JJRLl DISCUSSION PAPER H.eport No. DRD290 IMPLEM&~TING A COMPUTABLE GENERAL EQUILIBRIUM MODEL ON GAMS THE CAUEROON MODEL by Timothy Condon Henrik Dahl and Shantayanan Devarajan Hay 1987 Development Research Department Economics and Research Staff World Bank The World Bank does not accept responsibility for the views expressed herein t<~hich are those of the author(s) and should not be attributed to the ~orld .Bank or to its affiliated organizations.. The findings, int.erpretations, and conclusions are the re$~lts of research supported by the Bank; they do not necessarily represent official policy of the Bank. The designations employed, the presentation of material, and any maps used in this document are solely for the convenience of the reader and do not imply the expression of any opinion t.Jhatsoeve:r on the part of the World Bank or its affiliates concerning the legal status of any country, territory, city, area, or of its authorities, or concerlling the delimitations of its boundaries, or national affiliation. IMPLEMENTING A COMPUTABLE GENERAL EQUILIBRIUM MODEL ON GAMS THE CAMEROON MODEL by Timothy Condon World Bank Henrik Dahl* World Bank and Goldman Sachs and Co. and Shantayanan Devarajan* Harvard University April 1986 Revised May 1987 "/( Consultant IMPLEMENTING A COMPUTABLE GENERAL EQUILIBR!OM MODEL ON GAMS: THE CAMEROON MODEL Abstract Applied general equilibrium models have become a major tool for the economic analysis of developed and developing countries. Although the theoretical background for these models is well established, the technical skills required to formulate and solve such models have often limited their practical use. This paper shows how many of these practical difficulties can be overcome. Using a prototype model of Cameroon, it describes a framework for implementing numerical general equilibrium models on the General Algebraic Modeling System (GAMS). By separating the model from the solution algorithm, this system permits the user to concentrate on the economic aspects of the model. Also, because the syntax of GAMS closely resembles standard algebraic notation, the system facilitates the communication of model assumptions and results. The paper first describes the Cameroonian policy issues and outlines a general equilibrium model that captures these issues. Second, the paper describes some basic CAMS syntax, and shows in detail how the mathematical model can be implemented on GAMS. Third, it describes methods to test and debug the model, and finally the paper gives some examples of numerical simulations of the model. I. INTRODUCTION CAMCGE, a computable general equilibrium (CGE) model of Cameroon, is a prototype CGE model implemented on the General Algebraic Modelling System (CAMS), (see Meeraus (1983) for additional details). This paper first describes the model (section II) and then shows how it can be formulated in GAMS (section III). Several practical considerations concerning testing and debugging the model (Section IV) are followed by a description of some · simulation experiments (Section V). Finally, the concluding section discusses possible extensions of this particular approach to economy-wide modelling. II. A COMPUTABLE GENERAL EQUILIBRIUM MODEL OF CAMEROON Before proceeding to a complete statement of CP~CGE, we describe the context in which the model was built. We present a thumbnail sketch of the Cameroonian economy and of the policy concerns that led to the construction of the model. This helps to motivate the particular specification of the CGE model described in section II.B. AIJ The Cameroonian Economy and Policy Issues In the twenty-four years since independence, Cameroon has enjoyed modest but steady economic growth, with an average annual growth rate of GDP of over five percent. In 1981, its per capita GNP of $880 was one of the highest in sub-Saharan Africa. Agriculture is the most important sector, accounting for 32 percent a£ GDP and empl0ying 80 percent of the labor force.!/ In addition, of the $1.1 billion in export earnings (20 percent of !/ All statistics in this section refer to 1981 data. - 2 - GOP), over 72 percent came from cash crops -- mainly ~offee and cocoa. The industrial sector has been growing rapidly and now accounts for 24 percent of GDP. This sector produces a variety of exports and import-substitutes, including aluminum, pulp and consumer goods. Although the nontradable sectors -- construction, services and public administration -- have grown rapidly, poor infrastructure and low-levels of education remain the most-often cited obstacles to the country's development. The discovery of offshore oil in the early Seventies, and its subsequent production beginning in 1978, heralded a new era in Cameroon's economic development. No longer would the country be totally dependent on coffee and cocoa exports -- whose prices fluctuated wildly -- for its foreign exchange. Moreover, the oil revenues represented an additional source of savings to the economy. The savings, in turn, could be used to finance capital investment, releasing capacity bottlenecks and increasing productivity. However, for several reasons, the oil revenues are being viewed with caution. The oil sector is somewhat of an enclave in the economy. It uses imported materials and employs foreign labor (mainly highly skilled technicians), so that the effects of oil production on the rest of the economy, in terms of generating employment and backward linkages, are miniscule. The real impact of this sector, therefore, is the expenditure of net oil revenues. The latter are estimated to be about $1 billion in 1982 or about fifteen percent of GDP !/• While not all of this is patriated, even the For a more detailed analysis of Cameroon's oil sector and its relationship to the rest of the economy, see Benjamin and Devarajan [1985]. - 3 - fraction that is can crP.ate the "Dutch disease". That is, the appreciation of the real exchange rate resulting from oil revenue expenditures will make Cameroon's coffee and cocoa less co~petitive in world markets, and its import- substituting industries less con1petitive in domestic markets. The nontraded goods sectors, which have been plagued with capacity constraints, will face an increase in demand. It is important to note that these effects will occur although Cameroon•s official exchange rate is fixed (at 50 CFA Francs to the French Franc}. The injection of oil revenues will serve to raise domestic prices, making foreign goods more attractive. In short, the real exchange rate -- the relative price of traded to nontraded goods -- appreciates. Finally, Cameroon's oil reserves are limited. If no more than twenty years' production are forecast, allowing the non-oil traded goods sectors to contract is probably not the best preparation for the economy to enter the post-oil The advent of oil revenues, therefore, raises a host of policy issues for the government. In the medium-term, the questions are: how much of the oil revenues should be expatriated, how should they be spent, and wha·t will the effects of this expenditure be? If, as is suspected, the effects are those predicted by the Dutch disease literature, the next question is, how can the undesirable outcome be mitigated? In the Cameroonian context, these questions translate to the impact of oil revenues on agricultural exports, import-substituting manufactures and the nontradable sectors. As for policies to mitigate the shift in output mix, van Wijnbergen (1984] shows that protecting the non-oil traded goods sector may be desirable if there is "learning-by-doing." - 4 - protective tariffs are typically suggested. In particular, the government may consider protecting the food crops sector to prevent its demise in the wake of cheaper food imports. This policy is important for two other reasons. First, self-sufficiency in food is one of the country's goals in the futur•!· Second, given the intensity of rural-urban migration in Cameroon, a pro-agricultural policy may be necessary to stem this flow as well as to maintain food output in the face of declining rural employment. Among manufacturing industries, intermediate goods in general, and construction materials and base metals in particular, have been singled out as potential candidates for protection. Now, it is well-known that tariff policies have effects which go beyond the sector being protected. For example, a tariff on intermediate goods will raise costs for the purchasers of these goods, which, in turn, will alter prices elsewhere in the economy. For our purposes, the interesting question is how the direct and indirect effects of tariffs behave in the face of an injection of, say, half a billion dollars in oil revenues. Lastly, there is the question of how the oil reve~ues are spent and the impact of this expenditure on the evolution of the economy. A major priority of the government's is education and manpower training. Investment in this sector will presumably increase labor productivity and thereby reduce some of the inflationary effects -- particularly in the nontradables sectors -- arising from the oil boom. Investment to increase productivity in agriculture is also under consideration, the motivation being the goals of food self-sufficiency and lower rural-urban migration mentioned earlier. To analyze the implications of oil revenues and of policies to counteract Dutch disease effects, it is clear that we need a model of the Cameroonian economy. The model should be multisectoral, to show the - 5 - differential response between tradables and nontradables. Moreover, it should be price-endogenous, since the cru~ of the expenditure effect lies in its impact on relative prices. Also, the indirect effects of tariff policies are price effects. In addition, the model should allow for substitution between domestically produced and imported goods, since this substitutability is what underlies both the Dutch disease and the levying of protective tariffs to prevent it. In the following section, we present such a model. B. The Multisector CGE Model The computable general equilibrium {CGE) model to be described is a descendant of Johansen's {1960) pioneering work on the Norwegian econo~y. It follows mo-re closely the applications of CGE models to developing countries by,. among others, Adelman and Robinson (1978), Taylor et al. (1980), and Dervis, de Melo and Robinson (1982). Specifically, the present model is a variant of that developed by Dervis, de Melo and Robinson (1982). !