David F. Hendry 45apparent criticisms of selection have failed to note that key limitation. In the sim-
ulations described above, the same algorithm and selection criteria were always
applied to commencing from both the GUM and the LDGP, and only the addi-
tional costs attributable to starting from the former comprise search costs. Also,
when there are relevant variables with smallt-statistics because the parameters are
O( 1 /
√
T), especially if they are highly correlated with other regressors (see Pötscher,
1991; Leeb and Pötscher, 2003, 2005), then selection is not going to work well: one
cannot expect success in selection if a parameter cannot be consistently estimated.
Thus, although uniform convergence seems infeasible, selection works for parame-
ters larger thanO( 1 /
√
T)(as they are consistently estimable) or smaller thanO( 1 /T)
(as they vanish), yet 1/
√
Tand 1/Tboth converge to zero asT→∞, so “most”
parameter values are unproblematic. If the LDGP would always be retained by the
algorithm when commencing from it, then a close approximation will generally
be selected when starting from a GUM which nests that LDGP.
Additional problems for any empirical modeling exercise arise when the LDGP is
not nested in the GUM, due to the regressor set being incomplete, the functional
form misspecified or structural breaks and other non-stationarities not being fully
accommodated, as well as serious measurement errors contaminating the data or
endogenous variables being incorrectly treated as regressors. For very high levels of
collinearity between relevant and irrelevant variables, the selected approximation
may use the incorrect choice if that is undominated, but in a progressive research
strategy when there are intermittent structural breaks in both relevant and irrele-
vant variables, such a selection will soon be dominated. Phillips (2003) provides
an insightful analysis of the limits of econometrics.
1.6 Teaching “Applied Econometrics”
“Manners are not taught in lessons,” said Alice. “Lessons teach you to do
sums, and things of that sort.”
“And you do Addition?” the White Queen asked. “What’s one and one
and one and one and one and one and one and one and one and one?”
“I don’t know,” said Alice. “I lost count.” (Lewis Carroll, 1899)Both economic theory and theoretical econometrics are relatively structured sub-
jects to teach, whereas applied econometrics is not, so many approaches are extant.
The obvious way might be to include substantive empirical findings in the relevant
subject-matter part of other economics courses, and so effectively abolish the need
to teach what applied econometrics has established. This certainly happens in part,
usually with a lag after the relevant study was published, but seems less common
than courses specifically oriented to applied econometrics. I was taught in such a
course, the bulk of which concerned studying how the “masters” had conducted
their investigations, and what they found – essentially an apprenticeship. Other
courses focus more on the economic and econometric theory behind key studies,
with less attention to their empirical outcomes: systems of demand equations seem
to be addressed that way. Presumably the aim is to explicate the relation between