II Industrial Countries
- International Monetary Fund
- Published Date:
- July 1990
The long-run model of consumption and wealth is based on the work of Blanchard (1985), with extensions by Weil (1986) and Buiter (1988). Households maximize the discounted utility of current and future consumption subject to the constraint that the present value of consumption not exceed initial wealth. Wealth is defined as the sum of the real value of assets held by households plus the present value of the flow of after-tax labor income (“human” wealth). Because households are assumed to face a constant probability of death, λ, and the total population is growing at rate n, not all future labor income accrues to existing households. This is reflected in the rate used to discount labor income, which is the real interest rate, r, plus λ + n. Human wealth, WH, is then defined as:
where (Yt – Tt) is the flow of after-tax labor income at time t. Total wealth, W, is the sum of human wealth and asset wealth, A:
For instantaneous utility functions that exhibit constant relative risk aversion, that is,
C = α(r,σ,δ,λ) W
In terms of the equations and variable definitions that appear in the model, human wealth is expressed in discrete time as a function of its next-period discounted value and the flow of after-tax labor income in the initial period:3
where RBAR is the equilibrium real interest rate, 0.035 is an estimate of n + λ, (1 - β) is the share of labor income in total output, and TAXH is taxes on labor income.4 Asset wealth is defined as the sum of the real market value of the capital stock (as defined in the next section) and the real value of financial assets. Total wealth, then, is
where WH is human wealth, WK is the real market value of the domestic capital stock, M is nominal high-powered money balances, B is the stock of domestic government bonds, NFA is net foreign assets denominated in U.S. dollars, ER is the price of domestic currency in U.S. dollars, and P is the deflator for domestic absorption.5 The value of government bonds in equation (2′) is partially but not fully offset by the present value of associated tax liabilities embodied in WH—the discounting of future labor income at a rate that exceeds the real interest rate implies that a portion of government bonds are net wealth to existing households.
Changes in the real interest rate affect both the initialperiod value of human wealth and the propensity of households to consume out of wealth. Specifically, equation (3) can be differentiated with respect to the real interest rate to obtain
d(log(C)) = [d(log(α))/d(r) + (d(WH)/WH)/d(r)] d(r).
The long-term real interest rate is included in the consumption function to capture the combined effect on α and WH of changes in r.
In addition to wealth and real interest rates, consumption is assumed to be affected by changes in disposable income. This assumption is made because some households are “liquidity-constrained” in the short to medium run in the sense that their spending is determined by changes in disposable income as opposed to their longer-run wealth position. This is consistent with the strong co-movements in consumption and disposable income observed in aggregate timeseries data (see, for instance, Campbell and Mankiw (1989)).6 A demographic variable was added to the consumption function to account for changes in spending owing to “life-cycle” effects that are not captured in the infinite-horizon model of household behavior. Specifically, the elderly and the young consume while earning little labor income; this is reflected in the inclusion of a dependency ratio in the equation, defined as the ratio of the population aged under 15 and 65 and over to those aged 15–64 (DEM3).7 Finally, there is evidence of an upward shift in the consumption function in the 1980s for many industrial countries, perhaps owing to the effects of financial innovation on the borrowing costs faced by households. A dummy variable equal to one from 1980 on (DUM80) was added to the equation to account for this effect. Expressed in error-correction form, the consumption function then is
where RLR is the long-term real interest rate, and YD is real disposable income defined as net domestic product plus transfers less taxes.8 The error-correction model ensures that consumption is homogeneous of degree one in wealth in the long run, with the ratio of consumption to wealth depending on the real interest rate. A shock to disposable income affects consumption in the short run, but the effect dies out gradually over time at a rate determined by C1.
