Abstract
This paper describes minimod, a small international macroeconomic model. The construction of MINIMOD was undertaken for two reasons. The first was the desire to have a readily understandable and transparent model of manageable size suitable primarily for policy analysis rather than forecasting. Transparency of results is especially important because it is clear that models are only a rough, and often flawed, representation of reality; it is therefore important to be able to explain why simulation results are what they are, and to ensure that they are related to important economic linkages and not to errors of specification. This is much easier to do for a small model than for a large one. In the context of a multicountry model it is also an advantage to have small, identically specified models for all countries because they permit comparison of certain key parameters and identification of relationships that may explain differences of behavior between economies—for example, the degree of wage indexation or the interest elasticity of money demand.
This paper describes minimod, a small international macroeconomic model. The construction of MINIMOD was undertaken for two reasons. The first was the desire to have a readily understandable and transparent model of manageable size suitable primarily for policy analysis rather than forecasting. Transparency of results is especially important because it is clear that models are only a rough, and often flawed, representation of reality; it is therefore important to be able to explain why simulation results are what they are, and to ensure that they are related to important economic linkages and not to errors of specification. This is much easier to do for a small model than for a large one. In the context of a multicountry model it is also an advantage to have small, identically specified models for all countries because they permit comparison of certain key parameters and identification of relationships that may explain differences of behavior between economies—for example, the degree of wage indexation or the interest elasticity of money demand.
The second reason was a need for a macroeconomic model small enough to allow what are often called “rational expectations” simulations—that is, simulations where expectations are made consistent with the model’s predictions—to be performed inexpensively. Such simulations are perhaps better termed “consistent expectations” simulations, and this latter terminology is used in what follows.1 Although advances in computer technology have meant that the cost of simulations is not usually a factor for a model without forward-looking endogenous variables, the calculation of consistent expectations solutions can be prohibitively expensive for large nonlinear models. If a model is small, these costs are reduced considerably.
MINIMOD is a small, two-country model in which the equations for the United States and an aggregate rest of the industrial world region are based on the same theoretical framework. The model’s size is the minimum needed to capture the major macroeconomic relationships. The parameters of the model were obtained not by direct estimation but rather by simulation of a larger model. Endogenous variables in the larger model were aggregated and exogenous variables that are not relevant for policy simulations were dropped, yielding a much more compact version of the model while retaining its essential properties.
Section I describes the theoretical structure of MINIMOD. Section II explains how its parameters were extracted from the larger model using simulation techniques. Section III describes the results of several policy-simulation experiments using both consistent expectations and adaptive expectations, in which expectations are formed on the basis of past values of the variable. The final section contains our concluding observations and suggestions for further work. Appendix I presents the simulation model.
I. The Theoretical Model
MINIMOD is a model of two economies with the same structure (see accompanying table). The models are driven by conventional aggregate demand functions and are linked by goods and financial markets. Expectations of the future levels of inflation and of long-term bond rates in the two economies, as well as exchange rate expectations, are made explicit in the model. In the simulations discussed below, the model is simulated with both adaptive expectations and consistent expectations of these variables.
MINIMOD
Theoretical Model
Home Country
1. Real domestic absorption
2. Real domestic GDP
3. Real consumption
where
and
4. Net investment
where
5. Government budget constraint
6. Nominal tax receipts
7. Capacity output
8. GNP
9. Domestic absorption deflator
10. Inflation rate
11. Demand for m1
where
12. Long-term interest rate
13. Exports of goods and nonfactor services
14. Imports of goods and nonfactor services
15. Open parity condition
16. Accumulation of net claims on foreigners
Foreign Country
17. Real domestic absorption
18. Real domestic GDP
19. Real consumption
where
and
20. Net investment
where
21. Government budget constraint
22. Nominal tax receipts
23. Capacity output
24. GNP
25. Domestic absorption deflator
26. Inflation rate
27. Demand for m1
where
28. Long-term interest rate
Variables
* Indicates foreign variables
· Indicates a time derivative
EXOGENOUS
g = real government expenditure
m = nominal base money
μ = money multiplier
ξ= marginal tax rate
τ = time
= long-run expected inflation
ENDOGENOUS
Real Variables
a= absorption
c= private consumption
i= imports of goods and nonfactor services
k= capital stock
q= gross national product
w= wealth
x= exports of goods and nonfactor services
y= gross domestic product
yc= potential gross domestic product
yd= disposable income
Prices
p = absorption deflator
pq = gross national product deflator
π = inflation rate (rate of change of p)
πe = short-run expected inflation rate
Financial Variables
b= nominal stock of government bonds
m1= nominal money supply (M1)
f= nominal stock of net claims on foreigners (denominated in home currency)
t= government tax receipts, net of transfers
Interest Rates and Exchange Rates
cc = user cost of capital
e = exchange rate (the unit price of foreign currency in terms of home currency)
ee = expected exchange rate
r = short-term interest rate
rl = long-term interest rate
rle = expected long-term interest rate
PARAMETERS
α = proportion of a change in government expenditure that is directly offset by a change in private consumption
β = the relative share of capital in output
δ = the depreciation rate
λm = the proportion of base money that is included in wealth
λb = the proportion of government bonds that is included in wealth
λt = the degree to which the tax system is neutral with respect to the inflation premium in interest receipts
η = the speed of adjustment of the capital stock to its desired level
n = the sum of rates of growth of the labor force and of labor productivity, that is, the economy’s steady state real growth rate
A number of characteristics of the model are worth mentioning at the outset. Outside assets, in the form of government bonds, net claims on foreigners, and the physical capital stock, are endogenous to the model; budget constraints link these asset stocks to the appropriate flow variables.2 The investment function is specified as a lagged adjustment process of the actual capital stock to its desired long-run level, which is derived from a Cobb-Douglas production function. In the long run, the marginal product of capital is equal to the user cost of capital, which depends on the long-term real rate of interest and on tax rates.
There are two composite final goods in the model, with each economy specialized in the production of one of the goods. However, consumption and investment in each country includes both goods, and the deflators for consumption, investment, and government spending are assumed to be the same. Correspondingly, there are four prices in the model: an output price—that is, the GNP deflator—and an absorption deflator, for each of the two countries. The absorption deflator is a weighted sum of home output prices and of import prices, the latter being simply the trading partner’s output price expressed in the home currency.
The labor market is implicit in the model; both wages and employment have been solved out. MINIMOD contains an equation for the rate of change of the GNP deflator, which depends positively on the rate of capacity utilization and on the expected rate of change of the absorption deflator (with a unit coefficient). Such an equation can be derived from an expectations-augmented Phillips curve which determines contract wages; a price equation with a constant markup over actual wages calculated as an exponentially declining weighted average of contract wages; and an Okun’s Law relationship between unemployment and output.3 The absorption deflator enters the equation for the GNP deflator because it affects the real consumption wage relevant to workers. The rate of capacity utilization, calculated as the ratio of actual output to capacity output obtained from the production function, captures demand pressures on both prices and wages. The model implies that there is a normal rate of capacity utilization, which corresponds to a “natural rate” of unemployment, at which changes in output prices will equal the expected rate of change of absorption prices. Therefore, at this rate of capacity utilization, if import prices grow at a fully anticipated, constant rate, output prices will also grow at that rate.
Consumption depends on real wealth, real disposable income and real long-term interest rates. Real disposable income is defined to include only the real portion of interest payments and thus differs from the conventional national accounts definition. Taxes are a function of national income and the private sector’s interest earnings. There is a parameter, λt, that measures the neutrality of the tax system with respect to the inflation component in interest rates; if it is unity, then taxes are levied only on real interest receipts. Real wealth is defined as the sum of outside money, government bonds, and net claims on foreigners, each divided by the absorption deflator, and the real capital stock. Government bonds are assumed to pay the short-term interest rate, and to be fixed in price; net claims on foreigners are assumed to be denominated in U.S. dollars, and their foreign-currency value thus varies with the exchange rate, e. No attempt is made to explain the market valuation of the physical capital stock, as opposed to its replacement cost.
A parameter, λb, specifies the degree to which government bonds are net wealth: if it is zero, then Ricardian equivalence holds, and the choice between financing government expenditure through bond issues or lump-sum taxes has no real effect; if it is unity, the private sector does not offset anticipated future taxes needed to service the debt against any part of its current holdings of bonds. Correspondingly, one minus λb, multiplied by the change in government bonds outstanding, is subtracted from disposable income (see Hodrick (1980)). There is also a parameter, α, that measures the extent to which government consumption is a direct substitute for private consumption. Government expenditure is assumed to fall on home and foreign goods in the same proportions as private spending; thus import and export volumes can be expressed as functions of relative prices and total domestic absorption.
Perfect substitutability is assumed between home and foreign short-term bonds and between short-term and long-term bonds in each economy. The first assumption—open parity—means that the short-term home and foreign interest rates differ only by the expected exchange rate change.4 The second assumption implies that holding-period yields on short-term and long-term bonds, allowing for expected capital gains on the latter, are equalized.
II. The Empirical Model
The parameters appearing in behavioral equations of the theoretical model described above were for the most part obtained by simulating the Federal Reserve Board’s Multicountry Model (MCM). Our decision not to try to estimate the parameters directly reflected a concern that estimation of an aggregated model may give unsatisfactory results. Given the small samples that are available, data on macroeconomic variables are often dominated by special events and by institutional changes that heavily influence the historical data but may not be relevant to future periods over which the model will be simulated. Model builders often have to include dummy variables or make ad hoc adjustments for these past events; not to do so would distort the coefficients on the variables of interest. Such events may be considered random from a longer-term perspective, and hence in principle they should not bias the structural coefficients. However, in practice it is not possible in small samples to relegate these events to the error terms of structural equations; the change in parameter estimates owing to the addition of a few observations could be unacceptably large.5 A large part of the time spent in estimating a model consists of identifying and adjusting for these special factors; it is more straightforward to do so when a model is disaggregated and contains institutional detail. A small version of the resulting model can retain the interesting interactions, while discarding the extra exogenous variables that are needed to track the historical data but that are not relevant for simulations of future policy changes relative to a baseline path.
