Abstract
In this chapter a CGE model (the CGE mini model) is presented. The model is simple enough to be presented in a few pages and yet complicated enough to demonstrate the application of the general CGE structure. In short, the focus of this chapter is to provide examples of structural adjustment in an open economy. The numerical applications of this chapter will be an examination of the sensitivity of the model to systematic variation in key variables of the adjustment process. Here we emphasise the effect of changes (government intervention) in the fixed rate of real exchange and growth in the capital stock.
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- 1.
The CGE mini-model is included in the GAMS model library which is distributed with the GAMS system. The CGE mini-model is a minor version of an equilibrium model that originally comes from Chenery, Lewis, de Melo, and Robinson in their work in designing an equilibrium development model for Korea. The model is originally designed for the study of three development strategies. The first option was the strategy of export expansion, the second option was the strategy of import substitution, and the third option was a strategy between the two extreme cases. This model illustrates the basic use of CGE models. See further: Chenery et al. (1986), pp. 311–347.
- 2.
Note, that the export demand function (Eq. 4.35) is not included in the CGE mini model.
- 3.
In other words the word price in foreign currency is given. The reader must note, that price incentive policy such as taxes, subsides, and tariffs are now explicitly incorporated. Domestic prices can be altered by the government by changes in price incentive policy, and hence, affect the economic structure.
- 4.
In intertemporal models, agents have rational expectations and future markets are considered when optimising. Endogenous variables follow an optimal path over time and there are no incentives to deviate from this path at any point of time.
- 5.
For a discussion, see Dervis et al. (1982), pp. 192–197.
- 6.
The choice of which variables are to be exogenous is called the model closure. In all experiments in this book the exchange rate is fixed and the net flow of foreign borrowing is unfixed. Following this specification, the trade deficit is free to vary.
- 7.
Dervis et al. (1982), p. 183.
- 8.
Alternatively, the sectors can be defined in terms of input characteristics; labour-intensive, capital-intensive, and knowledge-intensive commodities.
- 9.
Note, that in equilibrium the expenditures of each household exhaust its income. However, in this chapter we consider saving. In any case, total income generated in the system always equals total national product at market prices.
- 10.
To compute benchmark equilibrium can also be an alternative if the benchmark year is not accepted as a representative equilibrium.
- 11.
This assumes that the benchmark year is a representative equilibrium.
- 12.
- 13.
As noted, the mini-equilibrium-model is included in the GAMS model library, which is distributed with the GAMS system. Readers who have access to the GAMS program can thus take an active part of the model developed here. Readers who also are interested in downloading the current version of the GAMS distribution will find necessary information in the appendix of this chapter and Chap. 4.
- 14.
See the end of the appendix for this chapter.
- 15.
- 16.
The J-curve describes the time lag with which a real currency devaluation improves the current account.
- 17.
For details, see the discussion in Chap. 3.
- 18.
Recursive-dynamic CGE models are those which can be solved sequentially (one period at a time): they assume that behaviour depends only on current and past states of the economy.
- 19.
The perfect competition theory defines the equilibrium state and not the process of adjustment. (Kirzner 1973).
- 20.
Schumpeter 1942 and 1976.
References
Armington P (1969) A theory of demand for products distinguished by place of production. IMF Staff Pap 16:159–178
Chenery H, Lewis J, de Melo J, Robinson S (1986) Alternative routes to development. In: Chenery H, Syrquin M (eds) Industrialization and growth: a comparative study. Oxford University Press, New York
Condon T, Dahl H, Devarajan S (1987) Implementing a computable general equilibrium model on GAMS – the Cameroon model, DRD discussion paper 290. The World Bank, Washington, DC
Dervis K, de Melo J, Robinson S (1982) General equilibrium models for development policy. Cambridge University Press, Cambridge
Freeman C (1974) The economics of industrial innovation. Penguin Books, Harmondsworth, Middlesex
Kirzner IM (1973) Competition and entrepreneurship. The University of Chicago Press, Chicago
Lofgren H, Harris RL, Robinson S (2002) A standard computable general equilibrium (CGE) model in GAMS, vol 5, Microcomputers in policy research. International Food Policy Research Institute, Washington, DC
Petersen TW (1997) An introduction to CGE-modelling and an illustrative application to Eastern European Integration with the EU. The Institute of Economics at the University of Copenhagen, Denmark. The working paper is only available on www.dreammodel.dk/
Schumpeter J (1942, 1976) Capitalism, socialism and democracy. Harper & Row, New York
Shoven J, Whalley J (1984) Applied general equilibrium models of taxation and international trade: an introduction and survey. J Econ Lit XXII:1007–1051
Shoven J, Whalley J (1992) Applying general equilibrium. Cambridge University Press, Cambridge
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Appendices
Appendix 1: The Mathematical Equations of the Model
5.1.1 Prices
5.1.1.1 Definition of Domestic Import Prices
\( p_j^{WM } \) is the world market price of imports, ER is the real exchange rate, tm j is the tariff rate on imports, and pr j is the import premium rate. Note, that the world market price of imports \( p_j^{WM } \) and the tariff rates are fixed. Depending on the exchange rate, the domestic import price \( p_j^M \) is flexible or fixed.
