MULTIMOD
A Multi-Region Econometric Model*

The paper describes a global model consisting of several industrial and developing country blocks built to analyze alternative economic policies in a medium-term context. The model, which has been used to construct medium-term scenarios for the World Economic Outlook, consists of aggregate demand and supply relationships, with endogenous determination of interest rates, prices, and exchange rates. Financing flows to developing countries depend on expectations of their ability to service debt. Expectations of interest rates, inflation, and exchange rates are modeled in a way that is consistent with the model’s solution, and budget constraints are imposed on governments.

Abstract

The paper describes a global model consisting of several industrial and developing country blocks built to analyze alternative economic policies in a medium-term context. The model, which has been used to construct medium-term scenarios for the World Economic Outlook, consists of aggregate demand and supply relationships, with endogenous determination of interest rates, prices, and exchange rates. Financing flows to developing countries depend on expectations of their ability to service debt. Expectations of interest rates, inflation, and exchange rates are modeled in a way that is consistent with the model’s solution, and budget constraints are imposed on governments.

I. Introduction

1. Purpose of model

MULTIMOD, or MULTI-region econometric MODel, has been designed to improve analysis of the effects of industrial country policies on major macroeconomic variables, both in the developed and developing worlds. It is a continuation of modeling work undertaken at the Fund in recent years, in particular the World Trade Model (Spencer [1984]) and MINIMOD (Haas and Masson [1986]), and it supplements individual country and sectoral models, as well as detailed analysis and monitoring performed by country desks. The focus of the model is on the transmission of policy effects, and in this respect therefore it accords well with the Fund’s surveillance role over the policies of major countries. More generally the model can be used to trace the effects of changes in the external environment facing developing countries on their economies in the aggregate. To a limited extent, the model can also be used to evaluate policies that developing countries might choose in order to improve their outcomes, for instance, through shifting demand away from consumption and toward investment. However, their monetary and fiscal policy instruments are not at present explicit in the model. The model has not been designed to do unconditional or “baseline” forecasts, nor is it our intention to use it for this purpose. Instead, the model has been designed to utilize a judgemental forecast that incorporates detailed knowledge of country desks as given, and to examine the effects of changes in policies in major countries and other exogenous changes in the economic environment on that baseline.

Given the focus on comparative scenarios, the model can be much simplified compared to a model that must be used to give baseline forecasts. Simplicity in a model is an important characteristic, since it allows easier understanding of the economics behind the model’s results; in addition, it allows faster solution of the model, which is important if computer-intensive simulations are to be run, such as those that impose consistency between the model’s final solution and model-generated expectations. 1/ A desire for transparency and tractability also motivated a precursor to this model, MINIMOD, which was simpler in structure and consisted of only two blocks—the United States and the Rest of the World. The present model, in order to be useful for considering various policy combinations and economic interactions among industrial countries, has more country disaggregation; in addition, it attempts to capture characteristics of developing countries, in particular their financing constraints and different economic structures.

The model at present includes three separate industrial countries—the United States, Japan, and the Federal Republic of Germany—and two blocks of the remaining industrial economies, one for the other G-7 countries, labeled the larger industrial (LI) block (France, the United Kingdom, Italy and Canada), and one for the smaller industrial countries (SI). 2/ The rest of the world (RW) has been divided into high-income oil exporters (HO) and developing countries (DC). On the developing country side, there is only one aggregate region, but its industrial structure is disaggregated between production of manufactures, of oil and of primary commodities. The region is assumed to be faced with an endogenous supply schedule for foreign loans that depends on a forward-looking assessment of developing countries’ debt service capacity. Given other countries demands for the region’s exports, imports are assumed to depend on the level of financing available less interest payments.

The high income oil exporters 3/ are treated separately, in simplified form; they are the residual suppliers of oil, whose price is exogenous in real terms, and their exports of other goods are exogenous. In addition, they are assumed to have explicit import demand equations, instead of a residual determination of imports from the balance of payments identity. Thus their holdings of reserves are modeled as the residual.

2. The transmission of policy effects

The main linkages among the regions modeled are the endogenous determination of prices and volumes of goods trade and the endogenous determination of exchange rates and interest rates. In this respect, the model is a dynamic version of the Mundell-Fleming model, incorporating many of the extensions to that model that have been developed over the years. That basic framework has proved a useful and robust tool for the analysis of economic policies. 4/ The signs of transmission effects of economic policies, and also the magnitudes of their domestic effects, depend on a number of key parameters, including the degree of price stickiness, the elasticity of expenditure with respect to interest rates, the degree of openness to trade, and the size of trade elasticities. 5/ Estimates of these key parameters are necessary to evaluate the transmission effects, which are calculated by computer simulation of the model.

An important linkage between industrial to developing countries is the level of capital flows and the interest rate on outstanding debt. Flows of financing between industrial and developing countries are assumed to depend on the ability of developing countries to service debt. The measure of servicing ability used is the ratio of debt interest payments, corrected for inflation, to exports. Expectations are assumed to be formed for that ratio: if it exceeds a threshold level imposed on the model, then additional financing will not be demanded or supplied. If it is less than the threshold, then financing will be available in an amount that depends on the difference between the expected level and the threshold level.

Developments in industrial countries influence the expected value of that ratio, since the level of interest rates on DC debt appears in the numerator, and demand for the developing countries’ exports affects both prices and volumes in the denominator. Increased developing country export price or volume will lead to greater financing flows from industrial to developing countries, and the greater the level of financing, the larger will be DC imports from the industrial countries; some of which will be associated with increased consumption, but the remainder, by increasing DC investment, will affect the capital stock and future growth prospects. Increased demand by industrial countries for manufactures produced by developing countries will first mainly lead to increases in the volume of DC exports, and over time in the price of those exports, while an increase in industrial country demand for primary commodities will lead in the first instance to an increase in their price, and only later to an increase in output. Conversely, any increase in protectionism in industrial countries, by reducing the demand for DC exports, will lead to smaller financing flows and less capital formation in developing countries.

3. Commodity disaggregation

Trade is disaggregated into three different types of goods: oil, primary commodities, and manufactures. Trade in oil is treated separately, and it is assumed to be subject to one world price, fixed exogenously in real terms. 6/ All countries and regions other than the high-income oil exporters have variables for oil production and domestic consumption, and for exports and imports of oil; typically, production is exogenous for the individual producer, while a domestic demand equation determines consumption and either imports or exports residually. 7/ For both the high income oil exporters and the DCs, production and exports are also endogenous, and are determined such that world demand and supply of oil are equal; increases of demand are shared between them in a fixed proportion. Inventories of oil are not explicit in the model; changes in inventories are implicitly included in consumption.

Primary commodities produced by developing countries are assumed to have a price that is perfectly flexible and moves to clear the market. An increase in the relative price (and implicitly, in the profitability of production) of primary commodities will induce a shift of resources into this sector, increasing the quantity produced and eventually bringing about an increase in capacity and supply.

The composite manufactured good is assumed to be produced by all regions, and imports and exports of all regions except the high income oil exporters are endogenous to the model. 8/ Furthermore, each region’s (or country’s) manufactured good is assumed to be an imperfect substitute for other regions’ manufactures, and relative prices of the different manufactured goods explain imports and exports. Base period export shares are used as weights for the calculation of relative prices. There is no single price of manufactures, and prices in each region move sluggishly.

