The following are specification changes that have been made to the US
model since the forecast dated October 31,
2005. Prior to this forecast the model is the version in Fair (2004) (except
for reestimation each quarter).
The latest estimates and exact specification of the model are
Appendix A: The US Model:
April 26, 2013. The estimates and specification of the version of
the model in Fair (2004) are in Appendix A in
Many of the specification changes are due to changes in variable
definitions in the NIPA and the Flow of Funds accounts. Responding to these
changes requires eliminating some variables in the model, adding others, and
changing some identities. These changes are tedious, but minor,
and they are not discussed below. If you want to
see the exact specification changes for each equation, you can compare
Appendix A in Fair (2004) to
Appendix A: The US Model:
April 26, 2013.
Beginning with the October 31, 2009, forecast, the forecast horizon was
lengthened to about 11 years. In the process of doing this the
exogenous nominal variables were tied to the GDP deflator. To be
precise, for an exogenous nominal variable y a real variable
x was created as y/p where p is the GDP deflator.
Then x was treated as exogenous, and the equation y = p*x
was added to the model. A "Q" is added at the end of a name of an
exogenous nominal variable to denote that the variable is real, and
equations are added linking the nominal values to the real values.
- In equation 1, which explains CS, the time trend T has been dropped.
Equation 9, which
explained MH, has been dropped. The recent data on MH, which are from the
Flow of Funds accounts, are not sensible, and so MH has simply been taken to
- In equation 14, which explains HF, the time trend T has been added.
- In equation 17, which explains MF, the interest rate variable is
unlagged rather than lagged once. Also, the dummy variable D981 has been
- In equation 19, which explains INTF, the long run restriction has
been relaxed and the weights on the short term and long term interest rates
in the interest rate variable have been changed.
- Equation 20, which explained IVA, has been dropped. The values of
IVA since 2007:4 have been extreme, and it does not seem possible to
explain them. IVA has thus been taken to be exogeous.
- Equation 21, which explained CCF, has been dropped. There have been
too many changes in depreciation tax rates for estimation to be sensible.
These changes are now incorporated into variable D6G, which is taken to be
- Equation 22, which explains BO, has been dropped. Similar to the
case for IVA, the values of BO
since 2007:4 have been extreme, and it does not seem possible to explain them.
BO has thus been taken to be exogenous. This means that exogenous variable
RD is no longer used in the model.
- Equation 27, which explains IM, is estimated under the assumption of
no serial correlation of the error term.
- In equation 29, which explains INTG, the long run restriction has
been relaxed, the weights on the short term and long term interest rates
in the interest rate variable have been changed, and the equation is now
estimated under the assumption of a first order serially correlated
- The identity explaining BR has been dropped, and BR has been
taken to be exogenous. This means that exogenous variable G1 is no
longer used in the model. Dropping this equation means that BR is no
longer tied to MB; it is simply exogenous. As with BO, the values of BR
since 2007:4 have been extreme, and it does not seem possible to
- Variables PKH and PSI14
have been added, and in equation 89, which determines the wealth variable,
has been replaced with PKH. PKH*KH is a better measure of housing wealth
than is PIH*KH. PKH is the market price of KH. It is based on data from
the Flow of Funds accounts. PKH*KH is the market value of the stock
of housing, KH. PKH is explained by a new equation, equation 55,
which is PKH = PSI14*PD,
where PSI14 is taken to be exogenous. Relative housing price changes
are thus reflected in changes in PSI14.
- In equations 47, 48, 90, and 91, POP has been replaced with
(POP*PH). This change ties the progressivity of the personal income
tax system to real per capita income rather than nominal
per capita income.
Also, nine variables were added to the list of variables that can be
examined using the output part of the web software.
Beginning with the January 28, 2012, forecast, equations 1, 2, 3, 4, 10, 12,
and 27 have been estimated under the assumption that the constant term
changes linearly between 1968:4 and 1988:4, where the slope is estimated.
In addition, the coefficient of the time trend (T) in equation 10 is
assumed to change linearly in this period, where the slope is estimated.
This introduces the variable cnst2 in the equations and the variable
TB in equation 10. This estimation method is joint work in
Don Andrews, where for the general method the beginning and ending quarters
for the linear change are estimated (along with the slope). For present
purposes the beginning and ending quarters have just been fixed at
1968:4 and 1988:4, respectively.
- RECGZGDP = RECG/GDP
- EXPGZGDP = EXPG/GDP
- SGPZGDP = -SGP/GDP
- AGZGDP = -AG/(4*GDP)
- INTGZGDP = INTG/GDP
- ASZGDP = -AS/(4*GDP)
- SRZGDP = SR/GDP
- PCGDPR4 = 100*((GDPR/GDPR(-4))**1-1)
- PCGDPD4 = 100*((GDPD/GDPD(-4))**1-1)