5.1.1.2 Definition of Domestic Export Prices
\( p_j^E \) is the domestic price of exports, \( p_j^{WE } \) is the world market price of exports, te j are the export duty rates, and ER is the real exchange rate. Note, the world market price of exports \( p_j^{WE } \) and the duty rates are fixed. Depending on the exchange rate, the domestic export price \( p_j^E \) is flexible or fixed.
5.1.1.3 Value of Domestic Sales
p i is the price of composite commodities, x i is the composite commodity supply, \( p_j^Z \) is the domestic price, \( x_j^Z \) are the domestic sales, \( p_j^M \) is the domestic price of imports, and M j is imports by sector.
5.1.1.4 Value of Domestic Output (Market Value)
\( p_j^Z \) is the average output price by sector, Z j is the domestic output by sector, \( x_j^Z \) are domestic sales, \( p_j^E \) is the domestic price of exports, and E j is exports by sector.
5.1.1.5 Definition of Activity Prices
\( p_j^Z \) is the average output price by sector, ITAX j is the indirect tax rate, PVA j is the value added price by sector, a ij are the input–output coefficients, and p i is the price of composite commodities.
5.1.1.6 Definition of Capital Commodity Price
\( p_j^{\mathrm{ K}} \) is the rate of capital rent by sector, p i is the price of composite commodities, and c ij is the capital composition matrix.
5.1.1.7 Definition of General Price Level
p index is the general price level, pwts i are the CPI weights, and p i is the price of the composite commodity.
5.1.2 Output and the Factors of Production
5.1.2.1 Production Function (Cobb-Douglas)
Z j is the domestic output by sector, AD j is the production function shift parameter, α j,lc is the labour share parameter, L j,lc is the employment by sector and labour category (lc), and K j is the capital stock by sector.
5.1.2.2 First Order Condition for Profit Maximum
\( P_{lc}^{\mathrm{ L}} \) is the average wage rate by labour category (lc), Wdist are the wage proportionality factors, L j,lc denote the employment by sector and labour category, and PVA j is the value added price by sector.
5.1.2.3 Labour Market Equilibrium
L j,lc denote the employment by sector and labour category, and L lc is the labour supply by labour category (lc).
5.1.2.4 CET Function: Exports (Domestic Output)
Z j is the domestic output by sector, AT j is the CET function shift parameter, GAMMA is the CET function share parameter, E j is exports by sector, ϕ j is the CET function exponent, and \( x_j^Z \) are the domestic sales. This function applies to commodities that are both sold domestically and exported. The equation above reflects the assumption of imperfect transformability between domestic sales and exports.
5.1.2.5 Export Supply
\( p_j^E \) is the domestic price of exports, and \( p_j^Z \) is the domestic price.
5.1.2.6 CES Function: Composite Commodity Aggregation Function
x i is the composite commodity supply, AC j is the Armington function shift parameter, \( {\delta_j} \) is the Armington function share parameter, M j is imports, ρ j is the Armington function exponent, and \( x_j^Z \) are the domestic sales. This function applies to commodities that are both produced and sold domestically and imported, i.e., composite commodities. The equation above reflects the assumption of imperfect substitutability between imports and domestic produced commodities sold domestically.
5.1.2.7 Cost Minimisation of Composite Good
\( p_j^Z \) is the domestic prices, and \( p_j^M \) is the domestic price of imports.
5.1.2.8 Domestic Sales for Non-traded Sectors
A first step toward more realism has been taken by introducing non-tradable commodities. Non-tradable commodities are commodities that are not subject to international trade. In general, most service as well as housing and construction fit this category.
\( x_j^Z \) are the domestic sales, and Z j is the domestic output by sector.
5.1.2.9 Composite Commodity Aggregation for Non-traded Sectors
x i is the composite commodity supply, and \( x_j^Z \) are domestic sales.
5.1.3 Demand
5.1.3.1 Total Intermediate Uses
x ij are the intermediate uses, a ij is the input–output coefficients, and Z j is the domestic output by sector. The sector balances of intermediate inputs (inter-industry matrix) form the basis of the input–output table. The input–output matrix is derived from the inter-industry matrix, by dividing each element in a column by the row sum of the corresponding row. The Leontief matrix is obtained from the input–output matrix by subtracting it from an n by n identity matrix. This changes the sign of all off-diagonal elements and makes all diagonal elements into their complements to one. Theoretically, the input coefficients are in physical terms. Empirically, the coefficients are in monetary terms. As long as we assume that prices are constant, the input coefficients should be the same either in physical or monetary terms.
