies to the government household which demands domestic and imported commodities in order to produce public goods and government services. Producers<9> combine primary as well as intermediate inputs in order to satisfy this final demand. They also use imported intermediate inputs and supply export commodities to the rest of the world.<10> Bilateral exports and imports are distinguished by destination and source region. Moreover, imports are distributed among specific domestic user groups, i.e.


private households, government and firms. This is especially important for the analysis of trade policy issues.

Finally, there are two global sectors in the model. First, there is a global bank which balances regional savings and investments and thus provides the so-called macroeconomic closure of the model. Producers, in addition to final commodities, also supply an artificial investment good, which is collected by the global bank and then distributed to regional households in the form of shares in a global portfolio, in order to satisfy their demand for savings. Second, there is a global transportation sector which accounts for the differences between fob export values and cif import values in international trade on a global scale (Hertel and Tsigas 1997, p.11).

2.2.2. Model Variables, Coefficients and Parameters

The structure of the GTAP model will be discussed by referring to Appendix A-2.1 where the readable text file of the standard model code is listed. The model code begins in Section A-2.1.1 with the definition of relevant files and sets. There are three types of files used in the modeling process: a data file with the base data in value terms, a parameter file with elasticity parameters, and a set file where various sets of commodities and regions are defined. There is a one-to-one relationship between sectors and commodities, i.e. each sector in the model produces only one good. Furthermore, there are three primary endowments, i.e. land, labor, and capital. Their initial levels are fixed for each region. By default, labor and capital are mobile endowments while land is sluggish, i.e. imperfectly mobile between sectors.

Following these initial statements, the model variables have to be defined. The GTAP database is formulated in value terms, e.g. the value of imports of a certain commodity from one region to another, or the value of a certain endowment used for the production of a certain commodity. Each of these value terms can be described by a quantity variable and a price variable. Quantities and prices are endogenously changed in the model which yields an updated value term after the model has been solved for a new equilibrium. In addition to quantity and price variables, there are technical change variables which can be implemented at various stages of the production technology.


Various taxes and subsidies are the policy variables in the model. They provide the linkages between market prices at various levels. For example, an output tax (to) can be implemented as a wedge between the market price and the price which the producer actually receives, the so-called agents' price in the GTAP terminology. Similarly, a tax or subsidy on primary inputs (tf) defines the difference between the input market price and the actual factor cost for the producer. Moreover, there are other tax instruments like source-specific import taxes and destination-specific export taxes available. A variable import levy can also be implemented by fixing the ratio between the world market and the domestic market price.

Furthermore, value, income and utility variables are necessary for calculating summary indicators which are based on the price and quantity changes resulting from a model run. Finally, there are several so-called slack variables. These are used in the model to change the closure rule for different modeling purposes. An AGE model has to be closed in a sense that all value flows have to be accounted for, i.e. in equilibrium there are no surpluses and profits. The model can be checked for consistency by applying Walras' law. Therefore, one market is dropped from the model formulation. In the standard case, this is the market for savings and investment. If all other markets are in equilibrium after the model has been solved, then the last market also has to be in equilibrium. This is checked by the endogenous variable walraslack<11> which has to be zero in a general equilibrium. The other slack variables are useful for partial equilibrium closure rules. For example, in certain cases one might want to look only at one country or region by creating a single-region general equilibrium model. This can be done in GTAP by fixing all trade linkages and keeping prices and income constant in all other regions, i.e. making them exogenous in the model. However, simply making certain variables exogenous would cause the solution algorithm to break down. The number of equations and endogenous variables would no longer be the same and, hence, the model could not be solved. This can be circumvented by making the relevant price variables exogenous, and at the same time making the corresponding slack variables endogenous. Thus, prices and quantities in certain regions can be kept constant, but the number of endogenous variables in the model remains the same.


After the variables have been defined, the base data have to be read by the modeling software. This is described in Section A-2.1.2 in the Appendix. Since the model is formulated in percentage changes, the value terms from the database enter the model as coefficients.<12> Value terms in the database are defined at three price levels: agents' prices, market prices and world prices. The difference, for example, between the value of output at agents' prices and market prices is defined by the level of output taxes or subsidies. Likewise, border intervention measures account for any difference between the value of exports, or imports, at domestic market prices and world prices.

The links between the values of output, government intervention, international transportation, and final consumption in the model are illustrated in Figure 2.6 .

Figure 2.6: Distribution of sales to regional markets

Domestic market in region "r"

Value of output at agents' prices


+ Output taxes/subsidies


= Value of output at market price


\|[xrArr ]\| Domestic sales, exports, and transportation


Value of exports at market prices


+ Export taxes/subsidies

World market

= Value of exports at world prices (fob)


+ Value of international transportation


= Value of imports at world prices (cif)

Domestic market in region "s"

+ Import taxes/subsidies


= Value of imports at market prices


\|[xrArr ]\| Import purchases of private households, government and firms

Source: Adapted from Hertel and Tsigas (1997, p.46).

Starting with the value of output at agents' prices in region r, output taxes or subsidies can be added which yields domestic output at market prices. Part of this is exported, and by adding export taxes or subsidies, the value of exports at fob world prices can be derived. International transportation provides the link to the corresponding import region s where imports are valued at cif world prices. Adding import taxes or subsidies yields the value of imports at domestic market prices in region s. Finally, these imports are distributed among private household consumption, government purchases, and firms' intermediate input use. In a similar way, all sales, purchases and government


interventions can be traced in the model. In the case of an input tax or subsidy on land, labor, or capital, there would be a difference between the value of input use at agents' prices and market prices.

After the value coefficients have been read from the data file, parameters defining substitution and income elasticities have to be read into the model from the parameter file. Finally, having set up the basic information from the database, the model calculates a variety of additional value and share coefficients which simplify the formulation of later calculations.<13>

2.2.3. Model Equations

The model equations, which are listed in Section A-2.1.3 in the Appendix, define the behavior of model agents as well as market clearing conditions, based on the theoretical foundation of the model. While the model is principally non-linear in the levels of the variables, it is nevertheless formulated in terms of percentage changes of the endogenous variables. This yields a linear form of the model which then can be solved for an equilibrium by using linear approximation methods.

Using Equation 1 in the Appendix Section A-2.1.3 as an example, at this point it will be explained how the non-linear model can be transformed into a linearized representation (Hertel and Tsigas 1997, p.15-20; Harrison and Pearson 1996, p.3.3). Equation 1 can be derived starting with the market clearing condition for tradable commodity i in region r:




= output of commodity i in region r valued at market prices


= domestic sales of commodity i in region r valued at market prices


= exports of commodity i from region r for transportation valued at market prices


= exports of commodity i from region r to region s valued at market prices.


This can be rewritten in terms of the corresponding quantities and a common domestic market price PM for i in region r:



= output quantity of commodity i in region r


= domestic sales of commodity i in region r


= export quantity of commodity i from region r for transportation


= export quantity of commodity i from region r to region s.

Dividing through by PM(i,r) yields the market clearing condition in quantities:


In a similar way, any market clearing condition in quantities can be converted into value terms by multiplying through by a common price. Hence, only value terms are required in the database, which also simplifies the problem of model calibration (Hertel and Tsigas 1997, p.16).

However, the behavioral relationships in the model are more conveniently written not in value terms, but in percentage changes of prices and quantities.<14> The non-linear formulation of the model in value level terms can be transferred into percentage changes by totally differentiating the values in the following way:



= value term


= price level


= quantity level


= percentage change in price


= percentage change in quantity.

Linearization of the market clearing condition (3) involves total differentiation which yields a linear combination of appropriately weighted price and quantity changes:


where the lower case variables are again percentage changes. Multiplying (5) on both sides by PM(i,r) yields the following equation:

This is the main part of Equation 1 in the model code described in Section A-2.1.3.<15> In addition, there is also the term VOM(i,r) tradslack(i,r) included in the equation. The slack variable is usually exogenous and zero, but it can be endogenized in the case of a partial equilibrium closure of the model.

In the linearized form of the equations, initial value terms taken from the database enter the model as constant coefficients. In a model run, percentage changes in endogenous prices and quantities are derived, and then the value terms are updated according to the update statements given for each coefficient in the model code. The updated value terms are stored in an updated data file which can be used for subsequent modeling purposes. Several approximation methods are available for solving a non-linear model via its linearized representation (Harrison and Pearson 1996, Chapter 2.5).

The first group of equations in the model code includes market clearing conditions for all traded goods, for mobile and imperfectly mobile endowments, and for private household expenditures. Furthermore, price linkage equations account for the differences in prices at various market levels caused by government intervention. All policy variables are called taxes in the model code, but in fact they represent taxes as well as subsidies depending on their sign.

Behavioral equations for producers

The second group of equations contains the behavioral restrictions for producers imposed by neoclassical economic theory. Figure 2.7 shows the so-called technology tree which illustrates a separable, constant-returns-to-scale production technology.<16>


Figure 2.7: The production technology tree in the GTAP model

Source: Adapted from Hertel and Tsigas (1997, p.56).

This production technology has a so-called nested structure. Based on certain assumptions about separability in production, firms are making their production decisions in the model in several independent steps. The separate nests are combined through elasticities of substitution. On the left-hand side of the production tree is the value-added nest, i.e. firms use primary inputs (qfe) which are combined in a constant-elasticity-of-substitution (CES) function. The elasticity of substitution is denoted sigmava. Firms also use intermediate inputs, some of which are domestically produced (qfd) and some of which are imported (qfm). They are combined in a CES function with sigmad as the elasticity parameter. Imported intermediate inputs are sourced from specific regions through bilateral trade flows (qxs), which is done according to the Armington assumption (Armington 1969). Again, a CES function is used with sigmam as the elasticity of substitution between imports from various regions. Finally, at the top of the production tree, the primary input composite and intermediate composite are joined in fixed proportions via a Leontief function, i.e. sigma equals zero, to produce final output qo. On each level of this production tree a variable for implementing technical change is


also available. Technical change in the GTAP model can be land, labor or capital saving, intermediate input saving, or overall Hicks-neutral.

The major advantage of the nested structure is that it significantly reduces the number of required model parameters and thus simplifies the calibration procedure. However, the chosen production technology is very restrictive in various directions, e.g. there is no substitutability between primary inputs and intermediates, which is certainly unrealistic. Moreover, the Armington approach to modeling international trade has been widely criticized, because the degree of product differentiation by region is given exogenous and not subject to the model exercise. Still, the use of the Armington assumption can be justified, because it is able to capture to some degree intra-industry trade, i.e. trade flows between regions in both directions for similar products (Hertel and Tsigas 1997, p.21-22).

There are two types of equations for each nest in the production tree. The first describes substitution between inputs within the nest. The second type is the composite price equation which determines the unit cost for the composite good produced by that branch. This composite price enters the next higher nest and determines the demand for this composite good. Both types of equations can be derived by starting with the definition of the elasticity of substitution (Hertel and Tsigas 1997, p.22-24). For illustrative purposes the example of two input goods and their inverse price ratio is shown here:



= elasticity of substitution

Q1, Q2

= quantity levels

P1, P2

= price levels.

From this, the following equations can be derived where prices and quantities are now expressed in percentage change terms (Hertel and Tsigas 1997, p.22-24):

Price equation:

p = theta1 p1 + ( 1 - theta1 ) p2

Quantity equation:

q1 = sigma ( p - p1 ) + q,




= price for composite input good

p1, p2

= prices for primary inputs


= cost share of primary input 1


= quantity of composite input good


= quantity of primary input 1

The first equation defines a weighted price p for the composite input good q. The second equation defines a firm's derived input demand for good q1, which is decomposed into two components. The first is the substitution effect, i.e. the product of the constant elasticity of substitution and the percentage change in the ratio of the composite price p to input price p1. The second component is the expansion effect, i.e. the percentage change in the output quantity of the composite good q. This simply assures an equiproportionate relationship between output and input, related to the assumption of constant returns to scale.<17>

The mobility of sluggish endowments, e.g. land, between sectors is governed by a constant-elasticity-of-transformation (CET) supply function which is analogous to a CES function on the demand side. As the elasticity of transformation increases, these endowments become more mobile between sectors. A consequence of imperfect factor mobility, in contrast to the perfect mobility case, are different factor prices for different sectors. If factor use is prohibited from full adjustment, factor prices have to differ in order to maintain a general equilibrium.<18>

Behavioral equations for households

The third group of equations define the behavior of households in the model. The overall regional household's behavior is determined by an aggregate Cobb-Douglas utility function which is specified over three categories: private consumption, government purchases and savings ( Figure 2.5 ). Although the allocation of savings is an intertemporal maximization problem, it is possible, by a proper specification of the utility function, to represent savings in a comparative static model (Hertel and Tsigas 1997, p.25). In a macroeconomic sense the model is savings-driven, as the share of regional income spent on savings is constant in the Cobb-Douglas function, and the level of regional investment has to adjust accordingly.


In order to derive a regional welfare measure, certain assumptions have to be made about the level of government purchases which are spent on the provision of public goods and services. The above mentioned regional utility function implies that preferences for public goods are separable from preferences for private goods, and the utility for public goods is identical across private households in the region. Furthermore, it is assumed that the initial level of public goods provided in each region is optimal (Hertel and Tsigas 1997, p.25). However, this assumption can be changed by exogenously fixing the level of government purchases. In that case, private household consumption alone has to provide full adjustment to changes in the regional economy. The regional Cobb-Douglas utility function is specified in a per-capita form with fixed expenditure shares on the three types of regional expenditures. Hence, in the case of a simulation period over several years, the population growth rate, represented by the variable pop(r), has to be taken into account for the calculation of regional utility.

Government spending on final commodities is allocated by another Cobb-Douglas function. First, expenditures are distributed in fixed shares among domestic and imported composite goods, and then imports are sourced by regions via the Armington parameters. Private household demand is treated differently, and this is a specific feature of the AGE model developed by GTAP. Private demand is clearly non-homothetic in nature, i.e. the expenditure shares of various commodities change as the level of income changes. This is important in a global trade model, where per-capita income levels differ significantly between regions. Moreover, a welfare increase, e.g. through trade liberalization, is likely to change the structure of private consumption. In the GTAP model, for the private household utility function the so-called constant difference of elasticities (CDE) form has been chosen. It is more flexible than the non-homothetic CES form, but it still can be calibrated to existing information on income and own-price elasticities of demand (Hertel and Tsigas 1997, p.26-27; Hertel et al. 1991). The parameters of the CDE function are initially calibrated to replicate a pre-specified vector of income and own-price elasticities. However, these elasticities are generally not constant, they rather vary with different expenditure shares and relative


prices. Hence, the elasticity values have to be updated with each iteration of the model.<19>

Savings and investment - the macroeconomic closure

The next group of equations covers a crucial area in any AGE model, the so-called macroeconomic closure. In order to close the economic system of resource flows as shown in the social accounting matrix ( Figure 2.3 ) and the stylized GTAP model ( Figure 2.5 ), a link between savings and investments has to be established in the model. GTAP does not account for any macroeconomic and monetary policies, which are usually the driving forces behind aggregate investment. In fact, there is no "money" in the model, as it is rather concerned with real resource flows and re-allocation effects caused by trade policy interventions or other exogenous shocks. However, the allocation of investment across regions has implications on production and trade through its effects on final demand. Because there is no intertemporal mechanism for the determination of investment in the model, the closure in a macroeconomic sense has to be provided in another way.