We therefore chose to profit from the work of other modellers and used the MCM because it is a well-documented model of five industrial countries with a large data base. The structure of the MCM is roughly consistent with the theoretical model described above; where there were conflicts, we imposed our theoretical structure and functional forms. For instance, we identified lagged price variables in the MCM’s wage equation as resulting from expectational lags, to be consistent with equations (10) and (26) in the table, and we scaled real interest rates in the consumption equation by GNP in order to allow consumption to grow with output in steady state. We have based the “home economy” of the MINIMOD on the MCM’s U.S. model and the “foreign economy” of the MINIMOD on an aggregation of the MCM models of Canada, the Federal Republic of Germany, Japan, and the United Kingdom. The model is, in principle, a closed model, as we scale up the foreign economy’s exports and imports to make them consistent with U.S. imports and exports, respectively. Implicitly, then, variables for countries not included in the MCM are assumed to move proportionally with those of the countries that are included.
The idea of creating smaller models from larger models is not new; in the mid-1970s a small structural6 model of the Federal Reserve Board’s MPS model was constructed in order to perform optimal control experiments.7 More recently, Malgrange and others have studied the properties of larger models by constructing “maquettes” of those models that capture the essential dynamic features but ignore “second order” linkages.8 Masson and others have applied these procedures to the Organization for Economic Cooperation and Development’s (OECD) INTERLINK model to obtain a small structural model that is in many ways a precursor to MINIMOD.9
An alternative to creating a small structural version of the larger model would be generating its reduced form, aggregated appropriately, and doing simulation experiments with that.10 This has two disadvantages for our purposes. First, it does not allow us easily to modify the model by replacing some of the structural equations or by changing some of the structural parameters. This may be desirable either because of perceived inadequacies of the large model or because of a desire to gauge the sensitivity of simulation results to certain key parameters. Second, the reduced-form approach means working with a linear model, which may not give satisfactory long-term properties. Though it is usually possible to linearize most of the model in the logarithms of appropriately defined variables, there are essential nonlinearities, for instance those resulting from budget or balance sheet constraints, that one may want to retain. The use of partial simulations in order to generate a small structural model allows one to do this.
The methodology used in the construction of MINIMOD is described in detail in Masson (1986b); however, it can be summarized as follows. First, sections of the large model that correspond to single equations in the small model are isolated. Right-hand-side (RHS) variables of the small-model equations are exogenous to the isolated block of the large model (though not necessarily exogenous to the model itself). Each of these variables is, in turn, given a shock, and the model is simulated for a sufficient number of periods so that the endogenous variable settles down to its long-run value. The “shock-minus-control” results of the left-hand-side (LHS) variable are then regressed on the “shock-minus-control” values of the RHS variables in order to generate coefficient estimates.
Following Jorgenson (1966), we have used ratios of polynomials in the lag operator to capture the dynamic responses of the model. By regression of the dependent variable on lagged values of itself, as well as on contemporaneous and lagged values of the independent variable, we were able adequately to model the dynamic patterns of the large model in a parsimonious way. In practice, lags of more than two periods on either dependent or independent variables were seldom required. We were able to capture the lag distributions to a high degree of precision using rational lags of this form.11
The MCM, as published in 1983, was used to generate the simulation results, with the following four exceptions. First, the link between capacity utilization and wage inflation in the United States incorporates more recent information. Second, the demand for Ml in the United States is based on work done by Brayton, Farr, and Porter (1983), also at the Federal Reserve Board. Third, the Ml demand function in other industrial countries is based on work done at the OECD and published in Atkinson and others (1984). Finally, we imposed a Cobb-Douglas production function with parameters that reflect the relative shares of labor and capital.
In each case the equations were estimated without a constant term; this ensures that when the RHS variables are at their steady-state values, so are the LHS variables. Two types of constraints were imposed in estimation: the effect of inflationary expectations on actual inflation is constrained to have a unit coefficient in the long run and, in the net investment equations, the coefficients on the desired and actual capital stocks are constrained such that the actual capital stock is equal to the desired capital stock in the long run.
III. Simulation Results
This section presents the results of several simulation experiments using MINIMOD. The simulations were performed with both an adaptive expectations version of the model and a consistent expectations version. In the adaptive expectations version, expectations of next period’s inflation rates and long-term bond rates in each of the two economies, as well as of the exchange rate, are formed on the basis of current and past movements of the respective variables (as generated by the model), with adaptation parameters, which, though chosen arbitrarily, roughly replicate the simulation properties of the MCM (see the Appendix for a list of the parameters used). In the consistent expectations version of the model, this period’s expectations of these variables are made to equal the model’s solution values for next period.
The consistent expectations solution—a more common, but somewhat misleading, term is rational expectations solution—was calculated using a version of the algorithm described by Fair and Taylor (1983). This algorithm is iterative, and, starting from initial guesses, it revises expectations of a variable on the basis of what the model calculates for that variable in a later period. Furthermore, it successively extends the horizon for the formation of expectations until variables differ between iterations by less than some predetermined tolerance. After experimentation, we discovered that the solution path could be quite sensitive both to the tolerance and to the values provided as initial guesses each time the horizon was extended. Consequently, we created a steady-state version of the model, calculated the long-run effects of the policy changes, and used these values each time the horizon was extended. For the steady-state solution to exist, we had to impose some further assumptions: from 1991 on, taxes are assumed to adjust so that eventually a given value for the stock of government bonds as a ratio to GNP is obtained; the two economies are assumed to settle down eventually to the same real growth rate; and the wealth elasticity of consumption spending in the United States is set equal to its long-run value in the ROW (.0438), rather than its estimated value (.0049).12
We begin by analyzing the results of fiscal shocks applied to each economy under the two alternative expectational assumptions. We then examine monetary and exchange rate shocks in a similar fashion. The policy simulations are done with all other policies fixed; thus the fiscal shocks assume all monetary aggregates are unchanged while the monetary shocks treat real government expenditure as unchanged. The results of all of the simulations are discussed relative to a common baseline for 1985-90 that reflects instructions of the organizers of a conference at the Brookings Institution.13
Fiscal Shocks
Chart 1 shows the response of the major macroeconomic variables to a previously unexpected, sustained U.S. fiscal contraction that is implemented when it is announced. Specifically, U.S. real government expenditure was permanently decreased by an amount equal to 1 percent of U.S. GNP in the first quarter of 1985. Narrowly defined money in both economies was fixed while interest rates were allowed to vary.
The differences in the two versions of the model are perhaps most apparent in the behavior of the exchange rate. In the consistent expectations (CE) version, the exchange rate jumps a good deal—the dollar depreciates by about 4 percent on impact—and then appreciates gradually. In the adaptive expectations (AE) version, the exchange rate depreciates very little initially, but continues to depreciate throughout the simulation. The long-run effects are, however, identical for both versions of the model, and a nondynamic version of the model was used to calculate them; they involve an appreciation, not a depreciation, of the dollar, by about 2 percent. The dollar appreciates in the long run because the fiscal contraction brings about an increase in net claims on foreigners, and hence an improvement of the balance on investment income: this is consistent with a lower trade balance and, ultimately, an appreciation of the dollar’s real exchange rate. As can be seen from Chart 1, even after six years of simulation the exchange rate is far from its long-run level. The CE simulations in fact solve the model some ten years beyond that point, using as terminal values for the expectations variables their calculated steady-state values.
The difference in dynamic paths for the exchange rate has a simple intuitive explanation. The interest parity condition implies that the expected rate of change of the exchange rate must equal the interest differential, or roughly (ee – e)/e = r – r*, where ee is the exchange rate expected for next period. The fiscal contraction in the United States, by lowering r more than r*, implies that ee – e must be negative—that is, the U.S. dollar is expected to appreciate in effective terms between this period and next. Under consistent expectations, actual exchange rate changes must therefore also be negative, after an initial jump when the previously unanticipated policy change occurs. Since in the long run the exchange rate appreciates, in principle the initial jump could be positive or negative, as long as it did not exceed the long-run appreciation. Given the size of the cumulative interest differential, however, an initial depreciation is required in our model. Under adaptive expectations, exchange rate expectations are given by
For ee – e to be negative, e must continually be greater than the value that was expected last period to prevail this period, since
and η<1. At the beginning of the simulation, e = ee; since subsequent changes in ee are a fraction, between zero and one, of movements in e, it must therefore be the case that e continually increases under adaptive expectations, even though it is expected to decrease.14
Reduction in U.S. Government Purchases
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Reduction in U.S. Government Purchases
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Reduction in U.S. Government Purchases
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Reduction in U.S. Government Purchases
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Reduction in U.S. Government Purchases
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Long-term interest rates in both economies also exhibit different dynamic patterns under consistent and adaptive expectations. In the CE version long-term interest rates fall more on impact and continue with a flatter trajectory than in the AE version. Steady-state effects on both long-term and short-term interest rates, in both countries, imply a fall of 16 basis points in response to the cut in U.S. fiscal expenditure, whether expectations are formed rationally or adaptively. The larger initial dollar depreciation and forward-looking inflationary expectations in the CE version of the model cause prices to move more quickly than in the AE version, but inflation rates in the long run are unaffected since money growth has been held fixed.
