A Forward-Looking Multicountry Model: MX3
Abstract
This is paper discusses the theoretical structure and empirical properties of MX3, a multicountry macroeconometric model with rational expectations. MX3 is a medium-sized quarterly model of the United States, Japan, and West Germany. The primary objective of the model is to analyze the effect of fiscal and monetary rules on national economies in an international context. By incorporating rational expectations into almost all of the model's behavioral equations, MX3 takes a large step toward addressing the "Lucas critique" of model-based policy analysis.
Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 359
August 1989
A FORWARD-LOOKING MULTICOUNTRY MODEL: MX3
Joseph E. Gagnon
NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgement that the writer has had access to unpublished material) should be cleared with the author.
ABSTRACT
This paper discusses the theoretical structure and empirical properties of MXi, a multicountry macroeconometric model with rational expectations. MX3 is a medium-sized quarterly model of the United States, Japan, and West Germariy. The primary objective of the model is to analyze the effect of fiscal and monetary rules on national economies in an international context. By incorporating rational expectations into almost all of the model's behavioral equations, MX3 takes a large step toward addressing the "Lucas
critique" of model-based policy analysis.
A FORWARD-LOOKING MULTICOUNTRY MODEL: MX3
Joseph E. Gagnon! INTRODUCTION
MX3 is a medium-sized macroeconomic model of the United States, Japan, and West Germany. In MX3, quarterly econometric models of each country are linked by trade and capital flows. To close the system, data from the four next largest industrial economies are aggregated as a proxy for the rest of the world (ROW), and are modeled as a fourth country in Mx3 7 Each country block in MX3 has 11 behavioral equations, 21 identities, 4 government policy rules, and 2 exogenous variables. The scale of MX3 is thus considerably smaller than the Federal Reserve Board's Multicountry Model (MCM). (The MCM has app:oximately 170 equations per country block.) This paper presents a theoretical description of MX3 and discusses its empirical implementation
and estimation.
1. The author is a staff economist in the Division of International Finance. This paper represents the views of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or other members of its staff.
I would like to thank Gwyn Adams for outstanding research assistance. I would also like to thank Sean Craig, Neil Ericsson, David Gordon, William Helkie, Dale Henderson, David Howard, Eric Leeper, Jaime Marquez, John Taylor, Ralph Tryon, and participants in the Division's Monday Workshop for helpful comments and suggestions.
2. One avenue for future research is to extend the ROW sector by collecting data from other countries and building separate models for blocs of similar countries. Possible country groupings include the rest of the OECD countries, the OPEC countries, the newly industrialized countries (NICs), the non-oil developing countries, and the socialist countries. It would also be of interest to model each of the seven largest economies separately.
The structure of MX3 is in many ways similar to traditional Keynesian macro models. Economic agents are separated into four groups- -households, producers, traders, and governments. Each of the main aggregates in the national income accounts is associated with the decision rule of one or more of these groups. For example, households determine aggregate consunption and producers determine aggregate investment. >
MX3 differs from traditional large-scale quantitative macro models in three important dimensions. The first, and most obvious, difference is that expectations are rational and forward-looking rather than backward- ooking. MX3 imposes "rational expectations" in the sense that unobserved expectations are set equal to the model's own prediction of the future .* Only in the past few years have modelers begun to introduce rational expectations into empirical macro models. Two notable examples are John Taylor's multicountry model and the International Monetary Fund's MULTIMOD .> MX3 builds upon the work of these two forerunners.
The second innovation of MX3 lies in its treatment of lags in the structural relations. In MX3, the behavioral equations contain only one lagged dependent variable and no other lagged variables. (The appearance of
a lagged dependent variable in the decision rule is a general result of
3. Even though the profits of producers and traders revert to households, the decisions of producers and traders are not directly coordinated with the decisions of households. A general equilibrium in the model is achieved only through the incentives given by market interest rates and prices.
4. Because it is not feasible to compute true expectations in a large stochastic nonlinear model, the expectations variables are solved under the assumption that future disturbances are identically zero, i.e. the model solution enforces certainty equivalence. This procedure introduces an approximation error. Simply put, the model solves nonlinear functions of expectations when the theory calls for expectations of nonlinear functions.
5. See Taylor [1988] and Masson, et. al. [1988] for a description of these models.
optimizing behavior with costly adjustment.) Higher-order dynamics in the behavior of any individual time series are assumed to reflect the transmission and equilibration of shocks throughout the entire system of equations. In other words, a system of several first-order equations typically gives rise to time series behavior of individual variables that is higher than first order. This research takes the view that the apparent significance of lagged variables in much empirical work can be traced to misspecification of the estimation equation and, in particular, to the lack of a good measure of expected future variables.
The third, and perhaps most significant, difference between MX3 and traditional models concerns the long-run properties of the model. MX3 is designed to exhibit the qualities of an optimal stochastic growth model in the long run. The ultimate sources of growth in this economy are exogenous increases in labor force and technology. MX3’s parameters are carefully restricted to ensure that changes in government policy and.permanent shocks
to supply are consistent with steady-state growth paths.
OBJECTIVES
The primary objective of this project is to develop a simulation model for analyzing fiscal and monetary policy. By allowing expectations to react endogenously to changes in policy rules, MX3 takes a large step toward addressing Lucas’ [1976] critique of model-based policy analysis.
The essence of the Lucas critique is that the "structural" equations of most macro models really are not capturing stable decision rules of economic
agents. Instead, these equations are better characterized as reduced forms
that combine the interactions of policymakers and private agents. Lucas demonstrated that one would not expect such a reduced form relationship to hold constant in the face of a change in the policymakers’ behavior.
Lucas’ prescription for macro modelling is to consider the decision problem for each class of economic agents. Lucas argued that for a wide range of decisionmaking environments, agents base their actions on expectations of future variables as well as the realizations of current and past variables.° Only when modellers have correctly identified the optimal decision rules and information sets of each class of agents can they hope to gauge the effects of different policy rules accurately.
Unfortunately, a fully satisfactory analysis of macroeconomic dynamics based on optimizing behavior has yet to be developed, and it is likely to be years away for models of the scale of MX3. The strategy behind MX3 is to build a tractable model now by appealing heuristically to the structural equations that might result froma suitably specified set of agents, tastes, and technologies. There are three guiding assumptions: First, in the absence of shocks, the economy approaches a perfectly competitive, steadystate growth path. Second, in the face of shocks, agents must undertake costly adjustments. Third, the different classes of agents--consumers, ‘producers, traders, and governments--do not coordinate their decisions except through market prices and interest rates.
Many of the structural equations of MX3 are based on the Euler equation
decision rules that characterize optimal behavior with quadratic adjustment
6. "Rational expectations" embody a simplifying assumption that ignores any learning process by agents about the nature of the economy or the shocks that have ocurred recently. Under rational expectations, agents know the true stochastic structure of the economy, including the policy rules in effect.
costs, / The decision variable is a function of its own past and the expected future discounted sum of the forcing variables. The coefficients on these explanatory variables are typically constrained to ensure an eventual return to an optimal growth path. The speed of adjustment to the steady state can be freely estimated.
A. second objective of MX3 is to learn more about the world economy through estimation and testing of the model. Ideally, all the private sector behavioral and government policy equations should be estimated simultaneously using a technique such as full-information maximum likelihood (FIML) .2 Unfortunately, the computational requirements for FIML in all but the smallest rational expectations models are prohibitive.
YX3 was therefore estimated using instrumental variables techniques. One acvantage of estimating each equation separately and using instruments for current and future endogenous independent variables is that one need not
specify the exact form of the government policy rules before estimating the
. : : 9 private sector behavioral equations.
7. See, for example, Sargent [1978].
8. The advantages of FIML are especially important in the context of ratioral expectations models because future expectations in the equations being estimated can be solved directly by the model's own structure. Moreover, the implied cross-equation restrictions of rational expectations
can be tested, both jointly across all equations and individually in particular equations.
9. The treatment of expectations during the estimation of MX3 thus differs from the treatment of expectations during simulation. In order to simulate the model all equations must be specified, including the policy equations. Because estimation of all the equations simultaneously (FIML) is too expensive, the parameters of MX3 were estimated equation by equation, using instrumental variables for the future expectations.
THEORETICAL STRUCTURE
Overview
MX3's fundamental structure is that of a stochastic growth model with Cobb-Douglas technology, perfectly competitive firms, and long-lived utility-maximizing households. In MX3, households and firms rationally forecast future income and real interest rates when making their consumption and investment plans. Growth in the model is driven exogenously by growth in the labor force and in technology.
With Cobb-Douglas technology and perfect competition, capital.’s share of total output is given by the exponent on capital in the production function. The capital-output ratio equates the returns to capital. with the cost of capital, which is in turn dependent on the real rate of interest. The real interest rate serves to equilibrate consumption and investment at the level of output given by the production function.
While it would be possible to build a model of the economy with only the simple relationships described above, such a model would not be able to explain the short- to medium-run dynamics evident in the data. The transmission of shocks throughout the economy is almost certainly influenced by adjustment costs, gestation lags, and delays in the assimilation of new information. These characteristics of the economic environment may prevent markets from behaving competitively in any given period, and yet market forces may move the economy to a competitive outcome over a longer horizon.
Only recently have economists begun to enrich the dynamics of growth models by solving the decision problems of agents with costs of adjustment or gestation lags. At present, this work has yielded only rudimentary
models that require the assumption of continuously competitive market
clearing in order to obtain a solution. Extending these models rigorously to allow for monopolistic competition and endogenous entry of new firms is a task beyond the scope of this project.
The structure of MX3 reflects the view that economic theory in its present state yields clearer insights about the long-run behavior of the economy than about short-run dynamics. The approach taken by MX3 is to enforce a competitive steady state in the long run, but to allow (heuristically) for imperfect competition and costly adjustment in the short run. In several instances, the model's dynamics are inspired by optimal decision rules in the face of convex adjustment costs. These decision rules determine the control variable as a function of its previous value and the discounted expected future sum of the forcing variables. However, with the exception of consumption, the structural equations of the model are not
derived from the maximization of specific objective functions.
Markets and Agents
Each country is composed of four different types of economic agents. Producers in each country produce a homogeneous good that is differentiated from the goods produced in other countries. Productive capacity is modeled by a Cobb-Douglas function in the capital stock and the labor force. Total production can deviate temporarily from capacity production, but these deviations will be associated with equilibrating price movements.
Traders do not utilize capital and labor; they are modeled as pure arbitragers. Domestic traders purchase goods from domestic producers to sell to foreigners. This trade is characterized by significant costs of transportation and adjustment that prevent the continuous equalization of
prices across countries. The preferences of households, producers, and
governments for foreign goods relative to domestic goods jointly determine the demand curve faced by foreign traders selling into the domestic market.
Households maximize utility from discounted future consumption subject to their budget constraint. Households own the firms that produce and trade goods, and the net income earned by these firms passes directly to the households. The notional labor supply of each household is constant, but actual labor supplied may fluctuate as output fluctuates around capzecity. (The model essentially enforces equal capacity utilization of capitel and labor.)
Governments determine the level of the monetary base and real government spending. The government budget constraint determines the level of bonds outstanding. Tax rates are modeled with an ad hoc adjustment mechanism to ensure that the ratio of bonds to taxable income returns to an exogenous target level. The target level of government debt and the speed of adjustment to that target may be considered as additional policy instruments of government.
Financial markets determine the levels of interest rates and exchange rates. These financial markets represent the combined behavior of the four sectors in the model. Production technology and the labor force are modeled as exogenous to the rest of the economy.
Appendix 1 (attached to this paper) presents a simplified overview of a typical country model in MX3 and lists the data mnemonics used in the paper. Appendix 2 (not attached, but available upon request) provides a detailed
listing of the equations in MX3; it also documents the model database.
Consumption In the absence of liquidity constraints, adjustment costs, and
information lags, the representative household consumes a constant fraction
10
of its wealth. Wealth is defined as the discounted sum of expected future
disposable income.
- -i 1. C= B =YD (b+ 2+ a-may, ote - PPA i]
——1
4 4
In equation 1, RL, i is the nominal interest rate at time t on a risk-
free bond maturing after i periods; TAU, i is the average tax rate on the
interest from such a bond; DPA, , is the average rate of inflation of the
t,i
domestic absorption deflator between period t and period t+i; and A is a risk premium. !+ C is total private consumption and YD is private disposable income. RL, DPA, and A are all divided by four to convert annual rates to
quarterly rates of discount.
Ceteris paribus, higher levels of current or future income lead to
higher current consumption; higher interest rates reduce current
10. This consumption relation can be derived for infinitely-lived households with time-separable, logarithmic utility.
11. The premium A has two components. The largest component derives from the fact that private rates of return typically exceed the rate of return on government bonds. This excess return may represent a risk premium, and it has an average value of 6 percentage points in the United States. (See Mehra and Prescott [1985].) The economics profession has made little progress to date in explaining this risk premium or its fluctuations. In MX3 it is assumed to take a constant value of 6 percent.
The second component of A is the probability that the representative consumer will not survive until the following year. The probability of death leads all consumers to discount the future at a faster rate than the market rate of interest. (See Blanchard [1985].) In MX3 the probability of death for the representative consumer is assumed to be 2 percent per annum, which implies that the representative consumer expects to live for 50 more years.
consumption. In practice, however, positive shocks to income will]. tend to raise interest rates via the money demand equation, with ambiguous results for current consumption.
There are two modifications of equation (1) that may or may not be important in modeling consumption. First, a fraction of consumers: may be liquidity constrained, so that they simply consume their current clisposable income. 14 Second, the non-liquidity-constrained consumers may adjust slowly
to shifts in wealth by smoothing consumption from period to period due to an
aversion to sharp changes in their spending habits. > 2. C. =~ Cy, + Cy,- 3. Cie = ayD,. ~ A L DPA, .) > 4. Cy = bC,,+°(1-b)(1l-a)B = YD Ae + _ + (1-TAU .)® tii - t i| t 2t : t+i t,i i=0 4 4 4 12. For a discussion of the empirical magnitude of liquidity corstraints, see Hall [1988] and Poterba and Summers [1987]. Given the asymmet:iry between
ability to borrow and ability to save, it may be more descriptive to call these consumers myopic.
13. These households also should be forecasting movements in wealth in order to smooth consumption optimally. It is easy to show that forecastable movements in wealth over short horizons are extremely small under a broad range of environments. Therefore, the current value of wealth is a close approximation to its expected value over the near horizon. For more on habit-formation and slow adjustment in consumption, see Nason [1969].
Even if individual consumers adapt their spending plans rapidly, there will be a lag between the date their plans are made and the date the transactions are recorded. This lag will vary depending on the individual
plans: a European vacation may wait until summer, while a new car may be purchased quickly.
-ll-
According to equation (2) total consumption consists of the sum of consumption by liquidity-constrained consumers, C); and consumption by slowly-adjusting, unconstrained consumers, Co. Liquidity-constrained consumers simply consume their current disposable income, and the parameter, a, represents the share of disposable income earned by liquidity-constrained consumers. The remaining consumers adjust slowly toward the target level of consumption; b is the lagged adjustment parameter. Equations (3) and (4) can be substituted into (2) to yield a simplified expression for total consumption. If liquidity constraints and consumption smoothing are
unimpertant (a=0 and b=0) equation (5) reduces to equation (1).
5. C. = aYD, + i (ae - aD, _1]
- “i + (1-a)(1-b)B z D3 (1 +24 ci-tau, ,)Beta - PPAt i| . i- 4 car
In order to eliminate the infinite sum of future variables in equation (5) consider the following transformation of equation (4) using the term
structure relation that is presented in a later section (equation (36)).
6. Cor = bCo. 41 ~ i-l -1 + (l-a)(1-b)B 3 4¥YD.., * I (2 +44 c-tau_,.)PSt4y - PPAceit1] . t+1 : t+j i=0 j=0 4 4 4 The one-period interest rate, RL. 1? has been abbreviated to RS, as has the
one-period inflation rate, DPA,. This relationship also holds in the
subsequent period.