The transactions may be valued at either the price received by the producer, producer’s value, or at the price paid by the consumer, purchaser’s value. The difference between these values is that transport margins, net indirect commodity taxes, i.e., indirect taxes less subsides, and trade margins are added to the basic producer’s values in the national accounts. Since the demand components are computed at purchaser’s values, production and imports are converted to these values too.
5.1.3.2 Inventory Investment
DST j is inventory investment by sector, DSTR j is the ratio of inventory investment to gross output, and Z j is the domestic output by sector.
5.1.3.3 Private Consumption Behaviour
p j are the price of composite commodities, CD j is the final demand for private consumption, CLES j,h are the private consumption shares, MPS h is the marginal propensity to save by household type, YH h is the total income by household type, and HTAX h is the income tax rate by household type
5.1.3.4 Private GDP
Y is private GDP, YH h is the total income by household type.
5.1.3.5 Total Income Accruing to Labour
YH h is the total income by household type, \( {P_{lc}}^{\mathrm{ L}} \) is the average wage rate by labour category, L lc is the labour supply by labour category, REMIT is the net remittances from abroad, and ER is the real exchange rate.
5.1.3.6 Total Income Accruing to Capital
YH h is the total income by household type, PVA j is value added price by sector, Z j is the domestic output by sector, DEPRECIA is total depreciation expenditure, \( {P_{lc}}^{\mathrm{ L}} \) is the average wage rate by labour category, L lc is the labour supply by labour category, FBOR is the net flow of foreign borrowing, ER is the real exchange rate, and YPR is total premium income accruing to capitalists.
5.1.4 Saving and Income
5.1.4.1 Household Savings
HSAV are the total household savings, MPS h is the marginal propensity to save by household type h, YH h is the total income by household type, and HTAX h is the income tax rate by household type.
5.1.4.2 Government Revenue
GR is the government revenue, TARIFF is the tariff revenue, NETSUB is the export duty revenue, INDTAX is the indirect tax revenue, TOTHTAX is the household tax revenue.
5.1.4.3 Government Savings
GR is the government revenue, p j are the price of composite commodities, GD j is the final demand for government consumption, and GOVSAV are government savings. It is an essential assumption for a real equilibrium model that the government must balance its budget.
5.1.4.4 Government Consumption Shares
GD j is the final demand for government consumption, GLES j is the government consumption shares, and GDTOT is the total volume of government consumption.
5.1.4.5 Tariff Revenue
TARIFF is the tariff revenue, TM j are the tariff rates on imports, M j are imports, \( p_j^{WM } \) are world market price of imports, ER is the real exchange rate.
5.1.4.6 Indirect Taxes on Domestic Production
INDTAX is the indirect tax revenue, ITAX j is the indirect tax rates, \( p_j^Z \) is the average output price by sector, and Z j is the domestic output by sector.
5.1.4.7 Export Duties
NETSUB is export duty revenue, te j are export duty rates, E j are exports by sector, \( p_j^{WE } \) is the world market price of exports, ER is the real exchange rate.
5.1.4.8 Total Import Premium Income
YPR is the total premium income accruing to capitalists, \( p_j^{WM } \) is the world market price of imports, M j are imports, ER is the real exchange rate, and pr is the import premium.
5.1.4.9 Total Household Taxes Collected by Government
TOTHTAX is the household tax revenue, HTAX h is the income tax rate by household type h, YH h is the total income by household type h.
5.1.5 Capital Formation
5.1.5.1 Depreciation Expenditure
DEPRECIA is the total depreciation expenditure, DEPR j is the depreciation rate, K j is the capital stock by sector, \( p_j^{\mathrm{ K}} \) is the rate of domestic capital rent by sector, ER is the exchange rate. As the capital stock gets older, the quasi-rent in the Marshallian sense falls and eventually becomes zero. The economic decision is then taken to scrap the capital object as obsolete.
5.1.5.2 Total Savings
SAVINGS are total savings, HSAV are total household savings, GOVSAV are government savings, DEPRECIA is total depreciation expenditure, FSAV are foreign savings. Thus, the sum of domestic and foreign savings in domestic currency.
5.1.5.3 Domestic Investment by Sector of Destination
In the CGE mini-model domestic investment by sector of destination is given by:
Thus, \( p_j^{\mathrm{ K}} \) is rate of capital rent by sector, \( I_j^{\mathrm{ D}} \) is volume of investment by sector of destination, \( K{I^{\mathrm{ o}}}_j \) are the shares of investment by sector of destination, INVEST is the total investment, DST j is inventory investment by sector, p j is the price of composite goods. The sector share parameters for investment are assumed fixed. Total investment is determined by savings in the economy (saving determined investment).
