xiv Editors’ Introduction
theory of theories. This chapter is deliberately thought-provoking and certainly
controversial – two characteristics that we wish to encourage in aHandbookthat
aims to be more than just an overview. For balance, the reader can consult Volume
1oftheHandbook, which contains two chapters devoted to the Bayesian analysis of
econometric models (see Poirier and Tobias, 2006, and Strachanet al., 2006). The
reader is likely to find familiar concepts here, such as probability and testing, but
only as part of a development that takes them into potentially unfamiliar areas.
DiNardo’s discussion of these issues is wide-ranging, with illustrations taken from
gambling and practical examples taken as much from science, especially medicine,
as economics. One example from the latter is the much-researched question of the
causal effect of union status on wages: put simply, do unions raise wages and, if so,
by how much? This example serves as an effective setting in which to raise issues
and to show that differences in approach can lead to differences in results.
For some, the proof of the pudding in econometrics is the ability to forecast
accurately, and to address some key issues concerning this aspect of economet-
rics Part II contains two chapters on forecasting. The first, Chapter 4, by Michael
Clements and David Harvey, recognizes that quite often several forecasts are avail-
able and, rather than considering a selection strategy that removes all but the best
on some criterion, it is often more fruitful to consider different ways of combining
forecasts, as suggested in the seminal paper by Bates and Granger (1969). In an
intuitive sense, one forecast may be better than another, but there could still be
some information in the less accurate forecast that is not contained in the more
accurate forecast. This is a principle that is finding wider application; for example,
in some circumstances, as in unit root testing, there is more than one test available
and, indeed, there may be one uniformly powerful test, yet there is still potential
merit in combining tests.
In the forecasting context, Clements and Harvey argue that the focus for mul-
tiple forecasts should not be on testing the null of equal accuracy, but on testing
for encompassing. Thus it is not a question of choosing forecast A over forecast B,
but of whether the combination of forecasts A and B is better than either individ-
ual forecast. Of course, this may be of little comfort from a structuralist point of
view if, for example, the two forecasts come from different underlying models; but
it is preferable when the loss function rewards good fit in some sense. Bates and
Granger (1969) suggested a simple linear combination of two unbiased forecasts,
with weights depending on the relative accuracy of the individual forecasts, and
derived the classic result that, even if the forecasts are equally accurate in a mean
squared error loss sense, then there will still be a gain in using the linear combina-
tion unless the forecasts are perfectly correlated, at least theoretically. Clements and
Harvey develop from this base model, covering such issues as biased forecasts, non-
linear combinations, and density or distribution forecasts. The concept of forecast
encompassing, which is not unique in practice, is then considered in detail, includ-
ing complications arising from integrated variables, non-normal errors, serially
correlated forecast errors, ARCH errors, the uncertainty implied by model estima-
tion, and the difficulty of achieving tests with the correct actual size. A number of
recent developments are examined, including the concept of conditional forecast