There are various solutions to this problem (Dewatripont and Michel 1987; Shoven and Whalley 1992, p.230-240; Sadoulet and de Janvry 1995, p.354-355; Hertel and Tsigas 1997, p.28-34). As mentioned above, like many other models, the GTAP model is savings-driven. The amount of savings is determined as a certain share of regional income, and investment has to adjust accordingly. One possibility in a multi-region model is to achieve the savings-investment equilibrium on a regional basis. The current account balance of each region can be fixed, and the difference between regional savings and investment always has to be equal to the current account surplus or deficit. However, the GTAP model also allows for a global closure. This is facilitated by a global bank as shown in Figure 2.5 . In addition to the production of traded commodities, each sector in each region also produces a certain amount of an artificial, homogeneous investment good, called capital goods.<20> The production of capital goods is modeled in the same way as the production of traded goods already discussed. However, only intermediate inputs, but no primary factors, are used in the production


function for capital goods. The global bank purchases these investments goods in all regions and sells them to regional households in order to satisfy their demand for savings commodities. Thus, the global bank provides a link between regional savings and investment on a global scale. The price for the investment good is the numeraire for all other prices in the model. However, the market equilibrium for capital goods is not enforced by a market clearing condition. This market is omitted from the equations, because it is used for checking Walras' law as mentioned earlier.

The GTAP model provides two alternative mechanisms for allocating investment across regions, which are explained in more detail in Hertel and Tsigas (1997, p.30-34). Under the first option, the regional rate of return on capital is equal across all regions. This is to say that the shares of regional investment in the global portfolio have to adjust in order to achieve a common global rate of return on capital. Under the second option, the regional composition of the global capital stock remains unchanged, and the region-specific rates of return have to adjust accordingly. The choice between the two options has to be made according to the specific modeling exercise. As long as a certain scenario is short-run and affects only a relatively small part of the global economy, it seems realistic to use the second option and keep the regional shares in the global capital stock constant. Under certain long-run scenarios, the choice of the investment allocation mechanism can significantly alter the size of international trade flows.

Global Transportation

The second global activity, apart from the global bank, is the service of international transportation which links exports from one region to imports of another region, and thus accounts for differences in the corresponding values at fob and cif prices. Transportation services are provided by a Cobb-Douglas production function which demands certain exports from all regions as inputs. Due to missing data these exports are simply combined into a composite international "transport good" with a common price. Again, the transportation activity is described by a price equation and a quantity equation as discussed with respect to the production technology. Commodity and route specific technical change in international transportation services can also be specified in the model (Hertel and Tsigas 1997, p.34).


2.2.4. Summary Indicators and Results

The final group of the model equations provides a number of summary indicators which are actually not necessary for computing an equilibrium, but which are useful for presenting the results of a model exercise. The basic results of a model run would consist of percentage changes in all the endogenous variables discussed earlier. In addition, several domestic price indices can be calculated, e.g. the regional terms of trade or the price index for private household expenditure. Then there is the percentage change in the value of GDP, which can also be broken down into a price and a quantity component. The overall change in welfare is calculated as the Hicksian measure of Equivalent Variation (EV) for each region and for the world as a whole.<21> The well-defined utility function of the regional household allows this calculation by multiplying the percentage change in overall regional utility by the initial level of regional income. Welfare changes are expressed in million US$, valued in the base year, i.e. 1992 in version 3 of the GTAP database. The change in world welfare is simply the sum of all regional welfare changes. It is important to note that the calculation of the Equivalent Variation is only valid in the case of a general equilibrium model closure. Once a partial equilibrium closure of any kind is chosen by endogenizing certain slack variables, the EV values might not be consistent any more and should be interpreted very carefully.

With respect to international trade there are several useful value indices as well as related price and quantity indices. Probably the most important price index in a global trade model is the world market price index for traded commodities. It is calculated as the weighted average of regional export fob price indices, using the value of regional production at fob prices as weights. Finally, the changes in regional commodity-specific trade balances and the change in the regional current account are provided. These are both given in value terms, i.e. in million 1992 US$.

This concludes the discussion of the standard GTAP model structure and the model code. The model is implemented and solved using the General Equilibrium Modeling Package (GEMPACK).<22> A typical modeling exercise would imply the following steps. First, the data and parameter files have to be specified. Then, the closure rules have to


be defined, and it has to be determined which of the variables are endogenous and which are exogenous in a certain application. Finally, the exogenous shocks to the initial equilibrium have to be listed. Shocks can be changes in policy intervention through taxes and subsidies, technical change of various kinds, population growth, or other endowment shocks.

2.3. The Global Trade Analysis Project Database

One of the most important achievements of the Global Trade Analysis Project is the construction of a global database for AGE modeling. This is an on-going project and the database is continuously improved and up-dated. It contains information based on individual countries' input-output tables, bilateral commodity trade between regions as well as data on international transportation and protection (Hertel 1997). Information for the database is provided by various national and international organizations, including the World Bank, the World Trade Organization (WTO), the United Nations Conference on Trade and Development (UNCTAD), the Organization for Economic Cooperation and Development (OECD), the European Commission, and the Economic Research Service (ERS) of the United States Department of Agriculture (USDA). In addition, many individual researchers have provided data on specific regions of their interest. Thus, GTAP explores the comparative advantage of a wide range of regional experts in the world economy. The global database also provides an opportunity for comparing the potential of various AGE models on the basis on a common data set. This is important, as differing results from different models are often explained by the fact that different data sets were used. This might not be true in all cases.

The complete database as well as the procedures for harmonizing data from many different international sources are fully documented in McDougall (1997).

Table 2.1 shows the complete list of regions and sectors included in version 3 of the GTAP database, which covers the global economy in the reference year 1992.<23>,<24>


Table 2.1: Sectors and regions in the GTAP database, version 3.

Model sectors

Model regions a

1 Paddy rice 1


2 Wheat 2

New Zealand

3 Other grains 3


4 Non-grain crops 4


5 Wool 5


6 Other livestock 6


7 Forestry 7


8 Fisheries 8


9 Coal 9


10 Oil 10


11 Gas 11

Hong Kong

12 Other minerals 12


13 Processed rice 13


14 Meat products 14

Rest of South Asia

15 Milk products 15


16 Other food products 16

United States

17 Beverages and tobacco 17


18 Textiles 18

Central America and the Caribbean

19 Wearing apparel 19


20 Leather, etc. 20


21 Lumber 21


22 Pulp, paper, etc. 22

Rest of South America

23 Petroleum and coal 23

European Union (EU-12)

24 Chemicals, rubbers, and plastics 24

Austria, Finland, Sweden (EU-3)

25 Non-metallic minerals 25

EFTA (Iceland, Norway, Switzerland)

26 Primary ferrous metals 26

Central European Countries (CEC-7)b

27 Non-ferrous metals 27

Former Soviet Union

28 Fabricated metal products 28

Middle East and North Africa

29 Transport industries 29

Sub-Saharan Africa

30 Machinery and equipment 30

Rest of the World

31 Other manufacturing



32 Electricity, water, and gas



33 Construction



34 Trade and transport



35 Other savings (private)



36 Other services (government)



37 Ownership of dwellings



a For details on the composite regions see McDougall (1997, Chapter 8).
b These are Bulgaria, Czech Republic, Hungary, Poland, Romania, Slovakia, and Slovenia. The group is called "Central European Associates" (CEA) in the GTAP documentation.

(Source: McDougall 1997)


Harmonization of data and other information from different international sources is a critical issue in the development of a global database. National input-output data, trade flows and estimates of government intervention heavily differ depending on the reporting institution. Problems occur with respect to different base years, different commodity and country aggregations, and simply inconsistencies and statistical errors. In order to achieve a database which represents a global equilibrium for a certain reference year, all these problems have to be overcome. Clearly, the outcome can only be a best guess based on the information available at a certain point in time. Nevertheless, the broad cooperation within the Global Trade Analysis Project assures that for most countries and commodities probably the best available data have been used. In any case, the current state of the database provides a sound basis for future improvements. Some of the data problems, with a special focus on the EU and the Central and Eastern European countries, will be briefly discussed in the following.

National input-output data

National input-output tables or SAMs are often difficult to obtain. Even for most industrialized countries they are only published at long intervals. Country tables usually differ with respect to reference years and sector disaggregation such that they are often not comparable. For many developing as well as transition countries the problem is even worse, as in many cases there exists no up-to-date information at all (Wahl and Yu 1997).

The collection and preparation of the regional data for the EU in GTAP is described in Brockmeier (1997). Input-output tables have been collected from national statistical offices and Eurostat, the statistical office of the EU. Although Austria, Finland and Sweden have already joined the EU, they are kept as a separate region (EU-3) to allow for analyses of European integration issues with the GTAP model. The member countries' information differs in the base years and sector aggregations. The most recent national input-output tables are from 1987 in the Netherlands and Luxembourg, while the other countries only have complete data on 1985 (Brockmeier 1997, p.16.2.4). The sector disaggregation is broader in most EU countries (59 sectors) than in the GTAP database (37 sectors). Hence, many sectors can be aggregated without problems. However, agriculture, forestry, and fishery products are combined into one sector in the EU classification. For their disaggregation, additional information from the Sectoral


Production and Income Model of Agriculture for the European Union (SPEL) has been used (Eurostat 1995). The input-output table for the EU-3 region was constructed from national statistics of the three recent EU members (Kerkela 1997). For input-output tables with an inappropriate base year or sector disaggregation, a statistical fitting procedure has been applied to update and modify the original data according to more recent macroeconomic information (McDougall and Hertel 1997).

The biggest problems concerning domestic data occur, of course, in the Central European countries and the Former Soviet Union (Wahl and Yu 1997). Most of the data used in GTAP were provided by the World Bank. However, all the original input-output tables are out-dated and have their base years between 1987 and 1989, i.e. still in socialist times. Moreover, the sectoral coverage is generally not in accordance with the GTAP disaggregation. Only for Hungary there was some additional recent information available. Hence, an extensive revision of the input-output tables for these regions had to be undertaken in which average values from other countries or regions at a comparable level of development were used. The strategy was to "retain the final demand structure of the contributed tables - that is, the commodity composition of consumption, exports and investment - but to replace the industry cost structures. The new cost structures ... are, in effect, averaged over many regions. ... This should be borne in mind in any application of GTAP data for Eastern European issues" (Wahl and Yu 1997, p.16.4.17-18).

Bilateral trade flows

The establishment of a consistent database on merchandise trade flows poses a different challenge than for other data components in the GTAP database. "The problem is less a matter of finding scarce data and more a matter of resolving inconsistent data. This is because one country's exports are also another country's imports, and imports and exports are reported by both partners. This reporting arrangement produces two trade records representing the same trade flows. Large discrepancies can be found when comparing a country's exports flows with its corresponding partners' import flows. Discrepancies in bilateral trade statistics pose a problem for use in the GTAP database" (Gehlhar 1997, p.11.1). In order to make trade data useful for a global AGE model, they have to be balanced in the initial situation. This means, the value of imports at cif prices for a certain commodity and region, minus the value of transportation services,


has to be equal to the value of exports at fob prices at the border of the trading partners. The reliability of the structure of trade is important for the credibility of the AGE model results. Various methods can be applied to balance all the bilateral trade flows in the database (Gehlhar 1997). The common objective is to generate the most reliable set of trade flows possible from the existing reported trade data. Of course, neither of the applied methods can be a substitute for insufficient source data.

The main sources of bilateral trade data are the COMTRADE database by the United Nations (UN), the World Bank's World Tables, the balance-of-payments and financial statistics by the International Monetary Fund (IMF), the FAOSTAT database by the Food and Agriculture Organization (FAO) of the UN, and the UNCTAD database. One side effect of establishing the GTAP database has been a quality assessment of the "raw ingredients found in bilateral trade statistics" (Gehlhar 1997, p.11.2). The results can be summarized as follows. In many individual cases large discrepancies in reported trade flows can be found. However, although 73 percent of the number of bilateral trade flows seem to be unreliable, these transactions contribute only 2 percent of the total value of trade in the database. On the other hand, over 75 percent of the value of individual transactions are reported with a discrepancy of less than 25 percent (Gehlhar 1997, p.11.20). Like the other contributions to the GTAP database, collection and derivation of reliable trade data is an on-going process.

Agricultural protection data

The outcome of any modeling exercises on regional integration and trade liberalization in agriculture and food products crucially depends on the initial protection levels in the database. It is a very demanding task to define unambiguous protection levels on a global scale, especially in agriculture and food sectors where an abundance of protection measures prevails in addition to simple import tariffs and export subsidies. The protection data in the GTAP database where mainly contributed by the World Bank and the WTO (Reincke 1997; Ingco 1997; Huff 1997).

The GATT Uruguay Round for the first time established international rules for trade in agricultural products. Important regulations agreed upon in the UR were the "tariffication" of non-tariff barriers (NTBs) and the introduction of bindings on the value and volumes of existing export subsidies. Since all participating countries had to


submit detailed descriptions of their initial protection levels, this was a unique opportunity to collect comparable agricultural protection data on a global scale (Ingco 1997, p.14.1). Of course, the UR results were not without problems, as many countries applied a so-called "dirty" tariffication. They took advantage of the difference in protection levels between the UR base period of 1986-88 and the actual levels at the end of the negotiations, which enabled them to increase their tariff bindings. For example, the EU and the countries in the European Free Trade Agreement (EFTA) set their post-UR tariff equivalents for "sensitive" products like dairy, sugar and grains significantly higher than their actual rates of protection in 1986-88.

Nevertheless, the UR results were used to establish two sets of protection data in version 3 of the GTAP database, pre-UR and post-UR protection levels. This facilitates the implementation of UR issues in the GTAP model. How various NTBs were converted into tariff equivalents is discussed in detail in Ingco (1997, p.14.10). For the use in the GTAP database all the protection measures had to be included in either of three categories: the difference between the value of imports at cif prices and domestic market prices (import protection level), the difference between the value of exports at domestic market prices and fob prices (export intervention level), and the difference between the value of domestic output at agents' prices and market prices (domestic support level).<25> These differences only define the initial protection levels in the database in the form of tax or tariff equivalents. However, starting from these levels, other policy measures like quantitative restrictions or variable levies can be implemented if required for any policy simulation.<26>

Elasticity parameters

As discussed earlier, the behavioral parameters in the GTAP model include elasticities of substitution between imported goods by source region, i.e. Armington elasticities, factor substitution elasticities, factor transformation elasticities, investment parameters, and consumer demand elasticities (Dimaranan et al. 1997). For many of these parameters external estimates or values from other AGE models have been used in the GTAP database. Armington and factor substitution elasticities have been mainly taken from the Australian SALTER model (Jomini et al. 1991). These were derived from a


review of international cross-section studies covering a wide range of countries and industries.

