The version of the US model that is part of the MC3 model, which is presented in Macroeconometric Modeling, is the same as the version used for the April 27, 2001, forecast (BASE011). The complete documentation for the US model that is part of the MC3 model is contained in Appendix A and the Chapter 5 tables at the end of this workbook and at the end of Macroeconometric Modeling.

The EMU began January 1, 1999, and so the estimation periods for the interest rate and exchange rate equations (equations 7, 8, 9, and 10) end in 1998:4 or 1998 for the EMU countries (AU, FR, GE, IT, NE, FI, BE, IR, PO, and SP). The one exception to this is equation 8 for GE, which is estimated through the end of the data. From 1999:1 on this equation is taken to be the term structure equation for the entire EMU. Greece (GR) joined the EMU on January 1, 2001, and so the estimation periods for the interest rate and exchange rate equations for GR will end in 2000. The treatment of the EMU for solution purposes is discussed in Section 1.8. Until Section 1.8, the discussion pertains to the model prior to the EMU regime.

1. The prediction period, where the default is 2002-2004.
2. Whether you want the entire MC3 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 MC3 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 2000:1 and to the predicted values in the base dataset (MC3BASE) from 2000:1 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 10 for LIMITA and 10 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.

Table B.1 shows that there are in the ROW model 20 variables per country determined by identities (identities I-10 and I-11 are no longer used), 5 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 5000 variables in the MC3 model.

The way in which the US model is imbedded in the MC3 model is explained in Table B.5. The two key variables that are exogenous in the US model but become endogenous in the overall MC3 model are exports, EX, and the price of imports, PIM. EX depends on X95$_US, which is determined in Table B.4. PIM depends on PM_US, which depends on PMP_US, which is also determined in Table B.4.

Feeding into Table B.4 from the US model are PX_US and M95$A_US. PX_US is determined is the same way that PX is determined for the other countries, namely by equation 11 in Table B.3. In the US case logPX_US - logPW$_US is regressed on logGDPD - logPW$_US. The equation is:

logPX_US - logPW$_US = q(logGDPD - logPW$_US)

This equation is estimated under the assumption of a second order autoregressive error for the 1962:1--1999:4 period. The estimate of q is .916 with a t-statistic of 24.74. The estimates (t-statistics) of the two autoregressive coefficients are 1.46 (20.03) and -.47 (-6.40), respectively. The standard error is .0116. Given the predicted value of PX_US from this equation, PEX is determined by the identity listed in Table B.5: PEX=DEL3*PX_US. This identity replaces identity 32 in Table A.3 in the US model.

M95$A_US, which, as just noted, feeds into Table B.4, depends on M_US, 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 MC3 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 MC3 model can now be considered. Because some of the countries are annual, the overall MC3 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 MC3 model is solved as follows:

1. Given values of X95$, PMP, and PW$ 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 M95$A for each country, the calculations in Table B.4 can be performed. Since all the calculations in Table B.4 are quarterly, the annual values of E, PX, and M95$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$, the third task is to compute the values of a_ij from the trade share equations---see equation 6.13 in Section 6.16 of Macroeconometric Modeling. This solution is also dynamic in the sense that the predicted value of a_ij for the previous quarter feeds into the solution for the current quarter. (Remember that the lagged value of a_ij is an explanatory variable in the trade share equations.) The fourth task is to compute X95$, 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 X95$ and averaging in the case of PMP and PW$.
3. Given the new values of X95$, 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=10 and k₂=10 leads to very little change in the final solution values, and so these are the default values.

Because the MC3 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 15 and 15, respectively.

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.
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 2000:3 when the basic prediction period is 2000-2004.
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 1671 coefficients in the equations. Unlike for the US model alone, however, you cannot add variables to the equations.

If you want to work with the MC3 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 MC3 model as apply to the US model. In other words, Section 2.6 is as relevant for the MC3 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.

For the EMU regime, which begins in 1999:1, the interest rate reaction functions of the 10 countries except GE were dropped from the model. For GE the coefficient estimates of the interest rate reaction function were retained but the right hand side GE variables were replaced with the respective EU variables. This equation is interpreted as the interest rate reaction function of the European Central Bank (ECB). What this means is that the ECB is assumed to have the same policy rule as the Bundesbank did except that the rule reacts to the overall EU variables and not just to the GE variables.

