|This chapter discusses practical things you should know when working with the MC3 model. It relies on Appendices A and B and on the Chapter 5 and Chapter 6 tables, all of which are at the end of this workbook. If you are reading this online and/or planning to work with the MC3 model, it may be helpful to print the appendices and tables for ease of reference.|
The complete documentation for the non-US part of the MC3 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
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.
|1.2 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. The two letters EU denote the European countries in the model that are part of the EMU. These are: AU, FR, GE, IT, NE, FI, BE, IR, PO, SP. (Luxembourg, which is also part of the EMU, is not in the model.) (GR joined January 1, 2001.)|
|1.3 Solution Options|
|There are five choices you can make regarding the solution of the MC3
|1.4 The Complete MC3 Model and How It is Solved|
|The size of the MC3 model is as follows. The US model, which is part
of the MC3
model, includes 30 stochastic equations plus one more when it is imbedded
in the MC3 model.
(This additional equation is discussed below.) There are 39 countries in
the ROW model and
up to 15 stochastic equations per country. If each country had all 15
would be a total of 585 (39 x 15) stochastic equations in the ROW model.
Because of data
limitations, however, not all countries have all equations, and there are
in fact 330
stochastic equations in the ROW model. Given the 31 stochastic equations
in the US model,
there are thus 361 stochastic equations in the MC3 model. There are a
total of 1671
coefficients in these equations, counting the autoregressive coefficients
of the error
terms. In addition, as discussed in Section 6.16 in
there are 1030 estimated trade share equations. Not counting the trade
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 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$US, which is determined in Table B.4. PIM depends on PMUS, which depends on PMPUS, which is also determined in Table B.4.
Feeding into Table B.4 from the US model are PXUS and
PXUS is determined is the same way that PX is determined for
countries, namely by equation 11 in Table B.3. In the US case
logPXUS - logPW$US
is regressed on logGDPD - logPW$US. The equation is:
M95$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 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:
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.
|1.5 Solution Errors|
|If you ask to solve the MC3 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 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.
|1.6 Changing Stochastic Equations|
|There are four changes you can make to any of the 361 stochastic
|1.7 Creating Base Datasets|
|If you ask the program to solve the MC3 model for any period
beginning 2002 or
later and you make no changes to the coefficients and exogenous
solution values for the endogenous variables will simply be the values
that are already in
MC3BASE. If, on the other hand, you ask the program to solve the model
for a period
beginning earlier than 2002, where at least some actual data exist, the
will not be the same as the values in MC3BASE because the model does not
(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 MC3BASE when you make no changes to the
and coefficients is when you are solving beginning 2002 or later.
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.
|1.8 Treatment of the EMU Regime|
As noted above, there are 10 countries in the model that are part of the
EMU beginning January 1, 1999: AU, FR, GE, IT, NE, FI, BE, IR, PO, and SP.
GR joined January 1, 2001. EU denotes the sum of the
10 countries for 1999 and
2000 and then the sum of the 10 countries plus GR beginning in 2001.
Each of these countries
has an estimated interest rate reaction function (equation 7), and each
country except FI, SP, and GR
has an estimated long term interest rate equation
(equation 8). In addition, GE has an estimated exchange rate equation
where the exchange rate explained is the DM/$ rate, and each of the other
countries has an estimated exchange rate equation where the
exchange rate explained is the local currency/DM rate (equation 9).
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 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
The EU exchange rate equation is
|1.9 Software Issues for the EMU Regime|
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.
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
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.