4. Estimation strategy

Unlike MINIMOD, whose parameters were not estimated, but were derived by simulation from an existing multi-country model, the parameters of the model described here were to a large extent estimated using historical data. The difference in approach is the result of different requirements on the models. One of the uses of the current model is to help generate medium-term scenarios in conjunction with the World Economic Outlook, and so it is convenient that the model explain data series used in that publication. Differences in data definitions may make the outputs of existing models produced outside the Fund inconsistent with WEO data. In addition, the coverage of regions—all the industrial countries and the developing countries—goes beyond many existing multi-country models, so that necessarily many parameters could not be taken directly from those models.

In estimating model coefficients, a high value is placed on comparability across countries and regions, at least as applies to industrial countries. Rather than specifying and estimating individual country models independently, in many cases a given equation was estimated for the five industrial regions using pooled cross-section, time series estimation. This allowed imposition of common coefficients where the data warranted it. The aim was to avoid differences in country model behavior that were the result of arbitrary differences in specification, rather than parameter differences that were statistically significant.

Therefore, common parameters occur quite frequently in the model, as is described below. Nevertheless, even with common behavioral parameters countries will respond differently to changes in exogenous variables, because of different structural features. For instance, the Federal Republic of Germany exhibits lower fiscal multipliers than the United States in large part because of a greater degree of openness, as exhibited by a higher import/GNP ratio. Similarly, the levels of net foreign assets and different trading patterns in the various countries will lead to different macroeconomic responses to the same shock. In addition, there is an asymmetry in the importance of countries in international monetary arrangements; foreign assets and liabilities are assumed to be denominated in dollars, and to pay a U.S. dollar interest rate.

II. Industrial Countries

1. Aggregate demand

a. Consumption behavior

Consumption behavior in each country or region is modeled in a fashion that reflects the correlation between current income flows and consumption, as well as the longer-term relationship between consumption and permanent income or wealth. 9/ The effect of current income flows can be explained by capital market imperfections, taking the form of constraints on borrowing by some households. The consumption equation therefore reflects the assumption that some consumers are only constrained in the level of their consumption spending by their net wealth, while others are also liquidity constrained. The measure of wealth used is financial wealth plus the present discounted value of expected future income, where income is defined as net national income (the value of output domestically produced, net of factor payments abroad) less taxes: it thus includes both physical capital and human capital, and is the net wealth of the private sector.

In calculating wealth a choice must be made of the appropriate rate of discount used by consumers. In the model, it is assumed to be the same as the government’s. 10/ As a result, expected increases in taxes offset increases in private holdings of government bonds in the calculation of wealth.

In the definition of wealth, therefore, neither bonds nor taxes appears explicitly since the present value of taxes equals the stock of bonds plus the present value of government spending. Instead, wealth equals the present value of expected net national income minus the government’s spending, plus the monetary base and net claims on foreigners. As a result, whether government spending is financed by taxes or bond issues has no effect on wealth, as calculated here. However, since current taxes appear in disposable income, what Barro [1974] has termed Ricardian Equivalence—the equivalence of bond and tax financing—will not hold, as the liquidity constrained consumers will consume less if current taxes rise, reducing their disposable income. 11/

As mentioned above, it is assumed that the private sector discounts the future at the same rate as the government, i.e. using the real government bond rate. However, any reasonable historical measure of real interest rates—either long or short—gives some years in the 1970s where the real interest rate is negative; clearly that rate cannot be used to calculate discounted present values. On the other hand, if we constrain the real rate to be a parameter, e.g. to equal the average over some historical period, then interesting valuation effects are lost. The prevailing ex ante real short rate is used to discount next period’s flows, but a discount rate that tends to return to the historical average real rate is applied to subsequent periods’ flows; the speed of adjustment of the discount rate is estimated using an autoregression on historical data.

The determination of wealth can be derived as follows. The starting point is the definition of net wealth of a representative consumer as being the sum of financial assets per capita and the discounted present value of future income:

W=(M+B+NFA/ER)/P+0er(s)sρ(s)Y(s)[1τ(s)]ds(1)

where M is outside money, B holdings of government debt, NFA net foreign assets, P the absorption deflator, r the short-term real interest rate, ρ the relative price of output and absorption, Y per capita net national product, and τ is the tax rate. Now the government’s budget constraint is given by the following equation, provided that discounted interest payments go to zero so that e-r(s)sB(s) ⇒ 0 as s ⇒ ∞:

B/P=0er(s)sρ(s)Y(s)[τ(s)g(s)]ds(2)

where g is the share of government spending on goods and services in net output. Substitution of (2) into (1) eliminates B and τ:

W=(M+NFA/ER)/P+0er(s)sρ(s)Y(s)[1g(s)]ds(3)

Suppose that ρ(s), r(s), Y(s), and g(s) are all expected to stay constant at their current values, that is ρ, r, Y, and g, respectively. Then equation (3) reduces to

W=(M+NFA/ER)/P+(1g)ρY/r(4).

Such an assumption is clearly too restrictive. In general, however, if those variables take arbitrary paths then we cannot collapse the integral in (3). We suppose that the real interest rate, the terms of trade, real output, and the share of government have normal values that correspond to long-run equilibrium, equal to r, ρ, Y, and g, respectively. For output, the long-run equilibrium value is clearly potential output, and hence it is convenient to work with the rate of capacity utilization, CU = Y/Y. Suppose that r, ρ, CU, and g move gradually from their current levels to their long-run equilibrium values:

Dr(s)=α[r¯r(s)]Dρ(s)=β[ρ¯ρ(s)](5)DCU(s)=γ[1CU(s)]Dg(s)=δ[g¯g(s)]

This implies that their future paths can be described by the following:

r(s)=eαs(rr¯)+r¯,(6)

and similarly for the other variables. Let the integral in equation (3) be called V. We linearize around the normal values, in the following way:

V=ρ¯(1g¯)Y¯/r¯+er¯sρ¯(1g¯)[Y(s)Y¯]dser¯sρ¯Y¯[g(s)g¯]ds+er¯sY¯(1g¯)[ρ(s)ρ¯]dser¯sρ¯(1g¯)Y¯[r(s)r¯]ds(7)

Given equations (5), the integrals in (7) can be collapsed to give the following:

V=ρ¯(1g¯)Y¯/r¯{1+(CU1)/(r¯+α)+(ρ/ρ¯1)/(r¯+β)(gg¯)/[(1g¯)(r¯+γ)](rr¯)/(r¯+δ)}(8)

Therefore, the normal value of wealth is modified by the deviation of the variables from their normal levels, and the faster they are expected to return to their normal levels, the less effect they have on current wealth calculations. Since the adjustment equations above are formulated in continuous time, the speeds of adjustment can approach infinity, in which case (8) reduces to

V=ρ¯(1g¯)Y¯/r¯(9)

The values of α, β, γ, δ, as well as r and g are estimated using historical data, using autoregressions over the period 1965-85. A regression of the form

X=aX(1)+b(10)

was run in order to infer the long-run value b/(1-a) and the speed of adjustment 2(1-a)/(1+a) corresponding to the parameters of (5). 12/ It was first verified that the variables considered above did seem to be stationary; no formal statistical tests were performed, but Figure 1 suggests that this is indeed the case. Capacity utilization, which is calculated in the data to be the ratio of actual output to its trend value, has a normal value of unity, which was imposed, as was the value for the ratio of the output to the absorption price (both are indices, equal to 1.0 in 1980). The speeds of adjustment and long-run values implied by the estimated autoregressions are given in Table 1 below.