The relatively larger dollar depreciation and larger declines in the long-term U.S. interest rate early in the simulations cause the decrease in U.S. GNP in the CE version to be smaller initially and to reverse itself sooner than in the AE version. In the long run, output will be higher in both the United States and the rest of the world as lower interest rates lead to capital accumulation by their private sectors. In the meantime, however, the U.S. fiscal contraction has a different effect on the rest of the world depending on the expectations formation assumption: under consistent expectations, long-term bond rates fall enough in the ROW that output actually rises in the short run.
Chart 2 shows the results of a fiscal shock in ROW. This shock is an unanticipated, sustained increase in real ROW government expenditure that is the mirror image of the U.S. spending decrease discussed above—the expenditure change is equal to 1 percent of ROW real GNP. The charts show that the resulting macroeconomic effects differ somewhat quantitatively—for example, the dollar depreciation is less than in Chart 1—but the qualitative results are similar. The dollar depreciates more on impact—but by less at the end of the simulation—in the CE version of the model than in the AE version; the initial increase in long-term interest rates is larger under CE, in both the United States and the ROW. These effects serve to moderate the changes in both ROW and U.S. output in the CE version of the model relative to the AE version. In the new steady state, the dollar appreciates by 2.5 percent, and interest rates decline by roughly 50 basis points.
Increase in Non-U.S. Government Purchases
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Increase in Non-U.S. Government Purchases
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Increase in Non-U.S. Government Purchases
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Increase in Non-U.S. Government Purchases
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Increase in Non-U.S. Government Purchases
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Monetary Shocks
Monetary expansions were simulated in each economy; in both economies the shock was a permanent increase in the money supply of 4 percent distributed evenly over the first four quarters of the simulation. The increase in the money supply was assumed to be unexpected prior to the initial period of simulation, but, under consistent expectations, agents are assumed thereafter correctly to anticipate the subsequent path of the money supply as well as of the other macroeconomic variables. Real government expenditure in both economies, as well as Ml in the economy not receiving the shock, was unchanged during the simulation.
Chart 3 presents the simulation results for the U.S. monetary shock. In the AE version the exchange rate begins to depreciate monotonically to its new long-run level, which is a 4 percent dollar depreciation. The same shock applied to the CE version of the model displays the well-known property of exchange rate overshooting. Sticky prices, combined with perfect asset substitutability, lead to an impact depreciation in excess of the amount required in the long run, as an interest differential opens up in favor of the ROW currency that must be compensated by an expected dollar appreciation. Long-term interest rates fall more on impact in the CE version than in the AE version, but, by the end of the simulation, their decrease relative to baseline is less than in the adaptive version. These interest and exchange rate effects are reflected in the behavior of U.S. output; the relatively large—but temporary—real exchange rate effects in the CE version of the model, combined with the initial sharp fall in long-term interest rates, lead to a more pronounced increase in output, but it is reversed more quickly. Output in ROW increases in the short run in response to a rise in U.S. activity; soon, however, in both versions of the model, output falls—more in the CE version where the exchange rate effects are larger. In other words, MINIMOD shows a negative transmission of U.S. monetary shocks abroad, as does a simple version of the Mundell-Fleming model. In the long run, money is neutral in the model, so prices in the United States go up by 4 percent and outputs in both countries return to their baseline levels. By 1990, in the CE simulation, U.S. absorption prices have increased by about three fourths of their ultimate change.
U.S. Monetary Expansion
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.U.S. Monetary Expansion
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.U.S. Monetary Expansion
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.U.S. Monetary Expansion
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.U.S. Monetary Expansion
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Chart 4 shows the results of the same monetary experiment in ROW. Qualitatively the results are nearly the same as those discussed above for a U.S. monetary expansion. The exchange rate overshoots in the CE version of the model, although by less than with the U.S. monetary expansion; long-term interest rates drop more in ROW on impact—but less at the end of the simulation period—in the CE version than in the AE version. Consequently, output in ROW increases more initially, but less by the end of the simulation, in the CE version of the model. One difference worth noting is the behavior of U.S. GNP. In the AE version of the model alone, the eventual decrease in the U.S. long-term interest rate is enough to cause U.S. output after four years to be higher in response to a ROW monetary expansion than in the baseline.
Exchange Rate Shock
In MINIMOD the exchange rate is an endogenous variable, and assets denominated in the two currencies are perfect substitutes for one another. These two facts make it impossible to view an exchange rate shock to the model in the same way as the two policy shocks discussed above or in the same way that an interest rate shock resulting from open market operations might be assessed. To examine the behavior of the model in response to an imposed exchange rate change, however, a residual was introduced into the open parity relationship that equates expected returns on dollar and nondollar assets. The simulation can be interpreted as an increase in the perceived risk of holding dollar-denominated assets that induces investors to demand an annual return on dollar assets that is higher by 1 percentage point.
Chart 5 shows the result of imposing this constant risk premium of 1 percentage point starting in 1985. In the long run, the risk premium will require U.S. real interest rates—short term and long term—to rise relative to ROW interest rates by 1 percentage point, as there will be no ongoing nominal or real exchange rate changes relative to baseline once the new steady state is reached. In equilibrium, this will result from an 80 basis-point rise in U.S. rates, and a 20 basis-point decline in ROW rates. In the meantime, however, U.S. rates do not rise by the full amount relative to foreign rates, and the increased expected return on dollar assets is obtained through expected dollar appreciation. In the CE version, this requires an initial large depreciation—a 6.5 percent decline in the value of the dollar—followed by a gradual appreciation. In the AE version, for the reasons discussed above, the exchange rate exhibits a continual depreciation during the simulation period.
Non-U.S. Monetary Expansion
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Non-U.S. Monetary Expansion
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Non-U.S. Monetary Expansion
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Non-U.S. Monetary Expansion
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Non-U.S. Monetary Expansion
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.
Increase in Risk Premium on U.S. Dollar Assets
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Increase in Risk Premium on U.S. Dollar Assets
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Increase in Risk Premium on U.S. Dollar Assets
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Increase in Risk Premium on U.S. Dollar Assets
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Increase in Risk Premium on U.S. Dollar Assets
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Long-term interest rates rise substantially under CE from the start of the simulation, and this more than offsets the stimulative effect on U.S. output of a fall in the real value of the dollar. Under AE, in contrast, output declines by a negligible amount in the first two quarters, and then remains slightly above its baseline value. ROW output is lower under both CE and AE after the first few periods, as the decline in interest rates does not offset the negative effects of ROW appreciation.
Announcement Effect Simulations
Additional experiments were undertaken with the consistent expectations version of MINIMOD to gauge the announcement effects15 of credible policy. Specifically, the same U.S. fiscal and monetary policies described above were applied to the model three years after the simulations began; this has the effect of providing agents with full knowledge of the policies, and their consequences, three full years before the policies take effect. Thus these agents can alter their behavior, and thereby affect macroeconomic variables, before the actual implementation of the policy changes.
Chart 6 reproduces the U.S. fiscal shock already discussed and shows, in addition, the results of the same shock announced at the beginning of the simulation period (first quarter 1985) but taking effect in 1988. Fiscal contraction causes the dollar to depreciate and long-term U.S. interest rates to fall. The announcement of a future fiscal contraction, combined with the assumption of consistent expectations, brings some of the future effects forward to the present; thus the expansionary effects of the exchange rate depreciation and the interest rate decline come into play before the contractionary effect of the actual decrease in government expenditure. Consequently, U.S. GNP rises for twelve quarters and by the fourth quarter of 1987 is about ½ of 1 percent above its baseline value. In the next period of the simulation, output declines in response to the government spending cut, but by a smaller amount than if the announcement and implementation were contemporaneous. The long-run effects of the two shocks are the same, however, and they were discussed above in the context of Chart 1. As for ROW output, it is higher throughout both simulations, aside from a few quarters near the end, but when there is an implementation lag, the stimulative effects are larger.
Reduction in U.S. Government Purchases, Under Consistent Expectations
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Reduction in U.S. Government Purchases, Under Consistent Expectations
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Reduction in U.S. Government Purchases, Under Consistent Expectations
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Reduction in U.S. Government Purchases, Under Consistent Expectations
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Reduction in U.S. Government Purchases, Under Consistent Expectations
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.Chart 7 presents the results of a similar monetary experiment; the U.S. monetary expansion described above is applied to the CE version of the model both with and without a three-year lag between the announcement and the implementation of the policy. The announcement of the policy is enough to cause the exchange rate to depreciate immediately even though monetary expansion occurs later—indeed the exchange rate overshoots its long-run value before the money supply is actually increased, at which point it depreciates further for two periods, then appreciates to its long-run level. As a result, the expansionary effect on U.S. output begins before the policy is implemented. The peak output effect in the United States is lower when the policy is announced beforehand, however.16
IV. Conclusions
In the construction of MINIMOD, we have deliberately sacrificed some detail from the Federal Reserve’s multicountry model, but have endeavored to capture the essential features of the larger model, including the nonexpectational dynamics and the key stock-flow relationships. We have not presented a direct comparison of full model simulations of MINIMOD and MCM because our purpose was not to create a replica of the MCM. For example, we have added some structure to the non-U.S. model to make it symmetric with the U.S. model, updated the wage/price block, and used demand-for-money functions as well as production functions from other sources. Nevertheless, the adaptive expectations version of MINIMOD seems to behave similarly to the MCM.
