Counting equations and variables and closing the CGE model

We have above formulated set of equations similar to those representing the optimal solution of the nation-wide resource allocation model NLP-2.2-2. They are different from each other in as much we have used the revised forms of the equations suggested above. This is also the reason that we have 2n more equations and variables than before. The total number of equations is 22n+4, and we have 22n+5 variables. All equations are homogenous in prices, therefore we can fix the price level by setting the value of one them, for example, pcv = 1.

Thus, the number of unknowns is equal to that of the equations, the equations system is regular.

Although we could expect the derived system of equations to have solution, the general equilibrium model is not yet complete and its specification provides opportunities for revision.

Consider first of all that yg and yjbn

are exogenous variables and ycv is set by Walras’s law, rather than by means of utility maximization subject to budget constraints. There are no budget considerations introduced explicitly into the model, despite the fact that the distribution and redistribution of incomes is an important constraint as well as means in generating final demand that matches total supply in a monetary economy.

Let us try to construct the budgets of the economic agents represented in one way or another in our model. They are the private households, in charge of making the private consumption and savings decisions, the government, who decides on public consumption and budget deficit or surplus, the firms (production sectors), who can be charged to make the investment decisions as well in addition to production decisions, and the foreigners, who represent the rest of the world.

One of the special advantages of the computable general equilibrium models is that they can cover all the major aspects of public finance including all substantial taxes, social policy transfers, public expenditures and deficit financing instruments. The models contain, usually in considerable detail, the process of income distribution and redistribution, which takes place via various channels. The primary incomes received can be interpreted in broader sense than usual, to include not only wages and gross operating surplus (labour and capital), various taxes, for example on wages, consumption, imports and exports. Secondary income generation takes place in the form of transfers between the above mentioned various agents.

Most of the transfers are assumed to be proportional to some activity levels, represented in the model, and are assumed to be set in real (valorised) terms so as to maintain the price homogeneity of the model. Here we will represent them only by their net outcome (± tr^a) in the budgets of the economic agents, which eventually define the net monetary savings (S^a) as the difference between disposable incomes and expenditures.

We will, thus, introduce for each agent a function, tr^a(·), representing the net result, the positive or negative balance of the transfers taking place between them. The net transfer functions depend on specific endogenous variables, which determine the levels of the various activities that form the basis of the transfers. The sum of the transfers is by definition zero, that is,

tr^h(·) +

Σ

j tr_j^f(·) + tr^g(·) + tr^rw(·) = 0.

We have to introduce also n+3 additional variables, S^h, Sjf

, S^g and S^w, to represent the net monetary saving position (savings or borrowings) of the households, the firms (production sectors), the government and the foreigners.

We will also add the same number of equations to the system, to define the budget conditions of the various agents that must be satisfied by the feasible solutions. The primary incomes received and the net result of the transfers will be presented on the left hand sides of the budgets, which defines thus the total income available for the given economic agent. On the right hand side one will find the expenditures and the net result of savings/borrowings.

To keep the presentation simple, we assume that the whole of c_i⁰ consists of committed private consumption. The budget of the private households will thus be as follows (wages plus/minus transfers equal to consumption expenditure plus net savings):

Σ

j w·djw operating surplus plus/minus transfers equal to investment expenditure plus net savings, typically minus borrowings): The government collects direct and indirect taxes, gives subsidies, redistributes income via transfers, finances public expenditure and the resulting balance will be equal to the budget Finally, the budget of the foreigners (rest of the world)

Σ

i v·p_i^wm·m_i + tr^rw(·) =

Σ

i v·p_i^we·z_i + S^rw, (E30) which could also be written as the sum of the current account and monetary transfers, which result in the balance of payments, represented by S^w:

v·d_e + tr^w(·) = S^w. (E30’)

The sum of the net savings/borrowings should be zero, that is, S^h +

Σ

j S_j^f + S^g + S^rw(·) = 0.

It can be shown that equations (E1) - (E26) imply the basic accounting identity that states that the value of final demand is equal to the sum of primary incomes, as required by Walras’s law. The same identity is implied by equations (E27) - (E30), if we assume that total savings and borrowings match each other. The above equilibrium condition will, thus, be automatically satisfied, so there is no need to introduce it separately.

As we have discussed it, equations (E1) - (E26) can be solved for the variables contained by them. Once we know their solution, equations (E27) - (E30) can be independently solved for the net savings/borrowings variables. This shows the specificity of the implied macro-closure of the CGE model specification derived, step-by-step, from the macro-programming model 2.2-2. Namely, savings adjust to the structure of final demand, which is set basically by fiat, externally, by considering public consumption (y^g) and net investments (y^nv) to be exogenously given. This choice of endogenous and exogenous macro variables can be called a programming macro-closure.