Figure 1
Figure 1

Industrial Countries: Plots of Historical Data

Citation: IMF Working Papers 1988, 023; 10.5089/9781451921014.001.A001

Table 1:

Implied Long-Run Values and Adjustment Speeds

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The autoregressions imply a much faster return to normal capacity utilization rates than for relative prices; hence, deviations from normal relative prices have a larger effect on calculated wealth. Equilibrium real short-term interest rates were calculated from the regression coefficients, as described above; surprisingly, they differ considerably across countries. Normal shares of output appropriated by governments, g (note that: transfers are excluded here), are remarkably similar for the different regions, with the exception of Japan. As noted above, there is also no evidence of trend over the period, suggesting that government spending and net national product are cointegrated. When estimated separately, speeds of adjustment to a normal government share were poorly determined; thus, a pooled time-series cross-section constrained the speed to be the same.

Using the wealth measure defined above, a consumption equation was estimated in error-correction form 13/ that constrained consumption to increase proportionately to increases in wealth in the long run. This specification allows the speed of adjustment to be estimated freely, but ensures that steady-state consumption equals some constant times wealth. The equation also includes the change in the real long-term interest rate ΔR (expressed as a decimal fraction) and the change in the log of disposable income, Δlog(YD). The equation was estimated using instrumental variables, 14/ with pooled data over 1970-85; individual coefficient restrictions were not rejected at the 5 percent level. 15/ The estimated equation has the following coefficients (t-ratios in parentheses; constant terms, which differ across countries, are not reported):

Δlog(C)=.117(2.5)log(W1/C1).451(1.4)ΔR+.555(6.3)Δlog(YD)R¯2=.867SER=.013(11)

In the long run steady state, the change in R is zero, and consumption and disposable income settle down to a common growth rate. Therefore, equation (11) implies that the level of consumption in each country or region i will be related to wealth in the following way:

Ci=κiWi(12)

The constant term κi in (12) depends on the country’s intercept in (11) as well as the steady-state rate of growth, which is equal to the exogenous combined rate of growth of the labor force and technical progress.

b. Investment behavior

Investment is modeled as a gradual adjustment to an optimal level for the capital stock; in the presence of adjustment costs, the adjustment is spread over time. 16/ As is the case for consumption, this process is modeled as an error correction mechanism. The optimal stock of capital is derived from the production technology: the profit-maximizing level of capital will equate the marginal product of capital to the user cost of capital, UC. In the simple Cobb-Douglas technology assumed here, the marginal product of capital is just the level of output times the share of capital (β), divided by the capital stock. Therefore, the optimal capital stock K* is given by

K*=βGDP/UC(13)

In the models for industrial countries, the user cost is defined in a way that takes into account economic depreciation of the capital stock as well as the tax treatment of depreciation and the non-neutrality of the tax system with respect to inflation. 17/ Such a measure of user cost gives values for UC for several countries that are close to zero in some periods, or even negative (for instance, for the United Kingdom during the 1970s). As a result, equation (13) does not give a useful measure of the desired level of the capital stock. Given measurement problems, the effect of the user cost on capital was estimated freely, instead of imposing the elasticity of minus unity implied by (13).

The adjustment to the optimal capital stock is modeled as an error-correction mechanism in log form. This permits imposing long run homogeneity of the level of capital with respect to output as is implied by (13) provided steady states with the same UC are compared. There is also a term that captures a short-run accelerator effect of current changes in output on investment.

Unfortunately, adequate data for the real net capital stock, excluding government capital, were not available for all industrial countries. Consequently, pooled estimates were obtained for six of the G-7 countries—all but Italy—and for the SI region. The same coefficients (except for the constant term, which was set equal to the average for the United Kingdom, France and Canada) were imputed to Italy. A dummy variable was included to allow for a shift in investment behavior after the first oil price shock: it is zero before 1974, 1 afterwards. The estimated equation was the following (separate intercept terms are not reported), where instrumental variables were used to account for the joint endogeneity of investment, GDP and the user cost: 18/

Δlog(K)=.56(8.5)log(GDP1/K1).085(1.8)UC+.086(1.5)Δlog(GDP).012(3.2)DUM74(14)R¯2=.960SER=.010

In the long-run steady state, K and GDP settle down to constant growth rates that are determined by the (exogenous) rates of growth of labor force and technical progress, and are reflected in the constant terms. From (14), in the long run K is therefore given by

log(K)=log(GDP).54UC+aconstant(15)

c. Trade volumes

For the industrial countries, trade flows are disaggregated as follows. Oil trade is treated separately from other goods; each country’s oil exports are exogenous, while imports of oil are determined residually, as the difference between domestic production (which is exogenous) and domestic consumption plus exports, if any. Domestic consumption of oil depends on relative prices and domestic activity. Industrial countries also import primary commodities from developing countries. 19/ Finally, each industrial country produces a manufactured good, (as do developing countries); each manufactured good is differentiated from other countries’ goods. For each country, there is an equation for the total volume of manufactured imports and one for the total volume of manufactured exports.

In modeling oil, it is assumed that there is one world price; this assumption is realistic for world trade but less so for domestic consumption. Consumption equations were estimated with pooled data, and the same long-run price elasticity was imposed, though in the short run, price elasticities are allowed to differ in order to permit different short-run responses of domestic prices to changes in the world price. An error-correction equation was estimated that imposed a unit elasticity with respect to GDP in the long run, as well as a short-run effect of activity on oil consumption, with coefficients differing across countries. Since oil serves as an input into production, GDP rather than domestic absorption served as the activity variable. For manufactured imports, in contrast, domestic absorption is the activity variable in the equation (see below). The form of the equation for oil consumption was the following, where the relative price RPO is the ratio of the domestic price of oil to the GNP/GDP deflator, and all variables are in logs:

Δlog(COIL)=κ+αlog(RPO1)+βlog(GDP1/COIL1)+γΔlog(GDP)+δΔlog(RPO)(16)

Estimated coefficients are presented in the following Table; coefficients α and β are constrained to be the same for all countries, as unrestricted coefficients showed a remarkable degree of uniformity across countries.

The estimates for α and δ imply strong and statistically significant effects of relative prices on oil consumption. The long-run relative price effect, equal to α/β, is about -0.7, but it has a mean lag of about 10 years. Short-run elasticity effects of economic activity on oil consumption are greater than unity for all regions except the United States and the smaller industrials; in the long run, the elasticity is unity, as discussed above. The short-run relative price elasticities are very small.

Imports of oil by each industrial country are determined residually, as the difference between consumption and production. For those countries that produce oil, implied elasticities of oil imports are considerably larger than those for consumption, since production is exogenous. For instance, if oil imports are one quarter of consumption, then the elasticity of imports with respect to either price or GNP will be roughly four times that for consumption, reported above.

As is the case for oil, one world price is assumed to prevail for primary commodities. Primary commodity imports are also modeled in error-correction form, but here the restriction that demand is unit elastic was rejected by the data. Writing RPC for the relative price of commodities and domestic output, i.e. the world price of commodities converted to domestic currency and divided by the GNP/GDP deflator, the equation for commodity imports ICOM can be written as follows:

Δlog(ICOM)=κ+αlog(RPC1)+βlog(GDP1)+γlog(ICOM1)+δΔlog(RPC)+εΔlog(GDP)(17)

Since the price of commodities moves to clear the market, it is clearly endogenous, and ordinary least squares are inappropriate. Instead, instrumental variables was used; GDP and the GDP deflator in all of the industrial countries were instruments. Results are presented in Table 3. Coefficients vary considerably across countries and regions; however, relative price and GDP elasticities are generally well determined. Only the estimates of ε for Japan and α for Germany differ from their a priori signs; neither is significantly different from zero, however. Estimates of long-run price elasticities, equal to α/γ, are less than unity for all countries except Japan; estimates of long-run GDP elasticities, equal to -β/γ, range from .25 to 1.1.

Table 2.