Let GERSOLD be the interest rate determined by equation 7 for GE prior to the EMU regime, and let GERSEMU be the interest rate determined by the ECB equation just mentioned. In the coding of the model the German interest rate (GERS) is taken to be (1 - EMU)*GERSOLD + EMU*GERSEMU, where EMU is a dummy variable that takes on a value of 1 from 1999.1 on and 0 otherwise. This treatment allows the estimated equations for both GERSOLD and GERSEMU to be included in the coding of the model.

Let ITRSOLD be the (short term) interest rate determined by equation 7 for IT prior to the EMU regime, and let ITRSEMU be the short term IT rate in the EMU regime. ITRSEMU is taken to be GERSEMU. In other words, the Italian short term interest rate in the EMU regime is taken to be the rate determined by the ECB equation (which is GERSEMU). The same procedure was followed for the other 8 countries. The coding of the model is the same for these countries as it is for Germany. For example, the short term IT interest rate (ITRS) is taken to be (1 - EMU)*ITRSOLD + EMU*ITRSEMU.

A similar procedure was followed for the long term interest rate as for the short term rate. For the EMU regime, the long term interest rate equations (equation 8) of the 8 countries except GE that have such equations were dropped from the model. The equation for GE was retained as is.

Let ITRBOLD be the interest rate determined by equation 8 for IT prior to the EMU regime, and let ITRBEMU be the long term IT rate in the EMU regime. ITRBEMU is taken to be GERB. In other words, the Italian long term interest rate in the EMU regime is taken to be the rate determined by the German equation (which is GERB). The same procedure was followed for the other 6 countries. The coding of the model is the same for the long term rate as it is for the short term rate. For example, the long term IT interest rate (ITRB) is taken to be (1 - EMU)*ITRBOLD + EMU*ITRBEMU.

Finally, a similar procedure was followed for the exchange rate as for the short term interest rate. For the EMU regime, the exchange rate equations for the 10 countries except GE were dropped from the model. For GE the coefficient estimates of the exchange rate equation were retained but the right hand side GE variables were replaced with the respective EU variables. This equation is interpreted as the exchange rate equation for the euro. What this means is that the euro is assumed to be determined in the same way that the DM was determined except that the explanatory variables are overall EU variables and not just GE variables.

Let GEEOLD be the exchange rate determined by equation 9 for GE prior to the EMU regime, and let GEEEMU be the interest rate determined by the euro equation just mentioned. In the coding of the model the German exchange rate (GEE) is taken to be (1 - EMU)*GEEOLD + EMU*GEEEMU.

Let ITHOLD be the exchange rate determined by equation 9 for IT prior to the EMU regime, and let ITHEMU be the IT exchange rate in the EMU regime. ITHEMU is taken to be the rate set by the EMU on January 1, 1999. The same is true for the other 8 countries. The rates (remember, relative to the DM) are: 7.0355297 for AU, 3.3538549 for FR, 989.999 for IT, 1.1267390 for NE, 3040.003 for FI, 20.625463 for BE, 402.67508 for IR, 102.50482 for PO, and 85.071811 for SP. The coding of the model is the same for the exchange rate as it is for the interest rates. For example, the IT exchange rate (ITH) is taken to be (1 - EMU)*ITHOLD + EMU*ITHEMU.

The treatment for GR is similar with EMU2 replacing EMU, where EMU2 is 1 from 2001:1 on and 0 otherwise. The EMU exchange rate for GR (relative to the DM) is 174.22272.

The overall EU variables that are used in the ECB interest rate reaction function and in the euro exchange rate equation are just the variables that pertain to the quarterly EU countries: AU, FR, GE, IT, NE, and FI. In future work this may be changed, but it is difficult to combine quarterly and annual data. The EU variables are:

• EUY=GEY+AUY/(AUE95/GEE95)+FRY/(FRE95/GEE95)+ITY/(ITE95/GEE95) +NEY/(NEE95/GEE95)+FIY/(FIE95/GEE95)
• EUYS=GEYS+AUYS/(AUE95/GEE95)+FRYS/(FRE95/GEE95)+ITYS/(ITE95/GEE95) +NEYS/(NEE95/GEE95)+FIYS/(FIE95/GEE95)
• EUYY=GEPY*GEY+(AUPY*AUY)/AUH+(FRPY*FRY)/FRH+(ITPY*ITY)/ITH +(NEPY*NEY)/NEH+(FIPY*FIY)/FIH
• EUPY=EUYY/EUY
• EUZZ=(EUYS-EUY)/EUYS
• EULPYZ=LOG(EUPY/USPY)
• EULEA=EULPYZ-GELE(-1)
• EUPCPY=((EUPY/EUPY(-1))**4-1.)