- 12 -
7. bec
Coed = Poe
re) i-l -1 + (l-a)(1-b)B 5 {ea * ae + : + (1-TAU,, 5 Ses - Parsi +1 } i=l j-
By dividing both sides of equation (7) by (1 + “+ (1-Tau,) Sse - or e+1) 4 4 mn
and subtracting equation (7) from equation (6), it is easy to show that
8. [2 + b/(2 + 4 + (1-TAU,) Se - Pact) co. = bCy, 4 4 4
4
PPAven) + (1-a)(1-b)p¥D,.
A RS +C (2 +" + (1-TAU,) ot - 2t+1 i tz z
Once again, the liquidity-constrained consumers are described by equation (3). Combining equations (2) and (3) with equation (8) yields a description of aggregate consumption that relies on expectations of only one
future period.
A RS DPA 9. C= b(Se-1- a? 4)/(1 + b/(2 + : + (1-TAU,) _ - “c1)}
A RS DPA + (Seat a¥D.43)/[1 +b +t i + (1-TAU,)—£ - Pett) + (a + (1-a)(1-b) 8) ¥D,. Fixed Investment
The model's investment equation is essentially neoclassical. In the
long run, the returns to capital should equal the cost of capital:
- 13- 10. ((1-Tav)Rs + (1-TAU)S - (1-TAU)DPA + | * K = a@(1-TAU)GDP.
The first three terms in the brackets on the left-hand-side of equation (10) represent the cost of holding a unit of capital for one period. The inte:‘est charge, RS, is reduced by the tax rate, TAU, because firms are allowed to deduct interest expense from their taxes. Similarly, the depreciation, 6, is also tax deductible. The inflation rate, DPA, represents a capital gain to the firm, so it reduces the cost of holding capittal. However, because the ability to deduct future depreciation from the firm's taxes is based on historical nominal cost rather than current value, inflation today increases the firm's future real tax liability. Finally, the model allows for a constant risk premium, 7, needed to induce agents to hold capital instead of risk-free government bonds.
The right-hand-side of equation (10) represents the returns to capital. With a Cobb-Douglas production function and competitive markets, capital’s share of output is simply the exponent on capital, a, in the production function. These returns are reduced by the average tax rate.
If it is costly to adjust the capital stock, even perfectly competitive markets are not sufficient to enforce equation (10) continuously. Some slowness in the adjustment process will generally be optimal. Equation (12) describes investment as a process that adjusts slowly to deviations between the desired and the actual capital stock. One explanation for slow adjustment of investment is that many capital-spending projects require multi-period commitments of a stream of investment that is costly to
change. !4 On the other hand, costly adjustment also provides an incentive
14. See Kydland and Prescott [1982].
-14-
for forward-looking behavior. A convenient way to capture both of these effects is to include a lagged dependent variable and expected future values of the target variables in the decision rule. Equation (12) does this without abandoning the long-run relationship in equation (10) and it
introduces only two new parameters. 11. cc, = ((1-Tav,) * (RS + 6 - DPA...) + n).
12. IF. = cIF, |
+ (l-c)(1-d) = a [ (a(1-ta0,, .)60P,,5/CCe,5) - (1-5)K
i~0 ces}:
13. K. = (1 - 6/4)K. + IF /4.
Equation (11) describes the one-period holding cost of capital. The term inside the inner set of brackets in equation (12) can be interpreted as the equilibrium capital stock in the absence of adjustment costs, as given by equations (10) and (11) .}5 The second term in the brackets is the capital stock carried over from the previous period. Equation (13) is the
perpetual inventory identity which defines the evolution of the capital
stock, 16
15. Equation (12) presents a causal relationship between expected output and desired capital. Future output is not exogenous, however, since it is affected by the amount of capital installed in the current period. Due to decreasing marginal returns to capital in the production function, there will be a unique combination of capital and output that satisfy. equation (12) in the steady state.
16. All stock variables refer to quantities at the end of the period. Because all flow variables are expressed at annual rates, they must be divided by four for purposes of stock accumulation. This rule applies to the capital stock, government bonds, and net foreign assets.
- 15 -
As in the case of consumption, it is possible to write equation (12) without the infinite sum of future variables. First, rewrite equation (12)
in serms of lag and lead operators (L and F): -1 14, (1-cL)IF, = (1-dF) (2(1-TaU,) GDP, /cc, - (1-6)K,_4)- Multiplying both sides of equation (14) by (1-dF) yields the following:
15. (l+ced) IF, = cIF + dIF.
t-l. 1
+ (1-¢) (1-d) (a(1-TAU, )GDP,/CC, - (1-8)K, 4).
Inventory Investment
Producers are assumed to hold inventories to adjust to expected and unexpected changes in demand. Thus, the net change in the,stock of inventories responds negatively to current output and positively to expected future output. The cost of holding inventories is the short-term real
interest rate.
16. Il, = €g + e,GDP.., - e GDP. - e3(RS_- DPA, 41) -
Export Prices
Traders are modeled as imperfectly competitive arbitrageurs who buy goods in their home country and sell them in a foreign country. The price of these exports reflects output prices at home and abroad. Export prices
are constrained to be homogenous of degree one with respect to output
- 16 -
prices. The foreign output price, PGNPW, is a weighted average of foreign prices converted to domestic currency at the exchange rate, E. The weights, w,, are fixed according to the average share of domestic exports destined for country i over the estimation period. The superscripts index individual countries. The home country is normalized at zero and its superscript is suppressed.
Over time, export prices in all developed economies have fallen relative to aggregate prices. This phenomenon is most likely due to faster technological progress in tradables than nontradables and it is modeled here
as a simple function of time.
17. log(PEX, ) = && + 8 log(PEX, |) + 8 log(PGNPW, ) + (1-8) -&5) log(PGNP ) - &3¢.
18. log(PGNPW,) = w,log(E-*pcnP!) + w,log(E2*PGNP2)
7 508 t OB ETE GNE gr OB, t
3 3 + (1-w, -wy)log(E,*PGNP_ ).
Export Volumes
Unlike many other econometric models, MX3 allows for different cyclical and secular demand elasticities in trade. The cyclical demand for exports depends on weighted foreign absorption relative to foreign productive capacity, AW/CAPW, and the price of domestic exports relative to the price of foreign exports, PEX/PIM. The secular demand for exports depends on the level of worldwide production capacity, CAPTOT. MX3 thus incorporates the assumption that long-run growth in trade is due as much to supply-side as to demand-side factors. (In equations (20) and (21) the weights, W;, are the
same as those used to compute PGNPW in equation (18).)
- 17 -
19. log (EX, ) = ho + hy log(EX, 4) + h, log (AW, /CAPW, )
+ h,log(PEX,/PIM,) + h,log(CAPTOT,).
I
1 2 3 20. log(AW, ) w, log(A,) + wo log(A,) + (1-w, -w,)log(A,).
1 2 3 21. log(CAPW, ) = w, log(CAP.) + w,log(CAP.) + (1-w,-w,)log(CAP_).
2
1 22. CAPTOT, = CAP. + CAP. + CAP.
+ CAPS. Import, Volumes and Prices
Because each country’s exports are the imports of the other countries, it would not be theoretically consistent to model imports and import prices independently of exports and export prices. MX3 thus estimates equations that describe the share of a country’s exports that are destined for each other country. These share equations incorporate the global trade balance identity. Country i's total imports are computed in both nominal and real terms by adding up the fraction of each other country’s nominal and real exporzs that are destined for country i. (The aggregate import price for country i is the ratio of nominal to real imports.)
Ideally, there should be two sets of export share equations: one set for nominal exports and one set for real exports. The allocation of nominal and real exports across trading partners need not be identical because the price of exports to different trading partners need not be identical. Unfortunately, on a bilateral quarterly basis only nominal trade shares are available. Both nominal and real imports in MX3 are computed using the same
share weights of exports.
As an alternative to modelling the export side, it would be possible to estimate behavioral equations for imports and import prices and use import share equations to compute exports and export prices. The former strategy is adopted by MX3 for two reasons. First, the assumption that nominal and real trade shares move together is more realistic for exports than for imports, as long as export prices are more closely correlated with the exporter’s price level than the importer's. Second, it is econome=rically easier to model the effect of relative prices on nominal export shares than on nominal import shares. An increase in the price level of one trading partner relative to another will unambiguously increase the share of nominal exports to that country by encouraging both higher prices and quantiities. However, an increase in the price level of one trading partner relative to another will have offsetting price and quantity effects on the share of nominal imports from that country.
The allocation of each country’s exports among its trading partners is modeled via a system of equations that captures the effects of changing relative prices while forcing the shares to sum to unity for each exporter, !” SHR1 refers to the share of country O exports destined for
country 1. sHRot refers to the share of country 1 exports destined for
country 0.
= . 17. In theory one also might want to capture the effects of relative
absorption and relative capacity, but empirically these effects were insignificant.
- 19 -
1
t
23. SHR1 = vy + Ty) o*SHRL, 4 + 7, )*1og[E t
+PGNP?/E;*PGNP?|
1
+ 7, y¥1og(Et
1.3 3 *PGNPE/EE*PCNP?)
1 1,,2 2 24. SHR2/= Ve + Too *SHR2, 4 - 7, p#log[Et*PGNPL/Ee*PCNP?|
2 2.3 3 + 1, ¥log{E-¥PoNP?/E>*PCNP?)
25. SHR3 = (1-4, -¥) - T *SHR1 | - T *SHR2
10 20 1
1 1,,3 3 - 7 y*1og [Et*PoNP)/E>+PGNP
2 2.3 3 :| - T, y#log(Ep*PoNPL/E?*PoNP®)
li pyl 2 2 3 3
26. IM, ~ SHRO | *EX) + SHRO|,*EX) + SHRO | *EX, .
1 1 loioyl 3 3
3 3 = * * 27. PIM. & PEX. SHRO | *EX +... + E,*PEX?*SHRO,+EX>| / IM, .
Finally, net foreign assets are the sum of previous current account
surp..uses. The currency denomination of all international assets is assumed
to be U.S. dollars, and the return on these assets is equal to the treturn on
U.S. government bonds. = * - * 28. NFA, (2 + RS, /4)NFAL 1 + PEX, *EX/4 PIM, *IM,/4.
Capacity
Capacity output, CAP, is given by a Cobb-Douglas production furiction. The labor force, L, and production technology, Q, are exogenous. The rate of capacity utilization, CU, is simply the ratio of domestic output to domestic capacity. In this model capacity denotes the sustainable, equilibrium level of output given the values of K, L, and Q, and the preferences of workers and managers. As discussed below, it is possible for
the economy to operate above or below "capacity" at any given time. fo4 = * 29. CAP. Qe Ke. 30. CU, = GDP, /CAP..
Prices
The model abstracts from the labor market in its description of aggregate price behavior; in other words, it treats workers’ wages as just additional prices in the system. The model therefore does not rely on
movements in the real wage to explain output fluctuations. 18 Instead, MX3
18. The traditional Keynesian explanation of the business cycle relied on countercyclical real wages caused by sticky nominal wages: during periods of high demand, firms would charge higher prices, thus reducing the ireal wage and encouraging more employment and output. The seminal work of Dunlop [1938] as well as recent studies by Bils [1985] and Roberts [1987] all conclude that the real wage is nearly constant over the business cycle.
- 21-
posits an expectations-augmented Phillips curve to explain price adjustment. In the model, the rate of inflation accelerates when output is above capacity or when output is expected to be above capacity in the future. Similarly, inflation decelerates when output is below capacity or when output is expected to be below capacity in the future. The model also is
characterized by a significant degree of inertia in the inflation rate. = - * 31. DPGNP Po*DPGNP. 4 + (1 Po) DPGNP 44 + P,log(cu.).
A Phillips curve that is both backward- and forward-looking, like equation (31), can be justified as a rough approximation to a model of staggered price contracts. 1? According to models of staggered contracts, firms and workers set nominal prices for a predetermined period of time and agree to supply whatever quantity is demanded during the contract period. If the contracts last for more than one period, lagged adjustment will be introduced into the inflation process. Because firms and workers try to predict conditions over the life of their contracts, there will also be a forward-looking element to price behavior.
When output equals capacity, CU = 1 and log(CU) = 0. In this state of full employment there is no tendency for inflation to accelerate or decelerate, according to equation (31). The real side of the MX3 model can therefore be in equilibrium at any constant inflation rate of the price level.
The absorption deflator is an average of the GNP deflator and the
export and import deflators. It is solved from the nominal GNP identity.
19. See Taylor [1980]. The dynamics induced by staggered contracts are more complex than those of equation (31).
- 22 -
The rate of inflation of output prices and the rate of inflation of
absorption prices are defined in annual rates by simple identities.
= - * * - * 32. PA *AL PGNP, *GNP PEX EX. + PIM, IM, RS. NFA, _1-
33. DPGNP = 4*(PGNP,-PGNP, ,)/PGNP. |.
34. DPA, = 4*(PA,-PA,_1)/PA,_1-
Exchange rate
The basic exchange rate equation is motivated by open interest rate parity. The difference in nominal rates of return, RS, across countries is exactly matched by the expected movement of nominal exchange rates. g, 20 There are three exchange rates in the model; U.S. dollars are the numeraire.
Equation (35) presents a typical exchange rate equation.
1
35. (EL - E41) / EY = (RS. - RS.) / 4.
Term Structure
The model incorporates the pure expectations theory of the term structure of interest rates. Long rates are a function of expected future short rates over the term to maturity. Because the other behavioral equations of the model use this term structure relation to simplify their expressions,
long-term interest rates are not needed to solve MX3. The implicit equation
DN : : : 20. It is possible to augment the equation to include either a constant risk premium or a variable risk premium that depends on the ratio of foreign
to domestic bonds (portfolio balance). See Dooley and Isard [1982] and Frankel [1983].
- 23 -
for the interest rate on a bond maturing in i periods is given below. The one-period interest rate, RL, L? has been abbreviated to RS ..
36. (1 + RL, > - (1 +RS,)(1 + RS (1 + Rs
t+1) t+i-L°
Money Demand - Money Supply
{t is possible to model either the short-term interest rate, RS, or the monetary base, MB, as the instrument of monetary policy. One of the main purposes of MX3 is to analyze the effect of different monetary policies on the overall economy. In the simplest case, one may consider a monetary policy that sets a constant growth rate for the monetary base.
The public demands real money balances, MB/PA. The absorption deflator and domestic absorption appear in the money demand equation on the assumption that cash balances are held to support spending. Nominal interest rates adjust to ensure that the public willingly demands the
quantity of money supplied.
37. MBL = mMB, 4.
38. log(MB, /PA,) = To + r,log(MB. _j/PA,_4) + rolog(A,) +r RS .. Fiscal Policy
Real government spending is denoted by G. Nominal tax revenues, TAX, equal the tax rate, TAU, times taxable income, TI. Taxable income is net national product plus interest on government bonds, B. The stock of government debt is given by the cumulation of past budget deficits minus
revenues from money creation.
- 24 - = *
= * - 40. TI PGNP | GNP. 6K
* * r PA, + RS,*B,_
t-1 1°
41. Be = (2 + RS_/4) Bey + (PAL *G,. - TAX, /4 - (MB. - MB. 1).
Based on equations (39)-(41) it would appear that governments are free to choose values of G and TAU independently and without constraints. However, when private agents form their expectations of future fiscal policy, they recognize that the government must satisfy its budget constraint (equation (41)) at every future date. Thus, an intertemporal budget constraint implicitly restricts the future paths of G and TAU. If the government is not allowed to default on its obligations, the national debt cannot grow so large that interest payments on the debt exceed the government’s ability to raise revenues. Assuming a positive interest rate
and a fixed rate of money growth, this feasibility condition places an upper
bound on the ratio of government debt to taxable income.71 21. When there are no liquidity constraints, risk premia, or finite
-horizons (i.e., a=0 and A=0 in the consumption equation) optimizing behavior places the following restrictions on expected future fiscal policy:
fo 0]
= - * - 42. By Fan {(7% e574 Par Cey 3/4 + MB MB 45-1)
/ i (2 + RS 44/4}.
i=1
j 43. limB.., / I (1 +RS_,./4) = 0.
