40 Methodology of Empirical Econometric Modeling
The New Keynesian Phillips curve is perhaps the best-known model which
includes expected inflation to explain current inflation. Models of this type are
usually estimated by replacing the expected value by the actual future outcome,
then using IV or GMM to estimate the resulting parameters, as in, say, Galí, Gertler
and Lopez-Salido (2001). As shown in Castleet al.(2008), since breaks and regime
shifts are relatively common, full-sample estimates of equations with future val-
ues can deliver spuriously significant outcomes when breaks are not modeled, a
situation detectable by impulse saturation (see section 1.5).
1.4.11 Estimation
“I was wondering what the mouse-trap was for,” said Alice. “It isn’t very
likely there would be any mice on the horse’s back.”
“Not very likely, perhaps,” said the Knight; “but if they do come, I don’t
choose to have them running all about.” (Lewis Carroll, 1899)Developing appropriate estimators comprises a major component of extant econo-
metric theory, and given any model specification, may seem an uncontentious
task. However, only in recent decades has it been clear how to avoid (say) nonsense
correlations in non-stationarity data, or tackle panel dependencies, so unknown
pitfalls may still lurk.
1.5 Model selection
In another moment Alice was through the glass, and had jumped lightly
down into the Looking-glass room. (Lewis Carroll, 1899)Model selection is the empirical route whereby many of the simplifications in
sections 1.4.2.2 and 1.4.2.3 are implemented in practice. In that sense, it is not
a distinct stepper se, but a way of carrying out some of the earlier steps, hence our
treating the topic in a separate section.
Selection remains a highly controversial topic. It must be granted that the best
approaches cannot be expected to select the LDGP on every occasion, even when
the GUM nests the LDGP, and clearly cannot do so ever when the LDGP is not a
nested special case. However, that statement remains true when the GUM is exactly
the LDGP, but conventional inference is nevertheless undertaken to check that
claim. If the LDGP were known at the outset of a study, apart from the unknown
values of its parameters, then if any specification or misspecification testing was
undertaken, one could only end by doubting the claim that the initial formula-
tion was indeed the LDGP. The least worst outcome would be weak confirmation
of the prior specification, and otherwise either some included variables will be
found insignificant, or some assumptions will get rejected, casting doubt on the
claim. That is the risk of undertaking statistical inference. The alternative of not
testing claimed models is even less appealing, namely never learning which ones
are useless. To quote Sir Francis Bacon: “If a man will begin with certainties, he