The parameters for the CDE demand functions of private households had to be calibrated to empirical estimates of income and price elasticities of demand. Income elasticities were taken from the World Food Model of the FAO (1993) as well as cross-country studies by Theil et al. (1989), Chern and Wang (1994), Zhi and Kinsey (1994), and Fan et al. (1995). In most cases, these studies had a different commodity disaggregation which had to be mapped to the GTAP structure of regions and commodities. With respect to price elasticities of demand there is much less information available in the literature. Using the available information on income elasticities, the values for own-price elasticities of demand were computed following a procedure developed in Zeitsch et al. (1991). The calculated elasticity values are presented and discussed in Dimaranan et al. (1997).

Reliable elasticity parameters are very difficult to obtain which is a problem for any empirical modeling project. Statistical estimation of elasticities is very demanding in terms of time and data requirements. At the same time, it is not a very rewarding activity any more in terms of methodological development. Consequently, not many researchers are actually undertaking broad-based empirical studies on elasticities. Moreover, in those cases where parameters are actually available for the use in simulation models, they are often fairly specific with respect to the regions, commodities or time period under consideration. This makes it difficult to implement them directly in an AGE model.

2.4. Recent Extensions to the Standard Applied General Equilibrium Model

In the recent literature on AGE modeling, several approaches for extending the standard modeling framework have been presented. Some possible extensions will be discussed in the following, i.e. systematic sensitivity analysis, welfare decomposition, implementation of quantitative restrictions, the introduction of imperfect competition, and more dynamic aspects like international capital mobility and accumulation.


Systematic sensitivity analysis

Results from any empirical modeling exercise are critically dependent on exogenous variables and parameters used in the simulations. As already discussed, especially in complex AGE models many parameters are not known with certainty or even missing altogether. One approach to solve this problem is sensitivity analysis with respect to key exogenous variables, behavioral parameters, or policy interventions. However, sensitivity analysis in large models is usually ad hoc, as a more or less arbitrary set of parameters has to be chosen for the investigation (Arndt 1996, p.1). This method is clearly unsystematic and provides little insight into the overall robustness of a model.

The core of the problem with unreliable model results is the mathematical fact that, for non-linear functions, the expected value E of a given function H is generally not equal to the value of the function evaluated at the expected value of an exogenous variable a, i.e. E[H(a)] ne H(E[a]). This implies that, if a complex model is only solved once using mean values of uncertain parameters, the deterministic results may be a poor approximation of the mean results (Arndt 1996, p.3). One solution to this problem would consist of an extensive Monte Carlo analysis, where the model runs would be repeated sufficiently often with a variety of parameter sets. However, for large multi-region AGE models this becomes impractical under normal time constraints.<27>

Another approach to sensitivity analysis is the so-called Gaussian Quadrature (GQ). In the GQ method, uncertain parameters and variables are described by a statistical density function. Consequently, the outputs of the GQ method are estimates of means and standard deviations of model results. In order to reduce the number of evaluations, a numerical approximation of the integral of the density function has to be applied. The special feature of GQ is the way how the weights are assigned in the numerical approximation to the integral of the density function. It can be shown that the outputs from this method, if applied to the GTAP model, are generally good approximations of means of model results and their associated standard deviations. They also provide valuable insights into the robustness of model results. On the other hand, GQ is applicable even under normal time and other resource constraints (Arndt 1996; Arndt and Pearson 1996).


Welfare decomposition

In the standard GTAP model, as discussed earlier, the regional Equivalent Variation is used as an indicator of the overall welfare effect which may be caused by a policy change or any other shock to the initial equilibrium. The model code can be enhanced by adding a facility for decomposing the total welfare change into several components which are related to certain policy instruments or specific quantity and price changes (Huff and Hertel 1996). By using this application, the interpretation of model results becomes much more detailed, as direct and indirect effects of certain taxes can be easily evaluated and linked to the relevant quantity changes in various endowments and commodities.

To give some examples, the total welfare effect for each model region can be broken down into the overall change in allocative efficiency and the terms-of-trade effect. Then, the regional change in allocative efficiency can be assigned to the individual sectors. Moreover, the allocative efficiency effects can be related to specific tax instruments, i.e. taxes on outputs, inputs, or international trade flows. Finally, the contribution of an import tariff to the regional change in allocative efficiency can be further broken down to the various sectors (Huff and Hertel 1996, p.19-20). Hence, the facility for welfare decomposition enables the modeler to identify the share of any individual economic transaction in the total welfare results of a simulation run. Moreover, the method is not specific to the GTAP model. With the necessary modifications, it can be used in other AGE models as well.

Quantitative restrictions

Standard policy instruments in the GTAP model include ad valorem taxes and tariffs at various levels of the production or demand functions as discussed in Section 2.2.2 . However, quantitative restrictions, i.e. quotas, on production and trade have become important non-tariff barriers to international trade, especially in agricultural and food sectors. For example, bilateral import quotas on grains were suggested by the Chinese government during the negotiations on Chinese membership in the WTO. Bilateral export quotas played a significant role in the Multi-Fiber Agreement as part of the Uruguay Round (Bach and Pearson 1996, p.4 and p.15). Moreover, quota restrictions for total imports into a certain region have been applied, e.g. by the EU on banana


imports from Latin American countries (European Commission 1993). Finally, production quotas on milk and sugar in the EU should be mentioned.

In a linearized representation of a non-linear AGE model it is not always straightforward to implement explicit value or quantity restrictions. As long as the quota restriction is binding, the relevant quantity variable can be fixed exogenously, while making the corresponding policy variable endogenous. However, in two cases this approach fails do work: first, if the status of a quota shifts from binding to non-binding, as it often occurs with bilateral export or import quotas; and second, if an export or import "tax" contains two elements, the tax equivalent of a quota and also an "ordinary" import tariff or export subsidy.

Bach and Pearson (1996) have developed a method to model any kind of inequality using the GEMPACK software package. The basic idea is to introduce additional value, price and quantity variables in those parts of the model where quantitative restrictions or other inequalities could be applicable. For example, concerning imports of a certain commodity into a certain region there are two relevant price levels in the standard model, the world market cif price (PCIF) and the domestic market price including any tariff or tax (PMS).<28> For modeling an import quota, an additional price (PIS) and, hence, value level is defined in between. Without import quotas, PIS would be equal to PMS. If the import quota is binding, however, PMS would be greater than PIS. Any "ordinary" import tariff on top of the quota can be modeled independently in the standard way, i.e. as a wedge between PIS and PCIF. In Bach and Pearson (1996) it is explained in more detail, how this can be included in the GTAP model code, and how the associated quota rents can be calculated. In order to derive sufficiently accurate results in the presence of quotas, a two-step solution strategy with different algorithms has to be applied.

Imperfect competition

One of the basic assumptions in many AGE models is the existence of perfect competition in all industries. This is clearly an oversimplification of observed economic reality, since output as well as input markets are frequently characterized by some degree of imperfectly competitive behavior. Main issues in this respect are product


differentiation and economies of scale. Swaminathan and Hertel (1996) show one possible way of how imperfect competition can be dealt with in an AGE model. However, modeling of imperfect competitive industries requires profound changes to the model structure.

Consumers in modern economies have very diverse preferences, i.e. their utility increases when there are many distinct varieties of the same product available on the market. This was termed the "love of variety" by Lancaster (1979). The same can also be observed with respect to firms' demand for intermediate inputs. Producers respond to this diversity by producing differentiated brands of principally the same good. The supply of differentiated products implies fixed costs for research and development (R&D) as well as marketing. Even if production occurs at constant returns to scale, the fixed costs give rise to increasing returns to scale in sales and, hence, imperfect competition. Firms determine their price by adding a markup to their marginal costs in order to recoup the fixed cost from R&D and marketing (Swaminathan and Hertel 1996, p.2). Typically, industries which are characterized by high expenditures on advertising or R&D include food processing, beverages, textiles, automobiles, electronics, and other durable goods. In these sectors imperfect competition is more likely to occur. On the other hand, primary agriculture, natural resources, and mining are assumed to be closer to perfect competition (Swaminathan and Hertel 1996, p.2).<29>

In addition to the more traditional treatments of oligopoly and monopolistic competition<30>, recent developments in industrial organization theory have strongly increased the number of different oligopoly models. However, many of these theoretical models are unsuitable for implementation in economy-wide AGE models, as they require information on the strategic interaction between firms in imperfectly competitive industries which is usually not available. Hence, the Chamberlin model of monopolistic competition (Chamberlin 1933) has been widely used in applied models. It abstracts from local firm rivalry and uses a representative consumer for modeling the preferences of all private households (Swaminathan and Hertel 1996, p.4). The Chamberlin model has been criticized for two reasons. First, firms can never really act


as local monopolists, as they have to face the competition of their direct neighbors. This situation usually would be better described by a local oligopoly (Kreps 1990, p.345-346). Second, if any consumer only buys one variety of a differentiated product at a time, he or she can hardly represent a whole group of consumers. Nevertheless, it is probably impossible to describe imperfect competition in a unique way, and the Chamberlin model captures at least some of the important aspects in a consistent way.

Implementing monopolistic competition in the GTAP model affects the behavioral assumptions on consumers as well as producers. Demand for final goods and intermediate inputs does no longer distinguish between domestic and imported goods. The Armington assumption has been criticized for being an ad-hoc product differentiation. It implies that in the standard model bilateral imports of a certain commodity only enter a region as an aggregate import good. In contrast, in the monopolistic competition model domestic as well as imported products directly compete for the demand of various agents in a certain region. This tremendously increases the model size in terms of new equations, variables and parameters. Also, the structure of the database has to be altered.

With respect to the structure of production, the modeler first has to decide which industries are characterized by perfect competition and which reveal imperfectly competitive behavior. Then, a markup on average variable costs is introduced which is dependent on the elasticity of substitution between differentiated products. Moreover, the number of firms within an industry enters the model as a new endogenous variable. It is important to note that there is a one-to-one relationship between varieties and firms. The possibility of endogenous entry and exit of firms into or from an industry assures overall zero profits, i.e. the difference between revenues and total costs, in each sector. The details of the necessary modifications to model structure and data, together with the model code, are discussed in Swaminathan and Hertel (1996, p.7-24).

Simulation results from the modified GTAP model include, in addition to the standard industry-wide results, changes in the number of varieties in a certain industry (variety effect) as well as changes in output per firm (scale effect) (Swaminathan and Hertel 1996, p.30). Hence, with this model specification the pro-competitive effect of trade liberalization can be explored. The monopolistic competition model might also be


useful for applications of GTAP to the transition countries, where market power and other market imperfections prevail in many formerly state-owned industries.

International capital mobility and dynamics

To conclude the section on possible extensions to standard AGE models, some dynamic aspects like international capital mobility, foreign ownership and growth will be briefly discussed. These issues also have implications for projection experiments. Although medium-run projections can be done with the comparative-static version of the GTAP model (Gehlhar et al. 1994), a dynamic version would yield an explicit time path and more realistic end-of-period results. However, dynamic modeling within the GTAP framework is still in a rather preliminary state.

Francois et al. (1996) explore the relationship between trade, investment, and growth with an extended GTAP model. This is not accounted for in the standard version with exogenously fixed savings rates and fixed regional capital endowments. However, classical growth theory suggests that trade liberalization potentially affects medium-run capital accumulation through induced changes in regional savings and investment patterns. With an endogenous savings rate the medium-run impact of trade policy reforms can differ quite substantially from the pure static effects. Capital accumulation can reinforce, but in some cases also reverse, the static results and should be given more attention in policy modeling (Francois et al. 1996, p.1-2). Together with economies of scale effects, as discussed earlier, the total welfare gains from trade liberalization are probably much larger than those obtained from pure static analysis.

Perfect international capital mobility can only be covered in a truly dynamic model. McDougall and Ianchovichina (1996) have developed a dynamic extension to the GTAP model in which regional capital stocks are endogenous and time is included as a new variable for determining the length of the modeling period. In addition, the reallocation of endowment capital across regions is made possible, which also has to deal with the question of explicit capital ownership, i.e. foreign or domestic. However, data on bilateral international capital flows are not available. Instead, a "global fund" is installed which handles all international capital transfers. In addition, investment is treated in a partial adjustment mode in order to avoid extreme volatility in the short-run (McDougall and Ianchovichina 1996, p.3).


The question of foreign capital ownership is also closely related to the appearance of foreign direct investment and multinational enterprises (MNE). Clearly, these are of growing importance in a globalizing economy and will most likely affect the results from trade policy analysis. The equilibrium theory of international trade has long been separated from industrial organization approaches to the multinational enterprise (Markusen 1998, p.1). Only recently there has been some progress in integrating MNE into AGE models. Basic conditions for MNE to evolve are firm-specific fixed costs as well as plant-specific fixed costs as well as trade and transportation costs and differences in factor intensities (Markusen 1998, p.6). If parameters for these conditions can be found, equilibrium trade and foreign investment regimes can be derived in relatively simple AGE models. This might be a good starting point for future implementations of MNE in a global trade model like GTAP.

Traditionally, the limits to complex economic modeling were set by the available computer hardware and software technology. This is hardly a restriction any more. Moreover, there is a huge variety of theoretical models for the treatment of up-to-date economic issues, like imperfect competition or multinational firms. The restrictions to more advanced AGE modeling are rather given by the limited availability of appropriate data, e.g. sector-specific information on firms' behavior, bilateral investment flows, or elasticity parameters in general. However, this section has demonstrated that, even under current circumstances, there are various promising extensions available for making AGE analysis more realistic.

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Appendix A-2.1 The Global Trade Analysis Project Model Code

This appendix shows the complete model code for the standard GTAP model.<31> The code is used for implementing the model in the GEMPACK software package. First, the relevant files and sets have to be defined, followed by the model variables. In Section A-2.1.2 the database coefficients and parameters are read into the model, and various derivatives of the base data are calculated. Section A-2.1.3 provides the equations which describe the theory of the model. Finally, in Section A-2.1.4 various summary indicators are listed.