U.S. Monetary Expansion, Under Consistent Expectations
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.U.S. Monetary Expansion, Under Consistent Expectations
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.U.S. Monetary Expansion, Under Consistent Expectations
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.U.S. Monetary Expansion, Under Consistent Expectations
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.U.S. Monetary Expansion, Under Consistent Expectations
Citation: IMF Staff Papers 1986, 004; 10.5089/9781451930696.024.A004
aIncrease indicates U.S. dollar depreciation.In contrast, the consistent expectations version of MINIMOD, in which expectations of the exchange rate and of U.S. and ROW long-term bond rates and inflation rates are made equal to their realized values next period, behaves quite differently. In general, this version exhibits greater flexibility of financial prices and, to a lesser extent, of goods prices, and the initial output effects of monetary shocks are smaller than for the adaptive version. In addition, the dynamics are quite different in the two versions.
The consistent expectations version of the model, because of its forward-looking expectations, allows experiments in which announcement of a policy change that is to be implemented later can have effects now (provided the announcement is believed). In these simulations, future contractionary fiscal policy can have an expansionary effect now because the exchange rate depreciates and long-term interest rates decline immediately. In contrast, future deflationary monetary policy has contractionary effects now, because interest rates rise and the exchange rate appreciates from the outset. However, in both cases, these real effects depend on expectations of future demand not having an offsetting effect on current demand. An obvious extension is to allow some middle ground between lack of forward-looking expectations (as in the adaptive version) and complete credibility of future policy (which we now impose in the consistent version). An example would be where announced fiscal policy was unsustainable because it involved a continual increase in the ratio of government debt to income. In these circumstances expectations would likely reflect the probability of an eventual change in policy, and a judgment as to what form the change might take.
Future work with MINIMOD centers on two areas: simulation work with the existing version of the model and further developmental work. There are a number of questions that can be addressed with the current version of MINIMOD. Among those is one that was just mentioned, the sustainability of fiscal deficits. The fact that financial wealth, the capital stock, and foreign indebtedness are all endogenous variables in the model suggests that it is well suited to address policy questions of this sort. Further development of the model will likely focus on disaggregating the ROW sector to make macroeconomic models of the Federal Republic of Germany and Japan explicit and the inclusion of an abbreviated developing countries model.
APPENDIX
MINIMOD: Equations and Coefficients
ADAPTIVE EXPECTATIONS VERSION OF MINIMOD.
CONSISTENT EXPECTATIONS VERSION OMITS EQS 68-72 AND FORCES EE = E(+ l), ETC.
SYMBOL DECLARATIONS
ENDOGENOUS:
| DELRP_PI | —PARTIAL EFFECT OF INFLATION EXPECTATIONS ON ROW INFLATION |
| DELUP_PI | —PARTIAL EFFECT OF INFLATION EXPECTATIONS ON U.S. INFLATION |
| E | —EXCHANGE RATE ($ PER FOREIGN CURRENCY) |
| EE | —EXPECTED VALUE OF E NEXT PERIOD |
| EPSILONE | —EXPECTED RATE OF CHANGE OF E AT ANNUAL RATES |
| F | —NET CLAIMS OF U.S. ON ROW (ASSUMED DENOMINATED IN U.S. $) |
| RA | —ROW REAL ABSORPTION |
| RB | —ROW NOMINAL STOCK OF GOVT. DEBT |
| RC | —ROW REAL CONSUMPTION EXPENDITURE |
| RC_W | —PARTIAL EFFECT OF ROW WEALTH ON CONSUMPTION |
| RC_Y | —PARTIAL EFFECT OF DISPOSABLE INCOME ON ROW CONSUMPTION |
| RCU | —RATE OF CAPACITY UTILIZATION IN ROW |
| RGDP | —ROW REAL GROSS DOMESTIC PRODUCT |
| RGNP | —ROW REAL GROSS NATIONAL PRODUCT |
| RK | —ROW REAL PHYSICAL CAPITAL STOCK |
| RMONE | —ROW MONEY SUPPLY (Ml) |
| RP | =ROW ABSORPTION DEFLATOR |
| RPGNP | —ROW GNP DEFLATOR |
| RPIE | —EXPECTED RATE OF CHANGE OF ABSORPTION PRICE IN ROW NEXT PERIOD |
| RRL | —ROW LONG-TERM BOND RATE |
| RRLE | —EXPECTED ROW LONG-TERM BOND RATE NEXT PERIOD |
| RRS | —ROW SHORT-TERM BOND RATE |
| RTAX | —NOMINAL ROW TAX RECEIPTS |
| RT1 | —ROW TAX PARAMETER |
| RW | —ROW REAL PRIVATE SECTOR NET WEALTH |
| RYCAP | —ROW CAPACITY OUTPUT |
| RYD | —ROW REAL DISPOSABLE INCOME |
| UA | —U.S. REAL ABSORPTION |
| UB | —U.S. NOMINAL STOCK OF GOVERNMENT DEBT |
| UC | —U.S. REAL CONSUMPTION EXPENDITURE |
| UC_R | —PARTIAL EFFECT OF REAL INTEREST RATE ON U.S. CONSUMPTION |
| UC_Y | —PARTIAL EFFECT OF DISPOSABLE INCOME ON U.S. CONSUMPTION |
| UCU | —RATE OF U.S. CAPACITY UTILIZATION |
| UGDP | —U.S. REAL GROSS DOMESTIC PRODUCT |
| UGNP | —U.S. REAL GROSS NATIONAL PRODUCT |
| UI | —VOLUME OF U.S. IMPORTS OF GOODS AND NON-FACTOR SERVICES |
| UI_ACT | —PARTIAL EFFECT OF U.S. ABSORPTION ON U.S. |
| IMPORTS | |
| UI_E | —PARTIAL EFFECT OF REAL EXCHANGE RATE ON U.S. IMPORTS |
| UK | —STOCK OF U.S. REAL PHYSICAL CAPITAL |
| UMONE | —U.S. MONEY SUPPLY (Ml) |
| UP | —U.S. ABSORPTION DEFLATOR |
| UPGNP | —U.S. GNP DEFLATOR |
| UPIE | —EXPECTED RATE OF CHANGE OF THE U.S. ABSORPTION DEFLATOR NEXT PERIOD |
| URL | —U.S. LONG-TERM BOND RATE |
| URLE | —EXPECTED U.S. LONG-TERM BOND RATE NEXT PERIOD |
| URS | —U.S. SHORT-TERM BOND RATE |
| UTAX | —U.S. NOMINAL TAX RECEIPTS |
| UT1 | —A U.S. TAX PARAMETER |
| UT2 | —A U.S. TAX PARAMETER |
| UW | —U.S. REAL PRIVATE SECTOR NET WEALTH |
| UX | —VOLUME OF U.S. EXPORTS OF GOODS AND NON-FACTOR SERVICES |
| UX_ACT | —PARTIAL EFFECT OF ROW ABSORPTION ON U.S. EXPORTS |
| UX_E | —PARTIAL EFFECT OF REAL EXCHANGE RATE ON U.S. EXPORTS |
| UYCAP | —U.S. CAPACITY OUTPUT |
| UYD | —U.S. REAL DISPOSABLE INCOME |
| DELRP_PI | —PARTIAL EFFECT OF INFLATION EXPECTATIONS ON ROW INFLATION |
| DELUP_PI | —PARTIAL EFFECT OF INFLATION EXPECTATIONS ON U.S. INFLATION |
| E | —EXCHANGE RATE ($ PER FOREIGN CURRENCY) |
| EE | —EXPECTED VALUE OF E NEXT PERIOD |