Coefficient Estimates, Oil Consumption Equations, 1964-85

(t-ratios in parentheses)

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Table 3.

Coefficient Estimates, Commodity Import Equations, 1965-85.

(t-ratios in parentheses)

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Manufactured trade equations are modeled in a conventional fashion, using a base period share matrix to weight up the growth in foreign markets and competitors’ prices. 20/ Import volumes are assumed to depend on the level of domestic absorption, A, as well as on the ratio of the import price to the non-oil GNP deflator. Export volumes depend on a foreign markets variable, defined as the weighted sum of other countries’ imports (with weights that are equal to base period shares of the home country’s exports in other countries’ imports) and on the ratio of the home country’s export price to other countries’ export prices. This latter variable incorporates other countries’ export prices using a double weighting scheme, reflecting both the importance of all other markets in the home country’s exports and the market share of its competitors in those markets.

The equations that were estimated for import volumes have the following form, with lags on relative prices and absorption included where dictated by the data. A time trend is also included in some equations, to capture secular changes in trade liberalization and hence in world trade that is not related to trend growth in absorption or output.

log(IM)=κ+αlog(A)+βlog(A1)+γlog(PIM/PGNPNO)+μt+φlog(IM1)(18)

Coefficient estimates are presented in Table 5 below.

Table 4.

Coefficient Estimates, Import Volume Equations, 1966-85

(t-ratios in parentheses)

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Notes: a Constrained to a constant.b Constrained to be equal to .c Constrained to equal 1-α.d First order serial correlation correction is -.50.
Table 5.

Shares of Manufactured Export Markets

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Note: The figures give the share of the country in the stub in the total exports to the country in the heading (also equal to that country’s total imports, if measurement errors are ignored).

The import equations have long-run elasticities with respect to absorption that are constrained to be equal to unity (this constraint being accepted by the data), in most cases with adjustment estimated to take place during the first year, the exception here being the Larger Industrial group. Price elasticities are equal to the following values, after lags are taken into account: -0.8 (US), -1.4 (JA), -0.7 (GR), -1.6 (LI), -1.7 (SI).

Export volume equations depend on weighted foreign demand for imports (FM) and the log of the export price relative to competitors’ export prices, (REER). These variables are defined as follows:

FMi=ΣjsijIMjE¯ij(19)
REERi=log(PXMi)ΣjλijΣkiskjlog(PXMkEik)/(1sij)(20)

where Eij are base period exchange rate indices, and λij measure the importance of country j in the exports of country i. The export share matrix sij is given in Table 5. The double weighting scheme in (20) can be condensed to a single set of weights, and the equation rewritten as follows:

REERi=log(PXMi)Σjwijlog(PXMjEij)(20)

The matrix of weights wij is given in Table 6 below.

Table 6.

Export Competitiveness Weights

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The variable REER for a given country compares its manufactured export prices (in logs) to a weighted average of other countries’ prices (in logs), converted to a common currency, with the weights appearing in the appropriate row of Table 6. It should be emphasized that this measure of the real effective exchange rate excludes competition in the home market; thus it is not a comprehensive measure of competitiveness. Each country’s export equation has the following form:

log(XM)=κ+εlog(FM)+νREER+φREER1(21)

Coefficient estimates are given below.

Table 7.

Coefficient Estimates, Export Volume Equations, 1970-85

(t-ratios in parentheses)

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Notes: a constrained to equal zero.b Serial correlation correction, ρ = .70.

The export equations give conventional estimates, with foreign market coefficients near to unity. To the extent that these elasticities differ from unity, these equations will not be consistent with a steady state with real growth, since a country’s export share of foreign markets will not settle down to a stable ratio. The sample period however produces estimates that differ significantly from unity, and alternative specifications with time trends to capture changes in market shares did not give satisfactory results. Fortunately, elasticities do not differ so greatly from unity as to give nonsensical results when the model is simulated, even as far as 30 years into the future; nevertheless, further experimentation with specifications that allow for transitory changes in market shares, converging to a stable long-run value, is planned.

Long-run effects of relative prices on manufactured exports differ considerably across countries, ranging from -0.3 for Germany and the LI and SI regions, to -0.5 for the United States and -1.1 for Japan. Price elasticities may seem low, but it must be remembered that the foreign market variable itself is implicitly a function of relative prices, since it is a weighted average of imports. Therefore, the Marshall-Lerner conditions are easily satisfied, at least for manufactures.

2. Government sector

The government sector does not include any true behavioral equations; however, in addition to identities that define the budget balance and total expenditures, there are technical relationships and simulation rules. Each country’s equation for taxes (net of non-interest transfers) relates tax receipts to a tax rate and a tax base, which is approximated by Net National Product plus interest receipts. 21/ In addition, in simulation tax rates are changed to prevent the stock of government debt from rising without bound relative to GNP.

The equation for tax rates is a simulation rule with imposed parameters; they have not been estimated from historical data. Given exogenous government spending, the logic of the government’s intertemporal budget constraint implies that tax rates must eventually be increased, provided that the real interest rate exceeds the real growth rate of the economy. 22/ If tax rates are not increased, then the government bond stock will increase without bound relative to GNP, as the government will be forced to borrow more in order to service the increased debt. If the government bond stock does settle down at a higher level, then even for an unchanged primary (i.e. non-interest) deficit, higher tax rates will be needed to service the higher debt.

A feedback rule was specified for tax rates that makes them respond to the government debt/GNP ratio and to the change in the ratio. Parameters were chosen on the basis of earlier work that studied the dynamics of MINIMOD, and formulated rules that made the model stable. 23/ Such a stability analysis has not yet been performed with the present model; this remains a project for further work.

3. Money and Interest rates

As in most theoretical macroeconomic models, monetary policy in MULTIMOD is specified in terms of the supply of money, in particular the monetary base. This, together with the demand for base money, determines the short-run interest rate that clears the money market. Short-term interest rates in turn have an effect on long-term rates and the exchange rate. The supply of money is however not exogenous; instead, there is a reaction function for the central bank’s behavior. What is exogenous is a target for the money supply; central banks are assumed to move short-term interest rates to close a gap between the target and the actual stock of money.

Demand equations for real money balances (deflated by the absorption price) were estimated as a function of real GNP and the short-term nominal interest rate. Base money includes both currency and the reserves of commercial banks held with the central bank. Demand for reserves therefore includes the demand derived from required reserves on the part of commercial banks, which depends on demand for their liabilities and the reserve requirement applied to them, plus commercial banks’ demands for excess reserves. Each of these components may be expected to vary with the level of economic activity and to be sensitive to interest rate fluctuations. Money balances may also adjust with a lag; this is captured by a lagged dependent variable and lagged independent variables, where significant: 24/

log(M/P)=κ+αlog(GNP)+βRS+γRS1+δlog(M1/P1)(22)

Results of this common specification are presented in Table 8. Tests were performed of equation (22) relative to more general specifications with additional lags; these tests accepted the more parsimonious specification in (22). Lagrange multiplier tests failed to find evidence of serial correlation up to fourth order (see Hendry [1987]).

Table 8.

Coefficient Estimates, Demand for Base Money, 1965-86

(t-ratios in brackets)

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Note: for the Smaller Industrials, the sample period is 1966-86.