A-2.1.1: Definition of Files, Sets, and Variables

FILE        GTAPDATA # The file containing all base data. # ;

FILE (TEXT) GTAPPARM # The file containing behavioral parameters. # ;

FILE        GTAPSETS # File with set specification #;

SET REG # Regions in the model #


















SET ENDWC_COMM # Capital Endowment Commodity # (capital) ;












Quantity variables

VARIABLE (all,i,NSAV_COMM)(all,r,REG)                              qo(i,r)
       # industry output of commodity i in region r # ;

VARIABLE (all,i,ENDWS_COMM)(all,j,PROD_COMM)(all,r,REG)            qoes(i,j,r)
       # supply of sluggish endowment i used in j, in r # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)                   qxs(i,r,s)

       # export sales of commodity i from r to region s # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)                              qst(i,r)

       # sales of i from r to international transport # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)                              qds(i,r)

       # domestic sales of commodity i in r # ;

VARIABLE (all,i,ENDW_COMM)(all,j,PROD_COMM)(all,r,REG)             qfe(i,j,r)

       # demand for endowment i for use in j in region r # ;

VARIABLE (all,j,PROD_COMM)(all,r,REG)                              qva(j,r)

       # value-added in industry j of region r  # ;

VARIABLE (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)             qf(i,j,r)

       # demand for commodity i for use in j in region r # ;

VARIABLE (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,s,REG)             qfm(i,j,s)

       # industry demands for aggregate imports # ;

VARIABLE (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,s,REG)             qfd(i,j,s)

       # industry demands for domestic goods # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)                              qp(i,r)

       # private household demand for commodity i in region r # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)                              qg(i,r)

       # government household demand for commodity i in region r # ;

VARIABLE (all,i,TRAD_COMM)(all,s,REG)                              qpm(i,s)

       # private hhld demand for imports of i in region s # ;

VARIABLE (all,i,TRAD_COMM)(all,s,REG)                              qpd(i,s)

       # private hhld demand for domestic i in region s # ;

VARIABLE (all,i,TRAD_COMM)(all,s,REG)                              qgm(i,s)

       # government hhld demand for imports of i in region s # ;

VARIABLE (all,i,TRAD_COMM)(all,s,REG)                              qgd(i,s)

       # government hhld demand for domestic i in region s # ;

VARIABLE (all, r, REG)                                             ksvces(r)

       # capital services = qo("capital",r) # ;

VARIABLE (all, r, REG)                                             qcgds(r)

       # output of capital goods sector = qo("cgds",r) # ;

VARIABLE (all,r,REG)                                               qsave(r)

       # regional demand for NET savings # ;

VARIABLE (all,i,TRAD_COMM)(all,s,REG)                              qim(i,s)

       # aggregate imports of i in region s # ;

VARIABLE (all,i,TRAD_COMM)(all,s,REG)                              qiw(i,s)


       # aggregate imports of i in region s, cif weights # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)                              qxw(i,r)

       # aggregate exports of i from region r, fob weights # ;

VARIABLE (all,r,REG)                                               qxwreg(r)

       # volume of merchandise exports, by region # ;

VARIABLE (all,r,REG)                                               qiwreg(r)

       # volume of merchandise imports, by region # ;

VARIABLE (all,i,TRAD_COMM)                                         qxwcom(i)

       # volume of global merchandise exports by commodity # ;

VARIABLE (all,i,TRAD_COMM)                                         qiwcom(i)

       # volume of global merchandise imports by commodity # ;

VARIABLE                                                           qxwwld

       # volume of world trade # ;

VARIABLE (all,i,TRAD_COMM)                                         qow(i)    

       # quantity index for world supply of good i # ;

VARIABLE (all, r, REG)                                             kb(r)

       # beginning-of-period capital stock, in r # ;

VARIABLE (all, r, REG)                                             ke(r)

       # end-of-period capital stock, in r # ;

VARIABLE                                                           globalcgds

       # global supply of capital goods for NET investment # ;

VARIABLE                                                           qt

       # quantity of global shipping services provided # ;

VARIABLE (all,r,REG)                                               pop(r)

       # regional population # ;

VARIABLE                                                           walras_dem

       # demand in the omitted market--global demand for savings # ;

VARIABLE                                                           walras_sup

       # supply in omitted market--global supply of cgds composite #;

VARIABLE (all,r,REG)                                               qgdp(r)

       # GDP quantity index # ;                    

Price variables

VARIABLE (all,i,NSAV_COMM)(all,r,REG)                              ps(i,r)

       # supply price of commodity i in region r # ;

VARIABLE (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)             pf(i,j,r)

       # firms' price for commodity i for use in j, in r # ;

VARIABLE (all,i,ENDW_COMM)(all,j,PROD_COMM)(all,r,REG)             pfe(i,j,r)

       # firms' price for endowment commodity i in j of r # ;

VARIABLE (all,j,PROD_COMM)(all,r,REG)                              pva(j,r)

       # firms' price of value-added in industry j of region r # ;

VARIABLE (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,s,REG)             pfm(i,j,s)

       # price index for imports of i by j in region s #;

VARIABLE (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,s,REG)             pfd(i,j,s)


       # price index for domestic purchases of i by j in region s #;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)                              pp(i,r)

       # private household price for commodity i in region r # ;

VARIABLE (all,i,TRAD_COMM)(all,s,REG)                              ppm(i,s)

       # price of imports of i by private households in s # ;

VARIABLE (all,i,TRAD_COMM)(all,s,REG)                              ppd(i,s)

       # price of domestic i to private households in s # ;

VARIABLE (all,r,REG)                                               pgov(r)

       # price index for govt hhld expenditures in region r # ;

VARIABLE (all,r,REG)                                               ppriv(r)

       # price index for private household expenditures in region r # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)                              pg(i,r)

       # government household price for commodity i in region r # ;

VARIABLE (all,i,TRAD_COMM)(all,s,REG)                              pgm(i,s)

       # price of imports of i by government households in s # ;

VARIABLE (all,i,TRAD_COMM)(all,s,REG)                              pgd(i,s)

       # price of domestic i to government households in s # ;

VARIABLE (all,i,NSAV_COMM)(all,r,REG)                              pm(i,r)

       # market price of commodity i in region r # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)                              pim(i,r)

       # market price of composite import i in region r # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)                              piw(i,r)

       # world price of composite import i in region r # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)                              pxw(i,r)

       # aggregate exports price index of i from region r # ;

VARIABLE (all,r,REG)                                               pxwreg(r)

       # price index of merchandise exports, by region # ;

VARIABLE (all,r,REG)                                               piwreg(r)

       # price index of merchandise imports, by region # ;

VARIABLE (all,i,TRAD_COMM)                                         pxwcom(i)

       # price index of global merchandise exports by commodity # ;

VARIABLE (all,i,TRAD_COMM)                                         piwcom(i)

       # price index of global merchandise imports by commodity # ;

VARIABLE                                                           pxwwld

       # price index of world trade # ;

VARIABLE (all,i,TRAD_COMM)                                         pw(i)

       # World price index for total good i supplies #;

VARIABLE (all,i,ENDWS_COMM)(all,j,PROD_COMM)(all,r,REG)            pmes(i,j,r)

       # market price of sluggish endowment used by j, in r # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)                   pms(i,r,s)

       # domestic price for good i supplied from r to region s # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)                   pfob(i,r,s)

       # FOB world price of commodity i supplied from r to s # ;

         ! i.e., prior to incorporation of transportation margin !

VARIABLE (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)                   pcif(i,r,s)


       # CIF world price of commodity i supplied from r to s #;

         ! i.e., subsequent to incorporation of transportation margin !

VARIABLE                                                           pt

       # price of global shipping services provided # ;

VARIABLE (all, r, REG)                                             rental(r)

       # rental rate on capital = ps("capital",r) # ;

VARIABLE (all, r, REG)                                             rorc(r)

       # Current net rate of return on capital stock, in r # ;

VARIABLE (all, r, REG)                                             rore(r)

       # Expected net rate of return on capital stock, in r # ;

VARIABLE                                                           rorg

       # Global net rate of return on capital stock # ;

VARIABLE                                                           psave

       # price of capital goods supplied to savers # ;

VARIABLE (all, r, REG)                                             pcgds(r)

       # price of investment goods = ps("cgds",r) # ;

VARIABLE (all,r,REG)                                               psw(r)

       # Index of prices received for tradables produced in r # ;

         ! Note: this includes sales of net investment in r !

VARIABLE (all,r,REG)                                               pdw(r)

       # Index of prices paid for tradables used in region r # ;

         ! Note: this includes purchases of net savings in region r !

VARIABLE (all,r,REG)                                               tot(r)

       # terms of trade for region r: tot(r) = psw(r) - pdw(r) # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)                              pr(i,r)

       # ratio of domestic to imported prices in r # ;

VARIABLE (all,r,REG)                                               pgdp(r)

       # GDP price index # ;                    

Technical change variables

VARIABLE (all,j,PROD_COMM)(all,r,REG)                              ao(j,r)
       # output augmenting technical change in sector j of r # ;

VARIABLE (all,i,ENDW_COMM)(all,j,PROD_COMM)(all,r,REG)             afe(i,j,r)

       # primary factor i augmenting tech change in j of r # ;

VARIABLE (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)             af(i,j,r)

       # composite interm. input i augmenting tech change in j of r # ;

VARIABLE (all,i,PROD_COMM)(all,r,REG)                              ava(i,r)

       # Value added augmenting tech change in sector i of r # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)                   atr(i,r,s)

       # tech change parameter in shipping of i from region r to s # ;


Policy variables

VARIABLE (all,i,NSAV_COMM)(all,r,REG)                              to(i,r)

       # output (or income) tax in region r # ;

VARIABLE (all,i,ENDW_COMM)(all,j,PROD_COMM)(all,r,REG)             tf(i,j,r)

       # tax on primary factor i used by j in region r # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)                              tpm(i,r)

       # tax on imported i purchased by private hhlds in r # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)                              tpd(i,r)

       # tax on domestic i purchased by private hhld in r # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)                              tgm(i,r)

       # tax on imported i purchased by gov't hhld in r # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)                              tgd(i,r)

       # tax on domestic i purchased by government hhld in r # ;

VARIABLE (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)             tfm(i,j,r)

       # tax on imported i purchased by j in r # ;

VARIABLE (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)             tfd(i,j,r)

       # tax on domestic i purchased by j in r # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)                   txs(i,r,s)

       # combined tax in r on good i bound for region s # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)                   tms(i,r,s)

       # import tax in s on good i imported from region r # ;

VARIABLE (all,i,TRAD_COMM)(all,s,REG)                              tm(i,s)

       # variable import levy -- source generic # ;

VARIABLE (all,i,TRAD_COMM)(all,r,REG)                              tx(i,r)

       # variable export tax (subsidy) -- destination generic # ;

Value, income and utility variables

VARIABLE (all,r,REG)                                               vxwreg(r)

       # value of merchandise exports, by region # ;

VARIABLE (all,r,REG)                                               viwreg(r)

       # value of merchandise imports, by region, at world prices # ;

VARIABLE (all,i,TRAD_COMM)(all,s,REG)                              viwcif(i,s)

       # value of merchandise regional imports, by commodity, cif # ;

VARIABLE (all,i,TRAD_COMM)(all,s,REG)                              vxwfob(i,s)

       # value of merchandise regional exports, by commodity, fob # ;

VARIABLE (all,i,TRAD_COMM)                                         vxwcom(i)

       # value of global merchandise exports by commodity # ;

VARIABLE (all,i,TRAD_COMM)                                         viwcom(i)

       # value of global merchandise imports by commodity, at world prices # ;

VARIABLE                                                           vxwwld

       # value of world trade # ;

VARIABLE (all,i,TRAD_COMM)                                         valuew(i)  

       # value of world supply of good i # ;


VARIABLE (all,r,REG)                                               vgdp(r)

       # change in value of GDP # ;                    

VARIABLE (all,r,REG)                                               y(r)

       # regional household income, in region r # ;

VARIABLE (all,r,REG)                                               yp(r)

       # regional private household expenditure, in region r # ;

VARIABLE (all,r,REG)                                               up(r)

       # per capita utility from private expend., in region r #;

VARIABLE (all,r,REG)                                               ug(r)

       # per capita utility from gov't expend., in region r #;

VARIABLE (all,r,REG)                                               u(r)

       # per capita utility from aggregate hhld expend., in region r #  ;

VARIABLE (CHANGE)(all,r,REG)                                       EV(r)

       # Equivalent Variation, $ US million # ;

         ! Hicksian equivalent variation. Positive figure indicates 

         welfare improvement !

VARIABLE (CHANGE)                                                  WEV

       # Equivalent variation for the world # ;

VARIABLE (CHANGE)(all,r,REG)                                       DTBAL(r)

       # Change in trade balance X - M, $ US million # ;

         ! Positive figure indicates increase in exports exceeds imports. !

VARIABLE (CHANGE)(all,i,TRAD_COMM)(all,r,REG)                      DTBALi(i,r)

       # Change in trade balance by commodity and by region, $ US million #;

         ! Positive figure indicates increase in exports exceeds imports. !

Slack variables

VARIABLE (all,j,PROD_COMM)(all,r,REG)                         profitslack(j,r)

       # slack variable in the zero profit equation #

         ! This is exogenous, unless the user wishes to specify

         output in a given region exogenously. ! ;

VARIABLE (all,r,REG)                                          incomeslack(r)

       # slack variable in the expression for regional income #

         ! This is exogenous, unless the user wishes to fix regional income!;

VARIABLE (all,i,ENDW_COMM)(all,r,REG)                         endwslack(i,r)

       # slack variable in the endowment market clearing condition #

         ! This is exogenous, unless the user wishes to fix

         the wage rate for one of the primary factors !  ;

VARIABLE (all, r, REG)                                        cgdslack(r)

       # slack variable for qcgds(r) #

         ! This is exogenous, unless the user wishes to specify

         the level of new capital goods in a region ! ;

VARIABLE (all,r,REG)                                          saveslack(r)

       # slack variable in regional demand for savings #

         ! This is exogenous unless the user wishes to fix the

         level of savings in a region.  ! ;

VARIABLE (all,r,REG)                                          govslack(r)

       # slack variable to permit fixing of real govt purchases #

         ! This is exogenous unless the user wishes to fix the

         level of government purchases. ! ;


VARIABLE (all,i,TRAD_COMM)(all,r,REG)                         tradslack(i,r)

       # slack variable in the tradables market clearing condition #

         ! This is exogenous unless the user wishes to specify

         the price of tradables exogenously !  ;

VARIABLE                                                      walraslack

       # slack variable in the omitted market #

         ! This is endogenous under normal, GE closure. If the GE links are

         broken, then this must be swapped with the numeraire, thereby

         forcing global savings to explicitly equal global investment. !  ;

A-2.1.2 Database Coefficients and Parameters

Base revenues and expenditures at agents' prices

COEFFICIENT (all,i,ENDW_COMM)(all,r,REG)                        EVOA(i,r)

          ! value of commodity i output in region r. ! ;

UPDATE (all,i,ENDW_COMM)(all,r,REG)

       EVOA(i,r) = ps(i,r) * qo(i,r) ;

COEFFICIENT (all,i,ENDW_COMM)(all,j,PROD_COMM)(all,r,REG)       EVFA(i,j,r)

          ! producer expenditure on i by industry j,

            in region r, valued at agents' prices ! ;

UPDATE (all,i,ENDW_COMM)(all,j,PROD_COMM)(all,r,REG)

       EVFA(i,j,r) = pfe(i,j,r) * qfe(i,j,r) ;

COEFFICIENT (all,r,REG)                                         SAVE(r)

          ! expenditure on NET savings in region r

            valued at agents' prices ! ;

UPDATE (all,r,REG) SAVE(r) = psave * qsave(r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)       VDFA(i,j,r)

          ! purchases of domestic i for use in j in region r ! ;

UPDATE (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)

       VDFA(i,j,r) = pfd(i,j,r) * qfd(i,j,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)       VIFA(i,j,r)

          ! purchases of imported i for use in j in region r ! ;

UPDATE (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)

       VIFA(i,j,r) = pfm(i,j,r) * qfm(i,j,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                        VDPA(i,r)