| EPSILONE | —EXPECTED RATE OF CHANGE OF E AT ANNUAL RATES |
| F | —NET CLAIMS OF U.S. ON ROW (ASSUMED DENOMINATED IN U.S. $) |
| RA | —ROW REAL ABSORPTION |
| RB | —ROW NOMINAL STOCK OF GOVT. DEBT |
| RC | —ROW REAL CONSUMPTION EXPENDITURE |
| RC_W | —PARTIAL EFFECT OF ROW WEALTH ON CONSUMPTION |
| RC_Y | —PARTIAL EFFECT OF DISPOSABLE INCOME ON ROW CONSUMPTION |
| RCU | —RATE OF CAPACITY UTILIZATION IN ROW |
| RGDP | —ROW REAL GROSS DOMESTIC PRODUCT |
| RGNP | —ROW REAL GROSS NATIONAL PRODUCT |
| RK | —ROW REAL PHYSICAL CAPITAL STOCK |
| RMONE | —ROW MONEY SUPPLY (Ml) |
| RP | =ROW ABSORPTION DEFLATOR |
| RPGNP | —ROW GNP DEFLATOR |
| RPIE | —EXPECTED RATE OF CHANGE OF ABSORPTION PRICE IN ROW NEXT PERIOD |
| RRL | —ROW LONG-TERM BOND RATE |
| RRLE | —EXPECTED ROW LONG-TERM BOND RATE NEXT PERIOD |
| RRS | —ROW SHORT-TERM BOND RATE |
| RTAX | —NOMINAL ROW TAX RECEIPTS |
| RT1 | —ROW TAX PARAMETER |
| RW | —ROW REAL PRIVATE SECTOR NET WEALTH |
| RYCAP | —ROW CAPACITY OUTPUT |
| RYD | —ROW REAL DISPOSABLE INCOME |
| UA | —U.S. REAL ABSORPTION |
| UB | —U.S. NOMINAL STOCK OF GOVERNMENT DEBT |
| UC | —U.S. REAL CONSUMPTION EXPENDITURE |
| UC_R | —PARTIAL EFFECT OF REAL INTEREST RATE ON U.S. CONSUMPTION |
| UC_Y | —PARTIAL EFFECT OF DISPOSABLE INCOME ON U.S. CONSUMPTION |
| UCU | —RATE OF U.S. CAPACITY UTILIZATION |
| UGDP | —U.S. REAL GROSS DOMESTIC PRODUCT |
| UGNP | —U.S. REAL GROSS NATIONAL PRODUCT |
| UI | —VOLUME OF U.S. IMPORTS OF GOODS AND NON-FACTOR SERVICES |
| UI_ACT | —PARTIAL EFFECT OF U.S. ABSORPTION ON U.S. |
| IMPORTS | |
| UI_E | —PARTIAL EFFECT OF REAL EXCHANGE RATE ON U.S. IMPORTS |
| UK | —STOCK OF U.S. REAL PHYSICAL CAPITAL |
| UMONE | —U.S. MONEY SUPPLY (Ml) |
| UP | —U.S. ABSORPTION DEFLATOR |
| UPGNP | —U.S. GNP DEFLATOR |
| UPIE | —EXPECTED RATE OF CHANGE OF THE U.S. ABSORPTION DEFLATOR NEXT PERIOD |
| URL | —U.S. LONG-TERM BOND RATE |
| URLE | —EXPECTED U.S. LONG-TERM BOND RATE NEXT PERIOD |
| URS | —U.S. SHORT-TERM BOND RATE |
| UTAX | —U.S. NOMINAL TAX RECEIPTS |
| UT1 | —A U.S. TAX PARAMETER |
| UT2 | —A U.S. TAX PARAMETER |
| UW | —U.S. REAL PRIVATE SECTOR NET WEALTH |
| UX | —VOLUME OF U.S. EXPORTS OF GOODS AND NON-FACTOR SERVICES |
| UX_ACT | —PARTIAL EFFECT OF ROW ABSORPTION ON U.S. EXPORTS |
| UX_E | —PARTIAL EFFECT OF REAL EXCHANGE RATE ON U.S. EXPORTS |
| UYCAP | —U.S. CAPACITY OUTPUT |
| UYD | —U.S. REAL DISPOSABLE INCOME |
DEFINITIONS:
| EPSILON | —RATE OF CHANGE OF THE EXCHANGE RATE, AT ANNUAL RATES |
| RCURBAL | —ROW CURRENT ACCOUNT BALANCE |
| RGDEF | —ROW GENERAL GOVERNMENT DEFICIT |
| RGE | —TOTAL ROW GENERAL GOVERNMENT EXPENDITURES |
| RPI | —RATE OF CHANGE IN ROW ABSORPTION DEFLATOR, AT ANNUAL RATES (DECIMAL FRACTION) |
| RRLR | —ROW REAL EX POST LONG-TERM INTEREST RATE |
| RRSQ | —ROW QUARTERLY SHORT-TERM INTEREST RATE |
| RRSR | —ROW REAL EX POST SHORT-TERM INTEREST RATE |
| RUCSTCAP | —ROW USER COST OF CAPITAL |
| UCURBAL | —U.S. CURRENT ACCOUNT BALANCE |
| UGDEF | —U.S. GENERAL GOVERNMENT DEFICIT |
| UGE | —TOTAL U.S. GENERAL GOVERNMENT EXPENDITURES |
| UPI | —RATE OF CHANGE OF U.S. ABSORPTION DEFLATOR, AT ANNUAL RATES (DECIMAL FRACTION) |
| URLR | —U.S. REAL EX POST LONG-TERM INTEREST RATE |
| URSQ | —U.S. QUARTERLY SHORT-TERM INTEREST RATE |
| URSR | —U.S. REAL EX POST SHORT-TERM INTEREST RATE |
| UUCSTCAP | —U.S. USER COST OF CAPITAL |
| EPSILON | —RATE OF CHANGE OF THE EXCHANGE RATE, AT ANNUAL RATES |
| RCURBAL | —ROW CURRENT ACCOUNT BALANCE |
| RGDEF | —ROW GENERAL GOVERNMENT DEFICIT |
| RGE | —TOTAL ROW GENERAL GOVERNMENT EXPENDITURES |
| RPI | —RATE OF CHANGE IN ROW ABSORPTION DEFLATOR, AT ANNUAL RATES (DECIMAL FRACTION) |
| RRLR | —ROW REAL EX POST LONG-TERM INTEREST RATE |
| RRSQ | —ROW QUARTERLY SHORT-TERM INTEREST RATE |
| RRSR | —ROW REAL EX POST SHORT-TERM INTEREST RATE |
| RUCSTCAP | —ROW USER COST OF CAPITAL |
| UCURBAL | —U.S. CURRENT ACCOUNT BALANCE |
| UGDEF | —U.S. GENERAL GOVERNMENT DEFICIT |
| UGE | —TOTAL U.S. GENERAL GOVERNMENT EXPENDITURES |
| UPI | —RATE OF CHANGE OF U.S. ABSORPTION DEFLATOR, AT ANNUAL RATES (DECIMAL FRACTION) |
| URLR | —U.S. REAL EX POST LONG-TERM INTEREST RATE |
| URSQ | —U.S. QUARTERLY SHORT-TERM INTEREST RATE |
| URSR | —U.S. REAL EX POST SHORT-TERM INTEREST RATE |
| UUCSTCAP | —U.S. USER COST OF CAPITAL |
EXOGENOUS:
| DUM | —DUMMY VARIABLE EQUALS 1 FROM 1991 Ql ONWARDS |
| RBRATIO | —EQUILIBRIUM RATIO OF ROW BOND STOCK TO GNP |
| RDELTA | —DEPRECIATION RATE FOR ROW PHYSICAL CAPITAL |
| RG | —ROW GOVERNMENT EXPENDITURE ON GOODS AND SERVICES |
| RM | —ROW MONETARY BASE |
| RMRT | —ROW MARGINAL TAX RATE (NET OF |
| TRANSFERS, CORPORATE AND PERSONAL) | |
| RMULT | —ROW MONEY MULTIPLIER |
| RPIBAR | —ROW LONG-RUN INFLATION EXPECTATIONS |
| RSCALE | —SCALE FACTOR IN ROW PRODUCTION FUNCTION |
| RT1BAR | —‘NORMAL’ VALUE OF RT1 |
| RT2 | —A ROW TAX PARAMETER |
| T | —TIME TREND |
| TRADSCAL | —MULTIPLIER THAT REFLECTS RATIO OF TOTAL U.S. TRADE TO THAT WITH MCM COUNTRIES (JAP, GER, UK, CAN) |
| UBRATIO | —EQUILIBRIUM RATIO OF U.S. BOND STOCK TO GNP |
| UDELTA | —DEPRECIATION RATE FOR U.S. PHYSICAL CAPITAL |
| UG | —U.S. REAL GOVERNMENT EXPENDITURE ON GOODS AND SERVICES |
| UGEXOG | —U.S. GOVT. TRANSFERS TO FOREIGNERS AND NET SUBSIDIES TO GOVT. ENTERPRISES |
| UM | —U.S. MONETARY BASE |
| UMRT | —U.S. MARGINAL TAX RATE (NET OF |
| TRANSFERS, CORPORATE AND PERSONAL) | |
| UMULT | —U.S. MONEY MULTIPLIER |
| UPIBAR | —U.S. LONG-RUN INFLATION EXPECTATIONS |
| USCALE | —SCALE FACTOR IN U.S. PRODUCTION FUNCTION |
| UT1BAR | —’NORMAL’ VALUE OF UT1 |
| UT2BAR | —’NORMAL’ VALUE OF UT2 |
| DUM | —DUMMY VARIABLE EQUALS 1 FROM 1991 Ql ONWARDS |
| RBRATIO | —EQUILIBRIUM RATIO OF ROW BOND STOCK TO GNP |
| RDELTA | —DEPRECIATION RATE FOR ROW PHYSICAL CAPITAL |
| RG | —ROW GOVERNMENT EXPENDITURE ON GOODS AND SERVICES |
| RM | —ROW MONETARY BASE |
| RMRT | —ROW MARGINAL TAX RATE (NET OF |
| TRANSFERS, CORPORATE AND PERSONAL) | |
| RMULT | —ROW MONEY MULTIPLIER |
| RPIBAR | —ROW LONG-RUN INFLATION EXPECTATIONS |
| RSCALE | —SCALE FACTOR IN ROW PRODUCTION FUNCTION |
| RT1BAR | —‘NORMAL’ VALUE OF RT1 |
| RT2 | —A ROW TAX PARAMETER |
| T | —TIME TREND |