Placing bounds on the ratio of debt to income is sufficient to ensure that (42) and (43) hold, provided that the nominal rate of interest exceeds the growth rate of nominal income.
(Footnote continues on next page)
- 25 -
In order to compute expectations of future fiscal policy in a manner consistent with the government’s intertemporal budget constraint, MX3 models the tax rate, TAU, as a reaction function that gradually adjusts to return the ratic of bonds to taxable income to some exogenous target value, BRATIO. The variable TBAR represents the tax rate necessary to return the bond to income ratio to its target, BRATIO, in one period. The actual tax rate, TAU, adjusts part of the way toward TBAR in.each period. 2? If desired, automatic stabilizers in the tax system could be added to equation (44). As with the monetary base, government spending and the bond ratio are left unspecified. However, in order to solve the model, some policy rule must be assumed to describe the future behavior of G and BRATIO. In the simplest
case, G prows at a constant rate and BRATIO is constant. 44. TAU, = wIAU, 4 + (1-w)TBAR, .
= * - 4* - 45. TBAR, (S. PA. + RS_*BL_, - 4*(MB, MB, .;))/TI,
- BRATIO, + B._j/TI,.
(Footnote continued from previous page)
If the rate of interest is smaller than the growth rate of income, a bounded debt-to-income ratio will still ensure feasibility of future fiscal policy, but it does not guarantee that equations (42) and (43) will hold. However, if households have finite lives or if they are risk averse, then (42) and (43) are no longer necessary for optimality. See Abel, et. al. [1987].
22. The adjustment parameter, w, is always bounded between zero and one. However, depending on the remaining parameters of the model, large values of w may not adjust the tax rate quickly enough to ensure stability.
- 26 -
47. BRATIO, = Z.
Accounting Identities
48. A. = Cc, + IF. + Il, + GC.
49. GDP. - A, + EX. - IM, .
50. GNP. = GDP, + RS .*NFA,_j/PGNP..
= * - - 51. YD, PGNP | GNP /PA, 6 TAX, /PA,
Kee + RS,*B,_1/PA, - (“Bet B, 1} *DPA,/PA,.
ESTIMATION
The equations to be estimated are consumption, fixed investment, inventory investment, export volumes, export prices, export shares, production capacity, price adjustment, and money demand. Since many of the variables in these equations are nonstationary, they must undergo appropriate transformations in order to eliminate heteroscedastic ~esiduals. For most equations, the relationships are estimated in logarithmic form. In
other cases, all the nonstationary variables are divided by a smoothly-
growing variable with which they are presumed to be cointegrated.?? 23. The presumed cointegrating relationships are that consumption and
investment grow proportionately with output in the long run. These relationships have not been tested with the MX3 data set because of the
short sample that is available. However, they are implied by the theory of the previous section.
The data available for estimation are 48 quarterly observations from 1976:1 to 1987:4. The data are expressed at annual rates. All equations are estimated over the maximum possible range after allowing for necessary lags and leads. The consumption, inventory investment, and fixed investment regressions were run in RATS 3.0. The remaining regressions were run in TROLL 13.0.
Wherever practical, MX3 uses common parameter estimates from pooled regressions. In some cases there are theoretical reasons for expecting a common parameter. In other cases a common parameter was imposed only if the
unrestricted estimates were not significantly different statistically.
Consumption
The. consumption equation (9) is highly nonlinear and it contains expectations of future variables. Hansen and Singleton [1982] develop a generalized method of moments (GMM) procedure for the estimation of nonlinear equations with future expectations. The procedure is based on the orthogonality condition between future disturbances and past information. This orthogonality condition is an implication of rational expectations: agents should use all available information, of which the instruments are a subset, in order to compute the expectations of future variables th-* concern them. Any deviation between their expectation and the subsequent realizat:ion of a variable ought to be orthogonal to all information that was availab’e at the time they formed their expectation.
In order to scale for growth over time, both consumption and disposable income “in equation (9) have been divided by production capacity. The equation was estimated for each country individually and in a pooled
regress:.on for all countries together. The instruments used were a
- 28 -
constant, one lag of consumption, one lag of disposable income, current government spending, a lagged interest rate, a lagged inflation rate, and lagged real money balances.
The liquidity-constraints parameter, a, was not significantly different from zero in any regression. After setting a=0, the equation was reestimated. None of the estimated parameters in any of the single country regressions ever deviated from the pooled estimates by more than two standard deviations. Moreover, the standard errors in the pooled regression were uniformly smaller than the standard errors in the individual country regressions. Therefore, the model takes the coefficients from the pooled regression for every country. These results are shown below:
52. 11 + b/f1 + 4 + (1-Tau_yBSe ~ PPALs iy Ic. = bc 4 t —— t t-l
4 4
+ Cuya/(2 +S + a-tauyBSe - PPAtea) + ppv, 4 ns ls t
b= 0.852 B = 0.00985 A= 0.08 J= 1.50 (2) (0.059) (0.00101) n.a.
The Hansen-Singleton J-statistic, which tests the orthogonality implications of rational expectations, is not significant at conventional levels. Formal tests of parameter constancy were conducted both over time and across countries. These tests are described in Andrews and Fair [1988]. The test for parameter constancy over time splits the sample into t:wo equal subsamples and tests whether the parameters estimated in each subsemple are significantly different from each other. This test was not significant at
the 10 percent level. There are four tests for parameter constancy across
countries. Each test compares the parameters estimated in a single country to the pooled estimates. None of these four tests was significant at the
5 percent level. The ROW estimates were significantly different at the 10 percent level, however.
In addition to tests of parameter constancy, the consumption equation was reestimated after incorporating a constant term and it was also reestimated after incorporating a lag of disposable income. In neither case was the extra term significant at the 5 percent level.
Returning to the estimated equation, one may interpret the economic significance of the coefficients b and 8. The estimate of b implies that consumers adjust to new circumstances at the rate of 15 percent per quarter. In other words, after a shock to permanent income, consumption adjusts 47 percent of the way to its new long-run level in the first year. The estimate of 6 implies that in steady-state, households consume 1 percent of
their wealth per quarter.
Inventory Investment
“he inventory equation (16) was estimated via GMM. The inventory investment and GDP series were first divided by capacity. The instruments were a constant, a lagged growth rate of GDP, current government spending, a lagged real interest rate, and a lagged growth rate of the monetary base. The equation was estimated on individual countries as well as pooled across countries. In every case the restriction e) = & could not be rejected. The estimated value of e, varies considerably across countries, but in every case the associated standard deviation is quite high. The pooled estimate lies approximately in the middle of the range. Results from the pooled
regression are presented here:
- 30 -
53. II, =e, + 2) (PPL - GDP.) - e,(RS_- DPA, +1): @9y = 0.0073 e, = 0.483 e, = 0.078 J= 5.35 (4) (0.0011) (0.570) (0.035)
The J-statistic is significant at the 10 percent, but not the 5 percent, level. Parameter constancy tests were conducted across time and across countries as in the case of consumption, and none of the tests was
significant at the 10 percent level.
Fixed Investment
The fixed investment equation (15) was also estimated using GYM. Once again, the series IF, GDP, and K were divided by capacity before estimation. The instruments were a constant, two lags of investment, a lagged capital stock, a lagged real interest rate, a lagged growth rate of the moretary base, and a lagged inflation rate.
The discount factor d is fixed at 0.97. This value was calibrated empirically as follows: The rate at which firms discount the future sequence of desired capital stocks ought to be related to the real discount rate and the rate of depreciation of capital. The sum of the average real after-tax interest rate, the Mehra-Prescott risk premium, and the measured rate of depreciation has averaged about 12 percent per annum, or 3 percent per quarter, historically.
The rate of depreciation, 6, and the share of output accruing to capital, a, were estimated independently. The remaining parameters of the fixed investment equation are the lagged adjustment, c, and the risk premium, x. Attempts at estimation were unsuccessful, as the lag
coefficient was approximately unity. In the end, the lag coefficient c has
- 31 -
been constrained at 0.95, and the risk premium, 7, has been estimated
independently for each country. 54. (1+ed)IF, = cIF, | + dIFL,, + (1-c) (1-4) (aGDP,/cC, - (1-6)K, 4).
where ce. = (RS, + 6 - DPA ) +n / (1-TAU,).
t+1
Germany Japan ROW USA ww (x100) 4.784 ; 6.707 6.707 6.796 (0.784) (0.951) (0.888) (1.621) c 0.95 0.95 0.95 0.95 n.d. n.a, n.a,. n.a. d 0.97 0.97 0.97 0.97 n.a. n.a. nea. na. J (x2) 7.75 0.01 27.3 35.4
eee
The J-Statistic is significant at the 1 percent level in the ROW and U.S. regressions. The test for parameter constancy is significant at the
1 percent level in every country.
Capital Stock
The depreciation rate of capital was estimated via ordinary least squares (OLS). The regressand is the series defined by KL -IF,. The regressor is Keeq: This regression estimates the fraction of capital that
; 4 aaa ‘ survives after one quarter.” The quarterly depreciation rate is the
24. Equation (55) is very nearly an identity, and it is treated as such in the model. In practice, statistical agencies estimate the capital stock at a disaggregated level, using different depreciation rates for each type of capital. If the proportion of investment in each type of capital good were
(Footnote continues on next page)
- 32 -
fraction that decays in one quarter, or unity minus the estimated coefficient. The annual depreciation rate is approximately four times the quarterly rate.
55. K. - IF, = 6*K, where 6 = 4 * (1-6).
t 1? Germany Japan ROW USA
§ 0.9879 0.9924 0.9836 0.9845 (0.0000) (0.0003) (0.0001) (0.0001)
F 0.0483 0.0304 0.0658 0.0623
R? 0.999 0.998 0.996 0.999
D-W 1.34 0.50 0.28 1.13 —_
Production Function
Under perfect competition, the exponent on capital in a Cobb-Douglas production function is equivalent to the fraction of output that accrues to the owners of capital. The value of a used in MX3 differs slightly between the four country blocks. It is estimated by taking the average fraction of after-tax GDP that is composed of capital consumption allowances and operating surplus, according to the OECD's National Accounts over the period
1976-1987. The values of a in Germany, Japan, and the United States are,
(Footnote continued from previous page) constant over time, then the aggregate depreciation rate would be constant and equation (55) would hold identically.
- 33 respectively, 0.35, 0.39, and 0.32. The value of @ in ROW has been arbitrarily fixed at the value estimated for Germany.
Technology, Q, is assumed to follow a log-linear time trend. This trend is estimated as the fitted value of the following OLS regression.
56. (Log(aDP,) - alog(K, 4) - (1-a) log(L,_1)) = [ + pt.
Germany Japan ROW USA
r 2.1990 0.3792 1.6272 2.0944 (0.0051) (0.0024) (0.0035) (0.0080) » 0.00116 0.00231 0.00140 0.00079 (0.00019) (0.00009) (0.00013) (0.00029) Rr? 0.45 0.94 0.72 0.14 D-W 0.41 _ 0.55 0.18 0.15 ne ea 2 © > > Se ©; © PO
Output Price
It proved impossible to obtain sensible estimates of the expectationsaugmented Phillips curve for the GNP deflator. Consequently, the coefficients on lagged and lead inflation have been arbitrarily set at 0.5 each, and the sensitivity of inflation to capacity utilization has been deternined by simulation trials to yield a reasonable responsiveness of prices to aggregate demand.
Since the process of price adjustment is central to understanding the transmission of monetary policy to the rest of the economy, the lack of a well-estimated structural price equation is a serious flaw in the MX3 model as it exists currently. The first step in the next stage of development
must be to consider alternative price adjustment mechanisms and estimation
- 36 -
Germany Japan ROW USA hy -0.612 -0.301 -0.373 -1.645 (0.192) (0.172) (0.187) (0.318) hy 0.775 0.937 0.864 0.476 (0.069) (0.033) (0.067) (0.101) hy 0.688 0.418 0.268 1.929 (0.223) (0.223) (0.112) (0.297) hy -0.260 -0.107 -0.120 -0.372 (0.075) (0.036) n.a. (0.092) hy, 1.000 1.000 1.000 1.000 nia. nia. nia. n.a. R2 0.97 0.99 0.98 0.96 D-W 2.02 2.00 2.05 1.75 __
59. log(PEX, ) = & + 8, log(PEX, 1) + B,log(PGNPW, )
+ (1-g)-B,)log(PGNP,) + B,log(PEX, |/PEX, 4) - 8, (1-g,)t.
Germany Japan ROW USA B 0.015 0.005 0.008 0.003 (0.002) (0.006) (0.003) (0.002) a 0.734 0.824 0.985 0.962 (0.050) (0.063) (0.037) (0.032) B, 0.076 0.120 0.000 0.000 (0.013) (0.046) nua. n.a. B3 0.408 0.136 0.527 0.728 (0.092) (0.123) (0.118) (0.119) b,, -0,0025 -0,0025 -0.0025 -0.0025 (0.0002) (0.0002) (0.0002) (0.0002) R2 1.00 0.93 1.00 1.00
D-W 1.67
1.09
1.27 1.70 __ neem ne
- 37 -
A likelihood ratio test for parameter constancy was run by reestimating the entire model over two equal subsamples. The test rejected parameter
constancy at the 1 percent level.
Export Shares
The export shares for each country are estimated as systems of equations so that the cross-equation restrictions on the parameters Ty can be imposed. Because the share equations sum to unity, as do the share data, the last equation in the system is omitted from the estimation since its residual is a linear combination of the other residuals. Estimation is by
FIML, treating the relative prices across countries as exogenous variables.
1
t
60. SHR1,~ ¥) + T))*SHRL_ | + 1 #Log(z .
*PGNPL/E,*PCNP S|
1 1.3 3 + 1 *log[etePonPteesponp?)
1 1.2 2 61.. SHR2)= Vo + To9*SHR2, 1 - 1 p#log[BExPcNPL/E?*PcNP?|
2 253 3 + T,#log(BC#PoNP2/EesPoNP?)
62. SHR3 = (1-¥) -¥,) - Ty *SHR1 4 - Ty 9*SHR2. oy
1 1.3 3 2 2.3 3 . 7, j*log(Et¥PoNP/E2+PcnP?) - 1, y*log[Ep*PGNP? /E>¥pcNP?)
- 38 -
German Japan ROW USA
¥, -0.003 0.007 0.137 0.063 (0.002) (0.004) 0.062) (0.014) v, 0.014 0.034 0.074 0.006 (0.005) (0.003) 0.031) (0.017) To 0.900 0.876 0.705 0.166 n.a. (0.006) (0.090) (0.166) Too 0.850 0.900 0.778 0.711 (0.059) n.a. (0.079) (0.118) Ty 0.000 - 0,002 0.041 0.005 (0.001) (0.003) (0.013) (0.004) T, 0.003 0.000 0.003 0.018 (0.001) na. (0.017) (0.007) T53 0.019 0.044 0.000 0.009 (0.007) (0.012) oe (0.010) RS 0.91 0.75 0.90 0.46 RS 0.91 0.97 0.88 0.68
In the case of German export shares, 1 and 2 refer to Japan and the United States, respectively. In the case of Japanese export shares, 1 and 2 refer to Germany and the United States. In the case of ROW, 1 and 2 refer to Germany and the United States. Finally, for the United States, 1 and 2 refer to Germany and Japan, respectively.
Two of the lag coefficients had to be constrained to avoid es:cimating unit roots. Two of the relative price coefficients were restricted from
taking the wrong sign. Together, these four restrictions could be rejected
- 39.
at the 1 percent level. A test for parameter constancy also rejected
constant parameters in favor of a break at midsample at the l percent level.
Money Demand
The money demand equations were estimated by two-stage least squares. The instruments are a constant, current government consumption, and one lag each of real money balances, the nominal interest rate, and total
absorption.