The consumption function was estimated using annual data over the period 1969–87 for the Group of Seven countries and the smaller industrial region. We constrain the parameters C1, C2, and C3 to be the same across the eight regions because of the few observations for each country and the lack of evidence that consumption behavior differs significantly across industrial countries. Instruments were used for wealth, the real interest rate, and disposable income to control for their potential endogeneity.9 Estimation was performed using a Zellner-efficient systems estimator, with the following results (absolute values of t-ratios in parentheses):
The long-run relationship between consumption and the levels of the right-hand-side variables, after consumption has fully adjusted to changes in its determinants, is as follows:
Consumption is homogeneous of degree one with respect to wealth; the long-run consumption-to-wealth ratio depends on the real interest rate and the demographic variable. An increase of 1 percentage point in the real interest rate lowers consumption by about 6.2 percent in the long run, while a rise of 1 percentage point in the dependency ratio raises consumption by 2.0 percent.
Gross investment is the sum of the change in the net capital stock and depreciation on existing capital:
where INVEST is gross investment in units of domestic absorption, K is the net capital stock, and DELTA is the (exogenous) depreciation rate on capital. The change in the net capital stock is determined by the gap between the market value of existing capital and its replacement cost, following the approach of Tobin (1969). The market value of capital is the discounted value of its stream of after-tax income. Conceptually this value can be represented as
where WKt is the real market value of the capital stock existing at time t,
The income of the period-t capital stock in future period s consists of the income of the total capital stock in period s multiplied by the share of the period-t capital stock in that income. The after-tax income of the total capital stock in period s is the value of its marginal product times the capital stock, less net taxes on capital income; the result is expressed in units of domestic absorption:
where YK is the after-tax income of the total capital stock, PGNP is the output deflator, MPK is the marginal product of capital, TAXK is taxes on capital, and P is the absorption deflator. The Cobb-Douglas production function used in the model implies that the marginal product of capital times the capital stock is a constant proportion, β, of total output. This allows equation (9) to be rewritten as
The net taxes paid by capital are calculated as the effective corporate tax rate times estimated capital income, with adjustments for depreciation allowances, the tax deductibility of interest payments on debt, and investment tax credits.10 Depreciation allowances are based on the historical cost of capital goods, which is less than their replacement value in an inflationary environment. The (nominal) historical cost of capital goods, VKHIST, equals the previous period’s depreciated historical cost plus the value of gross investment for the current period:
To calculate nominal interest payments, the replacement cost of the capital stock is multiplied by the estimated share of total financing represented by debt; interest is paid on debt based on a three-year moving average of the long-term interest rate.11 Taxes on capital are then
where CTRATE is the tax rate on capital, DSHR is the share of debt in total financing, and TXCRED is the average tax credit rate on investment.
Total capital income in time s is then divided into the component accruing to capital existing at time t and that due to new capital put in place between periods t and s. Since capital is assumed to be homogeneous (in contrast to vintage capital models), the share of the period-t capital stock in total capital income at time s is the ratio of the period-t capital alive in time s to the total capital stock. Given depreciation of capital at rate δ, and denoting period-t capital alive at time s by
Defining growth in the capital stock between periods t and s as γ, the total capital stock in period s is
Expressions (8), (10), and (15) imply that the market value of the period-t capital stock is
The equation in the model for WK is a discrete-time approximation to equation (16), where the present value of after-tax capital income beyond period t is replaced by the next-period discounted value of WK. The discount rate on capital income is the short-term real interest rate on government bonds plus a risk premium, RPREM,12 δ is the depreciation rate, and γ is the growth rate of the capital stock:
The higher the market value of the capital stock relative to its replacement cost, the greater is the incentive to undertake new investment; growth in the capital stock is assumed to be proportional to the gap between the market value and the replacement cost of existing capital:
We estimate equation (18) using annual data for the Group of Seven countries and for the smaller industrial region for the period 1968–87. A Zellner-efficient systems estimator was used on the equations for the eight regions. The parameter K1 was constrained to be the same for all regions, while the intercept term differed across regions. To control for the potential endogeneity of the market value of the capital stock—which is based on both current and future data—instrumental variables were used. The instruments were specific to each region and included the real monetary base, real government expenditure, the lagged capital stock, lagged real GDP, and the change in lagged real GDP (all in natural logarithms). The value obtained for K1 was 0.080, with an associated t-ratio of 24.1.
