7.3. Variance estimation: Autocorrelation, cross-sectional dependence, and
variance increases
While non-normality and biases in estimating the market model are unimportant
in tests for abnormal performance, the choice of variance estimator to
be used in hypothesis tests is of some concern, affecting both the specification
and power of the tests. For hypothesis tests over multi-day intervals, there is
evidence that the specification of the test statistic is improved by using simple
procedures to adjust the estimated variance to reflect autocorrelation in the
time-series of mean daily excess returns. However, the improvements are small,
and only apply in special cases, for example event studies concentrating on
AMEX firms, Non-synchronous trading, which can induce the autocorrelation,
appears to have a detectable but limited impact on the choice of appropriate
methodology.
When the implications of adjusting variance estimates to account for dependence
in the cross-section of excess returns are studied, only in special cases is
such adjustment necessary to prevent misspecification. Moreover, there is a
potentially large cost. In results reported in the paper, tests which assume
non-zero cross-sectional dependence are only about half as powerful and
usually no better specified than those employed assuming independence.
Finally, we illustrated how variance increases can cause hypothesis tests
using standard event study procedures to become misspecified. Several procedures
to deal with the possibility of variance increases were outlined. However, further research is necessary to fully understand the properties of alternative
procedures for measuring abnormal performance in such situations.