A Macro-Fiscal Modeling Framework for Forecasting and Policy ...

have developed some useful tests for endogenously determining multiple structural
breaks.
2.4 Estimating the Timing of Structural Break
In many applications the break date, i.e. timing of structural break may not be known by
exogenous or a priori information. In general, it may be best to infer the break date from
data. One possibility is to use the largest value of the Chow test sequence. Quandt
(1960) infact proposed taking the largest Chow statistics over all possible break dates. 2
Hansen et. al (2001) also discusses this and argues that this procedure may be reliable
only when the Chow test is constructed with the homoskedastic form of covariance
statistics. Bai (1994, 1997a) derives the asymptotic distribution of the break date
estimator and provides a method to construct a confidence interval around the break
date for a single variable. Chong (1995) and Bai (1997b) describe methodologies for
estimating multiple structural break dates by using the sum of squared errors as a
function of break dates, which have a local minima near each break date. The global
minimum can be used as the break date estimator and other local minima can used as
other candidate estimators for multiple breaks. Bai, Lumsdaine and Stock (1998) extend
the analysis to multiple time series with multiple break dates.
After extensive testing, Bai and Perron (2003) contended that most
macroeconomic time series are not characterized by the presence of a unit root and that
fluctuations are indeed transitory. Looking at the U.S. data, they find that only two
events had a permanent effect on the various macroeconomic variables: the Great Crash
of 1929 and the oil price shock of 1973. Implicit in this analysis is their postulate that the
Great Crash and the oil price shock were not a realization of the underlying data
generating mechanism of the various series. Instead, these shocks are taken as
exogenous. The exogeneity assumption time is used as a device to remove the influence
of these shocks from the noise function.
Some recent literature on multiple structural beaks includes Andrews, Lee and
Ploberger (1996), Garcia and Perron (1996), Liu, Wu and Zidek (1997), Lumsdaine and
2 Quandt (1960) also considered that y t is subject to a one time change in mean at some unknown
date T b , i.e., y t = 1 + 2 l (t>T b ) +e t where e t ~ iid (0, e 2 ) and l(.) denotes the indictor function.
He also introduced the Sup F test (assuming normally distributed errors). It is basically a
likelihood ratio test for a change in parameter evaluated at the break date that maximized the
likelihood function (Perron, 2005).
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