In many countries, the demand for money has been affected by financial innovations and deregulation that have occurred in the 1980s. 25/ Consequently, it is of interest to test whether the demand functions are stable when the recent period is compared with earlier data. In the first part of Table 8 above, the final column gives a test for stability, when each equation is estimated over 1965-85 (one fewer observation) and used to forecast 1986. If the figure in the final column is greater than the critical value of the χ2 distribution, which at the 5 percent level of significance (with one degree of freedom) is 3.8, then the hypothesis of parameter stability can be rejected. It can be seen that only for the United States does parameter instability seem to be present. 26/

Concern about the effect of financial innovation on money demand has led a number of central banks to abandon or de-emphasize monetary targeting. It is also true that even during the historical period, few central banks targeted the monetary base (the principal exception being the Federal Republic of Germany). Though over some periods and for some countries, other variables, for instance exchange rates, have clearly influenced monetary policies, the approach implemented in the model—imposing a reaction function in which short-term interest rates move to achieve money supply targets—has the advantage of simplicity; it also permits “money supply changes” to be simulated. Despite the deemphasis on monetary targeting, it is useful to associate a neutral stance of monetary policy with an unchanged money supply. An obvious alternative, making interest rates exogenous, provides no nominal anchor for the simulations, and as a rule for monetary policy in the face of shocks it is clearly inadequate.

Another key relationship in this sector is an arbitrage condition between short-term and long-term interest rates. This equation constrains the return on short-term bonds (RS) and the expected return on long-term bonds (RL, plus expected capital gains) to be equal. By assumption, long-term bonds are consols, 27/ so that the price is the inverse of the bond rate; consequently the expected rate of capital gain is just -(RLE-RL)/RL, where RLE is the bond rate expected for next period. The equation can thus be written as

RS=RL(RLERL)/RL(23)

In the consistent expectations solution to the model, the expected long-bond rate is equal to its actual value next period. Repeated substitution can then be performed using (23) to express the current long rate as a function of expected future short rates. Thus (23) embodies a pure expectations theory of the term structure, and there is, for instance, no direct effect of the stock of government debt on interest rates. Though it seems likely that when the stock of government debt becomes very large relative to GNP, interest rates would tend to be higher, regressions on recent historical data have had difficulty in isolating such an effect, probably because debt ratios have exhibited insufficient variability.

4. Price determination and aggregate supply

a. Domestic output price

The key behavioral relationship in this sector is a semi-reduced-form equation for the price of output—the non-oil GNP deflator. This equation captures price setting behavior by firms and wage setting in the context of overlapping contracts. Price setting by firms is assumed to depend on the level of capacity utilization, while wage bargains depend on the degree of slack in labor markets as well as on the expected real wage. Employment and wages are not modeled explicitly here; instead, they are substituted out, and the level of capacity utilization is used to proxy labor market conditions. 28/ Capacity utilization CU is calculated as the ratio of actual output, as determined by demand, to capacity output, as given by a Cobb-Douglas production function of capital and a trend term that captures both labor force growth and technological progress. As Gordon [1985] shows, an equation for the rate of change of output prices can be derived that depends on expected inflation, on the level of capacity utilization, and on the change in capacity utilization.

Suppose that wage bargaining is characterized by overlapping contracts, ranging in length from 1 period to infinity, and that furthermore the distribution of contracts remains constant over time. Let us call fi (i=0, 1, …) the proportion of contracts that were negotiated i periods ago that are in force at any given time. When any contract is negotiated, the wage is determined on the basis of current and expected changes in consumer prices (not output prices) over the term of the contract, and on current labor market conditions, as well as trend productivity growth α. Writing Δw(i) as the annual rate of change in the wage negotiated i periods ago, πt-i the prevailing rate of inflation, and πtie the annual rate of inflation expected at t-i to prevail over the life of the contract, we therefore suppose that

Δwt(i)=ηπtie+(1η)πti+φlog(CUti)+α(24)

Implicit in this formulation is that there is no front-end loading of wage increases: they occur smoothly over the life of the contract. 29/ It is also the case that expected inflation is assumed to be at the same rate, and not to be dependent on the length of the contract, but only when the expectations are formed. We further suppose that output supply is based on imperfect competition among firms that set prices on the basis of a flexible markup over variable costs, in this case just wages adjusted for productivity increases. The markup also depends on the rate of capacity utilization. Now labor costs are a weighted average of the various contracts in force. Calling ν average unit labor costs (in logs),

vt=Σi=0fi[wt(i)αt](25)

and the log of the non-oil output price pt (in the model listing, this variable has the name PGNPNO) is given by

pt=vt+βlog(CUt)+c(26)

Differencing (25) and (26) with respect to time, and substituting into (24), we can write

Δpt=Σi=0fi[ηπtie+(1η)πti+φlog(CUti)]+βΔlog(CUt)(27)

If the following assumption is made about the distribution of contracts, then (27) can be considerably simplified. 30/ Let the proportion of contracts negotiated i periods ago be (1-λ)λi. Then if L is the lag operator, (27) can be rewritten as

Δp=[(1λ)/(1λL)][ηπe+(1η)π+φlog(CU)]+βΔlog(CU)(28)

which gives an equation that can be estimated in the form

Δp=λΔp1+(1λ)[ηπe+(1η)π+φlog(CU)]+βΔlog(CU)λβΔlog(CU1)+ε(29)

where ε is an error term.

Estimated values are given below. Instrumental variables were used since both the capacity utilization rate (it appears in log form in the regressions) and expected inflation are likely to be correlated with the error in (29). 31/ Time series regressions were pooled, 32/ and all coefficients constrained to be the same, since the constraint of common coefficients was not rejected by the data. The constant term was omitted, as implied by (29). An iterative estimation procedure was used to impose the constraint on the coefficients for the lagged dependent variable and on the lagged change in capacity utilization. In particular, starting from an initial estimate for λ, say λ, a regression of the form

ΔpΔp1=α1(πeπ)+α2(πΔp1)+α3log(CU)+α4DCU+ε(30)

was run, where DCU - Δlog(CU) - λ Δlog(CU-1) and where coefficients were constrained to be the same for all countries. Using the estimated value for α2, a new estimate for λ was calculated, yielding a new series for DCU, and equation (30) was reestimated until parameter values converged. The resulting estimate for α4, equal to .11, was insignificant, with a t-ratio of 0.7. Consequently, this variable was dropped, and the equation reestimated, giving the following results:

ΔpΔp1=.397(2.9)(πeπ)+.545(3.7)(πΔp1)+.146(1.5)log(CU)R¯2=.516SER=.017(31)

The implied values for the parameters of equation (30) are λ = .455, η = .728, and ϕ = .269.

The degree of price flexibility is reflected in the size of effects of capacity utilization, and also by the smallness of λ. The mean contract length is estimated by λ/(1-λ); in the limiting case where λ equals zero, the rate of change of the output price depends only on expected inflation, not past price changes. The estimated value for λ implies a mean contract length of about 10 months. Another important determinant of price flexibility is the weight η applied to expected inflation relative to current inflation: a high value reflects large responses of current wage bargains to forward-looking, rather than backward-looking, changes in consumption prices. The estimated value for η suggests a large forward-looking component.

b. Trade prices

The model also includes equations for trade prices. As discussed above, each country is assumed to produce a non-oil good (which is identified as a manufactured good in the model, though in fact it also includes some semi-finished manufactures and primary commodities) which is differentiated from other countries’ goods. Moreover, the export price is distinguished from the domestic output price, since in reality there seems to be a considerable amount of price discrimination between home and foreign markets. 33/ (It is also possible that exporters discriminate between different export markets; this possibility is however not allowed for in the model).

Manufactured import prices are determined in the model as weighted averages of other countries’ export prices. The average price of imports of manufactures of country i, PIMi, is modeled as follows:

PIMi=Σjsij(PXMjEij)+ε(32)

where the sij correspond to the export shares in Table 6 above, PXMj is the price of exports of country j, and Eij is an index of the value of currency j in terms of currency i.