In the long run, a 1 percent increase in real GDP is associated with a 1 percent rise in the capital stock, ceteris paribus. The effect of a rise in the real interest rate depends on the baseline values for the real interest rate and the depreciation rate: for the United States, for instance, an increase in the real interest rate of 100 basis points causes a decline in the capital stock of about 6 percent in the long run.13 In addition, the level of the capital stock depends on the rate of inflation for two reasons: (i) depreciation allowances are a function of the historical cost of capital, and (ii) interest deductions depend on nominal interest rates, which rise with the rate of inflation in the long run. When inflation rises, the first effect increases taxes and lowers the market value of capital, while the second reduces taxes and raises the value of capital. The first effect dominates in the long run for all countries except Germany: an increase in the rate of inflation of 1 percentage point from the baseline value reduces the capital stock by an amount that ranges from 0.1 percent for Italy to 0.6 percent for the United States.14 For Germany, interest deductions are large relative to depreciation allowances, and higher inflation raises the capital stock by 0.3 percent.
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. 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.
Oil Consumption Equations
In modeling oil, it is assumed that there is one world price; this assumption is realistic for world trade but is less so for domestic consumption. Error-correction equations for oil consumption were estimated with pooled data for 1965–86, and the same long-run and short-run price elasticities were imposed across countries.15 A unit elasticity with respect to GDP in the long run was imposed. Speeds of adjustment and short-run price elasticities are also constrained to be the same for all countries, as unrestricted coefficients showed a remarkable degree of uniformity across countries. Coefficients for the short-run effect of activity on oil consumption were allowed to differ across countries. Since oil serves as an input to production, GDP rather than domestic absorption is used as the activity variable in the oil consumption equation. For manufactured imports, in contrast, domestic absorption is the activity variable in the equation (see below).
The specification and the estimated coefficients are presented in Table 1. The estimates imply strong and statistically significant effects of relative prices on oil consumption. The long-run relative price effect is −0.75, with a mean lag of over 10 years. The short-run elasticity of oil consumption with respect to economic activity is greater than unity for Japan, Germany, France, and the United Kingdom; in the long run, the elasticity is constrained to be unity, as discussed above. The short-run price elasticity is very small.
del(log(COIL)) = COIL0 + COIL1*del[log(GDP)] + COIL2*del[log(POIL/(ER*PGNP))] + COIL3*log[POIL(-1)/(ER(-1)*PGNP(-1))] + COIL4*log[GDP(-1)/COIL(-1)]
|Germany, Fed. Rep. of||–0.23||1.6||–0.046||–0.0478||0.064|
|Smaller industrial countries||–0.22||0.76||–0.046||–0.0478||0.064|
|SER = 0.042|
Imports of oil by each industrial country are determined residually, as the difference between consumption and production. For those countries that produce oil, the implied elasticities of oil imports are considerably larger than those for consumption, since production is exogenous. For instance, if oil imports are one fourth of consumption, the elasticity of imports with respect to either price or GNP will be roughly four times that for consumption, reported above.
Commodity Import Equations
The basic equation for imports of commodities from developing countries is an error-correction model that regresses the change in imports on the change in GDP and relative prices, on lagged values of these variables, and on lagged imports, with all variables in log form. Since the price of primary commodities in dollars (PCOM) moves to clear world demand and supply of commodities, instrumental variables were used to estimate this equation; the instruments used were the supply of commodities, industrial country real GDP, and the country’s real GDP and GDP deflator. Coefficient estimates, using data for 1965–87, are given in Table 2.
del(log(ICOM)) = IC0 + IC1*del[log(GDP)] + IC2*del[log(PCOM/(ER*PGNP))] + IC3*log[PCOM(-1)/(ER(-1)*PGNP(-1))] + IC4*log[GDP(-1)] + IC5*log[ICOM(-1)]
|Germany, Fed. Rep. of||–0.015||1.106||–0.483||0.577||0.055||1.51|
|Smaller industrial countries||–1.862||1.959||–0.452||–0.135||0.498||–0.599||0.722||0.034||1.86|
For some countries, the unrestricted estimates were implausible or insignificant. For Canada, the estimated speed of adjustment was 1.05, which would give nonsensical long-run results, so the equation was rerun in level form (imposing in effect instantaneous adjustment). For the United Kingdom and Germany, the equation in first-difference form worked best, with no lags on GDP or relative prices. Unlike the estimates in Masson and others (1988), in which Japan had no short-run GDP elasticity, it now has a small, but insignificant one.
