A major task confronting policymakers in recent years has been to predict the effects of changes in the various parameters under their control. Typically, the changes being examined are small—a slight shift in a tax rate, or a minor devaluation, for example. In such cases, partial-equilibrium models have normally been used for prediction, on the underlying assumption that the effects of the proposed changes are relatively minor and do not have reverberations throughout the economy. Such an assumption cannot be considered valid, however, when there are parameter changes that are specifically intended to bring about structural shifts in the economy. A country that decides to carry out a complete liberalization of its trade regime by relaxing tariffs would be such a case, since opening the economy to foreign competition is intended to bring about a restructuring of the domestic production technology. A long-term adjustment program, such as the extended Fund facility, is also intended to bring about major structural changes in a country’s economy, and thus does not lend itself to analysis by partial-equilibrium methods.
The aims of this paper are to construct a general-equilibrium model of an open economy and to develop a computational technique for deriving a market-clearing solution to the model. The model will allow for disaggregated commodities, taxes, and tariffs, so that the individual parameter changes that are often considered by a government may be examined. The model includes a government that is an active participant in the economy as a producer of public goods and that may influence the rate of savings by its actions. The model allows for different rates of substitution between capital and labor in each sector, so that a precise analysis of the impact of government policies on the relative shares of scarce factors can be made. Because of its general-equilibrium nature, the model can cope adequately with the type of large changes that would be considered in a program designed to bring about major adjustments.
As will be discussed, the main innovation of this paper, compared with other disaggregated general-equilibrium models, is to incorporate financial assets. The large-scale computational models currently in existence either ignore money altogether or include it in such a way that it is neutral, that is, has no effect on any real variables. Thus, it is not possible to investigate, for example, the impact of changes in monetary policy on real output. Conversely, those models that do allow the inclusion of nonneutral financial assets are unable to cope with large numbers of commodities and differentiated taxes.
Although this paper is purely theoretical, the eventual aim is to carry out an empirical version of it to be applied to the United States. This model could be of use to countries other than the United States, since some governments attempt to manage their currency’s exchange rates so as to maintain some type of parity between domestic and U.S. prices; for those countries where the rates are preannounced or are expected to be maintained for some time, it is important to be able to predict the effect of anticipated shocks or policies on future U.S. price movements. Because the relevant U.S. price level may not necessarily be the official consumer price index, it is important to be able to predict individual equilibrium nominal prices, so as to construct a suitable price index for the country in question to follow. Such prices will be the output of the model.
Section I discusses the strengths and weaknesses of various existing models of the open economy and gives a brief verbal description of the model to be developed here. Section II develops the technical structure of the model, while Section III summarizes the analysis and suggests directions for future research.
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Mr. Feltenstein, economist in the Special Studies Division of the Research Department, received degrees from Harvard and Yale Universities. Before joining the Fund staff, he taught at the University of Massachusetts at Amherst.
The theoretical foundations of the modern versions of this model are given in Debreu (1959), while recent computational examples, some with empirical content, are given in Dervis and Robinson (1978). Feltenstein (1979; 1980), da Fonseca (1978), Miller and Spencer (1977), Richter (1978), Shoven (1976), and Whalley (1977).
A survey of the attempts to introduce money into the Walrasian system is given in Grandmont (1977).
This is, of course, a great oversimplification of the characteristics of and differences between these types of model.
Richter (1978) has constructed a computational general-equilibrium model that emphasizes the production of public goods.
This particular financing rule is not essential to the model; the government might instead, for example, choose to set the quantity of bonds that it will issue, while letting the market price fluctuate.
Hahn (1971; 1973) and Kurz (1974) are the basic papers introducing transactions costs into the general-equilibrium framework. Grandmont (1977) offers a survey of the current state of the subject. The treatment of transactions costs in this paper is admittedly ad hoc, as it is not derived from axiomatic reasoning.
Ideally, one would like to be able to consider imported goods for which the country is a price setter, but doing so would require the specification of a world supply function for that good, a task that one might wish to avoid.
The production coefficients are not, actually, completely fixed, since a certain degree of substitution is allowed between domestically produced inputs for production and their imported counterparts.
A similar methodology is described in Whalley (1977). It is not true that scarce factors will have a constant share in the value of final output, since relative prices will change.
The input/output matrix referred to is I-A, so that negative entries represent inputs for a particular sector, while positive entries represent net outputs.