63, log (MB. /PA,) = 1) + vr log(MB, _4/PA,_1) + rolog(A,) + r4RS.. Germany Japan ROW USA ry -3.286 -1.805 -0.885 -1.395 (0.814) (0.746) (0.272) (0.190) r, 0.678 0.766 0.768 0.776 (0.081) (0.094) (0.063) (0.038) r., 0.477 0.271 0.139 0.193 (0.116) (0.110) (0.039) (0.026) re, -0.670 -0.840 -0.600 -0.390 (0.210) (0.270) (0.120) (0.050) R“ 0.99 0.99 0.96 0.99 D-W 1.82 2.31 2.25 1.74 cme SPY 20 PY 2
The German equation was estimated via Cochrane-Orcutt in order to correct for serial correlation. The estimated autocorrelation coefficient was 0.63. In order to check for homogeneity of the effects of the real interest rate and the expected inflation rate on money demand, the lagged
rate of inflation was added to the instrument list and the current rate of
- 40 -
inflation was added to the list of regressors. The estimated coefficient on the inflation rate was significant at the 5 percent level in the German equation, but not in the other countries’ equations. A Chow test for parameter constancy (see Fair [1987]) rejected parameter constancy at the 5 percent level for the ROW equation only. The U.S. equation failed at the 10
percent, but not the 5 percent, level.
Monetary and Fiscal Policy
The coefficients of the monetary base and real government consumption equations are "estimated" by the average rate of growth of these variables over the period 1976-87. The (presumed) constant target ratio of bonds to income, BRATIO, is simply the actual value of the ratio of bonds to taxable income in the fourth quarter of 1987. The coefficient w in the tax adjustment equation has been arbitrarily fixed at 0.95.
Obviously, the simple policy rules described here are not very realistic. One of the most attractive features of MX3 is the ability to consider alternative policy rules, both as descriptions of past behavior and as proposals for future policy. By allowing private expectations to fully incorporate the implications of a particular policy rule, we hope to obtain a more accurate characterization of the economy's behavior under that rule,
at least in the long run.
SIMULATION PROPERTIES
This section presents the dynamic response of the model to a simple
monetary shock and a simple fiscal shock. The monetary shock consists of a
2 percentage point increase of the U.S. monetary base in the first quarter of 1988. This shock has a permanent effect on the monetary base due to the simple growth rate rule for monetary policy. The second shock increases U.S. government consumption by 1 percent of total U.S. productive capacity in the first quarter of 1988. This shock also has a permanent effect through the simple fiscal spending rule.
In order to highlight the effect of expectations in MX3, each of these shocks is implemented in two different ways. In the "surprise" scenarios, the monetary or fiscal shock is first announced in the quarter of implementation, 1988:1. In the "anticipated" scenarios, the government announces its intention to change monetary or fiscal policy in 1986:1, eight quartiers before the planned implementation.
The results of these simulations are presented in terms of percentage deviations from the baseline path, except for real net exports, which are presented as deviations from the baseline path in percentages of baseline capacity output. The baseline path uses actual values through the end of 1987 Beginning in 1988 real variables increase at a constant 3 percent rate, prices increase at a 4 percent rate, nominal variables increase at a 7 percent rate, and interest rates and exchange rates are fixed at their 1987:4 values. Residuals are computed for each equation to keep the model on the baseline path. In other words, when the model is simulated with the residuals it tracks the baseline path. In the shock simulations the model is solved with the baseline residuals in addition to the monetary or fiscal
shock. The use of baseline residuals allows us to isolate the effect of the
- 42 policy shock under consideration. ”>
The first simulation is a surprise increase of the monetary base by 2 percent effective 1988:1. Because MX3 incorporates the long-run neutrality of real activity with respect to money, we know that prices must eventually rise by 2 percent and output must return to its baseline value. Figure 1 demonstrates that the model does perform as expected in the long-run. The domestic price, UPGNP, rises steadily from its baseline level to a maximum value of 2.5 percent over baseline in 1990:4. The price level then drops to a value 1.8 percent above baseline in 1993:3 before gradually approaching its long-run equilibrium of 2 percent above baseline.
Movements in the weighted foreign price level, UPGNPW, primarily reflect movements in exchange rates. Consistent with a long-run equilibrium, we expect that foreign prices will be unaffected by a domestic monetary expansion and that exchange rates will rise proportionally to the increase in the monetary base. The weighted foreign price level in domestic currency should therefore rise by 2 percent in the long-run. Figutre 1 shows that UPGNPW jumps almost 2 percentage points in the first quarter before falling sharply by 1 percentage point in the following quarter. UPGNPW remains at about 1 percent above baseline over the next three quart:ers before climbing back up to--and temporarily overshooting--its long-run value. The dynamic behavior of UPGNPW is primarily explained by lower
nominal interest rates in the United States during the first two quarters
25. An alternative approach is to use the baseline implied by the model with future residuals set at their expected value of zero. This procedure is much more computationally intensive. Moreover, to a first approximation, the effect of the policy shocks relative to baseline is unaffected by which baseline is chosen. If the model were linear, the effect of policy shocks would be completely independent of the baseline
- 43 - Figure 1
Surprise Monetary Shock
(Percent Deviation from Baseline)
UPGNPW
0.5
1Oo+
0.5
1992 1995 1986 1989
NETX *
1Oo+
0.5
1 1992 1995 1986 1989
“In percent deviation from baseline capacity output.
1992
1992
0.5
lo+
0.5
1 1995
lot
0.5
1 1995
- 44 -
and higher nominal interest rates in the United States over the following 12 quarters. Because of the open interest rate parity equations, movements in exchange rates are completely explained by interest rate differentials after the impact of the shock.
UGDP jumps about 0.7 percent for the first three quarters before returning gradually to its baseline value. There is a very slight, damped oscillation of UGDP about baseline. The minimum value is reached “n 1991:2 at -0.12 percent of baseline. Net exports increase by 0.15 percent of potential GDP in the first quarter and decline very slowly thereafter.
Next we consider the behavior of MX3 in the face of an anticipated monetary shock. (See Figure 2.) It is important to remember that traditional macro models cannot consider such an experiment since they do not incorporate future expectations.
The domestic price level responds in almost exactly the same manner as before, except that everything is shifted eight quarters earlier. By the time the monetary base jumps in 1988:1, the price level has already risen by 2.1 percent and it continues to overshoot its equilibrium value, reaching a peak of 2.6 percent above baseline in 1989:1.
Weighted foreign prices--and the exchange rates--do not jump up on the announcement of future monetary policy. Rather, UPGNPW rises steacily from its baseline value to a first peak of 2.3 percent in 1988:1. The subsequent dynamics are basically a damped version of the behavior of UPGNPW under the surprise monetary shock.
The stimulative effect of the anticipated monetary shock is smaller in Magnitude, but more persistent, than the effect of the surprise shcck. Despite the presence of rational expectations, there is still a small spike
in UGDP in the quarter of impact, 1988:1, when UGDP jumps to 0.5 percent
- 45 - Figure 2 Anticipated Monetary Shock
(Percent Deviation from Baseline)
UPGNP
2.5
1.5
0.5
1o+
0.5
1 1986 1989 1992 1995
UGDP
0.5
lOo+
1 1986 1989 1992 1995
UPGNPW
1986
NETX *
1986
*In percent deviation from baseline capacity output.
1989
1989
1992
1992
1995
0.5
lo+
0.5
2.6
1.5
0.5
1Oo+
0.5
1 1995
- 46 -
above baseline. A cyclical trough is reached in 1989:4 at -0.16 percent of baseline output. Net exports rise steadily to a peak of 0.18 percent of baseline capacity output in 1988:1 and fall slowly back to baseline.
The other shock to be presented is a permanent increase in zovernment consumption by 1 percent of capacity output. Figure 3 shows the behavior of the same four variables in response to a surprise fiscal shock. The domestic price, UPGNP, rises to a peak 0.5 percent above baseline in 1989:3 before falling back to baseline in 1992:1. Beginning in 1993:1 UPGNP gradually rises to a value 0.3 percent above baseline, where it remains permanently. UPGNPW initially drops 0.6 percent below baseline. In subsequent periods it quickly returns to oscillate about the baseline. What is not evident in Figure 3 is that UPGNPW eventually rises to a level about 0.3 percent above baseline after several more years. UGDP jumps 0.7 percent above baseline in the initial period, but it quickly drops below the baseline and it gradually settles at about 0.3 percent below baseline. Finally, net exports drop about 0.1 percent of baseline capacity output by the second period and then begin a gradual return to baseline.
In order to understand the long-run effects of this fiscal shock, we must review the consumption and investment relations in MX3. The increased government consumption necessitates an eventual rise in the tax rate in order to maintain the ratio of bonds to income. The higher tax rate reduces disposable income, and thus consumption, by an amount equal to the rise in government spending. Thus, to a first approximation, government spending fully crowds out private consumption, leaving all other variables unaffected in the long run. This analysis ignores a secondary effect of higher taxes,
however. The secondary effect works through the investment equation.
- 47 -
Figure 3
Surprise Fiscal Shock (Percent Deviation from Baseline)
UPGNP
1.5
0.5
lo+
0.5
1 1986 1989 1992 1995
UGDP
0.5
lOo+
0.5
1 1986 1989 1992 1995
UPGNPW
1986
NETX *
1986
“In percent deviation from baseline capacity output.
1989
1989
1992
1992
1995
0.5
1o+
0.5
1.5
0.5
lot
0.5
1 1995
According to equation (10) an increase in the tax rate will reduce the long-
run desired capital stock. 2°
It is the secondary effect that explains the permanent drop in UGDP evident in Figure 3. With lower absorption and a fixed monetary base, UPGNP must rise to reduce the level of real money balances. UPGNPW must also rise in the long-run to equilibrate relative prices. When relative prices across countries return to their baseline values and U.S. absorption equals U.S. production capacity, both real and nominal trade flows will reequilibrate. During the transition period the United States runs a real trade deficit, but the favorable terms of trade help to minimize both the nominal trade deficit and the associated decline in net foreign assets.
It is interesting to note that even in the short run, fiscal policy has very little expansionary effect in MX3. Both consumption and investment drop immediately when government spending rises. This crowding out occurs because consumers and investors know that tax rates will rise in the future in order to satisfy the government's intertemporal budget constraint. The strength of this crowding out is somewhat surprising in light of the fact that private agents in MX3 discount the future much faster than the real rate of interest on government bonds. Blanchard {1985] showed that such a wedge between private and government discount rates can reduce crowding out of fiscal policy.
Figure 4 shows that the announcement of a future fiscal expansion is strongly contractionary. Domestic output and domestic prices both drop
steadily until 2 quarters before the period of implementation. This
26. This effect hinges on the assumption that the risk premium is constant in after-tax terms. If the risk premium is constant before taxes, then the tax rate does not affect the desired capital stock.
- 49 - Figure 4
Anticipated Fiscal Shock (Percent Deviation from Baseline)
UPGNP 2 UPGNPW 15 1 0.5 + NS ° 0.5 1986 1989 1992 1995 1986 1989 UGDP 3 NETX * 1.5 0.5 + oO 0.5 1986 1989 1992 1995 1986 1989
*In percent deviation from baseline capacity output.
1992
1992
1.5
0.5
1Oo+
0.5
1 1995
0.5
1o+
0.5
1 1995
contraction results from the forward-looking behavior of investors and consumers, who foresee a long-run decline in desired capital anc. disposable income. After implementation, the expansionary effect of the ariticipated policy is only about two-thirds that of the surprise policy. The long-run
effects are the same for both surprise and anticipated fiscal expansions.
CONCLUSION
This paper has presented the theoretical structure, empirical implementation, and simulation properties of the MX3 model. The structure of MX3 represents a significant step toward incorporating more economic theory in macroeconometric models. In particular, agents are assumed to have rational expectations; short-run dynamics are constrained to. resemble behavior under costly adjustment; and the economy moves toward a competitive steady state in the long run.
The implementation of MX3 has been largely successful, but more work clearly remains to be done. Probably the first areas for further work are the price adjustment and fixed investment equations. Eventually, it would be desirable to expand the geographic coverage of the model so that it captures a more accurate description of global feedbacks to domestic policies.
While the simulations presented in this paper are of some interest for the insights they provide on the properties of MX3, the proposed shocks and the associated policy rules are not wholly satisfactory. It is clearly the case that monetary and fiscal instruments do not evolve exogenously with
respect to the rest of the economy. Rather, the monetary and fiscal
authorities must be responding in some manner to the shocks that originate in the rest of the economy. They also may respond to evidence on the effect their policies are having on the economy. A realistic policy rule must therefore include some reaction of the policy instruments to information on the economy that the authorities have available at the time the policy instruments are set.
One experiment that is particularly attractive--although it is not explored in this paper--is to consider the dynamic properties of the model under alternative policy rules with stochastic simulations. The objective is to discover the macro policy rules that are best able to stablize output, inflation, or other target variables in the face of shocks similar to those that typically occur. It is particularly important to use a rational expectations model when searching over alternative policy rules if one believes that the private sector will eventually learn about any new rule
and alter its behavior accordingly.
- 52 -
REFERENCES
Abel, Andrew B., N. Gregory Mankiw, Lawrence H. Summers, and Richard J. Zeckhauser, (1987) "Assessing Dynamic Efficiency: Theory and Evidence," National Bureau of Economic Research, Working Paper No. 2097.
Andrews, Donald W.K., and Ray C. Fair, (1988) “Inference in Nonlinear Econometric Models with Structural Change," Review of Economic Studies, 55, pp. 615-640.
Bailey, Victor B., and Sara R. Bowden, (1985) Understanding United States Foreign Trade Data, (Washington: U.S. Department of Commerce).
Bils, Mark, (1985) "Real Wages over the Business Cycle: Evidence from Panel Data," Journal of Political Economy, 93, pp. 666-689.
Blanchard, Oliver J., (1985) "Debt, Deficits, and Finite Horizons," Journal of Political Economy, 93, pp. 223-247.
Chouraqui, J.C., B. Jones, and R.B. Montador, (1986) "Public Debt in a Medium-Term Perspective," OECD Economic Studies, No. 7, pp. 103-153.
Dooley, Michael, and Peter Isard, (1982) "A Portfolio-Balance Rational- Expectations Model of the Dollar-Mark Exchange Rate," Journal of International Economics, 12, pp.257-276.
Dunlop, John T., (1938) "The Movement of Real and Money Wage Rates," Economics Journal, 48, pp. 413-434.
Fair, Ray C., (1987) "International Evidence on the Demand for Money," National Bureau of Economic Research, Working Paper No. 2106.
Frankel, Jeffrey A., (1983) "Monetary Portfolio-Balance Models of Exchange Rate Determination," in Jagdeep S. Bhandari and Bluford H. Patnam
(eds.) Economic Interdependence and Flexible Exchange Rates,
(Cambridge, Massachusetts: MIT Press).
Ghysels, Eric, and Alastair Hall, (1988) "A Test for Structural Stability of Euler Conditions Parameters Estimated Via the Generalized Method of Moments Estimator," unpublished paper, Universite de Montreal.
Goldfeld, Stephen M., and Daniel E. Sichel, (1987) "Money Demand: The Effects of Inflation and Alternative Adjustment Mechanisms," The Review of Economics and Statistics, 69, pp. 511-515.
Hall, Robert E., (1988) "Intertemporal Substitution in Consumption, " Journal of Political Economy, 96, pp. 339-357.
Hansen, Lars P., and Kenneth J. Singleton, (1982) "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, 50, pp. 1269-1286,
Kydland, Finn E., and Edward C. Prescott, (1982) "Time to Build and Aggregate Fluctuations," Econometrica, 50, pp. 1245-1369.
- 53 -
Lucas, Robert E., (1976) "Econometric Policy Evaluation: A Critique," Journal of Monetary Economics, Supplement, pp. 19-46.
Masson, Paul, Steven Symansky, Richard Haas, and Michael Dooley, (1988) "MULTIMOD: A Multi-Region Econometric Model," IMF Working Paper No. 88/23, International Monetary Fund.
Mehra, Rajnish, and Edward C. Prescott, (1985) "The Equity Premium: A Puzzle," Journal of Monetary Economics, 15, pp. 145-161.