Long-run elasticities are given in Table 3. GDP elasticities are generally well below unity, except for the United Kingdom and Germany; the data clearly reject the long-run unit elasticity that is imposed in the equations for imports of manufactures (see below). Price elasticities are about the same on average (about −0.5) as those estimated in Masson and others (1988); however, they are more uniform across countries in the present version.
|Germany, Fed. Rep. of||1.11||–0.48|
|Smaller industrial countries||0.83||–0.23|
Volume Equations for Imports and Exports of Manufactures
The trade model for manufactures in this version moves away from the parsimonious specification in Masson and others (1988), where common coefficients were imposed on export share equations in an attempt to ensure world adding up of exports and imports (in practice, a world trade discrepancy remained that had to be allocated). A more general specification for import volumes is applied here, using an error-correction model, as in much of the rest of the model.
The main differences between the new import volume equations and those described in the earlier study are (1) the use of an error-correction specification, (2) the use of exports and domestic absorption as activity variables, and (3) the addition of the trend-squared term to most equations (unless completely insignificant). The general specification is given in Table 4; it permits a short-run effect of the change in the log of absorption that differs from its long-run effect, which is constrained to have a unit elasticity. Moreover, the current change in relative prices is included, as well as its lagged ratio. Instead of just the log of absorption, however, a weighted average of absorption and of exports of manufactures, both in logs, is included. Since imported inputs are used in producing export goods, an increase in the latter may well be associated with higher imports. A grid search was performed on the weight IM7, yielding the estimates in Table 4 that minimized the residual sum of squares.
del(log(IM)) = IM0 + IM1*del(IM7*log(A) + (1 - IM7)*log(XM)) + IM2*del(log(PIMA/PGNPNO)) + IM3*log(PIMA(-1)/PGNPO(-1)) + IM4*(IM7*log(A(-1)) + (1 - IM7)*log(XM(-1)) - log(IM(-1))) + IM5*T + IM6*T**2
|Germany, Fed. Rep. of||0.72||–0.547||1.438||–0.783||–0.316||0.351||0.007||0.695||0.036||1.28|
|Smaller industrial countries||0.77||–0.790||2.104||–0.670||–0.597||0.511||0.008||0.761||0.035||2.07|
Sample period is 1966–87.
Sample period is 1966–87.
The estimates are generally quite plausible, with all price elasticities and activity elasticities of the correct signs. For the United Kingdom, the current change in relative price had a small, insignificant positive coefficient, and that variable was dropped. The squared-trend term gave insignificant coefficients for Germany and the smaller industrial country region, as well as lowering the significance of other variables, and it was therefore omitted for those countries. Short-run effects of activity are quite high—over 2.0 for four of the countries, and over 1.0 for all of them; this result is not simply an artifact of including exports in the activity variable, since the coefficients are similar to those when absorption alone is used (that is, IM7 = 1). Price elasticities are generally well determined, but vary considerably in both the short term and long term across countries. Speeds of adjustment also vary, with mean lags extending to several years, except for the United States, where the adjustment is quite fast.