At the degree of aggregation that would be used in any empirical study, the price indices for domestic goods and their foreign counterparts are different, indicating that they are not perfectly comparable.
Here, aij represents the total input requirements of the ith type of good to the jth sector, a requirement that may be made up from foreign and domestic sources.
These are considered functions of p—domestic prices—only, since world prices of imports are taken to be exogenous. In equation (2), it is assumed that for a particular commodity the coefficients and elasticity of substitution are constant across sectors, since in any empirical work it would generally be possible to estimate these parameters only on an economy-wide basis.
Thus, the government’s role in, for example, training human capital or building highways is ignored. Such roles, although obviously of great importance in the modern economy, are not germane to this model.
This admittedly ad hoc introduction of money has appeared in somewhat different form in various macroeconomic models of trade. See, for example, Weiss (1980). In Weiss’s model, however, the nominal stock of money is given exogenously, so that there is no possibility of analyzing changes in the money supply.
Both wE and πE might, in practice, be generated in a variety of ways. For the purpose of this paper, as is explained in greater detail in the next section, the consumer will be perfectly myopic, so that wE = (1 + πE) w, where w is his current wage and πE is equal to the current rate of inflation.
Here, income taxes are paid by the firm when it purchases labor and capital from the consumer.
An empirical study of the impact on money demand of withholding at the source has been made by Tanzi (1974).
It has been assumed that the consumer includes sales taxes, at their current rates, in evaluating the cost of his future bundle of consumption.
If there were a possibility of a change in the exchange rate, then parameter a would presumably reflect the consumer’s perception of exchange rate risk.
Here, p refers only to the prices of the financial assets.
Because the foreign consumer receives income from his sale of exports to the home country, his own levels of demand are subject to a wealth effect. This specification of foreign demand for exports is given in Boadway and Treddenick (1978).
When i = 1 (i.e., when the asset in question is money), pi = 1, since money is the numeraire.
When the tax is levied on inputs of labor, it represents the income tax withheld at the source that was mentioned earlier; when it is levied on capital, it can be interpreted as a profits tax.
There is thus the same tax rate applied to different types of capital, while different rates may be applied to different types of labor, although the rates will be uniform across sectors. Progressive income taxes are not introduced here for reasons of simplicity.
The introduction of export taxes (or subsidies) would pose no technical problem, but they are not currently in use in most industrial countries.
One notion of public goods is defense.
Thus, the introduction of a government allows the existence of a central bank that creates money. Unlike Grandmont and Laroque (1975), the author does not allow consumers to borrow directly from this central bank, thereby creating their own indebtedness.
Recall that goods k + q + 3 + 1, …, k + g + 3 + c are capacity constraints on the first c sectors. Thus, pk + q + 3 + j ≡ 0 if j > c.
Because of the possibility of substitution between domestic and imported goods in production, VAI(p) is not a totally satisfactory substitute for the domestic price index, as would be true if there were completely fixed coefficients in intermediate and final production. The justification for using this proxy is that producers look at, for example, changes in domestic labor costs in making initial decisions concerning the purchases of inputs.
Such elasticities are typically estimated in econometric studies. See, for example, Goldstein and Khan (1978).
This assumption is not a technical necessity but rather is motivated by empirical considerations.
Recall that prices of imported goods are exogenously given in terms of money, the numeraire.
Recall that TR, total transfer payments, is being treated as the H + 1st price.
These are not really factor prices, since domestic financial assets may be produced. Rather, they are the set of prices on which an equilibrium will be calculated.
Where D < 0, the transfer payments going to consumers, −D, are not, in general, equal to TR, the H + 1st price that enters the consumer’s budget constraint, as in equation (30). At the equilibrium that may be shown to exist, they are, in fact, equal.
Here, rk + q + 1 > rk + q + 2 refer to the total initial holdings of money and of domestic bonds, respectively.
As in equation (32), this amount can be calculated as
where the inner summation is taken over the set of all domestically produced goods for which there is an imported substitute.
A proof of this result is available upon request from the author, whose address is Research Department, International Monetary Fund, Washington, D.C. 20431.
The algorithm used here is based on Merrill (1971) and Scarf and Hansen (1973). Manne and others (1980) and Eaves (1976), among others, have constructed somewhat different algorithms to solve similar problems. A different approach, based on Newton’s method, has been employed by a number of other economists.