Nason, James, (1989) "Permanent Income, Current Income, Consumption, and Changing Tastes," unpublished paper, Federal Reserve Board.
Poterba, James M., and Lawrence Summers, (1987) "Finite Lifetimes and the
Effects of Budget Deficits on National Savings," Journal of Monetary Economics, 20, pp. 369-391.
Roberts, John M., (1987) "Two Studies of Price and Marginal Cost in U.S. Manufacturing Industry," Ph.D. Dissertation, Stanford University.
Sargent, Thomas J., (1978) "Estimation of Dynamic Labor Demand Schedules
under Rational Expectations," Journal of Political Economy, 86, pp. 1009-1044.
Taylor, John B., (1980) "Aggregate Dynamics and Staggered Contracts," Journal of Political Economy, 88, pp. 1-23.
_. (1986) “Improvements in Macroeconomic Stability: The Role of Wages
and Prices," in Robert J. Gordon (ed.) The American Business Cycle:
Continuity and Change (Chicago: University of Chicago Press) pp. 639- 669,
_, (1988) "The Treatment of Expectations in Large Multicountry Econometric Models," in Ralph C. Bryant, Dale W. Henderson, Gerald Holtham, Peter Hooper, and Steven A. Symansky (eds.) Empirical
Macroeconomics for Interdependent Economies (Washington, DC: The Brookings Institution) pp. 161-182.
World Economic Outlook, (1988) (Washington, DC: International Monetary Fund) April.
- 54 -
APPENDIX 1: SIMPLIFIED COUNTRY MODEL
I. Data Definitions
A
AW
B BRATIO Cc
CAP CAPTOT CAPW CC
CU DPA DPGNP
GDP GNP IF II IM
MB NFA PA PEX PGNP PGNPW PIM
RS SHRx
Absorption
Weighted Foreign Absorption National Debt
Target Ratio of National Debt to Taxable Income Private Consumption
Capacity Output
World Capacity Output
Weighted Foreign Capacity Output Cost of Capital
Capacity Utilization Rate Inflation Rate (Absorption) Inflation Rate (GNP)
Exchange Rate
Export Volume
Government Consumption
Gross Domestic Product
Gross National Product
Gross Fixed Investment
Inventory Investment
Import Volume
Net Capital Stock
Labor Force (exogenous)
Monetary Base
Net Foreign Assets
Absorption Deflator
Export Deflator
GNP Deflator
Weighted Foreign GNP Deflator Import Deflator
Production Technology (exogenous, estimated) Short-term Nominal Interest Rate
Share of Total Exports Destined for Country x
- 55 -
TAU Tax Rate
TAX Tax Revenues
TBAR Tax Rate Required to Hit Target Debt Ratio TI Taxable Income
YD Disposable Income
II. Private Sector Demand
Private Consumption 1.C= (vp, RS, DPA, TAU) Fixed Investment | 2. IF = IF (GDP, CC, TAU, R) Inventory Investment 3. II = 11 (AcDP, RS, DPA) Money Demand 4. MB = MB(A, RS) * PA
IIl. Aggregate Supply
GNP Deflator (Inflation Rate) 5. DPGNP = P(DPGNP, cu)
Capacity Output 6. CAP = F(Q, K, L)
IV. Exchange Rate and Trade
Exchange Rate 7. aEt = RS - rs! Expo::t Volume 8. EX = EX (AW/CAPW, PEX/PIM, CAPTOT) Export Price 9. PEX = PEX(PGNP, PGNPW, t}
Expoxt Shares 10. SHRI = siRi(etepene", ...,z°«ponp’]
V. Monetary and Fiscal Policy
Money Supply Government Consumption Target Ratio of National Debt
Tax Rate
VI. Identities and Definitions
Imports
Import Prices
Absorption
Gross Domestic Product Gross National Product
Disposable Income
Absorption Deflator
Inflation Rate (Absorption)
Inflation Rate (GNP)
- 56 -
ll.
12.
13. 14. 15.
16.
17.
18.
19.
20.
21.
22.
23.
24. 25.
SHR2 = sur2[et*pne?, ... e*xpenr’|
SHR3 = 1 - SHR1 - SHR2
AMB = m AG = g BRATIO = b
TAU = 0.95 * TAU_, + 0.05 * TBAR
1
IM = sHRO! «Ex! + SHRO?*EX? + SHRO°*EX?
1 1 1
PIM (surolen *PEX *EX” + ,
SHRO°*E?*PEX?*EX?] / IM
+
A=C+IF+II+G
GDP = A + EX - IM
GNP
GDP + RS*NFA_,/PGNP
YD = PGNP*GNP/PA - §*K_, - TAX/PA
+ (RS - DPA)*B_|/PA - RS*MB_,/PA
PA*A = PGNP*GNP - PEX*EX + PIM*IM
- * RS*NFA |
DPA = APA
DPGNP = APGNP
- 57 -
Taxable Income 26. TI = PGNP*GNP - §*K_,*PA + RS*B | Tax Revenues 27. TAX = TAU*TI Equilibrium Tax Rate 28. TBAR = (c*PA + RS* (By - MB_1)) / TI
- BRATIO + B_,/TI_,
Cost of Capital 29. CC = (1-TAU) * (RS + 6 - DPA) +x Capacity Utilization 30. CU = GDP/CAP Total World Capacity 31. CAPTOT = CAP + cap! + cap? + CAP? Weighted Foreign Absorption 32. AW = [at}oh [7]? [?}? Weighted Foreign Capacity 33. CAPW. = [car ret * (car? 2 |e * [car?}? Weighted Foreign Prices 34. PGNPW = [rowel ra [rone? wet]?
34.53] 03
* [powp3s E?| Capital Stock 35. K= (1 - §)*K | + IF Government Bonds 36. B= (1 + RS)*B_y + PA*G - TAX - RS*MB_)
Net Foreign Assets 37. NFA = (1 + RS)NFA_} + PEX*EX - PIM*IM
Note: Superscripts. denote foreign country variables. Variables with hats are future expectations. A denotes the percentage rate of change of a variable. 6 is the rate of depreciation of fixed capital. m is the risk premium for holding capital instead of government bonds. wl-w3 are fixed weights that sum to unity.
APPENDIX 2: MODEL LISTING AND DATABASE*
This appendix is divided into four main parts. The first three parts comprise a complete listing of the current version of the MX3 model: the equation listing, the variable and equation cross-reference table, and the variable definitions. The final part is a detailed description of the MX3 database.
The equation listing is grouped by country and then by sector. In this way, each country model is presented as though it were a separate
macroeconometric model using the following format:
1. Private Sector Demand
2. Aggregate Supply
3. Exchange Rate and Trade
4. Monetary and Fiscal Policy
5. Identities and Definitions
The sectors and variables in each country model are preceded by the first letter of the country name. For example, "G.1" is the first sector of the German country model (private sector demand). Likewise, "GGNP" is German gross national product. Although equations are grouped within sectors, equations are numbered consecutively throughout the whole model. Each equation is reported with its coefficient values and labeled with the associated left-hand side variable. (Estimation results and test statistics
are reported in the text of the paper).
1. Special thanks are due to Gwyn Adams for preparing this appendix.
The cross-reference table gives the number of each equation in which each variable in the model appears. It is grouped by endogenous and exogenous variables. The variable listing gives each variable alphabetically with a short definition. The variable listing is also grouped by endogenous and exogenous variables.
The variable naming convention uses the first letter of the variable name to indicate the country. The middle portion of the name describes the variable and the presence of a trailing "V" or "W" indicates a nominal value or fixed weighted value respectively. The existence of a final "_ERR" is used to indicate the error term for the equation describing the indicated endogenous variable. For example, JGDEBTV is current Japanese government debt, and GIF_ERR is the residual term in the German fixed investment equation. Also, the bilateral trade shares are represented in either a "XijS" or "XijS3" format. Both represent the share of country i’s exports
destined for country j. The trailing 3 indicates the export share with ROW
for G-3 countries.
GERMAN MODEL
1. GC: Private consumption expenditure - 1980 prices GC/GCAP = .852 * GC(-1)/GCAP(-1)/(1 + .852 /(1 + .2 + (1 - GTAU) * GRS/400 - GDPA(1)/400)) + GC(1)/GCAP(1)/(1 + .852 + .02 + (1 - GTAU) * GRS/400 - GDPA(1)/400) + (1 - .852 ) %* .00985 * GYD/GCAP + GC_ERR
2. GIF: Total fixed investment - 1980 prices
(l + .9& %* .97 ) * GIF/GCAP = .95 * GIF(-1)/GCAP(-1) + .97 * GIF(1)/GCAP(1) + (1 - .$5 )* (1 - .97 3 * (€ .35 * GCU * 100/(GRS + 4.83 - GDPA(1) + 4.78 /(1 - GTAUJ) - (1 - 4.83 7100) * GK(-1)/GCAP) + GIF_ERR
3. GII: Inventory investment - 1980 prices
GII/GCAP = .00733 + .483 * (GCU(1) - GCU) - .000778 * (GRS - GDPA(1)) + GII_ERR
4. GMB: Monetary base
LOG(GMB/GPA ) = -3.2863 + .6776 * LOG(GMB(-1)/GPA(-1)) - .0067 * GRS + .4771 * LOG(GA) + GMB_ERR
G2. AGGREGATE SUPPLY
5. GPGNP: Gross national product deflator - 1980=100.00
(GPGNP/GPGNP(-1) - 1) * 400 = .5 * (GPGNP(-1)/GPGNP(-2) - 1) * 400 + (1 - .5 J ® (GPGNP(1)/GPGNP - 1) * 400 + 10 * LOG(GCU) + GPGNP_ERR
6. GCAP: Total capacity output
GCAP = GQ * GK(-1)* * .35 * GLF(-1)**(1 - .35 ) + GCAP_ERR
G3. EXCHANGE RATE AND TRADE
7. GER: Spot exchange rate - US$/DM
(GER(1)/GER - 1) * 400 = URS - GRS + GER_ERR
8. GXGSNI: Exports - NIA basis - 1980 prices LOG( GXGSNI ) = -.612 + .775 * LOG(GXGSNI(-1)) + .688 * LOG(GAW/GCAPW) - .26 * LOG(GPXGSNI/GPMGSNI) + (1 - .775 ) * 1 %* LOG(CAPTOT) + GXGSNI_ERR
9. GPXGSNI: Export deflator - NIA basis - 1980 prices LOG( GPXGSNI ) -015 + .734 * LOG(GPXGSNI(-1)) + .076 * LOG(GPGNPW) + (1 - .734 - .076 ) * LOG(GPGNP) + .408 * LOG(GPXGSNI(-1)/GPXGSNI(-2)) - .0025 * (1 - .734 ) * TIME + GPXGSNI_ERR
10. XGUS: Share of German exports destined for US
XGUS = .01¢ + .85 * XGUS(-1) + O * LOG(UPGNP/( JER * JPGNP)) + .019 * LOGCUPGNP/(RER * RPGNP)) + XGUS_ERR
11. XGJS: Share of German exports destined for Japan
XGJS = -.003 + .9 ® XGJS(-1) - O * LOG(UPGNP/( JER * JPGNP)) + .003 * LOG{ JER * JPGNP/(RER * RPGNP)) + XGJS_ERR
12. XGRS3: Share of German exports destined for ROW
XGRS3 = 1 - .014¢ - -.003 - .85 * XGUS(-1) - .9 * XGUS(-1) - .019 * LOG(UPGNP/(RER * RPGNP)) - .003 * LOG(JER * JPGNP/(RER * RPGNP)) + XGRS3_ERR
G4. MONETARY AND FISCAL POLICY
13.
14.
15.
1é.