The sector capital stocks K j are fixed within periods. However, they change over time given aggregate growth of the capital stock and the sector allocation of investment. Sector share parameters of investment by sector of destination \( K{I^{\mathrm{ o}}}_j \) are assumed to be fixed. For information, the numerical values of the sector share parameters of investment are in these applications arbitrary assumed to be: 0.13 for agriculture, 0.29 for industry, and 0.58 for services. The sum is equal to one. However, the sector allocation of investment is here assumed to be adjusted over time (endogenously) to equate rental rates \( p_j^{\mathrm{ K}} \) in the industrial sectors by the terminal year.
5.1.5.4 Investment by Sector of Origin
The request for the volume of investment by sector of destination \( I_j^{\mathrm{ D}} \) (the sector capital accumulation) is translated into a demand for investment commodities by sector of origin \( I_i^{\mathrm{ S}} \) (producing sectors of capital commodities), thus investment by sector of origin:
\( I_i^{\mathrm{ S}} \) is the final demand for productive investment, IMAT IJ is the capital composition matrix, and \( I_j^{\mathrm{ D}} \) is the volume of domestic investment by sector of destination. In accordance with the production structure, as represented by the input–output model, the investment by sector of origin \( I_i^{\mathrm{ S}} \) is also known as final demand for productive investment. The summation of the capital composition matrix IMAT IJ is, as the sector share parameters of investment, equal to one. Following this application, the two sectors producing capital commodities are industry (the dominating sector), and a small fraction from services.
5.1.5.5 Balance of Payments
\( p_j^{WM } \) is the world market price of imports, M j are imports, \( p_j^{WE } \) is the world market price of exports, E j are exports by sector, FSAV are foreign savings, REMIT are net remittances from abroad, and FBOR is the net flow of foreign borrowing. In the experiments in this book the exchange rate is fixed and the net flow of foreign borrowing is unfixed. Following this specification, the trade deficit is free to vary.
5.1.6 Market Equilibrium
5.1.6.1 Commodity Market Equilibrium
x i are the composite commodity supply, x ij are intermediates uses, CD j is the final demand for private consumption, GD j is the final demand for government consumption, \( I_i^{\mathrm{ S}} \) is the final demand for productive investment, and DST j is the inventory investment by sector.
5.1.6.2 Objective Function
OMEGA is the objective function variable, CLES j,h is the private consumption shares, and CD j is the final demand for private consumption.
For full specification of the numerical input in the original input version of the model, see the computer program of the CGE mini-model. The CGE mini-model is a minor version of an equilibrium model that originally comes from Chenery, Lewis, de Melo, and Robinson in their work on designing an equilibrium development model for Korea. The model illustrates the basic use of CGE models. See further: Chenery et al. (1986). The model is included in the GAMS model library (korcge.gms). The reader can reach the GAMS homepage at www.gams.com.
Appendix 2: Some Parameters Assignments of the Model
PARAMETER ASSIGNMENTS
LABOUR SHARE PARAMETER IN THE PRODUCTION FUNCTION
LABOUR1 | LABOUR2 | LABOUR3 | |
---|---|---|---|
Agriculture | 0.38258 | 0.06740 | 0.00000 |
Industry | 0.00000 | 0.53476 | 0.00000 |
Services | 0.00000 | 0.16234 | 0.42326 |
INPUT–OUTPUT COEFFICIENTS
Agriculture | Industry | Services | |
---|---|---|---|
Agriculture | 0.12591 | 0.19834 | 0.01407 |
Industry | 0.10353 | 0.35524 | 0.18954 |
Services | 0.02358 | 0.11608 | 0.08390 |
CAPITAL COMPOSITION MATRIX
Agriculture | Industry | Services | |
---|---|---|---|
Agriculture | 0.00000 | 0.00000 | 0.00000 |
Industry | 0.93076 | 0.93774 | 0.93080 |
Services | 0.06924 | 0.06226 | 0.06920 |
WAGE PROPORTIONALITY FACTORS
LABOUR1 | LABOUR2 | LABOUR3 | |
---|---|---|---|
Agriculture | 1.00000 | 0.52780 | 0.00000 |
Industry | 0.00000 | 1.21879 | 0.00000 |
Services | 0.00000 | 1.11541 | 1.00000 |
PRIVATE CONSUMPTION SHARES
LAB-HH | CAP-HH | |
---|---|---|
Agriculture | 0.47000 | 0.47000 |
Industry | 0.31999 | 0.31999 |
Services | 0.21001 | 0.21001 |
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Norén, R. (2013). An Applied Model: The CGE Mini Model. In: Equilibrium Models in an Applied Framework. Lecture Notes in Economics and Mathematical Systems, vol 667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34994-2_5
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