It is, however, far not clear, which potential variables should be treated as exogenous and which as endogenous variables in the model. As a matter of fact, exogenous variables are partly used to counterbalance the shortage of the static model (see the discussion of the problem of macro-closure in the case of Walras’s second model), partly the lack of well tested theories to describe the complex interdependence of the main economic variables. Each exogenous variable represents in a sense an equation missing from the model. As a matter of fact, when we set the value of certain variables exogenously, we make a conditional (‘what if ) forecast in terms of the endogenous variables. By the same token, choosing one or another plausible specification possibility, we fix some conditions as corner stone for our analysis.

The above uncertainty and certain arbitrariness involved in the choice of specification can be counterbalanced by using alternative assumptions and test the robustness of the conditional forecasts. With each specification option we can generate an internally consistent forecast for the endogenous variables. In this way, we can derive “packages”, that indicate alternative, possible and consistent changes in macroeconomic variables (see, Zalai et al., 2002 for more details on this).

We will illustrate the macro-closure possibilities by some characteristic macro-closure options (see Dewatripont and Michel, 1987, Lysy, 1983, Taylor, 1983 and 1990 on a theoretical discussion of closure options). Let us take first the example of public consumption, the level of which (y_g) is usually set exogenously in the CGE models, because it is decided by economic policy makers in a way, which is difficult to model. Nevertheless, an alternative variable that could be exogenously set instead of y_g, is public deficit (S^g), which has become a growing concern in many countries nowadays. Yet another option is to fix both macro-variables, that is, both y_g and S^g, and free the general level of some tax rates (e.g., social security contribution, τjw

), by means of which the government collects income. That could to bring public budget into the required balance.

In the given specification of the model, there was no behavioural equation that would have explained the amount of the net savings of the households (S^g). It was rather adjusting to the level of private consumption. One might want to introduce such behavioural equation, for example, by assuming constant propensity to save or using the so-called ELES (Extended Linear Expenditure System) model, which would derive the level of savings from the optimizing behaviour of the representative household. That would require, in either case, the introduction of additional equation into the model, which in turn would necessitate to free some variable, considered to be exogenous so far, that would bring the households budget into

balance instead of savings. A new endogenous variable to play this role could be, for example, the general level of investments.

The general level of investments could be made endogenous also by fixing the level of some other components of savings instead. That would shift the Keynesian macro-closure towards a neoclassical one, in which investments adjust to savings. As a matter of fact, a major source of savings, the balance of payments, is to a large extent determined exogenously, as one can see it from equation (E30’), in which d_e is considered to be an exogenous variable. Again, to shift further towards a Keynesian macro-closure, one might make d_e endogenous and fix the nominal exchange rate (v) instead exogenously.

In typical neoclassical models, the supply of labour would be made an endogenous variable, the level of which would be also defined by the optimizing choice of the representative household. A radical shift in the direction of the Keynesian world would be to fix the nominal wage level (w) and let the labour market move out of equilibrium. This could be made technically feasible by introducing a new variable, the labour utilization index (l_u) and replacing L₀ in the labour market clearing condition with l_u⋅L₀. That would, of course, completely change the original meaning of that condition. It would simply set the level of the labour utilization index (l_u), which could be seen as an indicator of disequilibrium or tension on the labour market, rather than a resource constraint as before.

Another variant of this closure would be fixing the real wage rate instead, that could make more sense, especially in economies with strong labour unions. Instead of the real wage rate one could fix the level of utility function (the real value of consumption), that Taylor would classify as a Marxian macro-closure.

One may find difficult to justify the assumption of fixed capital stock, the scarcity of which determines the rate of return on capital, in a CGE model meant to generate a longer term perspective scenario. One could instead fix the rate of return and introduce a capital utilization index (k_u) as in the case of labour above.

As can be seen from the above examples, the macro-closure problem is closely related to the mechanism that sets the proportions between the main components of final demand, such as the general level of private and public consumption, investments and net exports, on the one hand, and the level of the key variables that determine the distribution of the national income, such as the general rate of wages, return on capital and foreign exchange. The above sets of variables compete with each other, that is, they can increase only at the expense of each other, because the overall level of the national income (net product) is determined practically by the available stocks of primary resources in our model. The two sets of macro variables are connected to each other through the income (re)distribution rules, which should secure that the demand generated by disposable income matches the emerging supply.

Some CGE models attempt to integrate the microeconomic general equilibrium models with macroeconomic IS-LM mechanism (termed as macro-micro integration), which has been traditionally used in Keynesian models (see for example Bourguignon, Branson, DeMelo, 1989, Capros et al., 1990). These hybrid models are designed to overcome the limitation of arbitrary closure rules, which must otherwise be adopted. In addition, due to the introduction of

financial market mechanisms and related structural adjustment, they allow to set the level of prices as well.

In document CGE Modelling: A training material (Pldal 92-96)