GRS: 3-month Treasury Bill rate
GMB = 1.0155 * GMB{-1) + GRS_ERR
GG: Real government purchases - 1980 prices
GBRATIO: Target ratio of government bonds to taxable income
GBRATIO = 0.262 + GBRATIO_ERR
GTAU: Actual income tax rate
GTAU = .95 * GTAUC-1) + (1 - .95 ) * GTBAR + O * LOG(GCU) + GTAU_ERR
-7-
GS. IDENTITIES, AND DEFINITIONS
17. GMGSNI: Imports - NIA basis - 1980 prices
GMGSNI = (XUGS * UXGSNI * 0.9169 + XJGS * JXGSNI * 4.424 + 1.181 * XRGS3 % RXGSNI * 1.173)/0.5505 + GMGSNI_ERR
18. GPMGSNI: I:mport deflator - NIA basis - 1980=100.00
GPMGSNI = (XUGS * UPXGSNI * UXGSNI + XJGS * JER * JPXGSNI * JXGSNI + 1.181 % XRGS3 * RER * RPXGSNI * RXGSNI)/(GMGSNI * GER) + GPMGSNI_ERR
19. GA: Absorption
GA = GC + GIF + GG + GII + GA_ERR
20. GGDP: Gross domestic product - 1980 prices
GGDP = GA + GXGSNI - GMGSNI + GGDP_ERR
21. GGNP: Gross national product - 1980 prices
GGNP = GGDP + URS * GNFAV(-1)/(GER * GPGNP) + GGNP_ERR
22. GYD: Disposable income - 1980 prices
GYD = GPGNP * GGNP/GPA - &.83 *% GK(-1)/100 - GTAXV * 100/GPA + (GRS - GDPA) * GGDEBTV(-1}3/GPA —- GMB(-1} * GRS/GPA + GYD_ERR
23. GPA: Gross domestic product deflator ~ 1980=100.00
GPA = (GPGNP * GGNP - GPXGSNI * GXGSNI + GPMGSNI * GMGSNI - URS * GNFAV(-1)/GER)/GA + GPA_ERR
24. GDPA: Rate of inflation of absorption prices
GDPA = (GPA/GPA(-1) - 1) * 400 + GDPA_ERR
25. GDPGNP: Rate of inflation of output prices
GDPGNP =: (GPGNP/GPGNP(-1) - 1) * 400 + GDPGNP_ERR
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
GTIV: Nominal taxable income
GTIV = GPGNP * GGNP/100 - 4.83 * GK(-1) * GPA/10000 + GRS * (GGDEBTV(-1) - GMB(-1))/100 + GTIV_ERR
GTAXV: Nominal tax revenues
GTAXV = GTAU * GTIV + GTAXV_ERR
GTBAR: Equilibrium tax rate
GTBAR = (GG * GPA + GRS * GGDEBTV(-1))/(GTIV * 100) - GBRATIO + GGDEBTV( ~-1)/GTIV 4 GTBAR_ERR
GCU: Capacity utilization rate
GCU = GGDP/GCAP + GCU_ERR
GAW: Trade weighted foreign absorption
GAH = UA®*0.0767 * JAX*0.0134 * RAX*0.9099 + GAW_ERR
GCAPH: Trade weighted foreign total capacity output
GCAPH = UCAP**0.0767 * JCAP**0.0134 * RCAP**0.9099 + GCAPW_ERR
GPGNPH: Trade weighted foreign gross national product deflator - 1980=100.00
GPGNPH = (UPGNP/0.8572 )**0.0767 * (JPGNP * JER/4.424)**0.013¢ % (RPGNP x RER/1.173 )**0.9099 * 0.5505/GER + GPGNPW_ERR
GK: Total net capital stock
GGDEBTV: Current total government debt
GGDEBTV = (1 + GRS/400) * GGDEBTV(-1) + GPA * GG/4G00 - GTAXV/4 - GMB(-1) x GRS/400 + GGDEBTV_ERR
GNFAV: Net foreign assets
GNFAV = (1 + URS/400) * GNFAV(-1) + (GPXGSNI * GXGSNI * GER - GPMGSNI x GMGSNI * GER)/400 + GNFAV_ERR
JAPANESE MODEL
36. JC: Private consumption expenditure - 1980 prices JC/JCAP = .852 * JC(-1L)J/JCAP(-1)/(1 + .852 7(1 + .02 + (1 - JTAU) * JRS/400 - JDPA(1)/400)) + JCCLI/JCAP(1)I/(1 + .852 + .02 + (1 - JTAU) * JRS/400 - JDPA(1)/400) + (1 - .852 ) * .00985 * JYD/JCAP + JC_ERR
37. JIF: Total fixed investment - 1980 prices
(1 + .95 * .97 J) * JIF/JCAP = .95 * JIF(-1)/JCAP(-1) + .97 * JIFC1)I/JCAP(1) + (1 - .95 }*% (1 - .97 3} ® € .39 * JCU * 100/(JRS + 3.04 - JDPA(1) + 6.71 /(1 - JTAU)) - (1 - 3.04 7100) * JK(-1)/JCAP) + JIF_ERR
38. JII: Inventory investment - 1980 prices
JII/JCAP = .00733 + .483 * (JCU(1) - JCU) - .000778 * (JRS - JDPA(1)) + JII_ERR
39. JMB: Monetary base
LOG( JMB/JPA) = -1.8045 + .766 * LOG(JMB(-1)/JPA(-1)) - .0084 * JRS + .2707 * LOG(JA) + JMB_ERR
- 10 -
J2. AGGREGATE SUPPLY
40. JPGNP: Gross national product deflator - 1980=100.00
(JPGNP/JPGNP(-1) - 1) * 400 = .5 * (JPGNP(-1)/JPGNP(-2) - 1) * 400 + (1 - .5 ) * (JPGNP(1)/JPGNP - 1) * 400 + 10 * LOG(JCU) + JPGNP_ERR
G1. JCAP: Total capacity output
JCAP = JQ * JK(-1)% * .39 ® JLF(-1)%*(1 - .39 ) + JCAP_ERR
-ll-
J3. EXCHANGE RATE AND TRADE
42. JER: Spot exchange rate - US$/DM
(JERC(1)/JER - 1) * 400 = URS - JRS + JER_ERR
43. JXGSNI: Exports - NIA basis - 1980 prices LOG( JXGENT ) = -.301 + .937 * LOG(JXGSNI(-1)) + .418 * LOG(JAW/JCAPNW ) - .107 * LOG( JPXGSNI/JPMGSNI) + (1 - .937 ) * 1 * LOG(CAPTOT) + JXGSNI_ERR
44. JPXGSNI: Export deflator - NIA basis - 1980 prices LOG( JPXGSNI ) = .005 + .824 * LOG(JPXGSNI(-1)) + .12 * LOG(JPGNPH) + (1 - .824¢ - .12 ) % LOG(JPGNP) + .136 * LOG( JPXGSNI(-1)/JPXGSNI(-2)) + (1 - .824 ) * -.0025 * TIME + JPXGSNI_ERR
45. XJUS: Shere of Japanese exports destined for US
XJUS = .034¢ + .9 * XJUS(-1) + .002 * LOG(UPGNP/(GER * GPGNP )) + .044 % LOG(UPGNP/(RER * RPGNP)) + XJUS_ERR
46. XJGS: Shere of Japanese exports destined for Germany
XJGS = .007 + .876 * XJGS(-1) - .002 * LOG(UPGNP/(GER * GPGNP )) + O * LOG(GER * GPGNP/(RER * RPGNP)) + XJGS_ERR
47. XJRS3: Share of Japanese exports destined for ROW
XJRS3 = 1 - .034¢ - .007 - .876 * XJGS(-1) - .9 * XJUS(-1) - .044 * LOG(UPGNP/(RER * RPGNP)) - 0 * LOG(GER * GPGNP/(RER * RPGNP)) + XJRS3_ERR
- 12 -
J4. MONETARY AND FISCAL POLICY
48. JRS: 3-month Treasury Bill rate
JMB = 1.0178 * JMB(-1) + JRS_ERR
49. JG: Real government purchases - 1980 prices
JG = 1.0085 * JG(-1) + JG_ERR
50. JBRATIO: Target ratio of government bonds to taxable income
JBRATIO = 0.283 + JBRATIO_ERR
51. JTAU: Actual income tax rate
JTAU = .95 * JTAU(-1) + (1 - .95 ) * JTBAR + O * LOG(JCU) + JTAU_ERR
-13-
J5. IDENTITIES AND DEFINITIONS
52. JMGSNI: Imports - NIA basis - 1980 prices
JMGSNI = (XUJS * UXGSNI * 0.9169 + XGUS *% GXGSNI x 0.5505 + 1.355 * XRJS3 % RXGSNI * 1.173)/4.424 + JMGSNI_ERR
53. JPMGSNI: Import deflator - NIA basis - 1980=100.00
JPMGSNI = (XUJS * UPXGSNI * UXGSNI + XGUS * GER x GPXGSNI * GXGSNI + 1.355 % XRJS3 * RER * RPXGSNI * RXGSNI)/(JMGSNI * JER) + JPMGSNI_ERR
54. JA: Absorption
JA = JC + JIF + JG + JII + JA_ERR
55. JGDP: Gross domestic product - 1980 prices
56. JGNP: Gross. national product - 1980 prices
57. JYD: Disposable income - 1980 prices
JYD = JPGNP * JGNP/JPA ~ 3.04 * JK(-1)/100 - JTAXV * 100/UPA + (URS - JDPA) x JGDEBTV(-1)/JPA - JMB(-1) * JRS/JPA + JYD_ERR
58. JPA: Gross domestic product deflator - 1980=100.00
JPA = (JPGNP * JGNP - JPXGSNI * JXGSNI + JPMGSNI x JMGSNI - URS * JNFAV(-1)/JER)/JA + JPA_ERR
59. JDPA: Rate of inflation of absorption prices
JDPA = (JPA/JPA(-1) - 1) * 400 + JDPA_ERR
60. JDPGNP: Rate of inflation of output prices
JDPGNP = (JPGNP/JPGNP(-1) - 1) * 400 + JDPGNP_ERR
él.
62.
63.
64.
65.
66.
67.
68.
69.
70.
- 14 -
JTIV: Nominal taxable income
JTIV = JPGNP * JGNP/100 - 3.04 * JK(-1)} * JPA/10000 + JRS * (JGDEBTV(-1) - JMB(-1)})/100 + JTIV_ERR
JTAXV: Nominal tax revenues
JTAXVY = JTAU * JTIV + JTAXV_ERR
JTBAR: Equilibrium tax rate
JTBAR = (JG ® JPA + JRS * JGDEBTV(-1))/(JTIV * 100) - JBRATIO + JGDEBTV( -1)/JUTIV + JTBAR_ERR
JCU: Capacity utilization rate
JCU = JGDP/JCAP + JCU_ERR
JAW: Trade weighted foreign absorption
JAN = UA®*0.2954 * RAX*0.6637 * GAX*0.0409 + JAW_ERR
JCAPW: Trade weighted foreign total capacity output
JCAPH = UCAPX*0.2954 %* RCAPX*0.6637 * GCAP%*0.0409 + JCAPW_ERR
JPGNPH: Trade weighted foreign gross national product deflator - 1980=100.00
JPGNPWH = (UPGNP/0.8572 )**0.2954 * (RPGNP * RER/1.173 )**0.6637 * (GPGNP x GER/0 .5505 )**0.0409 * 4.424/JER + JPGNPW_ERR
JK: Total net capital stock
JGDEBTV: Current total government debt
vGDEBTV = (1 + JRS/400) * JGDEBTV(-1) + JPA * JG/400 - JTAXV/G - JMB(-1) x JRS/400 + JGDEBTV_ERR
JNFAV: Net foreign assets
JNFAV = (1 + URS/G00) * JNFAV(-1) + (JPXGSNI * JXGSNI * JER - JPMGSNI * JMGSNI * JER)/400 + JNFAV_ERR
- 15 -
ROW MODEL
71. RC: Private consumption expenditure - 1980 prices
RC/RCAP = .852 * RC(-1)/RCAP(-1)/(1 + .852 /(1 + .02 + (1 - RTAU) * RRS/G00 - RDPA(1)/400)) + RC(1)/RCAP(1)/(1 + .852
+ .02 + (1 - RTAU) * RRS/G00 — RDPA(1)/400) + (1 - .852 ) * .00985 * RYD/RCAP + RC_ERR
72. RIF: Total fixed investment - 1980 prices
(1 + .95 *% .97 ) * RIF/RCAP = .95 % RIF(-1)/RCAP(-1) + .97 ® RIF(1)J/RCAP(1) + (1 - .95 )* (1 - 1.97 3 * ( .35 % RCU ¥ 1OO/(RRS + 6.58 - RDPA(1) + 6.71 /(1 - RTAU)) - (1 - 6.58 7100) * RK(-1)/RCAP) + RIF_ERR
73. RII: Inventory investment - 1980 prices
RII/RCAP = .00733 + .483 * (RCU(1) - RCU) - .000778 * (RRS - RDPA(1)) + RII_ERR
74. RMB: Monetary base
LOG( RMB./’RPA ) = -.8852 + .7683 * LOG(RMB(-1)/RPA(-1)) - .006 * RRS + .139 * LOG(RA) + RMB_ERR
-16-
R2. AGGREGATE SUPPLY
75. RPGNP: Gross national product deflator - 1980=100.00
CRPGNP/RPGNP(-1)} - 1) * 400 = .5 % (RPGNP(-1)/RPGNP(-2) - 1) * 400 + (1 - .5 ) % (RPGNP(1)/RPGNP - 1) * 400 + 10 * LOG(RCU) + RPGNP_ERR
76. RCAP: Total capacity output
RCAP = RQ * RK(-1)% * .35 % RLF(-1)%*(1 - .35 } + RCAP_ERR
-17-
R3. EXCHANGE RATE AND TRADE
77. RER: Spot exchange rate - US$/DM
CRERC1)/RER - 1) * 400 = URS - RRS + RER_ERR
78. RXGSNI: Exports - NIA basis - 1980 prices LOG! RXGSNI ) = -.373 + .864¢ * LOG(RXGSNI(-1)) + .268 x LOG( RAW/RCAPW ) - .12 * LOG(RPXGSNI/RPMGSNI) + (1 - (864) x 1 * LOG(CAPTOT) + RXGSNI_ERR
79. RPXGSNI: Export deflator - NIA basis - 1980 prices LOG( RPXGSNI ) = .008 + .985 * LOG(RPXGSNI(-1)) + 0 * LOG(RPGNPH) + (1 - - 985 - © ) * LOG(RPGNP) + .527 * LOG(RPXGSNI(-1)/RPXGSNI(-2)) + (1 - .985 ) * -.0025 * TIME + RPXGSNI_ERR
80. XRUS3: Share of ROW exports destined for US
XRUS:3 = .074 + .778 * XRUS3(-1) + .0¢1 * LOG(UPGNP/(GER x GPGNP )) + O * LOG(UPGNP/( JER * JPGNP)) + XRUS3_ERR
81. XRGS3: Share of ROW exports destined for Germany
XRGS3 = .137 + .705 * XRGS3(-1) - .041 * LOG(UPGNP/I(GER x GPGNP ) ) + .003 * LOG(GER * GPGNP/( JER * JPGNP)) + XRGS3_ERR
82. XRJS3: Share of ROW exports destined for Japan
XRJS3 = 1 - .074 - .137 - .778 * XRUS3{-1) - .705 x XRGS3(-1) - 0 * LOG(UPGNP/(JER * JPGNP)) - .003 * LOG(GER * GPGNP/{(JER * JPGNP}) + XRJS3_ERR
83.
84.
85.
86.
- 18 -
- MONETARY AND FISCAL POLICY
RRS: 3-month Treasury Bill rate
RMB = 1.0297 * RMB(-1) + RRS_ERR
RG: Real government purchases - 1980 prices
RG = 1.005 * RG(-1) + RG_ERR
RBRATIO: Target ratio of government bonds to taxable income
RBRATIO = 0.569 + RBRATIO_ERR
RTAU: Actual income tax rate
RTAU = .95 * RTAU(-1) + (1 - .95 ) * RTBAR + O * LOG(RCU) + RTAU_ERR
- 19 -
R5. IDENTITIES AND DEFINITIONS
87. RMGSNI: ‘Imports - NIA basis - 1980 prices
RMGSNI = (XURS3 * UXGSNI * 0.9169/1.3 + XGRS3 * GXGSNI * 0.5505/1.183 + XJRS3 * JXGSNI * 4.424/1.243)/1.173 + RMGSNI_ERR
88. RPMGSNI: Import deflator - NIA basis - 1980=100. 00
RPMGSNI = (XURS3 * UPXGSNI * UXGSNI/1.3 + XGRS3 * GER * GPXGSNI x GXGSNI 71.183 + XJRS3 * JER * JPXGSNI * JXGSNI/1.243)/(RMGSNI * RER) + RPMGSNI_ERR
89. RA: Absorption
RA = RC + RIF + RG + RII + RA_ERR
90. RGDP: Grass domestic product - 1980 Prices
91. RGNP: Gross national product - 1980 Prices
RGNP = RGDP + URS * RNFAV(-1)/(RER * RPGNP) + RGNP_ERR
92. RYD: Disposable income - 1980 prices
RYD = RPGNP * RGNP/RPA - 5.58 * RK(-1)/100 - RTAXV * 100/RPA + (RRS - RDPA) * RGDEBTV(-1}/RPA - RMB(-1) x RRS/RPA + RYD_ERR
93. RPA: Gros: domsetic product deflator - 1980=100.00
RPA = '\RPGNP * RGNP - RPXGSNI * RXGSNI + RPMGSNI * RMGSNI - URS * RNFAV(-1)/RER)/RA + RPA_ERR
94. RDPA: Rate of inflation of absorption prices
RDPA = (RPA/RPA(-1) - 1) * 400 + RDPA_ERR
95. RDPGNP: Rate of inflation of output prices
RDPGNP =: (RPGNP/RPGNP(-1) - 1) * 400 + RDPGNP_ERR
96.
97.
98.
99.
100.
101.
102.
103.
104.
105.