As for export prices, their rate of change is assumed to be a linear combination of the rates of change of domestic and foreign non-oil output prices, where foreign prices use the same doubly-weighting scheme as the real effective exchange rate, reflecting competition in all export markets. In addition, there is a term in the lagged difference (in logs) between domestic prices and export prices: this forces export prices in the long run to go up one-for-one with domestic output prices. Let PXM be the manufactured export price, PGNPNO the home non-oil output price, and PFM be a weighted average of competitors’ prices in foreign markets. The estimating equation can be written

Δlog(PXM)=κ+αΔlog(PGNPNO)+(1α)Δlog(PFM)+βlog(PGNPNO1/PXM1)(33)

Ordinary least squares estimates of coefficients are given below. The regions were pooled, and the coefficient β constrained to be the same; this restriction was not rejected by the data.

Table 9.

Pooled Coefficient Estimates, Export Price Equations, 1969-85

(t-ratios in parentheses)

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The estimates indicate a somewhat greater sensitivity of export prices of Japan and of the larger remaining G-7 countries to the rate of change of foreign prices than is the case for the either Germany or the United States.

5. International accounts and exchange rates

A final block of equations in each country’s model concerns the calculation of the current account balance, the net international asset or liability position, and the determination of exchange rates. The trade balance is the sum of a country’s exports of manufactures and oil, minus imports of those goods and of primary commodities. The current account is the trade balance plus net interest receipts, which are simply modeled as the product of a weighted average of U.S. short- and long-term interest rates and the country’s net foreign asset position. The latter variable, which is assumed to be denominated in dollars, is calculated in the model by cumulation of current account surpluses. Historical data for the major industrial countries do exist, and they differ from cumulated current accounts for various reasons, including valuation effects. However, such effects are not incorporated explicitly in the model’s equations, and hence they show up in the residual terms of the equations for the changes in net foreign assets.

The proximate determinant of exchange rates in the model is an equation for open interest parity between short-term interest rates in different countries; that is, the expected appreciation of the dollar exchange rate is set equal to the short-term interest differential in favor of the dollar. 34/ Such an arbitrage condition is analogous to the assumption described above that expected returns on long and short-term bonds are the same; as was the case there, asset stocks (in particular net foreign assets) do not directly affect the expected returns differential. Consequently, without further structure imposed on the model, a country would face a perfectly elastic supply of foreign funds, whatever its net indebtedness position. This is unlikely to be so, even for major industrial countries, and further work will attempt to capture the effects of limits to financing on exchange rates. However, as is the case for long-term bond rates, empirical estimation with recent historical data has had difficulty in uncovering a systematic link between asset stocks and exchange rates. 35/

The level of the exchange rate is thus strongly influenced by monetary forces that affect the short-term interest rate. However, it is also the case that exchange rate expectations—which are made to be consistent with the model’s solution for the exchange rate next period—reflect the general equilibrium of the model. Therefore, the exchange rate is the result of more than just monetary factors, and in particular, is affected by fiscal policy variables, the price of oil, and by productivity differences.

The model also generates a competitiveness index (REER) which is a measure of relative export prices, with weights that reflect the importance of other countries as competitors in all export markets (see equation 20 above). These variables appear in equations for the manufactured exports of each of the industrial countries and regions, and of the developing country block.

Of course, the bilateral exchange rates determined in the model can be weighted up in various ways, and it was judged useful to include equations defining the nominal effective exchange rates of industrial countries among themselves. These effective exchange rates are based on the MERM weights used in the effective exchange rates published by the Fund for 18 industrial countries, 36/ but the weights are collapsed to the 5 industrial countries/regions included in the model. The resulting weighting matrix is presented in Table 10.

Table 10.

MERM Weights for Industrial Regions in the Model

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Note: The effective exchange rate for any country in the stub is calculated by applying the weights in the row for this country to bilateral exchange rates for the countries in the heading.

III. Rest of the World

The rest of the world has been divided into two separate regions; high income oil exporters and the developing countries. While some variables and behavioral relationships are assumed to be the same in these two regions, it was necessary to separate them because a key feature of the model, constraints on external financing, are unlikely to be relevant for the high income oil exporters. Most of the discussion below concerns the developing country block, where financing constraints do apply.

The developing country model has a number of features that distinguish it from the structure described above for industrial countries. First, as a group they are assumed to be financing constrained, in the sense that they do not face a perfectly elastic supply of funds from the industrial countries. Instead, the amount available is determined endogenously, on the basis of a measure of ability to service additional debt. Second, because of the heterogeneity of the countries considered, the developing country model has greater commodity disaggregation; the region produces primary commodities as well as a composite manufactured good and oil. Third, lack of adequate data and the problems of aggregating dissimilar countries have induced us to include less detail on financial markets and on the effects of policy instruments. Finally, the existence of financing constraints implies that some category of expenditure in developing countries is not equal to its desired, equilibrium level. In the model, imports are determined residually by the balance of payments identity; correspondingly, the amount of domestic investment is the counterpart of the decision by foreigners to lend to the region: there is no separate investment function. These features are described in more detail below.

1. Financing constraints

A key feature of the model is the determination of the net flow of financing from industrial to developing countries. The availability of financing is assumed to depend on the debt-interest-to-exports ratio 37/, evaluated at expected real interest rates and exports in the future. 38/ Because of its forward-looking nature, it is a measure of solvency. The amount of financing available depends on the difference (if positive) between some critical upper limit for the ratio and its current level. If the gap is negative, developing countries are assumed to be constrained to run down net debt, that is, to run a current account surplus (adjusted for the inflation component in debt service). Therefore, from any initial level the interest ratio will tend to converge, in time, to the critical level, which is imposed exogenously on the model.

Algebraically, the financing equation can be written as follows. Call α the interest to exports ratio, r the U.S. interest rate minus the expected rate of change of U.S. prices (assumed to apply both to debt and to foreign reserves), PX and X are developing-country export prices and volumes, D is the stock of developing-country debt, FR are foreign reserves, and E is the dollar exchange rate. Then

αt=rt(DtFRt)/(PXtXtEt)(34)

The change in debt D is assumed to reflect both expected growth in developing countries’ exports plus an adjustment term that takes the interest-to-exports ratio toward its critical level, χ. Let g be the expected average annual growth rate of the dollar value of exports over some future period (in practice the horizon is taken to be 5 years). Let ρ be a fraction between 0 and unity, where ρ is a function of the ratio χ/α such that ρ goes to unity as the ratio goes to infinity and to zero as χ/α goes to zero. Then the financing equation can be written

ΔD=ρgPX1X1E1+μ(χPX1X1E1/r1(D1FR1))(35)

The proportion ρ is intended to capture the fact that within the developing country region there is a distribution of debt ratios, corresponding to a range of indebtedness. For those countries whose ratio far exceeds some critical level, new financing is unlikely to be forthcoming initially, even if exports rise. For other countries whose interest ratios are within the threshold level, financing is likely to grow with exports. However, a sustained growth in exports will tend to graduate countries in the first group into the second group, by bringing their interest ratios down to acceptable levels. The behavior of the average developing country ratio will in a rough way capture the proportion of countries that are below the threshold level at which they can obtain additional financing. In the model that is simulated below, the ρ is set to a constant, 0.3. In future work, its value may be endogenized, however.

Thus financing and repayment for developing countries is a function of the average rate of growth of the value of DC exports over the simulation period, the rate of convergence μ, and the interest to exports ratio α, (which depends on the inherited debt stock and the interest rate). The flow of financing changes as a result of forces largely beyond the control of developing countries themselves—interest rates and demand for their exports. The threshold level χ and the speed of adjustment μ were calibrated to give a realistic path for future financing flows; however, it is clear that these parameters may be influenced both by DC policies and regulations in industrial countries which affect the lending behavior of financial institutions.

