The MULTIMOD-Type-II-fixes have been carried out by optimal control, i.e. an additional equation is added to the model by which GDP-deviations from a one percent deviation from base of GDP are punished. This is easy to perform with MULTIMOD. For MSG2 and NiGEM carrying out a Type II fix is more cumber-some as these models run in their own software and for this reason are carried out as follows.
To perform a Type II fix for n periods, first a shock is applied for each of the n periods. The partial derivative is then calculated by which the size of the shock needed for the Type II fix can be determined. To give an example, assume ns2, and a shock g with response y. Shocking g by a1 in the first period gives a certain response in y, say b11 in the first period and b12 in second period, and subse-quently shocking g in the second period by a2 gives b21 and b22 in the first and second period. This can be formalized as
Ža10.g ª Žb11 b12.y,
Ž .3 Ž0 a2.g ª Žb21 b22.y,
where g and y are two-dimensional vectors. From this follows
b11 b12 y1 a1 0
gªy. Ž .4
ž
b21 b22/ ž
0 a2/
The shock size ensuring a one percent increase in y then is
Ž . Ž .
a b1 22yb21 a b2 11yb12
and Ž .5
U U U U
b b11 22yb b12 21 b b11 22yb b12 21
in the first and second period, respectively.
If there is no forward looking behaviour, b21s0. If a temporary shock only has
Ž .
a temporary instantaneous effect, also b12s0. In the case where b21sb12s0, the shock size for a one percent Type II fix is thus a1rb11 in the first period and a2rb22 in the second period. However, in the case of forward looking behaviour or responses that last longer than only the current period the calculation of the shock is evidently more complicated; it is no longer possible to divide merely the vector on the left hand side of the arrow in Eq. 4 by the vector on the right hand side ofŽ .
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R. Dou¨en, M. PeetersrEconomic Modelling 15 1998 163]195 193
this arrow6. This shows that obtaining a Type II fix is not a straightforward procedure in models with rational expectations andror dynamic specifications.
This also shows that the comparison of GDP responses of two countries, say country A and B, is not merely possible by a division of the GDP-responses of country A by those of country B. A one percent increase in GDP as a deviation from base is constructed in our analysis, and hence can be directly compared across countries.
Our objective is a 6 years Type II fix in GDP. Thus first six shocks are performed in MSG2, and then the size of the shock that gives a one percent increase in GDP during the first 6 years is calculated. As MSG2 is linearized and behaves well, no problems were encountered when carrying out this exercise. NiGEM is a quarterly model, so 24 shocks need to be performed to achieve the objective. For the government consumption and business investment shock no problems arose. For the money demand shock, on the other hand, some insurmountable problems occurred. First, the equation is dynamic by which a one percent increase in the first year is not achievable. Second, the money multiplier turns out to be very small for the US as well as for Germany. So very large shocks are necessary to obtain a one percent increase in GDP. This seems to lead to stability problems, in particular for
Ž Ž ..
Germany see also Turner et al. 1989 .
Tables 10]12 report the sizes of the exogenous shock performed in Tables 7]9, respectively.
Acknowledgements
This research was undertaken at the ESRC Macroeconomic Modelling Bureau at the University of Warwick with the support of the Leverhulme Trust and HCM
Table 10
Ž .
The shocks in MSG2 as percentage of GDP resulting in 1% increase in GDP during 6 years Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Years 7]50 US
A demand shock 5.39 5.37 5.68 6.17 6.59 7.06 0
A supply shock 1.00 0.64 0.68 0.70 0.72 0.69 0
A monetary shock 0.94 1.95 3.52 5.74 9.25 21.3 0
Germany
A demand shock 5.69 5.33 5.24 5.26 5.20 4.67 0
A supply shock 1.01 0.66 0.70 0.74 0.75 0.84 0
A monetary shock 1.01 1.94 3.24 5.00 6.23 21.4 0
6This would only be possible if the division is by the same amount in each period.
Table 11
Ž .
The shocks in MULTIMOD as a percentage of GDP resulting in a 1% increase in GDP during 6 years
Year 1 Year 2 Year 3 Year 4 Year 5 Years 6]50
US
A demand shock 13.57 25.55 40.10 52.37 59.79 0
A supply shock 11.21 22.31 28.96 32.96 34.33 0
Germany
A demand shock 17.38 32.37 42.07 50.12 53.79 0
A supply shock 5.02 7.46 10.18 11.93 12.21 0
Table 12
Ž .
The shocks in NiGEM as a percentage of GDP resulting in a 1% increase in GDP during six years
Quarter US GE
Research Fellowships from the European Community. For comments on the paper we thank Kenneth Wallis. For help and advice on the simulation results of the macroeconomic models we gratefully acknowledge Pete Mitchell and Joanne Sault.
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R. Dou¨en, M. PeetersrEconomic Modelling 15 1998 163]195 195
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