/ All CGE models attempt to simulate a market economy where prices and quantities for goods and factors adjust to equate supply and demand. The model can be used to simulate the effects of a change in government policy or in the external environment by introducing the change and solving for the new supply-demand equilibrium. The equations which govern supply and demand in the model, in turn, are based on individual optimizing behavior by agents in the economy: producers maximize profits, consumers maximize utility, etc. Material balance is required for each sector, so that supply must equal demand. Supply consists of domestic production and imports. The ];./ For other variants, see Lewis and Urata (1984), Michel and Noel (1984), Condon, Corbo and de Melo (1985), and Robinson and Tyson (1983). - 6 - different components of demand are intermediate demand, consumer demand, investment demandJ government demand and export demand. Since equilibrium is achieved by adjustment of prices, it is important to specify how each of the components of supply and demand depends on prices. We begin with imports. Import Demand In the classical theory of international trade, a traded good is assumed to be one for which (i) the country is a price-taker in the world market and (ii) the domestically produced good is a perfect substitute for that sold in world markets. This specification leads to the result that the domestic price of a traded good is equal to its world price. Now, for a country like Cameroon, the second assumption is particularly troublesome. First, quality differences are frequently observed between imports and domestic substitutes. Second, at a level of aggregation of eleven sectors, each sector represents a bundle of different goods. For example, the capital goods sector includes some goods (like machine tools) produced in Cameroon and others (like heavy machinery) which are not. Clearly, these two types of goods are not perfect substitutes. In our model, we resolve this problem by relaxing assumption (ii) for imported goods. Instead, we postulate that for any traded good, imports, Mi, and domestically produced goods, x~ 1 0 are imperfect substitutes. Domestic consumers are assumed to have a CES utility function over the two goods, Mi and (l ) c where A. l. ' o. l. are constants and a. 1 , the elasticity of substitution, is given by This formulation implies that consumers will choose a - 7 - mix of M~l and X~D l depending on their relative prices. Minimizing the tost of obtaining a "unit of utility 11 , P.X. l 1 = PD.X~D l l + PM.M. 1 1 (2) subject to (1) yields: M. PD. a. 0. a. ( PM~) l l l l. - ( ) (3) x~D - l 1-o. l l x~ 1 0 would have to be zero. Note that equation (3) allows for a M. richer set of responses, but as a. gets larger, the sensitivity of ~ to PD. 1 x~D changes in l. rises. Also, as a result of this specification, POi i§ no PM. 1 longer equal to PM 1 ; rather it 1s endogenously determined in the model. The variable PM 1 , however, is fixed exogenously (we retain the price-taker assumption of classical trade theory), and is linked to the world price in (4) vthere ER is the exchange rate between US dollars and CFA Francs (fixed parametrically in the model) and tmi is the tariff rate on sector i. Finally, it should be noted that the price of the composite good, Pi, is given implicitly from the model. - 8 - Exports Classical trade theory assumes that a small country faces a perfectly elastic demand for its exports. Again, this assumption may not be realistic for many developing countries. While they may not be able to affect the world market price with their exports, such countries may register a declining market share as, say, their domestic prices rise. To reflect this, we specify Cameroon's exports as facing a constant elasticity demand function: n. n. E. 1 = Eo (--1--) PE. 1 (5) 1 where ni is a weighted average of world prices for good i, E0 is a cnnstant, ni is the elasticity of demand, and PEi is the price of exports, (defined below). Furthermore, export supply may exhibit an excessively strong response to changes in domestic prices. As a domestic price rises, producers are induced to increase supply and domestic consumers to reduce their demand. The net result is a dramatic increase in exports (the difference between supply and domestic demand)~ However, in reality, exports may not rise this fast, for the domestically consumed and exported commodities in the same sector may be quite different. For example, "intermediate goods" includes both electricity (which is not traded) and wood pulp (which is). In addition, there may be a difference in the quality of exported goods vis-a-vis goods for domestic consumption in the same sector. To capture all this, we postulate a constant elasticity of transformation (CET) function between domestically consumed xXD 1 and exported (Ei) goods: - 9 - T $i + (1-y.) XX.D~i J1 /$i D = A.[y.E. X. 1 1 1 1 1 1 (6) D where X. 1 is domestic output, A! 1 and y. 1 are constants and the elasticity of transformation ~. is given by 1 l 1 - cp. • Maximizing the revenue from a l given output, P~ 1 X~ 1 = PD. 1 X~D 1 + PE.E. 1 l (7) subject to (6) yields the following allocation of supply between domestic sales and exports: E. PE. ~i l. -= x~D (PD~ ) (8) 1 l. is the elasticity of transformation. Note this leads to "'· 1 the export price PEi diverging from the domestic price PDi' that is defined as PWE.ER l. PEi = -1+-t-e-.- (9) 1 where PWEi is the dollar price of exports, and tei is the export tax. Domestic Supply of Goods and Demand for Labor Domestic supply of sector i is given by a constant-returns Cobb- Douglas production function, with three types of labor (Lli• L i, L i) and 2 3 - 10 - sector-specific capital, Ki, which is fixed in the short run 1/ (10) where and A. is a constant. 1 At this point, we must specify the labor market so that the dependence of D X. 1 on prices can be seen. Before we show how the demand for labor is determined, however, we must define the "net price" - the unit value added - of sector i: VA P = PD - E P a - td (11) i i j j ji i where aji is· the ( j, i) input-·output coefficient and tdi is the indirect tax rate in this sector. With perfect competition, profit maximization requires that the wage of each factor equal the value of its marginal product: D VA axi P· 1 aL ki = a1.kwk k = 1,2,3 (12) where wk is the average wage rate of skill class k, and aik is that proportion of the average wage earned by workers in skill class k and sector It is also possible to have CES production functions, with the elasticity of substitution estimated separately. - 11 - i. Equation (12) implicity defines labor demand. The dependence of domestic supply x?l on prices and wages is established through equations (10), (11), and (12). The labor market clears when total labor demand (across sectors) for each category k is equal to the (inelastic) supply of labor in that category, -s E L = L i ki k (13) Intermediate Demand As a result of the fixed-coefficient assumption, intermediate demand for material inputs Wi is derived as follows: D W =E a X (14) i j ij j Consumer Demand We assume there is only one representative household in this economy, which buys consumer goods according to fixed expenditure shares. If Ci is consumption demand for good i, then, a.ctot c. = __ 1._ l. P. (15) l. where ctot is total consumption and a.l. is the share spent on good i. Total consumption c, in turn, is taken to be a fixed fraction of disposable income Y: - 12 - ctot = (1 - s)Y (16) Recalling that we have only one household type, we see that disposable income Y is simply total factor earnings less total depreciation, DEPR: VA D Y =E P X - DEPR (17) i i i Note that {17) is based on the assumption that there are no direct taxes in Cameroon. DEPR is depreciation of fixed capital defined as a fixed fraction of the value of capital stock in each sector: DEPR = E D E P h K {18) j j i i ij j where h· 1J· is the fraction of capital good i in sector j's capital stock. Government Demand We assume the government keeps the real level of expenditure on each commodity fixed. Hence, government demand for commodity i is G. 1 = a~ 1 c;tot (19) In our model a~ 1 is zero for all sectors except public administration, for which !3~ 1 = 1. Investment Demand In our comparative static experiments, capital stocks are fixed. Therefore, investment does not add to the capital stock. However, for - 13 - accounting purposes, it is necessary to sp~cify the size and composition of investment demand. We assume that the level of investment is determined by the level of savings in the economy. The latter is the sum of private, public and foreign savings plus depreciation. VA D G S = st P X + R - EP G + DEPR + F.ER (20) i i i i i G VA D where R = ~td.P. X + tm PM + te PD E (21) 1 1 1 i i i i i i and F is the (exogenous) level of foreign savings (expressed in dollars), Having determined the level of savings {and hence investment) from (20) and {21), we must specify how the composition of investment is determined, First, we assume that the investible funds avail4ble to sector j are a fixed fraction Hj of S, Next, these funds are deflated by the price of a unit of capital in that sector, EP i h ij where hiJ' is the (i,j) element of i the capital coefficients matrix. Finally, investment by sector of origin is given by: HS j Z =E h i j ij EP h (22) i i ij Increased demand for investment translates to demand for capital goods. From equation {20), it follows that an increase in foreign savings (F) will, through equation (22), bring about an increase in demand for the capital-goods-producing ~ectors. Finally, we assume inventory demand is a fixed fraction of output: - 14 - D ST. 1 = v.X. 1~ (23) By applying Walras' Law to this system (including the investment- savings identity represented by (21)), we obtain: PD E i i E PW M ---------- = F (24) i i i ER (l+te ) i This can be viewed as an additional equation, defining the trade deficit as being equal to the level of foreign savings. 