Export volume equations have a number of changes relative to the earlier study’s specification: they incorporate an error-correction model; the scale variable is foreign absorption (FA) rather than foreign markets (FM); and the price variable takes into account the price of exports relative to prices in the importer’s home market, as well as competition in third markets. The equation is also more general than in the earlier version of MULTIMOD in allowing for lagged real exchange rate effects (REER, in logs).16 The most important changes are the use of weighted foreign absorption as an explanatory variable, and the inclusion of bilateral competition in the importer’s market in the relative price variable. Exports in the original MULTIMOD were based on the Samuelson-Kurihara formulation,17 in which exports are a function of a foreign market variable that combines the imports of foreign countries using base-period weights; movements in the real exchange rate determine gains or losses in market share. However, this formulation gave changes in market share that were not always sensible. Moreover, a disadvantage of this specification is that simulation of a single-country model is not straightforward, since the relative price effects operate not only through gains or losses in market share but also through the endogenous determination of other countries’ imports. As a result, comparison with conventional single-country export equations is difficult.
Foreign absorption in the current model is calculated as a weighted sum of the absorption in other countries/ regions, with weights equal to base-period shares of the home country’s exports accounted for by the foreign countries. The real exchange rate is calculated as the ratio of the home country’s export price to a foreign price that includes both foreign GNP deflators and a double-weighted average of competitors’ export prices (see coefficient listing for weights). Table 5 gives the weights used in calculating FA and also REER, based on the pattern of trade flows (for non-oil trade exclusive of primary commodity exports of developing countries) in 1980. Letting Xij be the exports of country i to country j in 1980, we define the following ratios:
|Exporter||United States||Japan||Germany, Fed. Rep. of||Canada||France||Italy||United Kingdom||Smaller industrial countries||Developing countries|
|Germany, Fed. Rep. of||11.8||2.2||—||1.2||23.7||16.2||12.2||72.3||38.7|
|Smaller industrial countries||14.3||7.1||53.2||2.1||30.6||16.5||27.6||72.8||55.1|
Excludes primary commodity exports of developing countries.
Excludes primary commodity exports of developing countries.
If we also let Eij be the i-currency price of currency j, and
The estimated equations reported in Table 6 constrain the coefficients on the change in foreign absorption, on the lagged dependent variable, and on the lagged real exchange rate to be the same for all countries and regions; however, coefficients on the change in the real exchange rate, on the time trend, and on the time trend squared all differ—as do constant terms. An F-test was performed on each of the restrictions, and for the latter coefficients, the data rejected the constraint of common values across countries and regions. The common coefficient on foreign absorption was thought desirable to minimize “unallocated” imports. The allocation of the remaining world trade discrepancy is discussed below in the subsection on the adding up of world trade and current balances.
del(log(XM)) = XM0 + XM1*del(REER) + XM2*del(log(FA)) + XM3*log(XM(-1)/FA(-1)) + XM4*REER(-1) + XM5*T + XM6*T**2
|Germany, Fed. Rep. of||–1.712||–0.225||2.003||–0.633||0.447||4.906||–0.051|
|Smaller industrial countries||–1.243||–0.242||2.003||–0.633||–0.447||2.696||–0.050|
|SER = 0.036||DW = 1.94|
Reported coefficient has been multiplied by 100.
Reported coefficient has been multiplied by 100.
The estimates imply a larger short-run elasticity of exports with respect to foreign absorption (2.0) than in the long run (imposed to be unity). This pattern—as well as the magnitudes of coefficients—is roughly consistent with import equations (see Table 4). Short-run price elasticities of exports differ across countries and regions but are typically smaller than the long-run elasticity (which is -0.64 for all countries). The common speed of adjustment is quite high—60 percent of the gap is closed after one year.
The government sector does not include any estimated 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 total taxes (net of noninterest transfers) relates tax receipts (TAX) to a tax rate (TRATE) and a tax base, which is approximated by net national product plus interest receipts on domestic government debt:
In simulations, 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, tax rates must eventually adjust to respect the intertemporal budget constraint, provided that the real interest rate exceeds the real growth rate of the economy. If tax rates do not adjust, the government bond stock can grow without bound relative to GNP, as interest payments compound on outstanding debt.
