292 The Basics of financial economeTrics
distinguished economists and physicists, the seminar introduced the idea that
economic laws might be better understood by applying the principles of phys-
ics and, in particular, the newly developed theory of complex systems. An
anecdote from the book is revealing of the issues specific to economics as a
scientific endeavor. According to Waldrop, physicists attending the seminar
were surprised to learn that economists used highly sophisticated mathemat-
ics. A physicist attending the seminar reportedly asked Kenneth Arrow, the
corecipient of the 1972 Nobel Memorial Prize in Economics, why, given the
lack of data to support theories, economists use such sophisticated mathemat-
ics. Arrow replied, “It is just because we do not have enough data that we use
sophisticated mathematics. We have to ensure the logical consistency of our
arguments.” For physicists, in contrast, explaining empirical data is the best
guarantee of the logical consistency of theories. If theories work empirically,
then mathematical details are not so important and will be amended later; if
theories do not work empirically, no logical subtlety will improve them.
This anecdote is revealing of one of the key problems that any modeler
of economic phenomena has to confront. On the one side, as with econom-
ics, the field of financial economics is an empirical science based on empiri-
cal facts. However, as data are scarce, many theories and models fit the
same data.
Given the importance of model selection, let us discuss this issue before
actually discussing estimation issues. It is perhaps useful to compare again
the methods of financial economics and of physics. In physics, the process of
model choice is largely based on human creativity. Facts and partial theories
are accumulated until scientists make a major leap forward. Physicists are
not concerned with problems such as fitting the data to the same sample
that one wants to predict—referred to as data snooping and explained later
in this chapter. In general, data are overabundant and models are not deter-
mined through a process of fitting and adaptation.
Now consider financial economics, where the conceptual framework
is totally different. First, though apparently many data are available, these
data come in vastly different patterns. For example, the details of develop-
ment of a financial system and instruments are very different from year to
year and from country to country. Asset prices seem to wander about in
random ways. Introducing a concept that plays a fundamental role in for-
mulating investment strategies explained in the next chapter, we can state:
From the point of view of statistical estimation, financial economic data are
always scarce given the complexity of their patterns.
Attempts to discover simple deterministic laws that accurately fit empiri-
cal financial data have proved futile. Furthermore, as financial data are the
product of human artifacts, it is reasonable to believe that they will not
follow the same laws for very long periods of time. Simply put, the structure