1/ Supply-Demand Equilibrium Having shown how the different components of supply and demand depend on prices and wages, we can now state the equilibrium conditions necessary to solve the model. X. 1 = W.1 + C. + Z. + ST. + G. 1 1 1 1 i = 1, ••••• ,N (25) Note that we assume all export demand is for the domestically produced good rather than for the composite commodity. In other versions of the Dervis-de Melo-Robinson model, either the level of foreign savings (F) or the exchange rate (ER) is an endogenous variable. Also, these versions include an equation which fixes the aggregate price level. In our model, we fix both F and ER, but allow the price level to adjust endogenously. - 15 - Equations (1)-(25) represent the model we use to simulate the impacts of oil revenues and tariffs. The result of the simulations can be explained by the assumptions underlying (1}-(25). First, by equation (20) we assume that oil revenues accrue to the government which saves all its additional income. 1/ By equation (22), this influx of savings gets translated to an increase in demand for investment goods, mainly capital goods and construction materials. It is not surprising, therefore, that the latter sectors benefit most from an oil boom. Second, equation (13) is essentially an assumption of full employment in the economy. Moreover, with fixed capital stocks, labor inputs determine output in each sector [equation (9)]. Now, if the nontradable sectors expand as a result of the increased demand (from oil revenues), labor is drawn to these sectors and away from the traded goods sectors. In this way, the traded goods sectors as a whole must contract, although some individual sectors may expand. Third, equation (1) states that imports and domestically produced goods in the same sector may not be perfectly substitutable. As a result, when the real exchange rate appreciates in the wake of an oil boom, consumers do not instantly switch all their purchases to imports. Rather, some of this additional demand is satisfied by domestic production. If the demand is significant, the import-substituting sector's output will have a milder effect on the domestic economy than classical trade theory would predict. Since the domestically produced good is only an imperfect substitute, it does net !1 This assumption is relaxed for some simulations. - 16 - register as strong an increase in demand, and hence in output, when a tariff is levied on the import. We turn now to an exposition of how the system of equations (1)-(25) can be implemented in GAMS. III. THE CAMEROON MODEL IN GAMS A. Some GAMS Syntax Before turning to a line-by-line description of the Cameroon model in GAMS, it may be useful to describe the GAMS syntax. The purpose of the naming convention is to make the GAMS statements' transparent. Since the GAMS representation is written in straightforward algebra, few of the operators require explanation here (See the GAMS manual for more detailed information). 1. Data The data in an economic model are generally of two types, parameters and variables. CAMS recognizes these types as well as a third, called SCALAR, which is a parameter of dimension une. Scalars and parameters are treated differently from variables in CAMS for the purpose of assigning values to them. In general, however, there are three ways of supplying values for scalars and parameters in GAMS: (i) by assignment: for scalars, ER0 = 1.0 for parameters, BETA(!) = 10; (ii) togeth~r with the definition: SCALAR ERi REAL EXCHANGE RATE I 1 I ; - 17 - (iii) in a tabular form: TABLE WLO(LC,I) WAGE BILL BY SKILL CATEGORY AND SECTOR DOMESTIC EXPORT UNSKILL 55.9 91.3 .SKILL 212.5 34.0; Note that each GAMS statement ends with a semicolon. 2. Supplying Values f~~ Variables In CAMS, variables may have a dimension of zero or greater, and they are associated with four values, the level value, the lower bound value, the upper bound value and the marginal value. Here we describe only the first three. The syntax for variables of zero dimension: X.L = 10 ; (the level value) X.LO = 5 ; (the lower bound) X.UP = 20 ; (the upper bound) In addition, it is possible to fix the level of a variable in one operation, by using the FX command: X.FX = 10 ; For dimensioned variables, the syntax is very similar. For example, to set a lower bound for the variable P defined on set I, P(I), the GAMS statement is: P.LO(I) = 0.01; The .L, .UP and .FX suffixes are used analogously. 3. Operators Like most other computer systems, GAMS uses the operators + , - , * ,I , and ** for plus, minus, Multiplication, division, and exponentiation respectively. In addition, CAMS has a special operator, the $ operator, that - 18 - can be read "such that". For instance, the statement X(I)$IT(I) = 1 ; reads "X of I, such that I is an element of IT, equals one", As another example: Y(I) = l$Z(I) ; reads "if Z(I) is non-zero then assign the value 1 to Y(I), otherwise assign zero. 4. Functions In the CGE models, we make extensive use of the SUM and PROD functions. These correspond to the familiar E and IT signs. For instance, E X is written as SUM(!, X(!)). Similarly, the expression IT X is written i i i i as PROD(!, X(I)). 5. Equality and Inequality Constraints GAMS identifies constraints by their name: PMDEF(IT) •• PM(IT) =E= PWM(IT)*ER*(l + TM(IT)) is an equality constraint (an equation) named PMDEF defined over the set IT'. The two periods following the equation name and its domain signal that what follows is the contents of the equation. The =E= is GAMS' way of saying that the constraint must hold as an equality. In addition to the =E=, GAMS recognizes =L= (less than or equal to), and =G= (greater than or equal to). 6. Models and the SOLVE Statement In GAMS, a model is a collection of constraints or equations. One must specify which constraints enter the model. This is done with the MODEL statement: MODEL CAMCGE CAMEROON MODEL I PMDEF, PEDEF, ••• , OBJ I ; states that the model named CAMCGE is the Cameroon model, and it contains the equations PMDEF, PEDEF, ••• , OBJ. It is possible to include several models, containing different sets of the defined equations, in a GAMS program. - 19 - The syntax for solving the mo~el is: SOLVE CAMCGE MAXIMIZING UTILITY USING NLP which states that we wish to solve the model CAMCGE, and our objective is to maximize the variable named UTILITY; the model being non-linear, we choose to have it solved by a non-linear optimization program (NLP). GAMS itself chooses the best available solver for us. B. CAMCGE The complete GAMS listing of the Cameroon model is presented in appendix 1. The program contains eight sections. In the first section~ all the sets and all the parameters containing base year data used in the model are specified. The input data are entered in the second section, and model calibration takes place in section three. The fourth section lists all the variables in the model and is followed in section five by a listing of all the eq~ation names in the model. The sixth section contains the actual equations, the seventh defines the initial values of the variables, and section eight closes the model by fixing the levels of the exogenous variables. 1. Sets and Initial Variables All CGE models require the definition of sets: the set of productive sectors, the set labor skill classes, the set of households, etc. These describe the level of disaggregation while providing a notation for indexing. In GAMS, the set of productive sectors I = {sector l, sector 2, ••• } is defined as: SET I PRODUCTIVE SECTORS /SECTOR!, SECTOR2, •• / j Note that in GAMS the slashes Hff" replace the curly brackets "{ }". As the GAMS listing indicates, in the Cameroon model, the set I contains the eleven productive sectors: - 20 - AG-SUBSIST (Food Crops) AG-EXP+IND (Industrial and Export Crops (Cash Crops)) SYLVICULT (Forestry) IND-ALIM (Food Processing) BIENS-CONS (Consumer Goods) BIENS-INT (Intermediate Goods) CIM-INT (Construction Materials (Cement) and Base Metals) BIENS-CAP (Capital Goods) CONSTRUCT (Construction) SERVICES (Private Services) PUBLIQUES (Public Services) The rationale for this level of aggregation is as follows: in the primary sectors, food crops and cash crops have different demand structures, and forestry differs from the other agricultural sectors in its production structure; in the secondary sectors, food processing has a very distinct pattern of intermediate consumption, and construction materials is important for industrial policy analysis; finally, in the tertiary sectors, public and private services are treated separately to allow for differences in their composition of demand. This distinction also allows an analysis of the competition in factor markets between the government and the private sector. The set LC of laBor skill categories contains RURAL (rural labor) URBAN-UNSK (urban unskilled labor) URBAN-SKIL (urban skilled labor) Two subsets are defined on these basic sets. They are: IT(I) (tradable sectors, containing food crops, cash crops, forestry, food processing, consumer goods, intermediate goods, and capital goods); and IN( I) (nontradable sectors, containing construction and private and public services) In the GAMS program, the contents of IT and IN are assigned dynamically according to the rule that a sector is traded (member of IT) if its base year imports are strictly positive; otherwise the sector is nontraded - 21 - (member of IN). This assignment takes place in section 2 of the GAMS listing. The statement "ALIAS (I,J)tt means that the set J is defined to be equivalent to I so that they can be used interchangeably and independently of each other in the same expression. The initial values of the model variables are treated as parameters and are used to calibrate the mode~, and to initialize the model variables. There is therefore a one-to-one m4pping between the parameters containing the initial values and the model variables. We follow a naming convention whereby the initial value parameter names are the same as the ·~ariable names except for the addition of a zero at the end. For example M~I) refers to sectoral imports, and MO(I) refers to the initial (parametric) level of impd~ts. 2. The Input Data The input data contains base year data as well as parameters such as input-output coefficients. The table IO contains the intermediate input- output coefficients matrix (blanks are zeroes) and by declaring it as a "TABLE" we can define it for reference in the model equations. The same applies for the capital composition matrix, called IMAT, the wage proportionality matrix, WDIST, and the employment matrix, X'LE. Table ZZ, however, simply contains the base year values of many of the parameters. The value of parameters are extracted from the ZZ table by assignments. 