EUY is real output of EU, EUYS is potential real output, EUYY is nominal output, EUPY is the output price deflator, and EUZZ is the output gap. The remaining variables are variables used in the EU interest rate and exchange rate equations, which are disucssed next. Note that EUY and EUYS are in units of 1995 DM and that EUYY is in units of current DM. The variable FRE95/GEE95 is the Franc/DM rate in 1995 and the variable FRH is the Franc/DM nominal rate (and similarly for the other countries).

The EU interest rate reaction function is

• GERSEMU = 0.1199618540 + 0.8355546364*GERS(-1) - 22.1521832804*EUZZ + 0.1999608193*USRS + 0.0260905973*EUPCPY

The EU exchange rate equation is

• GELE1EMU = - 0.624499483 + 0.096383148*EULEA - 2.098596175*GELRSZ, RHO1=0.326907848

The software allows you to change the EU interest rate and exchange rate equations. The "country" that you will click is EU. Remember that these equations are only relevant from 1999:1 on. Also remember that the equations that have been dropped for the countries from 1999:1 on are not part of the model from 1999:1 on. They only matter prior to this period. For GR the switch date is 2001:1.

There are a few features of the software regarding the EMU regime that you need to know, which are explained next. The following discussion is tedious, and you may want to print it for reference purposes when you are on line working with the MC3 model.

RB Equation
As discussed in the previous section, for countries AU, FR, IT, NE, BE, IR, and PO, the RB equation ends in 1998:4. If you are working with a period prior to 1999:1 and you drop one of these equations, you can then change the RB values using the "Change exogenous variables" option. The variable you change, however, is not RB but RBOLD. For Germany (GE), on the other hand, the RB equation pertains to the entire period through 2004:4, and the variable you change if you drop this equation is RB, not RBOLD. This is also true of all the remaining countries in the model.

RS Equation
For countries AU, FR, IT, NE, FI, BE, IR, PO, and SP, the RS equation ends in 1998:4. If you are working with a period prior to 1999:1 and you drop one of these equations, you can then change the RS values using the "Change exogenous variables" option. The variable you change, however, is not RS but RSOLD. This is also true for Germany (GE). For all the remaining countries in the model the RS equation pertains to the entire period through 2004:4, and the variable you change if you drop this equation is RS, not RSOLD.

If you are working with a period from 1999:1 on, the relevant RS equation for the EU countries explains a variable named GERSEMU. (See the discussion in the previous secton.) If this equation is dropped, you can change the EU RS values using the "Change exogenous variables" option. The variable you change is listed among the Germany variables. The variable is GERSEMU, not GERS.

E or H Equation
For countries AU, FR, IT, NE, FI, BE, IR, PO, and SP, the H equation ends in 1998:4. If you are working with a period prior to 1999:1 and you drop one of these equations, you can then change the H values using the "Change exogenous variables" option. The variable you change, however, is not H but HOLD. This is also true for Greece (GR) from 2001:1 on. For Germany (GE) the equation explains E, not H, and the variable you change if you drop this equation is EOLD, not E. For all the remaining European countries in the model the H equation pertains to the entire period through 2004:4, and the variable you change if you drop this equation is H, not HOLD. For all the non European countries the variable explained is E, the equation pertains to the entire period through 2004:4, and the variable you change if you drop this equation is E, not EOLD.

If you are working with a period from 1999:1 on, the relevant E equation for the EU countries explains a variable named GEEEMU. (See the discussion in the previous secton.) If this equation is dropped, you can change the EU E values using the "Change exogenous variables" option. The variable you change is listed among the Germany variables. The variable is GEEEMU, not GEE.

Dropped Equations From 1997:1 On

For the period from 1997:1 on the default is that the following equations are dropped: STH, UKH, DEH, NOH, SWH, GERSEMU, and GEEMU. If you want to add these equations back in for this period, click "Take equations to begin after the beginning of the prediction period" and change the -1 to 0. The GERSEMU and GEEMU equations are under country EU, not GE. If you go to EU, change the -1 to 0 for both equations (otherwise you will get an error message about -1). If you then want to keep one of the two equations dropped, click "Drop or add equations" and drop under country EU the desired equation.

Finally, when you click "Change exogenous variables," ignore the RS, RSOLD, RSEMU, RB, RBOLD, E, EOLD, EEMU, H, and HOLD variables that are not relevant. The only variables in this group that can be changed for a given country (after the appropriate equation has been dropped) are the ones mentioned above.