| TRADSCAL | —MULTIPLIER THAT REFLECTS RATIO OF TOTAL U.S. TRADE TO THAT WITH MCM COUNTRIES (JAP, GER, UK, CAN) |
| UBRATIO | —EQUILIBRIUM RATIO OF U.S. BOND STOCK TO GNP |
| UDELTA | —DEPRECIATION RATE FOR U.S. PHYSICAL CAPITAL |
| UG | —U.S. REAL GOVERNMENT EXPENDITURE ON GOODS AND SERVICES |
| UGEXOG | —U.S. GOVT. TRANSFERS TO FOREIGNERS AND NET SUBSIDIES TO GOVT. ENTERPRISES |
| UM | —U.S. MONETARY BASE |
| UMRT | —U.S. MARGINAL TAX RATE (NET OF |
| TRANSFERS, CORPORATE AND PERSONAL) | |
| UMULT | —U.S. MONEY MULTIPLIER |
| UPIBAR | —U.S. LONG-RUN INFLATION EXPECTATIONS |
| USCALE | —SCALE FACTOR IN U.S. PRODUCTION FUNCTION |
| UT1BAR | —’NORMAL’ VALUE OF UT1 |
| UT2BAR | —’NORMAL’ VALUE OF UT2 |
RESIDUALS:
| RES1 | RES10 | RES11 | RES12 | RES14 | RES15 | RES16 | |
| RES18 | RES19 | RES2 | RES20 | RES21 | RES22 | RES23 | RES24 |
| RES26 | RES27 | RES28 | RES29 | RES3 | RES30 | RES31 | RES32 |
| RES33 | RES34 | RES35 | RES36 | RES38 | RES39 | RES4 | RES40 |
| RES43 | RES44 | RES45 | RES46 | RES47 | RES49 | RES5 | RES50 |
| RES51 | RES52 | RES53 | RES54 | RES55 | RES57 | RES58 | |
| RES59 | RES6 | RES60 | RES61 | RES7 | RES9 |
| RES1 | RES10 | RES11 | RES12 | RES14 | RES15 | RES16 | |
| RES18 | RES19 | RES2 | RES20 | RES21 | RES22 | RES23 | RES24 |
| RES26 | RES27 | RES28 | RES29 | RES3 | RES30 | RES31 | RES32 |
| RES33 | RES34 | RES35 | RES36 | RES38 | RES39 | RES4 | RES40 |
| RES43 | RES44 | RES45 | RES46 | RES47 | RES49 | RES5 | RES50 |
| RES51 | RES52 | RES53 | RES54 | RES55 | RES57 | RES58 | |
| RES59 | RES6 | RES60 | RES61 | RES7 | RES9 |
COEFFICIENTS:
| ETA | ETARPI | ETARRL | ETAUPI | ETAURL | MUGNP | ||||
| Rα | RBETA | RC1 | RC2 | RC3 | RC4 | RC5 | RC6 | ||
| RIN1 | RIN2 | RIN3 | RIN4 | RIN5 | RIN6 | RM1 | RM2 | ||
| RM3 | RN | RP1 | RP2 | RP3 | RTAU | Uα | UBETA | ||
| UC1 | UC2 | UC3 | UC4 | UC5 | UC6 | UC7 | UIN1 | UIN2 | |
| UI1 | UI2 | UI3 | UI4 | UI5 | UI6 | UI7 | UI8 | UM1 | UM2 |
| UM3 | UM4 | UM5 | UN | UP1 | UP2 | UP3 | UP4 | UP5 | UP6 |
| UP7 | UTAU | UX1 | UX2 | UX3 | UX4 | UX5 |
| ETA | ETARPI | ETARRL | ETAUPI | ETAURL | MUGNP | ||||
| Rα | RBETA | RC1 | RC2 | RC3 | RC4 | RC5 | RC6 | ||
| RIN1 | RIN2 | RIN3 | RIN4 | RIN5 | RIN6 | RM1 | RM2 | ||
| RM3 | RN | RP1 | RP2 | RP3 | RTAU | Uα | UBETA | ||
| UC1 | UC2 | UC3 | UC4 | UC5 | UC6 | UC7 | UIN1 | UIN2 | |
| UI1 | UI2 | UI3 | UI4 | UI5 | UI6 | UI7 | UI8 | UM1 | UM2 |
| UM3 | UM4 | UM5 | UN | UP1 | UP2 | UP3 | UP4 | UP5 | UP6 |
| UP7 | UTAU | UX1 | UX2 | UX3 | UX4 | UX5 |
PARAMETERS:
| RLAMBDAB | —PROPORTION OF ROW GOVERNMENT DEBT INCLUDED IN ROW PRIVATE NET WEALTH |
| RLAMBDAM | —PROPORTION OF ROW MONETARY BASE INCLUDED IN ROW PRIVATE NET WEALTH |
| RLAMBDAT | —DEGREE OF ROW TAX INDEXATION OF INFLATION PREMIUM IN INTEREST INCOME |
| ULAMBDAB | —PROPORTION OF U.S. GOVERNMENT DEBT INCLUDED IN U.S. PRIVATE NET WEALTH |
| ULAMBDAM | —PROPORTION OF U.S. MONETARY BASE INCLUDED IN U.S. PRIVATE NET WEALTH |
| ULAMBDAT | —DEGREE OF U.S. TAX INDEXATION OF INFLATION PREMIUM IN INTEREST INCOME |
| RLAMBDAB | —PROPORTION OF ROW GOVERNMENT DEBT INCLUDED IN ROW PRIVATE NET WEALTH |
| RLAMBDAM | —PROPORTION OF ROW MONETARY BASE INCLUDED IN ROW PRIVATE NET WEALTH |
| RLAMBDAT | —DEGREE OF ROW TAX INDEXATION OF INFLATION PREMIUM IN INTEREST INCOME |
| ULAMBDAB | —PROPORTION OF U.S. GOVERNMENT DEBT INCLUDED IN U.S. PRIVATE NET WEALTH |
| ULAMBDAM | —PROPORTION OF U.S. MONETARY BASE INCLUDED IN U.S. PRIVATE NET WEALTH |
| ULAMBDAT | —DEGREE OF U.S. TAX INDEXATION OF INFLATION PREMIUM IN INTEREST INCOME |
EQUATIONS:
RATE OF CHANGE OF U.S. ABSORPTION DEFLATOR:
1: UPI= = (UP/UP(–1))**4 – 1
RATE OF CHANGE OF ROW ABSORPTION DEFLATOR:
2: RPI= =(RP/RP(–1))**4–1
QUARTERLY U.S. SHORT-TERM INTEREST RATE:
3: URSQ= =(1 + URS(–1)/100)**0.25–1
QUARTERLY ROW SHORT-TERM INTEREST RATE:
4: RRSQ= = (1 + RRS(–1)/100)**0.25 –1
SHORT-TERM U.S. REAL INTEREST RATE:
5: URSR= =(1 + URS(–1)/100)/(1 + UPI) –1
SHORT-TERM ROW REAL INTEREST RATE:
6: RRSR = = (1 + RRS(–1)/100)/(1 + RPI) –1
LONG-TERM U.S. REAL INTEREST RATE:
7: URLR= = (1 + URL(–1)/100)/(1 + UPI) –1
LONG-TERM ROW REAL INTEREST RATE:
8: RRLR = = (1 + RRL(–1)/100)/(1 + RPI) –1
RATE OF CHANGE OF EXCHANGE RATE:
9: EPSILON = = (E/E(–1))**4 –1
U.S. USER COST OF CAPITAL:
10: UUCSTCAP = = ((1 + URL/100)/(1 + UPIBAR) –1 + UDELTA)/(1 – UMRT)
ROW USER COST OF CAPITAL:
11: RUCSTCAP = = ((1 + RRL/100)/(1 + RPIBAR) – 1 + RDELTA)/(1 – RMRT)
U.S. GENERAL GOVERNMENT DEFICIT:
12: UGDEF = = 4*DEL(1:UB + UM)
ROW GENERAL GOVERNMENT DEFICIT:
13: RGDEF = = 4*DEL (1:RB + RM)
U.S. CURRENT ACCOUNT BALANCE:
14: UCURBAL = = 4*DEL(1:F)
ROW CURRENT ACCOUNT BALANCE:
15: RCURBAL = = (–4)*DEL(1:F)/E
NOMINAL U.S. GENERAL GOVERNMENT EXPENDITURES:
16: UGE= =UP*UG + URSQ*UB(–1) + UGEXOG
NOMINAL ROW GENERAL GOVERNMENT EXPENDITURES:
17: RGE = = RP*RG + RRSQ*RB(–1)
U.S. REAL ABSORPTION:
18: UA = UC + 4*DEL(1:UK) + UDELTA*UK(–1) + UG + RES1
U.S. REAL GROSS DOMESTIC PRODUCT:
19: UGDP = UA + UX – UI + RES2
PARTIAL EFFECT OF DISPOSABLE INCOME ON U.S. CONSUMPTION:
20: UC_Y = (1 – UC3)/(UC1 + UC2)*(UC1 *UYD + UC2*UYD(–1)) + UC3*UC_Y(–1) + RES3
PARTIAL EFFECT OF REAL INTEREST RATE ON U.S. CONSUMPTION:
21: UC_R = UC4*(1 – UC6)/(UC4 + UC5)*100*((1 + URL(–2)/100)/(1 + UPIBAR(–2)) – 1) + UC5*(1 – UC6)/ (UC4 + UC5)*100*((1 + URL(–3)/100)/(1 + UPIBAR(–3)) – 1) + UC6*UC_R(–1) + RES4
U.S. REAL CONSUMPTION EXPENDITURE:
22: UC = (–Uα)*UG + (UC1 + UC2)/(1 – UC3)*UC_Y + (UC4 + UC5)/(1 – UC6)*UC_R*UGNP/MUGNP + UC7*UW(–1) + RES5
U.S. REAL NET PRIVATE SECTOR WEALTH:
23: UW = ULAMBDAM*(UM/UP) + ULAMBDAB*(UB/UP) + F/UP + UK + RES6
U.S. REAL DISPOSABLE INCOME:
24: UYD = UGDP*UPGNP/UP – UDELTA*UK(–1) – UTAX/UP + URSR*(UB(–1) + F(–1))/UP – (1 – ULAMBDAB)*DEL(1 : UB)/UP + RES7
U.S. REAL NET CAPITAL FORMATION:
25: DEL(1 : UK) = UIN1*DEL(1 : UK(–1)) + UIN2*(UBETA/ UUCSTCAP*UGDP – UK(–1)) + UN*UK(–1) + RES9
U.S. GENERAL GOVERNMENT BUDGET CONSTRAINT:
26: DEL(1 : UB) + DEL(1 : UM) = URSQ*UB(–1) + (UP*UG – UTAX + UGEXOG)/4 + RES10
U.S. GENERAL GOVERNMENT TAX RECEIPTS NET OF TRANSFERS:
27: UTAX = UT1*(UPGNP*UGDP – UDELTA*UK(–1)*UP + URS(–1)/100*((UB(–1) + F(–1)) – ULAMBDAT*UPI *(1 + URSR)*(UB(–1) + F(–1))) + UT2*(UPGNP(–1)*UGDP(–1) -UDELTA*UK(–2)*UP(–1) + URS(–2)/100*(UB(–2) + F(–2)) – ULAMBDAT*UPI(– 1)*(1 + URSR(–1))*(UB(–2) + F(–2))) + RES11