A feedback rule was specified for the tax rate (TRATE) that makes it respond to both the level and the change in government debt relative to an exogenous target level, BT. The difference between the actual and target level is divided by nominal GNP, so that a given deviation in the bond stock relative to GNP elicits the same tax rate response across countries:
This rule is a variant of the one shown in Masson and others (1988). In that version of the model, the tax rate responded to the gap between the ratio of bonds to GNP and a target ratio. The original rule sometimes generated anomalous movements in tax rates owing to temporary divergences in nominal GNP from its equilibrium level, especially for countries with large baseline debt positions relative to GNP. For instance, a demand stimulus will initially cause output and prices to rise, temporarily reducing the ratio of bonds to GNP. With the old rule, this could reduce tax rates in a way that reinforced the initial demand stimulus, which occasionally caused problems with the dynamic stability of the model. At a conceptual level, this response was not consistent with the original motivation for the tax reaction function, which was to ensure that the government respects an intertemporal budget constraint over an extended period of time. The current rule substantially reduces the impact of transitory changes in nominal GNP on the tax rate: at the same time, BT is adjusted in simulation exercises to reflect permanent changes in nominal GNP, such as those arising from money level or growth shocks.
The parameters were originally chosen on the basis of earlier work that studied the dynamics of MINIMOD and formulated rules that made the model stable.18 Such a stability analysis has not yet been performed with the present model; it remains a project for further work. The parameter on the level of government debt in this version of the model has been raised relative to that in Masson and others (1988) to ensure that government debt returns to its control solution over the horizon typically used for model simulations. For some purposes, it is more natural to leave the tax rate unchanged and to allow debt to accumulate, in which case DUM can be set to zero as opposed to its usual value of one.
Aggregate taxes are divided into taxes on capital (TAXK) and taxes on labor income (TAXH) as follows:
The tax rate on capital income can be adjusted in simulation exercises so that changes in the aggregate tax rate affect the after-tax income of both labor and capital. The simulation rule adjusts the tax rate on capital income in line with the aggregate tax rate:
where DUMCT is a parameter that can be set between zero and one.19
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. The supply of money, 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 not, however, exogenous; instead, there is a reaction function for the central bank’s behavior. In the United States, Japan, Germany, the United Kingdom, and Canada, central banks are assumed to move short-term interest rates to close a gap between a target for the stock of money and its actual value. In contrast, in France, Italy, and the smaller industrial countries, central banks are assumed to move short-term interest rates to limit movements of their exchange rates vis-à-vis the deutsche mark. A central parity for the deutsche mark/local currency exchange rate is assumed to be set exogenously for those countries, consistent with their participation in the exchange rate mechanism (ERM) of the European Monetary System (EMS).
Demand equations for real money balances (deflated by the absorption price) were estimated as a function of real absorption and the short-term nominal interest rate.20 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. The money demand function is specified as
Estimation of equation (25) for individual countries yields widely varying parameters that are often of implausible sign and magnitude. This result is perhaps not surprising, given the effect on the demand for money of financial innovation and deregulation in many countries in the 1970s and 1980s. In the version of MULTIMOD described in Masson and others (1988), some simulations performed with money demand parameters that varied across countries produced results that were difficult to interpret. For instance, a standard fiscal shock produced substantially different paths for interest rates and hence exchange rates, solely because of differences across countries in money demand coefficients under a money-supply targeting regime. For these reasons, the money demand equations for the Group of Seven countries and the small industrial region were estimated jointly with the constraint that the parameters M1, M2, and M3 have the same values for all regions. Using a Zellner-efficient systems estimator for 1969–87 gives the following results (absolute values of r-ratios in parentheses):
The long-run elasticity of money demand with respect to absorption is 0.62, while the long-run interest semi-elasticity is –0.032; money demand is less interest elastic in the long run than in the previous version of the model.
As mentioned above, monetary policy is implemented in the model through a reaction function, which takes one of two forms depending on the country. Italy, France, and the smaller industrial countries are assumed to target their exchange rate with respect to the deutsche mark; the other industrial countries target their money supplies. In both cases, deviations from the target are permitted in the short run to avoid excessive interest rate volatility. At the same time, a nominal anchor is provided over the longer run by the exogenous money-supply or exchange rate target.
