38 Methodology of Empirical Econometric Modeling
1993). The main problem for economic forecasting using econometric models is
that coefficients of deterministic terms do not seem to stay constant, but suffer loca-
tion shifts, which in turn induce forecast failure (see, e.g., Clements and Hendry,
2005, 2006). While changes in zero-mean variables seem less damaging to forecasts
(see, e.g., Hendry and Doornik, 1997), such breaks nevertheless remain pernicious
for policy analyses.
1.4.9 “Independent” homoskedastic errors
“Contrariwise,” continued Tweedledee, “if it was so, it might be; and if it
were so, it would be: but as it isn’t, it ain’t. That’s logic.” (Lewis Carroll,
1899)Joint densities can always be factorized into sequential forms, as with martin-
gale difference sequences. Moreover, equations can often be standardized to be
homoskedastic by dividing by contemporaneous error variances (when these exist),
so this category may be one of the least stringent requirements.
1.4.10 Expectations formation
“What sort of things do you remember best?” Alice ventured to ask. “Oh,
things that happened the week after next” the Queen replied in a careless
tone. (Lewis Carroll, 1899)Surprisingly little is known about how economic agents actually form their expec-
tations for variables relevant to their decisions. Almost no accurate expectations
data exist outside financial market traders, so resort is usually needed to proxies
for the unobserved expectations, or to untested assumptions, such as “rational”
expectations (RE), namely the correct conditional expectationE[·]of the variable
in question (yt+ 1 ) given the available information (It). There is a large gap between
economic theory models of expectations – which often postulate that agents hold
RE – and the realities of economic forecasting, where forecast failure is not a rare
occurrence. The “rational” expectation is often written as (see Muth, 1961):
yret+ 1 =E[
yt+ 1 |It]
, (1.34)which implicitly assumes free information and free computing power as available
information is vast. The usual argument, perhaps loosely worded to avoid contra-
dictions, is that otherwise there would be arbitrage opportunities, or agents would
suffer unnecessary losses. But expectations are instrumental to agents’ decisions,
and the accuracy thereof is not an end in itself, so agents should just equate the
marginal benefits of improved forecast accuracy against the extra costs of achiev-
ing that, leading to “economically rational expectations” (ERE) (see Aghionet al.,
(2002)). “Model consistent expectations” instead impose the expectations forma-
tion process as the solved estimated model specification, so – unless the model is
perfect – suffer the additional drawback of imposing invalid restrictions.
While ERE may be more realistic than RE, it still assumes knowledge of the form
of dependence ofyt+ 1 on the information used: as expressed inE
[
yt+ 1 |It]
in (1.34),