Palgrave Handbook of Econometrics: Applied Econometrics

50 Methodology of Empirical Econometric Modeling

+ 0.06

(0.02)

I 35 + 0.07

(0.02)

I 36 − 0.08

(0.02)

I 38 + 0.07

(0.02)

I 41 + 0.08

(0.02)

I 43

+ 0.10

(0.02)

I 46 − 0.06

(0.02)

I 80

R^2 =0.86FM(12, 46)=23.9∗∗̂σ=0.019Far(2, 44)=0.14

χ^2 ( 2 )=1.27Farch(1, 44)=4.42∗Freset(1, 45)=0.01Fhet(14, 31)=0.69. (1.43)

Almost all the inter-war and war years are revealed as discrepant, with four
impulses in common with (1.40). Adding the 6 additional impulses found in (1.43)
to (1.40) and testing their significance yieldsFSExog(6, 40)=1.14, not rejecting.
Nevertheless, that there are four impulses in common is strongly against the exo-
geneity ofetin (1.40), especially as their signs all match, and even the magnitudes
are not too far from 0.67 times those in (1.43). It is not surprising that major shifts
in total expenditure are associated with shifts in expenditure on a subcomponent,
but sinceetis included in (1.40), the conclusion must be that agents altered their
decision rules more than that effect. Since a food program was in place for several
of the common impulses and rationing for the other, additional shifts do not nec-
essarily invalidate the economics behind the equation, so the overall outcome is
inconclusive.
An alternative check on the commonality of the inter-war and post-war periods is
to use the former to predict the latter, given the actual outcomes for the regressors.
We have implicitly done so via impulse saturation, which revealed only one post-
war outlier in 1970. TheF-test of constancy,FChow(37, 10)=2.02, does not reject.
Figure 1.7 shows the outcomes: panel (a) reports the fitted and actual values till
1952 and the predicted thereafter, with the full-sample fit shown immediately
below in panel (c), the residuals and forecast errors in panel (b), and one-step 95%
forecast intervals in panel (d). The outlier in 1970 is obvious, and otherwise there
is little difference between the sub-sample and full-sample fit. Such constancy in
the face of changing data behavior supports both the specification in (1.40) and
the use of the whole sample to estimate and evaluate these models.

1.7.1 An update

Everything was happening so oddly that she didn’t feel a bit surprised.

(Lewis Carroll, 1899)

The obvious extension is to update the data, and test the model on the extended
information. Unfortunately, Applied Econometrics is never that easy: the data have
been extensively revised. It came as a surprise even to an experienced empirical
modeler that data back to 1929 could differ so much between a 1989-based set
(denoted by a subscript 0 in the graphs) and a 2008 update when extending the
data to 2000 (denoted 1 ), but Figures 1.8 (data) and 1.9 (deviations) show the extent
of the revisions. Both food and total real expenditure have changed, the latter by
up to 15%, and savings have shifted by up to 5%, whereas the relative price of