          ! private household expenditure on domestic i in r ! ;

UPDATE (all,i,TRAD_COMM)(all,r,REG)

       VDPA(i,r) = ppd(i,r) * qpd(i,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                        VIPA(i,r)

          ! private household expenditure on imported i ! ;

UPDATE (all,i,TRAD_COMM)(all,r,REG)

       VIPA(i,r) = ppm(i,r) * qpm(i,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                        VDGA(i,r)

          ! government household expenditure on domestic i in r ! ;

UPDATE (all,i,TRAD_COMM)(all,r,REG)

       VDGA(i,r) = pgd(i,r) * qgd(i,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                        VIGA(i,r)

          ! government household expenditure on imported i ! ;

UPDATE (all,i,TRAD_COMM)(all,r,REG)

       VIGA(i,r) = pgm(i,r) * qgm(i,r) ;

COEFFICIENT (all, r, REG)                                       VKB(r)

          ! value of beginning-of-period capital stock, in region r ! ;

UPDATE (all, r, REG) VKB(r) = kb(r) * pcgds(r) ;


COEFFICIENT (all, r, REG)                                       VDEP(r)

          ! value of capital depreciation, in r (depreciation

            rate is exogenous and therefore does not appear in update) ! ;

UPDATE (all, r, REG) VDEP(r) = kb(r) * pcgds(r) ;

Base revenues and expenditures at market prices

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)             VXMD(i,r,s)

          ! exports of commodity i from region r to destination s valued at

            market prices (tradables only)  ! ;

UPDATE (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)

       VXMD(i,r,s) = pm(i,r) * qxs(i,r,s) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                        VST(i,r)

          ! exports of commodity i from region r for international

            transportation valued at market prices  (tradables only)  ! ;

UPDATE (all,i,TRAD_COMM)(all,r,REG) VST(i,r) = pm(i,r) * qst(i,r) ;

COEFFICIENT (all,i,ENDW_COMM)(all,j,PROD_COMM)(all,r,REG)       VFM(i,j,r)

          ! producer expenditure on i by industry j,

            in region r, valued at market prices ! ;

UPDATE (all,i,ENDWM_COMM)(all,j,PROD_COMM)(all,r,REG)

       VFM(i,j,r) = pm(i,r) * qfe(i,j,r) ;

UPDATE (all,i,ENDWS_COMM)(all,j,PROD_COMM)(all,r,REG)

       VFM(i,j,r) = pmes(i,j,r) * qfe(i,j,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)       VIFM(i,j,r)

          ! purchases of imports i for use in j in region r ! ;

UPDATE (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)

       VIFM(i,j,r) = pim(i,r) * qfm(i,j,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)       VDFM(i,j,r)

          ! purchases of domestic i for use in j in region r ! ;

UPDATE (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)

       VDFM(i,j,r) = pm(i,r) * qfd(i,j,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                        VIPM(i,r)

          ! private household expenditure on i in r ! ;

UPDATE (all,i,TRAD_COMM)(all,r,REG)

       VIPM(i,r)= pim(i,r) * qpm(i,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                        VDPM(i,r)

          ! private household expenditure on domestic i in r ! ;

UPDATE (all,i,TRAD_COMM)(all,r,REG)

       VDPM(i,r) = pm(i,r) * qpd(i,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                        VIGM(i,r)

          ! gov't household expenditure on i in r ! ;

UPDATE (all,i,TRAD_COMM)(all,r,REG)

       VIGM(i,r) = pim(i,r) * qgm(i,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                        VDGM(i,r)

          ! government household expenditure on domestic i in r ! ;

UPDATE (all,i,TRAD_COMM)(all,r,REG)

       VDGM(i,r) = pm(i,r) * qgd(i,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)             VIMS(i,r,s)

          ! imports of commodity i from region r to s, valued

            at domestic market prices ! ;

UPDATE (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)

       VIMS(i,r,s) = pms(i,r,s) * qxs(i,r,s) ;


Base revenues and expenditures at world prices

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)             VXWD(i,r,s)

          ! exports of commodity i from region r to

            destination s valued fob (tradables only)  ! ;

UPDATE (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)

       VXWD(i,r,s) = pfob(i,r,s) * qxs(i,r,s) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)             VIWS(i,r,s)

          ! imports of commodity i from region r to 

            destination s, valued cif (tradables only)!;

UPDATE (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)

       VIWS(i,r,s) = pcif(i,r,s) * qxs(i,r,s) ;

Regional income, utility and population

COEFFICIENT (PARAMETER) (all,r,REG)                             INC(r)

     ! initial equilibrium regional expenditure data INC is set equal to

       INCOME and does not change during a simulation !  ;

COEFFICIENT (all,r,REG)                                         URATIO(r)

     ! ratio of U(r), the per capita utility, to its presimulation value!;

FORMULA (Initial)(all,r,REG)  

     URATIO(r) = 1;

UPDATE  (all,r,REG)

     URATIO(r) = u(r);

COEFFICIENT (all,r,REG)                                         POPRATIO(r)

   ! ratio of POP(r), population in region r, to its presimulation value! ;

FORMULA (Initial)(all,r,REG) 

     POPRATIO(r) = 1;

UPDATE  (all,r,REG) 

     POPRATIO(r) = pop(r);

Technology and preference parameters

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                        SUBPAR(i,r)

          ! the substitution parameter in the CDE minimum expenditure


COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                        INCPAR(i,r)

          ! expansion parameter in the CDE minimum expenditure function! ;

COEFFICIENT (all,i,TRAD_COMM)                                   ESUBD(i)

          ! the elasticity of substitution between domestic and

            imported goods in the Armington aggregation structure

            for all agents in all regions. ! ;

COEFFICIENT (all,i,TRAD_COMM)                                   ESUBM(i)

          ! the elasticity of substitution among imports from

            different destinations in the Armington aggregation

            structure of all agents in all regions. !;

COEFFICIENT (all,j,PROD_COMM)                                   ESUBVA(j)

          ! elasticity of substitution between capital, labor, and

            possibly land, in the production of value-added in j  !;

COEFFICIENT (all,i,ENDWS_COMM)                                  ETRAE(i)

          ! ETRAE is the elasticity of transformation for sluggish primary

            factor endowments.  It is non-positive, by definition.! ;


COEFFICIENT (all, r, REG)                                       RORFLEX(r)

          ! RORFLEX is the flexibility of expected net rate of return on

            capital stock, in region r, with respect to investment. If a

            region's capital stock increases by 1%, then it is expected

            that the net rate of return on capital will decline by RORFLEX %!;

COEFFICIENT                                                     RORDELTA

          ! RORDELTA is a binary coefficient which determines

            the mechanism of allocating investment funds across regions.

            When RORDELTA = 1, investment funds are allocated

            across regions to equate the change in the expected

            rates of return (i.e., rore(r)).  When RORDELTA = 0, investment 

            funds are allocated across regions to maintain the existing

            composition of capital stocks ! ;

"Read" statements for model parameters and base data









READ (all,i,ENDW_COMM)(all,r,REG)                             EVOA(i,r)


     (all,i,ENDW_COMM)(all,j,PROD_COMM)(all,r,REG)            EVFA(i,j,r)


     (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)            VIFA(i,j,r)


     (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)            VDFA(i,j,r)


     (all,i,TRAD_COMM)(all,r,REG)                             VIPA(i,r)


     (all,i,TRAD_COMM)(all,r,REG)                             VDPA(i,r)


     (all,i,TRAD_COMM)(all,r,REG)                             VIGA(i,r)


     (all,i,TRAD_COMM)(all,r,REG)                             VDGA(i,r)


     (all,r,REG)                                              SAVE(r)


     (all,r,REG)                                              VKB(r)


     (all,r,REG)                                              VDEP(r)


     (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)                  VXMD(i,r,s)


     (all,i,TRAD_COMM)(all,r,REG)                             VST(i,r)


     (all,i,ENDW_COMM)(all,j,PROD_COMM)(all,r,REG)            VFM(i,j,r)


     (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)            VIFM(i,j,r)


     (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)            VDFM(i,j,r)


     (all,i,TRAD_COMM)(all,r,REG)                             VIPM(i,r)


     (all,i,TRAD_COMM)(all,r,REG)                             VDPM(i,r)


     (all,i,TRAD_COMM)(all,r,REG)                             VIGM(i,r)


     (all,i,TRAD_COMM)(all,r,REG)                             VDGM(i,r)



     (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)                  VIMS(i,r,s)


     (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)                  VXWD(i,r,s)


     (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)                  VIWS(i,r,s)


Derivatives of the base data

After the base data have been read, a variety of derivatives of these value flows can be defined. These derivatives are not directly stored in the database in order to avoid redundancies. Various share coefficients are also defined which simplify later calculations in the model. The value of total GDP in each region is also calculated from the base data in this section.

Values and shares


COEFFICIENT (all,i,DEMD_COMM)(all,j,PROD_COMM)(all,r,REG)        VFA(i,j,r)

          ! producer expenditure on i by industry j,

            in region r, valued at agents' prices ! ;

FORMULA (all,i,ENDW_COMM)(all,j,PROD_COMM)(all,r,REG)

      VFA(i,j,r) = EVFA(i,j,r) ;

FORMULA (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,s,REG)

      VFA(i,j,s) = VDFA(i,j,s) + VIFA(i,j,s) ;

COEFFICIENT (all,i,NSAV_COMM)(all,r,REG)                         VOA(i,r)

          ! value of commodity i output in region r. ! ;

FORMULA (all,i,ENDW_COMM)(all,r,REG) 

      VOA(i,r) = EVOA(i,r);

FORMULA (all,i,PROD_COMM)(all,r,REG)

      VOA(i,r) = sum(j,DEMD_COMM, VFA(j,i,r));

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                         VDM(i,r)

          ! domestic sales of commodity i in region r

            valued at market prices (tradables only)  ! ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)

      VDM(i,r) = VDPM(i,r) + VDGM(i,r) + sum(j,PROD_COMM, VDFM(i,j,r)) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                         VIM(i,r)

          ! value of imports of commodity i in r

            at domestic market prices ! ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)

       VIM(i,r) = sum(j,PROD_COMM, VIFM(i,j,r)) + VIPM(i,r) + VIGM(i,r) ;

COEFFICIENT (all,i,NSAV_COMM)(all,r,REG)                         VOM(i,r)

          ! value of commodity i output in region r. ! ;

FORMULA (all,i,ENDW_COMM)(all,r,REG)

      VOM(i,r) = sum(j,PROD_COMM, VFM(i,j,r)) ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)

      VOM(i,r) = VDM(i,r) + sum(s,REG, VXMD(i,r,s)) + VST(i,r) ;

FORMULA (all,h,CGDS_COMM)(all,r,REG)

      VOM(h,r) = VOA(h,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                         VPA(i,r)

          ! private household expenditure on commodity i


            in region r valued at agents' prices ! ;

FORMULA (all,i,TRAD_COMM)(all,s,REG)

      VPA(i,s) = VDPA(i,s) + VIPA(i,s) ;

COEFFICIENT (all,r,REG)                                          PRIVEXP(r)

          ! private consumption expenditure in region r ! ;

FORMULA (all,r,REG) PRIVEXP(r) = sum(i,TRAD_COMM, VPA(i,r)) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                         VGA(i,r)

          ! government household expenditure on commodity

            i in region r valued at agents' prices ! ;

FORMULA (all,i,TRAD_COMM)(all,s,REG)

      VGA(i,s) = VDGA(i,s) + VIGA(i,s) ;

COEFFICIENT (all,r,REG)                                          GOVEXP(r)

          ! government expenditure in region r ! ;

FORMULA (all,r,REG) GOVEXP(r) = sum(i,TRAD_COMM, VGA(i,r)) ;

COEFFICIENT (all,r,REG)                                          INCOME(r)

          ! level of expenditure, which equals NET income in region r

            (i.e. net of capital depreciation) ! ;


      INCOME(r) = sum(i,TRAD_COMM, VPA(i,r) + VGA(i,r)) + SAVE(r) ;


      INC(r) = INCOME(r) ;

      ! The above stores the initial value of INCOME as the parameter INC !

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)              VTWR(i,r,s)

          ! value of transportation services associated with

            the shipment of commodity i from r to s ! ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)

      VTWR(i,r,s) = VIWS(i,r,s) - VXWD(i,r,s) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)              FOBSHR(i,r,s)

          ! The fob share in VIW. ! ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)

      FOBSHR(i,r,s) = VXWD(i,r,s)/VIWS(i,r,s) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)              TRNSHR(i,r,s)

          ! The transport share in VIW. ! ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)

      TRNSHR(i,r,s) = VTWR(i,r,s)/VIWS(i,r,s) ;

COEFFICIENT                                                      VT

          ! The value of total international transportation services. !;

FORMULA VT = sum(i,TRAD_COMM, sum(r,REG, sum(s,REG, VTWR(i,r,s)))) ;

COEFFICIENT (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)        SHRDFM(i,j,r)

       ! the share, at market prices, of domestic prod used by sector j !;

FORMULA (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)

      SHRDFM(i,j,r) = VDFM(i,j,r)/VDM(i,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                         SHRDPM(i,r)

          ! share of domestic production used by private hhlds ! ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)

      SHRDPM(i,r) = VDPM(i,r)/VDM(i,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                         SHRDGM(i,r)

          ! share of imports from r in s used by gov't hhld ! ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)

      SHRDGM(i,r) = VDGM(i,r)/VDM(i,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)        SHRIFM(i,j,r)

          ! share of imports in r used by sector j ! ;

FORMULA (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)

      SHRIFM(i,j,r) = VIFM(i,j,r)/VIM(i,r) ;


COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                         SHRIPM(i,r)

          ! the share of imports in r used by private hhlds ! ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)

      SHRIPM(i,r) = VIPM(i,r)/VIM(i,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                         SHRIGM(i,r)

          ! the share of imports from r used by gov't hhld ! ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)

      SHRIGM(i,r) = VIGM(i,r)/VIM(i,r) ;

COEFFICIENT (all, r, REG)                                        REGINV(r)

          ! regional GROSS investment in region r,

          i.e., value of output of sector "cgds" ! ;

FORMULA (all, r, REG)

      REGINV(r) = sum(k,CGDS_COMM, VOA(k,r)) ;

COEFFICIENT (all, r, REG)                                        NETINV(r)

          ! regional NET investment in region r ! ;

FORMULA (all, r, REG)

      NETINV(r) = sum(k,CGDS_COMM, VOA(k,r)) - VDEP(r) ;

COEFFICIENT                                                      GLOBINV

          ! global expenditures on net investment ! ;

          ! here, GLOBINV is computed as sum of NETINV(r) !

          ! alternatively, GLOBINV may be computed as sum of SAVE(r) !


COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                         VXW(i,r)

          ! The value of exports, at fob prices, by commodity and region! ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)

        VXW(i,r) = sum(s,REG, VXWD(i,r,s)) + VST(i,r);

COEFFICIENT (all,r,REG)                                          VXWREGION(r)

          ! The value of exports, fob, by region ! ;


      VXWREGION(r) = sum(i,TRAD_COMM, VXW(i,r)) ;

COEFFICIENT (all,i,TRAD_COMM)                                    VXWCOMMOD(i)

          ! The value of world exports, fob, by commodity ! ;


        VXWCOMMOD(i) = sum(r,REG, VXW(i,r)) ;

COEFFICIENT (all,i,TRAD_COMM)(all,s,REG)                         VIW(i,s)

  ! The value of commodity imports, at cif price, by commodity and region!;

FORMULA (all,i,TRAD_COMM)(all,s,REG)

        VIW(i,s) = sum(r,REG, VIWS(i,r,s)) ;

COEFFICIENT (all,r,REG)                                          VIWREGION(r)

          ! The value of commodity imports, cif, by region ! ;


        VIWREGION(r) = sum(i,TRAD_COMM, VIW(i,r)) ;

COEFFICIENT (all,i,TRAD_COMM)                                    VIWCOMMOD(i)

            ! The global value of commodity imports, cif, by commodity ! ;


        VIWCOMMOD(i) = sum(r,REG, VIW(i,r)) ;

COEFFICIENT                                                      VXWLD

          ! The value of commodity exports, fob, globally ! ;


COEFFICIENT (all,r,REG)                                          VWLDSALES(r)

     ! The value of sales/purchases to/from the world market from/by r. ! ;

     ! NOTE: The difference between VWLDSALES(r) and         !

     ! VXWREGION(r) is that the former includes NETINV(r) !


      VWLDSALES(r) = sum(i,TRAD_COMM, sum(s,REG, VXWD(i,r,s)) 


                     + VST(i,r)) + NETINV(r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                         PW_PM(i,r)

            ! Ratio of world to domestic prices !  ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)

      PW_PM(i,r) = sum(s,REG, VXWD(i,r,s)) / sum(s,REG, VXMD(i,r,s)) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                         VOW(i,r)

            ! Value of region's r output at fob prices! ;

            ! INCLUDING transportation services !


     VOW(i,r) = VDM(i,r) * PW_PM(i,r) + sum(s,REG, VXWD(i,r,s)) + VST(i,r);

COEFFICIENT (all,i,TRAD_COMM)                                    VWOW(i)

           ! Value of world supply at world prices for i. ! ;                 

FORMULA (all,i,TRAD_COMM)                                           

        VWOW(i) = sum(r,REG, VOW(i,r)) ;

COEFFICIENT (all,i,ENDW_COMM)(all,j,PROD_COMM)(all,r,REG)        SVA(i,j,r)

          ! The share of i in total value-added in j in r.! ;

FORMULA (all,i,ENDW_COMM)(all,j,PROD_COMM)(all,r,REG)

      SVA(i,j,r) = VFA(i,j,r)/sum(k,ENDW_COMM, VFA(k,j,r)) ;

COEFFICIENT (all,i,TRAD_COMM)(all,s,REG)                         PMSHR(i,s)

          ! The share of aggregate imports in the domestic composite for

            private households, evaluated at agents' prices. ! ;

FORMULA (all,i,TRAD_COMM)(all,s,REG)

      PMSHR(i,s) = VIPA(i,s) / VPA(i,s) ;

COEFFICIENT (all,i,TRAD_COMM)(all,s,REG)                         GMSHR(i,s)

          ! The share of aggregate imports in the domestic composite for

            gov't households, evaluated at agents' prices. ! ;

FORMULA (all,i,TRAD_COMM)(all,s,REG)

      GMSHR(i,s) = VIGA(i,s) / VGA(i,s) ;

COEFFICIENT (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,s,REG)        FMSHR(i,j,s)

          ! The share of aggregate imports in the domestic

           composite for firms, evaluated at agents' prices. ! ;

FORMULA (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,s,REG)

      FMSHR(i,j,s) = VIFA(i,j,s) / VFA(i,j,s) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)              MSHRS(i,r,s)

          ! The share of imports by source, r, in the aggregate

            import bill of region s evaluated at market prices. ! ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)

      MSHRS(i,r,s) = VIMS(i,r,s) / sum(k,REG, VIMS(i,k,s)) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                         CONSHR(i,r)

          ! The share of private household consumption 

            devoted to good i in region r. ! ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)

      CONSHR(i,r) = VPA(i,r) / sum(m, TRAD_COMM, VPA(m,r)) ;

COEFFICIENT (all,i,ENDW_COMM)(all,j,PROD_COMM)(all,r,REG)        REVSHR(i,j,r)

FORMULA (all,i,ENDW_COMM)(all,j,PROD_COMM)(all,r,REG) ;

      REVSHR(i,j,r) = VFM(i,j,r)/sum(k,PROD_COMM, VFM(i,k,r));

COEFFICIENT (all, r, REG)                                        INVKERATIO(r)

  ! ratio of gross investment to end-of-period capital stock, in region r!;

FORMULA (all, r, REG)

      INVKERATIO(r) = REGINV(r) / [VKB(r) + NETINV(r)] ;

COEFFICIENT (all, r, REG)                                        GRNETRATIO(r)

          ! ratio of GROSS/NET rates of return on capital, in region r ! ;

          ! NOTE: VOA("capital",r) is GROSS returns to capital !

FORMULA (all, r, REG)

      GRNETRATIO(r) =   sum(h, ENDWC_COMM, VOA(h,r)) /


                  [ sum(h, ENDWC_COMM, VOA(h,r)) - VDEP(r) ] ;

COEFFICIENT (all,r,REG)                                          GDP(r)

      ! Gross Domestic Product in region r. Trade is valued 

        at fob and cif prices. ! ;

FORMULA (all,s,REG)      GDP(s)    = sum(i,TRAD_COMM, VPA(i,s) )

                + sum(i,TRAD_COMM, VGA(i,s) )

                + sum(k,CGDS_COMM, VOA(k,s) ) 

                + sum(i,TRAD_COMM, sum(r,REG, VXWD(i,s,r)) + VST(i,s))

                - sum(i,TRAD_COMM, sum(r,REG, VIWS(i,r,s))) ;

Computation of substitution, price and income elasticities

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                         ALPHA(i,r)

          ! one minus the substitution parameter in the CDE

            minimum expenditure function  !  ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)   ! (HT#F1) !

      ALPHA(i,r) = (1 - SUBPAR(i,r)) ;

COEFFICIENT (all,i,TRAD_COMM)(all,k,TRAD_COMM)(all,r,REG)        APE(i,k,r)

          ! the Allen partial elasticity of substitution 

            between composite goods i and k in region r  !  ;

FORMULA (all,i,TRAD_COMM)(all,k,TRAD_COMM)(all,r,REG) ! (HT#F2) !

      APE(i,k,r) = ALPHA(i,r) + ALPHA(k,r) 

                 - sum(m,TRAD_COMM, CONSHR(m,r) * ALPHA(m,r)) ;

FORMULA (all,i,TRAD_COMM)(all,r,REG) ! (HT#F3) !

      APE(i,i,r) =  2.0 * ALPHA(i,r)

                 - sum(m,TRAD_COMM, CONSHR(m,r) * ALPHA(m,r))

                 - ALPHA(i,r) / CONSHR(i,r)  ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                         COMPDEM(i,r)

          ! the own-price compensated elasticity of 

            household demand for composite commodity i ! ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)

      COMPDEM(i,r) = APE(i,i,r) * CONSHR(i,r) ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                         EY(i,r)

          ! the income elasticity of household demand for

            composite good i in region r  ! ;

FORMULA (all,i,TRAD_COMM)(all,r,REG) ! (HT#F4) !

      EY(i,r) =  {1.0/[sum(m,TRAD_COMM, CONSHR(m,r) * INCPAR(m,r))]}

              * (INCPAR(i,r) * (1.0 - ALPHA(i,r))

              + sum(m,TRAD_COMM, CONSHR(m,r) * INCPAR(m,r) * ALPHA(m,r)))

              + (ALPHA(i,r) - sum(m,TRAD_COMM, CONSHR(m,r) * ALPHA(m,r))) ;

COEFFICIENT (all,i,TRAD_COMM)(all,k,TRAD_COMM)(all,r,REG)        EP(i,k,r)

          ! the uncompensated cross-price elasticity of hhld

            demand for good i with respect to the kth price in region r! ;

FORMULA (all,i,TRAD_COMM)(all,k,TRAD_COMM)(all,r,REG)! (HT#F5) !

      EP(i,k,r) = 0 ;

FORMULA (all,i,TRAD_COMM)(all,k,TRAD_COMM)(all,r,REG)

      EP(i,k,r) =  (APE(i,k,r) - EY(i,r)) * CONSHR(k,r) ;



Computation of technical dummy variables

COEFFICIENT (all,i,ENDW_COMM)(all,j,PROD_COMM)(all,r,REG)        D_EVFA(i,j,r)

            ! 0, 1 variable for identifying zero expenditures in EVFA. ! ;

FORMULA (all,i,ENDW_COMM)(all,j,PROD_COMM)(all,r,REG)


        D_EVFA(I,j,r) = 0;FORMULA (all,i,ENDW_COMM)(all,j,PROD_COMM)(all,r,REG: EVFA(i,j,r) > 0 )

        D_EVFA(I,j,r) = 1;

COEFFICIENT (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)        D_VFA(i,j,r)

            ! 0, 1 variable for identifying zero expenditures in VFA. !  ;

FORMULA (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG)

        D_VFA(I,j,r) = 0;

FORMULA (all,i,TRAD_COMM)(all,j,PROD_COMM)(all,r,REG: VFA(i,j,r) > 0 )

        D_VFA(I,j,r) = 1;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)              D_VXWD(i,r,s)

            ! 0, 1 variable to identify zero expenditures in VXWD ! ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)(all,s,REG)              

        D_VXWD(i,r,s) = 0 ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)(all,s,REG: VXWD(i,r,s) > 0 )             

        D_VXWD(i,r,s) = 1 ;

COEFFICIENT (all,i,TRAD_COMM)(all,r,REG)                         D_VST(i,r)

            ! 0, 1 variable to identify zero expenditures in VST ! ;

FORMULA (all,i,TRAD_COMM)(all,r,REG)

        D_VST(i,r) = 0 ;

FORMULA (all,i,TRAD_COMM)(all,r,REG: VST(i,r)>0)

        D_VST(i,r) = 1;

Checking the base data

In this section the database is checked for consistency. According to neoclassical theory, in an initial general equilibrium there should be no extra profits, i.e. the total value of sales must be completely exhausted by the sum of payments to primary and intermediate factors of production. In addition, there should be no extra surplus, i.e. total income must be equal to total expenditure in each region.

COEFFICIENT (all,j,PROD_COMM)(all,r,REG)                         PROFITS(j,r)

          ! profits in j of r. This should equal zero. ! ;

FORMULA (all,j,PROD_COMM)(all,r,REG)

      PROFITS(j,r) = VOA(j,r) - sum(i,DEMD_COMM, VFA(i,j,r));

COEFFICIENT (all,s,REG)                                          SURPLUS(s)

          ! Economic surplus in region s. This should equal zero. NOTE: We

            first compute NET income from endowments and then income from

            various taxes. At the end we deduct private and government

            expenditures and net savings ! ;


SURPLUS(r) = sum(i,ENDW_COMM, VOA(i,r)) - VDEP(r)

           + sum(i,NSAV_COMM, VOM(i,r) - VOA(i,r))

           + sum(j,PROD_COMM, sum(i,ENDW_COMM, VFA(i,j,r) - VFM(i,j,r)))

           + sum(i,TRAD_COMM, VIPA(i,r) - VIPM(i,r))

           + sum(i,TRAD_COMM, VDPA(i,r) - VDPM(i,r))

           + sum(i,TRAD_COMM, VIGA(i,r) - VIGM(i,r))

           + sum(i,TRAD_COMM, VDGA(i,r) - VDGM(i,r))

           + sum(j,PROD_COMM, sum(i,TRAD_COMM, VIFA(i,j,r) - VIFM(i,j,r)))

           + sum(j,PROD_COMM, sum(i,TRAD_COMM, VDFA(i,j,r) - VDFM(i,j,r)))

           + sum(i,TRAD_COMM, sum(s,REG, VXWD(i,r,s) - VXMD(i,r,s)))

           + sum(i,TRAD_COMM, sum(s,REG, VIMS(i,s,r) - VIWS(i,s,r)))

           - sum(i,TRAD_COMM, VPA(i,r) + VGA(i,r))

           - SAVE(r) ;



A-2.1.3 Model Equations

Market clearing equations

Equation 1:        MKTCLTRD

! This equation assures market clearing in the traded goods markets.(HT#1)!


VOM(i,r) * qo(i,r) = VDM(i,r) * qds(i,r)

                   + VST(i,r) * qst(i,r)

                   + sum(s,REG, VXMD(i,r,s) * qxs(i,r,s))

                   + VOM(i,r) * tradslack(i,r) ;

Equation 2:        MKTCLIMP

! this equation assures market clearing for the tradeable commodities entering

  each region (HT#2)!


qim(i,r) = sum(j,PROD_COMM, SHRIFM(i,j,r) * qfm(i,j,r))

         + SHRIPM(i,r) * qpm(i,r) + SHRIGM(i,r) * qgm(i,r) ;

Equation 3:        MKTCLDOM

! this equation assures market clearing for domestic output (HT#3)!


qds(i,r) = sum(j,PROD_COMM, SHRDFM(i,j,r) * qfd(i,j,r))

         + SHRDPM(i,r) * qpd(i,r) + SHRDGM(i,r) * qgd(i,r) ;

Equation 4:        MKTCLENDWM

! In each of the regions, this equation assures market clearing in the markets

  for endowment goods which are perfectly mobile among uses. (HT#4) !


VOM(i,r) * qo(i,r) = sum(j,PROD_COMM, VFM(i,j,r) * qfe(i,j,r))

                   + VOM(i,r) * endwslack(i,r) ;

Equation 5:  MKTCLENDWS

! In each of the regions, this equation assures market clearing in the markets

  for endowment goods which are imperfectly mobile among uses.(HT#5)!


qoes(i,j,r) = qfe(i,j,r);

Equation 6


! For Equation 6 (zero profits condition) see the behavioral equations for!

! firms below.                                                            !   


Equation 7


! Equation 7 generates a price index for transportation services based on !

! zero profits. Refer to the global transportation sector equations below.!


Equation 8:  PRIVATEXP

! This equation computes private household expenditure as household income

  less savings less government expenditures. (HT#8)!


PRIVEXP(r) * yp(r) = INCOME(r) * y(r)

                   - SAVE(r) * [ psave + qsave(r) ]

                   - sum(i,TRAD_COMM, VGA(i,r) * [pg(i,r) + qg(i,r)]) ;


! This equation computes regional income as the sum of primary factor payments

  and tax receipts. (HT#9) The first term computes the change in endowment

  income, net of depreciation. The subsequent terms compute the change in tax

  receipts for various transactions' taxes. Note that in each of these terms


  the quantity change is common. This defines the common transaction which is

  being taxed. It is the prices which potentially  diverge.!


