42 Methodology of Empirical Econometric Modeling
Here we consider Autometrics, an Ox package (see Doornik, 2006, 2007a) imple-
menting automatic Gets modeling based on the theory of reduction discussed
above. The present implementation of Autometrics is primarily for linear regres-
sion models, but extensions have been derived theoretically to automatically
model dynamic, cointegrated, simultaneous systems; nonlinear equations; struc-
tural breaks; more variables (N) than observations (T); and testing exogeneity (see,
e.g., Hendry and Krolzig, 2005; Castle and Hendry, 2005; Hendry,et al., 2008;
Johansen and Nielsen, 2008; Doornik, 2007b; and Hendry and Santos, 2009,
respectively). Given any available theoretical, historical, institutional, and mea-
surement information, as well as previous empirical evidence, a GUM must be
carefully formulated, preferably with a relatively orthogonal parameterization, a
subject-matter basis, and must encompass existing models. WhenT N, the
GUM can be estimated from all the available evidence, and rigorously tested for
congruence. If congruence fails, a new formulation is required: but at least one has
learned the general inadequacy of a class of models. If congruence is accepted, it
is then maintained throughout the selection process by not following simplifica-
tion paths which are rejected on diagnostic checking (using the same statistics),
ensuring a congruent final model. WhenN>T, as must happen when impulse
saturation is used and can occur more generally (discussed below), misspecification
testing can only be undertaken once a feasible model sizen<Thas been reached.
Statistically insignificant variables are eliminated by selection tests, using a tree-
path search in Autometrics, which improves on the multi-path procedures in
Hoover and Perez (1999) and Hendry and Krolzig (2001). Checking many paths
prevents the algorithm from becoming stuck in a sequence that inadvertently
eliminates a variable which actually matters, and thereby retains other variables
as proxies (as in stepwise regression). Path searches terminate when no variable
meets the elimination criteria. Non-rejected (terminal) models are collected, then
tested against each other by encompassing: if several remain acceptable, so are
congruent, undominated, mutually encompassing representations, the search is
terminated using, e.g., the Schwarz (1978) information criterion, although all are
reported and can be used in, say, forecast combinations.
To understand why an automatic search procedure might work, consider a case
where the complete set ofNcandidate regressors is mutually orthogonal, but which
ones are relevant is unknowna priori, andT N. The postulated GUM nests the
LDGP. Estimate the GUM, then, squaring to eliminate signs, rank the resultingt^2 i
statistics from the largest to the smallest. Whencαis the criterion for retention,
letnbe such thatt^2 n≥cαwhent^2 n+ 1 <cα. Then select the model with thosen
regressors. That required preciselyonedecision – what to include, and hence what
to exclude. No issues of search, repeated testing, path dependence, etc., arise.
Goodness-of-fit is not directly used to select models; and no attempt is made to
“prove” that a given number of variables matters. In practice, the role of the tree
search is to ascertain “true” relevance when orthogonality does not hold; and the
choice ofcαaffectsR^2 andnthrough retention oft^2 n. Generalizations to other
maximum likelihood estimators, or approximations thereto such as IV, are feasible
(see Hendry and Krolzig, 2005; Doornik, 2007a).