3. Model Calibration The purpose of the model cali!>ration sector is to make sure that a solution of the model, using only base year data inputs, will yield the input data. This is done by finding values of shift and share par·ameters for ~ production functions, etc., that are consistent with the base data. For example, in the Cameroon model, the sectoral production functions a1:e - 22 - Cobb-Douglas. The production functions and the corresponding first-order conditions for profit maximization are (see 3.3.2.): x? l = A. l n L i,t te:LC ai,~ K (1 -nEe:LCai,n) k k (26) = a. n PV~-D .-~. (27) lpk l l The base year data contain information on the value of This information is sufficient to determine W. nL• n l,k l,~ (28) p~A X~ l l Knowing the set of ai,t means that we can find Ai from (26) by: (29) This procedure is also followed for the production functions, Armington functions and CET functions. 4. Model Variable Names All the variables, both endogenous and exogenous, that appear in the model are listed in the variable list section. The list groups variables for convenience; the order of the variables and the grouping have no effect on the model's solution. Note that an objective variable, OMEGA, is listed. This is mostly for convenience in case an optimization run with the model is attempted. Apart from giving shadow prices on constraints, the objective - 23 - function is irrelevant for simulation runs. This is so because for simulation purposes, the model must contain as many endogenous variables as equations (the system is said to be square). In such a case, the model will have a unique solution (if the model is well specified), and there will be no room for movement in the objective function (see III.6). 5. Equation Names The list of equation names follows the variable name list. Again a grouping of equations into blocks is presented for convenience only. A comparison of the variable name list and the equation name list is helpful when one is setting up the model. Of course, many of the endogenous variables are co-determined and it is impossible to say that equation 1 determines variable 1. However, for debugging purposes the matching of equations and unknowns is often useful. 6. Model Equations The actual model is written down in algebraic form in this section. The order of the equations does not conform to that in Section II. In the following substitution,, we will show the correspondence between the two sets of equations. Equation names appear first, followed by two periods. The symbol =E= is the GAMS representation of an identity restriction, and it is only used in the model equations. Elsewhere, in the Calibration section for· example, the ordinary equals sign is used. Th~ ordinary equals sign is interpreted, as in most computer programs, as a dynamic assignment, whereas the =E= is interpreted as a static identity condition~ Note that some equations are listed in the Equation Name section as operating over the entire set I but appear in the Model Equation section as indexed over a subset of I. This occurs in the case of the PMDEF equation. The rule we have followed with subsets is to use them in the Calibration - 24 - section, the Model Equation section, and the Initialization section, but to use the whole set index in the Variable !lame and Equation Name sections. When counting equati~~ns, however' the relevant set is that over which the equation is defined in the Model Equations section. Note finally that the objective function, OBJ, defines a Cobb-Douglas utility function. This is purely for convenience; the syntax of the SOLVE statement in GAMS requires that an objective variable be specified. As mentioned above, the inclusion of an objective function is superfluous in a square system. A solution will be declared optimal.as soon as a set of values for the endogenous variables has been found that satisfies simultaneously all the equations. However, one must be careful to specify the objective function so it does not contradict the rest of the model. In the Cameroon model, we assume a linear expenditure system for consumers. The underlying utility function is Cobb-Douglas. Therefore, when we specify the objective function as static consumer welfare, we do not conflict with the rest of the model. This choice of objective function has also been made to have an immediate economic interpretation of shadow prices. These will namely reflect the presence of bottlenecks in the economy that prevent a higher level of consumer welfare. Thus, the model yields much more structural information when solved with an optimization algorithm than t~ith an ordinary simulation system" Most of the equations should be self-explanatory. However, since their order is different we provide a. "key" linking the .model equations in section (II} to that GAMS equation listing. - 25 - Correspondence between Model Equations (Section II) and GAMS Listing of CAMCGE GAMS Equation Model Equation in Remarks Section II Price Block PMDEF 4 PEDEF 9 ABSORPTION 2 SALES 7 ACTP 11 PKDEF 22 PK is the denominator on the r.h.s. of (22) Output and Factors of Production Block ACTIVITY 10 PROFITMAX 12 LMEQUIL 13 CET 6 EDEMAND 5 ESUPPLY 8 ARMINGTON 1 COSTMIN 3 XXDSN XSN Accounting identities necessary because there are no exports or imports of Demand Block nontradables. INTEQ 14 DSTEQ 23 CDEQ 15 + 16 GDP 17 GREQ 21 GDEQ 19 TARIFFDEF 21 INDTAXDEF Second term on rhs. 21 First term on rhs. DUTYDEF 21 DEPREQ Third term on rhs. 18 TOTSAV 20 PRODINV 22 IEQ 22 CAEQ 24 EQUIL Implied by Walras' Law 25 - 26 - 7. Initialization To provide an initial point in the search for a solution, the model variables are set equal to the base-year levels. It is helpful to initialize as many of the variables as possible. The syntax is straightforward: for X.L(I) = XO(I), read "the level of variable X(I) is equal to XO(I)". B. Exogenous Variables In this last section, exogenous variables are fixed. The GAMS syntax for doing this is similar to the level assignment (see 2.5.2): For K,FX(I) = KO(I), read "the variable K(I) is fixed to its base year value, KO{I)". The model's closure is also specified here. We fix the households' marginal propensity to save (MPS). This is the savings-driven closure described by Dervis, de Melo and Robinson (1982, Chapter 7). Note that GAMS allows for great flexibility in specifying the model's closure rule. Thus, for instance, one could easily let MPS vary and instead exogenize government savings say by dropping the statement MPS.FX=xxxx and inserting a statement GOVSAV.FX=xxxx. The last step in the GAMS listing of the model are to name the model, we call it CAMCGE, and say that it includes "ALL" of the equations we have entered, and then ask for a solution of the model. Because the model is non- linear, we ask to use a non-linear programming (NLP) algorithm to solve it. IV. TESTING AND DEBUGGING THE MODEL Basic Tests For square CGE models there are two general consistency tests. First, the CGE model represents a circular-flow so there can be no leakages in the model. Second, the model must be homogenous of degree zero in pricea. - 27 - The first test of the CGE model's consistency amounts to saying that a solution should yield a balanced SAM. This condition can be tested by checking whether row sums are equal to column sums. If they are not, some inconsistencies are present in the model. The base year model solution should be a balanced SAM that reproduces the initial conditions data set with all domestic final good prices at unity. Having initial period prices equal to one is for convenience; it is helpful for interpreting the results of subsequent experiments. If the model solution in the base year is not the same as the equilibrium, initial conditions data, a problem exists. To help in debugging, limit the number of iterations to one and then examine the model results. Begin the search for the problem by examining the equations that determine the variables that have changed from their base year levels. The second consistency check, the homogeneity condition, can be tested by simply doubling the level of the variable that acts as a numeraire. The result should be a doubling of all absolute prices and nominal magnitudes, but no change in real quantities or relative prices. If this is not the case, the model contains at least ·one "implicit numeraire". An "implicit numeraire" problem can occur for a number of reasons. The most obvious case is that a price or a nominal magnitude is fixed independently of the numeraire. Of course, the level of the fixed price is expressed in terms of the numeraire, so when the numeraire is doubled, the fixed price should be doubled (exogenously) as well. The implicit numeraire problem can also be caused by mixed dimensions in equations. If the equation can be rearranged so that the left-hand side contains variables expressed in current values and the right-hand side contains real quantities, an implicit - 28 - . assumption has been made that the price of the right-hand side variables is unity and thus can be omitted. Check this by performing units analysis on the model equations. For example, suppose one forgets to inflate the capital stock divide total investment by the sectoral capital good's price when computing investment by sector of destination. The equation