There are some components of net debt that can be controlled directly by the country itself. In particular, foreign exchange reserves can be used to cushion shocks to the balance of payments; when there is a shortfall of export earnings or a fall in gross capital inflows, reserves can be run down temporarily, and subsequently built up to a normal relationship with, say, imports. Conversely, favorable developments in the terms of trade or export volumes may lead to temporary increases in reserves above their equilibrium levels; to the extent the favorable export performance is permanent, imports can be expected to rise over time, and reserves will therefore be run down in later periods. Thus reserves serve as a buffer to cushion the economy against shocks to the balance of payments; as a result, imports may not exhibit such extreme fluctuations. 39/ The model includes an equation for foreign exchange reserves FR of the form

ΔFR=γ[PXXE+ΔDr(D1FR1)]+δ[θPI1I1E1FR1](36)

where θ is the normal ratio of reserves to imports, so that in equilibrium,

θ = FR / PI · I · E

Equation (36), along with the balance of payments identity that states that the current account is equal to the change in debt minus the change in reserves, implies that imports are given by the following equation:

Δ(PIIE)=(1γ)[PXXE+ΔDr(D1FR1)]δ[θPI1I1E1FR1](37)

Thus, a shock to export earnings, for instance, will be cushioned by a decline in foreign reserves, so that imports decline not by the amount of the decline in exports, but by a proportion 1-γ that is less than unity. Over time, however, the normal relationship between reserves and imports will be reestablished—this is the role of the second term in equation (37).

2. The structure of the aggregate developing country model

As mentioned above, output of this region consists of a composite manufactured good, oil, primary commodities, and a non-traded good. The supply structure of these four goods is assumed to be quite different. The price of the manufactured good is not perfectly flexible, and does not move immediately to equate demand for the good and potential output. Instead, an increase in demand will increase both output and, over time, the price of the region’s manufactured good. Because manufactured goods are differentiated, producers have some market power to price their good differently from goods produced in other countries. The rate of change in the price of the DC manufactured good depends negatively on the gap between capacity output in this sector and actual output. However, since historical data did not exist for capacity output for developing countries as a whole, the coefficient could not be estimated. Instead, the effect of capacity utilization on price was given a value based on similar equations for industrial countries.

The non-traded good also is assumed not to have a perfectly flexible price and hence exhibits increases in output when demand increases. It is assumed that increases in consumption fall on non-traded goods in some fixed proportion. The price of non-traded goods is however not modeled explicitly, and furthermore it is assumed that there is no capacity constraint on the production of non-traded goods: output can be increased without shifting resources out of the other sectors.

In contrast, both oil and primary commodities are treated as a homogeneous goods, each with a single world price. In the case of oil, the price in real terms is taken to be exogenous, and the developing countries and high-income oil exporters are jointly treated as residual suppliers, such that world demand and supply are equal. For primary commodities, the relative price is endogenous, and moves immediately to clear the model. Supply of commodities is assumed to be given by the accumulated capital stock in this sector; the paradigm is a harvest or production from mines where individual producers are too small to influence the price, and where marginal costs of contemporaneous supply are zero. Therefore, an increase in demand for primary commodities will in the first instance bring about an increase in their price but not in the quantity produced. Only over time, as resources are shifted into this sector in response to improved profitability, will supply increase.

Given the quantity of exports and net financing less interest payments, the quantity of imports is determined residually. Implicit then is the assumption that the amount of financing constrains domestic expenditure; notional import demand (if it were made explicit), would be larger than actual imports.

Domestic demand is disaggregated only into consumption and investment; in the data, private and government demands are not distinguished. Consumption (C) depends on wealth (W) as well as the real flow of financing available, as a ratio to lagged consumption:

Δlog(c)=1.13(1.9)+.317(1.9)log(W1/C1)+.281(1.2)(ΔD/EP)/C1R¯2=.172SER=.016(38)

where D is the value in U.S. dollars of outstanding debt, E is the exchange rate and P is the absorption price. Wealth is calculated by capitalizing expected future income, as for the industrial country models, and adding net claims on foreigners (in the case of developing countries, subtracting net liabilities to foreigners). As in the industrial countries, where disposable income has an effect on consumption, here the flow of additional financing tends to lead to increases in current consumption. 40/ The amount of new financing that is not consumed is available for investment. This amount must be large enough to sustain the increased debt interest payments on the higher value of debt, since the model in calculating the amount of endogenous financing, uses the value expected in the future for nominal exports. Starting from an equilibrium with the interest payments ratio at its threshold level, it must therefore be the case that the marginal product of capital, times the proportion invested, must be greater than the rate of interest on an additional unit of debt. Otherwise, an additional dollar of debt will raise the numerator by more than the denominator. Because an assessment of the marginal product of capital is implicit in the equation for the supply of foreign financing, there is no additional investment equation; instead, investment is determined residually as the sum of domestic saving and foreign saving (that is, the current account deficit), with the latter determined by the solvency criterion. 41/

Investment is allocated by sector on the basis of rate of return considerations. There are a number of factors—taxes and subsidies, relative prices and wages, and shifts in production technology—that are necessary for a complete story. Neither the data nor the model are adequate for such a treatment; however, the model does focus on an important element, namely the sharp fall in profitability of producing primary commodities and the overhang of large amount of productive capacity that is the result of a capital stock that was accumulated when investment in this sector was attractive, for instance in mining. Given rates of depreciation that are low, and variable costs of production that are small relative to the capital costs, output may continue to be high even if no new resources are being shifted into the primary commodity sector. In the model, the share of new investment that goes into the production of primary commodities relative to manufactures is made to depend on their relative prices; below a certain level for this ratio, investment in the primary commodities sector is just equal to depreciation—that is, there is no net investment. Only when profitability in primary commodities reaches a certain level (taken to be its previous peak, roughly its 1980 level) will positive net investment in primary commodities resume.

The remaining additional investment will be directed to the production of manufactures; neither non-traded goods nor oil are assumed, for the purposes of the model, to involve capital. The desired supply of manufactures and the production of commodities will then depend on the existing stock of capital in that sector, and a time trend. In the absence of actual data on capital stocks by sector, production functions were not estimated but instead their parameters were chosen on the basis of plausible factor shares. 42/ Once in place, capital is assumed not to be mobile between sectors. Only new net investment will alter the shares of capital in the two sectors.

3. The high income oil exporters

This group of countries 43/ is treated separately, first because the countries are in general considerably wealthier than the developing countries discussed above, and hence do not face constraints on their balance of payments financing at the present time; and second, because their oil exports constitute so large a fraction of GNP that the structure of the model for this region can be made simpler.

In this model, trade volumes and prices are modeled in the same detail as for other developing countries, but domestic demand is not modeled nor is output of manufactures. Furthermore, imports are assumed not to be constrained by available financing; instead, import volume equations for primary commodities and manufactures each depend on the relative price of this region’s output (identified with the price of oil) and the import price of the relevant good. The balance of payments identity determines the region’s accumulation of net foreign assets.

IV. Some Standard Simulations

1. Industrial country monetary and fiscal shocks

In order to understand the model’s properties, it is useful to examine simulations of changes in the major exogenous variables. In particular, since the model will be used to analyze the effects of industrial country policies, we first look at standardized changes in the monetary and fiscal policy instruments in the three major industrial countries, the United States, Japan, and Germany. However, these simulations are not meant to suggest desirable or likely changes in exogenous variables, but rather to elucidate the functioning of the model. These simulations do not therefore serve the same role as those presented in the context of the World Economic Outlook.