INCOME(r) * y(r) 

 = sum(i,ENDW_COMM, VOA(i,r) * [ps(i,r) + qo(i,r)])

                    - VDEP(r)  * [pcgds(r) + kb(r)]

 + sum(i,NSAV_COMM, {VOM(i,r) * [pm(i,r) + qo(i,r)]}

                    - {VOA(i,r) * [ps(i,r) + qo(i,r)]})

 + sum(i,ENDWM_COMM,sum(j,PROD_COMM,{VFA(i,j,r) 

                    * [pfe(i,j,r) + qfe(i,j,r)]} 

                    - {VFM(i,j,r)* [pm(i,r) + qfe(i,j,r)]}))

 + sum(i,ENDWS_COMM,sum(j,PROD_COMM,{VFA(i,j,r) 

                    * [pfe(i,j,r)  + qfe(i,j,r)]}

                    - {VFM(i,j,r) * [pmes(i,j,r) + qfe(i,j,r)]}))

 + sum(j,PROD_COMM, sum(i,TRAD_COMM,{VIFA(i,j,r) 

                    * [pfm(i,j,r) + qfm(i,j,r)]}

                    - {VIFM(i,j,r) * [pim(i,r) + qfm(i,j,r)]}))

 + sum(j,PROD_COMM, sum(i,TRAD_COMM,{VDFA(i,j,r) 

                    * [pfd(i,j,r) + qfd(i,j,r)]}

                    - {VDFM(i,j,r) * [pm(i,r) + qfd(i,j,r)]}))

 + sum(i,TRAD_COMM, {VIPA(i,r) * [ppm(i,r) + qpm(i,r)]}

                    - {VIPM(i,r) * [pim(i,r) + qpm(i,r)]})

 + sum(i,TRAD_COMM, {VDPA(i,r) * [ppd(i,r) + qpd(i,r)]}

                    - {VDPM(i,r) * [pm(i,r)  + qpd(i,r)]})

 + sum(i,TRAD_COMM, {VIGA(i,r) * [pgm(i,r) + qgm(i,r)]}

                    - {VIGM(i,r) * [pim(i,r) + qgm(i,r)]})

 + sum(i,TRAD_COMM, {VDGA(i,r) * [pgd(i,r) + qgd(i,r)]}

                    - {VDGM(i,r) * [pm(i,r) + qgd(i,r)]})

 + sum(i,TRAD_COMM, sum(s,REG,{VXWD(i,r,s) * [pfob(i,r,s) + qxs(i,r,s)]}

                    - {VXMD(i,r,s) * [pm(i,r) + qxs(i,r,s)]}))

 + sum(i,TRAD_COMM, sum(s,REG,{VIMS(i,s,r) * [pms(i,s,r)  + qxs(i,s,r)]}

                    - {VIWS(i,s,r) * [pcif(i,s,r) + qxs(i,s,r)]}))

 + INCOME(r) * incomeslack(r);

Equation 10:  KEND

! Ending capital stock equals beginning stock plus net investment. (HT#10)!

(all, r, REG)

   ke(r) = INVKERATIO(r) * qcgds(r) + [1.0 - INVKERATIO(r)] * kb(r) ;

Equation 11


! Equation 11 computes changes in global investment. Refer to Equation 11'!

! in the investment equations section below.                              !


Equation 12:  WALRAS_S

! This is an extra equation which simply computes change in supply in the

  omitted market.  (HT#12)!

walras_sup = globalcgds ;

Equation 13:  WALRAS_D

! This is an extra equation which simply computes change in demand in the

  omitted market.  (HT#13)!

GLOBINV * walras_dem = sum(r,REG, SAVE(r) * qsave(r)) ;

Equation 14:  WALRAS

! This equation checks Walras' Law.  The value of the endogenous slack

  variable should be zero. (HT#14)!

walras_sup = walras_dem + walraslack ;

Price linkage equations

Equation 15:  SUPPLYPRICES

! This equation links pre- and post-tax supply prices for all industries.

  This captures the effect of output taxes. TO(i,r) < 1 in the case of a


  tax. (HT#15)!


ps(i,r) = to(i,r) + pm(i,r) ;

Equation 16:  MPFACTPRICE

! This equation links domestic and firm demand prices. It holds for mobile

  endowment goods and captures the effect of taxation of firms' usage of

  primary factors.  (HT#16)!


pfe(i,j,r) = tf(i,j,r) + pm(i,r) ;

Equation 17:  SPFACTPRICE

! This equation links domestic and firm demand prices. It holds for sluggish

  endowment goods and captures the effect of taxation of firms' usage of

  primary factors.  (HT#17)!


pfe(i,j,r) = tf(i,j,r) + pmes(i,j,r) ;

Equation 18:  PHHDPRICE

! This equation links domestic market and private household prices.It holds

  only for domestic goods and it captures the effect of commodity taxation of

  private households. (HT#18) !


ppd(i,r) = tpd(i,r) + pm(i,r)  ;

Equation 19:  GHHDPRICE

! This equation links domestic market and government household prices.

  It holds only for domestic goods and it captures the effect of commodity

  taxation of government households. (HT#19) !


pgd(i,r) = tgd(i,r) + pm(i,r)  ;

Equation 20:  DMNDDPRICE

! This equation links domestic market and firm prices.

  It holds only for domestic goods and it captures the effect of commodity

  taxation of firms.  (HT#20)!


pfd(i,j,r) = tfd(i,j,r) + pm(i,r)  ;

Equation 21:  PHHIPRICES

! This equation links domestic market and private household prices. It holds

  only for imports and it captures the effect of commodity taxation of private

  households. (HT#21)!


ppm(i,r) = tpm(i,r) + pim(i,r)  ;

Equation 22:  GHHIPRICES

! This equation links domestic market and government household prices. It

  holds only for imports and it captures the effect of commodity taxation of

  government households.  (HT#22)!


pgm(i,r) = tgm(i,r) + pim(i,r)  ;

Equation 23:  DMNDIPRICES

! This equation links domestic market and firm prices. It holds only for

  imported goods and it captures the effect of commodity taxation of

  firms. (HT#23)!


pfm(i,j,r) = tfm(i,j,r) + pim(i,r)  ;

Equation 24:  MKTPRICES

! This equation links domestic and world prices.  It includes a

  source-generic import levy. (HT#24)!


pms(i,r,s) = tm(i,s) + tms(i,r,s) + pcif(i,r,s)  ;


Equation 25:  PRICETGT

! This equation defines the target price ratio to be attained via the

  variable levy. (HT#25)!


pr(i,s) = pm(i,s) - pim(i,s) ;

Equation 26


! For Equation 26'refer to the equations on the global transportation sector!

! given below.                                                              !


Equation 27:  EXPRICES

! This equation links agents' and world prices. In addition to tx we have txs

  which embodies both production taxes (all s) and export taxes (r not equal

  to s) 



pfob(i,r,s) = pm(i,r) - tx(i,r) - txs(i,r,s) ;

Behavioral equations of producers

Equation 28:  DPRICEIMP

! Price for aggregate imports. (HT#28)!


pim(i,s) = sum(k,REG, MSHRS(i,k,s) * pms(i,k,s));

Equation 29:  IMPORTDEMAND

! Regional demand for disaggregated imported commodities by source.(HT#29)!


qxs(i,r,s) = D_VXWD(i,r,s) 

             * [qim(i,s) - ESUBM(i) * [pms(i,r,s) - pim(i,s)]];

Equation 30:  ICOMPRICE

! Industry price for composite commodities. (HT#30) !(all,i,TRAD_COMM)


pf(i,j,r) = FMSHR(i,j,r)*pfm(i,j,r) + [1 - FMSHR(i,j,r)]*pfd(i,j,r) ;

Equation 31:  INDIMP

! Industry j demands for composite import i. (HT#31)!


qfm(i,j,s) = qf(i,j,s)- ESUBD(i) * [pfm(i,j,s) - pf(i,j,s)];

Equation 32:  INDDOM

! Industry j demands for domestic good i. (HT#32)!


qfd(i,j,s) = qf(i,j,s) - ESUBD(i) * [pfd(i,j,s) - pf(i,j,s)];

Equation 33:  VAPRICE

! (Effective) price of primary factor composite in each sector/region. (HT#33)!


pva(j,r) = sum(k,ENDW_COMM, SVA(k,j,r) * [pfe(k,j,r) - afe(k,j,r)]);

Equation 34:  ENDWDEMAND

! Demands for endowment commodities (HT#34) !


qfe(i,j,r) = D_EVFA(i,j,r) * [ - afe(i,j,r) + qva(j,r)

             - ESUBVA(j) * [pfe(i,j,r) - afe(i,j,r) - pva(j,r)] ];

Equation 35:  VADEMAND

! Sector demands for primary factor composite. (HT#35)!


qva(j,r) + ava(j,r) = qo(j,r) - ao(j,r);


Equation 36:  INTDEMAND

! Industry demands for intermediate inputs, including cgds. (HT#36) !


qf(i,j,r) = D_VFA(i,j,r) * [ - af(i,j,r) + qo(j,r) - ao(j,r) ];

Equation 6':   ZEROPROFITS

! Industry zero pure profits condition. This condition permits us to determine

  the endogenous output level for each of the non-endowment sectors. The level

  of activity in the endowment sectors is exogenously determined. (HT#6)!


VOA(j,r) * [ps(j,r) + ao(j,r)] =

       sum(i,ENDW_COMM, VFA(i,j,r) * [pfe(i,j,r) - afe(i,j,r) - ava(j,r)])

       + sum(i,TRAD_COMM, VFA(i,j,r) * [pf(i,j,r)  - af(i,j,r)])

       + VOA(j,r) * profitslack(j,r);

Behavioral equations of households

Equation 37:  UTILITY

! computation of per capita regional utility (HT#37).  Note that private 

  utility has already been defined on a percapita basis. !


INCOME(r) * u(r) = PRIVEXP(r) * up(r)

                 + GOVEXP(r)  * [ ug(r) - pop(r) ]

                 + SAVE(r)    * [ qsave(r) - pop(r)] ;

Equation 38:  SAVINGS

! regional demand for savings -- generated from aggregate Cobb-Douglas

  utility function where the pop(r) terms again cancel (HT#38)!


qsave(r) = y(r) - psave + saveslack(r) ;

Equation 39:  GOVERTU

! Computation of utility from regional government consumption. In

  some closures this index of gov't activity may be fixed, in which case

  govslack is endogenized. In this case the mix of regional expenditures

  changes and the aggregate utility index no longer applies. (HT#39)!


ug(r) = y(r) - pgov(r) + govslack(r) ;

Equation 40:  GPRICEINDEX

! definition of price index for aggregate gov't purchases (HT#40)!


     pgov(r) = sum(i,TRAD_COMM, [VGA(i,r)/GOVEXP(r)] * pg(i,r)) ;

Equation 41:  GOVDMNDS

! Government household demands for composite commodities. Note that the pop(r)

  argument in per capita income and that in per capita consumption cancel due

  to homotheticity. (HT#41)!


qg(i,r) = ug(r) - [ pg(i,r) - pgov(r) ] ;

Equation 42:  GCOMPRICE

! Government household price for composite commodities (HT#42)!


pg(i,s) =  GMSHR(i,s) * pgm(i,s) + [1 - GMSHR(i,s)] * pgd(i,s) ;

Equation 43:  GHHLDAGRIMP

! Government household demand for aggregate imports. (HT#43)!


qgm(i,s) = qg(i,s) + ESUBD(i) * [pg(i,s) - pgm(i,s)] ;

Equation 44:  GHHLDDOM

! Government household demand for domestic goods. (HT#44)!


qgd(i,s) = qg(i,s) + ESUBD(i) * (pg(i,s) - pgd(i,s)) ;


Equation 45:  PRIVATEU

! This equation determines private consumption utility for a representative

  household in region r, based on the per capita private expenditure function.



yp(r) = sum(i,TRAD_COMM, (CONSHR(i,r) * pp(i,r)))

      + sum(i,TRAD_COMM, (CONSHR(i,r) * INCPAR(i,r))) * up(r)

      + pop(r) ;

Equation 46:  PRIVDMNDS

! Private household demands for composite commodities. Demand system is on a

  per capita basis. Here, yp(r) - pop(r) is % change in per capita income. (HT#46)!


qp(i,r) = sum(k,TRAD_COMM, EP(i,k,r) * pp(k,r))

        + EY(i,r) * [ yp(r) - pop(r) ]

        + pop(r) ;

Equation 47:  PCOMPRICE

! Private household price for composite commodities (HT#47)!


pp(i,s) = PMSHR(i,s) * ppm(i,s) + [1 - PMSHR(i,s)] * ppd(i,s) ;

Equation 48:  PHHLDDOM

! Private household demand for domestic goods. (HT#48)!


qpd(i,s) = qp(i,s) + ESUBD(i) * [pp(i,s) - ppd(i,s)] ;

Equation 49:  PHHLDAGRIMP

! Private household demand for aggregate imports. (HT#49)!


qpm(i,s) = qp(i,s) + ESUBD(i) * [pp(i,s) - ppm(i,s)] ;

Equations for sluggish endowments (imperfect factor mobility)

Equation 50:  ENDW_PRICE

! This equation generates the composite price for sluggish endowments.(HT#50)!


pm(i,r) = sum(k,PROD_COMM, REVSHR(i,k,r) * pmes(i,k,r)) ;

Equation 51:  ENDW_SUPPLY

! This equation distributes the sluggish endowments across sectors. (HT#51)!


qoes(i,j,r) = qo(i,r) - endwslack(i,r) 

            + ETRAE(i) * [pm(i,r) - pmes(i,j,r)];

Investment equations (macroeconomic closure)

Equation 52:  KAPSVCES

! This equation defines a variable for capital services, for convenience.

  (There is really only one capital services item.) (HT#52)!


ksvces(r) = sum(h,ENDWC_COMM, [VOA(h,r) / sum(k,ENDWC_COMM, VOA(k,r))]* qo(h,r));

Equation 53:  KAPRENTAL

! This equation defines a variable for capital rental rate. (HT#53)!


rental(r) = sum(h,ENDWC_COMM, [VOA(h,r) / sum(k,ENDWC_COMM, VOA(k,r))] * ps(h,r));


Equation 54:  CAPGOODS

! This equation defines a variable for gross investment, for convenience.

  There is really only one capital goods item. )  (HT#54)!


qcgds(r) = sum(h,CGDS_COMM, [VOA(h,r) / REGINV(r)] * qo(h,r))  ;

Equation 55:  PRCGOODS

! This equation defines the price of cgds for convenience. (HT#55)!


pcgds(r) = sum(h,CGDS_COMM, [VOA(h,r) / REGINV(r)] * ps(h,r)) ;

Equation 56:  KBEGINNING

! This equation associates any change in capital services during the

  period with a change in capital stock. Full capacity utilization is

  assumed. (HT#56)!


kb(r) = ksvces(r) ;

Equation 57:  RORCURRENT

! This generates the current rate of return on capital in region r.(HT#57)!