NATIONAL ACCOUNTS IDENTITY IN NOMINAL TERMS:
28: UPGNP*(UGNP – UX) = UP*UA – UI*E*RPGNP + URS(–1)/100*F(–1) + RES12
PARTIAL EFFECT OF INFLATION EXPECTATIONS ON U.S. GNP DEFLATOR:
29: DELUP_PI = UP4*((1 + UPIE)**0.25 – 1) + UP5 *((1 + UPIE(–1))**0.25 – 1) + UP6 *DELUP-PI(–1) + UP7*DELUP_PI(–2) + RES14
RATE OF CHANGE OF U.S. GNP DEFLATOR:
30: DEL(1 : UPGNP)/UPGNP(–1) = UP1*LOG(UCU) + UP2*LOG(UCU(–1)) + UP3*LOG(UCU(–2)) + DELUP_PI + RES16
MULTIPLIER RELATIONSHIP BETWEEN THE BASE AND U.S. M1 MONEY SUPPLY:
31: UMONE = UMULT*UM + RES15
PRODUCTION FUNCTION FOR U.S. CAPACITY OUTPUT:
32: LOG(UYCAP) = USCALE + LOG(1 + UN)*T*(1 – UBETA) + LOG(UK(–1))*UBETA
RATE OF U.S. CAPACITY UTILIZATION:
33: UCU = 100*UGDP/UYCAP + RES18
PARTIAL EFFECT OF FOREIGN ACTIVITY ON U.S. EXPORTS:
34: UX_ACT = (1 – UX2)*LOG(RA) + UX2*UX_ACT(–1) + RES19
PARTIAL EFFECT OF COMPETITIVENESS ON U.S. EXPORTS:
35: UX_E = (1 – UX5)*UX3/(UX3 + UX4)*LOG(E*RPGNP/UPGNP) + UX5*UX_E(–1) + (1 – UX5)*UX4/(UX3 + UX4) *LOG(E(– 1)*RPGNP(–1)/UPGNP(–1)) + RES20
VOLUME OF U.S. EXPORTS OF GOODS AND NON-FACTOR SERVICES:
36: LOG(UX) = UX1/(1 – UX2)*UX_ACT + (UX3 + UX4)/ (1 – UX5)*UX_E + RES21
PARTIAL EFFECT OF U.S. ACTIVITY ON U.S. IMPORTS:
37: UI_ACT = (1 – UI3)/(UI1 + UI2)*(UIl*LOG(UA) + UI2 *LOG(UA(–1))) + UI3*UI_ACT(–1) + RES22
PARTIAL EFFECT OF COMPETITIVENESS ON U.S. IMPORTS:
38: UI_E = UI4/((U14 + UI5 + UI6)/(1 – UI7 – UI8))*LOG(E*RPGNP/UPGNP) + UI5/((UI4 + UI5 + UI6)/ (1 – UI7 – UI8))*LOG(E(–1).RPGNP(–1)/UPGNP(–1)) + UI6/((UI4 + UI5 + UI6)/(1 – UI7 – UI8))*LOG(E(–2) *RPGNP(–2)/UPGNP(–2)) + UI7*UI_E(–1) + UI8 *UI_E(–3) + RES23
VOLUME OF U.S. IMPORTS OF GOODS AND NON-FACTOR SERVICES:
39: LOG(UI) = (UI1 + UI2)/(1 – UI3)*UI_ACT + (UI4 + UI5 + UI6)/(1 – UI7 – UI8)*UI_E + RES24
U.S. CURRENT ACCOUNT BALANCE (EQUAL TO THE CHANGE IN U.S. NET CLAIMS ON FOREIGNERS):
40: DEL(1 : F) = URSQ*F(–1) + (UPGNP*UX – RPGNP *UI*E)/4 + RES26
INTEREST PARITY CONDITION EQUATING EX ANTE RETURNS ON U.S. AND ROW SHORT-TERM BONDS:
41: 1 + URS/100 = (1 + RRS/100)*(1 + EPSILONE) + RES27
ARBITRAGE CONDITION EQUATING EX ANTE RETURNS ON U.S. SHORT-TERM AND LONG-TERM BONDS:
42: URS/100 = URL/100 – ((URLE/URL)**4 – 1) + RES28
DEMAND FUNCTION FOR U.S. M1:
43: LOG(UMONE/UP) = UM1*LOG(UGNP) + UM2*LOG(UGNP(–1)) + UM3*0.01*URS + UM4*0.01*URS(–1) + UM5*LOG(UMONE(–1)/UP(–1)) + RES29
ROW REAL ABSORPTION:
44: RA = RC + 4*DEL(1 : RK) + RDELTA*RK(–1) + RG + RES30
ROW REAL GDP (NET EXPORTS ARE SCALED DOWN BY THE SHARE OF MCM COUNTRIES IN U.S. TRADE):
45: RGDP = RA + (UI – UX)/TRADSCAL + RES31
PARTIAL EFFECT OF DISPOSABLE INCOME ON ROW CONSUMPTION:
46: RC_Y = (1 – RC2)*RYD + RC2*RC_Y(–1) + RES32
PARTIAL EFFECT OF WEALTH ON ROW CONSUMPTION:
47: RC_W = RC3/((RC3 + RC4)/(1 – RC5 – RC6))*RW + RC4/ ((RC3 + RC4)/(1 – RC5 – RC6))*RW(–1) + RC5*RC_W(–1) + RC6*RC_W(–2) + RES33
ROW REAL CONSUMPTION EXPENDITURE:
48: RC = (–Rα)*RG + RC1/(1 – RC2)*RC_Y + (RC3 + RC4)/ (1 – RC5 – RC6)*RC_W + RES34
ROW REAL NET PRIVATE SECTOR WEALTH:
49: RW = RLAMBDAM*(RM/RP) + RL AMBDAB*(RB/RP) – F/E/TRADSCAL/RP + RK + RES35
ROW REAL DISPOSABLE INCOME:
50: RYD = RGDP*RPGNP/RP – RDELTA*RK(–1) – RTAX/RP + RRSR*(RB(–1)/RP) – ((1 + URS(–1)/100)/(1 + EPSILON)/(1 + RPI) – 1)*(F(–1)/E/TRADSCAL)/RP – (1 – RLAMBDAB) *DEL(1 : RB)/RP + RES36
ROW REAL NET CAPITAL ACCUMULATION:
51: DEL(1 : RK) = RIN1*(RBETA*RGDP/RUCSTCAP) + RIN2*(RBETA*RGDP(–1)/RUCSTCAP(–1)) + RIN3*(RBETA*RGDP(–4)/RUCSTCAP(–4)) + RIN4*RK(–1) + RIN5*RK(–2) + RIN6*RK(–5) + RN*RK(–1) + RES38
ROW GENERAL GOVERNMENT BUDGET CONSTRAINT:
52: DEL(1 : RB) + DEL(1 : RM) = (RP*RG – RTAX)/ 4 + RRSQ*RB(–1) + RES39
ROW NOMINAL GOVERNMENT TAX RECEIPTS NET OF TRANSFERS:
53: RTAX = RT1*(RPGNP*RGDP – RDELTA*RK(–1)*RP + RRS(–1)/100*RB(–1) – ((1 + URS(–1)/100)/(1 + EPSILON) –1)*(F(–1)/E/TRADSCAL) – RLAMBDAT*RPI*((1 + RRSR) *RB(–1) – (1 + URS(–1)/100)/(1 + EPSILON)/(1 + RPI).F(–1)/ TRADSCAL/E)) + RT2*RTAX(–1) + RES40
PARTIAL EFFECT OF INFLATION EXPECTATIONS ON THE RATE OF CHANGE IN ROW GNP DEFLATOR:
54: DELRP_PI = RP3*((1 + RPIE)**0.25 – 1) + (1 – RP3) *DELRP_PI(–1) + RES43
RATE OF CHANGE OF ROW GNP DEFLATOR:
55: DEL(1 : RPGNP)/RPGNP(–1) = RPl*LOG(RCU) + RP2*LOG(RCU(–1)) + DELRP_PI + RES44
NATIONAL ACCOUNTS IDENTITY IN NOMINAL TERMS FOR ROW:
56: RPGNP*(RGNP – UI/TRADSCAL) = RP*RA – UX/TRADSCAL*UPGNP/E-URS(–1)/100*F(–1)/ErTRADSCAL + RES45
ARBITRAGE CONDITION EQUATING EX ANTE RETURNS ON SHORT-TERM AND LONG-TERM BONDS IN ROW: 57: RRS/100 = RRL/100 – ((RRLE/RRL)**4 – 1) + RES46
DEMAND FUNCTION FOR ROW M1:
58: LOG(RMONE/RP) = RM1*LOG(RGNP) + RM2*0.01*RRS + RM3*LOG(RMONE(–1)/RP(–1)) + RES47
PRODUCTION FUNCTION EXPLAINING ROW CAPACITY OUTPUT:
59: LOG(RYCAP) = RSCALE + LOG(1 + RN)*T*(1 – RBETA) + LOG(RK(–1))*RBETA
ROW RATE OF CAPACITY UTILIZATION:
60: RCU = 100*RGDP/RYCAP + RES49
MULTIPLIER RELATIONSHIP BETWEEN ROW MONETARY BASE AND M1:
61: RMONE = RMULT*RM + RES50
U.S. REAL GROSS NATIONAL PRODUCT:
62: UGNP = UGDP + URS(–1)/100*F(–1)/UPGNP + RES57
ROW REAL GROSS NATIONAL PRODUCT:
63: RGNP = RGDP – URS(–1)/100*F(–1)/E/TRADSCAL/ RPGNP + RES58
EXPECTED RATE OF CHANGE OF THE EXCHANGE RATE:
64: EPSILONE = (EE/E)**4 – 1 + RES59
TAX CHANGES TO STABILIZE U.S. GOVT. DEBT RATIO:
65: UT1 = UT1BAR + UTAU*DUM*(UB(–1)/UPGNP(–1)/ UGNP(–1) – UBRATIO) + RES60
U.S. TAX PARAMETERS ASSUMED TO MOVE TOGETHER:
66: UT1/UT2 = UT1BAR/UT2BAR
TAX CHANGES TO STABILIZE ROW GOVT. DEBT RATIO:
67: RT1 = RT1BAR + RTAU*DUM*(RB(–1)/RPGNP(–1)/ RGNP(–1) – RBRATIO) + RES61
ADAPTIVE EXPECTATIONS OF THE RATE OF CHANGE OF U.S. ABSORPTION PRICE:
68: UPIE = ETAUPI*UPI + (1 – ETAUPI)*UPIE(–1) + RES51
ADAPTIVE EXPECTATIONS OF THE RATE OF CHANGE OF ROW ABSORPTION PRICE:
69: RPIE = ETARPI+RPI + (1 – ETARPI)*RPIE(–1) + RES52
ADAPTIVE EXPECTATIONS OF THE EXCHANGE RATE:
70: EE = ETA*E + (1 – ETA)*EE(–1) + RES53
ADAPTIVE EXPECTATIONS OF THE U.S. LONG-TERM BOND RATE:
71: URLE = ETAURL*URL + (1 – ETAURL)*URLE(–1) + RES54
ADAPTIVE EXPECTATIONS OF THE ROW LONG-TERM BOND RATE:
72: RRLE = ETARRL*RRL + (1 – ETARRL)*RRLE(–1) + RES55
| ETA | 0.3 | ETARPI | 0.3 | ETARRL | 0.3 |
| ETAUPI | 0.3 | ETAURL | 0.3 | MUGNP | 1361.01 |
