1. Introduction
1.1 Documentation
1.2 Notation for the ROW Model
1.3 Solution Options
1.4 The Complete MC1 Model and How It is Solved
1.5 Solution Errors
1.6 Changing Stochastic Equations
1.7 Creating Base Datasets
1.1 Documentation
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. The prediction period, where the default is 1997-2002.
  2. Whether you want the entire MC1 model solved or just the individual country models by themselves. If you choose the latter, none of the variables in one country affect the variables in any other country. Each individual country model stands alone, and all foreign-sector variables in an individual country model are taken to be exogenous. The default is to solve the entire MC1 model.
  3. Whether or not you want the trade share equations used. If you do not want the trade share equations used, the trade shares are taken to be exogenous and equal to the actual values prior to 1996:1 and to the predicted values in the base dataset (MCBASE) from 1996:1 on. This trade share option is not relevant if you choose to have the individual country models solved by themselves since in this case the output from the trade share calculations does not affect any model. The default is to use the trade share equations.
  4. The number of within country iterations (denoted LIMITA) and the number of across country iterations (denoted LIMITB). The defaults are 4 for LIMITA and 7 for LIMITB. As discussed below, these options are useful for checking if the model has successfully solved.
  5. Whether or not you want to use the historical errors. The default is to set all the error terms equal to zero. If you use the historical errors and make no changes to any of the exogenous variables, add factors, and coefficients, then the solution values of the endogenous variables will be the actual values---a perfect tracking solution---aside from rounding error. This option can be useful for multiplier experiments, as discussed below.
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 tables.

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:

logPXUS - logPW$US = q(logGDPD - logPW$US)

This equation is estimated under the assumption of a second order autoregressive error for the 1962:1--1995:4 period. The estimate of q is .937 with a t-statistic of 26.47. The estimates (t-statistics) of the two autoregressive coefficients are 1.47 (19.49) and -.48 (-6.60), respectively. The standard error is .0121. Given the predicted value of PXUS from this equation, PEX is determined by the identity listed in Table B.5: PEX=DEL3*PXUS. This identity replaces identity 32 in Table A.3 in the US model.

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:

  1. Given values of X90$, PMP, and PW$ for all four quarters of year 1 for each quarterly country and for year 1 for each annual country, all the stochastic equations and identities are solved. For the annual countries "solved" means that the equations are passed through k1 times for year 1, where k1 is determined by experimentation (as discussed below). For the quarterly countries "solved" means that quarter 1 of year 1 is passed through k1 times, then quarter 2 k1 times, then quarter 3 k1 times, and then quarter 4 k1 times. The solution for the quarterly countries for the four quarters of year 1 is a dynamic simulation in the sense that the predicted values of the endogenous variables from previous quarters are used, when relevant, in the solution for the current quarter.
  2. Given from the solution in step 1 values of E, PX, and M90$A for each country, the calculations in Table B.4 can be performed. Since all the calculations in Table B.4 are quarterly, the annual values of E, PX, and M90$A from the annual countries have to be converted to quarterly values first. This is done in the manner discussed at the bottom of Table B.4. The procedure in effect takes the distribution of the annual values into the quarterly values to be exogenous. The second task is to compute PX$ using equation L-1. Given the values of PX$, the third task is to compute the values of aij from the trade share equations---see equation 6.13 in Section 6.16 of Testing Macroeconometric Models (MC1 Version). This solution is also dynamic in the sense that the predicted value of aij for the previous quarter feeds into the solution for the current quarter. (Remember that the lagged value of aij is an explanatory variable in the trade share equations.) The fourth task is to compute X90$, PMP, and PW$ for each country using equations L-2, L-3, and L-4. Finally, for the annual countries the quarterly values of these three variables are then converted to annual values by summing in the case of X90$ and averaging in the case of PMP and PW$.
  3. Given the new values of X90$, PMP, and PW$ from step 2, repeat step 1 and then step 2. Keep repeating steps 1 and 2 until they have been done k2 times. At the end of this, declare that the solution for year 1 has been obtained.
  4. Repeat steps 1, 2, and 3 for year 2. If the solution is meant to be dynamic, use the predicted values for year 1 for the annual countries and the predicted values for the four quarters of year 1 for the quarterly countries, when relevant, in the solution for year 2. Continue then to year 3, and so on.

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. Drop (or add back in) an equation. When an equation is dropped, the variable determined by the equation is taken to be exogenous, and it can be changed if desired. The default values for the variable are the historical values when they exist and forecast values from the base dataset otherwise. There are a few restrictions that you need to be aware of when dropping equations. For the US you should not drop the RB and RM equations (equations 23 and 24) without also dropping the RS equation (equation 30). Even though the software allows you to drop equations 23 and 24 without dropping equation 30, the results will not be right. Similarly, for all the other countries you should not drop the RB equation (equation 8) without also dropping the RS equation (equation 7). Also, for all countries except the US you should not drop the W equation (equation 12) without also dropping the PY equation (equation 5). Finally, for all countries you should not drop the PX equation (equation 11).
  2. Take an equation to begin after the beginning of the basic prediction period. When an equation begins later than the basic prediction period, the variable determined by the equation is taken to be exogenous for the earlier period, and it can be changed if desired. The default values for the variable are the historical values when they exist and forecast values from the base dataset otherwise. For quarterly countries the period that you want the equation to begin is a quarter, not a year. You can, for example, have an equation begin in 1997:3 when the basic prediction period is 1997-2002. The same restrictions apply here as apply to dropping equations. See the discussion in the previous item.
  3. Add factor an equation, where the add factors can differ for different periods. For quarterly countries the add factors are for individual quarters, not years.
  4. Change any of the 1434 coefficients in the equations. Unlike for the US model, however, you cannot add variables to the 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.