- 20 -
RTIV: Nominal taxable income
RTIV = RPGNP * RGNP/100 - 6.58 * RK(-1) % RPA/10000 + RRS * (RGDEBTV(-1) - RMB(-1))/100 + RTIV_ERR
RTAXV: Nominal tax revenues
RTAXV = RTAU * RTIV + RTAXV_ERR
RTBAR: Equilibrium tax rate
RTBAR = (RG * RPA + RRS * RGDEBTV(-1))/(RTIV * 100) - RBRATIO + RGDEBTV( -1)/RTIV + RTBAR_ERR
RCU: Capacity utilization rate
RCU = RGDP/RCAP + RCU_ERR
RAW: Trade weighted foreign absorption
RAW = UA**0.4593 % JAX*0.1956 * GA¥*0.3451 + RAW_ERR
RCAPW: Trade weighted foreign total capacity output
RCAPH = UCAP*®*0.4593 * JCAP**0.1956 * GCAP**0.3451 + RCAPW_ERR
RPGNPH: Trade weighted foreign gross national product deflator - 1980=100.00
RPGNPH = (UPGNP/0.8572 )**0.4593 % (JPGNP * JER/4.424)**0.1956 * (GPGNP * GER/0 .5505 )**0.3451 * 1.173/RER + RPGNPW_ERR
RK: Total net capital stock
RK = (1 - 6.58 7400) * RK(-1) + RIF(-1)74 + RK_ERR
RGDEBTV: Current total government debt
RGDEBTV = (1 + RRS/G00) * RGDEBTV(-1) + RPA * RG/400 - RTAXV/4 - RMB(-1) * RRS/400 + RGDEBTV_ERR
RNFAV: Net foreign assets
RNFAV = (1 + URS/400) % RNFAV(-1) + (RPXGSNI % RXGSNI * RER - RPMGSNI * RMGSNI * RER)/400 + RNFAV_ERR
-21-
U.S. MODEL
106. UC: Private consumption expenditure - 1982 prices
UC/UCAP = .852 *% UC(-1)/UCAP(-1)/(1 + .852 /(1 + .02 + (1 - UTAU) * URS/400 - UDPA(1)/400)) + UCC L)/UCAP(1)/(1 + .852 + .02 + (1 - UTAU) * URS/400 - UDPA(1)/400) + (1 - .852 ) * .00985 * UYD/UCAP + UC_ERR
107. UIF: Total fixed investment - 1982 prices
(1 + .,95 * .97 ) % UIF/UCAP = .95 * UIF(-1)/UCAP(-1) + .97 % UIF(1)/UCAP(1) + (1 - .95 )*% (1 - .97 3% ( .32 % UCU ® 100/(URS + 6.23 - UDPA(1) + 6.8 /(1 - UTAU)) - (1 - 6.23 7100) * UK(-1)/UCAP) + UIF_ERR
108. UII: Inventory investment - 1982 prices
UIT/UCAP = .00733 + .483 * (UCU(1) - UCU) - .000778 * (URS - UDPA(1)) + UITI_ERR
109. UMB: Monetary base
LOG( UMB,'UPA ) = -1.395 + .776 *% LOG(UMB(-1)/UPA(-1)) - .0039 * URS + .1926 * LOG(UA) + UMB_ERR
- 22 -
U2. AGGREGATE SUPPLY
110. UPGNP: Gross national product deflator - 1982=100.00
(UPGNP/UPGNP(-1) - 1) * 400 = .5 * (UPGNP(-1)/UPGNP(-2) - 1) * 400 + (1 - .5 ) % (UPGNP(1)/UPGNP - 1) * 400 + 10 * LOG(UCU) + UPGNP_ERR
111. UCAP: Total capacity output
UCAP = UQ * UK(-1)% * .32 *% ULF(-1)%*(1 - .32 ) + UCAP_ERR
-~ 23 -
U3. TRADE
112. UXGSNI: Exports - NIA basis - 1982 prices LOG(UXGSNI ) = -1.645 + .476 * LOG(UXGSNI(-1)) + 1.929 * LOG(UAW/UCAPW) - .372 * LOG(UPXGSNI/UPMGSNI) + (1 - .476 ) * 1 * LOG(CAPTOT) + UXGSNI_ERR
113. UPXGSNI: Export deflator - NIA basis - 1980 prices L'3G(UPXGSNI ) = .003 + .962 * LOG(UPXGSNI(-1)) + O * LOG(UPGNPW) + (1 - .962 - O ) * LOG(UPGNP) + .728 * LOG(UPXGSNI(-1)/UPXGSNI(-2)) + (1 - .962 ) * -.0025 * TIME + UPXGSNI_ERR
114. XUGS: Share of US exports destined for Germany
XUGS = .063 + .166 * XUGS(-1) + .005 * LOG(GER * GPGNP/( JER * JPGNP)) + .018 * LOG(GER * GPGNP/(RER * RPGNP)) + XUGS_ERR
115. XUJS: Share of US exports destined for Japan
xUJS = .006 + .711 * XUJS(-1) - .005 * LOG(GER * GPGNP/( JER * JPGNP)) + .009 * LOG( JER * JPGNP/(RER * RPGNP)) + XUJS_ERR
116. XURS3: Share of US exports destined for ROW
XURS3 = 1 - .063 - .006 - .166 * XUGS(-1) - .711 * XUJS(-1) - .009 * LOG(JER * JPGNP/(RER * RPGNP)) - .018 * LOG(GER * GPGNP/(RER * RPGNP)) + XURS3_ERR
117.
118.
119.
120.
- 24 -
- MONETARY AND FISCAL POLICY
URS: 3-month Treasury Bill rate
UMB = 1.0195 % UMB(-1) + URS_ERR
UG: Real government purchases - 1982 prices
UG = 1.0067 * UG(-1) + UG_ERR
UBRATIO: Target ratio of government bonds to taxable income
UBRATIO = 0.317 + UBRATIO_ERR
UTAU: Actual income tax rate
UTAU = .95 * UTAU(-1) + (1 - .95 ) % UTBAR + 0 * LOG(UCU) + UTAU_ERR
- 25 -
121. UMGSNI: Imports - NIA basis - 1982 prices
UMGSNI = (XGUS * GXGSNI * 0.5505 + XJUS * JXGSNI * 4.424 + 1.294 * XRUSZ % RXGSNI * 1.173)/0.9169 + UMGSNI_ERR
122. UPMGSNI: Import deflator - NIA basis - 1982=100.00
UPMGSNI: = (XGUS * GPXGSNI * GXGSNI * GER + XJUS * JPXGSNI * JXGSNI * JER + 1.294 * XRUS3 * RPXGSNI * RXGSNI * RER)/UMGSNI + UPMGSNI_ERR
123. UA: Absorption
UA = UC + UIF + UG + UII + UA_ERR
124. UGDP: Gross domestic product - 1982 prices
UGDP = UA + UXGSNI - UMGSNI + UGDP_ERR
125. UGNP: Gross national product - 1982 prices
UGNP = UGDP + URS * UNFAV(-1)/UPGNP + UGNP_ERR
126. UYD: Disposable income
UYD = UPGNP * UGNP/UPA - 6.23 % UK(-1)/100 - UTAXV * 100/UPA + (URS - UDPA) * UGDEBTV(-1)/UPA - UMB(-1) * URS/UPA + UYD_ERR
127. UPA: Gross domestic product deflator - 1982=100.00
UPA = (UPGNP * UGNP - UPXGSNI * UXGSNI + UPMGSNI * UMGSNI - URS * UNFAV(-1))/UA + UPA_ERR
128. UDPA: Rate of inflation of absorption prices
UDPA = (UPA/UPA(-1) - 1) * 400 + UDPA_ERR
129. UDPGNP: Rate of inflation of output prices
UDPGNP = (UPGNP/UPGNP(-1) - 1) * 400 + UDPGNP_ERR
- 2 -
130. UTIV: Nominal taxable income
UTIV = UPGNP * UGNP/100 - 6.23 * UK(-1) * UPA/10000 + URS * (UGDEBTV(-1) - UMB{-1))/100 + UTIV_ERR
131. UTAXV: Nominal tax revenues
UTAXV = UTAU * UTIV + UTAXV_ERR
132. UTBAR: Equilibrium tax rate
UTBAR = (UG * UPA + URS * UGDEBTV(-1))/(UTIV * 100) - UBRATIO + UGDEBTV( -1)/UTIV + UTBAR_ERR
133. UCU: Capacity utilization rate
UCU = UGDP/UCAP + UCU_ERR
134. CAPTOT: Total world capacity
CAPTOT = UCAP * 0.8572 + GCAP * 0.5505 + JCAP * 4.424 + RCAP * 1.173 + CAPTOT_ERR
135. UAW: Trade weighted foreign absorption
UAN = GA**0.0463 * RA**0.8532 * JA*®*0.1005 + UAW_ERR
136. UCAPW: Trade weighted foreign total capacity output
UCAPH = GCAP**0.0463 * RCAP**0.8532 %* JCAPxx0.1005 + UCAPW_ERR
137. UPGNPH: Trade weighted foreign gross national product deflator - 1980=100.00
UPGNPH = (GPGNP * GER/0.5505 )**0.04¢63 * (RPGNP * RER/1.173 )**0.8532 * (JPGNP * JER/4.424)**0.1005 * 0.8572 + UPGNPW_ERR
138. UK: Total net capital stock
UK = (1 - 6.23 /400) * UK(-1) + UIF/4 + UK_ERR
139. UGDEBTV: Current total government debt
UGDEBTV = (1 + URS/400) * UGDEBTV(-1) + UPA * UG/400 - UTAXV/4 - UMB(-1) * URS/400 + UGDEBTV_ERR
- 27 -
140. UNFAV: Net foreign assets
UNFAV = (1 + URS/400) * UNFAV(-1) + (UPXGSNI %* UXGSNI - UPMGSNI x UMGSNI 3/400 + UNFAV_ERR
VARIABLE
CAPTOT GA
GAW GBRATIO GC
GCAP GCAPW GCU GDPA GDPGNP GER
GG GGDEBTV GGoOP GGNP GIF GII
GK
GMB GMGSNI GNFAV GPA GPGNP
GPGNPW GPMGSNI GPXGSNI GRS GTAU GTAXV GTBAR GTIV GXGSNI GYD
JA
JAW JBRATIO Jc
JCAP JCAPW JCU JDPA JDPGNP JER
JG JGDEBTV JGDP JGNP JIF JII
JK JMB JMGSNI JNFAV JPA JPGNP
JPGNPW JPMGSNI JPXGSNI JRS JTAU JTAXV JTBAR JTIV JXGSNI JYD
RA
RAW RBRATIO RC
RCAP RCAPW RCU RDPA RDPGNP RER
RG RGDEBTV RGDP RGNP RIF
RII
- 28 -
CROSS REFERENCE LIST OF ENDOGENOUS VARIABLES AND EQUATIONS
| EQUATION NUMBER
i! NUE MORENO LO
78
112 23
16 22
23 137
34 26
26 23 24 22 35 35
27
35 55
55 89
72
86 92
18 137 104 104
96
134 65
29
29 24
32
33 35
26 23
52 58
41
64 59
32
68 70
61 40
70 42
90
73
99 94
32
100
66
35
28 25
88& 22
53 100
64
42
63 44
88 57
70 93
76
45
135
101
45
34¢ 26
122 26
87 135
101
53
69 56
122 61
87 135
99
46
134¢
46
45
28
88
134¢
56
57
63
88
134
47
136
47
46
34¢
121
136
58
58
69
121
136
53
53
47
122
67
60
122
67
67
67
70
61
77
80
80
80
80
88
81
81
81
81
91
82 88
82 102
82 88
82 102
93 102
102
114
102
114
105
114
115
114
115
114
115
116
115
116
115
VARIABLE | EQUATION NUMBER
RK RMB RMGSNI RNFAV RPA RPGNP
RPGNPH' RPMGSNI RPXGSNI RRS RTAU RTAXV RTBAR
UBRATIO uc
UCAP UCAPW UucU UDPA UDPGNP UG UGDEBTV UGDP UGNP UIF
UIT
UK
UMB UMGSNI UNFAV UPA UPGNP
UPGNPW UPMGSNI UPXGSNI URS
UTAU UTAXV UTBAR UTIV UXGSNI UyD XGJS XGRS3 XGUS XJGS XJRS3 XJUS XRGS3 XRJS3. XRUS3 XUGS XUJS XURS3
53 109
106
120 126
139 139
130 130 130 127 128
32 140 112
132 131
53 53
122 47
122 82
122 116 116
103 104 105
96 45
93 77
78 123
107
133 128
138 139 140
130 45
113 139
87
98 46
105 92
90 12¢
108
132 46
127 140
104¢ 47
122 96
93 127
111
139 47
140 58
112
- 29 -
67 75 79
98 104
105 121 122
133 134
67 80 81
70 77 91
124 127 140
91 92 93 95 96 114 115 116
82 102 110 113 125 126 127 129
93 105 106 107 108 109 #125 126
- 30 - CROSS REFERENCE LIST OF EXOGENOUS VARIABLES AND EQUATIONS
VARIABLE | EQUATION NUMBER
CAPTOT_ERR GA_ERR GAW_ERR GBRATIO_ERR GC_ERR GCAP_ERR GCAPW_ERR GCU_ERR GDPA_ERR GDPGNP_ERR GER_ERR GG_ERR GGDEBTV_ERR GGDP_ERR GGNP_ERR GIF_ERR GII_ERR GK_ERR
GLF
GMB_ERR GMGSNI_ERR GNFAV_ERR GPA_ERR GPGNP_ERR GPGNPW_ERR GPMGSNI_ERR GPXGSNI_ERR GQ
GRS_ERR GTAU_ERR GTAXV_ERR GTBAR_ERR GTIV_ERR GXGSNI_ERR GYD_ERR JA_ERR JAW_ERR JBRATIO_ERR JC_ERR JCAP_ERR JCAPH_ERR JCU_ERR JDPA_ERR JDPGNP_ERR JER_ERR JG_ERR JGDEBTV_ERR JGDP_ERR JGNP_ERR JIF_ERR JII_ERR JK_ERR
JLF
JMB_ERR JMGSNI_ERR JNFAV_ERR JPA_ERR JPGNP_ERR JPGNPW_ERR JPMGSNI_ERR JPXGSNI_ERR
JQ
JRS_ERR JTAU_ERR JTAXV_ERR JTBAR_ERR JTIV_ERR JXGSNI_ERR JYD_ERR RA_ERR RAW_ERR RBRATIO_ERR RC_ERR RCAP_ERR RCAPW_ERR RCU_ERR RDPA_ERR RDPGNP_ERR RER_ERR RG_ERR RGDEBTV_ERR RGDP_ERR RGNP_ERR RIF_ERR RII_ERR RK_ERR
VARIABLE | EQUATION NUMBER
RLF
RMB_ERR RMGSNI_ERF: RNFAV_ERR RPA_ERR RPGNP_ERR RPGNPW_ERF. RPMGSNI_ERR RPXGSNI_ERR
RQ
RRS_ERR RTAU_ERR RTAXV_ERR RTBAR_ERR RTIV_ERR RXGSNI_ERR RYD_ERR TIME
UA_ERR UAW_ERR UBRATIO_ERR UC_ERR UCAP_ERR UCAPW_ERR UCU_ERR UDPA_ERR UDPGNP_ERR UG_ERR UGDEBTV_ERR UGDP_ERR UGNP_ERR UIF_ERR UII_ERR UK_ERR
ULF
UMB_ERR UMGSNI_ERR UNFAV_ERR UPA_ERR UPGNP_ERR UPGNPW_ERR UPMGSNI_ERR UPXGSNT_ERR
UQ URS_ERR UTAU_ERR UTAXV_ERR UTBAR_ERR UTIV_ERR UXGSNI_ERR UYD_ERR XGJS_ERR XGRS3_ERR XGUS_ERR XJGS_ERR XJRS3_ERR XJUS_ERR XRGS3_ERR XRJS3_ERR XRUS3_ERR XUGS_ERR XUJS_ERR XURS3_ERR
44
79
113
-31-
MNEMONIC |
CAPTOT GA
GAW GBRATIO GC
GCAP GCAPW GCU GDPA GDPGNP GER
GG GGDEBTV GGDP GGNP GIF
GII
GK
GMB GMGSNI GNF AV GPA GPGNP GPGNPW GPMGSNI GPXGSNI GRS GTAU GTAXV GTBAR GTIV GXGSNI GYD
JA
JAW JBRATIO Jc JCAP JCAPW JCU JDPA JDPGNP JER
JG JGDEBTV JGDP JGNP JIF
JII
JK
JMB JMGSNI JNFAV JPA JPGNP JPGNPW JPMGSNI JPXGSNI JRS JTAU JTAXV JTBAR JTIV JXGSNI JYD
RA
RAW RBRATIO RC
RCAP RCAPW RCU RDPA RDPGNP RER
RG RGDEBTV RGDP
RGNP RIF
- 32 -
ALPHABETICAL LIST OF ENDOGENOUS VARIABLES FOR MODEL
EQUATION }
DEFINITION
Total World Capacity
Absorption
Trade weighted foreign absorption
Target ratio of government bonds to taxable income Private consumption expenditure - 1980 prices Total capacity output
Trade weighted foreign total capacity output Capacity utilization rate
Rate of inflation of absorption prices
Rate of inflation of output prices
Spot exchange rate - US$/DM
Real government purchases - 1980 prices Current total government deb
Gross domestic product - 1980 prices
Gross national product - 1980 prices
Total fixed investment - 1980 prices Inventory investment - 1980 prices
Total net capital stock
Monetary base
Imports - NIA basis - 1980 prices
Net foreign assets
Gross domestic product deflator - 1980=100.00 Gross national product deflator - 1980=100.00 Trade weighted foreign gross national product deflator - 1980=100.130 Import deflator - NIA basis - 1980=100.00 Export deflator - NIA basis - 1980 prices 3-month Treasury bill rate
Actual income tax rate
Nominal tax revenues
Equilibrium tax rate
Nominal taxable income
Exports - NIA basis - 1980 prices
Disposable income - 1980 prices
Absorption
Trade weighted foreign absorption
Target ratio of government bonds to taxable income
Private consumption expenditure - 1980 prices Total capacity output Trade weighted foreign total capacity output
Capacity utilization rate
Rate of inflation of absorption prices
Rate of inflation of output prices
Spot exchange rate ~ US$/DM
Real government purchases - 1980 prices Current total government debt
Gross domestic product - 1980 prices
Gross national product - 1980 prices
Total fixed investment - 1980 prices Inventory investment - 1980 prices
Total net capital stock
Monetary base
Imports - NIA basis ~- 1980 prices
Net foreign assets
Gross domestic product deflator - 1980=100.00 Gross national product deflator - 1980=100.00 Trade weighted foreign gross nationa. product deflator - 1980=100.)0 Import deflator - NIA basis - 1980=100.00 Export deflator - NIA basis - 1980 prices 3-month Treasury bill rate
Actual income tax rate
Nominal tax revenues
Equilibrium Tax Rate
Nominal taxable income
Exports - NIA basis - 1980 prices
Disposable income - 1980 prices
Absorption
Trade weighted foreign absorption
Target ratio of government bonds to taxable income Private consumption expenditure - 1980 prices Total capacity output
Trade weighted foreign total capacity output Capacity utilization rate
Rate of inflation of absorption prices
Rate of inflation of output prices
Spot exchange rate - US$/DM
Real government purchases - 1980 prices Current total government debt
Gross domestic product - 1980 prices
Gross national product - 1980 prices
Total fixed investment - 1980 prices Inventory investment - 1980 prices
Total net capital stock
Monetary base
Imports - NIA basis - 1980 prices
Net foreign assets
MNEMONIC
UPXGSNI URS UTAU UTAXV UTBAR UTIV UXGSNI UYD xGJS XGRS3 XGUS XxJGS XJRS3 XJUS XRGS3 XRJS3 XRUS3 XUGS XUJS XURS3
| EQUATION |
- 33 -
DEFINITION
Gross domsetic product deflator - 1980=100.00 Gross national product deflator ~ 1980=100.00 Trade weighted foreign gross national Product deflator - 1980=100.00
Import deflator - NIA
basis - 1980=100.00
Export deflator - NIA basis - 1980 Prices 3-month Treasury bill rate
Actual income tax rate
Nominal tax revenues
Equilibrium tax Rate
Nominal taxable income
Exports - NIA basis - 1980 prices
Disposable income - 1980 prices
Absorption
Trade weighted foreign absorption
Target ratio of government bonds to taxable income Private consumption expenditure - 1982 prices Total capacity output
Trade weighted foreign total capacity output Capacity utilization rate
Rate of inflation of absorption prices
Rate of inflation of output prices
Ueal government purchases - 1982 prices
Current total
government debt
Gross domestic product - 1982 prices Gross national product - 1982 prices
Total fixed investment - 1982 prices Inventory investment - 1982 prices