| Rα | 0. | RBETA | 0.383 | RC1 | 0.201055 |
| RC2 | 0.56857 | RC3 | 0.00634 | RC4 | 0.022152 |
| RC5 | 0.24771 | RC6 | 0.101305 | RGAMMA | 0.908193 |
| RIN1 | 0.0023 | RIN2 | 0.00534 | RIN3 | 0.00252 |
| RIN4 | 0.6545 | RIN5 | –0.66217 | RIN6 | –0.00252 |
| RMRT | 0.39995 | RM1 | 0.22 | RM2 | –0.518863 |
| RM3 | 0.72497 | RN | 0.00579 | RP1 | 0.052141 |
| RP2 | –0.03061 | RP3 | 0.241165 | RP4 | –0.182324 |
| RTAU | 0.1 | RT1 | 0.332668 | RT2 | 0.168227 |
| Uα | 0. | UBETA | 0.326 | UC1 | 0.252096 |
| UC2 | 0.021982 | UC3 | 0.594668 | UC4 | –3.05811 |
| UC5 | –0.456031 | UC6 | 0.42672 | UC7 | 0.043768 |
| UGAMMA | 0.934533 | UIN1 | 0.27905 | UIN2 | 0.02937 |
| UI1 | 1.37984 | UI2 | –0.722509 | UI3 | 0.711355 |
| UI4 | –0.070178 | UI5 | –0.016281 | UI6 | –0.099974 |
| UI7 | 0.761522 | UI8 | –0.087122 | UMRT | 0.494668 |
| UM1 | 0.259104 | UM2 | 0.099481 | UM3 | –0.339518 |
| UM4 | –0.130362 | UM5 | 0.616057 | UN | 0.00579 |
| UP1 | 0.02248 | UP2 | 0.048106 | UP3 | –0.032238 |
| UP4 | 0.17689 | UP5 | –0.10243 | UP6 | 1.4634 |
| UP7 | –0.53786 | UTAU | 0.1 | UTRATIO | 0.962673 |
| un | 0.242634 | UT2 | 0.252042 | UX1 | 0.78992 |
| UX2 | –0.03281 | UX3 | 0.023369 | UX4 | 0.106272 |
| UX5 | 0.882563 |
| ETA | 0.3 | ETARPI | 0.3 | ETARRL | 0.3 |
| ETAUPI | 0.3 | ETAURL | 0.3 | MUGNP | 1361.01 |
| Rα | 0. | RBETA | 0.383 | RC1 | 0.201055 |
| RC2 | 0.56857 | RC3 | 0.00634 | RC4 | 0.022152 |
| RC5 | 0.24771 | RC6 | 0.101305 | RGAMMA | 0.908193 |
| RIN1 | 0.0023 | RIN2 | 0.00534 | RIN3 | 0.00252 |
| RIN4 | 0.6545 | RIN5 | –0.66217 | RIN6 | –0.00252 |
| RMRT | 0.39995 | RM1 | 0.22 | RM2 | –0.518863 |
| RM3 | 0.72497 | RN | 0.00579 | RP1 | 0.052141 |
| RP2 | –0.03061 | RP3 | 0.241165 | RP4 | –0.182324 |
| RTAU | 0.1 | RT1 | 0.332668 | RT2 | 0.168227 |
| Uα | 0. | UBETA | 0.326 | UC1 | 0.252096 |
| UC2 | 0.021982 | UC3 | 0.594668 | UC4 | –3.05811 |
| UC5 | –0.456031 | UC6 | 0.42672 | UC7 | 0.043768 |
| UGAMMA | 0.934533 | UIN1 | 0.27905 | UIN2 | 0.02937 |
| UI1 | 1.37984 | UI2 | –0.722509 | UI3 | 0.711355 |
| UI4 | –0.070178 | UI5 | –0.016281 | UI6 | –0.099974 |
| UI7 | 0.761522 | UI8 | –0.087122 | UMRT | 0.494668 |
| UM1 | 0.259104 | UM2 | 0.099481 | UM3 | –0.339518 |
| UM4 | –0.130362 | UM5 | 0.616057 | UN | 0.00579 |
| UP1 | 0.02248 | UP2 | 0.048106 | UP3 | –0.032238 |
| UP4 | 0.17689 | UP5 | –0.10243 | UP6 | 1.4634 |
| UP7 | –0.53786 | UTAU | 0.1 | UTRATIO | 0.962673 |
| un | 0.242634 | UT2 | 0.252042 | UX1 | 0.78992 |
| UX2 | –0.03281 | UX3 | 0.023369 | UX4 | 0.106272 |
| UX5 | 0.882563 |
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The authors are, respectively, Assistant Chief and Senior Economist in the External Adjustment Division of the Research Department. Mr. Haas holds a Ph.D. from Duke University. Mr. Masson obtained his doctorate from the London School of Economics.
Simulation results similar to those reported here were presented to a conference at the Brookings Institution, “Empirical Macroeconomics for Interdependent Economies: Where Do We Stand?” March 10–11, 1986. The authors are grateful to the Division of International Finance of the Board of Governors of the Federal Reserve System for providing a recent version of its multicountry model, and to colleagues at the Fund for helpful comments. The authors are also indebted to William de Vijlder for his able research assistance, to Flint Bryton, Dick Porter, and Ralph Tryon for advice, and to the members of the Brookings macroeconomic modeling workshop for stimulation and encouragement.
The term “consistent expectations” was proposed by Walters (1971), but it has not been widely used by economists.
Base money is also included in the model, but it is exogenous.
Such a model is a restricted version of the model described in Taylor (1979), where expected unemployment (or output) during the duration of a contract is also important.
This equation in the model, however, has a residual that can be interpreted as an exogenous risk premium. In the simulations plotted in Chart 5 below, this residual is changed in order to gauge the effect of a portfolio shift away from U.S. dollar assets.
Sims (1980) has argued for treating regime changes as random errors. However, the resulting estimates of model parameters would be so unstable as to remove any confidence in simulation results.
The word “structural” is used here in opposition to “reduced-form.” The models are not structural in the sense of identifying utility function parameters.
Deleau, Malgrange, and Muet (1984).
Masson and Richardson (1986) and Masson and Blundell-Wignall (1986).
Such a methodology is used by Maciejowski and Vines (1984).
Measures of goodness-of-fit are available from the authors.
The importance of tax rules and wealth effects in consumption for the stability of the model is discussed in Masson (1986a).
”Empirical Macroeconomics for Interdependent Economies,” March 1011, 1986. The simulation results differ from those presented at that conference, because here they have been redone with a tighter convergence criterion. For most shocks, differences are minor.
Of course, since in the long run e is lower than in the baseline solution, at some point there must be a reversal, and this occurs when the interest differential moves in favor of the United States.
These simulations were performed in response to a request from John Taylor.
The fact that U.S. output actually falls slightly in the first quarter of simulation in the delayed policy scenario, but not in the contemporaneous policy scenario, can be traced to the behavior of prices. In both simulations real disposable income falls because output is valued at output prices but deflated at absorption prices and because absorption prices are more sensitive to exchange rate changes. The fall in real disposable income causes consumption and thus GNP to fall. This effect is transitory, and in the contemporaneous shock, it is more than offset by the effect of lower long-term interest rates on investment. In the delayed policy shock, higher prices cause all U.S. interest rates to rise, not fall. Short-term rates fall in the United States only when the money supply is actually increased.