In performing these shocks, care was taken not to depart from the historical experience of the countries concerned, nor to perform experiments that violate governments’ budget constraints, in the sense that governments are allowed to increase their debt as a ratio of GNP without limit. This would be the case, for instance, if the experiment were a permanent increase in bond-financed government expenditures, without an eventual increase in taxes. The model contains a tax rule that tends to stabilize the bond to GNP ratio, so that explosive growth in debt is ruled out. In addition, we prefer to perform experiments where the ratio of government spending to net national product does not change permanently, but only for some transitory period. The evidence cited above that the government’s spending share seemed not to have exhibited any marked trend since 1960 makes such a setup appropriate. Therefore, the fiscal shocks we report below are for a one percent increase in the government’s share of output in 1988, declining toward the baseline share with a speed equal to that implied by the historical estimates, namely a mean lag of 4.2 years, the time for half of the adjustment to take place (see section II.1.a above). Even if government spending declines to its baseline level eventually, the accumulation of government debt that has occurred in the meantime will imply some increases in taxes; however, in the simulations reported below, the tax increases are assumed to occur only starting in 1996, beyond the period of interest, which is 1988 to 1995.

A few words are necessary to explain how the simulations were performed. The exogenous and endogenous variables were first projected forward beyond the historical period; in most cases, the projections were simply those implied by the most recent WEO projections. The model was then used to calculate the residuals in the behavioral equations that would give the values of the endogenous variables, given the exogenous variables. Thus, the model is not used itself for making forecasts; instead the baseline projection is imposed on the model.

A complication in solving the model is the existence of expectations variables. These variables are constrained in the solution procedure to equal the values for the relevant future time period that the model produces—that is, the expectations are made to be consistent with the model’s predictions. This is achieved through a program that implements the Fair-Taylor algorithm, which constrains expectations and model solutions to be the same, to a preset tolerance, by iterating. 44/ In general, in order to avoid making the simulation results depend on arbitrary terminal conditions, the model has to be solved beyond the period of interest. In the simulations reported below for 1988-95, the model was in fact solved for 20 additional years, to 2015.

Appendix Table 1 gives the result of an increase in U.S. fiscal expenditures of 1 percent of GNP, declining back toward zero as described above. Because of the scaling, the initial effect on GNP has the interpretation of a standard fiscal multiplier, that is, the change in output resulting in a unit change in government spending. That multiplier is equal to 1.2 for the United States, which is slightly below the mean for existing multi-country models 45/ (and almost exactly equal to MINIMOD’s). With the passage of time, the positive effect on output disappears, and by the fifth year output is actually lower; this occurs because of crowding out of demand through two channels—higher interest rates and an appreciation of the dollar. The nominal effective exchange rate appreciates by about 2 percent on impact. Part of the fall off in the positive effect on output is also due to the decline in government spending. Since the model has cyclical mechanisms, such as the interaction of the spending multiplier and investment accelerator, output goes lower for a time; in the longer-run, however, it returns to its baseline path.

Effects on other countries of the fiscal expansion in the United States are also positive as concerns output; they benefit from increased expenditure in the United States as well as currency depreciation. However, interest rates rise in all countries, and this has some unfavorable effects on the developing countries because of higher debt service. Interest payments to export earnings rise, despite substantial increases in exports. Since the developing countries are assumed to peg to a basket of industrial country currencies, they tend to depreciate against the dollar in this simulation.

A U.S. monetary shock is presented in Appendix Table 2. In this simulation, the target for the U.S. stock of base money is increased by 5 percent in 1988, and kept at this higher level thereafter. Since the model is neutral with respect to nominal shocks in the long run, eventually the result will be an increase in the U.S. price level by 5 percent, and a depreciation of the dollar by the same amount. It can be seen that by 1994, the U.S. price level has increased by 5 percent; because the model reaches equilibrium in a cyclical fashion, the price level continues to rise for a time. In the short run, the monetary expansion lowers interest rates and stimulates output; the exchange rate also overshoots its long-run level (i.e. the U.S. effective exchange rate depreciates by more than 5 percent in the first year), as is to be expected in a model with price stickiness.

Effects on foreign economies are mixed. In keeping with the simple Mundell-Fleming model, monetary policy is negatively transmitted (after the first period) to other industrial countries, and output falls in Germany and Japan as a result of the appreciation of their exchange rates. Developing countries experience a small rise in GDP after the first year, and a substantial decline in their debt service ratio, as a result of lower U.S. interest rates. As mentioned above, the model takes the oil price (in real terms) to be exogenous, so it has not changed as a result of the shock, but the dollar price has risen. Moreover, the U.S. monetary expansion has raised world demand for oil, also increasing the GDP of the oil exporting countries.

Appendix Tables 3-6 give results for the same fiscal and monetary shocks for Japan and Germany. They are qualitatively similar to Appendix Tables 1 and 2. Fiscal multipliers are however considerably lower for Germany, which is natural given its greater openness. Another difference is that policy changes in Germany and Japan have smaller effects on other countries, since they are smaller economies.

2. A decrease in the price of oil

The model contains estimated equations for oil demand on the part of industrial countries, as discussed above. Any increase in demand brings about an increase in production, which is shared between the developing country region and the high-income oil exporters. Thus world demand and supply are brought into balance.

Appendix Table 7 reports a simulation in which the oil price was made exogenous in dollars and decreased by 20 percent, or roughly 4 dollars a barrel. It can be seen that this stimulates output in industrial countries as a group for several years, by about 0.5 percent relative to its baseline level. Interestingly enough, the stimulus to output occurs largely because long-term interest rates fall, anticipating downward pressures on prices that however occur only with a long lag. This mechanism—large effects on expectations, and hence anticipatory effects on long-term rates—is a feature that depends on having forward-looking expectations as in MULTIMOD. However, individual countries are affected differently; in Japan, because of the yen appreciation, output actually declines after the second year.

Developing countries generally benefit from the fall in oil prices, though, given their position as a net oil exporter, their terms of trade deteriorate. The high income oil exporters show an increase in real GDP, but not of course their real income nor their current account balance (not shown). Given a long run elasticity of oil demand of about 0.7, the value of their exports declines.

3. An increase in financing flows to developing countries

Appendix Table 8 presents a simulation in which the flows of financing from industrial to developing countries are increased by $20 billion each year over 1988-92 relative to their baseline levels. These financing flows are assumed to be the results of official loans at concessional rates and with reimbursement beyond the end of the simulation period, financed by increased budget deficits in industrial countries (on the basis of GNP shares).

Since the developing countries are assumed to be constrained by available financing, their imports go up one-for-one with the increase in loans. This increase in imports leads to higher economic activity in industrial countries, despite a small increase in their interest rates. Stimulus to activity varies by country, depending on the importance of trade with developing countries and indirect feedbacks. Industrial countries as a group show a substantial, and sustained rise in output. Output in developing countries also increases, as increased imports of investment goods increase the capital stock and aggregate supply.

Appendix I

Table A1.

Increase of U.S. Government Spending by 1 Percent of GNP

(PERCENTAGE DEVIATION FROM BASELINE UNLESS OTHERWISE NOTED)

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A POSITIVE VALUE INDICATES AN APPRECIATION.

Table A2.

Increase of 5 Percent in the U.S. Money Supply

(PERCENTAGE DEVIATION FROM BASELINE UNLESS OTHERWISE NOTED)

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A POSITIVE VALUE INDICATES AN APPRECIATION.