would read: ilK. ~ = H.Itot l. rtot is a value while K. is measured in physical units, and H. is ~ l dimensionless. The units analysis reveals that we have~ (value) = (quantity) which of course does not make sense. We have thereby specified as the implicit numeraire the sectoral price of capital goods, E b P j ij j Sorting Out Infeasibilities Infeasibilities in square CGE models occur because two different ways of determining the same variable always give different results for the set of data used. The reason for this can either be a misspecified model or inconsistent data. Here we shall only look at the data side. There are two typical sources of inconsistent data. The fi~st is that the base year SAM is not balanced. Enough has been said about this already. The second is that a number of coefficients do not satisfy adding-up conditions. A few examples of such conditions are: - 29 - Cobb-Douglas demand system coefficients must sum to unity. If this is not the case, the consumers' budget from the income side will differ from the use side and the model will contain a leakage. The column sums of the capital composition matrix and the sum of sectoral investment allocation shares must all be unity for a reason similar to that given above. Ex~onents of Cobb-Douglas production functions must sum to unity. If they sum to more than one there will be increasing returns to scale; if they sum to less than one there will be diminishing returns to scale. In both cases, a marginal productivity remuneration of factors of production will not exhaust the value added produced. Even small rounding errors on these coefficients may cause numerical infeasibilities. The safest procedure is therefore to calibrate the coefficients to satisfy the adding up conditions. Thus, it is generally advisable to compute n-1 of the parameters that m~st satisfy an adding-up n-1 requirement, then simply use (1- I parameter.) to denote to nth. i=1 1 A common problem is that the base year solution is s_lightly infeasible - all infeasibilities are very small - even though the above conditions are satisfied. In this case, small data errors may be scattered over the whole model. One possible way out is to do a very simple SAM balancing: Find a fixed variable that acts as a strong restriction o.n the model. In the prototype model this could be the balance of trade deficit, F, or the marginal propensity to save, MPS. Free up this variable - thus making the model rectangular - and solve the model again. If the change in the newly freed V"lriable is small, use the solution value as input data. - 30 - Runtime Errors and Slow Convergence Some possible problems in solving CGE models are due to limitations in the solution algorithms. Unfortunately, the perfect non-linear problem solution algorithm does not (yet) exist, so the user has to do something to condition the model for the algorithm. Fortunately, GAMS reduces this part of the user's job to a minimum. Here we shall give four hints of what the user should be aware of: It is in general preferable to set up equations with multiplications instead of divisions. (If the denominator approaches zero, the result of the division will aproach infinity). Exponents and logarithms can cause problems: if the variable that is exponentiated (or log'ed) gets very close to zero or becomes negative during iterations, these operations will cause runtime errors. Even though the algorithm may recover from such cases, it is advisable to put lower bounds of .01 or more on such variables. For CES and CET functions, one should attempt to restrict their domain to cases where p is not too small. Otherwise, the term 1/p will approach infinity and cause problems. As long as the solution algorithms do not automatically scale the model, the user may have to do so. The target of scaling is to get the level of all variables as close to each other as possible. Because some prices are usually set to one, this m"ans that scaling should be done so that the value of all variables ~re distributed around one. If necessary, scaling should be clone in a way that makes the results intelligible. Thus, scaling by powers of 1000 is in general advisable. To prepare for a possible rescaling of the model - 31 - - and a£ course for documentation purposes - one should always include the unit of measurement both on variables in the variable name list and on equations in the equation name list. A different - but equivalent - formulation of the model may cause the speed of convergence to increase. For example, the choice of which equation to omit in accordance with Walras' Law is of little importance from a theoretical point of view. Numerically, however, the model may converge more quickly with a particular equation omitted. Often, the original choice is to omit the current account equation. If this is the case, and it gives convergence problems, a good choice may be to omit the savings-investment balance ~nstead. These are generally chosen because they tend to be highly non-linear equations. V. SIMULATION USING THE CGE To this point we have only described the steps required to set up a CGE model. Most of the work in constructing a CGE model occurs during the set-up phase. Model design, the choice of issues to be addressed, data collection, model implementation and model debugging must occur regardless of the choice of software. GAMS allows some economies of implementation to be exploited because, due to its algebraic representation, it allows the model to be entered parsimoniously on the computer. Still, the full power of the software and the flexibility it permits can only be appreciated after all those important steps have been finished, and one begins to use the model for analysis. In this section we will provide some examples of simulation using the model of Cameroon described in chapter 3. - 32 - Simulation The majority of the applications with CGE models have been simulation analyses. In a simulation, one or more exogenous variables are perturbed from base or reference path levels, and the resulting values of the endogenous variables are compared with their base run counterparts. We now consider a series of simulations with the Cameroon model. We present first the results of some comparative static experiments where, from the base year, the model is driven to a new equilibrium by changes in some exogenous or policy variables. In these experiments, the capital stock and labor supply are held constant, whereas in the dynamic experiments they are updated in each period. We use the comparative static experiments to explore the effects of three exogenous changes: (1) an increase in oil export revenues (this could also represent the patriation of other types of foreign earnings or a sudden injection of foreign exchange from any source); (2) the pursuit of food self-sufficiency through increased tariffs on food imports; and (3) the institution of.an industrial policy which increases import tariff protection for intermediate goods and construction materials, to avoid deindustrialization. Since oil revenues were very small during the base year of the model, it provides a base case against which comparative static experiments with high oil revenues can be evaluated. We experiment with $500 million or 105 billion CFA Francs of oil revenues. The variable name in CAMCGE is FSAV. To run this experiment, two lines suffice: FSAV.FX = 500; SOLVE CAMCGE MAXIMIZING OMEGA USING NLP; The first sets up that experiment, the second asks for a solution. - 33 - In the Cameroon model, oil revenues are channelled directly into the total savings pool available for investment. In the first experiment, investment increases across sectors by an average of 34 percent; domestic prices rise 27 percent and wages 25 percent (see Table 1). Table 1: BASE FOREIGN EARNINGS EXPERIMENT Oil Revenues Channelled to investment Percentage change in: Investment 33.7 Domestic prices 27.2 Composite prices 20.7 Wages 25.4 This aggregate picture of the investment boom in the first ex- periment, with rising prices and wages, coincides with a general worsening of the trade position.. However, evidence of the Dutch diseas~ is best indicated in the sectoral breakdown of price, output, and trade changes. The rise of domestic goods prices in relation to foreign goods prices is most apparent in the prices of composite goods (see Table 2). Traded sectors show the smallest increase because the traded component holds constant at the world price while only the price of the domestically produced and sold portion responds to rising domestic demand. Thus the increases in domestic prices and wages worsen the trade position of the countr.":· both because productive resources move to more profitable nontraded s.ectors (where prices - 34 - are increasing faster) and because domestic traded goods face some price competition from foreign goods, depending on how substitutable they are, in both domestic and export markets. The investment boom generated in this experiment causes imports to grow by 21 percent and exports to fall by 13 percent. Some parallel results occur in changes in the structure of production (see Table 3). Production grows most significantly in construction--both a nontraded and investment good--while it declines severely in cash crops, the Table 2: BASE FOREIGN EARNINGS EXPERIMENT Percentage change Percentage change Sector in domestic in composite goods price goods price Food crops 25.1 24.9 Cash crops 22.5 9.4 Forestry 21.9 21.8 Food processing 26.0 18.2 Consumer goods 24.1 17.5 Intermediate goods 28.9 16.0 Cement & base metals 21.2 6.5 Capital goods 40.8 1.8 Construction 33.8 33.8 Private services 27.8 24.2 Public services 25.6 25.6 Total 27.2 20.7 traditional export sector, which loses competitiveness as domestic costs rise. But the expected pattern of output changes is broken by other tradable sectors, notably capital goods, which shows a high growth rate. This is due to the structure of demand for the capital goods sector as it supplies investment goods to the large investment boom. Another tradable sector, - 35 - cement and base metals does not suffer ~s much as might be expected given the importance of foreign competition, since the booming construction sector demands a large share of its output. The small expansion in two other tradable sectors, food crops and consumer goods, occurs because trade is so small in these sectors that they behave more like nontradables. Table 3: BASE FOREIGN EARNINGS EXPERIMENT Percentage Sector change in output 1. Food crops 2.7 2. Cash crops -14.2 3. Forestry -6.7 4a Food processing -7.4 5. Consumer goods 0.9 6. Intermediate goods -2.7 7. Cement & base metals -4.7 8. Capital goods 10.2 9. Construction 23.2 10. Private services 0.1 11. Public services -0.4 Total 0.7 !1 The effect of oil revenues on foreign trade is as could be expected (see Table 4). Imports rise in all traded sectors and exports decline, both because productive resources are drawn into nontraded sectors and also because domestic traded goods prices, not perfectly tied to international prices, are allowed to rise. Given our assumptions of fixed capital stock and a fully employed fixed labor supply, the total change in real output is insignificant in these comparative static experiments; only the intersectoral structure of output changes is relevant. These assumptions are relaked in the dynamic experiments. - 36 - Table 4: BASE FOREIGN EARNINGS EXPERIMENT Sector Exports Imports 1 Food. crops -11.5 44.0 2 Cash crops -14.4 7.2 3 Forestry· -7.8 4.8 4 Food processing ·-20. 