xviii Editors’ Introduction
literature in the 1980s and early 1990s, especially following the unit root litera-
ture. However, the integer restriction ondis not necessary to the definition of an
integrated series (see, in particular, Granger and Joyeux, 1980), so thatdcan be a
fraction – hence the term “fractionally integrated” for such series. Once the integer
restriction is relaxed for a single series, it is then natural to relax it for the multivari-
ate case, which leads to the idea of fractional cointegration. Gil-Alana and Hualde
give an overview of the meaning of fractional integration and fractional cointegra-
tion, methods of estimation for these generalized cases, which can be approached
in either the time or frequency domains, the underlying rationale for the existence
of fractionally integrated series (for example, through the aggregation of micro-
relationships), and a summary of the empirical evidence for fractionally integrated
univariate series and fractionally cointegrated systems of series. The various issues
and possible solutions are illustrated in the context of an analysis of PPP for four
bivariate series. It is clear that the extension of integration and cointegration to
their corresponding fractional cases is not only an important generalization of the
theory, but one which finds a great deal of empirical support.
One of the most significant developments in econometrics over the last twenty
years or so has been the increase in the number of econometric applications involv-
ing cross-section and panel data (see also Ooms, Chapter 29). Hence Part IV is
devoted to this development. One of the key areas of application is to choice sit-
uations which have a discrete number of options; examples include the “whether
to purchase” decision, which has wide application across consumer goods, and the
“whether to participate” decision, as in whether to enter the labor force, to retire, or
to join a club. Discrete choice models are the subject of Chapter 11 by Bill Greene,
who provides a critical, but accessible, review of a vast literature. The binary choice
model is a key building block here and so provides a prototypical model with which
to examine such topics as specification, estimation and inference; it also allows the
ready extension to more complex models such as bivariate and multivariate binary
choice models and multinomial choice models. Models involving count data are
also considered as they relate to the discrete choice framework. A starting point
for the underlying economic theory is the extension of the classical theory of con-
sumer behavior, involving utility maximization subject to a budget constraint, to
the random utility model. The basic model is developed from this point and a host
of issues are considered that arise in practical studies, including estimation and
inference, specification tests, measuring fit, complications from endogenous right-
hand-side variables, random parameters, the use of panel data, and the extension
of the familiar fixed and random effects. To provide a motivating context, Greene
considers an empirical application involving a bivariate binary choice model. This
is where two binary choice decisions are linked; in this case, in the first decision
the individual decides whether to visit a physician, which is a binary choice, and
the second involves whether to visit the hospital, again a binary choice: together
they constitute a bivariate (and ordered) choice. An extension of this model is to
consider the number of times that an individual visits the doctor or a hospital. This
gives rise to a counts model (the number of visits to the doctor and the number of
visits to the hospital) with its own particular specification. Whilst a natural place to