(all, r, REG)

rorc(r) = GRNETRATIO(r) * [rental(r) - pcgds(r)] ;

Equation 58:  ROREXPECTED

! Expected rate of return depends on the current return and


(all, r, REG)

rore(r) = rorc(r) - RORFLEX(r) * [ke(r) - kb(r)] ;

Equation 59:  RORGLOBAL

! This equation computes alternatively the global supply of capital goods

  or the global rental rate on investment. (HT#59) !



+ [1 - RORDELTA] * {[REGINV(r)/NETINV(r)] * qcgds(r)

- [VDEP(r)/NETINV(r)] * kb(r)}

= RORDELTA * rorg + [1 - RORDELTA] * globalcgds + cgdslack(r) ;

Equation 11':  GLOBALINV

! This equation computes: either the change in global investment (when 

  RORDELTA=1), or the change in the expected global rate of return on capital

  (when RORDELTA=0) (HT#11') !

RORDELTA * globalcgds + [1 - RORDELTA] * rorg = 

RORDELTA * [ sum(r,REG, {REGINV(r)/GLOBINV} * qcgds(r)- {VDEP(r)/GLOBINV} * kb(r))] 

+ [1 - RORDELTA] * [ sum(r,REG, {NETINV(r)/GLOBINV} * rore(r)) ];

Equation 60:  PRICGDS

! This equation generates a price index for the aggregate

  global cgds composite. (HT#60) !

psave = sum(r,REG, [ NETINV(r) / GLOBINV] * pcgds(r)) ;

Equations for the global transportation sector

Equation 7':  PTRANS

! This equation generates a price index for transportation services based on 

  zero profits. (NOTE Sales to international transportation are not subject to

  export tax. This is why we base the costs to the transport sector on market

  prices of the goods sold to international transportation.) (HT#7)!

VT * pt = sum(i,TRAD_COMM, sum(r,REG, VST(i,r) * pm(i,r)));

Equation 61:  TRANSVCES

! This equation generates the demand for regional supply of global

  transportation services. It reflects a unitary elasticity of substitution

  between transportation services inputs from different regions. (HT#61)!



qst(i,r) = D_VST(i,r) * [ qt + [pt - pm(i,r)] ];

Equation 62:  QTRANS

! This equation computes the global demand for international transportation

  services (i.e., variable qt). It reflects the fact that the demand for

  services along any particular route is proportional to the quantity of

  merchandise shipped [i.e., variable qxs(i,r,s) ]. (HT#62)!

VT * qt = sum(i,TRAD_COMM, sum(r,REG,

              sum(s,REG, VTWR(i,r,s) * [qxs(i,r,s) - atr(i,r,s)] ))) ;

Equation 26':  FOBCIF

! This equation links fob and cif prices for good i shipped from region r

  to s . (HT#26')!


pcif(i,r,s) = FOBSHR(i,r,s) * pfob(i,r,s) + TRNSHR(i,r,s) * [pt - atr(i,r,s)];

Equation 63: -

A-2.1.4 Summary indicators

Equation 64:  REGSUPRICE

! This equation estimates the change in the index of prices received for

  tradeable products produced in r. (HT#64)!


VWLDSALES(r) * psw(r)= sum(i,TRAD_COMM, sum(s,REG, VXWD(i,r,s) * pfob(i,r,s))

                       + VST(i,r) * pm(i,r))

                       + NETINV(r) * pcgds(r) ;

Equation 65:  REGDEMPRICE

! This equation estimates the change in the index of prices paid for tradeable

  products used in r. (HT#65)!


VWLDSALES(r) * pdw(r) = sum(i,TRAD_COMM, sum(k,REG, VIWS(i,k,r) *pcif(i,k,r))) 

                        + SAVE(r) * psave ;

Equation 66:  TOTeq

! Terms of trade equation computed as difference in psw and pdw. (HT#66) !


tot(r) = psw(r) - pdw(r) ;

Equation 67:  EVREG  

! computes regional EV (HT#67)!


EV(r) = [INC(r)/100] * [URATIO(r) * POPRATIO(r)] * [u(r) + pop(r)] ;

Equation 68:  EVWLD

! computes EV for the world (HT#68)!

WEV - sum(r,REG, EV(r)) = 0 ;

Equation 69:  PHHLDINDEX    

! computes change in price index for private household expenditures (HT#69)!


PRIVEXP(r) * ppriv(r) = sum(i,TRAD_COMM, VPA(i,r)* pp(i,r));

Equation 70:  VGDP_r

!  change in value of GDP (HT#70)!              


GDP(r) * vgdp(r) = sum(i,TRAD_COMM, VGA(i,r) * [qg(i,r)    + pg(i,r)    ]) 

                 + sum(i,TRAD_COMM, VPA(i,r) * [qp(i,r)    + pp(i,r)    ]) 

                                 + REGINV(r) * [qcgds(r)   + pcgds(r)   ]

   + sum(i,TRADCOMM, sum(s,REG, VXWD(i,r,s) * [qxs(i,r,s) + pfob(i,r,s)])) 

                 + sum(i,TRADCOMM, VST(i,r) * [qst(i,r)   + pm(i,r)    ])

   - sum(i,TRADCOMM, sum(s,REG, VIWS(i,s,r)* [qxs(i,s,r) + pcif(i,s,r)]));


Equation 71:  PGDP_r

!  gdp price index (HT#71)!              


GDP(r) * pgdp(r) = sum(i,TRAD_COMM, VGA(i,r) * pg(i,r) ) 

                 + sum(i,TRAD_COMM, VPA(i,r) * pp(i,r) )

                 + REGINV(r) * pcgds(r)

   + sum(i,TRAD_COMM, sum(s,REG, VXWD(i,r,s) * pfob(i,r,s) )) 

                 + sum(i,TRAD_COMM, VST(i,r) * pm(i,r) )

   - sum(i,TRAD_COMM, sum(s,REG, VIWS(i,s,r)* pcif(i,s,r))) ;

Equation 72:  QGDP_r

!  gdp quantity index (HT#72)!              (all,r,REG) 

qgdp(r) = vgdp(r) - pgdp(r) ;

Equation 73:  VREGEX_ir  

! the change in FOB value of exports of commodity i from r (HT#73)! 


VXW(i,r) * vxwfob(i,r) = sum(s,REG, VXWD(i,r,s) * [qxs(i,r,s) + pfob(i,r,s)]) 

                       + VST(i,r) * [qst(i,r) + pm(i,r)] ;

Equation 74:  VREGIM_is  

! the change in CIF value of imports of commodity i into s (HT#74)! 


VIW(i,s) * viwcif(i,s) = sum(r,REG, VIWS(i,r,s) * [pcif(i,r,s) + qxs(i,r,s)]);

Equation 75:  VREGEX_r   

! computes % change in value of merchandise exports, by region (HT#75)!


VXWREGION(r) * vxwreg(r) = sum(i,TRAD_COMM, VXW(i,r) * vxwfob(i,r)) ;

Equation 76:  VREGIM_s   

! computes % change in value of imports, cif basis, by region (HT#76)!


VIWREGION(s) * viwreg(s) = sum(i,TRAD_COMM, VIW(i,s) * viwcif(i,s)) ;

Equation 77:  VWLDEX_i   

! computes % change in fob value of global exports, by commodity (HT#77)!


VXWCOMMOD(i) * vxwcom(i) = sum(r,REG, VXW(i,r) * vxwfob(i,r)) ;

Equation 78:  VWLDIM_i   

! computes % change in value of global imports, by commodity (HT#78)!


VIWCOMMOD(i) * viwcom(i) = sum(s,REG, VIW(i,s) * viwcif(i,s)) ;

Equation 79:  VWLDEX

! computes % change in value of global exports (HT#79)!

VXWLD * vxwwld = sum(r,REG, VXWREGION(r) * vxwreg(r)) ;

Equation 80:  VWLDOUT

! change in value of world output of commodity i at fob prices (HT#80)!


VWOW(i) * valuew(i) = sum(r,REG, VOW(i,r) * [pxw(i,r) + qo(i,r)]) ;

Equation 81:  PREGEX_ir

! the change in FOB price index of exports of commodity i from r (HT#81)!


VXW(i,r) * pxw(i,r) = sum(s,REG, VXWD(i,r,s) * pfob(i,r,s)) 

                    + VST(i,r) * pm(i,r) ;

Equation 82:  PREGIM_is 

! the change in cif price index of imports of commodity i into s (HT#82)!(all,i,TRAD_COMM)(all,s,REG)

VIW(i,s) * piw(i,s) = sum(r,REG, VIWS(i,r,s) * pcif(i,r,s)) ;

Equation 83:  PREGEX_r   


! computes % change in price index of exports, by region (HT#83)!


VXWREGION(r) * pxwreg(r) = sum(i,TRAD_COMM, VXW(i,r) * pxw(i,r)) ;

Equation 84:  PREGIM_s   

! computes % change in price index of imports, by region (HT#84)!


VIWREGION(s) * piwreg(s) = sum(i,TRAD_COMM, VIW(i,s) * piw(i,s)) ;

Equation 85:  PWLDEX_i   

! computes % change in price index of exports, by commodity (HT#85)!


VXWCOMMOD(i) * pxwcom(i) = sum(r,REG, VXW(i,r) * pxw(i,r)) ;

Equation 86:  PWLDIM_i   

! computes % change in price index of imports, by commodity (HT#86)!


VIWCOMMOD(i) * piwcom(i) = sum(s,REG, VIW(i,s) * piw(i,s)) ;

Equation 87:  PWLDEX

! computes % change in price index of global exports (HT#87)!

VXWLD * pxwwld = sum(r,REG, VXWREGION(r) * pxwreg(r)) ;

Equation 88:  PWLDOUT

! change in index of world prices, fob, for total production of i (HT#88)!


VWOW(i) * pw(i) = sum(r,REG, VOW(i,r) * pxw(i,r)) ;

Equation 89:  QREGEX_ir     

! The change in volume of exports of commodity i from r.

  This is generated by deflating a value aggregate. (HT#89)!


qxw(i,r) = vxwfob(i,r) - pxw(i,r) ;

Equation 90:  QREGIM_is     

! The change in volume of imports of commodity i into s. 

  This is generated by deflating a value aggregate. (HT#90)!


qiw(i,s) = viwcif(i,s) - piw(i,s) ;

Equation 91:  QREGEX_r   

! computes % change in quantity index of exports, by region (HT#91)!


qxwreg(r) = vxwreg(r) - pxwreg(r) ;

Equation 92:  QREGIM_s   

! computes % change in quantity index of imports, by region (HT#92)!


qiwreg(s) = viwreg(s) - piwreg(s) ;

Equation 93:  QWLDEX_i   

! computes % change in quantity index of exports, by commodity (HT#93)!


qxwcom(i) = vxwcom(i) - pxwcom(i) ;

Equation 94:  QWLDIM_i   

! computes % change in quantity index of imports, by commodity (HT#94)!


qiwcom(i) = viwcom(i) - piwcom(i) ;

Equation 95:  QWLDEX

! computes % change in quantity index of global exports (HT#95)!

qxwwld = vxwwld - pxwwld ;

Equation 96:  QWLDOUT                                    

! change in index of world production of i (HT#96)!



qow(i) = valuew(i) - pw(i) ;

Equation 97:  TRADEBAL_i   

! computes change in trade balance by commodity and by region (HT#97)!


DTBALi(i,r) = [VXW(i,r)/100] * vxwfob(i,r) - [VIW(i,r)/100] * viwcif(i,r) ;

Equation 98:  TRADEBALANCE   

! computes change in trade balance (X - M), by region (HT#98)!


DTBAL(r) = [VXWREGION(r)/100] * vxwreg(r) - [VIWREGION(r)/100] * viwreg(r);


!                             END OF FILE                               !




Some examples will be given in Section 2.2 .


See Section 2.3 and Gehlhar (1997) for more detail.


In the recent literature there are some approaches to AGE modeling of international capital mobility and accumulation that will be discussed in Section 2.4 . For the impact of foreign direct investment in Central and Eastern European transition countries see Lotze (1998).


An overview of GTAP can be found at the Internet site http://www.purdue.edu/gtap.


For a detailed graphical overview see Brockmeier (1996).


The terms producers and firms are used synonymously throughout this chapter.


The rest of the world can be disaggregated into various single regions. They are structured in the same way as described in Figure 2.5 , but the details are omitted for simplicity.


See the section on "slack variables" in Appendix A-2.1.1.


The relationship between the value terms and the underlying quantities and prices will be discussed in more detail in Section 2.2.3.


These derivatives from the base data are not stored directly in the database in order to avoid redundant information (see Section A-2.1.2 in the Appendix).


In addition, percentage changes are usually also the preferred output from the model exercises.


The summation sign in the model code is written as "sum[s, REG, VXMD(i,r,s) qxs(i,r,s)]".


There are many other possible representations of production technologies in AGE models, according to specific modeling requirements and data availability (Shoven and Whalley 1992, p.94-100; Sadoulet and de Janvry 1995, p.349-356). In the GTAP model, the current specification has been chosen, among other reasons, to facilitate the calibration of the model to a global database.


Equation 30 to 36 in the model code (Section A-2.1.3) represent exactly these two relationships for the various nests shown in Figure 2.7 . At each stage, the relevant technical change variable are added to the equations.


Equations 50 and 51 in the model code determine prices and quantities for sluggish endowments.


The formulae for these calculations are given in section A-2.1.2. Huff et al. (1997) provide a detailed discussion on the CDE function. Private household behavior in the model is determined by Equations 45 to 49 in Section A-2.1.3.


The corresponding model variable is called cgds, with a respective price variable psave.


See Just et al. (1982, Chapter 6) for a derivation of the Equivalent Variation.


A detailed description of GEMPACK is given by Harrison and Pearson (1996). They also discuss various solution algorithms for large models. The internet site of GEMPACK can found at http://www.monash.edu.au/policy/gempack.htm.


In summer 1998 version 4 of the GTAP database has been released. It has 1995 as a new reference year and is extended to 50 sectors and 45 regions. Among other changes, labor has been split into "skilled" and "unskilled" labor, and "natural resources" have been introduced as a new primary endowment. For more information see the GTAP internet site at http://www.agecon.purdue.edu/gtap.


Usually, for specific model applications a smaller aggregation of the original database is used. GTAP provides the opportunity to aggregate certain regions and sectors into larger groups according to the focus of a certain modeling exercise.


See the GTAP model structure on policy variables discussed earlier (Section 2.2.2 ).


Quantitative restrictions will be briefly discussed in Section 2.4 below.


As an example, for sufficient confidence in the Monte Carlo results several thousand repetitions are necessary. If a solution run of the GTAP model took five minutes, which is not unusual, 1000 Monte Carlo repetitions would take about 3.5 days (Arndt 1996, p.1).


Upper-case letters are used for the variables here as the price levels are considered.


Of course, at a very disaggregated level probably any industry shows some degree of product differentiation. This is usually neglected in aggregated AGE models.


These include models by Cournot, Bertrand, and Chamberlin, which are discussed in Kreps (1990, Chapter 10).


This is the GTAP model file GTAP94.TAB. Throughout the Appendix, the model code is typed in Courier letters, while notes and comments are typed in Times Roman.

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