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GAMS models
A brief description of the models in the library.AGE3: Basic CGEmodelCGEmodel for a competitive equilibrium in a closed economy without government sector (see equations (3.18ad) of Ginsburgh & Keyzer (1997), GK for short). AGE4A: International tradeInternational trade is introduced by treating exports as the demand by an additional consumer who earns the imports as revenue (see equation 4.8 of GK). Though this model structure is often used in CGEmodeling, it has the severe limitation that equilibrium may not exist because of unboundedness in prices. The problem is due to the specification of the budget equation of the exporter whose income is equal to the countries imports (plus remittances). In this case, it may happen that the export price reaches infinity enabling the country to purchase very large quantities of imports, especially if substitution elasticities on imports are high. The problem is easily recognized in the welfare format, where the program's constraint set can become unbounded. AGE4B: International tradeThe specification follows the small country assumption (as in equations 5.21 or 5.22 of GK) by taking the prices of the tradable factors as given, but we associate it with Chapter 4 of the same book, because there are no taxes. Since for factors the export price is taken equal to the import price, there is no change in the price of commodities when the market shifts between imports, autarky, and exports. Hence, the formulation still fits within the (equality constrained) CGEframework. Note: the formulation does use translated instead of ordinary CES cost functions. For ordinary CES the slack on input coefficients should be expressed in total quantity terms or in value terms. The model is highly instable: the solution may be solver or even machine dependent. AGE4C: International trade in factors and switches between imports, autarky and exports,The model is the same as AGE4B, except that we allow for a wedge between import and export prices of factors. As there is now the possibility of a switch between imports, autarky and exports, the model has to be looked at as a nonlinear complementarity problem and can no longer be regarded as an equality constrained system. This is reflected in the product terms in the objective. The model is the same as AGE4B, except that we allow for a wedge between import and export prices of factors. AGE5: Tariffs, taxes, international trade in factors, switch between imports, autarky and exportsThis is a national model under the small country assumption which combines various features that often play a role in AGEmodels: taxes and tariffs, switches between imports, autarky and exports, and export quotas (see Chapter 5 of G&K). The main complication with respect to AGE4C is that due to the price wedges, the accounting becomes more complex and error prone. Therefore, we check the consistency of the accounts by computing the total accounting discrepancy (the variable GAP in TABLE7). AGE6A: Central buffer stocks, taxes, tariffs, international trade in factorsThis adds centrally held buffer stocks to the national model under the small country assumption (See Chapter 5, GK). Various price wedges are introduced caused not only by taxes but also by processing costs, including trade and transportation margins. Note: the formulation uses translated instead of ordinary CES cost functions. For ordinary CES the slack on input coefficients should be expressed in total quantity terms or in value terms. AGE6B: Drèze rationingHere we build uniform or Drèze rationing (Section 6.2.3, GK) into the open economy model under the small country assumption as in AGE6A with switches between imports, autarky and exports, taxes and tariffs, but without consumer tax. It is advisable in this model to avoid imposing rations when they are known to be not binding. AGE7: Recursively dynamic simulationThe model is similar to AGE6A, but with recursive dynamics (see Sections 7.2.3, 7.4.1 in GK). In a Tperiod formulation, all timespecific variables and equations would have to carry a timesubscript. The price normalization and the income would remain as they are, since they apply to the full period. Initial conditions would be introduced by treating the associated variables as fixed, terminal conditions through equations that only apply for the last period. AGE9: Nonrival consumptionThe model describes an equilibrium with Lindahl pricing of a single nonrival good (TV) (see Definition 9.1 in GK). Consumers share the cost of the nonrival commodity in accordance with their marginal utility with respect to that commodity. AGE10A: Marginal cost pricingIncreasing returns are introduced in the model AGE3, with marginal cost pricing for a good produced via a single output cost function that is concave with respect to output (see Section 10.5, GK. AGE10B: Efficiency wage relation and occupational migrationThe model allocates consumers of class i to state s, in order to achieve Paretoefficiency. The manpower supply of every consumer depends on his consumption. This is the efficiency wage relation. The model can be interpreted as endogenizing an efficient social security scheme (see equations 10.1314 in GK for a further elaboration of this model). Note that the model is a generalization of the one presented in Chapter 10 of GK:
AGE11A: Markup pricing of goodsThis introduces markup pricing of goods that are produced under constant returns to scale. The markup is a fixed fraction of producer cost and accrues to the owners of the firm (a markup can be interpreted as a tax: for treatment of taxes see AGE6A). AGE11B: Monopolistic competition among producers, single output firmsThe markup for good g is obtained as Lagrange multiplier of a maximization of producer g's profits subject to a price normalization condition and Walrasian excess demand at given levels of goods output (strategic supply). This strategic supply has the value generated in a markup ridden equilibrium, for a given markup rate. This rate is then adjusted iteratively until convergence is achieved (see Section 11.2 of GK). The markupequilibrium is represented as a basic CGEmodel like AGE3, but with markup pricing for all goods, Leontief technology and CES utility functions. AGE11C: Imperfect competition among consumers, strategic reservesA subset of consumers restricts its supply of factors. There is perfect competition in goods. Equipment is treated as numeraire. Producers are competitive. The markups are obtained via minimization of every consumer's net expenditure value keeping all strategic reserves fixed. AGE11D: Imperfect competition among consumers, strategic consumptionA subset of consumers adjusts its net demand for factors. Producers are competitive. The markups are obtained via separate maximization for every consumer of his net expenditure value keeping all strategic consumption fixed. AGE11E: Collusion among consumers, strategic reservesSame model as AGE11C, but the strategic consumers collude (without side payments). The markups are obtained via minimization of the net expenditure value of the coalition at fixed levels of strategic reserves. AGE12A: Transaction money (cash in advance)Transactions demand for money is a fixed fraction of consumer expenditure. All purchases are made at the beginning of the Hicksian week and financed through cash provided in limited quantity by a bank. If the constraint on this quantity is binding, the lenders who own the cash will receive an interest payment (see Section 12.1 in GK). AGE12B: NonhomogeneityThis model follows the specification of AGE7 (small country assumption under recursive dynamics) but has the additional property that it allows for nonhomogeneity in some revenue categories and for nominally fixed prices (see Section 12.3.1 in GK). AGE12C1: Incomplete asset markets (first approximation)There are two periods; period 1 (the present) is
certain, but S alternative states can occur in period 2. Every consumer
draws up a twoperiod plan, but is restricted with respect to the type of
financial assets that he can buy (the quantity of this net purchase of
assets is not restricted, however). A return function specifies the return
on every particular asset in every state in period 2. The equilibrium
determines the price of commodities in period 1 and all states of period
2, as well as the price of the financial asset in period 1 (see Section
12.2 in GK).
We present a version of the model with incomplete asset markets as was discussed in Definition (12.2) of the book. Though in the example given, iterative adjustment of the relevant parameters leads to reasonable convergence after about 25 calls of the Fullformat program in AGE12C1, it is useful, before preparing the accounts, to verify that the result does solve the true model with incomplete asset markets. This is checked in Phase II (AGE12C2). It may be added that after rather extensive experimentation (with settings on the OPTIONfile, with iterations between subsystems, with bounds, normalizations etc.) the Fullformat was the only stable implementation that could be obtained for this model within GAMS/MINOS, while for the other models convergence could be obtained through various schemes of computation. Running the second phase (AGE12C2) for finetuning of the optimal solution requires executing AGE12C1 with the SAVE option (GAMS AGE12C1 SAVE=AGE12C1). The application does this by default. AGE12C2: Incomplete asset markets (fine tuning)This is the second phase of AGE12C. It follows after AGE12C1, the solution by iteration over the Full format program. This second phase algorithm, which minimizes slacks in the ArrowDebrue format is quite unstable and should only be used for final finetuning. The application calls GAMS using the RESTART option: GAMS AGE12C2 RESTART=AGE12C1.
User's guide to models and additional utilitiesThis is a user's guide to a library of models covered in Ginsburgh & Keyzer (1997) written in General Algebraic Modeling System (GAMS). To make it relatively selfcontained this guide also reproduces some introductory material on the construction of an AGEmodel in GAMS. The library contains 18 models, starting with the simplest CGEmodel and gradually building up to models with a complete reporting and interactive parameter adjustment and more innovative applications on nonconvexity, efficiency wages and occupational migration, imperfect competition, monetary constraints and incomplete asset markets. The programs in the library are illustrative only. Though all will find an equilibrium solution for the parameter values given, we do not claim that the algorithmic implementation chosen is the most robust one or that it will find a solution after changes in parameters. By browsing through the applications the user will recognize various ways of controlling convergence. The guide is available in PDF. A free Reader from Adobe^{®} Acrobat^{® }can be downloaded from Adobe.
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