7 31.5 5 Consumer goods -·17 .5 33.3 6 Intermediate goods -9.9 14.6 7 Cement & base metals -·12.5 13.7 8 Capital goods 0.3 32.0 9 Construction o.o o.o 10 Private services ... 8.2 10.7 11 Public services o.o o.o Total -13.2 21.1 Real wages incrr~4se by 3.9 percent in the economy overall, but there is variation in the distribution ~cross skill categories: Qhange in Real Wage Rate Rural unski.lled 1.8% Urban unskilled 5.4% Urban skillt~d 5.5% The wage differential developing between urban and rural unskilled workers has serious implications for the effect of oil revenues on rural-urban migration and productivity in agriculture. Any differences in rural and urban household consumption patterns will multiply the effects of this shifting income distribution. - 37 - One common technique for achieving food self-sufficiency is to increase food import tariffs to restrict imports, support domestic prices, and thus encourage local production. We perform an experiment where this tariff rate is doubled. To simulate this, we create the file: TM.FX{"AG-SUBSIST") = 2*TM0(nAG-SUBSIST"); SOLVE CAMCGE MAXIMIZING OMEGA USING NLP; Again, the semi-complementarity between home goods and imports incorporated in the model constrains the transfer of demand from imports to domestic goods. Indeed, the near self-sufficiency in food crops in the base year makes it not surprising that an experiment doubling the level of the import tariff on food crops produces virtually no effect. The tiny drop in food imports is insignific~nt. Qomestic food crops output remains unchanged. ·output and trade in other sectors also show virtually no effect, and increase in tariff revenues is very slight. Thus the stability of output in the food crops sector can only be tested in the dynamic context where several years' enactment of different investment plans, population growth, and migration may affect that sector's productivity and draw people toward or away from the production of food crops. Another sectoral policy experiment, one that doubles import tariffs for intermediate goods and construction materials, has a more significant impact on the structure of output, relative prices, and trade. Doubling the tariffs is one possible industrial policy that would seek to protect and encourage output in these two manufacturing sectors. While this policy - 38 - succeeds in the case of construction materials, it fails for intermediate goods (see Table 5). Table 5: DOUBLE IMPORT TARIFFS SECTORS 6 AND 7 Percentage Sector Change in Output 1 Food Crops -o.i 2 Cash Crops 0.2 3 Forestry -0.1 4 Food Processing -2.9 5 Consumer Goods -1.8 6 Intermediate Goods -2.1 7 Cement & Base Metals 5.2 8 Capital Goods 5.6 9 Construction 6 .• 3 10 Private Services o.o 11 Public Services -0.1 The pattern of output is mostly explained by the structure of demand for the two sectors targeted by this policy. About half of the composite good in sector 6 is sold to final consumption, while in sector 7, all of the composite good is sold to intermediate consumption. In the model, intermediate demand does not respond to price changes since it behaves according to fixed technological coefficients; price changes merely alter the cost of production. As the increased tariffs in sectore 6 and 7 raise the price of those composite goods, the intermediate demand for construction materi-als remains inflexible to this change while the consumption demand for intermediate goods falls in response to the price incre4se •. It is also worth noting that sector 6 is a major purchaser of its own output, absorbing nearly half of the total supplied to intermediate demand. - 39 - Thus, raising the tariff on intermediate goods acts to increase the cost of producing them. This situation arises in part because of the diversity of the items which have been aggregated into sector 6. In contrast, the major consumer of sector 7 1 s output, buying nearly half of its total supply, is construction, a sector which grows significantly in this experiment. The higher tariffs cause government tariff revenues to increase 39 percent, and with government consumption fixed, this contributes to higher total savings and fuels an increase in total investment of 9 percent. This investment boom keeps demand for construction strong, so its output grows despite the fact that the sector must pay more for one of its inputs. The price changes reported in Table 6 reflect the influence of the new tariffs ~n the imported components of goods in sectors 6 and 7 and the pattern of direct and indirect demands in the economy. The impact of the tariff increases on the pattern of trade shows that imports of construction materials are hardly affected, dropping less than one percent, while imports o£ intermediate goods fall by 7.8 percent. Those sectors which must pay more for intermediate inputs because of the higher tariffs, have less value added to distribute to factors of production. In the course of this experiment, total value added falls and therefore household income and consumption decline as well. Real wages in particular fall by 3.3 percent on average. The distribution o£ real wage cbanges across sectors is as follows: Rural unskilled -3.4% Urban unskilled -3.1% Urban skilled -3.2% - 40 - In general, this policy is not particularly favorable to primary sectors nor to the rural unskilled workers whom they employ. . Table 6: DOUBLE IMPORT TARIFFS SECTORS 6 AND 7 Percentage change Percentage change in domestic in composite Sector goods price goods price 1 Food Crops -1.9 -1.9 2 Cash Crops -1.1 -0.5 3 Forestry -5.9 -5.9 4 Food Processing 0.9 0.7 5 Consumer Goods -0.3 -0.2 6 Intermediate Goods 1.6 7.3 7 Cement & Base Metals 10.4 17.4 8 Capital Goods 4.4 0.2 9 Construction 6.3 6.3 10 Private Services -2.0 -1.8 11 Public Services -1.0 -1.0 12 Total 0.2 1.4 CONCLUSION In this paper we described a multisector CGE model of Cameroon which would be used to analyze the policy questions arising from the country's oil revenues. We showed how the model could be solved using GAMS and presented and interpret€d some experiments with the model. The purpose of the paper was to show how a simple CGE model can be implemented on a software system hitherto used only for optimization exercises.!/ However, that GAMS is an optimization package permits a richer !/ See Dahl, et.al. (1986) for an optimization exercise within the same Cameroon model. - 41 - set of applications of CGE models. For example, dynamic optimization experiments can now be performed where we optimize over a sequence of equilibria. This, and the fact that GAMS allows changes in the model's equations without having to alter the algorithm, will broaden analysts' capabilities in using economy-wide models to understand development policy issues. - 42 - APPENDIX CAMEROON CGE MOOEL 05112187 22:35:46 PAGE GAMS 2.04 IBM CMS 2 SET I SECTORS a lAG-SUBSIST FOOD CROPS 4 AG-EXP+IND CASH CROPS 5 SYLVICULT FORESTRY 6 IND-ALIM FOOD PROCESSING 7 BIENS-CONS CONSUMER GOODS 8 BIENS-INT INTERMEDIATE GOODS 9 CIM-INT CONSTRUCTION MATERIALS 10 BIENS-CAP CAPITAL GOODS 11 CONSTRUCT CONSTRUCTION 12 SERVICES PRIVATE SERVICES 13 PUBLIQUES PUBLIC SERVICES I 14 Ii(I) TRADED SECTORS 15 IN (I) NONTRADED SECTORS 16 LC 17 ALIAS (I,J) LABOR CATEGORIES I RURAL • URBAN-UNSK , URBAN-SKIL I 18 19 20 *PARAMETERS 21 22 PARAMETER DELTA(!) 23 ARMINGTON FUNCTION SHARE PARAMETER AC(I) ARMINGTON FUNCTION SHIFT PARAMETER (UNITY) 24 RHOC(I) (UNITY) 25 ARMINGTON FUNCTION EXPONENT RHOT(l) CET FUNCTION EXPONENT (UNITY) 26 AT(I) (UNITY) 27 CET FUNCTION SHIFT PARAMETER GAMMA(l) CET FUNCTION SHARE PARAMETER (UNITY) 28 ETA(I) (UNITY) 29 EXPORT DEMAND ELASTICITY AD(I} PROOUCT:ON FUNCTION SHIFT PARAMETER (UNITY) .p. 30 CLES(I) (UNITY) w 31 PRIVATE CONSUMPTION SHARES GLES(I) GOVERNMENT CONSUMPTION SHARES (UNITY) 32 DEPR{I) (UNITY) 33 DEPRECIATION RATES DSTR(I) (UNITY) 34 KIO(I) RATIO OF INVENTORY INVESTMENT TO GROSS OUTPUT (UNITY) 35 SHARES OF INVESTMENT BY SECTOR OF DESTINATION (UNITY) TMO(I) TARIFF RATES 36 TE(I) (UNITY) 37 EXPORT DUTY RATES ITAX(I) INDIRECT TAX RATES (UNITY) 38 ALPHL(LC, I) (UNITY) 39 LABOR SHARE PARAMETER IN PRODUCTION FUNCTION (UNITY) 40 41 *DUMMIES TO HOLD INITIAL DATA 42 43 MO(I) VOLUME OF IMPORTS 44 EO(I) ('79-80 BILL CFAF) VOLUME OF EXPORTS 45 XDO(I) ('79-80 BILL CFAF) 46 VOLUME OF DOMESTIC OUTPUT BY SECTOR ('79-80 BILL CFAF) KO(I) VOLUME OF CAPITAL STOCKS BY SECTOR 47 I DO (I) ('79-80 BILL CFAF) 48 DSTO(I) VOLUME OF INVESTMENT BY SECTOR OF ORIGIN ('79-80 BILL CFAF) 49 INTO (I) VOLUME OF INVENTORY INVESTMENT BY SECTOR ('79-80 BILL CFAF) 50 VOLUME OF INTERMEDIATE INPUT DEMANDS ('79-80 BILL CFAF) XXDO(I) VOLUME OF DOMESTIC SALES BY SECTOR 51 XO(I) ('79-80 BILL CFAF) 52 VOLUME OF COMPOSITE GOOD SUPPLY PWEO(I) WORLD MARKET PRICE OF EXPORTS ('79-80 BILL CFAF) 53 PWMO( I) (UNITY) 54 WORLD MARKET PRICE OF IMPORTS (UNITY) PDO{I) DOMESTIC GOOD PRICE 55 PEO(I) DOMESTIC PRICE OF EXPORTS (UNITY) 56 PMO(I) (UNITY) 57 DOMESTIC PRICE OF IMPORTS (UNITY) PVAO(I) VALUE ADDED PRICE BY SECTOR (UNITY) CAMEROON CGE MODEL 05112187 22:35:46 PAGE 2 GAMS 2.04 IBM CMS 58 QD(I) DUMMY VARIABLE FOR COMPUTING AD(I) (UNITY) 59 XLLB(l,LC) OUMMV VARIABLE (L MATRIX WITH NO ZEROS) (UN! TV) 60 WAO(LC) AVERAGE WAGE RATE BY LABOR CATEGORY ('79-80 MILL CFAF PR WORKER) 61 LD(LC) EMPLOYMENT (1000 PERSONS) 62 LSO(LC) LABOR SUPPLIES BV CATEGORY (1000 PERSONS) 63 64 65 *BASE DATA 66 67 WAO("RURAL") = • 11 ; 68 WAO("URBAN-UNSK") = .15678 69 WAO( ''URBAN-SKIL") = 1.8657 ; 70 71 SCALAR 72 ER REAL EXCHANGE RATE (~NITV) I .21 I 73 GRO GOVERNMENT REVENUE ('79-80 BILL CFAF) I 179.00 I 74 GDTOTO GOVERNMENT CONSUMPTION ('79-80 BILL CFAF) I 135.03 I 75 CDTOTO PRIVATE CONSUMPTON ('79-80 BILL CFAF) I 947.98 I 76 FSAVO FOREIGN SAVING ('79.,..80 BILL DOLLARS) I 36.841 I 77 78 79 TABLE IO{I.J) INPUT-OUTPUT COEFFICIENTS (UNITY) 80 81 AG-SUBSIST AG-EXP+IND SVLVICULT IND-ALIM BIENS-CONS BIENS-INT CIM-INT BIENS-CAP CONSTRUCT SERVICES PUBLIQUES 82 83 AG-SUBSIST .03046 .30266 .00206 84 AG-EXP+IND .04120 .01518 .02043 . 