|The complete documentation for the non-US part of the MC1 model,
which is called
the ROW model, is in Appendix B and the Chapter 6 tables
at the end of this workbook and at the end of
Testing Macroeconometric Models (MC1 Version).
For the MC1 model forecast (dated May 21, 1997), the price and wage
equations for Korea have not been used,
although they are listed among the estimated equations.
They were not used because they seemed to have poor long-run properties.
The complete documentation for the US part of the MC1 model is in Appendix A and the Chapter 5 tables at the end of this workbook. As discussed in Model Versions and References, the version of the US model that is part of the MC1 model is slightly different from the version of the US model presented in Testing Macroeconometric Models (MC1 Version).
|1.2 Notation for the ROW Model|
|The notation for the variables in the ROW model is presented in Tables B.1 and B.2 in Appendix B. Two letters denote the country (CA for Canada, JA for Japan, etc.), and the abbreviations are given in Table B.1. Up to five letters denote the variable (C for consumption, I for investment, etc.), and the names are given in Table B.2 in alphabetical order. The complete name of a variable for a country consists of the country abbreviation plus the variable name, such as CAC for Canadian consumption, JAI for Japanese investment, etc.|
|1.3 Solution Options|
|There are five choices you can make regarding the solution of the MC1 model.
|1.4 The Complete MC1 Model and How It is Solved|
|The size of the MC1 model is as follows. The US model, which is part of the MC1
model, includes 30 stochastic equations plus one more when it is imbedded in the MC1 model.
(This additional equation is discussed below.) There are 32 countries in the ROW model and
up to 15 stochastic equations per country. If each country had all 15 equations, there
would be a total of 480 (32 x 15) stochastic equations in the ROW model. Because of data
limitations, however, not all countries have all equations, and there are in fact 297
stochastic equations in the ROW model. Given the 31 stochastic equations in the US model,
there are thus 328 stochastic equations in the MC1 model. There are a total of 1442
coefficients in these equations, counting the autoregressive coefficients of the error
terms. In addition, as discussed in Section 6.16 in
Testing Macroeconometric Models (MC1 Version),
there are 1041 estimated trade share equations. Not counting the trade share coefficient
estimates, all the coefficient estimates for the US model are presented in the Chapter 5
tables, and all the coefficient estimates for the ROW model are presented in the Chapter 6
Table B.1 shows that there are in the ROW model 18 variables per country determined by identities (identities I-10 and I-11 are no longer used), 4 variables per country determined when the countries are linked together, and 20 exogenous variables per country. Counting these variables, various transformations of the variables that are needed for the estimation, and the US variables (but not the trade shares), there are about 4000 variables in the MC1 model.
The way in which the US model is imbedded in the MC1 model is explained in Table B.5. The two key variables that are exogenous in the US model but become endogenous in the overall MC1 model are exports, EX, and the price of imports, PIM. EX depends on X90$US, which is determined in Table B.4. PIM depends on PMUS, which depends on PMPUS, which is also determined in Table B.4.
Feeding into Table B.4 from the US model are PXUS and M90$AUS.
PXUS is determined is the same way that PX is determined for the other
countries, namely by equation 11 in Table B.3. In the US case logPXUS - logPW$US
is regressed on logGDPD - logPW$US. The equation is:
M90$AUS, which, as just noted, feeds into Table B.4, depends on MUS, which depends on IM. This is shown in Table B.5. IM is determined by equation 27 in the US model. Equation 27 is thus the key equation that determines the U.S. import value that feeds into Table B.4.
The main exogenous variables in the overall MC1 model are the government spending variables (G). In other words, fiscal policy is exogenous. Monetary policy is not exogenous because of the use of the interest rate and exchange rate reaction functions.
The solution of the MC1 model can now be considered. Because some of the countries are annual, the overall MC1 model is solved a year at a time. A solution period must begin in the first quarter of the year. In the following discussion, assume that year 1 is the first year to be solved. The overall MC1 model is solved as follows:
This completes the discussion of the solution of the model. In the above notation LIMITA is k1 and LIMITB is k2. I have found that going beyond k1=4 and k2=7 leads to very little change in the final solution values, and so these are the default values.
|1.5 Solution Errors|
|If you ask to solve the MC1 model and the model does not solve, you will get an
error message to that effect. When this happens your dataset will not have been changed.
You will need to make less extreme changes and try again. The model has not been solved
when there is an abnormal abort, which usually means that the program has tried to take
the log of a negative number.
Because the MC1 model (unlike the US model) is not iterated until convergence (because k1 and k2 are fixed, it may be the case that the program finishes normally (no abnormal abort) but that the model did not really solve. If you are concerned about this, there is one check that you can perform, which is to increase LIMITA and LIMITB. If the model has correctly solved, it should be the case the increasing LIMITA and LIMITB has a very small effect on the solution values. You can thus increase LIMITA and LIMITB and see if the output values change much. If they do not, then you can have considerable confidence that the model has been solved correctly. The maximum values of LIMITA and LIMITB that you are allowed are 12 and 21, respectively.
|1.6 Changing Stochastic Equations|
|There are four changes you can make to any of the 326 stochastic equations:
|1.7 Creating Base Datasets|
|If you ask the program to solve the MC1 model for any period beginning 1998 or
later and you make no changes to the coefficients and exogenous variables, the
solution values for the endogenous variables will simply be the values that are already in
MCBASE. If, on the other hand, you ask the program to solve the model for a period
beginning earlier than 1998, where at least some actual data exist, the solution values
will not be the same as the values in MCBASE because the model does not predict perfectly
(the solution values of the endogenous variables are not in general equal to the actual
values). It is thus very important to realize that the only time the solution values will
be the same as the values in MCBASE when you make no changes to the exogenous variables
and coefficients is when you are solving beginning 1998 or later.
The only actual data for 1997 are US data, which are actual for 1997:1. If you have all the US stochastic equations begin in 1997:2 (which the software allows you to do) and you make no other changes, then a forecast beginning in 1997 will have the same solution values as are in MCBASE. Also, if you do not do this, but instead ask the program to use the historical errors, then a forecast beginning in 1997 will also have the same solution values as are in MCBASE if you make no other changes.
If you want to work with the MC1 model for a period for which actual data exist, you should read Section 2.6 of The US Model Workbook carefully. The same considerations apply to the MC1 model as apply to the US model. In other words, Section 2.6 is as relevant for the MC1 model as it is for the US model. This discussion will not be repeated here. The only new thing to note is that whenever you are making comparisons, you must treat the trade share equations the same for all runs---either use the trade share equations for all the relelvant solutions or take the trade shares to be exogenous for all of them.
An alternative to doing what Section 2.6 discusses should be done when working with a period for which actual data exist is to use the historical errors. When using the historical errors, the base prediction path is just the path of the actual values, and so any changes made are off of the actual path. An example of the use of this option is discussed next in Chapter 2.