For the EMS countries, the change in the short-term interest rate is a nonlinear function of the gap between the exchange rate versus the deutsche mark and an exogenous target level:21
The long-run nominal anchor is provided in this case by the German money supply. For the other industrial countries, the short-term interest rate adjusts gradually to a level (say RST) consistent with equality between money demand and the exogenous target money supply:
Another key relationship in the financial sector is the arbitrage condition between short-term and long-term interest rates. This equation constrains the expected holding-period yield on long-term bonds and the short-term interest rate to be equal. In the first version of MULTIMOD, long-term bonds were assumed to be consols. In this version of the model, we assume that long-term bonds are pure discount bonds with a maturity of five years—generally the maturity embodied in the data. The long rate is then a function of current and expected future short rates:
The short-term real interest rate (RSR) is defined as the nominal interest rate adjusted for growth in the absorption deflator over the current period:
The long-term real interest rate (RLR) is the long-term nominal rate adjusted for average rate of growth in the absorption deflator over the five-year life of the bond:
Price Determination and Aggregate Supply
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 a framework of overlapping contracts. Price setting by firms is assumed to be determined as a markup over variable costs that depends on the level of capacity utilization, while wage bargains depend on the degree of slack in labor markets as well as on expected inflation. Employment and wages are not modeled explicitly here; instead, they are substituted out. Capacity utilization 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.
If there are overlapping wage contracts, then nominal wages cannot adjust immediately to conditions in labor markets or to expected inflation. We assume that this inertia takes the following form:
where w is the log of average wages, ℓd and ℓs are the logs of labor demand and supply, respectively, and πe is the expected rate of change of consumption prices in the next period.22 The production function gives labor demand: it is the level of employment, given normal utilization rates and the existing capital stock, that would meet aggregate demand for output.
The Cobb-Douglas production technology of our model specifies that the log of potential output
Labor demand (at normal utilization rates) is thus
We assume that labor supply depends on exogenous demographic factors (embodied in
The log of the output price, q (in the model code, this is the non-oil GNP price, PGNPNO) is determined as a markup over nominal variable costs (here just normalized labor costs,
Equations (35) and (36) can be used to express ℓd–ℓs as a function of the real wage and of
then the difference between p and q is a function of the terms of trade, or the real effective exchange rate REER:
Equation (27) implies that real exchange rate appreciation increases output prices relative to consumption prices. Starting from equations (33)–(36), using equation (37) to substitute for wages and equation (39) to substitute for consumption prices, we can obtain a reduced-form inflation equation:
Thus, the rate of change of output prices depends on its lagged value, on the rate of capacity utilization and its current and lagged change, on expected consumption price inflation, and on the real effective exchange rate. Since 0 ≤ δ, Ψ, β, ≤ 1 and 0 < θ, γ, the signs of the coefficients on the right-hand side of equation (40) are expected to be positive for Δq−1, cu, Δcu, and πe, and negative for Δcu−1 and REER.
The equation was initially estimated in the form of equation (40). 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 equation (40). The regressions were first run separately for each country, and then they were pooled, and selected coefficients constrained to be the same. 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. Both separate and pooled estimates suggested that there was no significant effect for either the change in capacity utilization or the real effective exchange rate. Consequently, these variables were dropped; in addition, averaging capacity utilization gave somewhat more significant results: this variable is given as MCU below. The final equation, estimated over 1968–87, constrained the capacity utilization term to be the same, by expressing the dependent variable as the acceleration of inflation. The value of δ is allowed to vary across countries, as is the constant, which in all cases is close to zero (as is the mean of MCU over the sample period).23
The estimates, obtained using instrumental variables, are presented in Table 7.24 The degree of nominal flexibility is reflected in the magnitude of δ = P2, while real flexibility increases with the coefficient on capacity utilization, P1. In the limiting case where δ equals unity, the rate of change of the output price depends only on expected inflation, not on past price changes. The estimates indicate greater nominal stickiness, corresponding to longer average contract length, in the United States and Canada. The greatest nominal (but not real) flexibility is exhibited by Germany. These structural differences are broadly consistent with some earlier work on wage/price stickiness (Bruno and Sachs (1985); Branson and Rotemberg (1979)) and the greater prevalence of multiyear contracts in North America. Unfortunately, the data did not allow distinguishing between degrees of real flexibility, as captured by P1, which is constrained to be the same across countries. More work on this equation is in progress, in particular, to allow for stronger nonlinear effects of capacity utilization.