01123 .00669 as· SYLVICULT .00243 .02106 ~ 86 IND-ALIM .00341 .00629 .03241 .01234 .00503 .00092 ~ 87 BIENS-CONS .01532 .00105 .05385 .00435 .00103 .00338 88 BIENS-tNT .00676 .12385 .02095 .03794 .08309 .23461 .18289 .01567 . 14665 89 CIM-INT .00929 .08466 .00002 .00025 .00017 • 11238 .05095 .05593 .27608 .11722 • 18643 90 BIENS-1CAP .00041 .00018 .00971 .02427 .00931 .01229 .05259 .02053 .05013 .02622 .00389 91 CONSTR.UCT .00472 • 00113 .00318 • 10456 .01831 .05302 .00172 .00031 .01457 .00385 92 SERVlC~S .00375 .00394 .30649 .26666 • 10100 .26072 .23006 .11793 .09922 • 13692 • 13728 93 PUBLIQUES .00022 .24145 .00293 .00327 .00536 .00539 .00957 .00486 .00081 .00447 .00219 94 - 95 96 TABLE IMA~{I,J) CAPITAL COMPOSITITON MATRIX (UNITY) 97 98 AG-SUBSIST AG-EXP+IND SVLVICULT INO-ALIM BIENS-CONS BIENS-INT CIM-INT BIENS-CAP CONSTRUCT SERVICES PUBLIQUES 99 100 AG-SUBSIST .23637 101 BIENS-CAP .59530 .60608 .63876 .60608 .78723 .63876 .63876 .60608 .71728 . 17610 102 CONSTRUCT . 17610 • 16833 .39392 .36124 .39392 .21277 • 361 24 • 361 24 .39392 .28272 .82390 ,-03 .82390 104 105 TABLE WDIST(I,LC) WAGE PROPORTIONALITY FACTORS (UNITY) 106 107 RURAL URBAN-UNSK URBAN-SKIL 108 109 AG-SUBSlST 1.01890 .71491 110 AG-EXP+IND .49556 .34774 .29222 111 SVLVICULT 3.26280 2.28900 1 .92320 112 IND~ALIM 1.45710 1.02230 .85902 113 BIENS-CONS 1.13350 .79531 .66829 CAMEROON CGE MODEL 05/12/87 22:35:46 PAGE 3 GAMS 2.04 IBM CMS 114 BIENS-I NT 3.10740 2,.18060 1. 83230 t 15 ClM-tNT 6.32240 4.43640 3.72770 l16 BIENS-CAP 2 .. 50350 1 .. 75520 1. 47580 117 CONSTRUCT 2.92040 2.04920 1. 72200 ll8 SERVlCES 1.40390 .98502 .82776 119 PUBLlQUES 1.32630 1.11460 120 121 TABLE XLE(l,LC) EMPLOVMENI BV SECTOR AND LABOR CATEGORY (1000 PERSONS) 122 123 RURAL URaAN-UNSK URBAN-SKIL 124 125 AG-SUBS1ST 1654.43 162.8.9 126 AG-EXP+lNO 399.93 45.50800 5.05700 127 SYLVlCULT 7 .. 66200 1.78900 .59700 128 lND-ALlM 12.98900 9.43400 2.35800 129 BJENS-CONS 28.34400 37.46200 12.48800 130 BIENS-INT 18.33100 16~55300 8.30000 131 CtM-l'NT l .. 45800 1.31700 .66000 132 BIENS-CAP 3.11200 2.82000 1.20800 • 133 CONSTRUCT 22.58400 28.46200 7. 11600 134 SERVICES 121.20 125.8 61.96000 135 PUBLIQUES 83.029 32.77100 136 137 138 TABLE ZZ(*.I) MISCELLANEOUS PARAMETERS AND INITIAL DATA 1319 140 141 AG-SUBSIST AG-EXP+IND SVLVICULT INO-ALIM BIENS-CONS BIENS-INT CIM-INT BIENS-CAP CONSTRUCT SERVICES PUBLIQUES 14:2 MO 2.461 .t-- 8.039 .023 17.961 37.062 l38.57 Vl 143 EO 4.594 125.07 49.616 134.72 74.439 22.337 23.451 5.864 101.33 10.501 144 XDO 330.480 131.45 29.5P3 3.838 81.626 I 72.024 118.430 284.38 34.169 10.298 145 K 495.730 170.89 73.760 • 14E+03 174.12 615.79 163.98 146 DEPR 236.870 853.13 102.51 20.600 435.29 .0246 .0472 .0244 .0144 .0212 769.73 180.36 147 RHOC 1.5 .0335 .0335 .0111 .0232 .0637 .9 .4 1.25 1.25 .5 .0637 148 RHOT 1.5 .9 .75 .4 .4 .4 .4 .4 1.25 1. 25 .5 .75 149 ETA 1.0 1.0 1.0 .4 .4 .4 .4 4.00 4.00 4.0 4.00 150 POO 1 .o l.O 1. 0 1.00 1.00 1.0 1.00 4.0 4.0 4.0 4.0 151 TMO .2205 .2330 .278 1.0 1.0 1.0 1.0 .3534 .. 3826 .1768 .2633 .268 152 TE 153 !TAX .0020 .1910 .057 .038 .096 154 CLES .026 .014 .029 .034 .076 .2744 .00445 .05599 • 14099 155 GLES • 17738 .004 .31921 .02358 156 KIO • 11 .09 .06 .01 .04 1.00 157 OSTR • 14 .02 .01 .08 .34 .012203 .026694 .034742 .044291 .059958 • 100 158 OST 4.033 .012287 .042047 3.509 1.025 3.19 7. 101 3.494 159 ID 6.710 .433 160 ; 113.36 138. 13 161 162 163 •COMPUTATION OF PARAMETERS AND COEFFICIENTS FOR CALIBRATION 164 165 DEPR(l) :::: ZZ("OEPR".I); 166 RHOC(l) :::: (1/ZZ("RHOC"~I)) - 1 ; 167 RHOT(t) :::: {l/ZZ{"RHOT",I)) + 1; 168 ETA (I} :::: ZZ("ETA" ,I); 169 TMQ{I) :::: ZZ("TMO .. ,I): __Jl CAMEROON CGE MODEL 05/12/87 22:35~46 PAGE 4 GAMS 2.04 IBM CMS 170 171 TE(I) ITAX(I) = ZZ("TE",I); ::: ZZ("ITAX",I} 172 CLES(I) ::: ZZ("CLES".I} 173 GLES(I} = ZZ("GLES",I) 174 175 KIO(I) = ZZ("KIO",I); OSTR(l) ::: ZZ("OSTR".I); 176 XLLB(I.LC) = XLE(l,LC) + (1 - SIGN(XLE(I,LC))); 177 178 MO(l) ::: ZZ("Mo•• ,I); 179 IT( I) ::: VES$MO(l); 180 IN(I) = NOT IT(l); 181 182 EO(I) XDO(I) = ZZ("EO".I); ::: ZZ("XDO",I); 183 KO(I) = ZZ(''K'', I); 184 185 PDO(I) PMO(I) = ZZ("PDO",I); PDO(I) ; 186 PEO(I) = PDO(I) ; 187 PWMO(I) = PMO(l}/((1+TMO(I))*ER) 188 PWEO(I) = PEO(I)•(l+TE(I))/ER ; 189 190 PVAO(I) = POO(I) - SUM(J, IO(J,I)*PDO(J) ) - ITAX(I); XXDO(I) = XDO(I) - EO(I); 191 DSTO(I) ::: ZZ("DST",I); 192 IDO(I) = ZZ("ID",I); 193 LSO(LC) :::SUM(!, XLE(I,LC) ); 194 195 196 *CALIBRATION OF ALL SHIFT AND SHARE PARAMETERS ~ 197 0\ 198 * GET DELTA FROM COSTMIN, XO FROM ABSORPTION , AC FROM ARMINGTON 199 200 DELTA (IT)$MO(IT) = PMO(IT)/PDO( IT) *(MO(IT) /XXDO( IT))**( l+RHOC(IT)) 201 DELTA(IT) = DELTA(IT)/(I+OELTA(IT)) ; 202 203 XO{I) = PDO(I)*XXOO(l) + {PMO(I)*MO(I))$IT(I) ; AC(IT) = XO(IT)/(DELTA(IT)*MO(IT)**(-RHOC{IT)) + (1-DELTA(IT))*XXDO(IT)**(-RHOC(IT)))**{-1/RHOC(IT)) 204. 205 * GET INTO FROM INTEQ. GAMMA FROM ESUPPLV, ALPHL FROM PROFITMAX 206 207 INTO(!) = SUM{J, IO(I,J)*XDO(J) ); 208 209 GAMMA(IT) GAMMA(IN) = 0; = 1/{1 + PDO(IT)/PEO(IT)*(EO(IT)/XXDO(IT))**(RHOT(IT) - 1) ) 210 ALPHL(LC,.I) = (WDIST(I,LC) * WAO(LC) * XLE(I,LC}) /(PVAO(I)*XDO(I)); 211 212 * GET AD FROM OUTPUT, LD FROM PROFITMAX, AT FROM CET 213 214 215 QO(I) = (XLLB{I,"RURAL")**ALPHL("RURAL",l))*(XLLB(I,"URBAN-UNSK")**ALPHL("URBAN-UNSK",I)) *(XLLB(l,"URBAN-SKIL")**ALPHL("URBAN-SKIL",I))*(KO(I)**(l - SUM(LC, ALPHL(LC,I))) ) ; 216 AD(I) = XDO(I)/QD(I); 217 218 LO(LC) =SUM (I, (XDO (I) *PVAO{ I) *ALPHL(LC, I) I (WDI ST(I, LC) *WAO (LC))) $WDIST(I, LC)); AT{IT) = XDO{IT)/( GAMMA(IT)*EO(IT)*'-RHOT(IT) + ( 1-GAMMA{IT) )*XXDO(IT)**RHOT(IT) )**(1/RHOT(IT)) 21.9 220 221 *MODEL DEFINITION - VARIABLES 222 223 VARIABLES 224 225 *PRICES BLOCK CAMEROON CGE MODEL 05/12/87 22:35:46 PAGE 5 GAM$ 2.04 IBM CMS 226 PD(I) DOMESTIC PRICES 227 PM(I) DOMESTIC PRICE OF IMPORTS (UNITY) 228 PE{I) DOMESTIC PRICE OF EXPORTS (UNITY) 229 PK(I) RATE OF CAPITAL RENT BY SECTOR (UNITY) 230 PX(I) AVERAGE OUTPUT PRICE BY SECTOR (UNITY) 231 (UNITY) P(I) PRICE OF COMPOSITE GOODS (UNITY) 232 PVA(I) VALUE ADDED PRICE BY SECTOR 233 (UNITY) P\IIIM(I) WORLD MARKET PRICE OF IMPORTS . (UNITY) 234 PWE(I) WORLD MARKET PRICE OF EXPORTS 235 TM(I) TARIFF RATES {UNITY) 236 *PRODUCTION BLOCK (UNITY) 237 X(l) COMPOSITE GOODS SUPPLY 238 XD(I) DOMESTIC OUTPUT BY SECTOR ( 79-80 BILL 1 CFAF) 239 XXD(I) DOMESTIC SALES ('79-80 BILL CFAF) 240 E(I) EXPORTS BV SECTOR {'79-80 BILL CFAF) 241 M(I) IMPORTS ('79-80 BILL CFAF) 242 * FACTORS BLOCK ('79-80 BILL CFAF) 243 K(l) CAPITAL STOCK BY SECTOR 244 ('79-80 BILL CFAF) WA(LC) AVERAGE WAGE RATE BY LABOR CATEGORY (CURR MILL. CFAF PR PERSON) 245 LS(LC) LABOR SUPPLY BY LABOR CATEGORY 246 (1000 PERSONS) L(I.LC) EMPLOYMENT BY SECTOR ANO LABOR CATEGORY (1000 PERSONS) 247 *DEMAND BLOCK 248 INT{I) INTERMEDIATES USES 249 ('79-80 BILL CFAF) CD(I) FINAL DEMAND FOR PRIVATE CONSUMPTION ('79-80 BILL CFAF) 250 GD(l) FINAL DEMAND FOR GOVERNMENT CONSUMPTION 251 ('79-80 BILL CFAF) ID(I) FINAL DEMAND FOR PRODUCTIVE INVESTMENT ('79-80 BILL CFAF) 252 DST(I) INVENTORY INVESTMENT BY SECTOR 253 ('79-80 BILL CFAF) ..t:-- Y PRIVATE GOP '-1 254 GR GOVERNMENT REVENUE (CURR BILL CFAF) 255 TARIFF iARIFF REVENUE (CURR BILL CFAF) 256 INDTAX INDIRECT TAX REVENUE (CURR BILL CFAF) 257 DUTY EXPORT DUTY REVENUE (CURR BILL CFAF) 258 (CURR BILL CFAF) GDTOT TOTAL VOLUME OF GOVERNMENT CONSUMPTION ('79-80 BILL CFAF) 259 MPS MARGINAL PROPENSITY TO SAVE 260 (UNITY) HHSAV TOTAL HOUSEHOLD SAVINGS {CURR BILL CFAF) 261 GOVSAV GOVERNMENT SAVINGS 262 DEPRECIA TOTAL DEPRECIATION EXPENDITURE (CURR BILL CFAF) 263 SAVINGS TOTAL SAVINGS {CURR BILL CFAF) 264 FSAV FOREIGN SAVINGS (CURR BILL CFAF) 265 (CURR BILL DOLLARS) DK(I) VOLUME OF INVESTMENT BV SECTOR OF DESTINATION ('79-80 BILL CFAF) 266 *WELFARE INDICATOR FOR OBJECTIVE FUNCTION 267 OMEGA OBJECTlVE FUNCTION VARIABLE 268 ('79-80 BILL CFAF) 269 270 271 P.LO(I) = .01 ;PD.LO(I) = .01 ; PM.LO(IT) =.01; PWE.LO(IT) = .01 ; PK.LO(I) = .01 ; PX.LO(I) = .01 ; X.LO(I) = 272 XD . .LO(I) = .01 ; M.LO(IT) = .01 ; XXD.LO(IT):: .01 ; WA.LO(LC) = .01 ; INT.LO(l) = .01 ; Y.LO = .01 ; .01 E.LO(IT) = .01 ; L.LO(I.LC) = .01 ; 273 274 275 *MODEL DEFINITION - EQUATIONS 276 277 EQUATIONS 278 *PRICE BLOCK 279 PMOEF{I) DEFINITION OF DOMESTIC IMPORT PRICES 280 PEDEF(I) DEFINITION OF DOMESTIC EXPORT PRICES (UNITY) 281 ABSORPTION(!) VALUE OF DOMESTIC SALES (UNITY) (CURR BILL CFAF) CAMEROON CGE MODEL 05/12/67 22:35:46 PAGE 6 GAMS 2.04 IBM CMS 282 SALES{l) VALUE OF DOMESTIC OUTPUT 283 ACTP(I) {CURR BILL CFAF) DEFINITION OF ACTIVITY PRICES (UNITY) 284 PKOEF(l) DEFINITION OF CAPITAL GOODS PRICE 285 *OUTPUT BLOC!