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688 Chapter 16 Additional Topics in Time Series Regression

specific assumptions, derived from economic theory and institutional knowledge, of
what is exogenous and what is not. The discussion of structural VARs is best under-
taken in the context of estimation of systems of simultaneous equations, which goes
beyond the scope of this book. For an introduction to using VARs for forecasting
and policy analysis, see Stock and Watson (2001). For additional mathematical
detail on structural VAR modeling, see Hamilton (1994) or Watson (1994).

A VAR Model of the Growth Rate
of GDP and the Term Spread

As an illustration, consider a two-variable VAR for the growth rate of GDP,

GDPGRt, and the term spread, TSpreadt. The VAR for GDPGRt and TSpreadt
consists of two equations: one in which GDPGRt is the dependent variable and
one in which TSpreadt is the dependent variable. The regressors in both equations
are lagged values of GDPGRt and TSpreadt. Because of the apparent break in the
relation in the early 1980s found in Section 14.7 using the QLR test, the VAR is

estimated using data from 1981:Q1 to 2012:Q4.

The first equation of the VAR is the GDP growth rate equation:

GDPGRt = 0.52 + 0.29 GDPGRt - 1 + 0.22 GDPGRt - 2
(0.52) (0.11) (0.09)

- 0.90 TSpreadt - 1 + 1.33 TSpreadt - 2. (16.5)
(0.36) (0.39)

The adjusted R2 is R 2 = 0.29.
The second equation of the VAR is the term spread equation, in which the

regressors are the same as in the GDPGR equation, but the dependent variable

is the term spread:

TSpreadt = 0.46 + 0.01 GDPGRt - 1 - 0.06 GDPGRt - 2
(0.12) (0.02) (0.03)

+ 1.06 TSpreadt - 1 - 0.22 TSpreadt - 2. (16.6)
(0.10) (0.11)

The adjusted R2 is R 2 = 0.83.
Equations (16.5) and (16.6), taken together, are a VAR(2) model of the

growth rate of GDP, GDPGRt, and the term spread, TSpreadt.