del[log(PGNPNO)] = P0 + P1*[0.5*log(CU*0.01) + 0.5*log(CU(-1)*0.01)] + P2*del[log(P(1)) + (1 - P2)*del(log(PGNPNO(-1))]
|Germany, Fed. Rep. of||0.0037||0.159||0.520|
|SER = 0.0067|
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, although in fact it also includes some semifinished manufactures and primary commodities) that 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. Exporters may also discriminate between different export markets, but this possibility is not allowed for in the model. Prices for manufactured imports 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:
where the weights sij are as defined in the subsection on volume equations for imports and exports of manufactures, 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 export and output prices, where foreign prices use the same 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 term forces export prices in the long run to rise one for one with domestic output prices. Let PXM be the manufactured export price, PGNPNO the home non-oil output price, and PFM a weighted average of competitors’ prices in foreign markets. The equation and the coefficient estimates are given in Table 8. The regions were pooled, and the coefficient PXM2 constrained to be the same; this restriction was not rejected by the data. Not surprisingly, the estimates indicate a somewhat greater sensitivity of export prices by Japan, Italy, and France to the rate of change of foreign prices and very little sensitivity by the United States.
del[log(PXM)] = PXM0 + PXM1*del[log(PGNPNO)] + (1−PXM1)*del[log(PFM)] + PXM2*log(PGNPNO(−1)/PXM(−1))
|Germany, Fed. Rep. of.||0.000||0.749||0.077|
|Smaller industrial countries||–0.016||0.626||0.077|
|SER = 0.036|
International Accounts and Exchange Rates
A final block of equations in each industrial country model covers 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-term 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 cumulating current account surpluses. Historical data for the net foreign asset positions of 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. Such an arbitrage condition is analogous to the assumption described above that expected holding-period yields on long-term 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.
The level of the exchange rate is thus strongly influenced by monetary forces that affect the short-term interest rate. However, exchange rate expectations—which are made to be consistent with the model’s solution for the exchange rate next period—also 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 productivity differences.
Of course, the bilateral exchange rates determined in the model can be weighted 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 weights from the Fund’s Multilateral Exchange Rate Model (MERM), which are used in the effective exchange rates published by the Fund for 18 industrial countries.25 The weights for the smaller industrial country region are the result of aggregating the MERM weights for the smaller industrial countries.
Adding Up of World Trade and Current Balances
Published data contain discrepancies that imply that exports and imports summed across all countries are not equal; the problem is even more severe when an attempt is made to include factor service payments and receipts, as in current account positions. Nevertheless, it is a desirable property of a global model that incremental exports equal imports, whether or not their baseline levels are equal. Adding up is assured for commodities and oil from the way data are constructed and the imposition of market clearing in the model. For manufactures, adding up is achieved by allocating real and nominal world trade discrepancies to export volumes and import prices, respectively.
The model contains equations for “adjusted” exports of manufactures, XMA, that are equal to unadjusted exports, XM, determined as described in the section on trade volumes above, plus a coefficient times the excess relative to baseline of world import volumes over export volumes. The coefficient reflects the share of the country in total trade in manufactures. The remaining discrepancy in nominal trade flows is allocated across countries in a similar fashion by adjusting import prices PIM to get adjusted import prices, PIMA. In practice, world trade discrepancies for manufactures are not very large in simulation, so that the properties of the structural import and export equations dominate.
Given adding up of merchandise trade and nonfactor services, adding up of the world current account balance to zero is assured in simulation if, in the data, net foreign asset positions sum to zero across the world (since we assume that all claims pay the same U.S. dollar interest rate). This condition is met by defining the net foreign assets of the developing countries residually, as no reliable data are available for this group of countries.