< (UNITY) 286 ACT!VITV(l) PRODUCTION FUNCTION 287 PROFITMAX(l. LC) FIRST ORDER CONDITION FOR PROFIT MAXIMUM ('79-BO BILL CFAF) 288 LMEQUIL(LC) (1000 PERSONS) LABOR MARKET EQUILIBRIUM (1000 PERSONS) 289 CET(I) CET FUNCTION 290 EDEMAND{I) EXPORT DEMAND ('79-80 BILL CFAF) 291 ESUPPLV(I) EXPORT SUPPLY (UNITY) 292 ARMINGTON( I) (UNITY) COMPOSITE GOOD AGGREGATION FUNCTION ('79-80 BILL CFAF) 293 COSTMIN(l) FIRST ORDER CONDITION FOR COST MINIMIZATION OF COMPOSITE GOOD (UNITY) 294 XXDSN(l) DOMESTIC SALES FOR NONTRADEO SECTORS 295 XSN(I) ('79-80 BILL CFAF) \ COMPOSITE GOOD AGGREGATION FOR NONTRADEO SECTORS ('79-80 BILL CFAF) 296 •DEMAND BLOCK 297 INTEQ(J) TOTAL INTERMEDIATE USES 298 COEQ(I) PRIVATE CONSUMPTION BEHAVIOR ('79-80 BILL CFAF) 299 OSTEQ(I) INVENTORY INVESTMENT (CURR BILL CFAF) 300 GOP PRIVATE GOP ('79-80 BILL CFAF) 301 (CURR BILL CFAF) GDEQ GOVERNMENT CONSUMPTION BEHAVIOR ('79-80 BILL·CFAF) 302 GREQ GOVERNMENT REVENUE 303 TARIFFOEF TARIFF REVENUE (CURR BILL CFAF) 304 (CURR BILL CFAF) lNDTAXOEF INDIRECT TAXES ON DOMESTIC PRODUCTION (CURR BILL CFAF) 305 OUTVOEF EXPORT DUTIES 306 *SAVINGS-INVESTMENT BLOCK (CURR BILL CFAF) 307 HHSAVEQ HOUSEHOLD SAVINGS 308 GRUSE GOVERNMENT SAVINGS (CURR BILL CFAF) 309 DEPREQ DEPRECIATION EXPENDITURE (CURR BILL CFAF) 310 (CURR BILL CFAF) .s::-- TOTSAV TOTAL SAVINGS 00 311 (CURR BILL CFAF) PRODINV(I) INVESTMENT BY SECTOR OF DESTINATION (CURR BILL CFAF) 312 IEQ(l) INVESTMENT BV SECTOR OF ORIGIN 313 *BALANCE OF PAYMENTS ('79-80 BILL CFAF) 314 CAEQ CURRENT ACCOUNT BALANCE 315 *MARKET CLEARING (CURR BILL DOLLAR) 316 EQUIL{I} GOODS MARKET EQUILIBRIUM 317 *OBJECTIVE FUNCTION {'79-80 BILL CFAF) 318 OBJ OBJECTIVE FUNCTION 319 ('79-80 BILL CFAF) 320 321 •MODEL DEFINITION - PRICE BLOCK 322 323 324 PMDEF(IT).. PM(IT} =E= PWM(IT)•ER*(l + TM(IT)} 325 PEDEF(IT) •• PE{IT)*(l + TE(IT)) =E= PWE(IT)*ER 326 327 ABSORPTION (I) •• P(I)*X(I) =E= PD(I)*XXD(I) + (PM(I)•M(I))$IT(I) 328 329 330 SALES(!} .. PX{l)*XD(I) =E= PD(l)*XXD(I) + (PE(I)•E(I))$IT(I) 331' 332 ACTP(I) •• PX(I)*(l-ITAX(I)) =E= PVA(l) + SUM(J. IO(J.I)*P(J) ) 333 PKDEF(I) •• PK(I) =E= SUM(J. P(J)*IMAT(J.I) ); 334 335 336 *OUTPUT AND FACTORS OF PRODUCTION BLOCK 337 '1 4 CAMEROON CGE MODEL 05/12/87 22:35:46 PAGE 7 GAMS 2.04 IBM C~S 338 ACTIVITV(!)... XO{I) =E= AO(I) * PROD(LC$WOIST(I,LC)t L{l.LC)**ALPHL(LC,I) )*K{I)**{l - SUM(LC. ALPHL(LC.I)) ) 339 340 PROFliMAX(I .• LC)$WOIST(I .. LC) •• WA{I...C)*WOIST(I, LC)*L(l, LC) =E= XO(l) *PVA(I) •ALPHL(LC, I} ; 341 342 LMEQOIL(LC) ••. SUM(I. L(I-.LC)) =E= LS{LC) ; 343 344 CET(IT) •• XD(IT) =E= AT(IT)*( GAMMA(IT)*E(IT)**RHOT{IT) + ( 1-GAMMA(IT) )*XXD(IT)**RHOT(IT) )**(1/RHOT(IT)) 345 346 EDEMAND(l1) •• E(IT)/EO(IT) =E= ( PWEO(IT)/PWE(IT) )**ETA(IT) ; 347 348 ESUPPLV(IT) .. E(IT)/XXO(lT) =E= ( PE{IT)/PO(IT)*(l - GAMMA(IT))/GAMMA(IT) )**(1/(RHOT(IT)-l) ) ; 349 350 ARMINGTON{IT) .• X(IT) =E= AC(IT)* (OELTA(IT)*M(IT) ** ( -RHOC(IT)) + ( 1-DELTA(lT} }*XXO(IT} **( -RHOC(IT))) ** {-1/RHOC(IT)) 351 352 COSTMIN(IT) .... M(IT)/XXO{IT} =E= { PD(IT)/PM(IT)*OELTA{IT)/(1-DELTA(lT)) )**(1/(1 + RHOC(IT))) ; 353 354 XXOSN(IN)~. XXD(lN} =E= XO(IN) ; 355 356 XSN{lN) •• X{IN) =E= XXD(lN) ; 357 358 359 *DEMAND BLOCK 360 36'1 INTEQ(J) •• lNT(J) =E= SUM(I, IO(J,I)*XO(I) ); 362 363 PSTEQ{I).. DST(I) =E= DSTR(I)*XO(I) ; ~ 364 \.0 365 CDEQ(I) •• P(I)*CD(I) =E= CLES(l)~{l-MPS)*V 366 367 GOP •• V =E= SUM{I, PVA{I}*XO(I) ) - DEPRECIA 368 369 HHSAVEQ •• HHSAV =E= MPS*V 370 371 GREQ •• GR =E= TARIFF + DUTY + INOTAX ; 372 373 GRUSE. •• GR =E= SUM(I, P(I)*GO(l)) + GOVSAV 374 375 GDEQ(.IL. GO{l) =E= GLES(l)*GDTOT ; 376 377 TARIFrOEF •• TARIFF =E= SUM{IT, TM(IT)*M(IT)*PWM(IT) )*ER 378 379 lNOTAXOEF •• INDTAX =E= SUM(l. ITAX(I)*PX(I)*XD(l) ); 380 381 OUTVDEF,.. DUTY =E= SUM( IT 1 TE(IT}*E(IT)¥PE(IT) ) 382 383 OEPREQ ... OEPRECIA =E= SUM(Ip OEPR(I)*PK{I)*K(I) ) 384 385 TOTSAV ... SAVINGS =E= HHSAV + GOVSAV + .OEPRECIA + FSAV*ER 386 387 PRODINV(l).. PK(l)*DK(I) =E= KIO(l)*SAVINGS - KIO(I)*SUM(J, DST{J)*P{J)) 388 389 !EQ( I).~ ID(I) =E= SUM{J, IMAT(I,J)*DK(J)); 390 391 CAEQ •• SUM(IT • PWM(IT) *M(IT)) =E= SUM {IT, PWE(IT) *E(IT)) + FSAV 392 393 CAMEROON CG£ MODEL 05/12/87 22:35:46 PAGE a GAMS 2.04 IBM CMS 394 •MARKET CLEARING 395 396 EQUIL(l) •• X(I) =E= INT(I) +'CO(I) + GO(I} + I&(I) + OST{I) 397 398 OBJ •• OMEGA =E= PROD(I$CLES{I). CO{I}**CLES{l)) 399 400 401 *MODEl SETUP - I~ITIALIZATlON 402 403 X.L{I) = XO(l) ; XO.L(l) = XDO(I); XXO.L(l) = XXDO(I); CO.L(I) = CLES(I)*CDTOTO; M.L(I) = MO(I); 404 E.L(I) = EO(I); IO.L(l) = 100(1); DST.L(I} = DSTO(l); tNT.L(I) =INTO(!); PO.L(l): PDO(I); 405 PM~L(I) = PMO(I); PE •.L(l) = PEO(l); P.L(I) = PDO(I); PX.L(l):; PDO(I); PK.L(I) = PDO(I); 406 PVA.L(l) = PVAO(I); PWE.L(I) = PWEO(I); WA.L(LC) = WAO(LC); L.L(I,LC)= XLE(I,LC}; GR.L = GRO; 407 Y.L =SUM(!, PVAO(I)•,-.uQ(l)- OEPR(I)*KO(I)); FSAV.L = FSAVO; TM.L(IT} = TMO(IT) ; 408 409 GO.L(uPUBLIQUES") TARIFF.L = 76.548 = 135.03; 410 INDTAX .. L = 102.45 411 SAVINGS.l= 280.98 412 413 4t4 *CLOSURE 415 416 K.FX(I) = KO(l); 417 PWM.FX(I) = PWMO(I) 418 LS .. FX(LC) = LSO(LC) 419 TM.FX(IT) = TMO(IT) 420 FSAV.FX = FSAVO ; 421 MPS.FX = .09305; Ul 422 GDTOT.FX = GDTOTO; 0 423 424 M.FX(IN) =0; L.FX("PUBLIQUES ... •'RURAL .. ) = 0; 425 L.,FX( .. AG-SUBSIST", .. URBAN-SKlL") = 0; 426 42'7 E.FX(IN) = 0; 42B OPTIONS lTERLIM=lOOO.LIMROW=O.LIMCO~=O 429 430 MODEL CAMCGE SQUARE BASE MODEL 1 431 PMDEF. PEDEF, ABSORP'fiON, SALES, ACTP. PKDEF, ACTIVITY, PROFITMAX, LMEQUIL, CET 432 EDEMANO, E.SUPPLY$ ARMINGTON, COSTMIN, XXDSN, XSN, INTEQ, COEQ. DSTEQ, GOP, GOEQ 433 GREQ, TARl'FFOEF, INDTAXOEF, DUTYOEF, HHSAVEQ, GRUSE, DEPREQ, TOTSAV, PRODINV 434 IEQ, EQUIL. OBJ I ; 435 436 SOLVE CAMCGE MAXIMIZING OMEGA USING NLP; CAMEROON CGE MODEL 05/12/87 22:35;46 PAGE 9 SVMJlOL LlST!NG GAMS 2~04 IBM CMS SYMBOL TVPE REFERENCES ABSORPTION EQU DECLARED 281 DEFlNED 327 IMPL-ASN 436 REF 431 AC PARAM DEClARED 23 ASSIGNED 203 REF 350 ACTIVITY EQU DECLARED 286 DEFINED 338 IMPL-ASN 436 REF 431 ACTP EQU DECLARED 283 DEFINED 331 IMPL-ASN 436 REF 431 AD PARAM DECLARED 29 ASSIGNED 216 REF 338 At.PHL PAR AM DECLARED 38 ASSIGNED 2l0 REF 2*214 2*215 217 2*338 340 ARMINGTON EQU DECLARED 292 DEFINED 350 lMPL-ASN 436 REF 432 AT PAR AM DECLARED 26 ASSIGNED 218 REF 344 CAEQ EQU DECLARED 314 D~FINED 391 CAMCGE MODEL DECLARED 430 DEFINED 430 REF 436 co VAR DECLARED 249 IMPL-ASN 436 ASSIGNED 403 REF 365 396 398 coeo EQU DECLARED 298 DEFINED 365 IMPL-ASN 436 REF 432 COTOTO PARAM DECLARED 75 DEFINED 75 REF 403 CET EQU DECLARED 289 DEFINED 344 IMPL-ASN 436 REF 431 CLES PARAM DECLARED 30 ASSIGNED 172 REF 365 2*398 403 COSIMIN EQU DECLAReD 293 OEFINEO 352 IMPL-ASN 436 REF 432 DELTA PARAM DECLARED 22 ASSIGNED 200 201 REF 2*201 2*203 2*350 2*352 OEPR PARAM DECLARED 32 ASSIGNED 165 REF 383 407 DEPRECIA VAR DECLARED 262 IMPL-ASN 436 REF 367 383 385 DEPREQ EQU DECLARED 309 DEFINED 383 IMPl-ASN 436 REF 433 OK VAR DECLARED 265 lMPL-ASN 436 REF 387 389 DST VAR DECLARED 252 IMPL-ASN 436 ASSIGNED 404 REF 363 387 396 DSTEO EQU DECLARED 299 DEFINED 363 IMPL-ASN 436 REF 432 DSTR PARAM DECLARED 33 ASSIGNED 175 REF 363 \.Ti DSTO PAR AM DECLARED 48 ASSIGNED 191 REF 404 1-' OUT¥ VAR DECLARED 257 IMPL-ASN ,. 436 REF 371 381 DUTYOEF EOU DECLARED 305 DEFINED 381 IMPL-ASN 436 REF 433 l E VAR DECLARED 240 IMPL-ASN 436 ASSIGNED 272 404 426 REF 329 344 346 348 381 391 EDEMA NO EQU DECLARED 290 DEFINED 346 IMPL-ASN 436 REF 432 EQU!L EQU DECLARED 316 DEFINED 396 IMPL-ASN 436 REF 434 ER PARAM DECLARED 72 DEFINED 72 REF 187 188 323 325 377 385 ESUPPLV EQU DeClARED 291 DEFINED 348 IMPL-ASN 436 REF 432 ETA PARAM DEClARED 28 ASSIGNED 168 REF 346 EO PARAM DECLARED 44 ASSIGNED 181 REF 190 208 218 346 404 FSAV VAR DECLARED 264 IMPL-ASN 436 ASSIGNED 407 420 REF 385 391 FSAVO PARAM DECLARED 76 DEFINED 76 REF 407 420 GAMMA PARAM DECLARED 27 ASSIGNED 208 209 REF 2*218 2*344 2*348 GO VAR DECLARED 250 IMPL-ASN 436 ASSIGNED 408 REF 373 375 396 GOEQ EQU DECLARED 301 DEFINED 375 IMPL-ASN 436 REF 432 GOP EQU DECLARED 300 DEFINED 367 IMP(...-ASN 436 REF 432 GOTOT VAR DECLARED 258 lMPL-ASN 436 ASSIGNED 422 REF 375 GOTOTO PARAM DECLARED 74 D~FINED 74 REF 422 GLES PAR AM DECLARED 31 ASSIGNED 173 REF 375 GOVSAV VAR DECLARED 261 IMPL-ASN 43.6 REF 373 385 GR VAR DECLARED 254 lMPL-ASN 436 ASSIGNED 406 REF 37~ 373 GREQ EQU DECLARED 302 DEFINED 371 IMPL-ASN 436 REF 433 GRUSE EQU DECLARED 308 DEFINED 373 IMPL-ASN 436 REF 433 GRO PAR AM DECLARED 73 DEFINED 73 REF 406 HHSAV VAR DECLARED 260 IMPt..-ASN 436 REF 369 385 HHSAVEQ EQU DECLARED 307 DEFINED 369 IMPL-ASN 436 REF 433 I SET DECLARED 2 DEFINED 2 REF 14 15 17 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 43 44 45 46 47 48 49 50 51 52 53 CAMEROON CGE MODEL SYMBOL LISTING 05/12/87 22:35:46 PAGE 10 GAMS 2.04 IBM CMS SYMBOL TYPE REFERENCES 54 55 55 57 58 59 166 167 79 96 105 121 138 168 169 170 171 172 165 179 180 173 174 175 2*176 178 181 182 183 184 185 186 191 192 193 2*187 2•188 3*189 2*190 5*202 207 4*210 4*214 4*215 2*216 228 229 230 231 232 5*217 226 227 241 233 234 235 237 238 239 243 246 248 249 250 251 240 282 283 284 252 265 279 280 281 286 287 289 290 291 292 298 299 311 312 293 294 295 316 7*327 7*329 4*331 2*333 7*338 2*361 3*363 3*365 2*367 2*373 2*375 6*340 342 5*403 3*379 3*383 4*387 2*389 6*396 3*398 5*404 5*405 3*406 4*407 416 417 169 170 171 CONTROL 165 166 167 168 172 173 174 175 176 178 182 183 184 185 186 179 180 181 202 187 188 189 190 191 192 207 210 214 216 217 193 333 5*270 2*271 272 327 329 338 340 342 361 363 365 331 387 389 367 373 375 379 383 396 398 5*403 ro VAR DECLARED 251 IMPL-ASN 436 ASSIGNED 5*404 5*405 3*406 407 416 417 IDO PAR AM DECLARED 404 REF 389 396 47 ASSIGNED 192 REF 404 lEQ EQU DECLARED 312 DEFINED !MAT 389 IMPL-ASN 436 REF 434 PAR AM DECLARED 96 DEFINED 96 REF IN SET DECLARED 333 369 15 ASSIGNED 180 REF 2*354 2*356 CONTROL 426 209 354 356 423 I NOTAX VAR DECLARED 256 IMPL-ASN 436 ASSIGNED 410 REF' 371 INOTAXOEF EQU DECLARED 304 DEFINED 379 IMPL-ASN 436 379 INT VAR DECLARED REF 433 248 lMPL-ASN 436 ASSIGNED 271 404 REF lNTEQ EQU DECLARED 297 DEFINED 361 IMPL-ASN 361 396 1..11 INTO PARAM 436 REF 432 DECLARED 49 ASSIGNED 207 REF 404.• N IO PARAM DECLARED 79 DEFINED 79 !I SET REF 189 207 331 361 DECLARED 14 ASSIGNED 179 REF 180 3*323 6*200 2•201 202 8*203 5*208 8*218 3*325 327 329 9*344 5*346 7*348 407 419 CONTROL 9*350 7*352 3*377 3*381 4*391 200 201 203 206 218 2*270 325 344 346 348 2*271 272 323 ITAX 350 352 377 381 2*391 PARAM OECLAREO 37 ASSIGNED 171 REF 'il07 419 J SET 189 331 379 DECLARED 17 REF 79 96 2*189 2*389 CONTROL 2*207 297 2*331 2*333 2*361 2*387 189 207 331 333 361 387 K VAR DECLARED 243 IMPL-ASN 389 t