Terence C. Mills and Kerry Patterson xxiiithere are ways to “robustify” the empirical model and forecasts from it so as to
mitigate such possibilities, although challenges remain in an area that continues
to be of central importance in economic policy.
One of the key developments in monetary policy in the UK and elsewhere in
the last decade or so has been the move to give central banks a semi-autonomous
status. In part, this was thought to avoid the endogenous “stop–go” cycle driven by
political considerations. It also carried with it the implication that it was monetary
policy, rather than fiscal policy, which would become the major macroeconomic
policy tool, notwithstanding the now apparent practical limitations of such a
move. In Chapter 18, Brian Henry provides an overview of the institutional and
theoretical developments in the UK in particular, but with implications for other
countries that have taken a similar route. The key question that is addressed in
this chapter is whether regime changes, such as those associated with labor market
reforms, inflation targeting and instrument independence for the Bank of Eng-
land, have been the key factors in dampening the economic cycle and improving
inflation, unemployment and output growth, or whether the explanation is more
one of beneficial international events (the “good luck” hypothesis) and monetary
policy mistakes. Henry concludes, perhaps controversially, that the reforms to the
labor market and to the operation of the central bank are unlikely to have been the
fundamental reasons for the improvement in economic performance. He provides
an econometric basis for these conclusions, which incorporates a role for interna-
tional factors such as real oil prices and measures of international competitiveness.
Once these factors are taken into account, the “regime change” explanation loses
force.
The growth of financial econometrics in the last two decades was noted in the
first volume of thisHandbook. Indeed, this development was recognized in the
award of the 2003 Nobel Prize in Economics (jointly with Sir Clive Granger) to
Robert Engle for “methods of analyzing economic time series with time-varying
volatility (ARCH).” Part VII of this volume reflects this development and is thus
devoted to applications in the area of financial econometrics.
In Chapter 19, George Dotsis, Raphael Markellos and Terence Mills consider
continuous-time stochastic volatility models. What is stochastic volatility? To
answer that question, we start from what it is not. Consider a simple model of an
asset price,Y(t), such as geometric Brownian motion, which in continuous time
takes the form of the stochastic differential equationdY(t)=μY(t)+σY(t)dW(t),
whereW(t)is a standard Brownian motion (BM) input; thenσ(orσ^2 ) is the volatil-
ity parameter that scales the stochastic BM contribution to the diffusion ofY(t).
In this case the volatility parameter is constant, although the differential equation
is stochastic. However, as Dotsiset al.note, a more appropriate specification for
the accepted characteristics of financial markets is a model in which volatility
also evolves stochastically over time. For example, if we introduce the variance
functionv(t), then the simple model becomesdY(t)=μY(t)+
√
v(t)Y(t)dW(t),
and this embodies stochastic volatility. Quite naturally, one can then couple this
equation with one that models the diffusion over time of the variance function.
ARCH/GARCH models are one way to model time-varying volatility, but there are