Total net capital stock
Monetary base
Imports ~ NIA basis - 1982 prices
Net foreign assets
Gross domestic product deflator - 1982=100.00 Gross national product deflator - 1982=100.00 Trade weighted foreign gross national product deflator - 1980=100.00 Import deflator - NIA basis - 1982=100.00 Export deflator - NIA basis - 1980 prices 3-month Treasury bill rate
Actual income tax rate
Nominal tax revenues
Equilibrium tax rate
Nominal taxable income
Exports - NIA basis - 1982 prices
Disposable income
Share Share Share Share Share Share Share Share Share Share Share Share
German exports destined for Japan German exports destined for ROW German exports destined for US Japanese exports destined for Germany Japanese exports destined for ROW Japanese exports destined for US ROW exports destined for Germany ROW exports destined for Japan ROW exports destined for US
US exports destined for Germany US exports destined for Japan
US exports destined for ROW
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ALPHABETICAL LIST OF EXOGENOUS VARIABLES FOR MODEL
MNEMONIC | DEFINITION CAPTOT_ERR Residual term in CAPTOT equation GA_ERR Residual term in GA equation GAW_ERR Residual term in GAW equation GBRATIO_ERR Residual term in GBRATIO equation
__ERR Residual term in GC equation GCAP_ERR Residual term in GCAP equation GCAPW_ERR Residual term in GCAPW equation GCU_ERR Residual term in GCU equation GDPA_ERR Residual term in GDPA equation GDPGNP_ERR Residual term in GDPGNP equation GER_ERR Residual term in GER equation GG_ERR Residual term in GG equation GGDEBTV_ERR Residual term in GGDEBTV equation GGDP_ERR Residual term in GGDP equation GGNP_ERR Residual term in GGNP equation GIF_ERR Residual term in GIF equation GII_ERR Residual term in GII equation GK_ERR Residual term in GK equation
GLF Labor force GMB_ERR Residual term in GMB equation GMGSNI_ERR Residual in GMGSNI equation GNFAV_ERR Residual in GNFAV equation GPA_ERR Residual in GPA equation GPGNP_ERR Residual in GPGNP equation GPGNPW_ERR Residual in GPGNPW equation GPMGSNI_ERR Residual in GPMGSNI equation GPXGSNI_ERR Residual in GPXGSNI equation GQ Production technology GRS_ERR Residual in GRS equation GTAU_ERR Residual in GTAU equation GTAXV_ERR Residual in GTAXV equation GTBAR_ERR Residual in GTBAR equation GTIV_ERR Residual in GTIV equation GXGSNI_ERR Residual in GXGSNI equation GYD_ERR Residual in GYD equation JA_ERR Residual term in JA equation JAW_ERR Residual term in JAW equation JBRATIO_ERR Residual term in JBRATIO equation JC_ERR . Residual term in JC equation JCAP_ERR Residual term in JCAP equation JCAPW_ERR Residual term in JCAPW equation JCU_ERR Residual term in JCU equation JDPA_ERR Residual term in JDPA equation JDPGNP_ERR Residual term in JDPGNP equation JER_ERR Residual term in JER equation JG_ERR Residual term in JG equation JGDEBTV_ERR Residual term in JGDEBTV equation JGDP_ERR Residual term in JGDP equation JGNP_ERR Residual term in JGNP equation JIF_ERR Residual term in JIF equation JII_ERR Residual term in JII equation JK_ERR Residual term in JK equation JLF Labor force JMB_ERR Residual term in JMB equation JMGSNI_ERR Residual in "MGSNI equation JNFAV_ERR Residual in JNFAV equation JPA_ERR Residual in JPA equation JPGNP_ERR Residual in JPGNP equation JPGNPW_ERR Residual in JPGNPW equation JPMGSNI_ERR Residual in JPMGSNI equation JPXGSNI_ERR Residual in JPXGSNI equation JQ Production technology JRS_ERR Residual in JRS equation JTAU_ERR Residual in JTAU equation JTAXV_ERR Residual in JTAXV equation JTBAR_ERR Residual in JTBAR equation JTIV_ERR Residual in JTIV equation JXGSNI_ERR Residual in JXGSNI equation JYD_ERR Residual in JYD equation RA_ERR Residual term in RA equation RAW_ERR Residual term in RAW equation RBRATIO_ERR Residual term in RBRATIO equation RC_ERR Residual term in RC equation RCAP_ERR Residual term in RCAP equation RCAPW_ERR Residual term in RCAPW equation RCU_ERR Residual term in RCU equation RDPA_ERR Residual term in RDPA equation RDPGNP_ERR Residual term in RDPGNP equation RER_ERR Residual term in RER equation RG_ERR Residual term in RG equation RGDEBTV_ERR Residual term in RGDEBTV equation RGDP_ERR Residual term in RGDP equation RGNP_ERR Residual term in RGNP equation RIF_ERR Residual term in RIF equation
|
RII_ERR Residual term in RII equation
MNEMONIC
RK_ERR
RLF
RMB_ERI RMGSNI_ERI2 RNFAV_ERR RPA_ERR RPGNP_ERR RPGNPW_ERI RPMGSNI_ERI RPXGSNI_ERR RQ
RRS_ERR RTAU_ERR RTAXV_ERR RTBAR_ERE RTIV_ER#t RXGSNI_ERR RYD_ ERR
!
UAW_ERF!: UBRATIO_ERF: UC_ERF: UCAP_ERR: UCAPW_ERF: UCU_ERR UDPA_ERR UDPGNP_ERR UG_ERR UGDEBTV_ERR UGDP_ERR UGNP_ERR UIF_ERR UII_ERR UK_ERR
ULF
UMB_ERR UMGSNI_ERR UNFAV_ERR UPA_ERR UPGNP_ERR UPGNPW_ERR UPMGSNI_ERR UPXGSNI_ERR
UQ URS_ERR UTAU_ERR UTAXV_ERR UTBAR_ERR UTIV_ERR UXGSNI_ERR UYD_ERR XGJS_ERR XGRS3_ERR XGUS_ERR XJGS_ERR XJRS3_ERR XJUS_ERR XRGS3_ERR XRJS3_ERR XRUS3_ERR XUGS_ERR XUJS_ERR XURS3_ERR
|e |
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DEFINITION
Residual term in RK equation
Labor force
Residual term in RMB equation
Residual in Residual in Residual in Residual in Residual in Residual in Residual
RMGSNI equation RNFAV equation RPA equation RPGNP equation RPGNPW equation RPMGSNI equation
in RPXGSNI equation
Production technology
Residual in Residual in Residual in Residual in Residual in Residual in Residual in Time trend
RRS equation RTAU equation RTAXV equation RTBAR equation RTIV equation RXGSNI equation RYD equation
Residual term in UA equation Residual term in UAW equation Residual term in UBRATIO equation Residual term in UC equation Residual term in UCAP equation Residual term in UCAPW equation Residual term in UCU equation Residual term in UDPA equation Residual term in UDPGNP equation Residual term in UG equation Residual term in UGDEBTV equation Residual term in UGDP equation Residual term in UGNP equation Residual term in UIF equation Residual term in UII equation Residual term in UK equation
Labor force
Residual term in UMB equation
Residual in Residual in Residual in Residual in Residual in Residual in Residual
UMGSNI equation UNFAV equation UPA equation UPGNP equation UPGNPW equation UPMGSNI equation UPXGSNI equation
in Production technology
Residual in Residual in Residual in Residual in Residual in Residual in Residual in Residual in Residual in Residual in Residual in Residual in Residual in Residual in Residual in Residual in Residual in Residual in Residual in
RRS equation UTAU equation UTAXV equation UTBAR equation UTIV equation UXGSNI equation UYD equation XGJS equation XGRS3 equation XGUS equation XJGS equation XJRS3 equation XJUS equation XRGS3 equation XRJS3 equation XRUS3 equation XUGS equation XUJS equation XURS3 equation
Construction of the Database
Most data are taken from the OECD's Quarterly National Accounts. The trade shares are computed using data from the IMF's Direction of Trade Statistics. The exchange rate, interest rate, monetary base, and labor force are obtained directly from national sources.
All data are seasonally adjusted at annual rates.” Interest rates are expressed in percents, not decimals.> The data are expressed in billions of local currency units, except for data from Italy and Japan, which are expressed in trillions. Real quantities are expressed at 1982 prices for U.S. data, 1981 prices for Canadian data, and 1980 prices for all other data. Price deflators are equal to 100 in the base year.“ Exchange rates are the number of U.S. dollars required to purchase a unit of the currency in question, except for the cases of Italy and Japan, where the exchange rates are the number of U.S. dollars required to buy 1000 lire or yen.
The newly revised Italian national accounts data are not available prior to 1980. MX3 has spliced the old series onto the new series for the years 1976-1979.
The United States government consumption series differs from all other MX7 government consumption series because it includes public gross fixed capital formation. Thus, in the United States gross fixed capital formation
refers to private investment only.
2. Most of the data are available only on a seasonally adjusted basis. When the data are not available seasonally adjusted, we have adjusted them using Census X-11 as implemented by the SEASAQ command in TROLL.
3. For expositional purposes, the text assumes that interest rates are expressed in decimals. This convention allows for simpler notation.
4. For expositional purposes, the text assumes that deflators equal 1 in the base year.
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‘To create the ROW national accounts data, series from Canada, France, Italy and the United Kingdom were multiplied by their respective purchasing power parity (PPP) exchange rates in 1980 and then summed. The only exception is the Canadian data which are also rescaled from a 1981 base year to 1980. The PPP exchange rates were obtained from OECD National Accounts.
Factor payments abroad and factor receipts from abroad are available on an anrual basis only, and they were interpolated to yield quarterly figures. The nominal factor receipts and payments were deflated by either PGNP or PGDP, depending on availability, a procedure which ensures that PGNP will be identical to PGDP. For countries that report quarterly GDP, net factor receipts were added to obtain GNP. For countries that report quarterly GNP, factor payments were subtracted from reported imports and factor receipts were subtracted from reported exports. GDP in these countries is obtained by subtracting net factor receipts from GNP.
The share of U.S. exports to each trading partner is obtained by dividing nominal bilateral exports to that partner by total nominal U.S. exports. Japanese and German export shares are computed in the same manner. The rest of world (ROW) bilateral exports are the residual exports from those countries other than the United States, Japan, and Germany. Thus, ROW's export share to the United States is the total exports of ROW countries to the United States divided by total ROW exports to the G-3. For the purpose of computing trade shares, ROW includes all countries reported on the IMF Direction of Trade Statistics.
All trade weighted series are geometric averages and use the average
bilateral trade shares over the period 1976-1987 as weights. The
construction of each of these series is described in the text.
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The short-term interest rate is the 3-month Treasury bill rate waere available. In France it is the 3-month interbank rate. In Japan it is the 2-month Treasury bill rate.
Where not explicitly available, the monetary base is computed as the sum of all currency outside the central bank plus deposits held by private banks as reserves at the central bank.
In certain countries the labor force is computed as the sum of employment and unemployment. In France the labor force is reported o1 an annual basis and has been interpolated.
The capital stock series have been constructed by interpolating annual net capital stock series.” The primary source is the OECD's Flows and_ Stocks of Fixed Capital, 1960-1985. Missing components of these series have been approximated using estimates of gross capital stocks from the OECD's Sectorial Database and the ratios of net to gross capital for similar series in other countries as reported in Flows and Stocks of Fixed Capital.
Capital stocks after 1985 were extrapolated by cumulating fixed investment less depreciation at the estimated depreciation rate.
Except for Germany and Japan, the outstanding stock of-governmen: debt has been computed from a benchmark value by cumulating the public seczor deficits (at a quarterly rate) in successive quarters. The benchmark values are net public sector debt stocks at yearend 1982 and were obtained f--om
OFCD Economic Studies, No. 7, 1986, pp. 103-153. For Germany and Japan
public sector debt series were obtained from national sources.
5. The net increment to the capital stock over the year was allocated to
each quarter in a manner proportional to the measured flow of gross fixed investment in that quarter.
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Similarly, the stock of net foreign assets was computed by cumulating the current account balances over time. The benchmark values for these series are yearend 1982 from the IMF’s World Economic Outlook, April 1988, pp. 88-90. The current account balance is the sum of nominal net exports
and nominal net factor receipts.
Cite this document
Joseph E. Gagnon (1989). A Forward-Looking Multicountry Model: MX3 (IFDP 1989-359). Board of Governors of the Federal Reserve System, International Finance Discussion Papers. https://whenthefedspeaks.com/doc/ifdp_1989-359
@techreport{wtfs_ifdp_1989_359,
author = {Joseph E. Gagnon},
title = {A Forward-Looking Multicountry Model: MX3},
type = {International Finance Discussion Papers},
number = {1989-359},
institution = {Board of Governors of the Federal Reserve System},
year = {1989},
url = {https://whenthefedspeaks.com/doc/ifdp_1989-359},
abstract = {This is paper discusses the theoretical structure and empirical properties of MX3, a multicountry macroeconometric model with rational expectations. MX3 is a medium-sized quarterly model of the United States, Japan, and West Germany. The primary objective of the model is to analyze the effect of fiscal and monetary rules on national economies in an international context. By incorporating rational expectations into almost all of the model's behavioral equations, MX3 takes a large step toward addressing the "Lucas critique" of model-based policy analysis.},
}